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About Google Book Search Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at|http: //books .google .com/I T'h4sX1t-l'4. SCIENCEXEMESB. l^ ^m ILLUSTBATED GIFT BOOKS. lEEDICAL ANATOMT. ByPBANCi8SiB8ON,M.D.,F.R.0.P., F.B.S. Imperial folio. 21 Coloured Plates. Cloth, £2 28.; balf-morocco, £2 lOs. S1TB6ICAL ASATOMT. A series of Dissections, illastrating the Principal Regions of the Human Body. By Joseph Maclise, F.B.C.S. 8ecpertin of matter 12—19 I^efinite aggregation of mole- ealet Forms of crrttalB Primary ana secondary forms Law of symmetry in crystals ... Remarkable deriatkms Twin crystals ... ao— 22 i Dimorphoos snbstances 23,24 2o 28 29 27 28 CHAPTEE 11. ; Page 18. PIOPBBTIBS OF MASSES OF UATTBB — BXTBBHAL P0BCE8. DtfAision of gases ... ... 47 Ansell's fire-damp indicator ... 48 Transpiration of gases 48 DilTUsion of liquids W FricUon of sar&ees 62—65 Friction of cordage 56 Friction rollers 67 Gravitation 68-82 Weight 83,64 AUnettTe forces ... 30,31 Coheiion 82 Cohcsioa figmres of oils 33 Adhesion ... 84,35 Oi(ii»aiy attraction ... ... 86—40 capillary repulsion ... 41 Gaieoas adhesion 43 Apparent attraction and repulsion 43 E&r«AiaC8 — THB BEULTIONS OF BODIES IN UOTIOV. of motion [asure of Telodtj Beiative reloci^... Aeodexstin^ force Man ... 09/ Hydrostatic level 388 Artesian well 389 Level of liferent fluids ... 390 Level of the sea 891 Pressure on the base of a vessel 892 HydrosUtie'* paradox" ... 893 Bramah's ^ress 394 Hydranlicjack and punch ... 896 Vessel of greatest strength ... 396 Upward pressure 897 Lateral pressure ... 898—400 Centre of pressure 401 Besultant pressure ... 402,408 Equilibrium of floatiDg bodies 404,406 Metacentre 406 TABLE OF CONTENTS. StabOiiy of flotation ... 407,406 Equilibriam of immenod body 409 Principle of Archimedes 410, 411 Specific ffravity 412 Means or determining it 413—417 HTdrometer 418 Kicholaon's hydrometer ... 419 Hare's hydrometer 420 8tereometer 421 Temperaturo-rarrection of spe^ dfic grsTitics 428 Specific gravity of gases ... 423 luiamples 424 Table of specific graTlties ... 426 CHAPTEE VIIL ; Page 232. HTDBODYNAMICS— THE PROrSBTIES OF FLUIDS TN MOTION. Laws of sponting fluids 426, 427 Vena ooutracta 428 M. Lacontoure's results ... 429 Barker's mill 430 Velocity in channels 431 Springs and fountains 432 Geysers hi Iceland 433 ' Friction of li<)uids 434 Action of conical tubes ... 435 Lifting pump 436 Forcing pump 437 Stomach pump 439 California pump 439 Fire engine 440 Hydraulioram 441 Centrifhgal pump 442 Appold'spump 443 Chain ana bucket pump ... 441 Bope pump 445 The syphon 44A Tantalus' cup 447 Hiero's fountain 448 Persian wheel, &C. 449 Water wheels 450 Turbine 451 Paddle wheels 452 Screw-propeller 453 Windmill sail 464 Steam-engine 456 Watt's steam-engine 466 Non-condensing en^ne ... 457 Stationary, locomotive, and ma- rine engines 458 Water-engines 469 Steam-hammer 400 Gyrometric governor 461 Undulation of fluids 462,463 Reflection of undulations . . .464, 466 Interference of undulations ... 466 Inflection of undulations ... 467 Lateral accumulation 468 Undulations of elastic fluids 469—471 Theory of Tides 472,473 Sprinv and neap tides 474 Establishment of a port ... 476 Double tides 476 CHAPTEB IX.; Page 268. FNEUHATIC8 — THE PROPERTIES OF ELASTIC FLUIDS. Composition of the atmosphere 477 Finite extent of the atmosphere 478 Elasticity of the atmosphere . . . 479 Weight and pressure of the atmosphere 480—482 Water barometer 483 Mercurial barometer ... ... 484 Syphon barometer 485 Standard barometer 486 Correction for temperature ... 487 Correction for capillarity ... 488 Conical barometer 469 Horary variations 490 Mean diurnal height 491 Annual variation ... ... 492 Geographical variation ... 403 Height at difi'erent altitudes ... 404 Self-registering barometer ... 496 Vedy's aneroid barometer ... 496 Bourdon's aneroid barometer... 497 Bojrle'slaw 406—600 Weight of the atmosphere ... 601 Preesure-gaoge 602 Exhausting syringe 603 Air-pump 604 Smeotons air-pump 606 Cuthbert's and Grove's air-pump 606 Barometex^gauge 607 S}'phon-gauge 606 Condenser 600 Air-gun 610 Pneumatie experiments ... 611 TABLE OF 0OKTEHT8. Xt of tbe fttmofiphere. . . Vareef ■ sppantoa Hdgbt of aoifonn atraoc^here ^'^ of denritiw of dry air and Presrare of mixed gasM Prassore of airandvaponr ., Fl^irieal propertieB of yapoor Pmrare of fapoar 612 613 514 616 616 617 618 619 Premxre of steam 620 Lateral pressore of gaaee . . .621, 622 Pressure of wind 623 Anemometers 624 Self-registering anemometers 626 Forecasts of weather 626 Pneumatic lerer 627 Compressed air engine 628 Lenoir's gas engine 629 CHAPTER X. ; Page 204. acoustics; THB PBODOCTIOIT, TRANSMISSIOIV, AITD PBBCBPTIOll OF SOUND. Natvie of soond Isoehronooa Tibrations Inftrior numerical limit GoDdoctiDg medium essentia] Inteosity of soand 690 631 632 633 634—536 ...537,633 ofHelmhoItz ... 639 ion of sound ... 640 CoDcarrence of sounds ... 641 Velocity of sound in air 642-^644 Tdocsfcf of soond in varioos txidiea 645>-648 InterfereDce of sound 649, 650 Pboaographfl 661,562 Opdcal aeoostie fisfures ... 663 Bxamidas of interference ...664^ 656 riiiisur of sound through hete- Yogeaaoua media 666, 657 Ooatinnitj of direction 658, 669 Beflectioo of sound 660,662 EdkO ... ... ... ... 661 Be&adiOD of sound 563 Acoustic lens 664 Inflection of sound 666 Siren .•• ... ... ... 666 Timbre, or quality of tone . . . 667 Musical notes 668 Length of sound-waves 569, 670 Yariations of pitch 571 Normal diapason 672 Scheibler's tonometer 673 Musical intenrals 674 Harmonic sounds 676 Vibrations of chords 576, 677 Vibrations of rods 578 Vibrations of air in tubes 679—681 Modes of exciting them ... 682 Vibrations of plates 583, 684 Vibrations of membranes ... 586 Strehlke's experiments ... 586 Trevelyan's experiments ... 5S7 Vocal sounds 688 Vowel sounds 689 Forced Tibntions 690 CHAPTEB XL; Page 839. XAORBTISIC.— DIAMAGNETISIC. On^gin of magnetism 691 Magnetic field 692 P^iles of A magnet ... 698,594 Magnetic inductioii ... 695,596 Magnetism a molecular pro- perty 697—600 Hie mariner's compaae 601, 602 Devlatioo of the compass ... 608 Soorees of deviation 604 Varieties of deviation 606 HorixontAl and rertical induo- tkni ... ... 606 Hedii^ error •.• 007 Tonstrlal polaiity 609 Declination 609,610 Inclination— dipping needle ... 611 Aclinic lines Kraflt'slawofthedip Secular change of dip Solar diurnal variation of decli- nation 616,616 Lnnar-diumal change of deoU- nation ... ... ... ... Annual change of force Horizontal and vertical compo- nents of total force lyisturbance variations Periodicity of variations 612 613 614 617 618 619 620 621 zu TABLE OF CX>HTBKTB. HMDiofobMiTAtioii ... 622,623 Antomatio registration ... 624 Magnetie storms 626 Eanh-ourrents 626 Local changes of intensity ... 627 VagDetism a <(Jrec<»o« force ... 628 Consecutive poles 629 Manetio metals 680 Moaes of excitation 831 Single tooch 632 DoiU)letonch 633 Jaoobi's method 634 Gompoimd magnets 636 Magnetic capacity 638 Temperatore-change of force... 687 Magnetic metals 688 Law of magnetic attraction ... 639 Artificial magnets 640 Diamagnetism 641— -644 Diamagnetic bodies ... 646—648 Dinmagnetic fluids 649 Effects of msgneUsm ... 660,661 Influence of molecular aggre- gation on magnetism 662, 668 CHAPTER XIL; Page 366. FBAKKLnriC ELECTRICITT. Excitation of electricity ... 664 Attraction and repulsion ... 666 Positive snd negative electri- city 66B Conduction of electricity 667, 658 Insulation of electricity ... 669 Concurrence of opposite forms 660 Electroscopes 661—662 Baddiffb's electroscope 663 Coulomb's electrometer ... 664 Peltier's electrometer 666 Thomson's electrometer ... 666 Excitation of various bodies 667—669 Pyro-electric minerals 670 ETolution of light ... ... 671 Superficial distribution ... 672 Electrostatic laws 673 Potential depends on surfhce 674^ 675 Electric induction ... 676—678 Kind of electricity tested ... 679 Spedflc inductive capadtr ... 680 IvadaVs theory of induction. . . 681 Examplos of induction ... 682—684 Electrophorus ... 686—688 Theory of points and knobs ... 689 Earliest electric machines ... 690 Cylinder machine 691 Plate machine ... 692 Mode of using a machine ^ 693 Formstion oioxone 694 Development of potential ... 695 Action of amalgam 696 Ebonite plate 697 Hydro-electrio machine 696—700 Holt^ induction machine 701, 792 Brush and star 703 Sparks in Interropted oondoctor 704 Lane's discharger 706 Induction in a racuum 706^ 707 Heat accompanies a spark 706, 709 Henley's electrometer 710 Electrical toys ^ 711 Convective currents of air ... 712 Dynamic energy manifested ... 718 Spark evolves coloured light ... 714 Forms of discharge 716 Potential constrained 716 Induction on glass plates 717—719 Lerdenjar 720,721 Jomted discharger ... ... 723 Charge by induction 723 Leyden battery 724^726 Residual charge 726 Velocity of electricity 727 Charge not in the coating ... 728 Universal discharger 729 Eflbcts of discharge ... 730^781 Identity of electricity 732 Heat evolved l^ discharge ... 783 Light evolved bv discharge ... 784 Fiffures of Leuchtenberg ... 786 DifiVision of potential 736 Unitjar 737 Condenser 788—740 Multiple inductor 741 Applications of condenser ... 743 Lateral induction ... 743, 744 Unipolar bodies 746 Gradations of oondnctiTity ... 746 Potential of the atmosphere 747—763 Potential of clouds ... 764—766 Lightning conductors . . . 767, 768 cuiguiiies ... ... ... /Ov St Elmo's lights— Aoiota ... 760 TABLS OP OOHTKVTB. ••• XIU CHAPTEB XnL; Page 424. YOLTAIO ELEGTSICITT. Amrent flrrfUtion hj contact ofmetila ... ... ••• 761 Sflbet doe to ebemieal aotlon. . . 762 Beetric and ehamifal aotioii re- lated 763 ElaetrlcaeTiet of elements ... 761 Toltaie aetlon of zinc and copper 76 > Comae of tbe current 766 Conent dneio diemieal action 767—770 Saiee^a battery 771,772 Two flnids emplojed 773 Oaoieirs cell 774 Bkctrotype ... .*« ... 776 G rove's cdl •.. «■* ... 776 Booaen'seell 777 Scbonbeln'e cell 778 MOTnoothoell 779 Sobcrts's batteij 780 Leeson'g battery 781 PlsHnnm^potaasiiim comUna- tion ... ... ... ••• 782 ZfaM-csrbon battery excited by anlpbate of mercury 783 Modes of prodadngcarrenti 784—787 YolU'spile 78d»789 Pahrermaehei's cbsin-piila ... 790 Blrin^feUow'B battery 791 Marie Dayy'i pile 792 Crailuhanrs Dattexy 798 Snlell's battevy ... 79^795 Grovels battecy 796 Obm's theory 797 SadoedoDsfttmit ... 798^799 b's bridge 800 Form fVeqaently naed 801 Unitofresistaooe 808 Resistanoe coils 803 Kneostat ... ..■ ... ... 80a Condnctivity of metals 805 Kleotrio light 806—809 Serrin's electric lamp 810 Slratiaed discharnre 811 Inflaenoeofresistanoe... ... 812 Insolation by a vacunm ... 813 Inflaence of magnetism ... 814 Ignition of wire 816 Oalranio Icuife and canteiy ... 816 Cold produced by a current ... 817 Dry piles ... ... ... ... 818 Grove's gas battenr ... 819,820 Water decomposed ... 821,823 Ozone formed 828 Ozone generator 834 Definite electrolyiie ... 825—827 Voltameter 838 Secondary currents 828 Contrary energy... of th< 830 CondacCiTity ot the fluid !.'! 831 Electrolysis by one element 832—834 Beoquerel's battery 835 Seduction of metals ... 836—839 Reduction of ammonium 840,841 Electrolysis by a fl^nklinio cur- rent 842,843 Apparent anomalies ... 844—846 Bednctlon of salts ... 847,848 Franlilinio and voltaic currents compared 840 CHAPTEB XIY.; Page 478. ELECTRO-DTKAMICB. ActhmofaenrrentoD a magnet 850^ 851 1 Ampere's law 862 Law of amount of action ... 853 jBvenor ... ... ... ... 864 Galvanometer 856 Astatic needle 856 SquUfbrlnm of needle 857! Bensltfve galvanometer ... 858 Tlkomson's reflecting galvano- meter ... ... ... '•• 8)9 nomaon's marine galvanometer 860 Gaogain's tangent galvanometer 861 MagaetiamolAeo&diiGtor 862,863 Mutual action of ourrenta ... 864 Roget's galvanic spiral ... 866 Rotation of a magnet round a conductor 866 Rotation of a conductor round a magnet ... ... 867,868 Vibrating conductor 869 Spur wheel 870 M agnetic effects of a current 871, 872 Dels Rive's ring • 873 Rotation ofDe la Rive's ring 874 Electro-d>namic cylinder 875, 876 Ktoctro-magnets ... 877* 87B XI? TABLB OF COKTBKTS. Botation of magnets ... 879,880 Botation of one condootor round another ... 881,883 Theory of Ampere ... 883,884 Electro-dynamio engines ... 886 Induced, or secondary cur- rents ... ... ... 886 — 880 Self-indaction in a coil. . . 880, 891 Elongation of a bar by magne- tisation 892 Shock from seoondazy coil ^ 893 Currents in a revolving disc ... 894 Electro-magnetic machines 896—807 Inductorium 896—908 Faraday's original experiment 904 Magneto-electrio machines 906 — 907 Siemens and Halske's magneto- electric machines 906 Wilde's magneto-electrio ma- chines 911 Induced rotation ... 912,913 Induction on varioiu metals ... 914 CHAFTES XY. ; Page 614 ELECTRO-TELEGBAPHY. Ronalds' telegraph 916 Needle-telegraph 916 Communicator of needle-tele- graph ... ... ... ... 917 Alarum-bell 918 Wheat8tone*s rotating disc tele- graph ... ... ... ... 919 Wheatstone's magneto-telegn^>h 920 The first magneto-telegraph ... 921 Siemens' magneto-telegraph ... 922 Wheatstone's private tele- graph 923—926 Morse key 926 Horse telegraph 927 If orse alphabet 928 Horse printing telegraph ... 929 Belay ... ... ••• ... 980 Siemens' polarised relay ... 931 Bain's eieotro-chemical tele- graph ... ... ... ••• 932 Wheatstone's printing telegraph 933 Wheatstone's automatic tele- graph ... ... ... 084 Buewell's copying telegraph... 936 Conditions of long circoits ... 936 Submarine tel^raphy ... 937 Siemens and Ualske's cable ... 938 Hooper's core 939 F. Jenkin's diiforential gearing 940 Electrical teste 941 Resistances of metals and alloys 942 Resistances of copper, ftc., at various temperatures ... 943 Insulation teste 944 Induction teste 945 Teste for fkulte in a cable 946, 947 Teste for fkulte in land Unes ... 948 Tests of resistance of a battery 949 Electro-magnetic loom 950 Electric docks 951 Bain's electric clock 962 Shepherd's electric clock ... 963 Froment and Hardy's clock ... 966 Synchronous docks , 956 Wheatetone's chronbsoope ... 967 Chronofrraphs 968,060 Greenwich time-bell Electric regcdator 060 961 CHAPTEB XVL; Page 646. THEBKO-ELECTRICITT. Origin of thermo-dectridty ... 962 iniermo-series of metals ... 968 Current from one metal un- equally heated ... ... 964 Cmnent shown by attraction... 966 Thermo-dectric rotation 966,967 Thermopiles 968,969 Pdtier's hygrometer Beoonerd's and Marcus* thermo- Conversion of thermic and dy- namic onergy ThermoHsnrrente of low poten- tial w.— * ... ... ... ... Thermo-dectric oombinatioDS 970 Eleotro-thennio eflBMta... 971 972 m 974 976 TABLE OP COMTEHTS. XY CKAPTEB XVIL; Page 662. OBOANIO ELEGTBIdTT. SItetrielbhes 976 ToTpeik) 977 GymDotot 978 Fvadaj'B experiments on gjvch notofl 979 Direettooof emrrent in gymnotna MO Silanis 961 Electric imectfl 982 GahraBii's discovery 983 Yolta't experiments 984 Aldlni'f experiments ... ... 985 LawofVaUi 968 Kenro-electric theory ... 987,988 Vncealsr currents 989 Matteofid's fVotr-bftttery ... 990 Mstteood'a ftog rheosoope ... 991 Pigeon-battery 992 Dlieetion of currents 993 Proper corrent in frogs ... 994 BeseanhesofDaBois-BeynKmd 996 BeaeaRhesordianveaa ... 996 Fh^ological effects of a onrrent 997 Evidence in favoor of the dy- namic theory 996 PhvBiological effects not dne to direction of current . . . 999, 1000 Muscular and nerre currents subside with functional acti- vity 1001 Eckbard's experimimts ... 1002 Rate of transmission in nerves 1003 Time of - transmitting impres- sions 1004^1006 Electricity firom friction ... 1006 Electricity firom chemical changes 1007—1009 Liebig's theory lOlO Indications of potential 1011,1012 Piles of organic tissue 1013 Electricity in animal ftmo- tions 1014—1016 Vegetable electricity 1017 CHAPTER XVIIL; Page 676. LIGHT — CATOPTRICS AHD DIOPTBIC8. Naftnre of light ... ... ••• Undnlatory hypothesis Means of transmission Natare of wave-motion Analogies of sound and light ... Telodty of light Lizminoail7 1024^ Law of intensity Fhotocnetry ... •*• Cokored rays 1028, Modifications of light Direction of rays Law of illumination BeAeetaon of light ... 10S3— Bcflection from a plane Image defined ... ... ... Baecwaion of images Eefleetlon from a concave mir- ror-focus 1039 — '. BcAectlon firom a oonvez mirror Caustie carves Image in concave mirror Image in convex mirror SpheriMl aberration Least circle ci aberration ObUqiae reflection— focal lines CSrele of least confiiaion :oi8 019 .020 1021 022 .023 026 .026 .027 i020 .090 031 032 066 086 .087 038 .041 042 .043 044 .046 .046 .047 048 .049 Curve of sorfiMe of mirrors 1060, 1051 Fouoault's gloss speculum ... 1052 Method of silvering 1063 Refraction— law of sines ... 1054 Mutual direction of ravs ... 1065 Movable diagram of refraction 1066 Index of refraction 1057 Relative refraction 1058 Velocity varied in refraction ... 1069 Intemu reflection — limiting angle of refiraction 1000 Irregular refraction 1061 Newton's experiment 1062 Direction of refracted rays ... 1063 Prism 1084 Refiraction at a spherical sur* ilMiO 1065,1006 Caustic bvreflm^ion 1067 Forms of lenses 1068 Fochs of a sphere ... 1069, 1070 Refiraction through a lens ... 1071 Focus of lenses 1072 F06US of concave lenses 1073—1076 Focal length of combinations 1076 Images formed by lenses 1077, 1078 Magnifying power ... 1079^1080 Spherical i ition in lenaes 1061 ZTi TABLE OF CONTEVTB. CHAPTEB XIX.; Page 611, UQHT — CIIJU>MATIC8. Prismttlc deeompoeitioii Goloon in solar Bpectnun Beflraottre indices of coloured rays Kecompodtion of colourless MM^Mmw ••■ ■■■ ••• ■•• Leiwth and Telocity of waves of ooloared light LaTender band of Herschd ... Simple oolonrs Primary ooloors Superposed spectra ... ... Ccnnposition of colours Gornam's colour-top Absorption by transmission ... Absorptim solid to gaseous state 1428 Condensation of gases 1429 Heat of combination 1430 Water decomposed by heat ... 1431 Terrestrial heat 1432 CHAPTEB XXIV. ; Page 801. BADIAMT HEAT. Pereeption of radiant heat ... Heat reflected to a fucua 1434^ Theorj uf exchangee Identity of njiture of light and Bate of cooling by radiation ... Bate of oooHnff by convection. .. Proportiuns of heat reflected ... Forbes' thermopile Befraction uf heat CooTen^iice by a rock-«alt lens Beftaetion by prism of rock- ■BvW -•• *•• •■• ■•• Tramcolcncv and transparency contras'eu Hrat-spectmm of electric lamp Calorei>cett>-e BurfiMe-radiatlon Bate of cooling depends partly ooaarfluM « Terrestrial ntdiation Heaos uf comparing radiation Xoaer's fig*ires Thenperpetnal displacement of the planes of molecular isn^ution. But in the second case, the axis of rotation of the XXTl TNTRODDOTIOH. mass coincides in direction with those of the axes of molecular revoluiioni hence there is no displacement of the molecular orbits, and consequent!/ no internal friction, and ver/ little if any heat is generated. The rotatory character of the magnetic wave is further con- firmed by the known fact that if a plane polarized beam pass through a transparent solid in the direction of the lines of force of a powerful electro-magnet, the plane of polarization will be rotated the instant that the magnet is excited. The truth of a theory can be established only by the Terification of its necessary consequences; and it may not be too much to assume that in the present case the evidence already adduced by the writer is, in the entire absence of all contradictory evidence, strongly presumptive of the reality of the hypothesis. It has been authoritatively stated that ordinary electric and magnetic waves cannot both be assumed to be spirals, because each of these forms of energy notoriously evolves the other in a direction perpendicular to its course ; and the question is not without grave dynamical difficulties, but they may perhaps not be insuperable. It may possibly be that from some unknown con- straining condition or property inherent in magnetic bodies, a spiral wave, on being constrained into a spiral course, may lose its original spirality, and become a secondary spiral, having mole- cular motion in a direction perpendicular to that of the primary spiral. The relation between the various modes of motion, their physical results, and the sensuous perception of those results, having thus been inferred, the question next arises as to the nature of the media by which the several modes of motion are transmitted. It is unquestionable that sound-waves are transmissible by all kinds of matter, but can any valid reason be assigned in favour of the still prevalent opinion that other modes of wave-motion are in- capable of transmission by ordinary matter? — ^this incapacitpr being implied in the adoption of the self-contradictory hypothesis of an imaginary medium, not cogniasable by any known means of per- ception. It is a remarkable fact that in all the superseded crude notions of physical causation, each phase of physical energy has been presented in the garb either of impalpable, imponderable (in fact imm ing into a medium if they come on their heads, or bounding off, if they^ fall sideways against it. Then again, heat was supposed to oonsiat of material pacticies emanating from the source of heat; and aa a ball of ice placed in one focus of a concave mirror was found to lower the temperature of a thermometer placed in the conjugate focus, there were assumed to be particles of coU, aa well as of htal : it is needless to add how completely the theory of exchanges (1392) accounts for the latter fact. At length these wild speculations were superseded, and light and heat were admitted into the category of wave-motion ; but electricity and magnetism were still supposed to be either single or dual forms of " fluid" matter: and "Svca etism molll dora tanmtur sqoi i" these "fluids" are probably still running in the deep channels they have wpm in some philosophic minds. But the principle of admittiag imponderability into the cate- gory of legitimate physical hypothestes had become tacitly ac- oeptod ; and the conclusion was at once jumped at by the authors of the undulatory theory that the wave-motions of light and heat take place in an imperceptible, imponderable, highly elastic fluid medium, pervading all space, andaUmcUtert denominated "ether :" and this theory, with all its inconsistencies and inconsequences, is still probably entertained by many physicists. That some highly elastic and attenuated medium pervades infi- nite space, as the means of transmission of the energies of light and heat uom the centre of each solar system to its oependent satel- lites, is a necessary consequence of the dynamic theory: its ex- istence is, in fact, demonstrated by the periodic retardation of Eocke s Comet. Bat the remainder of the hypothesis, namely, that all palpable matter is pervaded by ether, tor the purpose of transmitting light- and heat-waves is by no means equally neces- sary, or even tenable ; for not a shadow of evidence of the inade- qoAoy of aU matter to transmit these motions has e ver been produced, xzriii nrrBODUcTiov. and in default of sncli evidence, the contrary hypothesis is at least eqnallj tenuMe : and this interstitial-ether theory (in common with all preceding physical theories involving imponderability) is hnr- dened with grave inconsistencies. In the first place the well-known phenomena of single anddouble refraction and p<>lariasation, whether of light or heat, necessitate the Romewhat viiJent hypothesis that the elasticity of (he supposed transmitting mediam, etner, is not, as it is in all cognizable fluids, a fixed and definite (jualitv capable of numerical estimation, but an ever- varying quality, depending quantitatively on the elasticity of adjacent matter, and in the case of double refraction, actually varying in tioo or in three directions, within the same svbttance : it would be not more re* pugnant to reason to assume that the elasticity of a gas is one thing in a glass bottle, and another in one of braes; or that the specific gravity of silver is a function of the moon's age, or the melting point of gold dependent on the- sun's zenith distance. Secondly, the fundamental ideas of inertia, energy, and *'work'' are inseparably associated with gravitation, and a contradiction of terms seems to be implied, in ascribing either inertia or energy, t.e., the capability of doing work, to an imponderable particle, which is consequently destitute of attraction for any other particle in the universe. The known enormous velocity, probably not less than 250,000 miles in a second, at which electricity travels through a cop- per conductor is complete evidence that ordinary matter is capable of transmitting aomeihing (whether matter or motion it signifies nothing for the present argument) at a considerably greater velocity than the waves of light and neat, why bhuuld not appropriate kinds of matter be assumed cspable of transmitting these also? and if so, the need of the interstitial presence of ether ceases altogether ; and it may with great advantage be excluded from the domains of ponderable palpable matter, by the very mild hypothesis that it is not miedble with air, any more than oil or ptupahU ether with water, but that it floata above the boundaiy surface of our atmosphere: this hypothesis is not repugnant to reason, nor adverse to physical experience. On this supposition it is no longer needed to impute to ether imponderability, t.€., an exemption from the otherwise universal law of gravitation ; it will then be imperceptible, only because it exists beyond the reach of observation : and thus imponderability will cease to he reckoned amongst the physical attributes of matter. Moreover, as there are no means of limiting the poeeihle amount of molecular dis- placement in a medium so attenuated as ether must be, an amount of energy is conceivable sufficient to impart effective motion to indefinitely denser matter ; and thus, witnout doing any violence to the fundamental principles of dynamics, this denizen of infinite apace may be assumed competent to ito divine mission of impart* nTBODDcnoir* zxix ing to material worlds thow essentials to corporeal existence,— the very mainsprings of organic lire, — light and heat. The question then natuitttly aris'^s — what becomes of the waves of heat and light, when they reach the confines of tiie atmo- sphere?— and is ordinary matter sufficient and effectual for their transmission ? Thin question can be answered only from analogy, which appears to infer an affirmative. That sound-waves are transmitted by air, and not by interstitial ether, is unquestionable; and if air be capable of transmitting S6,000 vibrations in one second, it will probably be difficult to aasigu any valid reason why the same medium is incapable of tnmsmitting the far more rapid waves of heat and light ; and if capable, then where lies the necessity for assuming the presence of another medium? Again, the refraction of sound, as demon- strated by the experiments of Hujech and Sondhaus (563, 564), is in exact accordance with the laws hitherto assigneil to the refrac- tion of light and heat. And it appears that the velocity of sound in solids and liquids is much greater than in air (545) ; in water it is nearly 5000 feet, and in iron nearly 17,000 feet in one second : is there, then, any known fact whatever that tends to assign a fimit to the powihU velocity of transmission of wave-motion through these and other material media? — ^if not, then the pre- sence of ether, as generally assumed, cannot be deemed essential to the transmission of light and heat ; and if not essential, why should the interititiaXrWier hypothesis be any longer entertained ? '* If eo Deat intenit, nisi dignot tindioe nodus Indderit.'* Moreover, Prof. Tyndall, to whom the progress of Dynamical Physics is indebted for many laborious and important researches, has observed that in various kinds of wood there is a remarkable hannony between their respective condnctivitiesfor sound and heat in three mutually perpendicular directions, namely, longitudinal, transverse-radial, and trms verse-tangential (546) : now although there is certainly no direct analogy between the conduction of heat, and the radiation of light and heat, beyond that of their coounon dynamic origin, a much closer analogy may nevertheless be traced through the phenomena of pho.«phorescence, fluorescence, and caloreseence. It appears to oe highly probable that the "caloresoence'' of a plate of platinizeuplatinum, the phospho- nscence by heat of the minerals Fluor and Apatite, and ordinary incandescence are analogous phenomena; differing only in the temperatare (t.e., the amonnt of thermic energy) at which heat- notion, impressed on the molecules of different substances, is im- parted as nght-rootion to the surrounding medium. And some phenomena of phosphorescence present further evidence of the in- tiointe relations existing between light, heat, and electricity : it XZX IXTBODDOTXOV. haB been observed that Flaor mtij be rendered phosphorescent by a very moderate application of heat ; but that it will not again Eoosnhoresce under similar circumHtances, until an electric spark as Deen repeatedly passed over its surface. But perhaps the closest analogy between the radiation of light and the conduction of heat may be traced in the observations of M. De Scnarmont, who has found that, in plates of ciystals cut in a direction coin- ciding with that of the optic axis, the relative conduction of heat, in directions parallel and perpendicular to the optic axis, is governed by precisely the same laws as those of optical elasticity, which determine the relations of the ordinary and extraordinary polarized rays : and moreover that in plates cut perpendicularly to the optic axis, thermic conductivity is, like optical elasticity, equal in all directions. It may also be remarked that the con- Terse permeabilities to light and heat of a crystal of alum, and one of dark smoky quartz, or a smoked plate of rock-salt, present striking examples of the existing yet unknown diflemnces of physical constitution, which are met with in the variiius kinds of matter, and which involve special capabilities of transmitting, or of arresting and diffusing, particular kinds of energy. The correlation of the various lornis of energy and their trans- mutations have been so well collated by Mr. Grove, and so fre- quently referred to in the preceding and subsequent pa^es, that repetition here w*ou1d be wearisome ; it will suffice to refer to the before-mentioned enormous magneto-electric engine dehigued for the illumination of lighthouses, and constructed also by Mr. Wilde of Manchester (91 1). Acting like those of Messrs. Wheat- stone, Siemens, and Ladd, on a principle of reduplication, or self- reaction, it is a grand instance uf the transmutation of energy ; and it may here be cited as a good example of a series of succes- sive conversions. In long bygone ages the energies of solar light and heat were occupied in the development of woody linsue, and this became gra- dually converted into coal, perhaps without much gain or loss of energy. The dynamic energy arising from the collision of the molecules of carbcm with those of atmospheric oxygen, in the act of combustion, f.e., combination, is yielded up as thermic energy to the boiler of a st-eam-engine, and generates steam, the elastic force of which, through the medium of the engine, drives round the annatnres of the electro-magnetit. Dynamic becomes now con\*erted into magnetic, and this again into electric energy, and an in- terrupted current of intense power is produced. This being trans- mitted between carbon electrodes, an immense amount of light and heat is produced by molecular friction at the point of great resistance to the passage of the current, and these are prodnced at the expense of electric energy, as proved by the loss of current ; here, theo, we have the final transmutation of electric into thennic ISTBODUCTIOV. ZXZl •Did pbotic* energy: the latter being so intense as to have thrown a shaditw a:rro88 the brightest sanbeam, and to produce an amoant of illomiDiition unattainable by any other known means. This entire series of transmutations ma^ be viewed as a complicated process of erolving stored up saudhine in an intensified form, for occa- sionaJ use. Having sufficiently considered the physical, it now remains to Rview the moral aspect of the large questionH that have been raised in the preceding pages. The Author cannot but feel that in thus seeking to simplify by generalization the conception of the powers of nature, and to unify their source, he may in some minds, misguided by the pride of human reason, unwittingly encourage the pantheistic tendencies of the present age ; than which nothing can possibly be further removed from his desire, or design. Where, it may be asked, is the faintest shade of difference between modern pantheism and the nature-worship of the oldest times, save that the mode of culture may have been humanized by civilization? in both alike reason and the objects of sense are deified, the thing created is set up on the Creator's throne, and the light of reve- lation, with it« priceless coiiseqnenceM, being invisible lo the mere carnal eye of sense, is practically extinguished. Ihe author vottid rather remonstrate openly with those who, conscious it maT be of great intellectual power, have unfortunately been led to Ignore ail things divine, tnat are not cognizable by unaided reason, and to aucn he would say, in the emphatic words of the peat Tishbite of old, *' How loug halt ye between two opinions ? if the Lord be God, follow Him ; but if Baal, then follow him :" and he would earnestly entreat them to reflect that between the two alternatives there can be no compromise. The grand mysteries of Crention must of course be ignored by all those who have closed their eyes against all things not visible m the light of unaided reason ; and accordingly it has not long siooe been asked before a large and intelligent audience, Whence came ihe fir^t elephant? *'did he fall from the sky (i.e., from the interplanetary space) ? did he rise moulded out of a mass of amoruhoDS earth or rock ? did he appear out of the cleft of a tree? ' — to which, responding in the same key, the writer answers so : — ^nor yet from the endless transmutations either of a sign-post, or a galinwM-tree ;-r>nor even from the adaptive efforts of countless generations of huge boar-pigs, inheriting from their primseval ancestor a weakness for the green tufts that grow on tall and leaf- less tropical stems; — ^nol — that wonderful mechanism of inter- Iscing niujvcular fibres, by which a boneless appendage can acquire abno*«t the rigidity of an outstretched arm, and the prehensile sensibi'ity of opposed digits, could only have come, and must have coiue direct, from the hand of an all-beneficent Creator. * ThA Greek roots are generallj adopted in all similar words. zzzii iHTBODucnoir. It may by some be thonght that tbeae remarks are ^xtra vires in a treatise on Phjsics, but the Anthor cannot ignore the apostolic injunction — " Whether ye eat or drink, or whatsoever ye dOj do all to the gloiy of God ;*' and he feels that when such language has been publicly proclaimed, he would fail in his Christian duty if he failed to give equal publicity to his earnest and indignant protest. ERRATA. N.B. — It will be foand oonvenient to make these corrections before reading the work. Line, Error. OMTtoAon* S3 i,note log Pi -log Pj p f «.tan^ w n log,I>i-log,P, 205 26 andiB and in the first column is SIS 126 casting forging 268 23 manytinieB much 289 16 M. Clement Desormes hai MM. Clement and Desormes hare 310 10 of the hypothetical me- } dele dium ether 312 86 % 313 8 in table s 0» 346 1, note 6A.lf. Sajc 887 1 potential electricity electric potential 308 632 176 16 TnieBuued (713) unTmcanlaed M 146 600 flOOO WW 126 800 8000 Ss Pig. 636 B» 10 coils B, 11 coils NATUEAL PHILOSOPHY. 1. Au. TBrietieB tnd drmi of nuttter ue nmiUrly composed, bring mule ap of an iDdefinile Dumber of extremelT, and mdeed inooDceiTtLblj, minute indcatmctible porticlei, irbich, from their not admitting of Further mecluQical oinBion, &re lenned atotnt* Soma philoaophen baie, bowaier, conceiied that no tma atom czi»ts, and that all matter ia capable of undetgoine diiinon to mfinitv. a atatement capable of being aatiibctori^ prored in r^snC to space, by the ooiuideration of matbemarical lines and HontB. Tbns, let ^ b, c d, -. . be lines drawn parallel to ^' ' cBchotber^drawuieabliqtw I line r o, aod ^m r on the I indefinite right Lne, c n, I take anv number o! equal I paitt,aerabed,&c. Ymm I B draw lines connecting ihis I point to ni» be infinite, H bllows Uiat the line r o ma; be infinitel; dirided by lines cod- Decting such points with ». Acgnmenta of this kind ongbt, however, to be regarded as qipficable onl; to mathematical lines and point*, wliich, the former being witLont breadth, and the latter withont magnitode.f * A, ud ■ri^rm, Hbido. t Endid, Book L itb. 1, 1. n bo ref^rded but ■« mental conceptions, md not plijsicnl 2. The nltimmte particles or alomi [I] of matter poawss the three funUiaZ cbnrnoterB a( impenetnAtliiy, txtetuion, Hodjiirure. Of thsMi properties, the first flows directly frotu the definition of sn at^nn, as it is obrious that nothin;; cnn be to impenetrable aa that which ia incapable of farther division. When anj solid 'bod; is immersed in a fluid, some portion of ihe latter is displaced, sndllinB, on a snperficial ticw, might ba supposed lobe penetrated bj the immersed body; it nil], however, be found that no real penetration occnrs, as a quantity of fluid becomes displaced, equal in hoik to the solid immersed. (Ch. VII.) On forcing a nail or a, ki.ifeinto a piece of wood, Iheultimate physical atoms of the latter are not penetrated, the instromentbeinK merely «*. »■ insinnaied into the interstices eiisti 05 between the indivisible molecules. Again, air and all them, are really as impenetrable as solids, allhough their particles arc tapable of mucli ^ater condensation bj nieclianica) means. If a glsBB receiver, *, be inverted over a lighted taper Ried on a cork floating en the surface of water, it can bo pushed to the bottom of the containing vessel, and the taper will thus con- , tinue to bnm under water so long ss sufficient 'b present to support combustion; a 3. The aeccnd chnraclcr, or erttniion, is also a necessary conse- quence of the delinilion of nn atom alrcndj ^ven, as that which possesses a pliysical existence must necessarily occupy a portion of space, and puiiiicss sides nod rurfnccii in relation to other atonis. "nie citpnsion iif bodies is oipTeased by the ibi-ee dimeneions of leDgth. breadth, and thiitness. 4. The third character, yti/ure or ^rm, is nl<>o essential to tlic existence of an atom, as nulhiug c;in bo conceiII^d aa phybicallv existing, unless it possesiies some determinate aliajie, althoush this ]iroperly is tiot tnmcient of itself to prove the material eiislonce ufan o^'cct ; for in sha^on-s and in spectral illusions, produced by various optical means, wo have cxbRiples of ligure or form wiiliout 5. Of the actual form or sixe of atoms, nolhinf; p'wiiive is knon-H, it is. however, probable that Ihov are sphorlcnl : hut In their difnenalont Ecarcely an app'oiimaliun can be oblnincd by MIKUTEXB98 OF ATOMV. 3 nnj meiuiB we are jet acquainted with. An ounce of gnid can b^ drawn into wire several miles in length (12), and jet no flaw, of evidence of separation between its atoms can be diflcoyered by the closest microscopic examination. Cbemistir affords ns eyidence of the ezcessiye minuteness of atoms, for when seyeral metals, as nickel, cobalt, or iron, are reduced from their oxides at the lowest possible temperature bj means of a current of hydrogen gas, the fitate of diyiMon of the reduced metal is almost inconcciyablt*. Each particle of metal slowlj evolving its ox jgen, forms a powder which maj be considered as composed of ultimate atoms. These are in everj case less than the one-hundred-millionth of an inch in diameter, so that bj a simple calculation it maj be proved that a cubic inch of them would, if extended on a level surrace so that they maj touch, but not overlap each other, cover an area of 218,166 square feet, or more than five acres of ground. 6. AnoUier illustration of the extreme minuteness of atoms is met with in the thin films of soap bubbles. These present fine iridescent coloured bands, and at the npper part ot each, it is demonstrated that the thickness of the film, just before it burets, cannot exceed the four-millionth of an inch ; and jet even this thin lajer is not composed of a single stratum of atoms ; as it must consist at least of the atom of soap and ono of water ; the former compoeed of soda, stearic, or margaric, and oleic acids, in the simplest view that cm be taken of its composition, and the latter made up of at least a molecule of oxjgen and one of hydrogen. We may likewise appeal to organic life for evidence of the un- limited divisibilitj of matter, in the extreme minuteness of definite structures that have been revealed bj the microscope, exhibiting the wonders of creation not less manifested in the most minute, than in the most stupendous works of which our senses are cogni- sant. Animalcules exist, so minute that mjriads can swim in a drop of water, and jet everj individnal possesses organs of diges- tion, circulation, and reproduction. The polishing-slate from Bilin in Bohemia, composed almost entirelj of the siliceous shells of infusoria, has been calculated to contain 41,000,000,000 in one cubic inch, which weighs 220 grains; consequentlj each shell, possessing nevertheless, the most exquisite beauty of structure, would weigh little more than the two nundred-millionth part of a grain. 7. The minute molecules composing masses of matter maj be, and often are, chemicallj compound, althongfa phjsicallj simple ; thus a piece of marble maj be divided into its ultimate molecules, each CQouisting of carbonate of lime, and here physical analjsis stops ; but bj chemical analysis we can separate each of these atoms into carbonic acid and lime, the former being asrain chemicallj divisible into carbon and oxygen, and the latter into calcium and oxygen. In physics, therefore, a molecule is reganled as simpio B 2 4 GBHEBAL PB0PEBTIE8 OF MATTER. when it cannot be farther diyided without separating its chemical elements. 8. The indestroctibility of matter must be regarded as one of its inherent properties. It is no more within the limited scope of human agency to destroy any of the ultimate material elements, than it is to create^ or even to commute them, as the alchemists of old vainly attempted. The tenns "destruction by fire,'* " destructive distillation," must be understood in a limited sense,as referring only to the previously existing form of matter, and not to the matter itself. The stick of charcoal is consumed, and leaves no vinbiU trace of its existence but a minute quantity of white ash : it is not however destroyed, an invisible gas has been gene> rated by the union of the carbon with the oxygen of the atmo- sphera, which manifests its existence by its power of extinguishing alike (and for the same reasons) die flame of a candle, and the vital spark of organic life. Many fluids, water for example, will readily evaporate ; but its particles are merely suspended invisibly in the atmosphere. This mav be rendered evident by their precipitation on any suitable cola surface, as on that of a glass vessel filled with iced- water. Tbe history of the earth's crust informs us that these wonderful transformations of matter have been progressively in operation during vast periods of time, of the extent of which the human mind can form no conception. £ven the humble "earth-worm that we tread on" plays an important part in the scheme of creation in continually reclaiming to a hi^ner grade of organiza- tion the organisable materials of the soil in which it lives and moves and Las its being. 9. Atoms and molecules are held together by means of a force denominated aUraction^ the finnness of their union being modified bv the presence of an opposing force, termed reptdtion; and upon the preponderance of one of these forces over the other, depends all the physical properties of matter, known as hardneu^ Boftnen^ JUiiaity, &c. ^ Tne intensihr of this molecular attraction varies considerably in different bodies, which thus acquire very varying degrees of coherence. If the mutual attraction of atoms be so considerable as to prevent a rigid body beine readily inserted between them, the mass is said to be hard; but if so feeble as to permit their easy separation, the resulting mass is soft; and &fiuui or a acueous body results, when the intensity of the mutual attraction between the atoms is so far counterbalanced, as to allow any substance to be moved between them without experiencing any considerable resistance. The hardness of many bodies is mucn influenced by external con- ditions ; thus most metals may be considerably hardened by ham- mering or rolling ; and the hardness <^ steel, resulting from sudden cooling, when at a red heat, is a familiar example. On the con- traiy, an alloy of one part of tin and four of copper is said to be -n DBH8ITT OF MATTES. 5 ductile when cooled enddeDlf , and Inittle when cooled slowly. Thne the varions states in which matter exists, as soUdj viteouSf Uqvidt or oasetnu, merely dej^nd upon the yaiying intensity of the moleciuar forces of attraction ana repnlsion. The property of emitting a sonnd on percussion is ascribed to the hardness ofbodies ; hat this property may be shown to be possessed hy hoth fluids and gaseous ixxiies. The water-hammer, a glass tube containing water, nt»n which the air has been nearly exhausted hy boiling the water in the tube, and then hermetically sealing it, emits a loud sound, prodnced hy the concussion of the water against the elass. The crack of a whip, or the peal of thunder, auke show the* effect of the concussion of the particles of air against each other, when they ha^ been separated by .anything passing between them with a -velocity greater than that with which air would rush into a yacnum. These seyeral states of matter are readily conyertible into each other by yarious mechanical means, and by alterations of temperature : thus, water at 32** F., and mercury at — 40** F., or 72* lower, are solids, the one being transparent, the other opaaue ; and at about — 90* F. carbonic acid may be obtained in the form of snow. At ordinaty temperatures the former are liquids, and the latter, gaseous : whilst at 212* F. water, and 670* F. mercury, become yapours or gases, both being transparent ; these seyeral changes depending merely on the neater separation of their atoms efiected by the repulsiye power of heat. The original yolume of &e fluid becomes amazingly increased by this separation of the oonsfiitnent molecules. The following table shows at a glance their enormous increase of yolume by yaporization, under ordinary atmoapherio pressure. 1 cubic foot of water expands into 1689*0 cubic feet of yapour. alcohol . . . 493'5 ether .... 21218 turpentine . . . 192*15 10. The most elastic gases can, h^ the application of sufficient pressure, be compelled to asmme a yisible form ; becoming liquids if the pressure be great enough to bring their constituent atoms sufficiently near to each other. it n n n It It ti ti it tt GSMt. Tamperatore. Sulphurous acid Chlorine . . . Carbonic acid . Nitrous acid . . 2 4 86 60 45* Fahr. 60 „ 32 „ 45 „ 11. The density of matter in any of its three states is measured 6 GENERAL PROPEETIES OF MATT&B. hy the quantity contained in a given bulk, and is expressed hy its specific gravity or relative weight, as compared with some body, taken as a standard ; thus, if a given bulk of water consists of 1,000 atoms of matter, an equal bulk of platinum Avill contain about 23,000, if each atom has the same weight ; of copper nearly 9,000, of iron 8,000, and of glass about 3,000 ; these several num- bers being proportional to the specific weight or gravity (Ch. Yll.) of the respective substances. Masses of matter moreover possess several properties which may be considered as accessorv, all depending upon the different de- grees of intensity with which the physical atoms are mutually tie- 1 together. Among the more important of these may be ranked DivmbiUti/, I^lexibilitVf TetiacUyi BritUeness, £lcwticUyf &c. 12. Divisibility or iJxtenaion of Maasea, — This character may be considered as well illustrating the extreme, and almost incon- ceivable, minuteness of phvsical atoms ; depending upon the im- mense, although finite number of parts into which a mass may be divided. Thus, an imperceptibly small portion of strychnia will render a whole pint of water bitter, and a single grain of the ammoniacal hyposulphite of silver will render intensely sweet 32,000 grains of water. One grain of iodide of potassium dis- solved in 480,000 of water, when mixed with a little starch, will tint every drop of the fluid blue on the addition of a solution of chlorine. In all these cases, we have at once evidence of the extreme minuteness of atoms furnished by the divisibility of the masses of strychnia, silver, and iodine by means of solution. Excellent illustrations of the same property are met with in many ])rocesses of art ; a sinde pound oi wool will furnish a piece of yarn 100 miles in length. Gold ander the hammer is reduced to such state of tenuity, that 360,000 of the leaves produced would, if piled on each other, only equal the thickness of an inch. Even this is far exceeded in the art of the wire-drawer, who, in the most economical mode of preparing gilded silver wiiy, extends two ounces of gold over a length of 1,351,900 feet, or rather more than 768 miles. The exquisitelv delicate wires of platinum made by the ingenious process of Dr. Wollnston, afford a remarkable instance of the extension of matter, no less than of the almost inconceivable minuteness of the component atcms. The finest of these wires is but the three-millionth of an inch in diameter, and 140 of them placed together would just equal in thickness a single fibre of silk. This extreme degree of tenuitv was attained by enclosing a platinum 'wire in a silver tube, tnen drawing both together, and lastly, dissolving awav the silver coaling by an acid. 13. Flexihility. — When any substance is capable of being bent in anv given manner within moderate limits, hj the application of sufficient force, it is said to he flexible. For a body to possess this property it is necessary that the distance between its contiguous ])articles should be capable of being slightly augmented, without removing them beyond the sphere of their mutual attraction. The TLEXIIUUTT. property of flexilnlitj maj be illnstrated by tbe followiDg simple aj^paratas : — ^Let ▲ b be a piece of whalebone, haviiig a number of viies CD, d vff &c., passed througb equidistant bolea : let ^« >• two series of balls c, c', &c., i>, ]/, &c., be fixed to tbe ends of tbe wires, and let a third series, b, e', &c., loose on the wires, rest on tbe piece of whalebone. If tbe rod be bent, as p o, the row of particles rs- presented by the balls c will oaTe receded from each other, and the particles d have become more closely approxi- mated, while the distance be- tween the particles b is not perceptibly altered. That such a change in the relative distance of the atoms really occurs, is rendered evident by merely inspecting the fignre of a thick wooden plank which has been allowed to become curved by _, . its own weight. Let a b, c d, ^* represent the section of such a p!ank supported at ita extre- mities c, D, it win be seen at QQce that the surfaces a b and CD represent two concentric cm^es, of which a b is the smaller, consequently the atoms nearest the Borface ab must be more closely approximated than those seaieat c d. The atoms lying in some line intermediate between A B and c D, undergo no change, the line b p, therefore, in which these lie, constitutes what is called the neutral €ucia of the body, and this portion mij^ht be excavated and removed ■without mate- rially diminishing the strength of the plank, provided a sufficient amoant of substance be left, to prevent the collapse of the surfaces ABandcD. ^ 14. On this principle, hollow cylinders of different materials are employed instead of solid ones, when used as mechanical supports. Inoeed, if all opposing causes in the shape of flaws, bad workman- ship, &c., are absent, such hollow cylinders not only have the advantage of lightness and economy of material, but are found in practioe to be actuaUy stronger than solid ones of equal weight. Tredgold found that when the inner semi-diameter of the hollow c^inder is to the outer as 7 to 10, it will possess double the strength of a solid cylinder of the same weight Similariy in the construction of ca6t>iron girders, for supporting the floors of buildings, it is found that the greatest strength is obta^ied by making the transverse action lu some degree to 8 MOLECULAR OB IMTBRHAL FORCES. resemble the itiverted letter Xi ^^® reBistance to oompressfon and extension being equally sustained by the upi>er and lower lamins respectively, the areas of the sections of which are as 1 : 6, while the yertical lamina serves to maintain the equidistant position of the former. Wroufht-iron is, however, now almost universally used for girders, ana as in this form of the metal, its powers of resisting extension and compression are much more nearly e^ual, the upper and lower laminn are usually made of equal dimensions^ the giraer, if small, being rolled between grooved rollers, like the railway rails ; or if larfi:e, being formed of strips of boiler plate and angle-pieces riveted together. 15. Tenacity. — This character is dependent u^n the intensity of attractive force existing between atoms bemg sufficient to oppose their ready separation, to such an extent as to cause the rupture or fracture of the whole mass. Consequently, all flexible, ductilOi and malleable bodies are tenacious ; althougn many sub- stances possess the latter property without the former. The tenacity of matter is well shown in the remarkable malleability of copper ; for from a flat plate of this metal the skilful workman forms a hollow vessel without any joint or seam by the use of his hammer alone ; and by well-directed and repeated blows, the vessel he has formed, however much differing in ngure from tne original plate, is everywhere of nearly the same thickness. Tenacity varies extremely in different substiuices : metals afford the best examples of it ; dius, a piece of steel wire of g^ven diameter is capable of suj^porting witnout fracture 39,000 feet, or seven miles and a half, of its own length.^ Wires of different metals of the same diameter require different weights to overcome the mutual attraction of their component atoms, as shown in the following table; the figures representing the number of pounds avoirdupois required to break wires of the metals enumerated, each being ono-tenth of an inch in diameter: — M«tals. POQDdfl. Metals. Pooiidi Bismuth . . 20-1 Silver . . 18713 Lead . . . 27-7 Platinum . 274-31 Tin . . . 34-7 Copper . . 302-26 Zino . . . 109-8 Iron . . . 54925 Gold . . . 16007 Cables constructed of fine iron wires of from tt ^^ rir ^^^^ in diameter, are stated to possess the enormous tenacity of 60 tons in each souare inch. It is this wonderful tenacity which renders wires of this metal so applicable to the construction of light sus- pension bridges. The followinp^ table shows the tenacity possessed by different bodies calculated m tons weight.* * MoMley'i *< lUnstntiona of MediMiifl%" p. 886. TEVACJTT. 9 Teaaoiif in tona^ p«r iqaireiiiolu Wrongbt iitm, in vire ^ to^ inch in diameter 60 — 91 „ in wire ^ inch diameter . . 36 — 43 in Iwn (English) 25i „ in bars nammered 30 „ in chains of six-inch links . . . 21 ( — 25 Cast iron 6 — 9J Steel, cast 44 „ Damascus 31 ■ 44 Ccnpper, cast 8^ wire 274 Silver, cast 8 „ wire 17 Gold, cast 9 „ wife 14 Flatinom 17 The tenacity of the fibres used in the mannfactnre of different &brica, has been found bj M. Labillaidi6re to be very different ; he has ascertained the tensile stoeugth of fibres of equal sectional area of silk, New Zealand flax, hemp, and common flaz^ to be nearly proportional to the numbers 17, 12, 8, and 6, respectively. 16. Tredgold has shown that many solids witt bear an enormous amount of pressure before they yield sufficiently to allow any ^r- maaent alteration in their shape. The fieures in the following table represent the weight in pounds required to effect a change in the figiue of a one-inch cube of the solids submitted to experiment. Malleable inm. . 17,8001bs. Cast iron . . . 15,300 „ Brass 6,700 „ Zinc 5,700 „ Tin 3,880 „ Lead 1,500 „ KedFir . . . . 4,2901be. Oak 3,960,, White Fir . . . 3,630,, Ash 3,540,, Ehn 3,240,, From a comparison of these tables it will be observed that the relative powers o£ resisting compression and extension differ consi- derably m different substances : thus while the tenacity of iron is to that of sine as 5 : 1, the resistance to compression is nearly as 3:1; hence the position of the neotral axis will differ in different mat^ials, and titerefbre likewise the sectional form of a beam of greatest strength in proportion to its weifcht, a point of great im- portance in the arts of constructioo. This may be further illus- tnted by the preceding ^paratus (13), in which the mutual recessioD of the particles o may be in any required ratio to the sppraximation or the particles d, by varying their relative distances Ami; * 10 UOLECULAJl OK 2KTBRXAL FORCES. Connt Rumford found that a cylindrical roll of paper, with the folds glued together, and presenting a sectional area of one square inch, would support a weight of 30,000 pounds. The tenacity of metals is greatly influenced bj their tempera- ture. At a certain elevation of temperature the readily fusible metals entirely lose this property, and assume the consistence of putty. This peculiar st^te is made use of in the arts, as in the formation of a plumber*s joint ; and lead pipe is mafle by the metal in this condition being forced through a round hole in an iron plate, with a concentric plug placed in the aperture. 17. £rUtleness,^TLh\H is obviously the converse of the last pro- perty of matter ; it points out that condition of a substance, in wliich the attraction between its molecules, althoughperhaps very intense, is mnch limited in its sphere of action. Hardness and brittlencHs are not incompatible qualities, but, on the contrary, Irequcutly coexist ; thus a piece of glass, notwithstanding its pro- verbial brittleness, will scratch a surface of polished steel. If, however, glass be spun into fine threads, or blown into thin laminie, it exhibits a high aegrec of flexibility as well as elasticity. The opposite properties of hanluess and brittleness, or ductility and tenacity, are frequently manifested by the same substance under different conditions of molecular arrangement ; thus cast-iron and hardened steel are brittle, while bar-iron and soil steel are amongst the toughest substltnces in nature. 18. JSlasticity. — A body is said to be elastic when, after being bent in anv direction, it spontaneoualv tends to recover its former shape on the force which had altered its figure being removed ; all elastic bodies must be so constituted as to allow a certain number of their atoms to be brought, at least momentarily, nearer each other than they previously were. If the body be a metallic rod, then, on being bent in the curved form a b D o. Fig. 4, it will have a tendency to resume its primitive rectilinear form on the removal of the coercing force, in consequence of the exertion of two forces, \iz., attraction between the partially-separated atoms on the out- side, and repulsion between the closely-approximated atoms on the inside of the curve. In this case, the cnange of form which brought into action the elasticity of the body is very obviouB, from the ourve produced by its flexure ; sometimes this change of figure, even in the most highly elastic bodies, is not evident to the eye, from its short duration ; still such change does demonstrably take place. Thus a ball of ivory is elastic, and this property causes it to rebound from the floor when forcibly thrown upon it, its figure, on impact, becoming altered and compressed ; as may be shown by causing onn ivory ball to impinge forcibly on another, smeared with some dark unctuous matter, as printing ink; the surface marked by the impact will be much larger thau if the balls were merely brought gently into contact with each other, thus showing that a mutual compression of the substanco of the balls hati taken MOLECULAR AGOBEOATION. 11 place (Inring the impact. Two balls of caoutchouc, which poMtesa a mnch greater degree of compreaaibility, will produce this effect io a mai« marked degree. 19. A body is said to be perfectly elastic, when the force with which it tenda to recover its original form, or as it is called, the force of rtHitviion^ w exactly equal to the compressing force. No kind of solid matter is perfectly elastic, bat many are elastic io a high deeree, the forces of compression and restitution being nearly ^qual. Different elastic bodies vary extremely in the extent to wiiich lliey will yield without rupture ; thus caoutchouc, and espe- cially the vulcemized variety, may be stretched to five or six times its original length, and will afterwards very nearly regain its ftinuer shape, nnleas the tenuion has been maintained for some time. Threads, and thin laminss of glass, and tempered steel springs are highly ehuitic ; unannealed iron, brass, and copper, are also elastic, but in a less degree than the former. Fluids, and especially gases, are the only forms of matter that exhibit the property of perfect elasticity : the latter, on account of their phy- sical constitution, will permit their atoms to be very considerably appcoximatod, by the application of sufficient force ; again sepa- rating instant jineousiy, and even with violence, on the removal of pressnre : the air-g^n, and condensed air-fountain are examples of this property in atmospheric air. 20. AIthriu|^h the scope of an elementary treatise forbids a de- tailed discussion of many important branches of phjrsical research, the sulject of molecular attraction would be incomplete without some notice of those remarkable conditions of pohmty in molecular aj!gregation, that ^ve rise to the formation of crystals. The term cry9tal originally implied transparency, bnt, in its more extended sense, it is applied to any portion of matter that has spontaneously assumed a definite geometrical form, bounded by four or more plane surfaces ; four planes being the least number that can enclose a fipace. Crystals that have been ibrmed by the agency of natural causes are tenned natural crystals, while tho^e that result arti- ficially from fnsion, solution, or any kind of chemical action, are called arf(^ScuzZ crystals. 21. The varieties of crrstalh'ne form depend on the different directions in which the forces of molecular aggregation act most pnweriiilly in different kinds of matter, and also on the relative mtensity of those forces. Some direct evidence of definite direc- tions of greatest molecular attraction may be derived from the fact, that many crystals will yield to any applied foix;c and break or hph't only in plane surfaces having a constant direction ; this pro- perty is callea cleavage. If a natiual crystal of Calcite, commonly Known as Iceland tpar^ or of the lead-ore called Galena, be broken into fragments, the surfaces of each fragment will have the same relative position as those of the entire crystal, or portion of a crys- tal, from which they were derived ; and if these migments be tri- 13 tanited in > morUr to an impalpable powder, and examined bj a micToacope, it will be foaiid tnateach particle is boundsd by plaiMi having the same mutual iDclinationB. 22. The lUreotiona of greatait molecnlar action CMDot in all cijitali be di«coTered hj cleavage ; bnt in all caaei, three lines of direction ma; be taken, pasting throngh the Bame point, bnt not lyinff in the (ame plane, which will bear some known relation to the direotioni of the molecnlar forces, or to the obterred inrfacei of Uie ctjita] ; ^eee three lines are called the Axe* of the crplal. 28. All the obeerved hnai ofetTstaU maj be referred te oite of nx AMentiall; diffenet ■jatems c^ crTstallixation, each of which may be defined by die relative podtion andmsffnitudeof the axes. The relative lengths of the axes, which define the formof a crystal, •re called voroiMlsrs. S4. In tnree sjatenu the ciystallographic axes ore all perpen. dicolar to each other. I. If the axes are all equal, the crjstal formed beloDKS to the QtUe system, of which common Salt, Alum, and Floor Spar are examples. Ctystals belonging to the cubic ^item are chiirac- terised by an appearance of symmetiy in whatever direction they tig. i. rsf. t. Silicate ofNickel are examples. Ciyslak of this class ftw^aentiy it tin mppearmnce of > iqiiare pyramid. When Tiawed in the .... ion at tbe mieqnal aiia, ttieu oatline U Brmmetrioal with regaid to the foitr ndei or eoniera of > aqnAre, bat when riewed In tbe directioii of either of the two equal axes, the ontline ii ijmme- trioLimlj with regard lo the opporite lidei of a rectansle : this taaj be imdentood bj a reference to the flgntet, in wbiob tbe nn- aqnal axes are TertkkL IIL If th« axes are nnequal'in ail three directiona, Ihe renilting fcrmatioa lepreaenta the iVitniatie B.vatem, of which tbe Snlpbatea of Folaab aitd Zinc, and Rochelie Salt are eiamplee: the latter salt, LoweTBT, fracjiKiitlj crjstalliEeB in half prianiB, ahowinE one of the irrwdariliea that occssionally occur in tbe (onoation of CTjstala. The fonns belonging to this ajslein freonently present a ijnunetrical bz«ng&«baped ontline, when view^ in the direc- tion of tbe «xi* of tbe priam, which is Tertioal in tbe entire ci7>taL FIg.t. [isles to each other in a _, .__ , but in a vertica! plana, ptiing tbrongh either of the other two, tbe OUtjue s^tem is eumpTified. Proto-snlpbate of Iron, Carbonate of Soda, and Tar- taric Acid, with nameroos other natural and artificial ciratals beknig to thia sjBtem. Ciystals of thia claee can be divided into two mnmetrical halves only by tbe plane in whioii the obliqae axis bee : thia paaaea through the edge at which tbe planes Mand n' meet, and tbrongh a diagonal of the plane p. T. If tbe three axea are eqoal and equally inclined to each other, Prttt-tM2fiat§ i^Itoi. 14 nil. 13 but not at right anglM, the B\omhoktdral iyilera reiulta. Tha crjutala nf thJH tjpo ubiibUj pntMnt a trianeular or bexaguiial STmmetrical ouclino, irben viewed in tho direction of the niia of the Rhombohsdran, wliich IB UBiMlly drawn verticallj, u in ibc following figure; but it muBt be obaeireJ ihat thiH niia in Hat One nr tlio crjstallo- graphic aiee, Calcite, and Quartz ar Rock Crriitiil, aa [t ia commnnly turmed, are fa- miliar examples of ihis clau. of the forcf^iag conditionx Hfe fulfilled, Uie O the AnoTthic Bj-Btem ; which although com- pnsing an alrncul endlesB lariet; of fnuiblo relntialia, hw verv few knnwn reproaeiitalivBH ID nature ; in which fact we rccogtiiae the universal tendency to STmmetrical and har- moiiiauB arrangnnient, thai Ih met with in all llic wonderful wurka of creation. biulpbnt« of Cop^r, and Aiiuite (Fig. 13), are ffiod iliualr«iionB of ihiii gjateni ; Ihe cry bUIb belonging tuwIiichSirBcliiirBcteriioil Aiifiit. \jy a total want nf syiumolry. Bft. Tlie position of the rariouB planes or faca at which the surface of a cryBtal !-> compoaed, is aometiiues determined lijtbeir relation to the facea of a paralleb^pipcd of the limpluBt form IliHt exbibils the characterigLicH of the eyBti^m to which it belongs. Thin ia called the prinurtf form ; and the planea by which its edges and angles an modified nro culled ttamdary planes. In tho pivreding figures the primary planes are marked by capital letters, and the secondary by italics. Jr. 14 26. 'He law of aymmelry, which prevBita to a remarkable eiteut amonff cryatala, re- quires that all simiUr edges and angles of the primary form should be similarly modilied ; hence in a Urge number of inatunccs, tbo ayni- nietrical arrangement of the aecundary pluneii will point out the Byslemto which thecrystiil ahoukl be referred. 27. In some crystals a deviation from the law ofs.vmmeti^ is obiicrved in the exiatencu nf only batf tlie comphto number of planeii, ticher the altemata or tho oppojiCe plnnen beinp Duiitted, aa in Fig. 14 : lUse are callcl ItejaihedTol fmma. In some of these tbere ii a correapondenco between the unajmmetricHl fiinn. and other phTeical ibnractora; as in aitKiQ nbich cithertbe right or Ihu kit huDil CTALS. 15 plines are omitted, as in tlie itnneied Heart, In tlieas an effect is pmdoced on n ray of l!f;ht trBnsmitt«d Inmugb > horizoutal slice flf the crjitsJ, which will ba Bubsequentlj explained aa righv or Wa-banded circular polsritation. (Cb. XXUL) In Ihe cubic sjstem two ilintinct cliasea nf bemihednl fnnns ara freoDentlj met witb. One oT tbeae, the heniiheitral ictlA paraBei face*, reiults from the alternate deficKnc; of o: ■hich the complete form 120 (that of wbich the indicia are 1, 3. 0,1 ia represented in a (Fig. 15) while the corresponding hemihedral form is b; in which of tbe pnirg of similar ptaneii a, b, in a, the plaaci a odIj are developed. The bemihedml form mth obliqut fane* ariwa from the defi- ciency of one of each pair of immiu pUnes, of Ibis the simplciit fxaaipk ii the tetTohedrori, which resuiis from the depoailioD of hucceMiTe lajera of molecules oa tbe alternate faces of the octa- hedron (Fig. 61 ; this is represented in a (fi^. IC); The tetmhe- dron ii unall/ dnwD in Ihe poaition b, in which position its retatioD to the oclAhednm is less apparent. anorthic si hemihednl formi of the obliqiH ; but no utiiiwtoi^ nnlt appear* U foUaw from this att«mptad genenluatioD. In PfTO^lectrie cr;»t»l», or thaw wbioh ezhilnt electrical pola- rity wben beated^ aa the TourmaliDe, a want of ajmmetrj between the two eitremlties ot the cryital ia nsuallj obaerred, 38. In many crjatiUine subttancei a remarkable, bat not un- ■ymmetrica], deviatioa Irom the nnialfbrtn ii oocanonallj obeerred. An; crjatal may be dirided into two equal and nmilar portione bj a plane passing throagh ita centre, sad parallel to one of ita faces, aa in Fig. IT, or (ai it i< in aome cases man ccmTtnienllj considered) perpendionlar to one of ita edges ; but the two halves are in a rSTenodjiaaliaQ u regarda each other. If, however, the aucoearire depoaition of particlea shoold take plaoe on opposite aides of thia median plane in Ihe tame dirMtion, the crrstal npre- sented in the seoond figure woold result, io place of tbe fonner; the letters 01^,0, Ac, showing the felatiooi of tbe planes in tha two fignrea. Crystsb of this kind are ealled twin oijttals or macles. The/ have also been called Henutroptt, beoanse the same resolt would be obtained if an ordinair ciystat were cut in half, and one portion tamed half ronnd on the other, a* maj bo easil; shown bj a model representbg these figures. «».iT. 'odiilinct forms not referable (0 the same class: tbns Calcite, which is rhombobedral, is chemically identical with Arragonite, which is Eriamatic; and natural crTatabofSulphar,as well as those obtaioed T anbiimation, and bv the slow araporatioD of a solution of Sal- pilar in bisulphide of Carboo, are pnraatic ; bnl those formed in the cooling of ^nlphor heated considerably ebave the point of tonon. HM occasionally, though rarely, those fonnedio the above- named sehition, bebng to tbe oblique system. Substances poa- sessiog tiiis property of aaanming two different fbrms are called dunorphout. Some substances also are trimoT^hovt, or oocorring in three different forma; thus Titanic acid in the mineral spedea Butile and Analase is pyramidal, bat the inclinations of tbe laces are very different, while in Brookile it is prismatic By moat recent aathors, the podtioD of any face of a crystal is h POemON OF A FACE DEFIITED. 17 detennined, without reference to a hypothetical primaiy form, by the relative distances from the origin (the point at which all the axes intersect each other) of the points at which the given plane intersects the axes: these distances are generally either in&nite, in which case the plane is parallel to an axis, or very simple sub- mnltiplea of the parameters (23) of the crystal : these submul- tiples are called tne indices of the face in question. In the language of analytical geometry a face of a crystal is defined by the equation A + B + c ^' in which A, B, C, are the parameters of the species, ajidp^ q, r, the indices of the plane.* * For ftirther i2if<»ination on tlda sabjeot the reader is referred to the Art. CrfBtallofraphy, in the " Encjdopsdi* Meiropolitanm," and to a reprodac- tianof Pfaiilipars "Mineralogy," Vj the late Mr. H. J. Brooke and Prof. W. H. Miller. 18 CHAPTER II. PHOPESTIES OF MAflSEB OF If ATTEB : — EXTERNAL FOBOSS. 30. ATTSAcnYE forces are capable of acting not only between atoms but also between masses, and form a very important sabject of consideration. The Molecular attraction of aggregation, which ties atom to atom, has been already alluded to. iVe have next to examine those forces which act between masses of matter ; these may be divided into two sections, the first comprehending attrac- tions at insensible distances, including cohesion and ecmjUarUy; the second, attractions at sensible, and eyen at unlimited distances, including gratfitation. 31. iAJl attractive forces, whether exerted between atoms or masses, diminish in intensity as the centres of attraction of the attracting molecules or masses recede from each other, snd gene- rally obey one law of the attractive force being invertdy as the equares of the distances between the attracting bodies. Attraction is always mutual, and exerted by one body on another, cceteris paribuSf in the ratio of their masses. As an example of the general law of attraction, let us suppose that two bodies, A and b, mutually attract each other when at a certain distance with a force equal to 1, at double that distance this force will be ^ instead of k of that when at a distance of 1, because the square of 2 is 4 ; at four times the distance the force will be diminished to ^, and BO on. ATTRACTION AT INSENSIBLE DISTANCES. Cohesion and Adhesion. 32. Wheneyer two smooth and clean flat surfaces of ax\j sub- stance are pressed together, a considerable resistance is expenenced in attempting to separate them ; this is owing to an attractive force called cohesion^ so termed from its causing bodies to cohere, or stick together. As an example of this force, if two clean surfaces of iron, at a white heat, be forcibly pressed, or hammered together, the cohesion is so perfect that they are subsequently inseparable : — this is the ordinary process of welding ; and some other metals are capable of being similarly united more or less perfectly. The mode of preparing black-lead for pencils, devised oy the lat« Mr. Brockedon, is another good example of the utilization of the force of cohesion. The plumbago is ground and finely levigated, all nit being csrcfall; ramOTftd ; Iha powdsr ii than labjected to njdnuilic premira, by which it i« to e(Hnp1el«lj oonnlidated a* (o be eqiul, or erea laperior, in hanlDflaa to the nataral runnaltoa. Two freshlT-cat Bomce* of lead or caontchono will, on being preaKd together, cohere w tightlj that it ii acanxlj poarible to aepaiste them : uid availing luinaelf of thia fact, ths chemist pi«- pam tabes of the latter valaable anbatance, applicable to numeiuiu important parposei id bia maDipalaCioDa. 33. Cohaion fyara. — Soma caiioDB obMrration* ham been made bj Hr. Tomhnsati* oo the Tariet; of figurea produced, when dropa 01 diSerent kinds of oil are drepprid on the surface of water. To tbeaa the name of cohenon-fignr^a has been applied, aa their difirencei most depend on the different dogreee of coheaion exiit- ing between the reapedive particles. These figures appear to bi very constant for the same kind of ail, bnt to dISer connderablj ii connderablj in taken as a teat of the purity of the oi diKient kinds ; so mnch ao indeed, that the figure may ■ ■ "leoil. Oli' M. Attraction takes place not nnlj between two portions of the aame tind of matter, but also between the a4)acent surface! of 4iifereDt substances, as between those of s soliil and a liquid ; this Tanety of attractJTe force has tieen termed adJiaiim. It fnnn one arm of a balance, a plate of copper, c, be anspendecl, and carefully counterpoised by weigbta in the scale auspen^ed from the oppoeite end of the beam, a very alight additional weight will cause either the plate or the acale Co prepondenite ; place a basin full of water, B, nnder the plate, c, in mch a manner that the latter may jnat touch the surface nf the water in b ; on placing weights in a, a very considerable reaistsnce is experienced to the aeparation • "Jaon^DTtlHSacMrrof Aru," 1M4, p.HS. 20 EZTEfiHAL F0BCE8. of c from the fluid surface, owing to this adhesive attraction. With a circular plate of smooth copper, presenting an area of 6*75 inches, Fig. 19, 4f^ l£ — ~ D miMt RkpillHrf InbM. Thna it will rise mDch higher in Jl tbnn ia B, in > than in o, &c. Tbis mnde of ftttroo- tion, eTiclently * modificBtion of ibo last-described pheaomena, ia ^, ji_ termed capillority tnm its beint most ob- vious in tabes of capillsrj orhaiiOike bores. He. height attaitjed by fluids ia tfaei^e tnbflH is constaot, and incT^aeea ioTerselj as tbe disnieten of the tuhea ; it bears do evident ratio to the density or speciBo gra- I vitj of the fluid emploji-d in the oxpvri- ' ment : for Moschenbriick* found that, in Inhes of equal diameter, fluids rose to the comparative heights shown in lh« IblJowing table : — Nun* of flaid. ElrrMioiu SulphDric acid ■ ■ ; I '30 Sulphuric ether, eoDtaining alcohol . . I'40 AnhydroQ* aloohol 1-80 H^rochloric acid .... Niti 207 2-53 3'40 Uil of turpentine ■ . Distilled water . . . SolutiDn of ammonia . Solution of carbonate of . H. Gay-Luasac hu ascertained tliat water, altobol, and m\ of turpentine, ascend in tubes of tiie diameter of -05 inch to the fol- luwiDg elevations : — PtuM. Speclfla gnvftf. SlvratiBo. Water 1*000 . 081 98 Atcuhol . . . Oil of turpentini 0-9415 0-37 0-33 0^9 comea ipto play equally between two fluids, aa in the case of lubes. If two platea of glass, i, B, touching at o, and aeparated at b at a very small angle, be plnneed into a trough D, filled with coloured the fiuid will, aHer a i^hort . rise between the platea, attaining the greatest elevation where the edges of the g! scribing II ectangular hyperbola. The utmoe • "DiM.P)>7Sla.Bip«lmaBt,L.B.."in«. CAFtLLABT ATTlUOnOV. 23 Fig.U. aittmed by the fluid in this arrangement is one-half of that which vodld haTO taken place in tubes having their diameters equal to the distance between the plates, and is always inversely as t lis distance. And the distance between the plates at any given point is, by similar triangles, proportional to toe distance of the point from the vertical edge, c ; hence the elevation of the fluid at any point multiplied by the distance of the point fi^)m the ver(icepre8Bion. 0-60 in. . . 0002 in. 0'60 „ . . 0*003 „ 0-46 „ . . 0 005 „ 0-40 „ . . 0-007 „ Diamet«r. Depreadon. 0-30 in. . . 0-014 in. 0-25 „ . . 0-020 „ 0-20 „ . . 0029 „ 0-15 „ . . 0044 „ 0-10 „ . . 0070 „ 0-35 „ . . 0-010 „ 42. Adhesive attraction (34) is exerted not only between liquids and solids, but is equally active between the latter and invisible gases. Thin films of air adhere by virtue of their attractive force to the surfaces of most solids, and become very obvious in glass tubes when mercury is poured into them ; the fluid metal, instead of closely and equally adhering to the inner surface of the tube, will be separated from it in several places by interposed bubbles of air, which adhere with the utmost obstinacy to the glass. This curious form of attraction is well shown in porous bodies, as cork, pumice-stone, charcoal, &c. When a fragment of either of these 18 immersed in water, and placed under the receiver of an air* pump, the escape of torrents of bubbles of air on exhausting the receiver is very evident. The term tibsorption is generally applied to this power of porous bodies in attracting gaseSj and is EHDOfiUOSS AKD EZ0BM06E. 25 remarluMT intense in the cftfie of fresbly-bomt charooaL Thus one cubic mch of this subatance will reaoily absorb^ 90 cab, in. of ammonia. 86 „ hydrochloric acid. 55 „ hydrosulpburic acid. 35 ,« carbonic acid. n 9*2 cub. in. of oxygen. 7*5 „ nitrogen. 17 „ hydrogen. 1} All hodies in the state of powder possess this property of absorbing air, which becomes obvious when they are immersed in water. Toleiably coarse iron-filings will thus actually float in water, if carefully sifted on its surface, being buoyed up by the adhering air, which appears like little gbbules of polished silTor in the water. 43. A class of phenomena referable to eaptUariiy is the appa- rent attraction and repulsion of small bodies floating on water, when placed at small distances from each other. If one of the bodies only be composed of a substance capable of being moistened by water, mutual repulsion will occur. But if both are incapable of being moistened, as two balls of wax, mutual attraction ensues. If the balls a, b. Fig. 26, be of wax, or cork, rubbed over with lyoo- podium or resin, the water is repelled, and two depressions in which the balls lie are producea. If thev are then placed suf- ficiently near each other, the repulsion of the opposed surfaces of the balls exerted on the water at c will ^^ 26. lender its surface concave, and the balls^ by the lateral pressure of the water beyond, will be pushed together, and appear to attract each other. In the second case, if the ball d be of clean moistened cork and e of wax, the reverse takes place, the water being raised by attractive force on all sides of the first, and repelled by e. There- ibre, on the balls being placed in con- tact, they appear to repel each other in consequence of d attracting the fluid, which is repelled by e, the Tatter being incapable of being moistened by the water. If both bodies are wetted by the fluid in which they float, as two clean cork balls, r, G, in water, they will be drawn together by the united effects of the cohesion of the particles of fluid, and their adhesion to the Rufaces of the balls ; and when in contact, the fluid will rise higher between the balls, than at any other part of their surfaces. 44. Closely allied to capillarity are the phenomena of endomioae and exosfnosCf discovered by Dutrochet. Whenever two liquids of di&ivnt densities, capable of being mixed with each other, are separated by a ii!iembranous or porous partition, two currents be- come esUblirheil, ona & currant or fluid proceeding from witbia to without (exoBinaBe, JE Bid iiafiit, impulse), uid anolLer in the contrar; direction (cndoB- moM, Iviov and uir/iic). If a gUu tube cloied at one end witb a piece of bladder, ±, be paitl; filled with a I tolution of sugar, aalt, &c., and immened In a teasel partly filled with pure water, the fluid will rapidl* rise ID the tuba b, the water having entered tbronK" jl the bladder b/ endosmoae, and, adding to tbe I contents of the tnbe, cause tbe fluid to be elevated much above its former level. If. now, the conditions be revereed, Bvrup being placed in c, and water in B, exosmoee will occur, b; which the tobe b will become nearlj emptied. Ab a general rale, liable, howerer, to Mveiil eicoptioos, it appears that fluids of tea tpe- dfic gravity have a tendency (o pass througb membranes and B bodies, to mix with those of greater density (provided thef .-iscibla), and consequently to dilute them.* Tbe general rule may probably be thus more correctly ex- pressed, that the fluid, between which and the porous paitilian the greatest amount of capillary attraction eiiBts, will usually pass through and mix with the other fluid. i6. These phenomena admit of a very simple explanation, (banded on tbe capillary attraction or repulsion- exerted by the porous diaphragm npon the fluide expoeed to ita influvnce. In the case of a piece of bladder, this is readily moislened by water, but not bjr alcohol. Let the tube b be partly filled with alcohol and then immenied in water, Tbe first action in this coae ia the ~ ID of the membrane to the water, whilst it repels the alco- hol. A portion of water permeates the bladder, ia immediately mixed with the alcohol, and is do longer attracted by tbe bladder. A fresh portion then enters, and this continucB mitil the al(»hal is considerably diliit«d. Ths moBt conTcnient form of apparatus for demonatrating endoamosa or eioamoae is a amall rnnnel-sbsped flaaa vessel, tbe month of which ia about two inchcB in diameter, and fur- niahed with a rim, over which a piece of thin bladder may be aecorely tied. Int« the neck of this a piece nf barometer tube about 18 inches long, and O'l in internal diameter ia ground. By this means tbe veaael may be readi^ filled and emptied, and the area of tbe acting sarface Ib bo large compared witb tbe section of the tuba, that the fluid will nae two or three inches in the tube in s quarter of an hour. Tbe endoamose or influx of fluid is always attended by an > "IIaaT.l(MtMnih.iBrrKiido«ao«*,"lU,pwH.Dilncbat. Fuda, 1898. mdfttinn of > ceitki'n porticni of the liquid confinod by the poron» diaphragm, Thii ihiit bo illmrtrslBd bypUcing in the tube ■ aolation ^ sulphate of iron, unci immening it in water. In * short time the lolution will ri«e in the tube from Ihe FDtnoce of water ; and if then a few dropi of tincture of galls be added to the water is the external lessel, the purple colour which ia produced will saliafactorilj prove that a portion of Ihe solutioD of iron has really ainded through the membrane. The onuotic foireof dillerant saline solutions difiers considerablv; tbns a ■olulion of chloride of almniDUEn is, according to Mr. QTshain, 45 times more eneigetic than one of chloride of sodiam. 46. If the capillary action of the two ffnids on the diaphragm ia nearly equal, the endoBmose and eioamoee will be rery feeble ; bat will take place with considsrablo actirity in the direction of a gal- Tank current transmitted throuzh the flaids. This fact maj be ludjly ahown thua : take four pieces of glass tabe (hat will suc- ceniTcly pass within each olher, close the oaler one with a piece of cvtk, through which the poaitiTe electrode of a Tollaic battery may be paaaed, and tie a piece of Chin mem- hnne oTer the ends of the olher three. 'V- ^ If a satmsted solution of gallic acid be placed in the Srst and fourth tube, and a weak solntionorprotoaulphate of iron* in the aBcond and third, and the tabes be | placed one within (hs other, and a current pissed throDgh the whole, by dipping the iiegatiTB electrode in the flnid con- tained in the inner tube, the formation oTgallate of iron in the second and fourth lobM will immediately indicate the pas- sage of gallic acid in one case, and of prcto-enlphale of iron in the other case, aoooTding to the direction of the current. "* This fact ia important in Physiology in + indicating the probable manner in which the nerToos syitem influences the tarioos animal Beoratians. 47. Analogous phenomena are also eihiblled hj gases or seri- (bnn fiuida. If, fur instance, a glass Teasel full of airliaTs a piece of thin bladder tied firmly OTer its mouth, and he then placed in ajar of bydroEen, the gas will permeate the membrane and enter l>w Teasel. The contents ofthe latter areconseqaently increased; the snrface of Ihe bladder becomes comex, and if safGciently thin will erentaalty burst. It has been demonstrated by Hr: Graham, who has moat elaborately examined these phenomena, that gaaea difler in tlieir tendency to difluse Ihemselves through membrane* or poroua diaphragnu. This tenilencj diminishes with *(IT. ofnlBeuid, and 7or8 (r. arprDtaaalphaleotima, each in 1) «. le of density ot the gtn, boing inTeraely proportional lo root of tbis deDBitj. It maj b« rBmarked. tlat the ipplies lo tbe relative Telocity with which diSerent giweB will be discharved from bd orlGce into a Tacnum : cLia fact seeme to comiborale the brpotheaii of Dallon, that any one gu acta aa a Tacnnm ia relation to another. hydrogcD, oxygen, and nitrogen will b« aa fallowe : — Oi;g«n . . Dene. 1105 . . Diff. 0'94S Nitrogen . . „ (C972 . . „ 1014 Hydrogen. . „ 0-069 . , „ 3*807 If a long tahe be closed with a p)a^ of dry plaat«r of Paris, inverted in a cup of iiRiai(m of Idqnids ; *• Phil. Trama." I860, Part I. 80 BXTEBKAL FOBCEB. fourth was diffused dnrio^ the fint two days, the qnftiitities dif- fused during each remaining period of two dajs being yery nearly- equal. The following table exhibits the relative quantities of rarioas substances diffused at a temperature of 60'5' F. daring eight days, from solutions containing 20 parts to 100 of water: — Sulphuric acid . . . 69'32 Chloride of sodium . . 68*68 Nitrate of soda . . . 51*56 Sulphate of magnesia . 27*42 Treacle 32*25 Glucose . . , . . 26*94 Cane sugar (crystals) . 26*74 Gum arabic . . ... 13*24 Albumen . . . .' . 3*08 Salts of different bases may be separated by difiusion, for the quantities of the carbonates of soda and potash diffused in the same time from a solution containing equal parts by weight, were found to be as the numbers 35 and 65, very nearly ; and while the quantity of magnesia in the salts obtained from sea-water was 6 per cent., the proportion in the salts diffuRed was only 4 per cent. In some instances the difiusive power appears to be sufficiently energetic to effect the decomposition of tnple salts, such as alum, and the ammonio-sulphate of copper. 52. Friction is the resistance to motion which any portion of matter offers to another portion in contact with it; and beinf? analogous to adhesion, may be most appropriately considered in this chapter. Friction is of two kinds, one of which opposes the commencement of motion of one body in contact with another, but ceases to act when the body is actually in motion, the other con- tinually resists and retards the motion. To these forces the terms »t(ttical and dynamiecd friction have been applied : but, to avoid any error from the'confusion of terms. Dr. Whewell has proposed to designate the former atiction^ a simple and intelligible term, retain- ing firiction to express the latter force. We may therefore desi^ate these retarding forces by their initial letters, J?* and /Sf respectively. Between two plane surfieu^es, either of the same or of different materials, F is proportional to the pressure P by which the two surfaces are held together, or, in other words, p is a constant quantity : but at the same time .r'is independent of the extent of the surfaces in contact. This may be shown by the apparatus represented by Fig. 32, m which a weight, a, placed in a scale attached to a strinz passing over a pulley, b, is employed to drag a mass, c, along the horizontu surface of a table, de. The mass c, whether of wood, iron, or other material, is in the shape of a rectangular parallclopiped, .the breadth of which is B or 4 Fig. 32. nuonoH or smrACES. 81 tiiDM tke height, and baTing one of the broad sides hollowed ont BO as to leave only two narrow margins. K a is jtui iuffident to keep c in motion, it will be fonnd to have the same effect, whether c rests on the broad or narrow side, or on the two maigins, here represented uppermost. ^ Also, if one or more weights, each equal to c, be placed on it, in either jiosition, a proportionai increase of the weignt, a, will be foand eqaivalent to tae increased friction. 63. The retarding force represented by S increases from the mstant when both sor&ces are qniescent, and attains its mazimnm e&ct in the course of a few minutes. It may be yery readily coanteracted by jarring the surface of the table slightly, but re- peatedly, by the hand, during the time of the preceding experiment. When the weight, a, has been determined ezperimentallv, and the body, c, then allowed to remain qniescent for a short time, it will be found to require a considerable increase of weight, in some instances eyen greater in amount .than c itself, in oraer to start the body, c, from its position of rest* The added weight will re- present the resistance, 8. Sh^B been found by experiment not to be independent of the extent of sur&oes in contact, or proportional to the nressure, and therefore not to follow the same laws as JFl No dennite law has hitherto been assigned to this Quantity. 54. Between hard surfaces, P is found to be an uniform retard- ing force ; but between soft surfaces, as those of felt or leather, it increases with the yelocity of motion. i^is fonnd to be diminished by coating the surfaces in contact with any unctuous Rubstance. S may or ma^ not be diminished by the same means. It appears from the experiments of M. Morin, that if a complete stratum of the unguent be interposed, F is the same for all substances. This result is manifest, as in this cafie' the retarding force is the cohesion of tbe unguent., and not the friction of tne opposed surfaces. Finely powdered plumbago, either dr^, for sumces of wood, or inixed with pease for those of metal, is found to have tbe greatest effect in diminishing friction. In many instances ^is dimi- _. Dished by polishing the surfaces *^' in contact ; 8 is generally in- creased by the same means. 56. The yalue of ^ may like- wise be determined by the fol- lowing method. One edge of the tiulace, A B, under experiment, is raised from the horizontal plane until the body, c, placed on it^ will just slide down, and the angle of eleyation deter- mined by a graduated arc, d e, •i in the annexed diagram. ir this angle be celled f, then ten ^ {the trigonometricel tan- gent of the mgle) ia called the coefficient of friction, and the angle itself bu been called the iliijin^ angie, or limiting angle of railtanet, becaoite, If two jilane surfaces of any kind of material rast againgt each otber, it is evident that no nmount of preaauro will caute the surfacss to alids over each other, if they •re inclined at an angle leaa than p to a plane perpendicular lo the line of preaaure. The limiting angle of reaiatance ia important ia the arts of conatruction, aa, lor instance, in delemiining th« neceasar; direction of the joints of archea, and of the alopea of The value of f having been thua determined, the value off +:S ma; be aimilarly determiiied bj allowing the bodies to remain for a abort time at rest, and then gradual!; raiaing the plane, until Friction between cjlindrical .aarfacea is found to follow the aame law, bnt S ia said not to eiist between cylindeia. This, however, has been found not to be the caae, if a hollow and a solid cylinder are very accuratelr fitted to each otber, as ia the caae in Whit- worth's cyhndrical gaagea. 56. If a cord pasiing over the anrfac« of a wboci or cylinder is emplojed lo soatuQ a weight, bb in the capstan, or to coroinnni- cate motion, as in tbe driving parts of machiner;, the amoont of friction dependa oa the angle of contact between the cord and auTface on which it reals, and ia independent of the radiiia of tbe surface ; it ia alao greater when the cord testa in an angolar groove, than when resting on a curved auriocc, or on tbe aurface of the cjlinder, aa may be thua abown : — l^ake three caat-iron vlieels, one of two or three inchee, A, and another a foot or more in diameter, b, with similar angular groovea, and a third, c, of any oonveoient diameter, withsplunrim; take, alao, apiece of hempen cord, vitb two equal weights, Fif-U. II, K, attached lo each end of it. "- Jjet the cord be placed in the grooves *, b, aucceaeively, and " It will be found that in both cases the same weight, r, is necBBsary, when attached to one of the weights, n, to just drag up the otber s ; but that asmaller weight, f, will suffice, ' if the cord be laid on the plun rim, c. When the weights are ^ freely suspeuded, it is mani- fest that the oord will be in contact with the groove through theeileut of a semicircle, or 180°. If tbe cord be now carried from tbe wheel, a, horlion tally over a pulley, a, it will bo in contact with the wheel through a quadrant. a&lYlTATIOV. 88 or 90* ool J. It win now be foand that ■ wiU juH move with a weight, F, Buch that, ifD+jraKs in the latter instanoe, then i>+P=K*B would giTe the ralne of f in the former. Thoa, if in the case of the strinf in contact with a quadrant of the circle, d and B being each llb^ f (including the scale) were also lib., then woold Ks2 ; and when the string is in contact with the whole semicircle, d and b remaining the same, k' woald be 4, and the weight, F (including the scale), would be Slbs. Ctmaeqnentlj, in the capstan, the amount of friction depends on the number of coils of the rone ; this amount for each sucoesrive coil is, in fact, in geometrical progression, and between a wet hempen rope, and a cylinder of oak, the common ratio is 8 Tery neanj : thus, if the rope were held on with a force of 1 cwt. the weights sustained by 1, 2, and 3 coils respectiyely would be about 8 cwt, Si tons, and 25i tons.* 57. In the working of machinery friction gives rise to a oon- siderable expenditure of motive power, as well as wear and tear of material : but as there is no friction between surfaces that roll on each other without any sliding, this source of loss may be in a great measure obviated by the introduction of what are termed fnetionrToUerf gt frictionrwheeU. The axis of a fly-wheel, or other heavy rotating piece of a machine, is sometimes made to rest on the drcomference m a wheel at least ten or twelve times the diameter of the axis, eiiher before or after passing through the bearing collar : or if there be no considerable pressure on the circumference of the wheel, the axis may rest in me obtuse angle formed by the cir- cumferences of two wheels, placed near each other, and overlap- ping each other about one-third of their diameter ; in which case no bearing-collar or axle-box is required. The axes of the friction- wheels must of course sustain a certain amount of friction, but it will be small compared with the friction saved, on account of the slowness of their motion. ▲TTBJLCnOirB AT 8BKS1BLB DIBTAHCBB. Qraviiation, 68. When a heavy substance is permitted to fall from the hand, every one knows that it rapidly reaches the floor ; and doee not rise towards the oeiHng, nor move laterally towards the walls of the room. A stone being mere inanimate matter, and consequently absolutely inert, this phenomenon cannot depend upon anj iamaU tendency to reach the lower part of the room, as one of the enmitial * If Ian ^ be the ooeffldent of fHctioii between the rope and Bovlhea in ooBtaot with it. mod 9 the angle of oontaot ; alio Px, the weight rastslnedby Pi end the lirieiioa jointly, then Pj=P,f*-*"* or logPi— k)gP,=«.ttti^. 8ee ICoeeley's " Meehanieal Prineiplei of Bngineering and Arobiteetve" for farther infonoatJon on this sal^iect. 34 ETRBHAL VOBOB. ^.35. properties of matter ia its utter incapaciW to change ita porition. CoDseqQently, the rimple phenomenon of the falling of any hodj towards the earth mnst anse from the exertion of an attractive in- flnenoe or force emanating from the latter, and to this the name of OravUatian is applied, m consequence of its caasing that efiect which we recognise hy the term weiaht : the weight of any sub- stance being merely a measure of toe attraction of the earth for it. This form of attraction is exerted not only at comparatively small, bnt at all distances, however vast : thus, this force acts as effectually on the planet Herschel at the distance of 1,800,000,000 miles, as on the falling apple, in which Newton is said to have first recognised its existence. If a mass of lead be suspended by a string it will, when left iiee to move, point towards the centre of the earth; now the same thing occurs in India, in America, and at our antipodes ; a fact proving at once that the lead does not obev a nahaxU im%deney tofaU; tor the plum- mets, A, B, point in opposite directions, aa alao do c, d, ac- cording as they are situated at the opposite poles or at east and weat ; all pointing towards the centre, e, of the earth. 59. Gravitation, in common with other attractive forces, obeya most strictly the ffeneral law already announced (31), its intensity being inversely as the square of the distance of the gravitating boay. Thus our moon, which is placed at a distance of sixty of the earth's semi-diameters from its centre, is attracted according to this kw with a force of 60 x 60=3600 times less than bodies are on the surface of our globe. The force of gravitation must always be considered as acting from the centre of g^vity of any body from which it emanates. Fig. 96. From this circumntance it is theoretically impossible for two plumb-lines freely sus- pended to hang perfectly parallel. Let A and B be two lines, each having a leaden ball suspended to it ; they will point towards the centre, c, of the earth, and of coarse, instead of being perfectly parallel, will form an angle with each other, which at small distances is so slight that it may be almost neglected _ in reality, althougn it can never entirely vanish. In small distances, even to the tK^^m^-:stmm^mmB^^Kmtrwr'^^mmr ORAVrTATIOH. 35 extent of some hundreds of feet, the lines of gravity indicated br two plnmb-Iines may, on account of the magnitude of the semi- diameter of the earth, be regarded as parallel ; but when these lines are some miles apart, their convergence must be calculated accord- ing to the curvature of the earths surface; this will amount to about one minute in a FSg, 87. geographical mile, and consequently to one degree m sixty miles. LetABCDirbea section of the earth at the meridian of Paris, and ▲ a; its axis of rotation. Paris will be situated at c. and a pltunb>line freely suspended there will point in the direction of b o c. Dunkirk will be d St an angular distance of 2*^ 11' 6" from Paris, and its plumb-line will coincide with P D e. Barcelona will be at b, at an angular distance of 7" 28' 29' from Paris, and a plamb-Hne there will coincide with the line o B e, forming an angle of 9* 39' 35" with a omilar plummet at Dunkirk.* 60. The intensity of the attraction of gravitation varies, not onh- with the mutual distances of the attracting bodies, but also vitn the quantity of matter contained in them. In this wav the great centre of our universe, the sun, from its enormous bulk, its mass being greater than that of all the planets taken together, \b capable of attracting even the most remote, as Uranus and Nep- t^me, although placed at the enormous distance of hundreds of millions of miles. This force being mtUuaUu exerted between bodies, they idways move to meet each other : hence when a book or a stone falb towards the earth, the latter rises to meet it: this motion is of course almost infinitely small, because the attraction of these bodies for the earth being in the ratio of their masses, the enormous preponderance in favour of the earth would prevent its movinjT an appreciable distance to meet the stone, whilst it wonld be sufacient to enable our globe to attract the latter at a distance of several millions of miles. As a necessary consequence of this mntoal attraction of masses, elevated builuinss and mountains might be expected to gravitate towards each other, an effect pre- vented by the superior attraction of the earth which tends to keep them on their bases, and by the attractions at insensible distances which firmly bind their integral portions together. For whenever graritatton and cohesive or capillary attraction are opposed, the tatter within the limits to which they are confined are most ener- getic, instanced in the ascent of fluids in capillary tubes (37), above their level, aud in opposition to the gravitative attraction of the earth. Still, lateral attraction is exerted, for Dr. Maskelyne, in a • PoaiUet, " moments de Physique." d2 86 KXTSBITAL FOBCK. set of ezperimentB peifonned in 1772 near the moantain Shehallian in Scotland, found that a plummet was really drawn from the per- pendicular by the attraction of the mountain to the extent of 54". The same thing took place in the researches of the French astro- nomers, whilst engaged in America in determining the measure of the meridian ; nuinerous sources of fallacy arising from &e lateral grayitation of their instruments towards the surrounding moun- tains, opposing themseWes to the correctness of their results. The lateral attraction of Chimbora9o, the loftiest of the Andes, although much diminished by the existence of an enormous vol- oanic cavity in its centre, was found by M. Bonguer to deflect a plumb-line 7' or 8" from the perpendicular. The mutual attraction of bodies free to moye is beautifully illustrated in the celebrated Cavendish experiment,* which has lately been repeated by the late Mr. Francis Bailv.t In this noble experiment the attrac- tion of a large mass of lead for a given mass of light matter waa rigidly determined, and thus by comparing the attraction of the mass of lead for the light body with that of the earth, the meaa density of the latter was determined to be 6*6747 times that of water. 61. The ascent of vapours and balloons into the air, like that of light bodies, as corks, m water, is produced by the attraction of gravitation. For this attraction being greater in proportion to the quantity of matter, the denser bodies, as the atmospheric air or water, are drawn forcibly downwards ; and those containing a less quantity of matter in a given bulk, as the balloon in the former case, and cork or wood in the latter, are forced •^'^^ to rise by the denser fluid bodies sinking beneath them. Let the vessel ▲ be filled with water, and a solid body, as b, be placed in it ; both the fluid and the bod^ b will be attracted by the earth. If B be heavier than an equal bulk of water, it will be more attracted by the earth than the fluid it displaces, and will sink : but if it be less heavy than an equal bulk of water, the fluid will obey the preponderating fravitative attraction of the earth, and b will oe forced to nse to the surface. Thus the floating of light bodies in fluids of every de- scription, is a direct and legitimate consequence of the law of gravitation. 62. The spheroidal form of our earth, and of the planets of oar system, appears also to result from this law. For as attraction is equal at equal distances, and virtually emanates from the centres of the masses, we may conclude, that the earth, when in a fluid or semi-fluid state, must necessarily have assumed the spherical form ; • ••rUL Trans." 17B8,p. 409. t ** Mem. Astrononioal Boo." vol xiv. OBAYTTATIOV. 87 becaofle no^figore bas every part of the line bounding its penpbery eqnidistuit* ttom the oenfane, except a circle : which would have been the exact figure of a meridian section of the earth, if the cen- trifi^^ force arising from its rapid rotation had not interfered, by opposing gravitation in the equatorial regions. 63. As weight is an acquired property of matter, and prodaced by an attractive force r58) emanating from the centre of our earth, hot dinunishing as tne distance from that point increases; it follows that a mass of matter would not appear so heavy on the top of a lofty mountain as on the earth's surface, because it will be there further removed from the centre of the earth. And ao cordingly it is found that a mass of lead weighing 1000 pounds at the level of the sea, loses two pounds of its weignt on being ele> vated four miles above the surface : and if carried to the surtace of the moon, and thus removed 240,000 miles from the earth, the attraction of the latter for it would not exceed five ounces. For this reason, bodies weigh heavier near the poles than at the equator, on account of the former being nearer the centre of the earth than the latter ; and if it were possible to place any body in a cavity at the centre of the earth, it would be equally attracted on aU sides, and consequently remain suspended w space, like the fabled coffin of Mahomet. 64. It may here be mentioned, although the scope of this treatise precludes a rigorous demonstration of the fact, that be- neath the earth's surface the force of gravity varies, not inversely as the square, but directly as the distance from the centre, and con- B, two weights suspended by a string passing over them ; from any point, I, of the strmg another weight, p, less than the suni of o and n, is suspended ; b o, b h, s c, are three wooden rods jointed together at I, and Ko and kh are two similar rods jointed to a clamp sliding on BK, and connected by sliding clamps wiUi bg and Bfl. The rods are all marked in inches measured fiom the paints of connec- tion. Let us suppose the weights, a x>, p, to be 3, 4, 5 oa. reneo- tively ; then take b o, b h, any lenjg^ths proportional to 8 and i, as 6 sad 8 inches, and xnake kh, k o equal to b o, b h, respeotiv^y ; then BOKH is a parallelogram. Kow let the slidinj; piece, k, oe moved im or down until the anfle o bh coincides with the angle ABi^ which the string assumea when the weights were left free. It wUl be found that the dia^nal of the parallelogram b k is in a vertical position, and that its length is ten inches ; it therefore besrs the same numerical ratio to the weight p, that the sides b o, b B, do to the weights, c, n, respectively. Now the weight p would evidently be supported by an equal pressure acting vertically up- wards &t the point ■, which will be Tepraeetited hj s i, u 0 und n r«preMiita in magnitude and dirsc- tion the leenltant of two preHure& which are themselTeB repreeeDtH in magnitude and directian by the ±xat aidea, ta, an. If, then, required to 6nd tbe reniltant be obtained bj completing tha parallelognun a b, of which the dia- Ithe diagooal * n is the resnituit of A B And 1 0 : then complsU the panllslogram d k, and 4 F is the resDltaBt of 1 D and A ■, that is, of A B, A c, and A B, and so on. Faan the comtniclioa it ii clearlf immaterial whether a b, a c^ A B, &c., ai« all in the same pUne or not. 72. It ibllowB from the preceding pnipoaition that a'point will ho kept Bt rest, if acted on b/ three preuures, which are repi«Beiit«d in magnitode aad direction b; the three aidea of a triande taken m order, ij. is the aame direction, a> Aa ob, b a, in the anneied diagiBm (ilg. 4S]. For if we complete the parallelogram ■ d, tbs sideOD is equBlacd parallel to b a, and will therefore represent the ot the joint eSect of o b and 0 D, which is represented bjr c A (70), it will therefore connter- act the nniled eflecta of cb and B A, and, if acting with them, will keep the point oiaclion at rest If the aides of a triangle are retpeo- I tions of three preasnrea which keep a point at i«tt, thej will repreaeat the preasnrea in magnitnde, for if tbe three sides of one triaogla are rsspectivelv peipendicnlBr to the thiM side* of another, the triangles are amiitar to each other. 78. Bj an eiteasion of rimilu' reasoning, it may be ihown that a pdnt will be kept at rest bj anj nninDer of prsssares rspre> MDted in Du^itDd« uid du«ction b^ the aim of ft pnlj'cr h U inunstenkl whether thi niiltw of the polygon Bra hi u fbmt or not. Tha tmth of this ni>7 be thus ihomi bj sxnri- ^V* ^■ nwnt. On * nrtickl bmrd draw >nT polygpn, u i D, of vhich the ■idea are in any ■smmied nome- rical proportion, aa 3, 6, 8, ID, and 7 inchea reepecdvelj; insert a pin at linj point, o, and place a tr it; attach polleyB ilhatH&eapaadng .. ._.» the point OEoaj be pnaHel to the nqwctiv* ridee of the paljgan, and in the aaoM dinctiai ftom o, aa the lidee taitm M order (bdicated b; the AB,DitOBC,OCtOCD,OdtaDB, ud 0 a to K A. Let aa manj atricgi be hooked on to the ring at 0, ukI TeighCa attached to them, ptoportional to tha aidee to the.T VB mpectirelf ouallel, aa S, 6, 6, 10, and 7 ooncea, he ivnun^ from o, a rlghla weigh^ aa one ounce lor initance, tbe ring « The mn maj dov he ivnun^ from o, atid the "itifi' But il either (rf the wei^hta be incraawd or diminiBhod by •mall weight, ai with nlScient ima peaitioa, that ia, provided the polleje more jitae. Let the angle a of the polygvo be not in the aame plane ae Ibee otbera, a, o, d, then draw . ._p „_ JOD, i%. 44, andjon d^bb; then the pres- J me B A i« eqninlent to b ■, ■ a pi); and ad is eqmTalmt to A ■, id; tharafoie ba, ad, which are together eqniTalent to b K, B A, A ^ ■ D, are eqniTalaot to B ■, ■ D, bacaaae ABandiA neatriJize each other. 14 'Die method bj which coal ia raited Dot of the hold of the cdlien ia a practical illaitmtion of the reenltant of «e*eral prea- nrei in difiereat pUnea. Sereral email ropea are attached to the end of a laiger one, which paaaea orer a pulley placed overhead, ud ie then carried down to the coal-basket. Each email rope ii beU b; one ohui, and all jumping down nmoltaneonaly from a ttiKd step, the loaded baeket ie laiaed by a jerk ; hence the term " ooal-whipper.'' 75. Hie raenhant of two eqnal praeeorea acdng in parallel a tt 42 9TAT1GB. directions, is a pressure equal to their snm, acting at the middle point between them : thas, when the two sides m a balance are equally loaded, the pressure of the beam on its support is its own weight together with the sum of the weights in the scales. This proposition, the truth of which is almost self-eTident, may be thus illnstrated by experiment. Take a small rod, ▲ b, similarly shaped J. ^ at both ends, and to its mid- ^' die point c, attach a string, which, passing over a pulley, D, supports a weight, k, which =f====^="s«^^o just sustains the rod. If 1 D now two equal weights be 2' suspended from the eztremi- Qf ties of the equal arms, and a weight, F, equal to their sum, be attached to s, the whole will remain in eouuibrium : for the equal weights, ▲, b, being suspended from equal arms, cannot have any tendency to preponderate on one side more than on the other ; and the two weights, ▲, b, will have jnst the same e£R3ct in sup- porting F, as they would have if suspended from c, the middle _ point between them. ^' *•• 76. We may hence de- duoe experimentaUy the -resultant of two unequal parallel pressures, and the point of its application. Let ▲ B be a balanoed bar tumine on a pin passing through the centre o, the upper edge of which is straight, and in a line with the centre of motion ; and let the edge be notched at equal distances (of one inch, for example) finom the cen- tre, as indicated by the figures; also let egual weights (as of one ounce each) be suspended Irom the odd diTisions i, •, &c. t, t, &c. It is clear that each pair of weights, i, t: s, t, &c., being equal and equidistant from the centre, will balance each other, and the whole will remain in equilibrium. If now the weights suspended from the points 6 and 7 be both suspended from 6, the middle point between them, their weights will have the same effect on the oar as before (75), and the equilibrium will not be disturbed. Similarly the weights at t and t may be suspended from t with tiie same recnilt, and the pairs of weiguts i and t, t and r, may be successively collected at the same point, without disturbing the equilibrium. We shall dow find that we have a ^ight, 6, acting at a distance, 2, from the point of support balancing a weight, 2, irmrn Mctii^ at k dittaDce, 6; but And benee ■we nuj inler gcnerkUj th»t >n j two panllel pre vam vilJ balance each other, when tbej ve luTenelj prupoitioiul to ibeir dulancea from the pmiit of giijipoit. 77. The nwmcnt of on; prewnre ■■ it* teadeDc; to more i bodj to which it ii applied round any given ceotre, aai is meMur«d by the prodnct of the prestuTe, ftnd x parpeadicattu' line dnwn from the centre of motion to the line o{ directioii of the pTMsnie. It ■ppnmiB, fnm the preceding propoeitioa, that wbeo two premuM an in eqmlibriiim, iheir momenta roond the cealre of motion, nr wuDt of rapport, ve eqiul ; uid they «re alao in opponte direction*, for each of the weights ainglj wonld turn tbo rod in adiraalioti tmitztaj to the other. 78. And if any amnber of preaurea in th> eame plane, tending to prodoce motion roond a given point, are in e^oili- brinm, then iho ram of the monMnta which act in one Erection ii eqoal to the ram of tboae acting in Ibe con- ttij directiou, •« ma; be ■hown by the following ei- periment :— * a ii a circle nd to find eipeniuenbUlj the position of the reBiillaiit. For this par- Applj & wrieB of weights r,. P^ Ac, the itringi of thoM which « intend to act upwards, passing Terticallj OTer pulleji. We ahau find that there u some poiot at which a siDgte presBUTe majr bo applied, which will maintain the rod in its honiontal poaitioD, nnless the sum of the weights actins upwards sbonld equal the ■nm of those acting downwaida, in which case the lod will be ma- tained without furUier rapport. But if them sunn of the weights ■IS not equal, the resnhant will act in the diivctiou of the greater sum, and the single premire, to counteract it, must conwqnentlj be in the oontraiy direction, and it will be eqoal in amoont to the difference of the above sums of weights. In the example here given, the weights p„ p„ ^- *>■ Ty are 8, 3, and 6 oonoea reapectiTelj, and are sus- pended at diatanoei of 1, I 12, and 17 inches from th« end a; and the weights F„ F„ are 2 and 5 onnces, acting upwards, at dia- tsnces of 3 and 14 inchea from A. W« shall find that the whole sjitem will be Bnstained hj a support placed under the diiision o, distant B inches from a, and the dis- tances of op„ op- tc„ will be 7, 6, 4, fl, and 9 inches respectJTely: and the sum of the poiilive momenls round the point □, or those which tend to turn the tjstem tht sans looy a* the Aondi of a dodc nuws, wiU be equal to the son of the negative moments, or those which tend to turn the sTStam the eoMraty maj, for (p^!x6 + W8x4 + (p^6>c9-(p,)8x7+(pJ6x6. Btit the snm oT the weights acting downwards is (p,)8 + (pJ8 + Cp.)B-17; and the sum of thoM acting upwards is (FjS + (p,>fi-7, and conaeqnentlj the difierence of these >unu is 17—7 = 10; that is, the resnltant oftbe sjrstem of pressures is a presinreof 10 acting downwaida at o; and if we attach a wei^tof lOoancM to ■qmLiBum o I, Thsic is k puticalu cms of tbe i eqtialit7 of oppoaite monieiits, tl»t lequireB notice, on accooot of it* prac- , ticBl importiuice. If equal weighU, r, be raapeiided from anj tbrse poinU, i A, B, c, Bqniilistaiit Ktim each other ind fiinn the oentre of tha moveable boaid, thej ir!ll be in eqnilibriom in anj pod- Let the diagram lepretent anj pom- titm, joio B c, and bisect it in i> ; join A D, and producs it to meet the Terbcal Koe throngh b in ■ ; aim produce the vertical throngh c to meet as in p; then, because a b c ia an equilateral trian^. A B is peipendicalai' to a o, and fHiri Ihrnnrii n; also A o ia twice o d. Bnt bjniiaiUrtiiaDglaa, V i>— D B, and therefore and tlis momenta ronnd o in oppoeite directjooa are eqaaL TUa eiplaina the advantage of emplojing three pmnpa, the piltooi of which are attached to a three-throw crank, m all kioda ,=0, (fat ^ tb* o^itntaiJ HiHi cf tlie mmaiti roDBd O ^0, wUsli i> aiFrtaaaa br HP.O,)-0. niH ma Ibe nnoil «iiidltlinHofM|idUbriiiaiofa>iiv*r*t«ia of panUel H—IIW ■iillin iiimiililliiiilj ir iinjlii iilmiiiiiil Mill lliii liiiiaiiiiialliiii ■■d aiiiiUwi, M eppliai] lo Uaa, mtnij busb npodte dliMiiiliHia i llaM Moc eouldarcd niaiiliTe, irtuoli aie diavn is ■ duwtion oDntrar to tbu pliiiTi ■iiMwiilie til ni nndtJTn Prom left to rifht, np«fd>» aad lowerda a. m naaallj emiiiinl ■• th* poiltiv* XnaUoat g ud lh>m rifbt to lift, Aoinaard^ tad UneUr baa lu, tht BafUJn. 81. Tlura ii a p*rticnbr cms of panllel prnmres in which no reiultoDt can b« obtained, that it, when tb« ajatem of prenorea maj be radncfd to two equal preuuraa acting ia opponte direo- _. tiona, but not at tbe rame point, which '•"^ majbelbmelnciJalad;— Lelp, p^ba ■ an; two preaiuren acting at the pomta I Pi-Pf '" '''B same direction, and let I p, xon, ^ rjXO^,; then o istbepoint I to which the ntBulunt mult be applied, I and a pressure p, -f r, applied at o in I a direction conlmrjr to p„ and F, ■ will produce equilibrium (TG). Sun I Fi " "Pi = ■•. " Fl = f,''P>Pt■. that ii, p, ii the pirint about wbicb the momenta of p, + p, and p, are equal, and at which, conaeqaontl;, their reaultant mutt be ap- plied : also, IB the 87Btem ia in equihbnuin, the remltant must be equal in magnitude to p„ and mnat act in a contrary direetion to p., that ia, in the direction of Pi + p^ We may, therefbre, remark, that if two unequal parallel preamrea act at any two points in ap- posite dlrectjona, ihotr resultant ia a preaanre e<|ual to their difier- ence, Rcting net at an; point between the giren pointa, but at wroe p int of the line joining them, produced in the direction of tb« gireater preasure. But when p, ia diminiihed in vaiae, r, -l- p, and p. become more nearly equal to each other, and at the aame time iha point p, becomea more remote, becauae the product P, X op, remaiua conatantly equal to (he aame quantilr P, x op^ _ .. and when f, becomea indeSnitely amall, and Op, indefinitely large, the preasures at o and p, ap. [ proach equalitv. We may henca conclude that ' - equal pi '" ' -• ■ - I that is to say, there ia no point at which their ol parallel prenures acting in oppoail Itant, I' ■■ . B joint action can be Juatcounleracted by aaingle I preaauic. Two auch preaeures as f, p, acting ■ Ht the points AB(Fig.51],arecalledaeoiit)^; I A c, toe perpendicnjar diatance between their I liaea of direction, the arm of tht onipb; and ™ p x * c, the moment of the eoupU. 82. As the IKO pressures cnnslituting a coaple are equal and in -^ — - -_ - * familiarly illna- ODlrifugol drill (Fig. 62), in which a rotatory impulse ia oiimmDnicAted to the weight a, by forcibly unwinding the strings &om the alem, a ; also spinning a lop, and trundling a mop, Bat the b«(t practical flliiitra- rf ooA or wcxJd, kept ir - " . _ ._. ._, ■ loantuD jet ptajing against o of it, bat witbont anj ebange of place, so loag aa the fore* of lbs jat TeiDaiDB perfectly onifonn (Fig. 68). In this oaae, the fwce of the jet acting opvaidi agwiut tlu loHhae of the kail b exact]; eqnal to the fbrae of gntn^ ar'' — ■" ' — ' rft.a. t S3. It may be tlated geaerallj, that aaj namber of prenmreB tctinf; in any direction, al the tame petal, maj atwaTS be reduced to a nngle leanltant, which vil1= 0, in caae of eqmlibriimi ; but if acting at diftrenl points, tbsj maj be reduced to a nngle RfilUnt, and a rSBollant couple, either or both of which ina/ = U. Ad eipenmebtal demonBtratioD of this wnnld, hovever, ho too fomplieated to be raadily intelligible, and a mathematjoal proof ii incompatible with the objects of this trsaliK. 84. Han; problenu relating to the coDdltiooa of eqailibrinm of bodice, Tanouil; connected and supported, are of laat importance in the arts of ooDBtmctioD ; and occaaiuDally verv curioui and unex- pected reBaitBareobtained. Thus, for instance, U we insh to obtain tlie but poaition in which any number of beams can be piactHi, n s« to form a roof of a given epan, that it may be uniformly Btrong in fitrj part, we have only to join loosely together an equal iDmber of rods of unifurm . weight and proportional length, and mapend their two free amis y^ ^^ fjoto two pointe at a pre- pmioDal distance in the I ume bonzonta! line, when I it wit] be foand that the I form which b;^ their own I wei^t Ihey will spontane- I ontly •nume, caTled thr I finicolar polj^on, is, when iavetted, lbt> strangeit fonn di which the beaioB can be placed 49 STATICB. order to nipiMrt k weiglit nnifbmily digtributed orar tbem. Agun, the rorm of the gracefiil calen&r; curve, that whicb, u its ^, ((, name impIieB, a chain umnies when framj' auspcDded from two points, is an impartatit problem, as being the bans of the con- atmction of sospensicD bridges ; bnt for the foil inveetigation of this Bobject OUT readers must be refeired to the standard treatisea 86. Tbecentreof gravity of anybody, or mass of matter, is that ptnnt about which the bodf will be balanced in all positioDB. This point eridently coincidee with the centre of parallel preseares (79), erery particle of the body being considered as a poiot sepa- rately act«d on by grsvity. And as this is the point of apphca- tioa of the resultant, that is, of a single pressnre Eaving the same eSect 88 the individual pressures co^jomtly, it followe that the veisht of the body would in ell cases have preciael; the same Blalical effect, if it were all collected or concentrated at the centre of gravity. j^^ gg_ SS. To End the centre ef gra- Ivitv of any body, let it be con- sidered as a syetem or aaaemblage of material points, and of theee taE« any two, f,, p.; also lake any point o, draw o p, horimntal, and there- fore at right Angles to the verticals throogh p, aod r,; let o, be the centre of ^vitv of p, aod p, and o, g, a vertical throagb o,, then (76) 'i^Pi9i = ''t'^PiSi't biitj',y, = oji, — oP|, andp,y, =op,— o j„ therefore "■j xoy,-P,xoj), = p,xoj.,-p,xoff„ or ?,>toy,+p,Koj,-p,jcop,-hP,xoft, «■ ('•. + '-,)'>ft = Pi' figure A d c d. In like I maonerpoin ft.with <; by the line c« ■ ; then e will I be the centre of gravity of the whde In a circle the centra of gravity is in its geometric centre; and in an oval, at that point where its trana- terae and longitudinal diametere intersect. M. If a body be freely eaapended by any point, it will remun at rent when a perpendicular line let fall fnim that point paosea through its centre of t^ravity. becaaae the upward preuure which gupporte the body most be in the same vertical line as the resultant of its Ac a^regate grvvity. This law afiorda a ready mode of determining the centre of gravity of any bodyby experiment. For let A C a D, Fig. 60, lie an irregnlarly.Bhaped body, OS a board, &«ely aiuipenaed at a, a plumb-line, abb, hanging on the same support. The attraction or the earth will cauHO the line a n to hang pcrpendicnlariy downwards, and, acting ouacbd, will "■ -TB of gravity to fall BqtUUBUDH. o of letl in another directioD, itill bsvins the centre of ennt; ia Ihe conn« of the rgrticaJ line described b; the plumb-line : let this line be a ■>, then the point o, where A D anit ct D intermct each other, correepondi vitb the ceDli« of graTJtj of the figure a b b d. 91. The centre of ^ritjiibj no menni Ko- «. neceaurily placed within Ihe mosa of the ■ faodj itself; in a nag for example, aa i b, I thia point will be the centre, c, and cod- I ■eqnentl; in the space midway fima eTei^ I portioD of the solid. ■ 92. If a body be not of nnifonn dendt;, I the centre of gruTitj ia not sitoaCed in ihe I places abore described. In a hom^^neona | circnUi Spin it correaponda. as above stated, with the Reometno cei in difierent pula, it becomei eccen- tric. Let 4 B c Kg. 6S, be^ an in- clined plane and ■ bmij of cylindrical bnt in one of unei|ual dunalty figure i> s a, be placed upon ; be composed of matter of eqnal den- iitv, o will be the centre of grarity, and being attracted hy the earth m the direction na, falling below the point aapported b j the plane, the bodj will necesaarilj roll down. Bat if the portion a of the figure le composed of i leuC the n , __ .. C the remaining portion bring [rf* tight wood, as alder, then a bulk of the latter weighing 800 grains, will correspond in iiie to a mass of the former weighing 11,360 graios: these nnmbcrs being in the ratio of the reapectiTo specific gravities, or densitiea. of the two bodiea. The attraction of the earth will now act Tecy differantly on the cinmlar figure n, for the centre of gravity will do longer be at the geometric centre, bnt at a point nearer o, as at a. OraritatioD will act on t in the direction » t, cansing it to asanme tike loweet point, Ihe noint s will obev Ihia attraction, and the aicolar figure d will roll ap the inclined plane ^ remaining at rest when a line let fall from the centre of grUTity B passes through the point lopported by the ^lane. 93. A body reating on its boae cannot remain in a state of permanent eqnilibriDm, nnless a perpendicular line, passing through the centre of giaTitj, &11s within the base. Thus in the figme a B, f^g. 63, s represents the centre of grsiity, and a line falling ftom that point pM«™ through the b«o, wh^h » mpported bTtlwt.ble: the figura tlierefore 8Und« wfelj. But pUce on it» wmmit wither piec«, o n, tha oeutre of giavty T ' ^,»?f** *J o ud u a perpeodiculir hne dr.wn from that point falli bejond ' tha supported base, the body necesisnly Fit. in. falls. And the same effect w!ll_ be pro- duced, if B portion of the material, as r, ba removed near the base. Hence the dangsr of loading waggons too high, and of building walla, if necesaaril; inclined, too loftv ; the leaiun^ tocera of Pi»» and BoSogna, may, accident a^rt, stand for ever, as long as perpendicular lines drawn from their centrea of grarity Ml vithin the bases of the buildioga. Thii is indeed the case with both these re- markable structures, for the tower of Pisa ii S15 feet higb, and has an incli- nation of ia-4 feet from Iha perpendicalar ; and that of Bologna, with an elevation of 134 feet, baa an inclination of but 92 feet. 91 A body, not acted upon by any external fbrcea except gravitation, will be in » state of tqiiiJibrium when ita centre of iravity ia aupported. But the equilibnum may ba of cither of three diffbrent kinds, vii., ttabU, umtabU, or lAdiffertnt. A body ia «id lo he in a aUte of stable equilibrium, whenever its cenlra of Rravity occupies a loiwr pooLion than it would do il Ihe Iwdy were moved a little in either direoUon; for as the toUl weip;ht would act in the same mwmer if collected at ita centre of gijvity, that point would tend to descend if the body were moved, that is, lo return to ita fonner position. And the amount of this tendency to return, or the itabauy of the body, is measured by the amount of a$ctnt of the centre of grtvity correapondipg to a given move- ment of the body. . - L ,1 IS Let J. B, Pig. G*, he the base on which the preceding fignre rests, am) a its centre of gravity ; then if Fig.t*. the body be tilled over towards A or B, the I centre of gravity will describe the circular ansae or UD, of which a is the loweat point. Take the angle O i C ■— O B t>, ihrongh o draw the vertical line o B, and draw c E and D F horizontal, then o ■, a r, will represent the relative elevationt of the centre of gravity when the body ia moved round the points ± b, respec- tively : hence we see that the stalnlity of tbe body will be much greater towanb A than towards B, or, in other words, it will be more difBcult to ovenum tha body in tbe fonner direction than in the Utter. Hence tlie atilit; of eitendiiig the baie of a bnildiDg bj iiie4nB of bottreneB, eapecisU; vhen the walla ore luliject lo the lateral (hraat of a roof of wide ipan, aa in catbedraU ami otIieT loft; edifieeB kavinff the iDterior apace entirely open. 9&. The Blabilitj of a ntapencled bod?, ami conaeijaently the re- aiitanca it oppoaea to diatorbaace of itseqailibrium, increaaeB with the distance of its cenire of gravity belov tht poiat of aopport. Hence in the coaBtnictionof very delicate baiancea, it ia necesaary for the centre of graTity to be but joat below the point of anpport, otherwise ao great a force would be required lo disturb the equili- bfinm of the beam aa to render its indicationa in the eatimation of unall weighta nearly naeleaa. 96. The eqailibriuin of a body is unstable, when the centre of graiity occupies a higher position than it would do if the body were displaced in any direction. In thia ease, the body will, if inoTed a little, recede still further from its poaition of reat, since the centre of gravity will then, by the auppoailion, descend. Thia if the condition of equilibriam of all bodies balanced, or supporled on a lingle point ; and the art of balancing any heavy body con- sists in repeatedly shining the point of support, ao as to keep it CtnitiDoally under the centra of gravity. 97. If when a body is moved, the centre of gravity neither rises Dor fklls, bat moiea in a horizontal line, that body is in the cod- dhioti of indifferent equiiibriuni, and when disturbed from its poaition, it has no tendency either to ad- Rn, m. vaoce or recede. The equilibrium of a sphere or cylinder, resting on a horizontal phne, is of thia kind, for it ia manifest thai tn theae bodies the centra of gravity will atWBya move horizontally, since all radii of s circle sie equal. 98. Whenever the path of the centre o< eratity of a moving body is a curved line, Uier« wilt be a poaition of stable squili- brinm at the lowest point of the curve, where the convexity in downwards, an4 one <£ unstable eqnilibnum at the highest, where the convexity is upwards. Tons, if any body, AB, of which s is the centre of gnnty, is raapended fram o, and capable of moving round that pant, the path of o will be a circle of which* o is the centre; there will be a position of stable equilibnum at a, the lowest point of the circle, and one of onstable cqailibrinm at o', the highest poiut. 99. This point may thus be further illustrated : — Take an oval board, thick enough to stand edgewise, with a hole in the centra Inge enongb to admit a pencil, and let this be railed along a ■trkieht e<^, A b, ll£. 66, resting on a sheet of paper ; a pencil pawiK throDgh the Eok will trace the corie, c d, the path of the centre of gravity. When tha grsftter oxia ii honHmtal, u at b, » .. Iho oentra of gTsntTvill oc- . cupjr tbe lowert point of Uie I curre, auiI tUe oquilibrium ii ■table ; when the aune axis U vertical, aa at v, tbe centre I of gravity it bigheat, and the equilibriiim it unalable. 100. Stable eqnilibiiniii in one direction tdkj, nnder I certain conditions, coexist I with nnstable eqnilibriam in another. For example, in the preceding figure, there are points of inflexion between the J. „ bigheat and loweat ptunta of Aa curve, OD, or pointi at which the cnriB changpB Ironi conveiitj to ODD- :a*i^, or vice vtrt&; lets be a point It which the oval reita on a a, when ts centre ia at a point of inflection, and draw a line through the centra and the point o. If now a be railed above n tiDtil the line through o ia vertical, the oval will then be aup- ported in thia poaition. In thia caie the path of the centre of gnvitj IB horiaontal juat at the point of equilibrium, a ; it uceoda towards o, and the equilibrium ii therefore itable in that direc- tion, hat \» nnatable towarda l>, in which direction the patb deacenda. Kg.w. Again, if we plaoe the oral I board on a amall horiiotital ojlinder, in. Fig. 68, with it« greater biib parnllel to the axi* of tbe cylinder, tbe equilibrinm will be atabla towarda a or b, bat tmstahln tranaverael}' beyond a very small diilance from ita vertical position, as indicated by tbe dotted tinea. _ These, however, which may be called cues of mixed equilibrium, are . altogether exceptional. Qenerally tbe equilibrium of a body will be (ound to be wholly atable, unstable, or iodiflerent. tOl. If nn portion of the path of tbe centre of gravicv tM bori- tontal, there will be no poailion of equilibrium, and tbe body will tend to move in the direolion tovraida which the path deacendi. Tbe motion of a doohie cone, or of a billiard-ball, ^/pareMly ■QDILIBklTBD 1 up mn incUned ^aue, coniiatiD^ of two rodi pUced at a imall a^s, witli the open ends nuad, maj be eipUined on this pnndple. 102. The cona premnta a good ezunple of a body capable of beinE placed ander all the three oonditiona of eqnihbnum. When lUooiDg on ita base, *, Fig. 69, its eqoilibrium ii ilAble ; when praaed on ita apex, it is nniuble, b ; and when retting on iti BlaDt lide, c, the eqailibrium ii indifierent. 103. One of Ibe moat important practical applicationa of the comditionfl of equilibrium la in the conitraction of the arch ; a atmeture compoaed of heai; masaea in contact, which eupport each other b; the matoal preaanre arising from their weight. The aepsnte maaaea of which an arch is competed are culled eouaaotra, which collectivelj conrtJtnle tha archnng, and this leata on two firm anpparta, the abvtmttiU. The external and in- ternal outlines of the iirch-ring are called the extradoi and inf ratio*. The lateral smfoce of the arch is called afaee, which ia supposed to be a vertical plane, nnleaa otherwise eipreased. IW. We will, in the first place, oonaiderwhat muit be therela- tire weight of the vonatoin, and the direction of their surfaces of The line of pressure at each joint of an equilibrated arch maat be parpeiidicnlar to the Joint. Suppose Iti.jo. the line of pressure a b, nc. TO, not • to be perpendicular to the joint CD. I Take aec.bb and di«w At, ea I peipcmdicnlar to CD; then the I pnMore A ■ is equiTalent to a r and I pa, and bb to bo and bb, of I which a r and b o will support each I other, and tha Touaaoin v., t^ being I OTged in opposite directiona bj the I preasnrea P a, • E, will slide over each other, which is contrai7 to the suppodtion, therefore a b mnst be perpendicular to a d. 105. Let T„ y„&c, FI5. 71, be Ibe vouisoire of the aemi-arch AiCD, and r, q„ &c. the loint*. Draw o x vertical, and ivhori- ■ratal, and o t„ &c. pantllal to r, q,, &a. Then for any Toussoii M T, the comiponiling trinngle T, o T, has its rides Derp«DdicnIar TeBpectlvelj to tlie directioni of ihe three preuureB that keep the ToiuBoir at rest, for the preunrei sC the joint are perpeDdicnur to OT,, OT,, oad the we[ght acts Tsrticalljr, that it, perpendicularly to T, T„ therefore o i„ o t^ and r, t, represent raipectivelj the 17. ti tireMQreB on the joiota P,«,, and the weight of T, (72). id as precisely the same reasoning will apply to the roc- cessive triangles t, ot^ &c., the presaiirei at the joints will be repreeented by the linesoT,, &c., to which the joints are reBpectiTcly parallel, and the weights of the ToaBSoirs v„ v^ &e., by xt„ T, T„ &c. Bnt the lines zt,. it„ Sk., are tho tangents of the angles zot,, XOT^ &c., ox being the radiun ; hence it,, t, t,, &c, are Ihe diSarenteB of the tangents nf these aiigles, that is, the weights of the Toussoin are as the diftBrenoes of the tangents of the angles which their respectite joints make with the vertical. 106, If the depth of the TDuasoirs be small and onironn, and the joints perpendicular to the curve, Ihe curve of the eqnilibntted arch will be a catenary. Let Ad be the cDrre ^- ^*' A D, inverted with refer«DCB to a horiioDta] "ine, and let PQ,, r'Q', be two of the joints; raw the verticid lines rp, t'p. If a li b« (he catenaiy curve (84), it is evident that anj' por- tion, ^^, which may be supposed to havA be- come rigid, after having assumed its posilioa of equilibrium, is snppnited b; its Own weight and 'ly two tensions in the direction of the cnrro It the points pij/; but the portion p r' of tho arch Is kept in equilibrium by its weight and ' 0 pressures perpendicular to the joints, that , in the direction of the cum; the form of (be arch being datemuned by the same con- diticna, must therefore agree with the cale- The funicular polygon (84) is a case of equilibrium inverted, precisely similar to the preceding. 107. £mitibriuni of Jre&ei in praefiM. — We have hitherto conaidered the condition nf equiltbrium of an arch, supposing the surfaces of the voussoirs to oBer no resistance to shi^ng. But the surfaces of building materials offer a considerable resistance to sliding, and it is therefore necessary to consider ihe practical Gooditions of equilibrium. For this purpose it i« desirable to take ■ thut ckn exhibit tbe rarioiu pr»- pertiea of an arch, vix., one connating of lonr TOUMoira, which, for tbe convenieDce of tiperimeDt, maj bt purtioDi of m rectangiiUr b«am of wood. Let B D B*, Fig. 73, bo the web J^- »■ the TOUBoin of which mt on th« kbntnieDtB at a b, a' b', and against ••ch other at the oUique pianei p 4, r' q', and tbe Terlical plaDp s t>. Let Di Snt BDnpaw the beami to be withimt weight, «nd tbe joiniB witboDt friction, m order to deter- mine tlie cooditioni of eqniMbriam when tlte areb ii acted od b; vcighta at the erov* e, and tbe lunmcJUf q, q'. Dnw o x t ai in Iig. 72, tboD ihe weight* at ■ and « tout be at z T to T T <106). Let unawsappose tbe weight at the crown tobeiiicreMed,uid let the we^u at X and qbe aixDto dt; join o d aod draw r i per- pemticular to o o, then ai the pmaBnra of the weight at s was And D q[ will ilide inwards at ihe with friction, if tbe angle d r a be lew than the Unudng Migle of TCBiteuce (S5) for the giren materiaii. It is *lao rtKiainte that the line ■ r ihonld not fall be;oild the Irtoal enrtiico of either of the iobts, Bnif ao. tbe Tonaaoir DDwill lum inimd tbe outer angle at i or the burt at p, ai in Fig- 75- In like manneT, let the weight be mereafed at the haonchei, and let tbe weight at « be to that at q aa T.. vTT inin oTand drawQD per- or. We ihaU now find thtt the haonchm will alide inwsrdi u in Fis. TS, nnteu tbe angls DQE (Fig. 75) b« ]«■■ tbaathe limitinfr mngle of reiialADoe. fff_ 77, It is aim nece«BBr; that ihe lioe I QD should not fall beyond thcaurfaoe ofeither of tbe joints; forifitdoso, then the Toowoir will turn round tbe point D or Q, or both, u in Fig. 77. By an eitenaion of praciialjr nmilar reiBoning, tbe aame piin- dplcB may be applisd to tba lereral parts of an u^^b, «t actually ooo- Btrncted, If ire luppose the arch to be in equilibrium, tbe line of prewur* will be a poljgoa pautng through tba centrot of gravity of tbe »ou«aoir«, as repreaented in Fis. 78 by a dotted line. If a veigbt b« now added at tbe ctdwd ■, the line of pr«imiro ascends towards a, and descends towaids r at tbe liaunches ; or Hf,K. '^ *^ '"''^ weigbU at tbe haunches, the Une of pres- sure ascends towaids <], and descends towards d, aa showD in tbe figure; in either of these catei the arch breaks, us in the pre- ceding Sgores, whenever tbe hoe of pressure fall* ' beyond tbe snrface of tba joints. If tbe line of pres- sure does not pass beyoad either the eitradoi or Ihfi intrados, it may pass very near either of these boundaries of the areh, as in the ngure : dius by over- loading tbe orown there is a tendency to crush Ibe material in the inside under the banncbes, and by overloading tbe baunchea, there isa teodenc; to croab the keystone in tbe inside at the crown. iOS. From what has pracaded, we may gather that the two con- ditions essential to the stability of an arch are: — (1.) That tbe lines of pressure pass within the limits of the sur- faces which are in contact. {!.> That the lines of pressure meet the joints in such diracliani that tbe angle contained between each and tbe normal to the jirint may be less than Ibe limiting angle of rasistauoe. We have here considered only the structure of tbe direct areh in which tbe face is perpendicular to the iqffit* or inner carved surface of the areh. For the construction of tbe oblique areh the reader must b« referred la tbe standaid treacle* on eagmeetiug.f 59 . CHAPTER IV. OF THE MSCHJLHICAL F0WBB8, OB SIMPLE MACHHOBB. 109. The mechanical powers comprise the most simple instni- ments that can be employed for the purpose of raising or snp^rt- Ibg weights, or communicating motion to bodies ; and all machines, howerer complicatod, with which the ingenuity of man has {ormshed as, are nothing more than combinations of these simple machines. By means of these it must not be supposed that we beget or increase force ; all that we do, is to apply force in a con- venient and economic manner. Thus, if a man could raise to a certain height 200 pounds in one minute, with the utmost exertion of his stren^h, no mechanism could enable him to raise 2000 to the same height in the same space of time. If left to elevate the mass by his own unaided strength, he would be obliged to divide it into ten different portions, and raise each separately ; whereas, bv means of one of these simple machines, he will be enabled to raise the entire mass at once, requiring, however, for the perform- ance of the task, ten times as long as ne required to raise the 200 pounds. Thus it is, in Umne, obvious that we exchange time for ])ower in using simple machines ; and this is true with all the varieties of impanatoB to which that term has been applied. Toe simple machines may be divided into three classes : — 1. The lever ; 2. the pulley ; 8. the inclined plane ; the theoretical properties and peculiarities of which, with their chief modifications, we shall now briefly describe. The screw and the wed^, commonly classed amonest the mechanical powers, may be considered as modifications of the inclined plane. 1. THE LEVEE. 110. The lerer, theoretically considered, is a ^rfectly straight inflexible rod, destitute of weight, and moving without friction on a point of support called Afidarwnt. Precisely tne same line of argument, and the same apparatus that has been already employed to demonstrate the relations of parallel pressures ^7^, may here be employed to determine the conditions of eqnifiorium of a straight lever, acted on by two pres- sures perpendicular to the arms. We may here remark that the theoretical consideration of the lever being without weight cannot be fulfilled in practice ; but we may arrive at the same results, if 60 iracnAncAL rowsM, ob siaru machihu. the pin on which the levnr tarns be mide to cmncide with the cantre of grarity of Iho leier ; for the Mmtn. of gr»»lty beinir nip. ported iQ all pomtiona of the lover, its weight cannot, in any poM- t(on tend to prodnce any motiou. We shall then find, Bret, that equal preiBurea applied per- peadicnlarly to the equal I armsofastraight lever, will I keep the lever at reet ; and secondly, that any two prea- I luree applied perpendica- larlj to the armi of a lerer, I will keep it at real, if the presBurea are inversely u the lenD;th of the arms. If p and w are the preaaarea Dsnally wiled the power and weight, in relation to the lever, and p, w, their pointa of application, alao f the fulcrum, we shall have nple given, the diitanoes o(p and ui from f are 3 and 7 i the weight! of r and w are 6 and 14 ooncei ; and 3yl4 = 43 = 6x7. 111. The pointa p and to are not neceaaarily on oppo- [ Bite Bidet of f : the only ii»- ceaaary condition is that f and w mnit tend to tnni the ' oiind T in contrary di- IS, coDsequeatly if ther I act both on the same side of IP, mn»t»ct „. 80. p, s w (produced if necessary), may tonch the eiTcles in the points j/, u/, respectively ; then if the weights be in the ratio of 5 : 3, ks 10 and 6 ounces, and the lai^r be attached to the string touching the smaller circle, and vice versdj the lever will remain at rest when left to the action of the weights, or, if diitnrbed from that position, will return to it more or less exactly, acondiDg to the amount of friction at the points d, e, f. Ip this case we have p (10)x Fjp'(3) = 30 =* w (6) x f «/ (6). In the experimental determination of the equilibrium of moments (78) a carefol measurement of the radial distances is necessary. If, however, it be desired to obtain integer results, this may be effected as above, by describing concentric circles on the board, the rsdii of which are multiples of one inch, and attaching the several strings, so as to touch these circles respectively, and selecting suitable weights, as in Fig. 82. 114. One of the most familiar practical applications of the lever is the common balance, or beam and scales. In its commonest finrm this instrmnent consists of a flattened bar of iron or other hard metal, tapering a little toward both ends, resting on its sup* port by an obtase knife-edge in the centre, and having an eye at each end to which the scale is attached by means of a hook. In sll beams of bettor construction, each scale is suspended from a knife-edge that passes through a box at each end of the beam. The centre of gravity of the beam is usually placed considerably below the point d suspension, in order to give due stability (92) to the balance; bnt the points of support of the scales when in the same horizoDtal plane, are a little above the point of support of the centre of the beam, that it may acquire sufficient sensibility, by the diminntion of its stability, when loaded. 115. The most perfectly constructod balances are those which ea timCBAXKAL POWKU, OK atKPt.B MAOBim. an iwed in chemical inTesligationB, for detarnuning atomic ««ij^ta IT eaDiWenU, and ipeciEc graviliea; or in aiBa;iiig, tLatiB.de- ^rmiDJnc the amount of imparity in the precious meUllj theae ■ ... - tjn^ anneied diagram (Fie- 83)nipreBeutsone of the beat deicription of these, coostructod bj Mr. Oeitling. The beam, l, is ao acute pieresd rbomh, com- bining liehtness with sdSiwsi. This ii fhmiihed with a fine knire- edge at Uie centra, which reit* on an agate plane cemented to the top of the pillar, b, and two kiii(»«dg«« attached to its extremities, ~~ which the scats planes, oemented to the snspeiinoli of the . „.P . .. '-iMoftheicr' ■cales, rest. When not in nse, the agate plant linit lifted oCT their knife-edges br a rising sufmo . __ m of which, the beam itKlf U raised off its bearing. This anpport if raised bj au ecoentrio at b, rooted bj the batton, d. The scal^-pana, when out of gear, are kept stoadv bv a tDOrahle support benealh them. B; means of a sliding liAjng-piece, r, which passes out through the side of the glazed case, o h, a noaU weight ti of wire maj be deposited on the upper edge of the beam, gr. placed in the scale- le whole rests on three —J „— - , , ate seen in the drawing. The inmoation of horiiontal position of the beam ie given b; a kmg slender indsi, l, attached to the beam, beneath the pomt of wbuh a scale of decrees i> ^aced. In the adjastmeat of a baUnca of this deicnption, it is necessary that the knife-edges pan ; and smaller parts in proportion. Tl adjusting screws; two only of which, k, i, The inmoation of horiiontal position of 63 attached to the heam ahould he parallel, and in the same plane, and that the tenmnal knife-edsea should he equidistant from that at the centre of the heam. T^e centre of ^yity of die heam is sdjnsted to ahont 0*01 inch helow the knife-edspB, which causes the heam to oscillate in ahont 40*. The drawing represents a 12-inch beam, designed to bear 1000 grains in each scale, and to indicate 0*001 grain. 116w Aa a smaller weight may be made to counterbalance a greater, by lengthening one of the arms of the lever when arranged as a balance, the dishonest vendor is thus frequently tempted to cheat the unsuspicious buyer. This is readily detected, by weigh- ing the substance to be purchased first in one scale pan and then in the other; if the balance be correct, it will weigh the same in both, but if inoorrect, its apparent weight will be different in each Kale-pan. To determine the true weight of a substance with such a bdance, weigh it first in one scale-pan, then in the other ; multiply thew two wei^ts together, and take the square root of the product. Tkm if a sub^ance weighed 253 pounds in one scale and 251 in the other, 1^251 x 253 = nearly 252 pounds, the true weight. This may be readily proved algebraicjdlv. Let a, b, be the un- equal arms of the balance, A, b, the weights which, appended to these anns respectively, balance x, the true weight ; then (110) a : h :: X : Af also a : 6 :: B : a;, therefore b : x :: x : a: hence o^ = a x b, and x = ^axu. 117. Another process for weighing accurately with a false balance haa been devised by Borda, wnich indeed furnishes us with the most accurate mode of ascertaining the exact weight of any sub- stance, even with a good balance.^ For this purpose accurately coonterbalimce the rodv to be weighed by means of any heavy matter, as fine leaden shot, or sand. Then remove the body and leplaoe it by weights carefully introduced into the scale-pan, until the shot or sand be counterbalanced, and equilibrium re- stored. These weights wiQ give the true weight of the body firee from any error arising from imperfections in the balance. Ijiis is called the method of double weighing. 118. In the lewr with un- j^, 94, equal arms, it is obvious that the spacea through which its extremities move are very diilerent. Let the line a f 0 represent a lever, turning on the folcram at f as on a centre, and suppose a weight to be attachea to the end, c, 64 ¥BCH^KICAL POWBRS, OB SIMPLE MACHIXES. and a power applied to a, sufficient to move it Then, while the end, C| describeB the arc, d c b, the end, a, will jpass through the arc, E A o, the length of each arc heing in the direct ratio of the arms of the lever. The power applied at a, and the length of the arm, a f, remaining the same, as the weight applied at o is in- creased, the arm f c must be proportionablj diminished, and the length of the arc, b d, or the space described by the weight, will be aiminished, as the weight increases ; consequently, the time occupied in causing the weight to describe the same space will be proportionablj increased. From this reasoning we become convinced of tne truth of the statement we set out with, that the application of the mechanical powers is an exchange of time for power (109). 119. The difference in the spaces described by the unequal arms of a lever, and consequently of the time required by the ends of each to traverse a given space, is well illustrated by the solution of the celebrated case assumed by Archimedes of Syracuse. Iliie philosopher, seeing the immense power capable of being exerted oy a lever, declared, that if he had a place to stand on, and were provided with a sufficiently l(»ng lever, he would move the world. If it be granted that he could exert a force of 30 pounds in pulling an arm of a lever through 10,000 feet per hour, he would, to raise the earth a single inch, nave to cause the end of the long arm of a lever to pass through an arc which would require the continued labour of 8,774,994,580,737 centuries to accomplish, supposing Archimedes worked 10 hours per day. 120. The common steelyard is an example of a straight lever with unequal arms. In this instrument the weighing is effected by attaching the substance to be weighed to the short arm, and then shifting a constant weight along the longer arm, until equilibrium is obtained. In the steelyard. Fig. 85, p is the movable weight, Pi^p^t &c., the divisions, each representing one pound : f, the fulcrum, and w, the weight, suspended from ^' ^' the point to. As the short arm is not made sufficiently heavy to balance the Ions arm, let o be ^ ^ , the point at which the weight, p, must be applied in order that the steelyard may balance itself, then the graiduation must com* mence from that point, and not from F. Let us suppose w to be 1 pound, and to be balanced by P at^*, then w is sustained partly by f and partlv by the weight of the long arm, which by the supposition is equivalent to p x o f, therefore wxwf=pxof + fxfp,=«pxo/},; and iipiPtj P%P» ^i ^ taken, each=io f, since to fsoj),, we shall have 2wxwF=p>«2o|)i=Pxop„ 8w X w F=p X 3 0^1 ■ p X o|)g, S DIFFEREHT KIKDB OF LBVXBS. 65 and 80 on; that is, p, raspended homp^jp^ &c., will respectlTely Bopport 2 lbs., 3 lbs., &c., at tr. JA tlie steeljards in common nse there are two hooks for suspend- ing anj substance to be weighed, at difierent distances from f, and two corresponding gradnations on the opposite edges of the bar, which may then bs emplojed either way upwards. When f tr is the ihorter, a mater weight maj be ascertained, bnt with less accnracy . 121. The levers jnst described have been termed levers of the fiist class, and are characterisEed by having the Ailcrom at some poinl between the power applied and the resistance to be over- come. Those leveiiB in which the fulcrum is at one end, and the resistance at an intermediate point, liave been termed levers of the second class ; whilst ihoae m which the power is applied be- tween ihe folcram and resistance are placed m a third class. But it appears unnecessary to make more than two classes : the only leai CDstinction that it is necessary to make, is between levers in which the fulcrum is between the power and the resistance, and those in which the fulcrum is at one end. The proportion between the pressures to produce equilibrium is expressed in the same tenns in each case (110, 111), the chief difference between them being, that when uie fulcrum is intermediate, as in the lever already adverted to, the pressure upon it is equal to the sum of the pressures api^ed, and to their difference, when the fulcrum is lenninal. 122. The power, weight, and resistance of the fulcrum being oooflidered as three pressures by which the lever is kept at rest, it may be remarked generally, that the two terminal pressures must always act in the same direction, and the intermediate pressure in the opposite direction ; and further, that the intermediate pressure must always equal the sum of the other two. This consideration irill frequently be found useful in determining the direction in which s^ gi^en pressure must necessarily act. 123. That modification of the lever, in which the power is applied between the fulcrum and resistance, is not very frequently met with; indeed, on account of the mechanical disadvantage at which the force is necessarily exerted, it is never used except to gain considerable velocity, or to overcome _ smaU resistances. Kkpf, Fig. 86, '^•^• represent such a lever moving on a hmge as a fulcrum at f, and the power be applied at f, it is obvious that whilst p moves through a small ■pace, K will describe a larpe one ] and as both are performed in equal times, the velocity of the end, r, is considerably greater than that of the point, p. The common tongs, used to supply the fire with fuel, 66 mBOSAHICAL POWERS, OB SDtFXM ICAGHnTES. afford an example of this kind of lever; the sheep-slieara and sogar-tongB are similar examples. 124. Of the first described leyer, in which the fblcmm is inter- mediate, examples are met with in the crowbar, scissors, pincers ; and in the ordinary poker, when it rests on the bar, in the act of stirring the fire. Of the seoond kind of lever, in which the fulcrum and power applied are both terminal, an oar will aflbrd an ex- ample, the water being the fulcrum, the boat is the resistance, and the hand of the rower is the power. The chipping-knife used hy druggists, in which the end is fixed to a board, the common nut- crackers, the chaff-cutter, and the treddle oi a lathe, are also instances of this kind of lever. The following figures of the crowbar. Fig. 87, chipping-knife, Fig. 88| and forceps, Fig. 89, afford examples of the tnree forms Pig.SV, Fig,B9. i^.88. ^ of lever ; the letters p, f, b, respectively point out the position of the power, fulcrum, and resistance. «.. ^ A good practical illustration of the bent *^' lever is met with in the truck. Fig. 90, by which sacks of com. or coal, or other heavy goods, are removed irom one part of a whan or warehouse to another. In this machine the axis of the wheels, f, is the fulcrum, against which the foot is placed while the weight at n is raised off the ground by the hand applied at p. 125. The compound lever is a system in which two or more levers are made to act on each other; by which means a vast in- crease of power is gained. The system re- presented in Fig. 91 consists of three levers, a b, b c, o d, of which the arms are respectively 6 and 1, 4 and 1, 5 and 1 ; and they are so placed that the short arm of a. b acts on the long arm of b c, and the short arm of the latter on the long arm of c d. Thus a ^w pBnrciFLE OP TnnuAL telocities. 67 yreastae 1 at a will siisfain 6 at b ; and as 1 at b will iMtlaDce 4 at c, 6 at B will balance 6 x 4 or 24 at c ; consei^aently, 1 at a will balance 24 at c. Similarly, 1 at a will sustain 5 x 24 or 120 at D ; thus, for instance, 1 ounce troy suspended at a will sustain 10 pounds suspended at d. The short arms of the levers here LW W W W *** represented are made heavy, that each may separately balance itself on the pin which forms the fulcrum. If o^, i^; a^b^; &c., be the long and short arms of any system similar to tne above, in which b^ acts on a,, &, on o^ and so on, we shall have equi- librium when p : w : : &, X (, X &c. : a^xa^x &c. ; that is, in any system of combined levers, the power is to the weight as the product of the short arms is to the prcduct of the long ones. 126. Prineiple of Virttud VdocUies. — ^There are two other modi- fications of the lever which it is desirable to notice on account of their important practical applications ; but the action of these cannot be readily rendered intell^ble without the application of a very important mechanical principle, that of virtual velodtieSf which may be here explained, although a rigid general demonstration is inadmissible. The velocity of a moving body (Ch. YI.) is measured or represented by the space described in a given time, but in re- ference to statics means only the space that would be described, if ihe body were put in motion ; and tne virtual velocity of any point, p, acted on by a pressure, p, is the space which that point will pass over, measured in the direction of f'b action. The general oondition of virtual velocities is, that if p^, p,, &c., are any number of pressures acting on any system or macnine at the points ^i,j},, &a, and Vj, v, &c., the virtual velocities of these points respec- tively, then in the case of equilibrium, p, xr,+p,xt;,-f- &cao; which may be expressed by Z(p x v) a o. The aiffebraical sum of the quantities (p x v) must be here un- derstood, for it is evident that in the case of equilibrium, some of the virtual velocities must be in a direction contrary to that of the others, and consequently that some of the quantities, v, must be negitive (vide 79, note). nut we may here confine our ideas to two pressures acting at F 2 > machiDe, mi tendiDg to prodoM tDOtion in oppoule There >re many cues in practice in vrbicfa it unmld be tediooa or difGcult la follow out tbe relations of preHares from their poiota of appll cation, to other potnta at which tbeir efiecta must be eiti- nial«d ; but in tlieae cajea, on the contriin, the lirlDsl velocities may without difficulty be determined. Thii will be readilj nikder- rtoodfrom the foUowmg '— 137. The principle of virtual Telocities is manifestlv tme in the case of the Btmi^ht lever; for if 'y**- thelaver, prK,Fig.92,kept«t it bj p, ij acting verticBll;, e moved into (be pontion, 'ra*, and vertical linea be I drawn through r' and k', ! meeting r s i" P, f, than t'p, t!T will be the ipacee traversed br r, s, respecavetv io the direction of tlieir actions, and will therefore represent their virtual tolocitiet. But b; similar triangles, and b; the topposition pf : pk :: a: p, therefore f*; ; s'r ; : » : p. In this case the ratio of the virtus) relociHes is constant, wbstber tho space described bv the lever be great or small ; but in manj initaaces, the ratio of the ipacei auccesaivel; deBciibed bv p uid K is not constant. The ratio of the virtual velocities is then repreaenlfld bj the ratio of very small cormBponding spaces, or Diore Btrictlj speaking, of indefinitely amall B[iacei; in otber words, the ratio oT the virtual velocities is the limiting ratio of ths corresponding spaces described. We will now proceed to the explanation of the two examples proposed. '*'■ W- 128. SobetvoTi Balance.— Two ir .^; levers *b, od, Fig. 93, are attached at their middle poiols, E, p, b; pins on which Ihej turn, to a verti- cal support, I r. The arms, a e, BB, cr, FD, are all et^ual, and their extremities are jomled to two vertical supports at the points «, c, B, n, so that the diatancea, A C, B r, B D, may be all equal. The sapport* AC, BD, ~ ' * bf Iioriiontsl tables, o, b,oq vbich the veighti are placed. Joid ■ r, r D, D B, B E, then i r D ■ it a parallelogram, and wiU coDtiDoe to oe UiB same, in whateTer pooition the leTen, jk B, c D, maj be pbceJ ; coneeqaentlj A c, B D, will in atl pouCiona remain parallel to ■ r, that n, will be alwajs Terlical ; and therefore the tabtei a, B, will moTe parallel to tbemwlTei, and all points nf their surfnces will moTe thnragb eqaal spaces, which wiU likewise be eqnal to tiKMe passed thraogb 07 a and b. If, therefore, weights are placed ■njwbeie on ihe tables oh, their virtaal Telocitiea will be equal to those of the points a b, that ia, thej' will be nibject lo the con- ditions of equilibrinin oF the ordinarj balance ; but with this ex- ception, that, nnlike the arms of a connnon bulance, it is imnw- terial on what parts of the table the weights are placed. 129. The weighing machine is comtmcted on this principle -rbea heavj goods are reqoiitid to be weighed, '*•*■ as io the weighing no- m chines at toll-gates and I nilwaj stalioDS, the I arms, a K, b b, are Tar; I ■maqpal, attd Ihe effect I of the connlerpoise is I rorther incresied b^ its I being attached to the | koser arm of a lever, as E. m Fig- W. 130, The Anou.— This term has been applied to a combination of lerara b; wbich a preasnre is effected un precisely the same principle as that on which the weight of the body ii ■ • ■ - the erect position by straightening the knees- Machines are thus constructed in which a iarge amonnt of Dresmre is required lo be exercised through a nttali space, •Dch as ooptiuR and printing preaMB, and the tike. Let a b c d be the ftameofapress, Bthe centre of the riidng piece, snd rou a bent lerer tuning on o. the middle [Kant of A D, and jointed at n to a fink, which is also jointed lo the IV- M- rf ijet F, s H, I, tig. 96, F,QH,B,. be fonr positions of the knee and hwidle, snch that the angle r, e r,— r, a r„ and conse- E, E„ and I, Ell then !,ap and p,f„^i, qoentlj H, OH. = H,aB,. Join r, r-r,r, when the angle Fj a f, is very small, r, »■« =1 "p , will represent the cMresponding virtnal velocities of tl 70 r and e. Bat while p, f, - p, f, , b, e, , acid s, i. are manireatlj Tei7 tmeqiuJ ; let p be the oousiHiit preuure on the handle tt r, J.. ^ Aod R, B*, the comaponding ^' preasum eiertedbeCireanK,^ ■od B, Bj respectiTelj, ttieQ (137)»x»,B,=pxr,F„ = b'x^b''; orii:B'::B,E.;E,B,; coDBeqaiinlJjr, ai e,b, becomea eicaeoingly atatll, compared with B, B, when the knee, h, approaches very netr]y to the stmit^ht poaitjon, the preaamv k' becomea exceedingly great relatively to k; but it mnat be romanibered, that thia great preesnrs is exerted through oalj a ver; small apace, and thereFore in practice, the presa requires carafal a^jaatment, in order to develop it» fall power. 131. The wheel and axle is a modificatiou of the lever, in which conaiderable mechaoical adiantage is gained. The machine consists of a cjUnder, A, Fig. 97, termed the axle, tnnuDK on a centre, sod connected with a larger circle of wood or other snbataDce, a, called the wheel. Sometimea this ia replaced hj a ^^e, as a, fixed into 4, to the eod of which the power ia applied. The resistajice to be _ „ OTercome is Gied to one end of ^' a rope wound round the small cylinder a, whiEat the power is applied to the circi^mfeience of B, generallj by meana of a rope r, acting in the direction * of a tangent to b. Here the radiua M the smaller circle, er axle, maybe conaidered ascor- reeponding to the abort arm, and the radius of the larger (or wheel), or the length of the apoke fixed into *, to the leneer arm of a straisht lever. And accordingly wa find that equilibrium ia obtained when the power applied is to the WsisUnc ■ ' the a«n:e ratio aa the radiu irf the axle ia 0 that of the wheel. THB PULLET. 71 OtDmg tlie ndhiB of the wheel w, and tliat of the axle w, we have PXWaBXtO. The winch, wmdlefl% capfftan, and crane, afford examples of the practical application of this naeful modification of lever. In the nDowing ngana, representing several varieties of the wheel and axle, the same letters of reference are nsed as in the diagram last described. JV-9S. Jl^« 9Va ^.100. JV* 101- 2. TBB POLLBT. 132. The sinaplest form of pulley is naed onljr to change the dirsction of motion. As osaally constracted, it is a small wheel moveable aboot in its centre, in Ihe cir- cuniiBrenoe of which a groove is formed, to admit a rope or flexiUa chain. ^ In the single fixed pdle^ moveable round itscflotre, G, Fig. 101, no mcrease of power is gained ; it is merely a convenient in- stnment for changing the direction in which a given pressure acts. If a rope AB be pasKd over the pnDev, eqnui- briun wiU oocnr when the weights n and p ne equal ; the tensions of the string win be equal on both sides of the pulley, uid as these tend equaUy to tuip the poOeyin opposite directions, it will ne- oasianly remain at rest. 133. Bv a single moveable pulley we sxe enabled to sustain a resistance of 2 ^ a power of 1. Let the rope a o, Fig. 102, be fastened to afixed pomt at ▲, and passing under the groove of a moveable poUey D, be brought over a fixed pulley b, so placed that the Kveral portions m the string may be parallel to each other : tbe Cj^J untu it meets o b at i. Then, if d e be ^-^ taken to represent the amount of power at p, it may, by the^ resolution of pres- sures (69\ be considered to be the re- sultant or two pressures, one acting in the direction e c, and efiective in raising the weight b ; the other, c d, being coun- teracted bj an equal and opi>08ite pres- sure arising from the tension or the string E o ; and as the two folds of the string, OB,' be, are equally active in ■K ) suBtamingB,2cE will represent the whole weight sustained by the power f, and p : b:: de: 2 CE ::rad : 2 cosdbo. When the strings become parallel, the angle dec vanishes, and ita cosine becomes radius, then p : b : : 1 : 2 as already explained (1S3). The pulley has been referred with great justice to the lever, of which indeed it may be considered as a modification ; the diameter and radius of the single moveable pulley, representing the arms of a lever, on which the power and resistance respectively act^ by means of the string. 138. The DifferenUal PuUey. — ^A combination of the wheel axle with the pulley, to which this term has been applied, affords an advantageous means of employing considerable power. One end of the string passes over the wheel a d, and the other is wound round the aue, b. The tensions of the strings b b, d f being each equal to ^b, a D may be considered a lever kept at rest by three pressures, p at a, and 4b at b and d, consequently iBx[DC=] CA = iBXCB + PXCA; theiefore iBx(oA~CB)=pxcA, 4bxab=pxc a; or whence p : B :: ab : [2ac =]ad. I \ k difleTcntuJ pnlleT worked fay an endless chaia. Wie. 108, hw htflj come connderablj into use in buiJilina; ; in this tiie gnxirM of tin doabls piJley are hollowed oat to fit the Hueceiaii'e Unks of the chain, ami the awenJinj; chain is prevented bwa ilipping 01 theinil^y bj passing under a — "— Ine Cbinese capstan, of »liich Dr. O. Gregory niet vilh anne drswiiKS mora than a centniT old, acts npoi thii prisaplB: the csp- •Ud coDsuto oftwo parli of diSerenl sine, and the rope is Boqiid on to the latKer, while it is nnwoiuid rrom the nuaDer, as in Fig. 109. The power will iocreaM as the difierence between the two portions of the capstan is diminished. 139, aigiditji of Cordagt. — The conditions of ttatieal eqmli>- brimn of the tarioiui sjatems of polleje have been correclly deter- nuted ; bat when an eiceas of power, beyond what is required to ^nce eqnihlnium, is applied to raise the weight, or to OTeroome the Kiiitaiice, it must be borne in mind that a certain portion 1^ this win be oonsmned in orercoming the resistance of the machine iUel^ ofwhic^ the rigidity of the cord f, also b e and a p pnpendicalar to a a Then the pres- •ure D p maj be resolved into Iwo (72], D A in the direction of the plane, and Ap perpendicnUr to it, of which 1 r CAD have no oBect in moring tha point D along the plane, and i f d p npnsentB the whole presnire p, a s will repRMDt the eSectife part of it, ■hich therefore : p :;AD:DP,aiidcon- >e<]aenU7 Similarij the vertical fKtean d a may ho reeolTed into d b and B X, oT vbicb B B acting perpendicalarlj to tlie pluie bu no tendency to move d along its sorfaca. Therefore the eflectivs part of B : B : : D E ; D a, and canseqaenU} = RX— = KX^(hy aim. triangleB}=«, lin fi ; itat D being at reat, the preisorea JD oppoaite directions mn^t be «|Da!, thcr^ore p. cos a = B. ua 0, If r acta parallel to the plane, we have aimplj p — s. nn J3; T p : K ; : height of plane : its leogth. If p acta horizontallj, a^fi, and then p.coa^ = R.BinAorp = B.Un(3; Of p: b; : height of plane: length of base. Hi. The conditioDB of equilihrinm on the inclined plane maj be eanlj ihown experimentallj. Two boards a b, b o, are hinired to- Ecilier at B,_Rg. 113; one of " tKem, B c, is placed borixon- tilly, and has a gradoated arm, de, allached to it, to vhich A B inar be clamped bj a KTCw. The edge ab is L dirided into inches, aa well as ' a narrow slip of wood or metal, A T, attscbed at A Ini a pin on wbich it can moTe &eelj ; thii slip hazing Tertically by its om gravity, shows the height of Iha plaw when Aia rawed. A weight k is placed on ayerj light carriage, coiaiiling of a thm plate of wood with fnnr small light wheels, sjid IS BBatainnl hy another weight r attached to a siring, which passes owr a pulley at A, and is fastened to the carriagB. When the wiglita are as the numbers of inches in A B and * p, they will be m esmlibnnm but if the plsne is raised or lowered a little from thu pomtion, the equJilnum wiU be destroyed, and « wiU ascend 78 MBCHARTCAL FOWXB8, OB BnOlM MACHnrn. or deecend accordingly on the inclined plane ; especiallj if aided in starting, by a jar on the table on which the pUuie rests. Here, as in the other mechanical powers, time is lost as power is gained, for the Tertical height to which the body is raised by means of the inclined plane, u e^nal only to the height of the plane, while the space through which the power descends is equal to the length of the plane ; and the less the height of the plane the greater the weight that can be raised on it by a gi?en power. 143. The Screw. — If an inclined plane be supposed to be wound spirally around a cylinder, in a manner similar to thst in which IW. 114. spiral paths are carried round mountains to ^ lessen the steepness of ascent, we have a 9creWt one of the most useful of simple machines. The edge of a flexible inclined plane a, Fig. 114^ an angular piece of naper, for example, wound round a cylinder b, represents the thread of the screw, which projects to a certain distance beyond the cylinder on which it is supposed to be wound. In order to appl^ the screw, a hollow spiral is carved in the mside of a block of wood or metal, termed the female screw ; this hollow spiral must be of such a size as to admit the projecting thread of tne first, or maJe screw. Thus constructed, the male screw is generally turned by means of a lever, fixed into its head ; thus, indeed, form- ing a compound machine, the power of the lever being added to that of the simple screw. The power of the screw increases with the circumference of the circle described by the lever, l, Fig. 115, to which the power is applied, and with the diminution of the distance between two conti^ous threads of the screw, measured m a direction parallel to the axis. Calling this distance d, and the circumference of the circle described bv the lever, l, equilibrium will be obtained, when p : B : : D : L. This is true by the principle of virtual velocities, for as the screw is raised or lowered tnrough the space of one thread, by one complete revolution, d : l : : (v) b : (o) p, and hence p : b : : (v) b : (v) p. 144. JBunter's, or the Differential Screw, — If a very large amount Fig. 116. 79 Fifi.iie. of pnmue h required to be exerdaed, the threads of the screw QULit be Tery ^aie, and are therefore more likely to be torn off the crlinder on which they are cut. To obviate tnis inconTenience, the laige screw that works throueh the head of the presi^ as in Fig. 116, is nollow, and bas a thread inside, less coarse than that on the oatside of it. A male screw fitting the preceding hollow screw is firmly fixed in the rising piece. In this machine it is evident that while the larger screw descends throoeh the space of one thread, daring one revom- tiooofthe handle, the smaller will ascend vithin it through the similar space ; conse- rtljT the descent of the rising piece, or ▼irtnal velocity of b, will depend on the ^fiBsrence of the spaces between the two thretds, wluch may be made as small as we please : and consequently the resistance, b, will be limited only bj the strength of the materials of which the press is composed. 145. The Wed^. — ^When two inclined planes are placed with their bases approximated, as a b, Fig. 117, we have a wedge ; which is a triaogolar prism, bounded by plane sides, of which two that are Fig. 117. opposite are equal and Pj^ndlol trian^es, the others wing parallelograms. This is occasionally used as t mechanical power to lift heavy weights to small elevations, but is more generally used for the puipose of splitting timber; the edge being introduced into a deft maoeto receive it, and the wedge forced in by repeated blows of a haojmer upon its biusk. The great saTaatage of tiie wedge appears really to depend upoo the percussion used to urge it into the mass of timber, &c., exciting vibration between the particles of the solid, and thus permitting the edge to insinuate itself between them. Certainly the diiect action of a weight preoing upon the back of the wedge, can bear no comparison with the immensely greater effect gained by percussion. The amount of weight necessary io^reu a common nail into a board, compared mth the weight of a hammer that will readily drive it, is slmost incredible. 146. Theoretically speaking, it has been Boppoeed that the power gained by the wedge bean the same proportion to the resistance to be overcome as naif its back does to its height; but this applies only to the equilibrium of the wedge when at rest : for friction enters so largely mto the consideration of any motion that might result from pressure on the back of the wedge, that the only part of this theory which is really supported by 80 MECHANICAL POWEBfl, OB BIlCPLB MACHIKBS. practical observation is the fact, that the power of the wedge in- creases as its width or back diminishes. Many of our domestic instmments are modifications of wedges ; a saw is composed of a series of them, and knives, scissors, razors are nothing more than fine saws. Needles, pins, &o., may be considered as acate circular wedges. 147. Another important modification of the inclined plane, of lig, 110. constant application in machinery, is the cam; this is a projecting piece attached to a revolving axis, on which an arm, or lever rests, which is periodicaUy raised as the cam passes between it and the axis in the course of its revolution. The eccentrics of a steam-engine, and the stampers of mills for crush- ing ore are examples of the ac- tions of cams ; large shears are moved by the same means at the iron works, by which iron boiler plates half an inch or more in thickness, are trimmed into shape with no more personal labour than that of holding them. 148. In that elab<)rate and wonderful part of the animal economy the muscular system, we have much to admire in the adaptation of power to the movement of the bony levers constituting the skeleton. Here, where great strength, rapidity of movement, and elegance of figure, are equally attended to, we find evidence of infinite wisdom in the adaptation of mechanical power, apparently the least advantageous, to the most important motor functions of the body. In considering the mode in which extension of the limbs, especially of the upper extremities, is performed, we see a set of levers of the first kind (121) called into action; or those in which the power and resistance are at opposite ends, and the fulcrum intermediate. In the flexion of the limbs, we have a set of beautiful examples of levers of the third, or that kind in which the resistance and fulcnim are terminal, and the power intermediate. And in some other muscular efibrts, as depressing the lower jaw, we have examples of levers of the second denomination, m which the resistance is intermediate between the fulcrum and power. The action of raising the body on tiptoe has been commonly, but erroneously, considered as an illustra- tion of the second class of levers, which ic could not be unless the upper end of the muscle, instead of reacting on the parts from which it arises, were attached lig.UO, LEYEBS ni THB ANIMAL ECOHOKT. 81 to a post or some otber fixed poiut external to the irame. For let A F be the bones of the leg, f b the foot, b p the muscles which raise the heel, and for oonTenience, let b p, the line of action of the moscles, vgpwards at p and downwcnrds at b, be parallel to A F, in which the weight of the body acts ; then p actiog apwards at jp sustains the parallel pressares p and w acting downwards at f; consequently or PX pBsPXFB + WXFB, P X [p B — F Bs3 ] p F=B W X F B ; that is, the conditions of equilibrium are precisely those of a lever ofthe first kind (110). 149. By the insertion of a muscle near the fulcrum, we gain a mat increase of velocity at the further extremity of the lever (123), a rapid motion best fitted for many of the purposes of animal life is thus obtained. In the act of flexing the arm for example, the fulcrum f is formed by the condyles of the humerus at the elbow j«int, the resistance is the weight, b, in the hand, and the power is applied at p, by the contraction of the muscle attachea to the radius. When this muscle (biceps flexor cabiti} contracts, the hand b describes a much longer curve in a Ftg. 121. given time than p, therefore, although the power of the hand is much less than the contractile force of the muscle, still that power is capable of being exerted through a much larger space. 150. The following* are some among many examples of levers in the human body. > A. Fvlcrwn behoeen the Fewer and Bmstance. POWBB. Muscles arising from tuberositiesofischia, and inserted into the lower extremities. Muscles connectinff the occiput and spine. FULCBUM. Heads of femora. The Atlas. BESISTANCE. Weight of the trunk, - when flexed upon the thighs. Weight of the head, acting at its centre of gravity, in front of the fulcrum. 82 IdSCHANICJLL FOWBBS, OR BDfPLV MJLCHINEB. B. Ffdcrum terminalf Beaietance intermediate. POWER. Digastricus, and other aepressors of the lower jaw. FULCRUM. Articulation of the lower jaw. KE6I8TA1ICE. Action of the tem- poral and masse ter muscles. C. Fvlcrum terminalj Power intermediate. Biceps flexor cuhiti and hrachialis. Deltoid. Condjles of hume- rus. Glenoid cavitj of scapula. Weight of arm and hand. Weight of the arm. 151. Of compound pulleys we should scarcely expect, where all is characterized hy beautiful simplicity, to find any examples ; of simple pulleys, merely to alter tlie direction of motion (132), we have a few instances. The structure of the pulley-like or^n is always extremely simple, usually being merely a groove m the bone covered with cartilage, sometimes a bony hook, and in another case a tendinoas ring. The tendon of the obturator in- ternus, which, in passing out of the pelvis, glides in a groove in the ischium, so as to alter its direction ; and the hook-like process through which the tendon of the circumflexus palati glides, so as to alter its direction to a right angle, and the tendinous ring in the depression of the frontal bone, through which the tendon of the obliquus superior muscle of the eye glides, being thereby bent to an acute angle, are examples of the simple pulley in the human body. 152. We have no illustration of the inclined plane, or its modifications, in the human skeleton. The sacrum is certainly not an example of the wedge, notwithstanding its figure. The only approach to a wedge in animal structure which the authors aro acquainted with, is the bony apparatus discovered by Sir Philip Egerton, in the neck of the ichthyosaurus, an extinct ante- diluvian reptile. Three wedge-like bones have been described by him as connected with the cervical vertebrae, and fitting into spaces between them ; these wed^s are supposed to have been withdrawn when the animal flexed the head upon the trunk, and to be introduced between bodies of the vertebrss when the head was raised: so as to diminish that vast muscular effort which would otherwise be required, to keep the enormous and dispro- portionate heads of these animals extended. 83 CHAPTER V. PRI2ICIPLE8 OF MECHANISM. 153. In the preceding chapter the conditions of equilibrium of the gimple macnines have heen ascertained, some of their leading mudiHcations explained, and their various applications in the ftniual economy illustrated. The object of the present chapter is to point out the various relations of tne parts of machines to each otkBr, the objects desired to be attained by machinery, and the mean s adapted for attaining them. A cursory notice of the leading features of so wide a subject is obviously all that the limits of an elementary treatise will admit ; and it will be found convenient, in the following treatment of this subject, to confine our ideas as much as possible to the mere relation of motion as existing between two parts of a machine, without any reference either as to tbeir actual velocities, or to the force employed in moving, or required to be exerted by the machine, or the mode of connexion of the parts in question with the framework of the machine. These points belong more properly to a practical treatise on the c<»i8truction of machines.* 15}. Any combination of mechanism is called a £ratn, consist- ing of several parts, OT pieces, variously connected with each other in succession. Of two successive pieces, that which communicates niotion is called the driver^ and that which receives it, the follower. 155. The line in the direction of which the action of the driver on the follower takes nlace, is called the line of action; and when- ever the driver and follower are moveable in tne same plane, about fixed points, the line joining those two points is called the line of centres. 156. Motion may be communicated from the driver to the fol- lower either by direct contact of their surfaces, or by some inter- mediate communication. If the surfaces roll on each other without rubbing, as the circumference of one cylindrical surface on another, the action is called rolling contact ; but if the surfaces do not roll on each other, as when a projecting pin rests on a cam or an eccentric (147), in the Btamping machine, for example, the action is that of sliding contact, in many cases the contact partakes of * The Authors are indebted for the subttance of this chapter to the ** Pdadplefl of Kechaaiim/' bj Prof. WiUit. Cambridge, 1841 . Q 2 84 PRIirClPLES OF IfECHAKIBM. Vig. in. both characters : thua, let A c, Fig. 122, be the driver, and b d the follower, their surfaces being in contact at fn, and let A e, B -. __ TABLB OP BLEKBlfTABT OOMBniATIOXS. 85 spices deseriW in the timeB t|, <,, &c., then since the yelodtj- ratio is constant, s, : #1 : : V : V. nmilarlj therefore, 8, : «, : : Y : V. &c. &c. 8,+aj + &c. :»,+«,+&c. ::y:v. And this is equally tme when the qnantities, s, «, and t, hecome so small that the changes in y and v hecome continuons ; and hence, The vdodty^ratiot when conttant, is obtained hy comparing the entire spaeee deecribed in the eame time^ whatever ekanges the aetwU vdodtiee mt^ have undergone during that time. SIXBOnOVAl MMhAXlOS— (2) CHAirewo Mova ov (1) COaiXAVT. mxonxcALLT. coavaziov. dans A. Class B. Class C. Vtloeiif^ratio rOoei^'ratio varffing. eoiutant or varp' ing. Pxnsioir a. BoDing cjlinden. Boiling carves. Mangle wheels. BjBottiog Cooteet. oones, aod hyper- and rolling ourre Mangle racks. bokridft. wheels. Kscaping gearings. Geaeral ftmiige- Eccentric wheels. nentandfocmof Wheels with inter- toothed wheels. mitted teeth. Pitch of wheels. Boiling corre levers. Dimiox' b. Forms of the indi- Fin and slit lever. Pfa» and slit lever. Bt Sliding OoDtoci. ▼fdoal teeth of Cams. Cams in general. wheels. Unequal worms. Bwash-plate. Cmdb. Geneva stop, and Double screw. other intermit- Bscapements. Bndlees screws tent motions. Propehnenu. and their wheels. Dinnov e. Bends in genersl. Conical poUeys. Curvilinear pulley Bt Wnppiog OoDiMotorfl. Forms of tbeir pol- lers. Curvilinear pul- leys. and lever. Guide pulleys. Fusees. Oesring chains. Bxpanding pul^ Modes of oommn- leys. nioating limited ^ Dcnsiov d. Cranks and link- Link-work. Cranks, eooentrics. work for equal Hooke's joints. and other link- rotations. work. Cranks for limited Batchet wheels motions. and clicks. BeD-crank work. Intermittent link- work. 86 PRIKCIPLBS OF MBCHAHjSlf. Hg. 1S3 II. To determine the Vdodty-raiio in Link-tcork. 162. Let A p, B Q, Fig. 123, be two anns moving on fixed centres, A and B ; and let them be connected by a link, PQ, jointed to their extremities, p, Q. L«t AK, BB, be perpen- diculars from A and B on PQ (produced if necessary), and let AP, PQ, QB be moved into the new positions, a p, pq, a B, very near to the former. Draw pm and -Qn porpendica- lar to PQ and join ^ A B, cutting p Q in T ; then in the ripht- angled triangles, p J) m, A p R, P|7 is perpendicular to a p, and p m to a r ; therefore the angle jpp ma the angle par, and the triangles are similar. In like manner the small triangle, Qng, is similar to bqb; whence, p^ : pm :: AP : A R, and qn: qq : ms :Bq\ also at:bt::ar:b8. (1) by similar triangles art, btb; and vm^^n ultimately, since p Q and p a are tlie same link. By compounding these proportions, omitting iaentical terms, and inverting a t, b t, a p, b q, we obtain AP * Bq' BT : AT . (2); but — ^ and ^ are the angles simultaneously described by p AP Bg and Q,^ and may therefore be taken to represent their angular velocities; also t is the point at which the line of centres (155) cuts the link p q, therefore in any g^ven position of the link. The angular vdodties of the arms a p, b q, are to each other in- versely €u the segments into which the link divides the line of centres. Cor. 1. By compounding the ratios (1) and (2) we obtain —2 : 3Ji : : BB : ar: AP B^ that 18, The angular velocities of the arms a p, b q, are inversely YKLOCnr-RATIO. 87 Of the jperpendiculari firom their eeatrei of motion on the line of aetkm. Cob. 2. Produce ap, qb to meet in x, and draw kl perpendi- cular to F Q, then pm : pm : : pl : kl, and qn :Qn ::kl:ql; whence bj componnding, |>m:Qn::PL:QL, and conseqnently l is uLtimately the point of interseetion of two conneeutive positions of the link. Cos 3. If the paths of the points of action p, q, ha^e no fixed centre, the results obtained above are inapplicable, but pj7, q^, being gmall portions of the paths described simultaneously, repre- sent the linear velocities of p and q, and vpxcoapvm=Fm = qn-qqxcos, m n, which are ultimately perpendicular to am, bm. Hence in the small triangle upn the sides Mj7, M n, j9 n, are respectirely per- pendicular'to am, bm, md, and conseouently the latter lines make with each other angles equal to those oi the small triangle, therefore pn sin jp M n sin a m b ^ p M sin ^ n M sin b M D ' in which expression -^ is the ratio of the sliding to the entire pu motion of the point of contact in one of the pieces, b m d is the angle between the nonnal and the radius of contact of the other piece, and sin AMB=iBin (bam+abm), as the sine of the sum of the angular distances of the radii of con- tact from the line of centres. a> n 1 \.L • P^ sin AM B Similarly we obtain • ■^— ^-r- . ' flM SmAMD 165. l^Vom these expressions it appears that in the small triangle pnUjpn can become indefinitelv small, compared with n m or jp m, only when sin a m b vanishes, that is, when the radii of contact coincide with the line of centres ; but when p n vanishes, there is no ilidingj and the contact becomes rolling contact. Hence it appears that In rolling contact^ the curves must he 8o formed that the point of eoTitact shall always lie on the Une of cevires, 166. Also, as the line of centres and common normal both pass through the point of rolling contact, it follows from (163) that In rolUng contaetj the angtdar velocities are inversiy as the segments into which thepoiiU of contact divides the Une of centres. BOLUKQ COHTAGT. 89 167. In wrapping connexions, the yelocity-ratio is the same a£ has been already foaod in link- work (162);. for in any given pod^n, the action of two pieces connected by a band is the same as that of two rods drawn from the centres to the points of contact, connected by a link ; hence in this case also, 7%e angular velociHes of the nieees are to each other inversely as the segments into wMch the oonneetor divides the Une of centres. 168. If the Une of direction of the link in link-work, of the common normal to the curres in ooutact motion, and of tne con- nector in wrapping motion, be severally termed the Une cfactionf the preceding propositionB may be considered as particnfar cases of tne more general condition, that I%e anguuar velocities of any two consecutive pieces are to each other inversely cu the segments into which the line of action di- vides the Une of centres; or inversely as the perpendiculars from the centres of motion upon the Une of action. 169. In the preceding propositions, each pair of connected pieces has been supposed to have circular motion in the same plane round fixed ^mts ; many of the conditions existing with regard to circular motion may be extended to rectilinear motion, by consi- dering the rectilinear motion to take place in a circle with an indefinite radius. Thus the conditions of motion of a rack and pinion are the same as those of a wheel and pinion. These general conditions having been established, some of the more important elementary combinations may now be separately considereo. CL. A : Drv. a. — Communication of Motion by BoQing Contact. 170. As in this case the point of contact must always lie in the line of centres (165), and ifivide that hne into two segments haying a constant ratio, the yelocity-ratio being constant (167), it is clear that none but surfaces of reyolu- tion can fulfil the required condition. If the axes of motion be parallel to each other, portions of two cylinders, the axes of which are parallel, and the radii of which are in the required yelocity-ratio, iviU attun the proposed object. If the axes be not parallel, but in one plane, two cones, or any portions of them, the vertices of which coinoide with c, Fig. 126, the intersection of the axes of motion ag, bo, and of which the corre- sponding radii, a d, b d, are in the given velocity-ratio, will fulfil the required conditions ; for it is evident that the drcumferonces of all corresponding sections of the two JV.126. { 90 PRniCIPLES OF ME0HANI8M. cones, made parallel to their bases, that meet each other at anj point in the hne cd, will have a constant ratio, and will therefore roll together. 171. If the axes be neither parallel nor meeting each other, the required surfaces of contact will be traced out bj the revolution of a line, intermediate in position between the axes, round each of them successively. These surfaces are called hyperboloids.* 172. In the practical application of rolling surfaces it is found necessary to cover them with leather or some other yielding ma- terial, and also to allow a sufficient mobility to one of the axes to ensure their contact by means of pressure : but the application of such means of communicating motion is very limited Fig. 127. A new mode of fnctional gearing has been devised by Mr. Robertson of Glasgow, which is represented in Fig. 127. In this a series of equal acute angular grooves are turned in the circumference of the wheels, which fit ^ into each other, and possess a considerably increased amount of holding surface. The amount of hold, or resistance to slipping, will depend partlv on the acute- ness of the wedge-shaped edges, and Partly oc the pressure on one axis towards the other. This will pro. oably work more satisfactorily than any kind of rolling contact hitherto proposed; but the necessary mobility of the bearings of one of each pair of contiguous axes is always objectionable. If great accuracy in the relative motion of the driver and mllower be required, as in clock-work, or if any con- siderable resistance must be overcome, as in mill-work, the contact motion is communicated by toothed wheels ; the employment of which is as extensive, as that of simple rolling contact is limited. 173. The total action of toothed wheels upon each other is analogous to rolling contact, because as equal lengths of the cir- cumferences contain an equal number of teeth, they must evidently pass the line of centres in the same time ; but the action of the individual teeth upon each other is by sliding contact, and will be subsequently considered. In reference to large wheels, the por- tion of the circumference occupied by one tooth and one space between two consecutive teeth, is caUed the pitch of the wheel, and two circles which would roll on each other m the same manner as two given wheels actually roll, are called the pitch circles^ or geometrical circles; the latter term is used by manufacturers of clock and watch-work. Oearing is a term applied to trains of toothed wheels : they are said to be tti gear when their teeth are engaged together, and out ofgeoTj when they are disengaged from each other. * See Hjmen' " Analytical Geometry," p. 142, or any other tareatiie on the same labjeot. TOCrmED WUEIU. 91 IT4. Toothed vheeli with fevteetb its termed ^'nioiu, tnd the tcFtb of these, Iranei, because thev are iiiu»U; made much longer in Ihd direction uf the aiia ihaa tie teeth of larger wheels, for the uke of rtrength, 'JTie teeth of vheeli may be made either in ooe ■W*- "*■ piece with the rim, as in vatch- vlieela, or(;onnatoriepsrat« piece) — (nmed into the rim ol' the wheel, an in large mill work ; the teeth are then cslli^ aw». The former me- thod is miiaUj adopted in metal nhee] work, and the lalter in w^ioden wheela. The small prwbeela, or pinions, in wooden wheel-work, fr«|uentl7 cnniiat of two parallel disrs, separated b; an inlerval a little wilier than the thickness of the wheel : this space is traversed hj ■ series ofeqoi Ji slant ejlindrical pins, called ttava, between which the o^ saccessiveij pass; awheel thus cnnstmcted is called a trutulie, nr lamtm. The con are made of some well-seasoned hard wood, SI mouD tain-beech, tiombeam, or hickory, tha grain of the wood being in the radial dirccti^in ; these are driven into grooTes or tnortioei in the rim of the wheel, and secured by pins passed throneh ihem inside the rim. Fig, 128 represents a large wooden o^-wueel. A, aad trundle, a, as usuallj constructed in mill-work. The pinions of Dolch clocks are umilarl/ constructed ; in then the pins are iron wire. 175. In modem mill-work, the wheels are nniall; of caat-iron ; bnt when the wheels are very large, and the power transmitted considerable, they are found to wear better and to work much more smoothly, if one of them, uaoally the larger, is supplied with wooden digs, instead of iron teeth; a wheel thus constructed is called ^- '••■ a mortUe-vh^. 1T6. In the wheels hitherto con- sidered, ihe leeth have been sup- posed to stand out radiallj from the rim ; these are called tpurvhetU. If the teeth project sideways from tbo face of tha wheel, ' pinion ofao ordinary vertical walcli : m which the axis a, is at right angles to the szi* b. In crown-wheels tha rei^aiaite s 92 PBIKCIPX.E8 OF MECHANISM. obtained by giving snfficient depth to the rim, but its thickness mast be inconsiderable, otherwise the amount of wearing would be sensibly increased by the oblique action of portions cf the surfaces in contact. For the same reason, the diameter of the pinion must be small compared with that of the wheel. In some cases the place of teeth is supplied by equidistant pins, standing out perpendicularly to the face of the wheel, as in Fig. 130 ; wheels tnus constructed are ctMed pin-wheeU ; Uiey are now rarely used, except in clock escapements. Fig. 190. Fig. 131. If a wheel be required to drive a pinion in the same direction in which it is movinfi", the teeth are cut in the intide of the rim, as in Fig. 131. A wheel thus constructed is called an annular wheel; the action is very smooth, but it is seldom employed, owing to the difficulty of construction. 177. If the motion required be that of two conical frusta (170), the teeth are cut on their surfaces, as in Fig. 132 : these are called bevil-toheele. In these, the teeth and •^* 1^ spaces are all directed towards the apices of the cones, a, and thus con- tact takes place along the whole sur- face of the tooth, and not in points only, as in the crown-wheel and pinion (176). ^. U3. ..A^ 178. If the path of one of the pieces be rectilinear, the teeth are then cut on the edge of a straight bar, and the piece is called a rackf the extent of motion of which is practically limited by its length ; Fig. 133 represents an ordinary rack and pinion. 179. A much greater smoothness of action may be obtained by cutting the teeth obliquely on the rim of a wheel and pinion, as in Fig. 134, but the construction is more difficult than that of ordi- naiy teeth, and the obliquity of the teeth produces an endwise rOBMB or THE TUTH OP WHBBLB. 93 preasare on the axiB, which would in man? cases be ^g- 134. objectionable ; especialJy where considerable power is required to be transmitted. Having now sufficiently considered the general formfl of wheels, the forms of the individaal teeth belong to the second division of the subject, as the action of one tooth on another, is that of sliding contact. Cli. A : DiT. h. — Chmmumeatian of Motion hy Sliding Contact, 180. The axes being supposed parallel, it has been shown (163^ that the angular velocities are in the inTerae ratio of the segments, into which the normal to the curves at the point of contact divides the line of centres. Hence when one toothed wheel is driven by another, it is necessary that the normal to the point of contact of any two correniionding teeth should always pass through the point of contact of the pitch circles, that being tne point at which the line of centres is. divided in the re- auiied ratio. Let a, b, Fig. 135, be ^V' 135. ie centres of the pilch circles h l, k m in contact at t, and let the tooth h d L be generated bv the revolution of the carve t s d on the outside of the pitch circle h l ; and the corresponding space KDM, by the revolution of the same curve, T X D, on the inside of the pitch circle k m ; then if the tooth and space be in contact at o. the normal to the point D will pass through t : for if the generating curve be brought into the position THD, so as to touch the circle H L in T, T D will be a normal to h d at d: and that the curves hl, km, may be in contact, the generating curve must toQch K M in T, that is, it must be in the same position for both the curves, H L, K M, and consequently t d must be a normal to both, that is, they wiU touch in d, and the line of action will pass through t. 181. In order, therefore, to find the form of the tooth of a wheel, that will work correctiy with a given tooth of another wheel, it is ceoesaary to find the curve which by rolling on the convex surfaoe of the pitch circle of the latter, will generate the curve of the given tooth, which may always be done ;* then the same curve, by rolling on the eoneatfe surface of the pitch circle of the former, will eenerato a space in which the given tooth will work correctly. In order • See Airy on the Teeth of Wheels ; Camb. FhiLTr. vol ii. p. 279. 94 PRIMCIPLBS OF UECHAMISir. Fig. 136. that the solution may be practicable, it is necessary either that the convexity of the tooth shoald be greater than the concavity of the space, or that the two curves should be convex towards each other. 182. This problem also admits of a simple mechanical solution. Let the curved edges of two boards, a b. Fig. 136, be portions of the given pitch circles. Attach to one of them. A, a piece of card-board, or other convenient material, c, having the shape of the given tooth, and to the other, b, a piece of drawing-paper, D, the piece, c, being raised a little, so as to allow o to pass under it. 1 hen keeping the circular edges of the boards in contact, and making them roll to- gether, the outline of c may be traced on D in several successive positions. A curve, e/, which touches all these suc- cessive outlines, will give the required form of the tooth of b ; for, from the mode by which it has been obtained, it will, if. cut out, touch c in every position, and therefore the contact of the two curves will be equivalent to the rolling action of the pitch' circles. A solution thus obtained is evidently impracticable, if the convexity of any part of either curve be not greater than the concavity of the opposed portion of the other curve. Having shown how the general solution of the problem of the requisite forms of corresponding teeth may be obtained, we may now ascertain the forms which may be most conveniently applied in practice. 183. Two particular solutions of the preceding general problem have been employed in practice. In one of these, the generating curve is a circle, and the curves described by a tracing point in its circumference, while rolling on the convex side of one pitch circle, and the concave side of the other, are called respectively Bpiey- doida, and ffupocycUnds. Let a, b, be the centres of the pitch circles, otto, 6 T n, in contact at t, and Thkthe gene- rating circle ; and let t c be the epicycloid described by the point t, when the circle Tbk rolls on T m, and t f the hypocy- cloid similarly described, by rolling on Tn. Now suppose the three circles, ar m, erfijTbkio roll together until the points which were coincident at t, assume the positions a, e, 6, then it is evident that the point 6 must be common to both curves, also they are in contact at 6, and rOB10 OF THB TEETH OP WHEELS. 95 (t IB a normal to both, for an indefinitely Braall arc of each curve, of which h is the middle point, may be considered as a circular aro described by the radius t 6, round the centre, t : since, therefore, the common normal to the point of contact, 6, always pisses through t, the point of contact of the pitch circles, the Teiocity- ratio will be constant when motion is produced by the pressure of one of the curves, ae^ «/, upon the other. It is also evident that 6, the locus ofeotUaet of the curves a 6 c, e &/*, must alwavs be in the circumference of the generating circle, rok. The following two individual cases of this solution have been frequently employed. 184. When the diameter of the generating circle is equal to the radius of one of the pitch circles, b t, the hypocycloid, e & b, Fig. 138, becomes a radius of the pitch circle : consequently, when epic^cloidal teeth are described on one pitch circle, by a circle of which the radius is half that of the o4her pitch circle, these teeth wiil work correctly with radial teeth, placed within the ciicnmference of the latter pitch circle. Jf^. 138. 185. When the generating circle is one of the pitch circles, the hypocycloid is reduced to a point in its circumference : consequently, when an epicycloidal tooth is described by one pitch circle on the oUieT, as a 6 c, Fig. 139, it will work correctly with a small pin, 5, in the circumference of the describing pitch circle. 186. The second^ particular solution is that in which the radius of the generating circle becomes infinite, or, in other words, when the curve is generated by a straight line rolling on a circle. This is most readily effected by unwinding from the circumference of a circle, a string with a tracing point at its extremity, and the curve thus generated iB called the InvoitUe of the circle. 96 PBIKCIPLES OF MECHAKIBM. f ^ Let A, B, Fiff. 140, be the centres bf.the pitch circles in contact at T ; through t araw d t e at any angle, and ▲ d, b e perpendicuUr to it, and with radii a d, b e draw the circles, d h, e f ; then by similar triangles, ad : be : : at : bt. Through the point t draw htk, the involnte of the circle d r, and F T G, the involute of the circle, b f ; then by the revolution of the circles DH, BF, let the involutes assume the new positions, /f^, htkf which last, in fact, are involutes described by the point t, for from the mode of describmg the involute, the line D E must be a common normal to all involutes of the circles, e f, d h, that intersect it; hence, when the action takes place between the in- volutes, the^point of action is always in the line' d e, and consequently the line of centres, ab, being always cut at the same point, t, by the line of action (168), the velocity-ratio is constant 187. If the circles, ef, dh, l Bcribed, corresponding to the same given velocity-ratio. 188. The theoretical principles on which the forms of the teeth of wheels depend having been given, the methods b^ which the teeth are practically constructed may now be explained. The simplest case is that in which teeth in one wheel act against pins in the other, as in the lantern or trundle, already mentioned (174). In combinations of this kind, it may be observed, that the toothed wheel is o/tpays the driver, and the pin wheel the follower. It has been shown (185) that an epicycloid will work correctly against a pin, which was not, in Fig. 139, supposed to have any sensible magnitude. In order to apply this principle to practice, with a radius at=b, Fig. 141, describe the pitch circle of the drivinfl^ toothed wheel, and with the radius btt, that of the following pin wheel ; and let the pitch be the arcs of equal length, T a, T c : round the centres t and e describe two equal circles, to represent the staves, the diameters of which are osaally somewhat leu thin half the pitch ; and {ram the points t and a dMcribe in opponM directians the epicy- ~ ,,, dmd.Ti,ai. meetin^int; **'"■ joia Aiaod bc, cutting a tin f, »nd thfl circumference of the BtAic in b. Take any namber of points, fun, &c^ in the tpicjcloids, T fc, Qit, anil roncd tun points dcacribv circular am with radii equal la be; and drav the curv», pb, ba, loncbing all the circlea in the pdnCa, q.r, &c^ then vill the uliun of this curve npoa the ilBie be the same as that of llie epicjcloid upon the pin ; ibr if any point, n, of the ep'cvcloid were brought to co- indde with e, then the curve p 6 and the Emrlace of the itaTewonld tridentlf touch each other at r. 189. Id order tbat there may be no intermpUon to the action of tlie teeth on the staves, it is neceesary that when the point ( of the tooth p 6b it on the point of qnittine contact, and therefore on the lineftf action re, the centre, t, of the next »tave muat be on the line of centres a b, and that stave commencing contact with the Mit tooth at (. LetTBe,tbe pilch-angle of the pin-wheel=^, at — e, b T=r, theiiBA&.half the pitch angle of the toothed wheel will be )-^, Wanse the pitch-arcs of the two circles are equal; and let k be the ratio of the diameter of the pin to the pitch, then c b, the ndina of the pin,'^ i krf. In the triangle b as ?giii=(^.)-_i^^ 0) im7«6" siB(ABe-hflAe) br aDcbe = tm{bee+bee), -ain^I-lABO + ABS+BAsV = CCs(iAB« + ,A«); tlienbjgnbstitiitiDg the valoe of CB in (1), and redDciDg,nc obtain 98 FRIKCIFLES OF XBCHAJnSM. B7 Babstitating in this equation any particular yalue of ^ expressed in parts of radius, and also of—, the necessarj value of k may be T obtained, wbich will cause one tootb to commence action, at the moment that the next is ceasing to act. Should the value of X; come out negative, the case is thus shown to be impossible; and if X;=o, the pin cannot have any sensible thick- ness. In practice it would not answer to construct wheels so that one pair of teeth should quit contact at the instant of commencing contact of the next pair; for in that case any error in the form of the teeth would be very injurious; if the error were in excess, the teeth would lock into each other and break ; if in defect, either originally or from wearing, an interrupted jarring motion would result. The constant difference between the width of a tooth or pin, and that of the space in which it is to work, is termed hpti«d with teeth ; and the form commonlj adopted i* a ewn. bioatian of the radial line and epicycloid (183, 184). A paur of ■heela the teeth of which are Ihna eeortracted U repreKQted iii Kg. **■ ^* Hi, where A and B are the centre! gf the pitch circles in contact at T ; tbe complete side of each tooth, as CTO, dtAto, coneista oftwo parts, one of which, ct, ot&t, liesuttjUii Ibe ratch circle, and ia called the . fan; and the other, i a, or tg, | Bee ioitlioat, and is called the /oee ) Df the tooth. The Saake of the teeth ia both wheels are radial lines, and the faces, epicjcioide ; of which T a is geoeraied bj the dnzltTJbB, andT^ b; t/a. The tonn of the curve ede, which con- oectt two coneecntiTe teeth, is immaterial; it is onlv necesearf that in the action of the teeth it should keep clear of the pointy; it is iberebre called the cUaring. As the teeth of both wheels an similarly conBtmcted, and are ejmmetrical with regard to a radial line produced to their points, either maj be emplojed to drive the other, and in either direction. 191. To examine the action of two coiresponding teeth, let the lower wheel drive the DpperinUiedirectionofthearcow; thenthe senicirda a/t will be the locni of contact in approaching the lino ' of centres, and TjfcB,iD receding. The contact, tiierefare,Degins at tbe root irf the driTer'a tooth, and ends at the point, and ^ reverie 100 Uksa place vitb the follower ; ud tbe length of f>ce is inneb greater thin the correapondiDg teagth of flank, forifvith ■radius B^BoiroleiB described cnltiiigT/A in e, and rith a rsdins as, a drale 8 (, cutting a t in (, then t and t will be the extreme points of contact of the flsnlc tc, and t( is manifeatly mach ihorter 192. It bos been ibown (IM^ that BpicTcloidul _t««lh de- »crib«don one pilch circle, by s circle of which tbe diameter is half that of the other pitch circle, will work correctly against _ ,„ ndial lines on the latter. In Fie. 143 let **■'"■ A be tbe centre of the driyer, and a that of the follower, and t the point of contact of tbsir pitch Hrclea ; t d a a tooth of the former, and ndm a radial line or tooth of e latter, wilh which tbe face ad baa ten in contact during its motion trnoi T to The semicircle rda is the locus of contact ; let the apex d of tbe tooth rad be quitting contact at tbe moment that the leit tooth ia commencing, (hen d will be n tbe aemicircle rdB, and the base of the leit tooth will coincide with t. Join bd. hen if ij were a pin in a wheal rds, Tbd woold be the pitch angle ; but in the pre- t inatance Tnif is the pitch angle, which- ^Tiii; it follows, tberafbre. that The taut numher of radii that mill vmrk icith a given mmiher ef epieydoidal teeth it tqaal to twice the leatt RmnMr of puw. 193. The line radim of a wheel exceeds the geometrical or pitch radios br the distance of the point of the tooth from the pilch ciirle ; this quantitj is called the addendum. If it ia the true radius, and athe nnmber of teeth of tbe driver, andu, w, those of tbe follower, the Tshie of- in mill-work is usnallj — -„ nearly, in which case the addendtim is abont y'j of tbe pilch for both In dock-work, however, a different valoe U aaaignod bj a recent antbor on this snbjecl,* namely, which gives the addenda lo the driver and follower | and J of tbe pitch ieiipectiTalj,+ 194. The following practical roles are Iboie commonly adopted in the tonitmction of mill-wheels, a portion of a pair of which in gsaris represented in Fig. 144, man, e as, being the pitch lilies i • B«ld-| Bomlogj, p. 114. t Bea WiUli' PrlMiplM of Uinhudsm, p. ST. ^^ •' LBSeTH OF TBITB. 101 Fig.l4L n >f tt tt Addendnm, or depth to pitch line, Je=^ pitch. Woilang depth, df=^ Whole depth, <^ ^ = iV Thickness of tooth, 00=^ Breadth of space, he=^ It here appears that a back-lash of ^th pitcQ is allowed to preTent the teeth from locking, and ^^th pitch is alloired in depth to prevent the teeth from httUuig, or striking the bottoms of the spaces: these pro- portions, however, differ slightly in different localities. 195. The necessary length of the teeth of wheels will depend on the conditions of the contact that takes place between them. Let a, b, be the centres of the driver and follower, t the point of contact of their pitch circles, and d the point at which the tooth of the driver is just quitting contact. Join xdf cutting the pitch circle iny, and join Bd^ err, then, as contact is ceas- ing at d^Td must be perpendicolar to dm. The arc t/ is called the arc of receding actum. If the diagram were reversed, and the wheel b were sup- posed to be the driver, then t/ would be die arc of approackkig action. Fig. 145. LetAT=B, BT=r,/rf=:B, andTBD=tf. We have Ad"=AT"+Td"— 2 ATXTcicoe atJ; snbetitadng the valaes of these quantities, and reducing, we obtain by expanding this in series, and neglecting the higher powers of 9, we obtain »^2Br+r' B 2 B« • B and n being the nmnber of teeth in a and b respectively, and c, the pitch, we have 0=?^?!?=?^** . n 103 PRI1IC1PLB8 OF MBOHAmSM. and if the arc of action t m, or r 0=f c, by sabBtitoting and re- dncing we obtain - == "* I ~+ - ) • 0 \ll 11/ Similarly, b^ reverBing the diaffram, and making the arc t m that of approaching action, e the addendum of the follower, /the ratio of the arc T m to pitch, and interchanging n and n we shonld obtain whence from which formula the relative values b and e may be obtained by Bubstituting appropriate Talues for f and /, n and n, it being remembered that at least f + /must= 1. The friction of two corresponding teeth that takes place before reaching the line of centres is accompanied by greater pressure, and ifl of a more injurious character than that which takes place during the receding action. It might hence be supposed desirable to render the are m approaching action as small as possible ; but, on the other hand, the amount of sliding, and consequently of friction, increases rapidly with the distance of the point of contact from the line of centres, and hence (since the sum of the arcs of approaching and receding action must at least be equal to the pitch) as much, or perhaps more would be lost than gained, by g'ving a very small value to the are of approaching action : — ^the >st method, then, is so to adjust the adaenda, that there may be less action before the line of centres than ailer it. 196. The following table of the values of -is calculated for c Value of 11 n Correspondingvalues i of- when e • V F = 2/. F=V2/. 1 F=/. Back follows . . . 0 2 1 0-5 rxV 2-3 11 0-6 2*4 1-2 0-6 Pinion drives . . h ^ 2-6 1-3 — •^ 2-8 1-4 0-7 ^ 3-2 1-6 0-8 f 1 4 2 1 2 5 2-6 1-2 Wheel drives . . . 4 6 8 1-6 • 6 6-5 3-2 1-6 iio 7 3-3 _- Back drives . . QD 8 4 2 rOBMS OP TBB TBBTH. 103 thiee different ratios of the two arcs of action, namely, when the arc of approachine action is equal to, or two-thirds nearly, or one- half that of Tece£ng action. Example, — In clock-work tiie wheels always dri^e the pinions, and the ratio of their nomhers Taries from 8 to 10. From the last colomn of this tahle it appears that 1*5, the ratio of the addenda in Mr. Reid's nile, is scarcely enongh to gire an equal action he- £)re and afYer the line of centres, and that it wonld he hotter to take a ratio of 3, which would give the simple rule D w + 3 tt^n+l' This role gives an addendum of ahoat k pitch to the driver, and ^ to the follower, and may safely he adopted when the wheels drive ; but when the pSnion drives, it appears that it will be safe to employ 197. The forms of teeth determined by the preceding articles are those most commonly employed in practice ; Imt they are sub- ject to this inconvenience, namelv, that any given wheel will work correctly only with that for which it was desiffued, since the form of the teeth of each depends on the radius of the pitch circle of the other ; and in the manufacture of cast-iron wheels, now mostiy employed in heavy machinery, this would be a serious inconve- nience, as it renders a multiplicity of patterns necessary for wheels even of the same size and pitch. In order to obviate this, when- ever a series of wheels are required to work with each other indis- criminately, it is^ found desirable to employ the radius of the least wheel of the series, as the diameter of uie common generating circle for all the curves of the teeth, consequently (180) the faces of the teeth will be epicycloids, and the flanks hypocycloids, and ^' ^^■ any one wheel will work co^ recUy with any other of this series. 198. Involute teeth (186) di£for from the epicydoidal teeth al- ready described in having . the entiro working surfSsu^ of the tooth, both &ce and flank, formed of a continuous curve ; the side of an epii^cloidal tooth being made np of two difierent curves jcnned at the pitch circle, f^g. 146 rroresents a ||ortion of a pair of^ wheels with involute teeth, in which A, B, are the centres of the pitch circles in contact at t ; a d, B 1^ the radii of the bases of the involnte^ and ]> e their conmion 104 PBIHCIPLE8 OF MBCHAHIBM. tangent, which is the locus of contact of the teeth (186). As in the preceding forms of teeth, the point of approaching contact lies within the pitch circle of the dnver, and of receding contact within that of the follower. Let the point b, of the tooth e m of the driver, be jast quitting contact at e, then r is the extreme point of action of the follower. With a centre a, and radius ▲ e, describe an arc K kj cutting A B in ib ; then the point b will coincide with k on the Une A B, and a clearing hollow of at least the depth of k must be formed within the base circle, as in the figure. Let h be the point of the tooth H F of the follower ; with centre b, and radius b h, aescribe an arc H A, cutting d t in A, then h will be the first point of contact, and the approachii^ and receding actions will be as ^t : te. The chief objection to involute teeth rests on the obliquity of action, which is always in the line d e, and by which a consider- able amount of pressure is thrown upon the axes of the wheels ; this is not the case with epicycloidal teeth, in which the action is perpendicular to the line of centres, at the moment of crossing that line. Their peculiar advantage consists in the property of working correctly at different distances of these centres firom each other. The distance of the centres of a pair of involute wheels may be so a4justed by trial, that they will just pass each other, by which means the back-lash is reduced to the least possible quantity : this is an evident advantage in the cgnstruction of those machines, such as dial-work, in which the object is the transmission of correct motion, not of working power. 199. In the practical construction of the teeth of wheels, a cir- cular arc may be found which will differ from any proposed curve by a quantity quite within the limits of error of workmanship ; but the methods commonly adopted for finding the required centre are merely tentative. The author already mentioned has fully investigated this subject ;* and has devised a very ingenious in- strument, the OdcnUogrqphj by means of which the forms of the teeth of large wheels may be traced with as much accuracy as is practicable. 200. In concluding this subject, it may be remarked that the chief points of excellence in the construction of toothed wheels, are iodformUy of action^ durdbilUy^ and strength. The first is attained by the epicycloidal form of the teeth ; tne second, by so arranging the form, that the curves may roll on each other, with the least attainable amount of sliding, and also that the approach- ing may be smaU, compared with the receding contact ; and the third, oy enabling as many teeth as possible to engage with each other at the same time. 201. In the preceding investigations respecting toothed wheels, the wheels have been assumed to be in the same plane ; when this is not the case, bevUled wheels must be employed, of which the pitch surfaces will be two conical frusta (170), which will roll on • WflliB, Prinoiplet of MeohaniRD, p. 123 tt ««29* THB EKDLESS BCREW. 105 Vig. 147. each other willi the required velocity-ratio. The forms of the teeth of these may be determined by deacribiag the requisite curves for the neater and lesser bases of the conical frusta, considered as pitcS^rdes. By tracing these curves in corresponding positions oo Uie bases, and cutting away the substance of the cones until a strsight line, passing through the common apex of the cones, will touch both curves, and the intermediate surface, a series of teeth will be formed that will work correctly with each other. - 202. When the axes of the required motion are perpendicular to each other, bat do not meet, a constant velocity-ratio may be obtained by a screw and nut (143), in which the nut will advance throngh the space of one thread during each complete revolution of the screw. A screw is called right- or left- kaoded, accordingly as a line touching the |hread rises to tne right or to the ien, as in Fig. 147 : the direction of the motion of the nat, in relation to that of the screw, win be determined accordingly. 203. The threads of the screw may be in contact with a rack instead of a nut, as in Fig. 148, in which case the linear movement of the rack will be tbe same as that of the nut. When the teeth, instead of being on a rack, are cat on the circumference of a wheel, as in Fig. 149, the I^,\4», ng,\4B. combination is called the endUia icrewj which is frequently em- plojed in machinery. In the rack, the motion is limited by the tsngth of the rack, or of the groove in which it works, but in the enUesB screw the motion is unlimited. The form of the teeth is di&rent from that of ordinary teeth, in consequence of the oblique action of the screw : the best mode of obtaining the requisite form ii, after roughly catting the requisite number of teeth in the wheel, to convert the screw itself into a cutter, by making one of steel, and cnttine notches in the threads of the screw in the direction of the axis. By rotating this with pressure against the teeth of the wheel, the oeoessaiy ibm of the teeth will be obtained. 204. If lbs incliDAtion of the tliread of Ihe screw to the aiia be conBiderable, one or tnore intemediatetbreadB ma; be added, aa in Fig. 160 : in which caae the screw is said to be double or triple, ac- cording to the number of separate spiral threads. As each otie of these will pass its own wheel-tonth across the line of centres in each revolutioa of the screw, it follows that as many leeth will pass the line of centres during each revolution of the screw, as there are threads in the screw. 20D. If we suppose the number of threads to be ver; great, for Fta- W. example, equal to that of the wheel-teeth, then the screw and wheel may be made exactly alike, as in Fig. 151 : this is an example of le of the disguised forms, which some com- gement maj be made ' S06. Where great smoothness, and the ' ' ' Dt back-lash are required in a „ ati»e motion, they may be at- 1 by means of the ingenious device of Messrs. Callen and Riplejr, the principle of which may be thus ex- plained : — Describe two circles touching each other at c (Fig- 152), ,, and let 1 0 be the radius of the larger and the "'' diameter of the smaller- Draw any line A B I cutting ths two circles in d and E, and having bisected a c in a, join i> a. Then, because the angle d a c is double of k i c, but the whole circumference DC equal to half the circum- ference EC, it follows that the arcs CD, CB, are of equal length ; and cousequently, if the inner circle rolTin the outer, the pomt a in the circamfcreDoe of the former will always lie in >. a, the radius of the latter- And conae- qnently if d b were an arm revolving round a, with a prqjeding Tig. Ita. P"* •' "• "'^ ■*" "S" * pi*** t*- volviw roond a, and having a dia- metnu groove bf, tbe pm will aiwan bo in the groove, if they revolve with unifbira velocities in 9 the ratio of two to one, and if ■ there be two or mo)^ correspondinB^ [Hns and grooves, eiUier of the axes carrjing these may be employed ta drive tie other. 207. Fig. 1S3 represenU an ar- tkngemant of thia kind, in which tb* mupnvo oonrecTOBB. 107 mM A curies three eqoidiBtaiit arms, fnrniBhed with friction loilera, and the pUte on the axis b, three equidistant grooves : this is probahlj the most convenient number ; and either ▲ or b may be advanta^naly employed to drive the other. If the leqnind veioci'tv-ntio be anv other than 2 : 1, the grooves will be nypo- cydoids, but the velodty-ratio will always hd that df the number of pins and grooves respectively. CL. A : Dmsiom e. — (hmmunieation of Motion by Wrapping Connectors. 206. Any two curves revolving in the same plane, whose wrapping eonnector cats the line of centres in a constant point, will main- tain a constaot angular velocitv-ratio (167). In practice, sarfiioes of revolution are employed, which revolve rouna their axes, and niaiiifettly possees the required property. In order that the communication of motion may ^' ^^ be cantinuoufl, the two ends of the wrapping ooonectoc are joined, so as to form an endu leas band, which embraces a portion of the paQey, and is stretched sufficiently tifht, that the friction of the band on the pimey (56) mayexoeed the resistance to be over- come. The band may be direct as at a, or crossed as at b, in Fig. 154 : in the former case, the axes will revolve in the same, in the latter, in the opposite direction, as indi- cated bj the arrows. Motion communi- cated in this manner is remarkably smooth and free from noise, and any sudden slight checks or inequalities of motion are relieved by a yielding of tiie band. Endless bands aie commonly employed in all kinds of machineiy, in which a very eocact velocity-ratio is not necessary ; and they are capable of tnnsmitting large amounts of force. 309. Bands may be either round or flatf and are formed of various materials. The round bands most commonly employed in machinery, are either cat^t or gutta percha ; the ends of a catgat band are sometimes umted by splicing, but more frequently hy a hook and eye, both of which have a screwed socket, into which the ends of the got are forced by twisting, having been pcevionaly dipped into a little rosin, and the hook or eye warmed to keep mb rosin fluid while the^gut is twisted in. The dn^gging out of the socket when in use may be further prevented, by searing the end of the gut protruding through the socket with a hot wire. Crutta percha Mmds have this advantage, that their ends may be completely united, without any bulging or increased diameter, by meltmg the extremities with a hot iron. The use of hempen ropes in ooane machinaiy is now frequently superseded by the 108 PSIM0IPLB8 OF KBGHAVXSM. I%ff. 165. f?Ofl rMi m M C O e emplojinent of iron-wire ropes, which poflseas &r greater dura- bihty, if exposed to much attrition. AVhen considerable power is required to be transmitted, flat bands are commonly employed. Leather belts were formerly almost universally employed in large machinery, but are now frequently superseded by those of gutta percha. ^ In mining work flat bands are employed to prevent twisting durine the ascent or descent of the backet : the hempen buids formerly employed for this purpose, are now generally superseded by woven wire bands. 210. The form of the groove in the pulley is important, as it affects the adhesion of the band : the principal forms are represented in Fig. 156, in which the groove of a is angular, of b, circular, and of c, flat. ' The groove may be supplied with a series of teeth, as d, or a series of pins, as e ; both these forms give more hold to the band, but at the same time they greatly increase the wearing, unless the connector be a chain, the links of which are adapted to the successive pins or notcnes. The pullepr p has no groove, but, on the contrary, a slight con- vexity at its middle point. 211. If a tight flat band run on a revolving oone, the direction of the approaching band being perpendicular to the axis, as in Fig. 166, it will generally advance towards the hase of the oone, instead of receding from it, as might have been ex- ricted at first sight ; for the edge of the band towards the base is more stretched by the increasing diameter of the cone than the other edge, and consequently has a constant tendency to become convex, and to assume the position b h ; the commencing convexity at b thus continuallv advancing towards the base of the cone. Advantage is taken of thia curious property in foimine pulleys for flat iMinds, which are made a little convex in the middie, as f, in the nreceding figure, and the band, haviuff equal tendencies to recede from either edge, remains in the midlljiiTe*eDt«dbyiinsny timei u maj ba Deoeuar; OD the dram, and fiiung tbc end* to the drum: thiu tb« oarriue, b, Fig. 168, nmi backwudi and forwarda on the rollen, «/ and deiirea iti Bkotioii fiom the dnim, a, moanted on an aiii abota it, by neani of two bands fixed to, and wonnd round th« dnun and attached to the carriage at eand d: thia is tbo conitructioD of Ute common manglo. Fig. IK. IV- !■>. 216. In order to maintain a conrtant velocitj-ratio, it ii neces- aary that the band ihonld not be permitted lo become heaped op on the dmm. This maj be readilj pretented by cutting a spiral groove on the drmn, in which a cord or chain will wry readily arrange ileelf, aa in Fig. 159. Thie plan is unuaUj adopted in the bwrels of weigbt-clooka. CL. A : DiTmum d. Chmnuutieatifm of Motion &y Link4eort. 317, It haa been shown that when two anni, BtoreaUe round liied centres io the same plane, are connected 'V- "«>■ by a link, their angular vclooiliei aro inveiMly as tho segments into which the link dindcs tbo lineorc«ntiosn62). This relation is cooataotly changing, as the onns reTolve, [uless the point of inlenection, T (Fig. 123) be removed tou indehnile distance by making rq parallel to a > in all podtiana, which can happen only when Ibe arms are equal, and the link eqnal in length to the distance between the centres, in which caae the angular Telocilies of the arms will always be eqnaL Let a, b, be the centres of motion, A 1, c D, the equal arms, and c d ( = a b) the link ; with tho centres A and a, and radina Ac B D, describe circles cutting the Une of cen- :s in o and h, and the same line prodnced in >nd 6. If a D be carried round the drcle,BC will always be a parallelogram ; but in any giTOn position of one of the arms, h d, not coinciding with the line of centres, there are two poasible corresponding position* of the JV- in. ■nn AC, tor i. cirele with oeatn Duid radini dc will eni the circle a c somawherc else, u &t ■, ftnd D s will bo tha ucond possibla poaitioD of the link ; bnt in thii poaitioa the velodtj-retio is not tODitiuit, becum the pniat r the intereectioa af a b and o ■ ia not ■ fixed poial. When the liak c d coincidss with thelineofoeotnis in either of the poBlioni ao or ft H, the an^u- moremaDt of oDe ana hu no power o( commanicating motion to the other arm. 'I'heiie two poiitioni of the link are called the dead pmntt of ihe 218. When the preceding arTaQftement ia emplojed in craniau- nicjting m cunBtant Telocitv-tatio, lome rapplemeDtaiy coatHnnce if requisite U> preTont the link from ■hifhug frota the pAnllel to the cnne pomtion at either of the dead poiuta ; thii may be eSected hj three different methoda. I. Bt introdQciiig a third arm equal to the other two, the centre of motion of which maj be od the line of centres, aa e. I^^. 161 , and the moreable end connected with the link c D at r ao that % r maj be parallel to ic or HP: Drtbac«n(re of molion E maj be in an; other place, aa t, and the end. /, cunnectM with the points c, D, br links reapectiTel; equal to a A, e B. In ihe' former case B F, E c mnit alwavi cimtiaue rectangles, and in the tatter, tbe triangle, en/, formed b; the links is con- strained to move patalkl to ihe equal tri- angle, ABC. It maj be remaned, that the latter arrangement obTiatea the difficulty of the Ices m power at the dead points, tor it ia ol link onlj can coincide with a Hue of centrea at an; one time: the former does not poseeaa thia adTantage. II. A a, B fc an the two norallet sies, a f, b q the parallel anus, and r q the link ; let equal parallel arms, ap, ~^ .„ 69. be attached to the other eod of the axes *' _ and connected bj a link, pq, equal to pq, in auch mannerthataplane pasaingtbroagb A, a, and p ma/ be perpendiciilar to aoolher plane Hssing through n, i, and r. In this caae both links will cflospire in communicating nnifuna motion from one axia to Ihe other, aod when either link ia at one of the dead points, the other ia perpendicnUr to the arms with which it ia connected, anil is iherefbre in the moat faTOurable positian for action.* It is immaterial whether the link pq ia car- ried by two anna, or by discB, aa in Kg. 1S2, the equality of the isdial diitaooes of tbe • Thii priiviFle ku beaa silaptWI bj Uu 112 PROICIPLES OF VECHAMIBM. Fig. 163. points of connexion from the centres of motion being the only- essential condition. If either axis be carried across the plane of motion of the link. Fig, IM. ^^®7 ^^^ come in contact, and continuous motion would be impossible; this is ob- viated by bendine the axis into a loop, called a cranky Fi^. 163, beyond which the axis may oe indefinitely prolonged. This is the prin^ ciple on which power is con- tinuously employed in rota- ting the cranlc axis of a lo- comotive or marine engine. In these cases, however, the links are not driven by another crank, as in the figure, but by the piston rods. III. In the third method, two or more links are attached to two discs at the extremities of the axes, at points equidistant from the centre, and from each other, as in Fig. 164. The planes of rotation of the discs must be removed to a sufficient distance from each other to allow the links by their obliaue position to pass clear of each other. Tnis method is rarely, if ever, employed in practice. 219. It has been shown that a continu- ous constant velocity-ratio can be com- municated between two axes by link-work only when they are parallel, and revolve in the same direction in equal times; if, however, motion be required through a small angle only, it may be communi- cated with an approximately constant velocity-ratio, whatever may be the mag- nitude of the ratio, or the relative position of the axes. It has been shown (162), that if two arms, at and bq, Fig. 165, or b^, moving in the same plane, be connected by a link, p q or p ^, and placed in such a position that the intersection, t or f, of the link and line of centres, shall coincide with the perpendicular, kt or Kt, upon moreable ourved needle for pMsing a ligatare oonseeatiTelj thrrmgh both sides of a deft pelate, in the operation of atapfajloraphj : » mo^eabJe pieoe at the end of a stem eanyinK a curved needle ia connected by two linki with another nOTeable piece at the junction of the atemand handle, firom which motion prodooed lij the linger ia oonunonioated to the needle. 1^.186. X. H3 tha intenection of the ) will be monientarilj coastant, and will continoe laSciently so Cot practiciil pniposes, if the moliaD of the arms be conGnM to a imall angle on each nde of Ibe mBui notitiini : and the angolar vekicitieH of the ■mu will be iaTereel; m tT.BT, or it ■ Bt. Wben pnctioble, the ampleet mode of arnaging t^M poeitioae, IB to make the lick perpeodicnlar to both anne, aa l P and on or r D ; in thia caie, the angnlar Telocitiea are inTenely ai the .aima theiaaelTea. 210. If the aiea be neither parallel nor in one plane, as a e, >/ Fig. 166, let ef be their comntoo peipendicalar, draw eg panllel to B/ arrf in tSe pUdo ieg ^ ,„ draw BO, oc wrpendiGnlar , to 1 e, e jr, and let the ratio of B A : c 0 be inTerulj aa the angular Telocitiea of the axes a. e, b/ reepeclivelj. Draw bK, eu puvtlel to ^ xe, ce respectiTelj, and cntdng each other in ■; join e ■ and prodnce it in- definitel/ to A. From anj point, A, draw Aa, A^, per- pendicnlan to A e, e ^, male Bf=«g, draw bI — and pa- nllel to; A, and join AI, which is parallel to ef, since aghl, and B«e/ aie parallelcgrama ; and ■■ the planes e i A, /b I are there- iif^ , 1I~I LI i- ^-^A^^A. __._J.'.-I i-.i- .. . I > - > theai that is, invenel; u ob: ce, or in the reqim., 221. Hie mecbaniim of organs, pedal haipii, bell-hanging, and Tarions other portions of machineiy, cominonly called i«ii-eroni vonbi&lUaDdertbisclsBS of sensibly eqoal imall angular motions. Thia dMB of work frequently re- j(^_ Igj qniiea a cfaan^ in (he direction and lelatire velocity of small molions, which may generally be efleoted by a single axis with two arms. If the motion be in one plane, let da, ab. Fig. 167, be the lines of direction ^ meeting in a. Draw a b, d f, pei^ pendicnlar loab, ad, and take b x : Dr in the ratio of the required ts- locitiea in the directions ah, da, nmectiTely, and draw Bi, fa i*- nllel to ba, da, and intaraecUng in 114 PRIH0IPLE8 OP MXCHAHISlf. A *, join a A and produce it to o. In a c take any point, c, and from c draw cb^cd perpendicular to abf ad^ then a crank consistingof the two arms, ch, cd^ will communicate the required motion, dj remoying the point c to a greater distance, the angular motion of the arms will he diminished, and consequently the inequali^ of the velocity-ratio, through the required extent of motion. This oontrivance is called a heU-arankf as the term crank is commonly restricted to a hent axis (Fig. 163). 222. If the given directions of motion intersect, as in the pre* ceding figure, we obtain four angles round the point of intersection, in one of which the directions of motion are hoth towards the point of intersection ; in another, hoth diverge from the point ; hut in the two remaining angles, one motion approaches, and the other recedes, in either of which the axis c may he placed. If tho directions of motion are parallel and opposite, tne axis will lie hetween them ; but if paitdlel and similar, beyond them. In tho latter case, if the required motions are likewise equal, the axis is removed to an indefinite distance (refer to couples, 81), and the crank becomes practically impossible ; but the reouired change of motion may then be efiected by the following metnod. 223. Let the two directions of motion be a (2, c&, not in the ifmie plane ; find their common perpendicular, cd^ draw ee parallel to a df and in the plane bee construct the re- quired crank, 6 b 6 (221) ; draw bx perpendionlar to the plane bc, and take BA=ae; draw a a parallel, and ^ necessarily equal to b «, then will A B be the axis and a a, b o the arms necessary to convert the small motion in ad, into the re- quired small motion in c b. If the arms a a, b 5 are parallel and equal, the construction will meet the case which was shown to be impossible by a crank in the same plane with the two motions. The preceding arrangements are of constant occurrence in the construction of organs; the crank is termed a back-faU when its arms are in the same horizontal straight line, and a iquare when they are at right angles. An axis with arms as in the pre- ceding figure is a roller^ and the links are stiken when they act by a thrust, and trackers when they act by tension. JV^. 168. GLASS A.'^Elementary Combinatwtu m Trauu. 224. Whenever the required velocity-ratio of the driver and fol- lower is very large, or veiy small, especially in the employment of toothed wheels, to which these remarks principally apply, it is found practically more convenient to employ two or more elemen- COXBISATIOHS IH TRAIirS. 115 tai7 oombiiiations, the product of whose velocity-ratios will be the required ratio. If any number of axes bave each a wheel and pinioD moonted on them, and be so placed that the pinion of the nnt axis shall be in gear with the wheel of the second, the pinion of the second with the wheel of the third, and so on ; and m?i, ^, w radii of the pitch circle of the first wheel and pinion, to., j?- those of the second, and so on ; then the velocity-ratio transmitted hj tlie train will be fg, X tPg X &C. X Wn . p^ X^, X &C. Xpn* or if the wheels be supposed to be all of the same pitch, then the qoantitieS) «7,|), may M the numbers of teeth and leaves in the wheels and pinions ; for it has been shown (125) in a system of «*«« acting successively on each other, that w : p : : product of long arms : product of short arms ; ^^ w : F : : virtual velocity of p : virtual velocity of w, >pd as these levers may be supposed to represent the radii of the pitch circles of the wheels and pinions, the truth of the above pro- position 18 obvious. . ^5. In a train of wheels consisting only of ^r wheels and I»^ons with parallel azep, the direction of rotation of the first, ^'i^ &c, axes will be the reverse of that of the second, fourth, •c. ; consiequently, if the train consist of an even number of axes, «« extreme axes will revolve in opposite directions ; but if of an ^ number, the revolution of the extreme axes will be in the same "'Bctioii. If a wheel, c, be placed in gear, with two other wheels , a JJ« >, the velocity-ratio of a and b will be we ttme as if they were in contact, for it ^' ^^• "erident that for every tooth of a that PjJ'es the line of centres of a and c, a woth of B will pass the line of centres of * and c Bat the direction of rotation of «e axes of a and b, which would be re- ▼ereed if they were in contact, will be rendered the same by the action of the jntennediate wheel, c: such a wheel is wnned an uUe wheeL When the shafts •^'wo wheels, a and b, lie so close together that they cannot be placed in the same plane without making ^m inconveniently small they may be fixed as in Fig. 169, so J*i ^°^^^ o°® another, and may be connected by an idle '■wel, c, of the thickness of a and b, tction i^a tawn of iriieel-work, than bj eipUiniiig the conitrncticai of & clock of Ihe iinipleit kind, which i« repruwated in Fig. 171. The weif^t w is attached to a cord or chain that ia wound Toead a groond bairel, ± ; npon tha aama adf^ ot arbor* ig fixed a toothed wheel b, which drirea a piDiDD ( on the aecood arbor b c, ^' ^^• which also carriea a wheel o; '' thia wheel driTca the piaion e on 1 the tfaird arbor, opon which ii ahio fixed a toothed wheel, D, with teeth of a peculiar form, termed a iwiag-whtel, or letm- Khted. AboTe the aca,pe-wheel ia j an arbor d a, taimed tbs verge, which ia oonuected with the pen- dnlniD, i> r, bj means of a forked piece, K. The verge also canim a pair of knni d, with a toolh at the end of each, called jiaUeit, which are altematelf engaged with th« scape-wheel, d, in such a maimer that at each oscillation of the pendulum one tooth of the wheel escapee, and aiiother fsjla oo the opposite " - -' ' ■ karing passed t osile pallet, the wheel ^ J Med through a apace equal to half the pitch, i t, m n, are the pUlea, which are msin- taXned in a parallel position b; pOlan, which are here omitted, to aroid cenfimon : the small endg, at mmlt, of the arbors run in holea in the platea. If we hare a aecoods' pendulum and 30 teeth in the swing- wheel, it will reTolTs once in a minnie ; and if b have 45, and c 48 tee th^ and the piniong, b, e, each 61eatea,then r,,T, being the times of iTochronal rotatioQ of the arbor e d, and the barrei.arbor. bnt the clock is also required to indicate the hours and minutes bj hands on a dial, g k ; this is effected bj wheels placed outside the frame, klvtn, called molion ahedt, Tha barrel-arbor panea • ^rkr ii (bs watoluuksn' term f« in Hi*. 118 BRINOIPLES OP MBGHAHlSlf. through the plate, m n, and two wheels, b, f, are fixed on it. Be- low these a stud, «, is fixed in the plate, and a tuhe is placed on this stud, to one end of which the minute-hand, m, is attached, and to the other, the wheel e in gear with e ; a second shorter tuhe is fitted on that of the minute-hand, which carries at one end the hour-hand, h, and at the other, the wheel f in gear with F. As the barrel-arhor revolves once in an hour, tne wheels E and 6 must be equal ; and as the hour-hand usually revolves once in twelve hours, the number of teeth in / must be twelve times that in the pinion f. The dial, g A, is placed in front of the motion wheels, and if a hand, «, were attached to the arbor, c d, prolonged to pass throngh the dial, it would indicate seconds, but m the train represented in the diagram would move backwards ; for as there are two intermediate axes between those of i>, and of e and/, h and m will move in an opposite direction to s (225) ; to make them move in the same direction, a second axis must be introduced between A and d, or the wheels e and / must be on the barrel-arbor, and e, f, on the stud s. 229. In order to exhibit the relative motions of the different parts of a machine, without regard to their relative positions, which can only be represented oy a drawing, some kind of nota- tion may be employea. Various modes of notation to represent clock-trains have been proposed by different authors; the following, which differs somewhat from precediug methods, appears to be well adapted for the purpose : I 40- I -72 — hour-hand -40 — ^minute-hand I 48- Barrel 6 30— swing-wheel. 45- This diagram represents intelligibly the preceding clock-train ; the long horizontal lines are the frame, the short ones between figures represent gear, and the vertical lines, axes. The figures represent not only the numbers, but the juxtapositions of the wheels and pinions. With the train just described, a clock would require to be wound up every day, on account of the number of revolutions of the barrel : it is not found convenient in practice to allow more than 15 or 16 turns to the barrel, consequentlv, if the barrel- arbor make one revolution in about 14 hours, the train will go for a week ; for this a different train from the preceding wiU be required. 230. In clocks of the best kind it is usual to employ high nnm- OOMBIHATIOSS Df TRAIHB. 119 beicd pinions, sncb as those with 10 or 12 leaves, on account of tlie smoothness of their action: the following will be a good train lor an 8-daj dock : — 10 I 54- •80 — ^hour-hand 36 — ^minnte-hand Bar I i*el 108- •12 108- I -12 I 30— swing-wheel 100 I 10 13*»30". I'^SO". 10' 1™. — ^periods in which the barrel will revolve once in 134 hours, and will go for rather more than eight days with 144 turns. In smaller clocks, the pendulum will make 100, 120, or 150 oscillations in a minute, the numbers will then require to be pro- portionabljr altered.* 231. Much ingenuity has been in former times bestowed on finding the requisite numbers for trains which will approximately represent the motions of some of the heavenly bodies, such as the period of one year, which is 365* 6** 48°* 50* very nearly ; as, how- ever, such machines appertain to the extensive category of inge- nions, bat useless mechanism, any details may be considered un- necessary ; the more curious reader is referred to an able digest of this subject in the work previously quoted.f 232. Calctdating Machines. — ^The present subject would be in- * As a farther illustration of the above-mentioDed notation, the foUowinff traia it given, wh^ch has been employed by the Author in the oonBtroction ot tine^eoeSj in which the boor-luuid is employed in carrying round the cylin- ders oekmging to his aelf-regictering raagnetie apparatus : the hour-hand one rerolntion in 2i hours; and in order to avoid the nnsteadinesB of the hoor-faand, which in ordina* y movements results from the necessary play of the teeth of the motion-wheels under the dial, the central axis, whicn carries the hour-hand, carries also an idle wheel in the train, and the axis which carries the miottte.hand is placed out of the centre : also the numbers of the teeth of the wheels and pinions in gear are as far as possible prime to other. hour-hand minutes seoonds r r I I •IS I 72- I -10 60- eel 62 11 76 9 14~icape- wheel L_ I I I I J 13i>48">20*. 24>>. lb. !«. —periods, f See Willis, Prindplei of Mechanism, p. 223. 120 nmroiFLKS or kbohahism. complete without some aoooant of these eminently ingeiiiouB and practicallj uaefbl contriyanceB. All these xnachines act on the principle of Boccessive addition; one wheel carrying forward another wheel in gear with it or connected with it hy some in- termediate mechanism, so many teeth or divisions as there are units in the digit or figure it is set to represent. But they ai'e of two essentially different kinds; one bemg designed to ac- complish merely the multiplication or division of numbers, the other, to which the name of difference engines has been applied, is designed for the calculation of lo^rithmic and other tables, by the addition of successive orders of differences. The principle of construction of the simpler forms of calculating machines, of which the Arithmometer of M. Thomas, of Colmar, . is a favourable example, may be apprehended Fig. ITS. by reference to the diagram. Fig. 172. Let jl be a pinion of 20 leaves, of which one, two, three, &c., tenths of the entire length are suc- cessively cut away, and let b be a wheel of 20 teeth, capable of being set at any noint on its axis, and in gear wil^ the pinion. If now it be required to multiply 6 by 4, the wheel b will be brought by suitable means to the indicated number 5, which will place it opposite the middle of the pinion, where 6 out of 10 successive leaves will have been cut away, and consequently each half revolution of the pinion will carry the wheel on 6 teeth, and four half revolutions will carry the wheel on 20 teeth, as the result of the o^ration, and that result will be shown on fi^re wheels in connexion with B. The carrying is effected by a pm in each figure wheel, which carries on the next wheel one unit, when the former arrives at the cypher, 0. The same contrivance is applied in the counting apparatus of gas- and water-meters, &c. These machines are, however, not of any great practical utility, rince the multiplication and division of numbers, containing many places of figures, is almost always effected in practice by tne aid of a table of logarithms, in a shorter space of time than the result can be elaborated by the machine. 233. The Difference Engine. — The first conception of this im- portant machine is due to Mr. Babbage, who constructed one in the year 1821, and a year or two afterwards commenced the con- struction of a more elaborate and perfect engine of the same kind, under the auspices of the British Government. In this provision was made for stereotyping the calculated results, b^ impressing corresponding figure punches in a soft plate. Dunn^ the con- struction of Uiis, the idea of a much more comprehensive ennne presented itself to the mind of Mr. Babbage, some notion of which may be given by stating that it is to the difference eneine what the Jacquard is to the simple loom. In consequence of this new discovery, the completion of the machine in progress was abui- iaaai. The fivdwd portion of tbe diftrsODe eneine hw be«n dspodtod bf Um aa>«niin«iit b tha HoMom of Kidk'b Collegfl-, and > deUQad deaaintioii of it will ba fbiuul in the '' Edinfaunh deriTcd tlie omccptioD of cotiitmctiiig a aimplar form of maohine, to KcompliBh tin msm object aa that of Mr. Bttbb*^, nunelji that of calcnlatiiig and dmnltaneoiul; printing namencal tablea. AR«r coDtending with man; difficnllieii, and more eapeciallr with want of meaoa, he eomphited, with the aid of hit aon, Mr. &. Schanta, a workiDg model of hia madujie in IMS ; bat from the want of sulEi^nt iiinda, the machine waa not finallj complalsd nntil Octt^r, ISAS. Thii nueUne waa exhibited for same weeka tntiuacoDObrr; itwaambeeqiientlxidarod in the Paria UniTeraal Exhibition of ISSS, and a edd medal waa then awarded to the inrenloT ; it wM finallj niTonaaad bf an enterprinng and libera] Bifaii ail merchant, and now balonga to tiw Diidlej Ubaerratorj at Albanj in that eoontiy. Another maohina waa anbaequent^ eonatmcted bj Heaara. Donkin, fnm the deaigtu of Hr. Schauta, br the naa (tf tha affioe of the B^^iitrar-Oeneral, where it baa pecfinmed modi naefid work in the calcnlation of tablea. ^.173. The machine oonaiita of two prinapal part* : — 1. The nalcnlatinB apparataa, compriatDg the TSrtical apindlec and rowa ttH^an whaela occupTin^ the entire front of ¥Q. ITS, ■od the carTTmg oama and traverting carriers, or " traTBllerB," of which one, o, tniTatMa in finat of the Egnie wheela, and the other behind them ; the latter being oat of sight. 3. lie joiDtii^ apjaratni, which ii placed at the npper and back part of the machine, and conaiila of the horiiontal ipindlea, with their oomaponding toothed and cam wheeli, pnlleya, 'racks, and tjpe wheela, partJaDiy nen in the Egore, V22 Tfaere is >Ibo a counting apporatns, or eaumenttor, not Men in the figure, which indicBtes the number of reenlM completed. The calculaCine apparatua containa fifteen vertical, and fire hnnHmtsl rows of figure wheels ; it will therefore comput* fifleen plnces of G^res, but of these only the eight first are in connexion with the printing apparatus ; and as the last five places are neg- lected, a consideralile time will elapse before an; sensihle eiror arisiog from figures neglected bejond the fifteenth place con occur in the tabulated reault. The first, or upper, of the five hotiEon- tal rows shows the result of each complete action or "stroke" of the machine: the four succeeding rona corrospond with the first four orders of differences. The figures on the first, third, and fifth rows read from left to right, and their motion is [direct,* those on the aecond and fourth rows rciui from ri(i;ht to left, and their motioD is r^rogradt; the latter are in relation with the traveller behind. In worliing (be machine, the handle is turned coutinnoual; in one direction, and the inotion being transmitted to a mangle- wheel. A (251 )j which b; means of a toothed aegment, s (periodi- cally bmught into action by a projcctiog atud at the back of the mangle-wheel), acts on a rack in gear nith a seriea of pinions on the opper enda of the vertical epindlea, and canseB them to make a complete revolution, firat in one direction, and then in the other; and these two contrary revolutions constitute a complete "atroke" or action. These spindles pass through the open centres of all the figure-wheels, but without touching them, ac that without the adding mechanism they would have no action on the wheels. As each figure wheel must necessarily bn el rest while ita num- ber Ih being Carrie^ or added to the wheel above. It followa that the nitematc horizontal raws only can be in motion at one ^me ; consequently, by the fl™t revolution of the spindles, or "half- u iTi stroke," the numbers on the third and fifUl J'lj. 17*. ^^g ^^ carried up to the second and fourth ; but durinj:; the aecond or reverse half stroke, 3 theae remain at rest, while their numberi are carried up to the first and third rows reapec- tlvely, the adding mechanism being such as to fct in one direction of rotation onlj. The figure wheels are cylindrical rings, resting and working in rebated bearinsB on their respective ahelvas, and admit of being reailily rotated cither by Che hand, or by the action of the adding apparatus. , The fewer part of each wheel it cot into ten parallol sided teeth with sloping faces, wliich correspond with the figures above THB D17FSBBVCB SKOIHB. 123 tfaem, and tbe direction of the slopes corresponds with the sequence of the figures. These teeth project below the shelves, as seen in Fig. 174, and are in gear with the adding arms beneath, which maj be thus described. In the interral between each two wheels in a Tcrdcal row there is a small stage, b, attached to the spindle, to which a rising piece, h, is jointed. From this riser a pin or finger, c, projects forwards, and an arm, d, downwards. Tlie finger, when oot of action, rests in a notch in the tumbler, k, the short arm of which falls nnder this finger when raised, and keeps it up until the tumbler is thrown back by coming in contact with the fixed stud, L, when the finger again drops out of gear. The arm, d, reaches nearly to the top of the figure wheel below ; and as the spindle reTolves, it carries this arm, or grapnel, with it. From toe Qpper edge of the wheel below there projects upwards a small catch, E, which ia balanced at its centre, and as the spindle re- volves the grapnel meets with an obstruction in the catch, the effect of which contact is to raise the finger of the riser, and to cause it to enter a notch in the undei^ part of the wheel above, and carry that wheel round until the riser falls, and the finger drops fiDm its hold on the wheel above. it thus appears that the amount of action on any figure wheel, or the number of unita it is carried forward, depends on the bterval between the raising of the finger, c, in the space beneath it, by the action of the ciftch e on d, and its falling by the action of L on the tnmbler, k, and this corresponds with the figure shown on the wheel beneath. It will be noticed that, with regard to the bottom row of wheels, no provision is made such as has just been described, and, therefore, whatever number is set on those wheels remains unchanged throughout the operation. When any figure wheel is set to 0, as nothing is then to be carried to tne wheel above it, the little catch, e, Fig. 174, is brought under a fixed arm, r, which depresses it below the reach of the grapnel, and the position of the figure wheel above will remain uniutered. Thus the action of the machine may be cur- tailed, by setting one or more of the lower horizontal rows to zero ; and if every wheel in the machine were set to zero, the spindles would revolve ad infinitum without changing the position of any of the wheels. After each act of addition has been performed, whenever the sum of the added digits exceeds 9, it is necessary that 1 should be carried to the next figure-wheel in the same horizontal line, which is thus ingeniously enected : — Each wheel has a small stud placed on its figured surface in such a position that, as the 9 passes and the 0 appears in front during the rotation of the wheel, it presses against the short arm of a bent horizontal lever, a, which has a cam at the end of the longer arm, standing in front of the next wheel to the left, and throws the cam forwards. The cams in front of the first and third wheels are shown in Fig. 174, and the commencement of the arms in front of the adjacent wheels. 124 PBDrOIFUBB OF lOBCHAXnil. Then, by means of an endless cbain geared to the mangle- wheel, an upright ^t traverses in a groove in front of the figure- wheels. ^ Tnis moving post, b, Fig. 173, — ^the " traveller," as it is called — ^is fitted with arms working on pivots, and these arms grope along the line of march for any obstmcting levers which ma^ have been thrown forward during the calculation as an indi- cation that a carriage needs to be made. Whenever the arm of the "traveller** comes in contact with a projected lever, the arm is raised, so as to brinf its finger against a tooth of the figure- wheel in front of whicn it is passing, and carry that wheel round one place: the traveller then replaces the lever in its position of inaction. This process of carrying is independent, and oomea into action between the rotations of the spindles. The printing apparatus is at the back part of the machine, and is brought into play by means of weights and pulleys acting upon a series of horizontal spindles connected in the front with the calcu- lating-wheels, and at the back vrith a set of racks geared to a cor- responding set of type-wheels, e. Whilst the calculation is being penormed, all the type-racks are kept fixed by a bar, p ; but as soon as the line of figures represented on tne top row of calculating-wheels is ready for printing, the bar is withdrawn, and the racks are left to the action of their weights, which is regulated by the motion of a snail, d, similar to that of a common cfock. The snail in this instance drops down on to a notched spital cam, o, attached to the top row of calculating- wheels, and the position of the type-racks, therefore, depends upon the corresponding positions of tne snail and the spiral cam. When the type-racks are thus regulated, the type-wheels will have ranged themselves in proper order for stamping the result of the calculation upon a plastic surface fixed in the printing-rack, which, by a simple contrivance, is passed along gradually underneath the type, and by the action of an eccentric is raised up to receive the impression, and then pushed forward so as to leave a clear space for the next line of figures. The material used for receiving the impression of the steel dies is papier mcichS, in slips of about eight mches lon^ by two inches oroad, and of moderate thickness, the surface bein^ rubbed over with black lead, so as to give greater facility in casting the stereo- type plates. From this mould an ordinaiy stereotype plate is cast, and thus the errors incidental to the calculator, the com- positor, and the printer, are alike eliminated. 234. The principle of action of the difierenoe engine may be thus explained : — Ut Ux be any quantity involving as, to which a series of- numerical values may be assigned, by giving to x suo- cessive values differing by unity; thus let ttx^xl^t ^^^ ^^ series &c. It.,, ttoi «i» ««f «•» «4» Ac- will be represented by the numbers &o. 1, 0, 1, 16, 81, 266, &c THB DIITBBXXCB XHGIRX. 125 being the biquadrates, or fonith powers of the natural numbers, poadve and negative. Further, let UkU^f Atf|, All,, All,, Att4, &c. be the differenees resulting from successively subtracting each term firom the following, and similarlj let A*Up, A*tt„ a"«,, A"l*g, &C. be the differences of these, or the $econd differenoeB^, and so on. The following table ma^ now be constructed, in which the nume- rical value, in the particular case that has been assumed, is Buh< jotned to the general expression : — &C. tt . «•«,«•«. u,, &c. 1 1 «• 0 1 16 81 25( -1 1 \ Att, 15 Att, Att, 65 175 2 1 ' 14 , tJr^ AS 50 110 a'u., 1 aX A«tt, 12 36 60 A*tt., A*«, 24 24 From the numerical values {pven in this table, the machine ma j be set for the calculation of this particular series of numbers. This is effiscted by setting the initial number of the series, 1, on the last printing figure wheel, all the rest being 0 ; then the first and second difierences of the preceding term (calculated backwards), which in the given example will be 1 and 14, on the first and iecond diffisrence wheels beneath it ; and then the third and fourth difierences of the term before that, which in the present case will be 12 and 24, on the third and fourth difference wheels beneath the preceding ; and all the unoccupied figure and difierence wheels are set to 0. The machine is now ready for work : by the first half- stroke the even differences are added to the odd ones, giving the tueeeedina odd differences (in the example, 15 and 36), as may be seen by tne above table, and the numoer on the first horizontal row is printed : and by the succeeding half-stroke, the last obtained odd difference are added, one to the first teftn, giving the second term 16» and the other to the second difference 14, giving a new second difference, 50. This will probably be more readily com- prehended by the aid of the following diagram : — A», ti, = 1 1 J ... 16= tt, 16 J ,.. 81= tt, »P=H... 15$ 15=Att^) ... 65} 65=AM, ,Mw=14) 14 ) ... 60 = A»u, ( 60) ...110 = A% A,tt, = 12) ... 86 5 36 = aXI •• 60 5 60 = A>M, A,i«.,=24 5 24 24=A*tt.5 24 24=Alrtics]lsTertig*liaBoflliu,iHWmu, Prine,arit«&p.Ml. VASTIBG YSLOCITT-RATIO IH WHKBD-WOBK. 129 7^.179. greatest and least radii are d k, d l^ and major axi«, d k + i>U and proceed in the same manner as before ; transferrine the radial dis- tances to hi, the semi-lobe of p. It will be founa that any two of these corves, or a pair of the same curves, will roll together. 238. When these rolling cnrves are employed in practice, they are nsnidly supplied with teeth like ordinary spnr-wheels, as in fig. 179 : which represents A ^r of wheels emploved in a printing-machine b^ Messrs. Saoon and Donkin. The iorms of the teeth are epicy- ciosdal corves, as in ordmaiy spar-wheels (190), bat the forms of consecutive teeth are not precisely alike, because the pitch-line is not a circle. 239. The following; is one of the simplest modes of efiecting a varying velodty-ratio by common epnr-wheels alone : the centre of a moveable ial&>wheel, c, Big. 180, is connected by links with the centres of two wheels, a, d, of wluch d revolves on its central axis, and a on an eccentric axis, b, which must be j>laced suffi- ciently iar from d, that the distance of b from the ciroumference of D may be greater than the larser segment of the diameter in which B lies, as indicated by the dotted lines : it is clear that by this arrangement a varying velocity-ratio will be communicated horn B to i>. JKff.190. Fig. l«i. ^.nTWIx, 240. If the axes of the driver and follower be at right angles to each other, a varying velocity-ratio may be obtained by an eccentric crown-wheel, F, rotating on an axis, a b, the teeth of which are in gear with a long pinion, o d ; the angular motion corresponding to each tooth of the crown-wheel will be inversely as its distance from the axis, a b. This arrangement has been employed by Huyghens. 180 FBUGXriiES or HSCHAVBIC. CL.B: Diymiovft. CknnmuMcatianofMaUonhySUdmgChnU^ 241. The Bimplest mode of obtaining a ▼ariable ▼elocitjr-ratio between parallel aies is by tbe pm and alit. In Fig. 182 a a, b (, are tlie axes, placed with their ends opposite each other ; ▲ a has an arm carrying a pin, d^ which works freely in a long slit in an arm 6/ carried by b&; either axis will commnnicate to the other a Tariable velocity-ratio, for the pin in revolring is oontinoally changing its distance from b. 242. An intermittent motion is con- veniently produced by the Geneva stop, a contrivance for preventing overwind- ing in Geneva watches. The driver a, has a projecting tooth, flanked by two hollows, r, «; the follower, b, has a number of hollows (usually five) for re- ceiving the tooth, tbe spaces between which are hollowed out so as nearly to fit the plain ^ part of the rim of a, to prevent any motion in ^h B except when the tooth is passing the line of centres, and having entered a notch, d, is car- nring the notch along with it. A portion of tne circumference of b is left convex, as off against which the tooth strikes after passing each notch across the line of centres, and fur- ther motion is prevented. During tiie unwind- ing of the spring the driver, a, moves the re- verse way until again stopped by the convex surface, /0. A similar contrivance, except that a single pin at the back of the driver is substituted for a tooth, is miule use of in the registering wheel-work of gas-meters, as well as in other registering machinery. 248. Any required variation of angular velocity-ratio may be produced by an arm resting on a cam-plate. The requisite form of the cam ma^ be traced out by taking any number of equidistant radii,, and makmg their lengths proportional to the required changes of velocity-ratio of the arm. CL. B: BrviBioR c. Oammunieatum of Motion hy Wrapping Ckmnectort. 244. A contrivance frequently employed under this head is that of placing two equal conical frusta m reversed positions, but with their axes psrallel, and connecting them by means of a flat band. isL this airangement care is required to maintain an equable ISt of tbft btuid to JV IM. e of tb» cooi tnTsl toward* the bue of »Ub cone (21 1) thii diffica1t7 will, bowsTcr, be lent Mt when the cones are pUced u near etch other m U the nrjing leiuion of the wrapper will I permit ' If a, fig. 164, be the driver, aod B P the foIJower, it ia evident that the telocltj I ratin trill be continiullj dlminiahed, *■ the I band Inveli from A towjrda a. It ie deairable that the conee ahoiiM n hiTO ■ IsTge angle, since tbe Tariatioa in tl teniion of the band then becomee conriderable !45. The Jwte te the mott important contriTance under thii bead. jkn. b&, Yig. 185, are parallel aiea, one of wbicb A.a, carriea a solid conical pnlley, or fueea, apoa the aurface oS wbicb ia tnced a apiral eroove lo receive a cotd or chain ; tbe aiit a h eairiej a plain cf Hnder, and one end of the connecting band ii attached to ihe fiuee at m, tbe other end to the barrel at n. The extent o[ motioo will be limited onlj bj the iiamber of tnint b the fhaee. It is clear that the Telodt^nlio wiU graduallj ^- '»■ Tary during the whole extent of motion ; and if a power be , ■pptied to Bfr that thall be alwaja iniereely as the nuliui ^^ of the fiiEee, the axis of the ' latter will rcToWe with ani- form power ; this, in clock- I work, ia eflected by a main- tpring in Ihe barrel B, which la woand op b^ winding the cord from the larger to the imaUer end of the fiuee. 346. iJjTKMinpfii&y.— Inwmsfonnaofinechaniani.eapeciallj in spinning machinery, it is Tery important to posuaa some ready and accarate meani of varying the Telocity- 'V- !*•■ iBlio of a driver and ■ fuUower connected by a I band ; aa, for example, I for the purpose of van- 1 ing Ihe speed of thi' I bobbina, in roving and I ■Inbbing frames. An in- 1 geniona contrivance fori Baling ibia object has ■ been patented by Henrs. Combe, of Beirast; — an gipanding pallej.* Tbe two aidea of tlua pulley, a, b, Pig. ISS, are iep«rate and compcaed oF alternate riba and slots, which mutually pMi each • 8« Finy-i Bigtuiinii PiUey : Bm^ Crdapwdia. I 2 other, and an sppnuiniUsd hj meuia of righi- and left-handed ■cren (SOS) c, d, on an aiia that pasaei through them. The ap- praximation of a and b, and conaequent expansion of the pulley, or MM vtni, VI eSected b; meani of the wheel a. An in thu arranKemenl the length of the connector andentlj nriei conii- deraU;, iti tennon ii rendered uniform hj paesiiig it over a pnlley attached to a loaded moreable ann. CL. B: DiTiBioad, Ootmrninieation of Motion bg Liniyieorh. DOlice il the Hooke'l Joint, a method of connecting two aiM, tbe direccione of which meet in a point. Let "»-^- .Ld, B& be the two aiea whieb, if pro- '' dnoed, would meet in X. Two lemicircnUr « attached to the aiea, tne enoa oi theie to a rectangular 18, of which tbe anng ce, nd^ intenect . .. A ball or rioK msij be SDbUitaled for tbe croeg, the 011I7 neoeuarv conditioo being that tbe pointi of connexion, c, c, o.d, and the point of interaaction, x, ■bould be in tbe aame plane. 34S. Ibjndthe AngiJor Vthaly-raiio of tmi Axe* emnecUd bga ffookt'4 Joint, — Letobetlieiiilereectianof theaxea, abd (he J. circledeeoribedbytbeaniiB of the driTinft ^' axie, which is eupposed to be perpendicn- lar to Ihe plana of the paper; let the plane in which both axes lie intersect the paper in BCL, and let the ellipse, a^d be the pro- jection of the circle described b; the arma of the follower. If 6 be the angle con- tained between the axes piodaced, wo Let F 0 o be any position of the arms or the cram connected wtth the driving axis, then h c 1, the projection of tbe arms connected with tbe rollowiofl: axis, will be perpendicular to r o. Now in the projection, A i n, lines parallel to ad are not altered in length; henoe am, perpendicnlar toBC, is the sine of the angle ^ thmogfa which the follower has been mured, reckoning from a c, and draw- ing A b fc through H, parallel to BC,Bch it that angle; am) tba conespondina angle, a, throogh which the drirer haa been immd i* A c F, whicD m B c H ; then tanfi _ coto _ Bi _ 6£ _ B00KE*8 JOIHT. 133 If we trace the progress of the arms round the circle, it appears tbat the angles dascrihed coincide at the points a, b, ]>, l ; and that stsrtiag from n, the follower moves slower than the driver, but the motion afterwards becoming accelerated, it overtakes the driver at D ; bevond that point it precedes the driver, and then becoming retarded, the? complete the second right angle simultaneonslv. The motion through the third and fourth right angles corresponds ^th that through the first and second. The amount of variation of the velocity-ratio will dej^nd on the magnitude of the angle 0 ; and if two or more such jomts be em- ployed, the axes being either in the same or in dinerent planes, the amount of variation will depend on the product of the cosines of the angles 9, provided the arms of each following axis be in the plane in which it and its driving axis lie, at the commencement of motion. 249. If, however, two Hooke's joints be employed, and the in- termediate axis be equally inclincKl to the first and last axis, and also the positions of the driving and following axes reversed, as regards the common plane, then the second variation of the velocity- ratio will exactly counteract the first, and on the whole a uniform motion will be transmitted ; this is the purpose for which a double Hooke's jcttnt is frequently employed. Uniform motion may eri- dently be communicated between parallel axes by means of this irrangement. 250. If a Hookers joint be made use of as an universal joint of flexure, the nature of the motion it would permit may be readily nnderrtood, by stating that if the arm were attached to the shoulder by a Hooke's joint, and the forearm had no rotatory movement from the elbow, the arm might be moved in all directions, but the palm of the hand would always be turned the same wav. In order that the direction of the palmar aspoct of the hani might be changed at will, as weU as the direction of the arm, it woiild be necessary to have a third motion round an axis not in the pUne of the other two, and which would be most advantageous, if the third axis of motion were at right angles to the pkne of the other two. The joints bv which the limbs of cmstaceous animals and insects are moved, and which are all formed between consecutive portions of the external skeleton, are from the nature of their formation, essentially different from the joints formed between the adjacent pieces of the internal skeleton of the higher animals; they furnish many beautiful examples of the principle of the Hooke's joint. For each separate joint in these animals is a hinge-joint very curiously constructed, but possessing but a single axis of fiexnre ; these joints are, however, so grouped as to form universal joints, in the manner just expUined. The front claw of the common crab may be taken as a good example. This consists of five separate pieces a, d, g, d, e, beodes 134 PBIHGIPLES OF MSCHAHlBir. F, the moveable jaw of the claw itself; of these, c and e may be considered the principal members, a, b, and d being the interme- diate pieces of Hookers joints. The piece ▲ is jointed to the bodj by an axis 1, 1 ; and to a second piece b, by an axis 2, 2, which is nearly at right angles to ^.189. If 1- The piece b is jointed to c by an axis 3, 3, nearly perpendicular to the other two, which is vertical in the plan, and consequently appears only as a point. By combined motions round these three axes, the limb may be turned in any required direction. The powerful members c and •^•4 Bare likewise connected by an intermediate piece D, the axes of motion between which and the former are 4, 4, 5, 5, which cross at k and are nearly perpendicular to each other ; by the combined action of these two joints, every requisite variety of motion is provided for. CLASS C. DutSCTIONAL BbLATIOH CHANQIHO. DiYisioir a. CommuniccUion of Motion hy Boiling Contact, 251. If a spur-wheel revolving constantly in the same direction drive another spur-wheel, the axis of the latter will revolve in a ^. 100. contrary direction ; but if the follower be an annular wheel, its axis will revolve in the same direction as the driver (176). If then the follower be a pin wheel, and the pins be so arranged that the driver may be in gear with them alternately inside and outside, the axis of the follower will move periodically in opposite directions: this combination is called a mangle-wheel^ from the machine in which it was first employed^ but it is now of frequent use in macninery. In this arrangement a groove is cut in the surface of the disc, concentric with its axis, except where the inner and outer portions are connected b^ a short curve ; the axis of the driving pinion prolonged rests in, and is guided by this groove. ir tbs ivlocitj-ratio vera raqnirad r, tba ptck-liiie of tlie nuuielo-whsel in *UT required i In R( Ig. 191, vbich re- oier it* H ^ . pTHuli ft mangle-wlKel emplojed i amtb'e eelfaoiiiig mole, lb« groote Ic I ii uKtl; ndial, and tberefbre the pinioD tQI not oeounaiiicftle any motion to the ■heel, when prooeading in thii portion of it! path. In thii wheel teeth are em- plojed in the place of pins, u the luoe wt cannot ftct on both eide*. 253. If the reciprocating piece moie backwards and fbrwarde ia I right liDe, which ia freqoentlj the case, it is called a manph- rati; thii admits of ao airangement b; whicb the inconTsnieat ■biftiDg motion of the pinion maj be obnated. The man^e-iack nprewnted in Fig. IBS, is G^m Cowper'e cylinder printing ma- chine. In thiH the reciprocating piece b6 ia guided between roUen; the aiia ofthe driving -^ ,„ niuoB * ia fixed, and the tit- va. • aeepanle i © __l°1 U,' '- ■ I — e teeth o •f the prajecting the gnide-g] Dde-gToore within the of teeth. The ^ lack i« connected with bj two gnide rods of eqnal ^-' ^~' feneth, OMrhioh the ends k, i, are jointed to b i, and Uie ends c, t, lathe rack; the middle points of the two rods are abo connected hj a monaUe croM-pieoe km. Bt these means the rack will, at Mch aitnmity e^heelf as it is called, is now usually a spur-wheel, with slender pointed teeth. If the vibrating piece OBC move on an axis distinct from that of the balance ^eel of a watch, which is universally the case in practice, it is called a detached escapement. 1^.197. FBOPELMEKTS. 259. In all escapements, properly so called, the wheel is em- ployed to drive, and its teetn successively escape from, the reci- procating fbUower ; bQt in Bome formi of mecbaninn, m in alecMcal clocki and dial-telegraphs, tha nciptocating piece may be employed to drire the vlieal, aDd to this modiGcation the term prop^meiU has been applied. Several arrange men tg have been devtaed for thia purpose, but it vitl suffice for the present to describe an in- genious maohuiiam applied by Profeasor Wheatatone, in his very elegant and efleotiTa dial- telegraph. In this a reciprocating ai Flt.lM. noTingoi natcd by an electro-magnet (Ch.XV.J, carries at ils extremity a spur-whee!, a, which ia driven by pallets at the ex- tremity of two fixed springB, d, b. The acrowB indicate the directions of the alternate motion ofB,duringirhich thej respectivelj act ; and the direc- tion of the motion of the wbeel is also shown by an arrow. Tha piece, B, IB repraMnted near tha middle of ils motinn from Tight to left, and (he tooth, r, ia abont to be held by the pallet, D, while the onward motion of B canies the wheel round, and the tooth o slips over the pallet, s, to be held by it daring the reverse movement of ■ from left to right, during wbidi the next tooth, h, slips under the pallet, n, and the same actions are repeated. In all these contrivancei some means must be osed to prevent the backward action of the wheel, and to ensure its progioeaive, though interrupted, motion ; this is evi- dently provided for, in tha propalment here described. CL. C : DiTisioM d. — OotnmvmcatUm of Motion by LitJMBork. S60. If it be required to oommnnioate ■ reciprocating motion bj link-work, the reault is moat frequenll; obtained by means ofa crank (21B), or eccentric (354), the reciprocating point q. Fig. 199, fff^ l^ being either constrainad t n the line a Let A F be the radius of the circle described by iha point r round the fixed centi^ a, and FQ the link; take nn, nd eacb = PQ, then Odin tha dis- tance through which the ptnnt Q oscillates. The distance a r is called the ihraa of the crank, or eccentric, and in aod « are the dead points of the nstem. 2S1. In the ecoanttio, which is the most common form, the link is t«muaated by t, hoop ab, Fig. 119, which embrdcss TABT1M TmUXWT-miTtO W I,t«-»■ made in two balvei, ooDDCCted by scram »t o, 6, in order to enable it to enter tb« rman. The thro* of Uw eccen- trie )* endentlj tbe diitance betwMn ihe centre of the disc and ibe centre of the uie on which it ie fiied- . - j i_ a6! A »«ri»tion in (he Tflocitj.nitio may be obtained bj 'mj' mg Ih'e pomtion of ihe link with raspect to the mtu portion of the drinng mm : a mpidly retarded Telocity maj bo Uiiw ptodoeod. centre of motion offtBc^and oofod, and let the anna ji(i,B&,aiidBCDdbo (ODDected by Unka 06, ed. I*t io,, 1 a- « a« be three eqnidiatant pootiona of iIm ann io; a, midway between a, aado,; and i„fcpt,; e,. 61, "Jj ; ^i. <*!. be oonMponding poations of the pomts fr c, (i, and let the poaition of ■ be inch that the line 6, 6, produced nearly bi»act« a. a Then it 11 evident that the ipaoe b, fc'oorreBpondioR to a, a, will be mncb ereater Iban 6,6, which correeponda with 0,0,; and if the arm od hew placed aa to be parallel to e, e- when in the poai- tion n iL, it ie also evident it wiU remain ment from e, 10 e^ that ii, doring the moiement of tba ann *« A.^^imtemhe,ed, da maybe connected with afc, 10 thai the arm d d would reat during tbe motion from 0, to o, ; thH u tbe principle of oonatrnction in Erarde donblftacbMi harp. for »4jn»ting the qoantily of mo- from 0 np to w commnmeated bj ■ aimple hnk connecting b and 0, which we may call unity, or 1. For thii puipoae tet *B •BHwit>a lure for thaos ' "'- .^. A »ery ingenione pli tion transmitted by link- work baa been deiised , by Prof. WtUis. For ex- ample, let it be required to ttinsmit any given emonnt of motion from the crank 4B, Fig. »01, to ooDDSctpd with » fixed piece, f a, b; > link, b ■, and an urn I r, a little longer than Sad. Then let a triansnlar liok h e L be joined at k to aa arm ems, moreable ronnilii, and capable of leing flxed in ita pmition (h by a screw and Dut noving in a groove o f), and let tbe pomt L be oonueeted at the point > wilb the arm e r by a link l >, iDoh that the distanco between tbe centres he, kl,lh, eh, fB,LR, may each be equal to S a b. When by the moTement of h towards o, Uie pranti f, e, and coo- •eqaeDtfy the poinla u, b, are made to omndde, the motion ia the same as if tbe points h and b were connected. If h ba moved in the opposite direction towanli r, nntil the pointa r and i. coincide, then the arm ■ f will oommanicate no motion to the point i. and coueqaentlytotheanncD. Ai the paints advances from P too, the EnotioD of the point c will increass nearly imifonnly from 0 to I. The ^ore represents this mechanism in ita mean position, in which the distance between ths extreme positioa* o( the point c «». SM. 'il •* nearly equal to * b. 364. If it be required to moltiplj oacillatifnis bylink-woik, letoAcFig. 303, be an OKnllating arm, moviug ronnd the centre a, and let a, a Cj, a,AC„ ba its extreme and a, a e^ its mean posi- tion, and let the aim a 6 ba so placed that, in ila extreme positions, tbe points h„ i, may be in the line a, e,, and let the two arms be Munected by • link b e, then, when e reaches c„ h will reach b^ and will retnm to £, when e arriTes at e^ so that (, and b, will cobcide ; thus a doable ntoiement of B & will result from a sinsle movement of a a. The motion transmitted by link-woTk may be vari- onslj mndified by oomtnnations of this and the preceding MnanRemsnts. S65. The ratclutvihea and tSei is an anangement frequently employed for oonunnnicating an intermittent nkotion from an •ItematinE driter to a revolving follower. The driver is an arm of wMch ths centte of motion is a, Ft«. 303 ; the follower ia J^, ]0g_ the ratchet-wheel, having teeth fortited like those of a aaw. lie piece b c ii jointed to tbe d[iving«nn at B, and resta on the wheel by its weight. If tbe arm be moved into the poution a h, tbe extremity of the piece c will puah the radial side of the tooth against which it rest*, so as to turn the wheel in tbe direction of the arrow ; when tbe arm retunu to it* former positicii, tbe piece BC will slipover the slanting side of the tooth, and fall into another epaoe. To inaors the wheel agwnat any aod- denUl backwATd motioD, uiotheT •im, dw, or ke, actiDg by it« wei^t, or n**, actiog bf ft iprtDg, » (idded to detain tbe vlteol; this U cklled > deleM, uid ths piece b n j^ j^ ■ cUei. In order that tbe click maj hold the whe«I efbctnall}', it ia necMaar^ that ■ itt piw»niu on tbe looth, i««oli«d in the I direclioa of ita inrfac* (71), maj act I tmtdfxb the centre of tba wfaesl. I 366. The dririDK-piece maj be made I to act on the ratchet-wheel dimnBits I motion in both dirsctiona, il, aa in Ft((. I 304, a click ab be attached to the drir- I ing-arm at a, and another, e ^ at a point c, equidistant with a from A. 367. With doe attention to the reqninie dit«clion of the line of action, a click or detent may be applied to a common spur- rig. Mf. wiiect aa at A, Hg. 305, or to a pio-wheel, aa at B. A detent i* mnetimea required lu retain the wbeel in an exact position : for this pnr- poae it rbonld reat on two cooaecntiTe teeth aa at c. Or if the detent be not required to witlutand much resiatance, it may be fomiahed with a roller, aa at d, which wilt render ita action mora easy. The aereral doited lines show the nonnala of contact. 268- In click-wurk, the slipping and ci ntcbet prodnced much noiae and wear ; theae incooreniencei may be cbriated br tbe employment ot the tiUai didi. one of the aimpteat fbnna of which is repreaentea in Fig. S06, in which the wbeel d is concentric with ths arm d, which cairies the click ph, joined to it atjr; itiesnu Ao la also conoentric with tbe wheel, and ia connected with the click by a link e/, jointed at « and /. Tbe motion of the arm ac on the piece n, ia limited In- two pina, a, 6. When the end of the arm c i* raored downwards, the click will carry the wheel in the dinectioD of the arraw; but of tbe click and Fig.iM. 142 pRnroiPLBS or mbchakibm. when it ii nised into the poaition a c, proTided the frictinn at the points A. e,/, j7, be less than the resistance to the motion of the wheel, tne click will be raised out of the space between two teeth, and then the piece b will be carried round the axis a, leaving the wheel at rest. When the arm c is again depressed, the click h will be brought into another space ; the motion of the arm will then be communicated to the wheel ; thus the first part of each alternate action of the arm a c is employed in silently engaging or disengaging the click. 269. An intermittent motion may be ]^roduoed hj link- work, by makingf a slit at either end of the link, m which case the motion will be intermitted, while a pin working in the slit is passing from one end of it to the other. Having now investigated the mora simple oombinations of ele> mentary mechanism, our readers must be referred to the treatises on machines for a detailed account of those more complex arrange* ments by which either an aggregate velocity ratio may be ob- tained; such as the complex trains of wheelwork for lunar, sidereal, or e(}uation clooks, and orreries ; or an aggregate motion in space, as in the parallel motion of the piston-rods of steam engmes ; or a combination of both, as in the various motions required in planing, boring, slotting, shaping, screw-cuttingi and various other kinds of machinery. 148 CHAPTEB VI. BTHIMICS; THB SELATI0V8 Or BODIES UT MOTION. 270. Th£ preceding chapter on Statics bas been devoted to tbo ooosideration of matter in a state of rest ; the properties of matter in motion, constitnting the science of Dynamics, nave nert to be inTOStigated. Bj motion is miderstood the act by which a body changes its posilioii. It has been divided into several species ; thns a body is said to be in abtolttte motion when it is actaally movinf from one part of space to another, instanced in the moTcments of the planets; and to be in a state of relatwe motion, when its position is con- sidered only in relation to some other body : thus a man standing in a sailing vessel is in motion with relation to the shore, and at rest in relation to the several parts of the ship ; in this case also his motion is said to be eommom, with that of the vessel. Besides these, there are some other divisions of motion which it is im- portant to understand ; thus the motion of a body is vnifarm, when it passes over equal portions of space in equal times ; it is acoderaJted, when the successive portions of space passed over are increased ; when diminished, it is said to be retarded; and when this increase or decrease of motion is constant, the motion is said to be unifomdy accelerated, or retardedm The motion of any body is wwifter or «2otoer, in proportion as the space passed over in a given time is greater or le«s. The degree of rapidity with which a body moves is termed its velocity^ and is measured by the space uniformly passed over in a given time. The number of feet traversed in one second is the usual measure of velocity ; if this number be called v, and « the space described in (^ (t seconds), then evidently «» t x v. 271. If the velocity of a moving body be variable, its measure at any given time is the number of feet that would be uniformly described in 1', if the velocity remained the same. This is what is meant by the term rate in common parlance ; as, " the train was going at the rate of fifty miles in an nour," "the winning horse came in at the rate of a mile in a minute ;'' meaning, not that a mile was, or could be, actually passed over by the horse in one minute, but that it would have been so, if the speed had continued uniform for that period of time. 272. The releiive velocUy of two bodies is the rate at which 144 DTVAMICS. they recede from, or approach, each other; if they move in the same straight line, the reUtive velocity will be the snm, or dif- ference, of the absolute velocities, accoraingly as they move in an opposite, or in the same direction. 273. In the chapter on Statics, the effects of pressures producing equilibrium, or rest, have been investigated ; it remains to consider in the present chapter, the effects of pressures producing motion. Accelerating force is measured by the velocity generated in 1" by the continuous action of an uniform pressure ; and if the pressure be not uniform, by the velocity which would be generatea by the given pressure acting uniformly for 1'. If we call ihe accelerating force ^ then /will be the velocity generated in 1", and if v is the velocity generated in <•, then v =/x *. 274. The nuue of a body, or the quantity of matter it contains, is measured by its weight, at any given place ; and generally, it is measured by the weight divided bv tne accelerating force of gravity, which is not uniform at dirorent points of the earth's surface (63). 275. The votume of a body is its bnU^ or the space which it occupies ; the unit of volume is one cubic inch. The denaity is the quantity of matter contained in an unit of volume. If we call u the mass of a body, d its density, and v its volume, that is, the number of units of volume that it contains, then h =y x d : and if w be the weight, and g the accelerating force of gravity, then WaspXMsspXy XD. 276. The momeiUwn of a moving body is its mass x its velocity ; but the moving force is ihe momentum generated in 1", that is, tne product of the mass and the velocity acquired in 1* : it is neces- sary that the distinction between the terms momentum and moving force should be clearly recognised, as they have been sometimes confounded together. 277. It follows as a conseauenoe of this definition, that when the momenta of two moving bodies are equal, their masses must be inversely proportional to their velocities *, and conversely, if the masses of two bodies are inversely proportional to their velocities, their momenta will be equal. Also, a light body will, by having its velocity, and therefore its momentum, increased, possess as much momentum as a heavier one, having a proportionably slower motion. A cannon ball, of 3 pounds weignt, possessing a velocity of 300 feet in a second, will possess as much momentum, as one of 30 pounds moving at tbe rate of 30 feet per second, for 300 X 3 = 30 X 30. The existence of momentum explains why the large masses of loaded ships or icebergs, althougn moving but slowly, are capable of exerting such enormous force upon bodies with which they come in contact. The term momentum has been applied indifferently to the quantity of motion existing in a body, and to its striking force, or power of overcoming resistance : the latter, hereafter explained as the vis viva of a moving body (338), unsTiA. 145 depends on the 9qujaTt of the Telocity, conseqnently the striking force of the small cannon hall above-men tioned is 10 times that of the larger one, and not simply equal to it, as it sometimes is re- presented to he. 278. All forms of matter, whether in the atom, or in the mass, are alike inert, and incapaUe, hy the exertion of any spontaneous force, of changing their state or position : loAereoer a body is placed hy any external cause, there it must remain forever, unless acted upon by some disturhing force. This property of matter is termed its Inertia, or passiye resistance to a change of position. JHe amomd of tnertia increasei with the qttantity of matter. The resistance experienced on first settine any body in motion, and the difScnlty experienced in stopping it wnen moving, arise equally from this cause ; for being absolutely inert, it follows that matter must retain its state of motion, as well as of rest, for ever, unless acted on by opposing forces. 279. The ' following are examples of the effects of inertia: in turning a fly-wheel, hy means of^a winch, a decided reaiatance is at first experienced to our attempts ; this is gradually overcome, and then the wheel continues to move rapidly by the continued application of a force, just sufficient to overcome the resistance oiBered by the medium in which it moves, and the friction at the points of support. In a team of horses attempting to move a neavily-laden waggon an immense exertion of muscular force is required to overcome its inertia, but this once effected, the horses continue to draw that weight with facility, which at first they were scarcely able, hy the utmost exertion of their physical force, to move. A traveller sitting in a coach, on the horses starting, is thrown backwards: his inertia opposing a resistance to his body acquiring at once the movement of l£e vehicle, and therefore tends to leave him hehind-; and on the coach stopping suddenly, he is thrown violently onwards, from the inertia of his body tending to retain the mo- tion previously acquired. J^. 207. A hoDet thrown at a pane of glass hreaks it in the direction of numerous lines radiating from the point of impact, but fired from a rifle at the glass, it merely pierces a circular hole, the tnertia of the glass pre- venting the surrounmng portion from yielding to the rapid motion of the bullet, and oonsequentlj that portion only which is opposed to the impact is carried onwards, and participates in the I. rapid motion of the ball. Similarly, a. common (allow candte, when fired out of a musket, will pierce a bole in a deal board; and aatick, of whicb tbe enilii rest on two wine-glasees, Fig. 207, mnj be broken b;n smart blow with & poker in its ceotro withoDt injuriog its brittle aupportB. The eiistenoe of inertia maj likawiae be demonetrated b; a more familiar experiment. Let a card witli a coin, of not too Boiull a aize, laid upon it, be poised on the point of the finger ; tiien by a dexterous Sip of a finger of the other hand against the edge of the card, it may be displaced, teaving behind it the coin ntill poised on the finger. This remll is due to ^S inertia of Uie coin, which is, however, to a small extent displaced by the friction of the card against it, 230. The Conaation Fuxe, — An admirable illustration of inertik utilized is met with in Sir W. Armatrong'g oonousaion fuM. The object of this ingenious deiice is to insure the explosion of ■ shell the ingtant that it strikes any object against which it is fired, bnt by such means aa will not cause explosion at any slight concoa- KioD, such as a fall on the ground from (h'- band, or tlie upsetting of an ammmiition waggon. Many different kinds hare been con- g^ 2(i§ Btrucled to meet special pnrpoeasi that repre- sented in_ Fig. 208, is intended to be enclosed in the interior of a shell supplied also with a time- ' , in order to ensure explosion, in case the >r fails, or has been adjusted for too lone a J ; and is so placed aa to move, on projection, in the direction of the arrow. It consists of an iron cylinder closed b^ a plate at both ends ; in- side this is a brass cylinder, a, capable of sliding in the former, and anneil with a steel polut, c, which, when It slides forward, strikes and ignites a small portion of percussion powder, in a plug of wood, d. This in ita tnm ignites the p-iwdcr, #, in the top of the fuze, whicb again, through a hole in the plate covered with gaoze, ignites the charge of the shell. Bat the firing pin and cylinder is fixed in a safe position by a sling of severaTsmall vires, b. b, which is soldered to the bottom of a, and to the oatude of the fuze. The ilin^ is sufficienllj strong to hold the pin in its place during any accidental concussion, but when fired from a gon the velocity of projection is so great, that the inertia of a breaks the sling, and the cylinder retiree to the bottom of the fnze ; but it is now free to move, and the instant the motion .J efi'ected. Moreover, the seecient- shell of the same ingenious inventor, the most destractive misBile for field parposee that has hitherto been devised, is a further illostration of the application of inertia. Thi« shell coniislt of ■ large number of rkdial eegmenta of flat rings SBWTOIi'8 FISST LAW OF MOTION. 147 packed close tc^ther in a thin cast-iron case, and sarroonding a sdulII cyUndrical carity in the centre, which contains just enough powder to burst the outer iron skin, but without scattering to anjr great extent its fragments, or the contained segments: these pursue a slightl? diyergent course, by their own inertia, and are probably as fatal in their effects as they would be if fired from a six-poundeT blunderbuss at the point where the shell bursts. 281. In consequence of the inertia of all bodies, force must be applied to cause them to assume motion. If it be merely intended to caose the body to move in the same horizontal pl&ne which it preriously occupied, the applied force must be sumcient to oyer- crings, as that which occurs in the torsion of a single filament, as in the first example ; the torsion of a spiral sprine correspODds with the flexion or bending of a fila- ment or thin lamina. The same law is observed in the extension and compression of caoutchouc ; this is most readily shown in the extension of a thread, or narrow strip of a lamina, of this substance. 291. The third law of motion having been established without reference either to the amount of a force, or the period of time during which it acts, must hold with respect to impact; conse- quently in the direct impact of two bodies, whatever momentum IS lost by one of them, the same is gained by the other. Let the masses of the two bodies be m and m', and their velocities before impact V and v', and first let them be supposed inelastic, in which case they must move together, after impact, as there is no force tending to separate them. Let x be tne momentum communi- cated m>m m to m', then m,v — a; = the momentum of m after impact, m'.t/+x= „ „ ml „ „ and "" = the common velocity after impacts — '—. — whence a:=^^,(t;-tO (a); therefore the velocity lost by m= — = — ; — > (v— t/) . . (6 : fn fn+m * . . . gained bym'=—/=s —- — -,(»—»') . . (c): coLusioM OF nrxLAsnc bodixb. 153 and the common Telocity after impact w- If the masses are equal, m^ml^ and (d) becomes \ (v+v'). If the Telocities are also equal, and in opposite directions, t/a -v, tnd (<2) disappears altogether ; that is to sa^, two equal inelastic bodies meeting each other with equal yelocities will, after direct impact, remain at rest f» If t/=o, (d\ becomes ,0, and if also me m' U[\ becomes h v. 392. The troth of these and many other corollaries may be thus shown experimentally: — Let two hollow Fig,tiO, vooden cylinders, of equal weight, one of which is furnished with a conical pin capable of entering a hole in the other, be suspended by equal strings from a nori- ^ lODtal frame, gd, Fig. 201, the quadruple Rtapeosion being designed to ensure steadi- ness in direct impact. If one of these, a, be raised by the hand, and allowed to im- pinge on B at rest, the two will remain in contact after impact, and will describe an arc very nearly naif that through which a descended:* and if either of the cylinders be loaded so as to make it double, treble, &C., the weight of the other, then corresponding spaces, according to the formuu, will be found to be described. If both cylinders be equally raised, they will remain at rest after impact, if equal ; or if unequal, they will moye through a corresponding space, in the direction of the motion of the heavier weight. 293. Let us now suppose the bodies to be elastic, and c to be their elasticity ; then, m consequence of the force of restitution, 111 will lose and nti will gain an addit^nal quantity of momentum, which will be c X, and the whole momentum lost bj m and gained by m' will be but (291, a) a: =5 x-htjXj or (l+f)a?. X IK therefore TeL lost by «»==»(l+«)-=»(l + e)r-ri-i(*^— «0 • X m and yeL gained by m'=(l+e)^=(l+e)^^;^,(»-«^)- • to) and if « and tf' are the yelocities of m and m' after impact, then * BtffetlT speakiBf , the yarsed sineB of the ana desoribed will be as 1 : 2 ; and gMMnulyf as m : •+■•'. 154 DTHAMICB. (») tt=« — (1 +g)^:rr^(p— ty^)= ^ . ^/ —«rr;;p (t>— t;') . wi+w^ ' fn+m 111+ 111 If e be made^o, then the second terms of {h) and {k) disappear, and their values both coincide with (d). ' If the elasticity were perfect, e=l, and (/), (g\ become 2m' (»— rO, and 2tn ■dv'V); Fig. 211. «l + OT V - " fll + m' therefore when the bodies are perfectly elastic, the velocities respectively lost by m and gained by w» , are double what they would be, when the bodies are whoUy inelasttc (291, &, e). If flisfn', i/so, and € = 1, the quantities (/) and (^) become each = v; that is, if the bodies are equal and perfectly elastic, and one impinges on the other at resl^ the impinging Dody will re- main at rest, and its whole velocity will be transferred to the other body. 294. These and other deductions from the general expressions (/)» (9)t (^). (^)i may be thus shown by experiment: — Let two equal ivory balls, a, b, be suspended bpr equal threads from the hooks, o, d : if one of these, as a, be raised by the hand, and allowed to impinge on b at rest, it will be found that ▲ will re- main very nearly at rest in b*8 place, and b will swing into a position b', nearly equidistant with that from which ▲ de- scended; B will then descend, and impinging on a, will occupy its place, and a will be driven back nearly to its former position. If the balls were perfectly elastic, the same motion would continue, until gradually ex- hausted by the resistance of the atmosphere; but owing to their imperfect elasticity, uiey begin to oscillate in the same direction, after three or four suc- cessive impacts. 295. If instead of a single ball, b, a row of equal balls be suspended from equidistant hooks in the frame o d, b will receive nearly the whole momentum of a, and will transfer nearly the whole of what it has received to o, and so on ; and the last ball in the series will recede from the preceding one, with the momentum transmitted frt>m A through ine entire series. On the return of the last ball, its momentum will be transmitted through the series back again to A, and the same movements will be repeated. It may be remarked, that the transfer of the momentum through the entire O wtieioflnUaUkea place in u tlmost iiufipTeoiabl; miKll space If a Domber of iioir balla, iiutead of being BUipended, be placed OD a table, bo that tbeii centree lie in the »anie right lino, or (as Ibe '*■ '"■ ui obtow angle, anil one of them, a, Fi^. 312, being eeparated ftno the icet, be propelled towards a with a certain degree of ntulico a, the iiit«rmediale ipheraB being nnaffected, except in the impennptible manner jnit deuribed. 296. IneuletkX ontJ JUfleetion. — If an elastic bodj impinga oUiqaelj on a plane aBrfaoe, the lorca of raatltation will, after impact, ^- *•*- cairy it awaj from the plane. Let ( p b« ikg elasticity of the body and plane, ud lei CD represent in magnitude I ud diiectioD the Tclacil; with which I Ibe bodj strikes the pUne at D. I Draw D ■ perpendicular, and c B pa- I nUeltothepWejtakeDr-ixDC, I ibranghp, draw Ffl parallel and eqoal I lo CB, and join De; tben will ds * represent in magnitude and directirai the Telocity of the bodj after Let c D ■ 1:3 6, which is called the 01^ o^ ineidewM, andEra = 0', „ „ ibe angle of r^/ketion ; now c D, rep reseating the Telocity of incideace, may be resolved (284) Into the two TelocitieB, c a, B D, of which c i beine in the direclirai of the plane, will be unaltered hy impact, and mtty be n^irasented by an eqnal and pantliel line, r a. Bat the Telocity I □, will be eipended in compreaeion, aad a corresponding Telocity, nr, will be generated by reatitntioa ; consequently, do, the re- nllant of ■> r and r u, will represent the Telocity and direction of tb« body after impact.* •od t=^„! fhRB vUcli two BqnatioK tt thm of the qnaotMei r, t*. 0, ff', « ba j^Tn (ineofwliHliuiiKbeatdfnhj) tlw other tao ni>j be deUnnined . 166 DTHAMIOS. 297. Impact has been termed "a prefsnre of aliort duration,'* bat practicallj there is a great difference between the effects of pressnre and impact : thus, for instance, a very lai^ weight will be reaujred to press a nail into a block of wood, which may be readiljr oriven into it bj a small hammer ; the reason of this is, that a longitndioal compression of the nail towards the head is the immediate effect of the blow ; this is followed by restitution, and these actions follow each other towards the point, consequently the friction of the nail against the portions of matter in contact with it is oTer- come at successive pomts, and not over the whole surface at once, as when pressure is emploved. Thus the nail eirters by a kind of vermieuiar action, precisely analogous in its kind, although Tery different in its duration, from that by which an earth-worm is observed to progress. The great power of the wedge in splitting the touffhest materials depends solely upon impact, and may be similar^ explained. The Pile Engine and the Steam Hammer are conspicuous examples of the impuJsiye application of great forces. Hardness in the impinging oody is obviously advantageous in avoiding loss of force by compression ; thus a hammer with a hard steel face will do its work much better than one of soft iron. Also, when impact is employed to communicate motion to one body relatively to another, tne amount of effect produced depends greatly on the immobility of the latter ; thus, many more dIows will be reonired to drive a given nail into a loose board, than what would suffice if it were resting against an immovable support; mach of the force in the former case being spent in communicating motion to the board itself. There are, however, certain cases in which the effect of impact is diminished by a firm support ; thus, hard and tough mineral substances may be more readily broken by a hammer if resting on a cushion, than if placed on an anvil, or other heavy mass of solid matter ; probably m the latter case the effect of momentum on the successive particles is interfered with by a contrary momentum generated by restitution. The effect commonly known as " deadening*' the force of impact is due to the gradual exhaustion of the momentum of a moving body ; thus, a bullet may be arrested in its fatal course by a son cushion, or even by a loosely-suspended silk handkerchief. The well-known art of catching a stone or other hard substance without inconvenience, by withdrawing the hand at the instant of contact, may be similarly explained. ▲CnOH OF 17HIF0BM AGCKLEKATIVO F0B0B8. 298. OrapUation. — Among the forces which are the most ener- getic in producing motion on the sur&oe of our globe is the at- traction of gravitation <59) ; this force, whilst acting on bodies under its infloence and approaching the earth, is a uniformly ac- celerating force, becoming as uniformly retarding on bodies receding ACnOH OF UHIFOBM AOGBLESATIBO FOKOBS, 157 froa Uie earth. So tliat a body acted upon hy it» passes through dtflfereiit poriionB of space in different times, and vniLst approach* mg the earth, would m each instant pass through a greater space than th*t which it traversed in the preceding instant of time. If a ball be let &11 from the hand, it can readilj be caught during the first few inches of its path, but its Telocity afterwards so rapidly increases, that it cannot be intercepted by the most aeile arm without difficulty. Even if the descending body fall obliquely, stin the same rapid increase of velocity is perceived ; this is well illustrated by the falling of bodies down steep descents, or long inclined planes: for the nrst few yards the mass appears to move slowly ; gradually, however, it increases in velocity, and, as for example in the fall of a eranite block from an afpine ridge of ToA, or of the more terrific avalanche, acted upon by the con« Btantiy accelerating force of gravity, it acquires such an accumu- lated energy (2^3). as to enable it to overcome the resistance of almost any obstacle it encounters. 299. If # be the space which a body describes from rest in t aeconda by the action of a uniform accelerating force,/, then Let A be the point from which the body be^ns to move, a b the space s described in t",* and v the velocity acquired at b. Let us now suppose the body to be projected from b Fig. 314. towards a with a velocity v, and to be also subject to the a accelerating force,^, in the contrary direction, a b, then since the accelerating force is uniform, the velocity that is being subtracted at any point of the line c, is equal to that which was being added at the same point on the farmer supposition ; hence the velocities being the same at B, they will be the same at every other jxnnt of the line ab: in the time <", therefore, all the initial velocity, o, with which the body left b will have been exhausted, and the space described in that time will be s. But by the second law (Amotion (283), a constant pressure produces the same effect in a given time, wneiher the body on which it acts were previouslv m motion or at rest ; wherefore s will be the space through which the accelerating force,/, will prevent the body from moving in t", when projected with a velocity, v, in a direction contrary to that of the force ; and the space actually described bv the body in <", on being projected from b with a velocity v, will be v.i—S'f but it has been shown that this space is $ ; therefore «=<. v— s, whence §=z^v.i; {a) but (273) »=/.«, therefore »=i/.<*. (6) * The diaraeten I™, <*, are now oommonly aaed to denote t minutes or Moonds (^Umtf while If, f, denote t muratas or Beconds of at^, or angular It sppean turn (a) that Ihe naee daeribed, roabmiu^-oM the beginning of tnolion, it half Inat wkieh leovld be dttcrioed w the tame time, miik llie latt aequirtd vdodty continued vniform. 300. If s body be mOTBcTfrom a stala of rest _bj the action of a aniform acceleratiiig force, Ibe apaoes described in equal HacceHiTe portioDB of time, reckoning from the benaoing of motion, will be as the odd numbers, 1, 3, 6, T, &a. For the ipace dewribed ia r being I/, t*, tbat described n r— I'wiUbe !/((-■)■; conse- qaentlj the Bpac« described in iJie f second is, i/C-i/('-l)' = i/(2<-l), and writing for t, 1, 3,-S, &c. BQCcoMiTel;, tbe spaces described in SDCcesBiTe seconds are \f, |/.3, 4/.fi, &c., that is, they an as the numbers 1, 3, S, &a. 301. Mcrin'i Apparattii. — Ths aboTe relation (b) between time and space nu; be verifled bj the appantof of H. Morin; this consists of a vertical cjlinder, covered with paper, and made to rotate with uniform velocity. A falling weight, with a pencil attached to it, which rests on the paper, is liept' parallel to the cjlinder by wire guides, and IS released from its support while the cylinder is rotating. On subsequently temoving the paper fmm the cylinder, a curve, a p, Fig. 215, willbe fbandlrHced upooit, enda straight line, oi, drawn before the weight descended. Draw o i perpendiculAr to o x (or draw it on the cylinder, by allowing the weight to fall, while the cylinder in at reet). Take any point r in the curre, and draw Ti, rr, parallel to OT, OT, rvspectiTtlj, and call them x, y ; then g represents the space fallen through in the time represented by t, -.nd it will be foand that x*= A y, and tbe carve p ia a parabola, as in projecrilee. SOS. A bodj leFt free to more, and acted upon direetlr by the force of gT^ritation, all opposing forces being eicladed. will, in the latitude of Greenwich, descend throngh 16'0954 feet in a second of time, acquiring by this motion a velocity of 331908 feet, or 3S6'iB96 inches per second. This velocity, expressed in nnmbers, is termed the ybriw o/'prority, and is represented bj 3. Th« space traver>ied by a fallinz body in a second is hence v«iy nearly equal to 16 feet 1 inch; which is sufficiently correct for ordinary calca- lations, and to enable os to avoid decimals, which are very incon- venient, unless we nse logarithms to lessen the number of Ggat«i: and the space described in t* it (^,t*. 303. AttiMod't MaMae. — It is difBcult to submit the resnlts , here obtained to tbe test of eiperiment, by means of bodies Ealling freely by the action of gravity, both from the space reqoiute, and I Ibe mMrtaintj of obHiriiig rapid motiom ; but meana hsTS been ikrued bj which the force of graritj mtj be so fnr diluted, u U> U snecepcible of euy obMrratian. If two bodicB, r uid q, oT wbicb e jg the grester, be cODDeoted br > itrine pesfiing OTor • bed pnllej, r by ita greeter weiebt viu deieeLd and draw op q. Lei tfae moring force (ST6) be f{r + n), neglecting (he inertia ol ,\. „ii ^ jhe rigidiljof the string (13), bnt "■• -*-^-- >f gravitj i»y (p— Q); coMequBntly, /{l-+Q)-ff(F-«), Md/=^-=^ff. If two equal seighia of 7) oi. be taken, and a weight of 1 oz. ba added to p, then —" will be ^, and the force,/, will be ^ p nrj ftearij ; f will conaeqoentlj descend from net one foot in a ncgod, and will aci^uire a Telocity of two feet per Mwnd. In order that prejudicial reeiituiceB may be ■• far M pOMlble re- mored in Attwoiid ■ machine, Fig. !16, the pnUej i* made to run nerj lightly on friction- '*'■ *•* ipilen, F (57) ; the ptiUey thua fnmiahed ii nppnted fay a ■tandud, or pillar, and a rod, B.gndnated in feel and inches to indicate the •paceBdeacribodbytbedeacendiagweigbt. At- tached to the atem ia a aeconda penduhun a, ■hich when drawn totratdi a, and released, at the moment it passee its central poeil loo, re- \ateM Ihe weight, p, by meam of a lever, n ; tlw veight r in ita descent drawing ap q. The tnoat conveiiient arrangement ia to make the ■eighia r and q equal, and to place on f an •cceJemting weight, h, which may, when reqnired, be detached from f in the coarse of If the weighta be bo adjnated that the de- fMndiiu; weight will deacribe exactly one foot in the Gnt second, marked by the beat of the •ecoodi peadulum, it will be found to descend tluoogh three feet In the next, and fire feet >a the third second. It may aleo be ahown by this machine, that Ibe apace deacribed from rest, by the action of a unirorm accelerating force, is half that which ■ould be unifomly described in the same time, by a body moving uniformly with the Ism acqaired Telocity (2»9) : for if, at the end "f one second, the accelerating weight, n, be arreated by a per- Cunted atage, b, through which the descending weight pasaea, it 160 DTHAinOB. will DOW be found to descend uniformly throngb two feet during each BQCceeding Becond : and if the weight be detached after the end of two seconds, four feet will be described daring die third second. This may be shown by placing a second stage, c, on the graduated rod, o, so as to be struck by the descending weight at the end of the required period. 304. The practical application of the preceding formulsB will be best understood by an example : thuSj if the space be required through which a heavy bodv will descend by gravity in 23', re> ferring to the expression B—^g^ (301), we have i^=16'095, and <-i23; consequently, «-16*0954x [23'»] 529«8511'4666 feet. The height of any lofty building, or the depth of a well or shaft may thus be roughly estimated ; for by lettmg fall a pebble from the top of the one, or into the mouth of the other, ana noting the number of seconds which elapse before the sound of its striking the ground or water is heara ; then, on sqnaring this number of seconds, and multiplying the product by 16^^ feet, or, more accu- rately, by 16*0954 feet, the height of the biuMing or distance of the water from the mouth of the well may be approximately dis> covered. This process is of course open to the error arising from the time requireid for the sound produced by the pebble striking against the ground or water to reach the ear ; and consequently the calculate length of the path of the pebble will be somewhat greater than the truth. 805. Also, knowing the time required for the fall of any bodv through a given space, we can readily discover the velocity witn which it moves ; and by knowing its velocity, we can of course ascertain the time required for its fall through any g^ven space. The following formulas will be sufficient to answer every question connected with this subject : — v being the velocity of the falling body, t the time of its descent, a the velocity acquired by the body after moving for a second of time, and $ the space passed through in the time <, then (270, 273, 299), 9 «-»-L*= /!J. 806. When a body is acted upon by any projectile force inde-. pendently of the attraction of gravitation, the motion it assumes 18 a compound one, produced by the combined influence of the im- pulsive force, which is momentary, and the gravitative force, which IS continuous. If a body, instead of being acted upon by ^vita- tion idone, be proje^ed downwards wiUi a given velocity per MOTIOH OV PBOJBCriLES. 161 Mcond, tluB 18 to be taken into account, and being expiewed in feet, and multiplied by the nnmber of secondB, the product is to be added to the space, also expressed in feet, which the body would bare^ tcaTeraed in the same time, if acted upon by the force of gravitj alone. Jfj on the contrary, the body be projected yertically ppwaids, its coarse being opposed to the attraction of gravitation, instead of being added, the effect of the latter is to be iubtraeUd from the space passed through by the projectile, if acted upon by the force of prqiection only. The following examples will illustrate these remans : (A.) To what height will a body rise in three seconds if pro- jectea upwards with a Telocity of 100 feet per second ? The space described by force of projection alone wiU be 100x3=300 Space through which the body would fall, if acted upon by gravitation alone daring that time will be 16095 x 9=14485 The diffsrenoe of these quantities is . 155*15 and conwquently the height attained will be but 155*15 feet. (B.) Where will a hodj, projected perpendicularly upwards, with a Telocity of 80 feet per second, be in 6 seconds ? By the force of projection alone, 80 x 6=480, .... graTitation alone, 160954x36=579*4344, and 480-579*4344 = -99*4344. The body will therefore be nearly 99^ feet lower at the end of 6 seconds, than the spot from whence it was first projected ; pro- vided no mechanical obstacle be present to preTent this taking pUoo. (C.) What space will a body pass through in 4 seconds, if pro- jected Terticafly downwards with a Telocity of 30 feet per wcond? Space due to projection alone = 30 x 4 = 120, .... graTitation alone = 1 6095 x 1 6 = 257*52 The answer is 377*52. The body will consequently pass through rather more than 37 7} feet in four seconds. MOnOV OV PHOJECTILBB. 307. The only motion hitherto considered has been that of a body acted on either by an accelerating force alone, or bjjr an impulsiTe force conjointly, but in the same straight line with the former. Bat if a body be projected in any other direction than Tertically npwards or downwards, and consequently in a course obliaue to tnat of graTitation, it will not follow the direction of eitner of these foroes, but its path will be determined by the joint action of both the foroes. Thos let a body placed at ▲ be projected in 162 DTVAMIOB. the direction ▲ b, with a Telocity v, Dnw ▲ b perpendicnlar to the horison ; then let a e be the space ^' ^"' over which the velocit j of projection X will carry the body in a given period of time, <*, and ab the distance it would traverse in the same time when acted upon by gravitation alone : now • draw BC paraUel to ae, and bo to V ▲ B, completing the parallelognun ▲ c. \ Then, in consequence of the united ^ action of these two forces, the body -^ will be found at the end of the given time at c instead of e, having de- scribed the curve ac by the com- "^ bined action of the two forces of projection, A b, and of gravitation, a b. By this, which may be called the " parallelogram offerees," the place of the moving body at the end of the given time may be determined, but neither the diagonal, nor the curve AG can be called a "resultant*' in the sense in which that term has been previously applied (70, 284). The line ae, representing the direction in which the force of projection alone would have carried the body, is a tangent to this curve at the point a. 308. But A e has been taken to represent t. v, and ab^J^. t* (302) ; also b o » a e ; therefore, Bc*=t»xi;«=g.<« xif7«=?^xAB; 2 o <7 whence (Hymers* Conic Sections, Art. 93^ the path of the body is a Parabola, of which the Axis, bein^ parallel to a b, is vertical. 309. If A be the space through which a body must fall freely from rest under the accelerating force of gravity, m order to acquire the velocity with which the body is projected from a, then (805) A = ^- ' and the preceding equation becomes bc'=4A'xab; and 4 h being thus the parameter at a, h is the distance of ▲ from the directrix of the parabola ; hence, The vdocUy of Projection i» that which a body would acquire hy faUing fredy from the directrix to the point o/ projection, 310. Let a be the inclination of the line of projection to a hori- Bontal plane ; then a is called the elevation of the projectile. As the velocity of the projectile in a horizontal direction is not a£fected by the accelerating force of gravity, it will remain con- stant ; let, therefore, the imtial velocity be resolved into two velo- cities (284) in the horizontal and vertical directions ; thus, v. cos a is the conetarU horizontal velocity, and v. sin a is the iniUal vertical velocity; in consequence of which the body will oon* KA.NOB OP A PBOJEOTXLB. 163 tmiie to rise above the horizontal plane, until the efiect of the aooelerotxng force of gnmiy has destroyed the vertical Yelocitj ; coBseqaentlj, the greatest height to which the body will ascend is equal to the space throagh which it most fall to acquire that Telocity, and this, since <=»- (305), is — (sin a)', or h (sin a)*. 311. Daring the time of flighty or the interval between the period of projection and the reium of the projectile to the same norizontaf piane, the initial vertical velocity will have been de- stroyed, and, since the body will have descended through the same vertical space throagh which it ascended, a vertical velocity downwards, equal to the initial vertical velocity upwards, will have been generated by gravitation ; therefore, the time offUght of a pro- jectile U twice the time of acquiring the initial vertical velocity by the action of gravity. Let this time be represented by T, then since generally < = -7. (2 73) m 2v . T= — sm a. y 312. The horizontal range of a projectile is the distance from the point of projection to the point where the projectile returns to the horizontal plane, and this is the space described daring the time of flight with the constant horizontal velocity (310); but generally e^t.v (270) and if in this case the range be repre- seoted by B, then, r» 2t7 . v*^ . «» . « £= — 8inaxi7.coea=:— 2 Binaxcosa = 2^. 8in2 a. ff . ^ . 313. The value of B just obtained will evidently be greatest, fin- the same value of A, when sin 2a is greatest, that is, when 2aB90®, and consequently, 0 = 45**; therefore, with a given velo- city of projection, the greatest horizontal range is obtiuned at an elevation of 46*. Also, any ranre ^^ less than the greatest may be ob- '^' tained at two difierent elevations, * A,ff . . 0 as in Fig. 218; for sin (90*'+2/3) ** a' 4.5 =a sin (90* — 2j8) ; consequently, whether we make the elevation 46'+ A or 45' -ft {B being any angle less than 45*) the range will be the same. This property is fre- ___^____.._ quently important m the art of c ^ gunnery, in enabling an olject, a, to be struck at the higher elevation, which would be protected from the lower, by an obitacle b o. H 2 164 DTXAMIC8. Tliese poinU may b« illustrated ezperimentallj by dischai^ging a bullet trom a tuoe furniBhed with a spiral spring, and trigger, and capable of being ac^usted to any angle of elevation, bj means of a vertical graduated arc. 314. In all tbese observations, the resistance of the medium in which the body under consideration moves, as well as the inter- ference produced by friction, have been neglected ; they fnmish, however, very important sources of opposition to the regularity of motion. Cceteris paribus^ the denser tne medium, the greater the opposition to the passage of the body moving through it ; and in the same medium the resistance opposed to the movement of the body is proportioned to the square of its velocity. It has been demonstrated by Newton, that when a spherical body moves iu a medium at^ rest, of equal density to itself, it loses half its motion before it has descrioed a space equal in length to twice its diameter. This resistance is a consequence of the molecular inertia of the medium, preventing the particles opposed to the moving body acquiring instantaneously a degree of movement cor- responding to that of the body. The atmospheric resistance is Bufncient to prevent projectiles describing a strictly accurate {)arabolic curve, as required by the theoretical considerations, and imits the ranj^e of the projectile in a remarkable degree. Accord- ing to Vega, it appears that a cannon-ball weighing four pounds, and which in vacuo would traverse 23,226 feet, will, when passing through the air, travel over only 6437 feet ; also a 24-pound shot discharged at an elevation of 45** with a velocity of 2000 feet per ¥ig, 219. second, would in vacuo reach (the hori- zontal distance of 125,000 feet, but the resistance of the air limits its range to 7300 feet. The curve actually described by a ijro- jectile in the atmospnere, when its resist- ance is taken into account, is not the parabolic curve, ▲ b, but a curve, a c i>, which continually approaches to a ver- tical asymptotet ef.* 316. Principle of the Rifie. — The resistance of the atmosphere not only retards the progress of a projectile, bnt also frequently causes it to deviate laterally from its course. If a ball be fired from a common gun, a rotation will probnbly be communicated to it, the plane of which will be determined by the last point of resistance to the exit of the ball. Let the ball, c d, be projected in the direction ▲ b, and let the plane of rotation coincide with that of the paper; " also, let the rotation of the ball be in the direction of the arrows, c, d. Then it is • See Wbewell's Dynamics, p. 180. ^ft^^'^m'^^r^rmi . , - m. • ■ — — ■ •* - — ■ ■■ ■ -jixj. BOTATIOV AND TBANBLATIOK. 1^ dear that the actual velocity of the side, o, of the ball will be greater than that of the side d, the former being the sum of the ▼elocities of projection and rotation, and the latter, their difference ; coneeouently, the ball will experience more resistance at c than at D, ana will therefore be deflected in its course towards n : and as both the direction and yelocitr of rotation are purely accidental, the direction and amonot of deflection of the ball are not deter- minable. To remedy this uncertainty, the barrel is rijledf that is, spiral grooTes are cut on its interior surface, by which a definite rotation is communicated to the ball in a plane perpendicular to the tine of projection ; this rotation has no effect in altering the comparative velocities of any two opposite points of the projectile, and consequently does not cause deflection. 316. The form of a body is found to influence considerably the amount of resistance ; thus, a projectile of given weight, with a S'ven velocity of projection, will have a much greater range if it i of a conical, or still belter, a parabolic, form, than if it be sphe- rical : this &ct has been applied in the construe- «^ ^, tion of the Mini^ ball, Fig. 221, which has also a canty in the wide end, as in the figure. The ad- vantage of the cavity is twofold ; first, the centre of gravity, g, is brought more forward, and the lighter portion of the mill acts like the shaft of the arrow, or the stick of the rocket, in steadying its motion ; secondly, the tlnn tubular pordon is more readily pressed into the grooves by the expansive force of the charge. 317. The flight of a rocket is a practical example of the resultant of two accelerating forces ; the path of the projectile is nearly straight, instead of being the parabolic curve resulting firom an impulsive projection. In point of fact, a Gongreve rocket is com- monlpr observed to deviate upwards in the latter part of its course ; this 10 due to the altered position of the centre of gravity (85), in eonsoquence of the exhaustion of the chaige, the stick then pre- ponderating more and more. 318. If a spherical body, a b, receive an impulse in the direction of a tine, dcb, passing thraugh its centre of gravity, c, all its parts Fig. 222. will move with equal velocity in a straight line. But if the force ap- plied do not act in the direction of a tine passing through the centre of gravity, uie particles of the body will possess unequal velocities, and* the whole mass wiU acquire a revolving or a rotatory motion, at the same time that it moves on- '^ wards under the influence of the apptied force. Thus, the earth is a body which revolves on its 166 DyxAHics. own axis, at the same time tbat it moves thron^h space ; and if these motions have been ac(|uired from a single impulse, it must have been exerted upon a point situated about 25 miles from a line passing through the geometric centre of the earth. The communication of a rotatoiy as well as a j^ro^ssive motion to a billiard-ball, hy means of a slightly eccentric impulse from the cue, is an artifice well known to billiard-plaverB. 319. As in the instance of the musket-ball already mentioned (315), so, whenever the progress of any portion of the surface of a moving body is more impeded than that of other parts of the surface, a rotatory move- "^' ^^' ment will ensue. This may be shown by placing a watch-glass, or convex lens, on * a smooth in- clined plane, Fig. 223, as a pane of glass ; having previously dipped the convexity of the watch- glass in water. Thus arranged, the glass, on sliding down the plane, will rapidly revolve around a vertical axis ; whereas, if the plane and glass be perfectly dry, it will slide down and reach the bottom of the inchned plane without revolving. This rotatory motion is explained by the adhesion produced by the drop of water, not being exactly the same on Ojpposite sides of the point on which the carved surmce rests. The side on which the adhesion is greatest is more retarded in its progress than the opposite side, and thus commefices the rotation round an axis passing through the point of contact, which continues, from the same cause, until the moving body reaches the bottom of the inclined plane. CEMTEIFDOAL FOBCB. 320. In consequence of the inertia of bodies causing them to persevere in rectilinear motion, it is found that when revolving in a circle they constantly endeavour to recede from the centre. This is termed the centrifugal or centre-flying force. If a ball affixed to a cord, c, be made to revolve rapidly in a circle, from a fixed point, s, as a centre, it will de- scribe the circle ▲ b d. If whilst rapidly moving the cord o be cut with a sharp knife, the inertia of the ball will cause it to continue in motion, not, however, in a circle, but in a right line corre- sponding to a tangent tc the circular path it described whilst the line o was entire. The force which caused ▲ to fly off in the direction of a tangent is the CBHTBIFUOAL TOKCB. 167 cadrifugpl or centre-flying force : and the cord c, represents the direction of a centripetal or centre-seeking force. Thus, consider- ing the circle to be composed of an infinite dumber of lines, the ball will tend to follow the direction of one of these lines, and msh off at a tangent to the curre. This circumstance, taking place the instant the force which binds a to the centre is overcome, shows that the centrifugal motion is the result of the tendency which bodies possess to move in rectilinear paths (282), and is not owing to the deTelopmeot of any new force. If a body moTO with a velocity, o, in a circle of which the radius is r, the general expression for the value of the force is, centrifugal force =— • The expression — may be put into a more convenient fonn if we call the anffular Telocity of the rotating body oi, then its linear velocity in its orbit will be <■» r ; the expression for the cen- w »r» trifngal force will therefore be , or t^r. 321. The truth of this proposition may be shown experimentally hy an apparatus called the whirling-table, Fig. 225. This con- FSg.226. sxsis of a horizontal frame, a b, to which are attached a wheel o d, and two small tables, b, f, each fixed parallel to the frame by means of three legs. Two rotating vertical axes pass up through * Eanitfaaw's Dymmies, p. 80. Koteley's Mechanical PrinoipleB, p. 123. 168 DTHJLiaOB. the centres of theie tables, underneath which pulleys are fixed on the axes, and to these rotation is communicated by a cord, bod, passing round them Imd the wheel. Two pulleys, o, h, are usually fixed on each axis, the diameter of one being aouble that of the other, and the diameter of the corresponding pulleys on the two axes being exactly equal. By means of these the axes may be made to rotate either with equal angular yelocities, or with Kuch that one angular velocity is exactly double the other. A frame is attached to each of the axes, so constructed that a weight, k, sliding on wire guides, may, wlien it has acquired sufficient centrifugal force, draw up by means of a string a weight, l, en* closed in a circular cage, concentric with the axis of revolution. One only of these frames is represented in the figure, the screw at the end of the axis to which the other may be attached being visible at e. If now equal weights be placed at k and x', and at L and l' (k', l' being the corresponding weights in the other frame), and the distances of k, k' from the centres of motion be exactly equal, it will be found that, when put in rotation, they will at the same instant acquire sufficient centrifugal force to draw up l and l'. It* now the weight k be placed at double its former cUstanoe from the axis of motion, and the weight l be doubled, or, more generally, if the distance of k from the axis and the weight l be either increased or diminished in the same proportion^ it will be found that the two weights, l, l', will still be raised at the same instant : thus showing that when the angular velocity remains constant, the centrifugal force of a given weight will vaiy as its radial distance from the axis of motion. Again, let the cord be placed over the smaller pulley at h, so that the angular velocity of x may be double that of x', and let the distances of x and x' from their respective axes of motion be eqnal. It will now be found that when the weight l is Quadrupled, it will be raised at the same time as l' ; that is, when tne angular velocities are as 2 : 1, the centri- fugal forces are as 4, or 2^:1, the radius remaining constant ; and if the an^lar velocity of x were increased or diminished in any other ratio, l being at the same time increased or diminished in the square of that ratio, the weights l and l' would be raised simultaneously: hence it appears that the centrifugal force of a mass m will be , 822. It may likewise be shown, by means of the whirling-table, J. 2«ii ^^^^ ^^^ connected bodies will '^' rotate round each other, if the C A B D axis of rotation pass through f>— O- - QJ f) their common centre of gravity. / \ / \ Let two spheres, i, b, be connected JL> g (jjv bjr a small tube, through which a > r< wire, c, passes, which is kept ^ ^ tense and parallel to a bar of tbs oommoa oenira of gnntj of a and b ba marked oa the Alwlrt the bftT, bf, be atUcbed to ana of the n*oInag ■___ ... ill middle point, lo that the «Hrs, o d, maj reTolte in ■ tunixontiJ plane. It willnowbefboadthatifthepoiDt abenudetoaoiDdde vfth the aiia of rotstioD, tbe cantrifog^ forceii of the two Iradiea will be sqiia], uid the; vill cootiiiae to rotate rouiid each other ; bat if the point o be displaced on either aide of the axis of roU- tion, the nyalem vill, vhen rotated, Sj off in the ume direction. This would foUow as an immediate dedoction from the expns- ROD giTen above for the centrifagsl force ; fbr if m and m' are the tDssaes of the two bodieg, and rand f' the distances of their centres of grsTitj &oni tbe axis of rotation, then, their angular Telocitiea baing the sanH, we have, if thair centrifugal forces are equal, or, m.r = TO'.r'; therefore (85) the centre of graTiCr lies in the axia of rotation. 333. We see magniScent examples of this force in the revolution of the spheres of nor nniierse. The earth and ntber planpta re- nrire roand the sun as a centre, with sDonaoDa velocity, eTerywbere tending to rush off into infinite space in the direction of a tAUgent to their elliptic orbits, and prevented onlv by an equsUj powerful oantripetat force, the grantative attraction of the sun. Equally balanoed between theaa opposing forces, the elenMnts of our uiu- verae faave rarolTed for myriads of sgei around the great centre of SOT sjatem, presenting a wonderfuT spectacle of infinite wiadom and urmooy. 324. The form of our own globe presents a remarkable instance of the e&eots of this force, from its revolving on its own axis at the Tate of 135 miles in a minute at the equator. An ener^tic cen- trifugal force is generated at the eqoatorial parts, by which, at an FIg.lX!. :s 17 miles Krester than its polar diameter. This alteration in Bgore admit* of anesay ■Qoatration, by rapidly revolving two elastic iron hoope placed transvaraelj. These are fixed to the iron axis at i, and are loose at B ; OD tomiag the handle c, so as to rotate them rapidly, the moveable ends of the j hoopa wQt nse up the axis to d, and will bulge oat at the sides. Thus repreeentiDK tbe figure of a holtow Satteneu spheroiiC ■0 long as the rapid motion continues; wlien thia ceuei, the looae psripheriea oT tho hoopi will d«K«ad and regsin their oripnal fiRnra. On ftccoont of the eiceu of the eqaatonsl aboTe the polar diameUr of the earth, bodies wei^ Ion at the eqaalorlhanat thapolea: JOOOpoands at tho latter corra- ■pondinff to 996 at the equator, from the diminiahed fotw ot grantjTSS). The projection of a atone by a aling ; the iparka from a grinder't wheel ; the aoattaring of dropa of water from tlie wet reTdvii^ camage wheel, or honaemajd ■ mop ; are so awar fatailiar eiaiii~ plea of the action of centrifugal force. S35. A lorther illiutratioD of this force will be roond in the Xa,^. fiwmaMon of the pluiet Saturn's ring. The formation of aa annaliu by the acUon <^ oentrifngal force may lie thm oonfeiiteDtlk. „;i — II ■-offfromtha OHCIU^nON OF £ PAMICUI. sphere, the velooity acquired ia tha sl_. as that which woold be acquired by the I body falling freely through tbe hwght ot I the plaoe. Let A B, Fig. 229, be an inclined plane, no its base, and AC its height, draw OD I ptrpendicnlar to ab. Let the vertical line, A c, be taken to represent tbe force of graTi^ ; this may be resolred into two, a d in the directiaD of the plane, and d c perpendicular to it, of which d a can have no eflect in moviog the Iwdy along the plane i ai> therefore repre. ssnta the efiective portion of the force of gravity. But bf ainulai triangle*, therefore a d cb a o x ▲ B' and die effective force of gravity on the inclined plane is ^ x MOnOS OV CDBYE8. 171 ▲ 0 L tne inclined plane is ^ x Bat since generally v^=2g^ (305), A C (velocity)* acqnireddown abs2^x — xab^ A B «2^XAC = (velocity)' acquired down Ao; or, as it Lb commonly exprossed, the vdodJty acquired hff a body in daeending an ineUnea plane is thait due to the height of the pUme, ^ 327. When a body nnoppoeed hv friction, or resutance of the air, descends a series of superposed inclined planes, the velocity acquired by it is equal to that which would be acquired in fiJIing through tlie vertical height of the series, as in the case of a sinrie niane (326) ; supposing that no motion be lost by concussion of the tiody in passing from one plane to another. Let ABCO represent tne planes, and let do and ob be pro* dnoed until thev meet ab in o and e. The velocity acquired by a body falling from a to b is equal to that which it would acquire in Calling from g to b, for the planes, «. ^3^ AB, o b, nave the same perpendicular ^* height ; and when this is the case with any two planes^ the velocities acquired in falling down their whole lengths aze eqnal, as the acquired velocity has been shown to depend on the height of the plane alone. The body bavmg reached b,- will descend b o with the same velocitv^ whether it &11 down A B or o B ; toen the velocity acquired at o will be the same, whether the body fall down gbc or Bc; and finally, it will pass down to d with the same velocity as if it had descended directly from b. The same reasoning will apply to bodies falling down curves, for their figures may be considered as made up of an infinite series of planes : hence, Jf a body descend hy gravity along a smooth continuous curve situated in a vertical plane, its velocity at any point will be the sasne as if it hadfaUenfredu through the same vertical space. 328. All bodies free from oostaoles will »^ 231 have their motion as much accelerated, whilst descending, as retarded, whilst as- cending a curve. Let gab be a curve, and a ball be placed at c, the attraction of gravitation will cause it to descend to IT! a; U thU motiaii it will uqnira ui unoimt of monentum (STG) ntkient to c»nj it onwardi to a point, b, at tho auae height (Mgtecting friction uid resiatuice) aa a abore the horitonlai pUn^ from which point it will descend by graritj to a, and the m thus guiented will carry it onwaids to c ; it will aguD ~. w ., «nd ao on, oscillaling from o to b, nntil opposing caoaoa tang It to a aUle of rest. The whole time of awwol to b or c will be eqaal to the time of descent to A, tu the velocitiea at oao&l ahituds" wiU be aqnal. ^ 829. For the pnrpoee of caoBing the bodj to move in a curved path with aa little reiiatance aa poasible, it may be altioW lo ■ au»- pended wire or rtriog, and then pormittad lo oacillate ; u ingtm- ment thus conalraoted ia tenned Aptndulum. Thia, theoraticatlv considered, consist* of a heavy particle suapended bj a tHramd, unacted upon by anj opporingor reaiating foroes. If ihe Wl t- Fiff, 233, be raised to i and allowed ^-'^ toM, itpaaaea through c to BJD the manner alreail; described, and the / '\ whole movement afthe bill lirom a to B, oi B to a, ia termed an 04eiUatiim ; from * to c, its moremeut ia termed the deecendinr, and Ironi c lo b ita ascending Hmt-osctUoJ ion. The diir tance t a, measured in degrees, is termed the amplUwU of an oadtla- tion; and the auralion of an oscilla- tion is the time required lo effect thia ~ moTement from A to B, or rics serafi . 33(1. 7%e Cydmd.—Tbia oune is described by a tracing point in the circumfereaoe of ■ circular diec, which la rolled along ■ straight edge laid on a sheet of paper. Let c a e, Fig. 233, bo a Ki ea. cycloid, described by rolling • circle, of ^' which the diametena A B along the line Ice: it has this remarkable properly, that if we produce a b to ■, making BB-AB, and through ■ draw omd equal and parallel to ce, and on db, Ei{ describe two semi -cycloids, bc, bc, equal to c a, a c, then a tracing point at the end of a string unwound from b c will describe 0 A ; and simiUrir, wiU de- scribe AC as it is wound ufon ic; consequentlj, if tbe cnnre* c^ Be be placed in a vertical plane, and a heavy panicle, r, occupy the place of tbe tracing point, it will oacillate in the Cjcloid, C AC* Anouier important property of the i^oloid is that if we take * For ■ noof of thli, ind ottanr sooimoii prapcrtlBi at Ib« crgtotd, ••• Bjtata; lodhBDlwX or *>>r •taodird treufaeoathe DiSknatiil Cslsalaa. Lrtc the !« , . Tcrtical, and iW bme, BC, iori... . Let 1. bo the point froni whicli the body b^ns to descend ; then ihe time complete OKilUtioD, vluch ii the bu tbo time« of the deBcendingond &Bcend- ing MtDi-occillationi |339), ii equal to I ■ ■ » the time of dencandinc ihroagh Divide L A into Tary Bmall prntBiOfi Di»w the borizoDtal lines, L Kmidrcle, calling th, un ia «, n; jom An, bid, tuid Ant, sn, cnttiDg eacfa olber in o. Then since v, the Telocltj at ii, ii the nme u that soquired in Uliog throagh »t (327), t= yjpxat: •nd if X ■ be supposed so ■mall tbat the Telodtj acquired in poss- mg tbroDgh H n may be neglected, compared vith the Telodty at K, or, in other ward*, that &e velocity may be considered onifono throng KH, then since generally (~ — (270), the time of moving throorii m a =—, — • . 3, the chords ... .a iolenect the geeerating circle de- scribed on the diameter, a b, ore respectively eqaal to %/abxat, and ^ a b >f a u ; and as the an» A K, an, are respectivelydonble the length of these chorda, m « moat be doable their diSbrence, or H s = 2 {v^iT.ri^- y nrr^= 2 yA B c /* T - ^'A o) i hence the time o[ moving throngh h ■ _VAB(yAT-y>p) 2AB yAT-^AI 174 DTHAMICH. 2a»x!!L£ ultimately,. ~V 9 g Bw because as m h is diminisbed, a o n approaches a rigbt angle, and tbe yalne of ▲ m— ▲ n approaches m o. Bnt^^=sin f»&o,=arc subtending the angle msn, ulti- Rfn natelj, because as the angle is diminished, the arc and sine approach equality ; consequently the time of moving from v to h X arc subtending the angle m b n : and as the same 9 may be prored for the time of moving through each of the other small portions into which l A is divided, the sum of the times, or the time of moving through the arc l a ^(the sum of tbe arcs subtending the small angles m b n), 9 2ab t. 9 2 = / -^ (arc subtending the right angle a b l), = / ■ /2ab Hence the time of making a complete oscillation =ir./ —- , and as the point l is arbitrary, it follows that the times of descent from all pomts of the curve to A are equal, and consequently that all oscillations in a cycloid are uochronous^ or performed in equal times. Since a b = b b, Fig. 233, a e the length of the pendulum = 2 a b ; calling this l, and the time of a complete oscillation t, we obtain •=v^ L and g being numerically expressed in parts of a foot. 332. Oscillations in a true cycloidal arc are practically unattain- able, but a small arc of the cycloid, of which a is the middle point, coincides very nearly with a circular arc described round the centre e with* the radius e a (Fig. 233) : and therefore the time of an oscillation in a small circular arc coincides with the above formula for the time in a cprcloidal arc. As, however, the cycloid c A c, must evidently lie within the circle described by the radius E A, because straignt lines joining the points e p, e c, must be shorter than the curved lines e f p, e f c, it follows that the time of an oscillation in a lai^ circular arc, will be greater than that in a corresponding cycloidal arc, that is, greater than that in a small circular arc. If we take unity ap the time of an oscillation APFUOXTIOHS OF THI PBXD0LUM. 176 in an indefinitely small circular arc, then the times of osdllationa in Uoger arcs will be as follows :* In an arc of 2* the time is 1*00003 „ 6" „ 100012 „ 10» „ 100190 „ 15' „ 100426 „ 36' „ 101676 833. Since t=w^-- -y-x v^l, and x=531416 nearly, an4 ^ in the latitude of Greenwich « 32*19 feet nearlj, therefore ; -^=0-66372; hence in order to determine the time required for a pendnlam of an J given length to complete an oscillation in the latitude of Greenwich, it is only necessary to take the square root of the length of the pendmnm computed in feet, and to multiply this result hj the decimal 0*65372. Thus, if the pendulum were nine feet in length, it would perform an oscillation in 1*66 seconds, for V^9x 0-66372 =1*66116. . Also T*=ir*x-, consequently l=^,xt*, but •^=8*2616 in the latitade of Greenwich, therefore, in order to ascertain the length of a pendulum which is required to perform a vibration in a given time, in this latitude, we have only to multiply the square of the number of seconds bjr the number 3*2616, and the jproduct will be the required length in feet. Thus, if it be required to find the length of a pendulum beating double seconds, Ls2*x 3*261 6s 130464 feet=:13 ft. ) in. nearly. ^ 834. Let L and l' be the lengths of two pendulums, and t,'!' the times of their oscillations in equal arcs, then TIT':: * X yL: ' X v^L', : : ^l : -/l'; that is, in a given latitude, the time of oidUation of a pendulum ii propcrtionid to the square root of tie len^h. And as the number of oscillations in a given time is inversely as the duration of each, it follows that in a given latitude the number of oscillations of a pendulum in a given time is inversely proportional to the square root of its length. 336. As the movements of the pendulum depend upon gravita- • -v| { ^ -(i) ^( j-;j)*(A)'H^.)'(k)'-*- }. I fa the vctsed >iae of the mad^ito of mcmation. -Baimliaw's Dj- p. 127. 176 DTVAMICS. tion, and as this force decreases in intensitj as we recede from the earth*B centre in the proportion of the inverse square of the distance from that point (31), this instrument forms a most valuable mode of determining the intensitj of gravity, and consequently, the distance of the surface of the earth from the centre, m different parts of the globe. This is done either by ascertaining the time required to complete the oscillation of a standard pendulum : or, the length of a pendulum requisite to complete an oscillation in a given time. The length of a pendulum required to vibrate seconds in the latitude of Greenwich is 39'1393 inches » 32616 feet. ir«L Since T=ir\/—,^ = ^ — j-, consequently in the latitude of Greenwich, ^s (31416)' x 32616 £9et=32'19 feet, nearly. 336. Let T and t' be the times of oscillation of a given pendu- lum, and g, ^ the accelerating forces of gravity at two given points of the earth's surface, then _. wVl irv'L 1 1 Let B, b' be the radii of the earth, at the two given points, then smce we obtain . • »___ • * It ' VT therefor© t:t'::e:r'; hence the radial dUtancea of any two poitUs of the earih\B surface from its centre are to each other as the times cfvihrattcn of an invariable pendulum at those points. Having then determined the radius at any one point by actual measurement of a known arc of the meridian, any other radius may be found by a simple pro- portion. . ^ . ^ ., 337. In practice, however, it is more easy to measure the length of a pendulum vibrating in a given time, in one second, for example, than to maintain the length of a pendulum absolutely invanable. Since then g=v*J. generally, when t=1, the values of g may b© readily found when the values of l are known. The following are the resulte of some measurements of the seconds pendulum, at different parts of the world : — FUoe. LatAtnde. iValne of l. Obterren. Spitsbergen . Leith . . . Loudon . . Jamaica . . Ascension . Sierra Leone 76' 49* 6S" N. 66" 68' 41" N. 5V 31' 08" N. 17* 66' 07" N. 7* 66' 48" S. 8' 29' 28" N. 39*21464 3916640 3913908 3903608 3902406 39*01964 Gen. Sabine. Capt. Kater. Do. Gen. Sabine. Do. Do. A* «n example of the Die of Ihia table, mppoM that the force of grsTity at Sierra Leone U reonired ; at thii place Oeoeral Sabine hse detenoiiieil the Talus of l to be S9'019M iochei, con- Mqnently, by logarithnu, Slog)r.0OT430 hg L- 1-59136 tbair Bom = 2-56663 - log SS6-1, ccrreapondiiig coDBeqaeDtlr to 3851 iDcboB, which will be the tetodt; acquired by a bodj falliug freely doling one wcond at Sierra Leone. findtht -_ Let B be the particle nupended Iram A., and let a B ^ a, and B the angle conluned between b a. and the Teriical AC; m the maw of b, and ( the teniiion of the euEpennoa A a ; then the tanlion t wouM prodnce dd m an accelerating Ibne = — in g force. ThiB foite may be reaolTod into two, - sia 9 in the direction a c, and — coa S, acting vertically iipwardi ; bnt unce by 3=icc«9. (I) Tha oentrifngal fbrce of a body moring vith a nlocity v circle whose raJioaiirii ~(320}, andiatliiecaaeiB — ,or — , But from (I) Laae therefore >^, whence «• ,''-I'(""^',and Batdnct ithe motion of B ie tini motion,! -- (210), hera '"v coee" lifomi, and geuerally in uniform time of rsTolutJQn drcomftrence S ir .a /^. V "-9 - - -J a COB S- Since tbii remit depends < t of a revohdwa of ' •rUth vikaXeBerbt Oie length of the lutpetuioH, provided the aUitiuie of tie cone Ttmaat the tame. This m*f be ihown eiperimentallT bj ittiching three or faar htiXi t)y wireg of different lengths to the top of i veiiickl rotatiDg uia : when the vhole ia mule to ralste wilh ■ufBcwnt ra)Hdit7, it will bo ab*enr«d that the balls will be all in th« wme horiioDlal SS0. Thii i« one of the important principles tfaat are freqnentlj fonadto be of great aerrice in the iiolution of d.vnamical queslioaa ; it may be thui enunciated. If the forces impreutd on the Mrersl paita of a ijiitem, howaoever related, be each reaolred into two others, ono of which is effective, uid the other, fiom the given condilioni, wholl; ineffective, then the ineffective reaolved ^irvea would, if acting on the avetem alone, pradace equilibrium. Thii will perhapa be better understood hj a aimple "t- **■ illuitration._ Let * D be a parallelognun ; Ithco (TO) if two preasarea mpreaenled in magnitade and direction hj A B, ac, actoD a lodj at A, their resultant will bia represented in magnitude and direction b? ad; coune. qaenll;, the effective parts of both preainres maat act in that direction. Draw be, cr, perpendicular to A D, then the resolved puis AP, AC, of the preaaurcB ab, Ao, are wholly effective, ajid their sum is AD, since a ■'"E d; also, the rcaolved parts, s b, pc, are wholly ineffective, being perpendicular to the direction of th« re. auttant ; thej are also equal, and in opposite directions, and would thpreforo, if acting alone, produce equilibrium. n't ^--iplemay othenriiO be atated thus : — If theefleo- ceiofthese ' - ' tive accelerating force* of the several parts of a connected aysteiu b« applied to them in direciione contrary to those in whic' " act, tbey will, lopether with the impressed accelerating satisfy die statical coodiiiona of equilibrium. This mode prMsion is eridsntly the aatne in effect aa tha fonner. 179 PRINCIPLE OP THE GOKSEItVATlOX OP VIS VIVA. 340. The vis vi?a of a body in motion is the product of its mass and the square of its velocitjr ; or since (275) w - ^ x m, VIS viva = — v*. 9 If the force of a body in motion be measared by the whole effect which it will produce before the velocity is destroyed, or by the whole e£Ebrt that has been employed in generating that velocity, without regard to .the time, it must be measured by the product of the mass and the velocity*. Thus, balls of the same sisse, pro- jected into a dense resisting medium, as a bank of moist clay, will penetrate to the same depth, provided the product of their weights and the squares of their velocities is the same. Force, thus mea- sured, is called vis viva, in contradistinction to force measured by miimentum, which is proportional to the pressure, or dead puu^ producing it. The principle in question is this: — If the jparticUs componng a 9^tkm m any measure connected or constrained in their motions^ or otherwUe, he acted on by arCy continuous forceSf then the change of vis viva of the system, in passing from one given position to (mother^ is the same as if the connexions of the system had been ditsoHvedf and each part of iJie system had been suffered to move frtdyfrom its former to Us latter position, Ml. When a system of bodies iu motion passes through a posi- tion of stable equilibrium, the vis viva will be a maximum at that point; and if tnrough a position of unstable equilibrium, the vis viva will then be a minimum. This is evident, since it appears (98) that the centre of gravity occupies the lowest point of its patD in a position of stable equilibrium ; the centre of gravity must therefore descend in approaching this point, and the vis viva will be aagmented by the accelerating force of gravity; but after passing it, gravitation will tend to diminish the vis viva, which must therefore have had a maximum value at the point of stable equilibrium. Similarly, in a position of unstable equilibrium, the centre of gravity occupies the highest point of its path; conse- quently, gravitation will tend to diminish the vis viva before reaching, and to augment it after the system has passed the posi- tion of unstable equilibrium ; the vis viva will therefore have a minimum value in that position. .Thus, for example, the vis viva of a moving pendulum is greatest at the lowest point of its oscil- lation ; and if a pyramid resting on its base were overturned by a horizontal thrust against the upper part, the vis viva of the moving pyramid would be a minimum, when, its centre of gravity reaches a vertical plane passing through the edge on which the pyramid id turning. In respect to rotating bodies it may be shown that the vis viva N 2 180 DTHAMICB. due to rotation U equal to the moment of inertia (846) of , cm ' cm and the effective moving forces are these quantities multiplied by the masses of the corresponding particles, or f.m, /•"•'"', fP'^P; cm cm also c m, c ft, c^, are perpendicular to the directions of these forces, and therefore their moments round c are the products of these moving forces and corresponding perpendiculars, namely, f.m.cm, /•»•'"'*, fP-^J^; cm cm but the impressed moving forces are the weights of the particles, or flr.wi, g.Uy g,py and the moments of these round c are (77), g.m.cmy ^.n.cn, g.p.Gp\ but by D*Alembert*s principle (339), the sum of the moments of the impressed forces = the sum of the moments of the effective forces, therefore f ,m,cm-t^- +*—^ *- ^g,m.cm+g,n,cn+g,p,cp. cm cm*' " if f jTi whence .cm,g(mcm-^ncn^p.cp) m . c m' + n . c n' + j> . c j?" and the form of the expression would be the same, whatever number CBXTBE OF OSCILLATIOX. 183 ef particles we assume. Bat m.Cfn+n.ci» + &c. has been repre- sented by S (m .cm) and it has been shown (86) that S (m . cm) B c o . 2 (m), and m.cm' + ».cn' + &c.= S(m.cm') ; therefore y^cm. cg .y. 2 W (1) •^ 2(m.cm«) ^ ' 347. The Centre of OeciUation. — Let it be now required to find a point in the system, that will be accelerated exactly as much as if the system consisted of that point alone. Let o, a point in C6 produced, be the required point ; then substituting o mr m in (1), we shall have 1 1- r co.co.fl.S (m) . accelerating force on o= — =-; — — i\ » £ (m . c m ) but if the system consisted of the point o alone, then accelerating force ono = g: therefore equating these values according to the supposition, co.oo.^.2(m) ^ S(m.cm«) ' whence S (m.cm')=co.oo.S(m), ^ _- r(m.cm*) /ON c o . 2 \tn) The point o is called the eeiUre of oscillation of the system, because the accelerating force on that point being the same as if the whole mass of the system were collected there, it follows that an oscillation of the system will take place in the same time as that of a simple pendulum of the lengtn c o. 348. Join Qm,aiiif op, Fig. 237, then by the property of the triangle, we have cm* = co' + om' + 2co.od, similarly on' = co*+om*— 2co.oe, &c. multiplying these equations hj m, n, &c. respectively, and then adding them together, we obtam S(m . c m*) = c o*.S(m) + 2 (m . o to') + 2 c o (m . o d - « . o e + &c.); but since o is the centre of gravity, therefore (86) m . o c2— n . o e + &c. s o, whence it follows that 2(m.cm')=2(m.om*)+co*.2(m), (3) that is, the moment of inertia of a system about any point c is equal to its moment of inertia about the centre of gravity added to the moment of inertia t^tout c of the whole system coUeeted at its centre of gravity, OoroQary. Since co*. 2(m) must always have a positive value, it follows tliat the value of 2 (m . c m') in (3) will be a 184 DTHAlflGB. immmiMK, when cosO, henco the moment of inertia of a tyHem about an axie paseing through the centre of gravity ^ is lew than it would he about any other parallel axis. 349. If we call 2 (m) or tne aggrogato masa of the flystem, m, then a distance h may be found (depending on the form of the system] such that m . A;* =» S (m . o m*), then ib is called the radiue of gyration of the system : for the rota- tion of the system is precisely the same as it would be if all its material particles were collected in the circumference of a' circle of whicn h is the radios. If these ralues of S (m .urn'), and 2 (m) be substituted in (3), this equation becomes 2 (m . 0 m') = Jfc* . M + c G* . M ; and if this value of 2 (m . o m*) be substituted in the equation (2), we shall obtain ^^ M^ + M.CO* C O OB _ - M.CG therefore CO co»co=sGO=s — , or CQ.oosAr: CO from which it appears that the jwinte c and o may he interchanged, that is, if o be the centre of oscillation when o is the point of sus- pension, then 0 will be the centre of oscillation when o is the point of suspension. 350. The above relation of reciprocity between the points c and o is the principle of construction of a very ingenious instrument, jl^ 2j^ Kater'e Pendulum, which has been employed in deter- '^* ' mining the absolute length of a seconds pendulum. It follows from this property of reciprocity, that if a pen- dulum have two fixed centres of suspension, and a weight or weights be so adjusted upon it, that it will oscillate in exactly the same time on either centre, then the centres must corren>ond to the points c and o, and the distance between them will be exactly the eouivalent length of a simple pendulum, oscillating in we same ^ ^ time as the compound pendulum actually oscillates. (Zj9 ' The following is the construction of Eater's Pendu- ]l lum. A brass bar, c n, Fig. 238, is.'fumished with two ■ transverse axes passing perpendicularly through it at the points c, o; these consist of triangular stoel bars, or, as they are commonly called, hnife-edgee, similar to those on which a balance of fpood construction is usually supported. Besides the principal weight, d, there are two aclJUBtable sliding weights, b p, of which the lai^;er, By is near to c, and the smaller, f, in an intermediate CBKTSB OP PBSCtJOSIOH. 185 podtion. In aoing this instrament, it is made to oficillate Alter- nately on the edges c and o, and the times of oscillation r3ndered nearW eqaalbr utering thepoBition of the heavier sliding weight, B. omail £flerences of the times of oscillation are then corrected bj acynating the smaller vreight, f, which is to he moved a little towardt ^e axis about which the number of oscillations is gretUest in a given tune. The number of oscillations was d*itermined by placing the pendalum in front of a clock pendulum oscillating in nearly the same time, and obserying the intervals at which the motion of the two pendulums coincided.* It is not essential to the correctness of the result thus obtained, that the centres of motion should present very fine knife-edges ; for if the axes of motion, c, o, were cylinders with equal radii, the distance between their opposed sur&ces would still correctly lepreeent the length of the ^mchronous simple pendulum.'f 351. Tke Centre of Terevaeion. — If a body, moveable about a fixed axis, be struck in a direction perpendicular to the plane passing through the axis of motion, and its centre of gravity, then the centre of percossioo is that point at which the impact mnst take place, in oroer that it may produce no pressure on the axis. This point is identical with the centre of oscillation (347), for as the acceleration of this point is the same as that of the entire mass of the body, it IS dear that the vis viva of the body, when moving, will be the same as if the mass were collected at the centre of oscillation : the vis viva, or dynamical force of the body, may be therefore sup- posed to be concentrated at the centre of oscillation, just as the statical pressure is in effect concentrated at the centre of gravity, ukl can be counteracted only by a force applied at the same point in an opposite direction. If a force acting in the same direction be applied at any other point, it will be expended partly in oppos- ing me vis viva of the moing body, and partly in producing pres- sure on the axis. And the same will be true with regard to any impressed force, as a blow, if the body be at rest. AJso^ if a body moveable about a centre strike another body at the centre of percussion, the whole accumulated work (343) is effective upon the body struck, but if the impact take place at any other point, the accumulated work is partly expended in producing pressure on the axis, and the blow is therefore less/om^Ie. The centre of oscillation of a rod suspended by one extremity is two- thirds of its length from the point of suspension ; consequently, if one end of a bar of wood of uniform thickness be held in the hand, it will strike the hardest blow at two-thirds of its length — pro- vided it is moved from the wrist, not from the shoulder, in which case the point will be differently situated ; and if a fixed obstacle be struck by the rod at any other point, pressure on the axis will • For (brther information on this sabjeot, see Capt. Eater's aoooont of tbe prooeM,- la Pbil. Trans, for 1818, p. 88. t irbmU, Dynamin, p. 888. Pratt^ Meeh. Philosophy, p. 408. 166 be rendered STident b; an nnpIeuiaTit jar upon the hand, wbich will JDcreatw with the dintance of the point of impact rrom the centre of pcrousBion. Tliia fact i« well known to cricks tplajers, wlieoETOr the bail ii not iitnick by the bat at the ri^t poiui. 352. The centre of oecillation or percnssion of a circDlar disc of uniform thicknesB, oacillaCin); in its own plane abont ■ point in the circumrerencc, ii a point in the diameter distant j of the diameler from the point of BuspesBioD ; and if the disc oKillate about ■ tdngent, the diBtance u | of the diameter. Tbia may be readily ohown by BuBpending a small heavy ball by a string of the len^h above nUted, in front of the disc in the former case, and b; the aide of it in the latter, wheu the disc and Btriog will be obierved to OBcillite in tlie name tima. S&3. Tlie centre of oscillation of any imgnlar body nay be determined experimental]; b; ascertaimng the length of a simple pendulum that will oacilhite in the sBine time ; it being remembered that the centres of en>pens!on, of gravity, and of Caciliation, or percnssion, vill always be in the same straight line. 354. As all bodies are acted upon by changes of lemperatnre, so that their length btrcomes altered, it is of extreme importance to have a pendulum constructed in such a manner, as to be unaffected by such changea. Several modes have been proposed lo effect ao desirable bq olg'ect ; of theae, the plan formerly most uauallj adopted was the well-known gridiron-pendulum, composed of two metalu, bo armnged that the eipimsion of the one counterbalance! that nf the other. In ita Bimplest fonn, this contrivance cooaists of a parallelogram of steel, ABoa, fixed to the Fig. 136. rod, K, by which the whole pendulum ia suapeuded. The braai ivd, F a, bent twice at right angles, is fixed by its lower ends to the trwuvene oieoe, C D ; and to the upper part of r O, the stonl rod supporting the ball of the pendolnln is affixed, wbich pasaes through a bole in the transveraa piece o D. It is obvioui, that as a brass rod expands much more in length than a steel rod by equal eleva- tions of temperature, in the proportion of 0-00193 to O'OOlltl, if the length of the sleel and brass ban be properly a^osled, when any elevation of tem- perature takes place, the increase in length of the steel ban, together with the snspendiDg rods, will be completely counteracted by the excess of the expansion of the braaa bars in the opposite direc- tion. The Importance of an arrangement ot this kind is snfBciently obvious, as an alteratioD of 30* of temperature, trould, by affecting the length of a simple pendulnm with an iron rod, inlro- dnce an error of eight seconds in twenty-foni oT stcet mnd bna> rodi, the fbllmrmg plaD has met with much ftTonr uiongst Continentml cbcknukera. The coDipenuted pen- dalatn, Fig. 340, coasislsora Keel rod,e, cUiuped FI^.UO. at the upper end to two bnw rodi, b>, all of which paai throoRh the upper port of the drcalar weight, or bob, which hu a caiitj at its cent The gtael rod, s, has a bent cnMs-piece at its Ion end, to which two ebort Ibtbh are jointed at ud c. The lower ends of the brow rode, b, b, rcK on the iiuer eitremitiea of these lever while the bob reste on the outer, by meaua of t* pioi, D, m. It ii endent that as the inner eD< of the leien are depreued hj the exceu of eipuiaion of the brara rods, the pointa, d, ■ will he railed; and the amount of elenUdon of the bob, required to compensate the eipaneion of the iteel rod, ma; be obtained b; B Rotable adJuBtmeut of the emu of the leven. In the preienl construction of English aatronomical clocka and i^nlatora, the mercuria! pendulum is uniTersally adopted. This couiita of a iteel itid, connected at ita lower end with an iron or glsM TSBsel ooDtsiniDE mercnry, a abort colamn of which, hj the great excess of its hnesr eipanajon abore that of sl«el, com- pensates for the whole length of the steel rod. 356. A correction of the errors of a pendulum anMug Iron that duage of length which is due lo change of temperatup' ■- — ' hownref, all that ii i^---—' '— ■' - - = ' • ancB of an astranomic that the time of oacillation in a circular arc ii inoeaees with the amplitude of the arc, which depends upon the amount of accelerating force transmitted U> the pendulum. Thia fince is subject to minute Tariations, owing to theraryins amoont of friction between the contact surfacrs of the icape-wbeel and pallets (22S}, &nm dust, naciditr of oil, &c. ; and as these sources of error are quite indefinite, a satinfacCorj method of equalising the amplitade of the arcs of libratlon has long been an acknow- ledged derideratom in horologj. This, however, has been in^ nieoal; snpplied by Mr. Loseby. A loop of balance-spring wire, tbout three inches in diameter, ia Eied in front of the penanlum, the plane of the loop betni( parallel to the plane of oscillatioD. A pb attached to the pendnluni elongates this loop towards the eibeme of its eicnraion, and it Is endeat, that the more the loop is elongated, the more its elasticity will accelerate the recoil of the {nndalam, and therefore tend to diminish the time of oscilla- tion in huger arcs. The magnitude and podtioo of the loop must ise of conrM beniiitleniof oiperiment; bnt, wh on carefully »4)'i"*e<'. it hat been found, that evea doubling the clock-weight produced a TBTj amsll vsriation of the rate. 367. While diiciiHiag the aubject of OHcilUtioni, it rDa|r not be nnintoreating to our renders to iDTeallgale a, piublem which com- inftDdad n much laipir ahtre of public attention Ibiin, perhaps, it iras entitled to, nnmely, the rotalion of the plaae of OKiUation of the pendnlom. . If a heavj ball be anspended from a conaidenble altitude, ao RB to oscillate Teij ilovly, and cnnaequentlj, to con- tinue itg oacillntlntin for a conaiderable length nf time, it ii obserred that the plane, io which the pandiilum iscilbitei, will graduall; rotate on a vertical line drawn throuefa the P"int of inspeniion aa an axis. This hai hfta anpposed to afford an independent proDf of (he rotation of the earth, and it will preaentljbe ahown that the time of a complete rotation of the plane of the pendalaia will varr from the exact length of a dav at the pole, to a period of indefinite dnratioD at the equator. The eipprimenl ie, however, an unialiHfaetoiy one. The diflicnlties of mechanical adjaitment are vet7 great. Jt ia indiepenaable that while the pendulan ' force! would immediately be brought into play, which would the apparent plane, or in thi« caae the principal plane (359) ot ine conical anrface generated hy the pendulum ilowly to rotate. Thia motion, which may be called an apiidal motion, is analoKou* to the motion of the itptida of thn orbite of tbe planeta, uidwhich arisea from the action of forcea eomevhat analngoua. In Fig. S4I, let H, H, be the polea of the earlh, o in centre, and ■ q the equator; and let A be a point in the earth's surface at ffg_ }()_ which a pendulum in oacillating in the plane of the meridian, which here coincides wilh the plane of tbe paper ; let l be the latitude of A. and let b be another point in the same parallel of latitude, at which the pendolnm make* its second awing. Draw tangents to the meridians A K, bh at (ha poinla, A,B, ) which will therefore meet each other, and the aiis of the earth, s a, produced, in the a&me I point, t: join ao, and draw at perpen- I dic'ilar to ot. Let a cone, of which the iqiex ia T, be auppoxed to envelope the earth — a sphere — along the drcle of latitude where haTJng aa many ai ^ twenty-four houn. Let ua suppose the n wcillation in the meridian av, which ooincides with at at a; it will make ita second awing in a line parallel to a t, the inclins- tiuD of which to IT ia equal to atb. But the direction of the n BOTATION OF ▲ RIOJD BODY OB BTSTSM. 189 meridian daring the second swing is the line bt. Hence the angle atb is the deviation from the direction of the meridian at the end of the second swing. Therefore, in twenty-four hours the BQi&ce of the oone ronnd the vertex t will he the measure of the whole deviation in that time. But if the cone were opened ont on a plane, the anenlar space round t would he measured hy an arc of a circle equju in length to the circumference of the parallel of latitude divided b j its radius a t. But the circle of latitude = 2«-.AC = 2ir.AO.oo8i^ and A T s A o . cot L, hence the deviation in 24*» =s '- '— 1 AO.COtL = 2ir.sinL. ConBequently, the plane of oscillation will make a complete rotation at the pole, and half a rotation in lat. 30** during twentj- four hours, and will remain stationary at the equator. 358. The rotation of the pendulum has been experimentally illustrated in a very ingenious manner by Prof. Wheatstone. A horizontal piece of wMd, a c. Fig. 242, ^^ 242. toming round freely on a heavy foot, e, BQpports a vertical graduated semicircle, ABC, furnished with a sliding clamp, b. A piece of spiral wire spring is attached to b and to d, the centre of the semi- circle. If this elastic wire be made to oacillate, by drawing its middle point a ^ nnall distance from its position of rest CZ—jV. by the finger and thumb, and then releasing it, it will be found to oscillate slowly and visibly. If the semicircle be rotated round a vertical axis passing through its centre, the plane of vibration will be constrained by tne attachment of the wire to pass through the centre, in the same manner as the plane of oscillation of the pen- dnlmn by the force of gravity, and the conditions of vibration ^11 be precisely similar to those of the pendulum. If, for example, the slider be placed at 30°, and the wire made to vibrate in the plane of the semicircle, then on turning the semi- circle half round, or through 180", the wire will be found to vibrate at right angles to the semicircle, the plane of vibration having made a quarter of a rotation, which agrees with the pre- ceding formula. KOTATIOH OF A BIOID BODT OB SYSTEM. 359. The complete and general investigation of the rotatory motion of a rigid system re(][uires a higher range of analysis than that which is compatible with the scope of this treatise; for this the more advanced reader must be referred to one of the standard sDilTlkal treitisea on djnamici: but by id apprcpriale M:kcIion of tnu lypical form uf ■ rotnling bodj, ihe impaitanl principlei inTolTcd in this drparlmcnt tf ciyniiniicB maj be luRicicnll; tiuci- ciated. Let us then auppose the aru. It may alto be remarked that Ibvae three aiei are per- pendicular to each other, and are called ^inripal arti. And it nmy be ahown gi^nerally* i]\M everii rtgid ig4ten hat three prin- cipal 03-et 0/ rotation, perpendiailar to eath other; rotaliau •bout either of ichich prodncei no preeture oa Ihe axit. AImi a plane, in which any tvo of the principal aiei lie, ia called a prindfal plane; conaequfntly, rotation in a principal plane prouuees no pr«a«ure on ths "'- -' -■-■--- [ia paaKing through tber (be Dii.jur or :ilh:r case thu body alien, and iliat ihe I aide of the axia ia be contrary 360. ir however, the body rotate round an aiia pamltel to eilbrr [ra, aa loy, Fig. 343, paralfel to a a, it U evident that Ibe ceutrifugHl force of each particle of tho principal Kff.W. ibove B b ia counteracted by an equal fon tbit line, Bod CDDBequently the rotation of (he ' ' '" ' " ' " produce angular irtot ist, the < iaof n But the centrifugal force ut t bi/ r.ol being ci balanced by Ysy, there will be a preaaure on the axia of rotation, which may be rapreiented by a single roenllant acting in iho diraclion o b. And the aame propui-IHoQ ia genendly true, namely, that if a rigid body rolatt abend an axi* parat- Ul lo either of the jirincipat oxet, tha raaltanl prtMtiTt on the axit maiibe repreievteil bg a tine perpendicular to it, and pa$ting through Ihe centre of gravity of Ihtbodg. 361. If the body b« now auppoaed to ratale alout an aiia paaaing ibraugh the centre of Kravit^ , but not coinciding wiih eilberof tbe principal aiea, let the ana cf rotation, ly, Fig. !4i, - tating body ; the form of this solid may M iinderglood ai that of a long e^ flattened sideways. In any solid of revolntion, that is, a solid of which the sarfaoe is generated bj the reiolution of a geometrical figure abont a straight line, snch as a cone, cylinder, spheroid, or paraboloid, one of the principal aiea is the geometrical aiis of the solid, tiio other two are any two lines at right angles to each other in the plane of reTolotion which passes tbrongh the centre of grarity of the solid. The geometrical axis may be either that of graateat or least moment of inertia, and conseqnenlly of stable or onstable eqnilibrinm of rotation ; but the slaiHll^ of rotation will always be equal about Ibe other two princiral axes. 364. It may now be desirable to illustrate by some examples the priiiciplei that haie been invest is'ated. The most ounrenient appa- ratus for this purpose is an npright standard with a foot to it, to which a horiiontal ana is atlacbed, carrying at its extremity a vertical mandrel, with a small grooved pulley on it, lo which rapid rotation may be communicaled by a band possinj; over a wheel attached to the upright piece, TarioDS bodies may be inspeuded b}; a cord (or still better, by a bundle of Ihraads) from the extre- mity of tho mandrel; and when the rotation is sufGcientty rapid for the centrifugal force lo overoome that of gravitation, the bodiea Bt.Ui. will all be found, afier a litlle time, to assume that poeition which the axis of rotation coiacidea with the principal axis »'■ Djaaniof, p. ISl. 193 moment of inertia, vhich ii slso tW of stable eqniU- In Fig. 245, tbe dotted line in eich esse showg ths poii- of the centre of ^n\itj Tertic&lly under the point of sapport. Tbo body a is an ellipeoid ; in the poBitlon which this anumes, the two greater aiea lie in a harizontd plane, and the leait ia TorticaL B i» a cone, the centre of graritj, o, of nhich liel in itt aiit, at a diataoce of ane-foorth of ita length torn the baae. Tbe ftiis of the cone vill be found to asanme a hariaontal podtion, the axis of rotation paniog tbrongh o. In Ihig caae nn; two aiei pcTpeodicnlar to each other, in the plane of rotation throngh o, will be eqoal axes of least moment of inertia (35fi) ; if the oone had an elliptic baae, the nuyor axis of the ellipse wonld become TOntsl position, the a beads, or ballets, with holes throagb them. These, afier a varietj of QDcertain moTementa which it is not Decessar]^ to investinte, will aasnme tbe poaidon of a boriioatal circnlar ring, similat^ to the ring c. If these bodies be Strang on an elastio cord, as the velocity of ntation increases, the drcle will be fonnd to expand nniformlj, leaving nearly eqnal spaces between the bodies : this eiperimenl afibrds farther evidence of the existence of centrifagal force. 365. The phenomena of rotatei^ motion have been aptlj illus- trated by tbe gyroKope, an instmment long since G0li*tmctad,juul .,_ ^ ,.. ._._ _..-._ ,._ ., „. jj^, -f|^j^ more recently bronght into notice by H. Foucault.* instmment consists of a heary ring of metal, o. Fig. *•«), attached centrally by a tbin plate to an axis, the pivots of which work in two centres, k, r, paasina; thtocgh the circamfetetice of a ring, n, waich ib attached by 'V- IM. pivota at right sngles to i, r, to a semicircnlar " BDpport, 0. This IB fixed on the top of a ojlin- dncol stem that moves roond freely in the tubalar I support, B, which itself rests on a heavy foot, j(. It ■ is uecessaij that a line joining the pivots of the I rotating axis should accarataly pass thionffh the I centre of gravity of o; ^eo that a line joiomg th" • pivots that sapport D sbonld likewise puss tbrooj the same pmnt ; tbe wheel when at rest will tht be in tbe condition of indi9erent eqnilibriam (97). I Tlie axis of a is fbmisbed with a snail projectiDg I pin, to bold the loop at the end of a piece of string | to be wound roand the axis, which is thea made to rotate r^iidly by fordbly onwinding the string, as in apinniog a ehild't top. As the vis viva of a rotating body, that ii, its energy t or tUi Und m bron^t from Italr In 1817 bf l£r. -'"-' — noTlJiuliiatniniSBtinsBHdbjlIr.Alrjinhh fixed on the aiia, vhicb is capable of being placed in gear with the lut of a train of mulliplving vbrnU, the first of which ia tnmed br a winch. By theae means, especiallT if the diac b« large and beary, a much higher Telocity of rotatTon maj be com- mnnioaled to the diac than that otpnble of being prodnced by meana of tbe itring. NumeroDa illuntration] of rotatiDn may u thni giTen, but the foUowinK are tlie more importaLt. If a imsll weight, h, of two or three ooncea (the diac being foar inches in diameter), be aaepended at one extiemity of the axis, u P, the ring, u, being honwntal, the point, f, wiU be im- mediately drawn down by the wciglit, ai represented in the figure ; bnt if the disc, a, be in rapid rotation, the weigbtwill prodnce no Tiiibie deflpiion of the point, r, bat only a luw hotiaontal mic- tion ; and if the weight, h, be remoTed &om r, and samended at K. or if H be allowed to remain at f, and a heavier weight be ma- ^nded at a, tlie horizontal rotation will lake place in tbe oppoaita The eiplanalion of tbia fact will be beat underatood bj re- Xg. M7. ference to the diagram, Fig. S47. Let tlic motion of rolaiion of a particle at a be repre- ■enled in magnitude and direction by the arc A B, and let the motion of the piant «, dne to (he weight, h, Buapended at r, be re- presented in magnitude and directtnn br A c, an arc of a great circle paiatng thnnwh Ibo axis ; then completing on ihs sphere t^e paTallelogram, ca, and drawinj; the great circle, adk, through its opposite angle i>, the particle at A will, in obedience to tbe two modona, move in the plane a d e, and consequently Ihe pirat at r will more boHiontally m the direction rr". It is evident that if the accelerating force, a c, bad acted in (be contraij diredian, tbe weight being inspended at I (Fig. S46), the movement of the point r wonid also have been in Ihe contrary diiectioD to f r*. If^ when tbe horizontal motion of the axis bf is proceeding, it be arrested br bolding the arc, c, by the bands, do mvltoiif motion can take place, and tbe point r will be deflected by tbe weight a, aa it would be, when the disc is not in rotation. The preceding experiment may be made in another fbnn hj detscbing the ring, d, from tbe stand, and haviDg produced a rapid rotation of the disc, suspending the ring by a stnng attached at B, or F, as in Fig. S4tl ; in this case tbe weight of the machine {(•slf will act in the same manner aa the weight, h, in ths fanner CMS, mnd tbe rin? vill roUto round the ati in m horizontal pla^e, in apparent vioUtiat tlte law ofgraiiUlioD. From those eiperimeola it appean that a force applied to more the rots- ting bodj prodnces a motian of i(e aiis a right onjrie in advance of that wbich it wonld prodoce er by Mr. Bridge, in the PhUoeoiSacal Mftfuiae for Kovcoiber, 1857. reetiUnew potitiint, bot it will go beyond thu con- ^- MO- ■iderablj, becomiDg comd is the opposite direotioo, End diiu s seiiea of vibraltoM, each deCT«uing in \^\^ Wtf magnitode, u ihown by the dotted correa io tlie y; [j./ fiKore, will continue for same time ; bat at length V L / l£jy iriU op«ae, and tho Kid onra more be left in its * |' origiiully Tsrtics] positioD. A little reflection will F (hotr that dnring tbii aerie* of movemenCa, the i~ M. cnnatitQent atomi of the rod moii h»Ta been alter- [\ ^~\ nstelf wpanted and appraxinuited, acoording as \] ( one or other of the ddw M the rteel becMoe convex or coDcare [13]. Some bodies vill, in consequenoe of their natural eluticitr, readily assume these motions; others are made suffidentl/ elastic b; artiGdatlj hardening tbeA, as in the tempering of iron and steel; or by tension, a« by sttetching cords anil membraDSB, as in the Aiings of a barp, or the bead of a drum. 371. Vibratai7 motion may be snccessively Sig, iSV. cODUDnmcaled to every part of a body, or be partidiuled in by every part at once. To illnj- trate the fonner of these conditions, attach one and of a rope to a sapport, a, Fig. 2&1, grasping the other end, k, in the hand ; on ^ving the end a sharp jerk, or Btill better, on drawing aside the rope at the poiut a by the finger and thumb of the other hand, and releasing it, the primary defieiioD prodaced at a will be obtervod to travel •long the rope successively asanming the posi- tioiia h, c, he., and after reaching the Sied end will be propagated back again in the tome plane, bot on tA< eovirary side nf the position of rest, d; wheitce tho wave will travel back to the These phenomena are best demonstrated by «mployiDg a piece of vulcanised india-nibber toM about hall an inch in diameter, filled with •and, a* on account of its weight, the undulation travels slowly ; and if the tube be about ten feet long, and be slightly stretched, and attached to two blacks fiied at the enda of a vertical board^ the undolalion will be seen to travel up . down from end to end several times in e Tlua is termed a prcgruitve nndnlalion, and if B second impulse be communicated at a when the first reaches b, and a third when it reaches 198 DTHAMIOS. 372. Vibrations are tenned stationary when every part of the body assumes motion at the same time, as when a rope is fixed at A and B, Fig. 253, and being drawn at its middle from the recti- linear position, ultimately recovers it, after performing a series of vibrations in which every portion of the rope simoltaneoosly participates. 373. When a body is made to assume a series of stationary vibrations, the points where the phases of elevation and depression intersect are always at A B, which has been made to assume a series of sta- tionaiy vibrations, the parts marked n will be in a state of rest, and pieces of paper resting upon them wul be undis- turbed; whilst, if placed on the intermediate portions, thev would be thrown off immediately. These points are called nodtU paints. When a plate is made to vibrate, these nodal points of rest always exist, ana may be easily detected (see Acoustics). A ready mode of rendering the nodal ]>oints visible is by means of a piece of elastic spring wire, five or six feet long, one end of which is fixed, and the other held in the hand. On stretching the wire slightly, and communicating to it a number of equal successive impuues by a vertical movement of the hand, at such intervals that the advancing and reflected waves ma^ coincide, the nodal points will be rendered distinctly visible. This may readily be accomplished by a little practice. The same thing may lie aocomplisned by means of the loaded india-rubber tube already mentioned. 374. Elastic rods or wires may easily be made to vibrate, and when uniform in structure, in equal times ; the number of vibra- tions increases with the diminished length of the rod, being in- versely as the square of its length. Thus, if a rod twelve inches long perform three vibrations in a second, it will, if shortened to TlBXATIOm OF BODS. 199 one balf, perform twelve TibratioiiB, and if of bat three inchee in length, forty-eight in the same time. 375. A -vibrating cord or wire, or an elastio rod fixed at one end^ will not neceflsarily vibrate in a plane, bnt any one of its points may describe either a circular or an elliptic path. The circnlar vibration of a oord has been aptly illnstrated by Prof. Tyndal by attaching one end of the cord to a rapidly-rotatioe mandrel, at a point slightly eccentric, the other end of the cord being attached to a fixed support, with the intervention of a swivel By properly timing the rotation, the cord will divide itself into several vibra- ting spindles, separated by nodal points. * To the mnltitnde it is probable that the facts of science are more acceptable when decked oat with adventitious ornament, and in deference to this taste. Prof, l^ndal has employed a cord covered with tinsel, or a strioff of bright beads, and has illuminated the fusiform subdivisions with coloured electric light.* Also, it is a law of vibration, that a body may have two or mors modes of vibration* impressed upon it simmtaneously ; thus a cord or rod mav vibrate in its entire length, and ?rith one or «^^ 266. more nodal subdivisions, at the same time, and the motion of each particle is the ag^^te of its separate motions : this is called the jmneijple of the super- po§iHon of small motions. This may be beautifully seen by the Oaleidophone, a contrivance of Prof. Wheatstone, made by fixing a silvered glass bead ik. Fig. 255, on the top of a steel wire B. On making this wire vibrate, the curved ^th of its extremity will be visible by the motion of the httle spot of light reflected from the surface of the bead. Manv curious and interesting combinations of on- eqaal vibrations, in two planes at right angles to each I otner, may be produced oy making use of rectan^lar /^ [^ wires or rods, the width of the sides of which is in L, J some simple numerical ratio, as 1 : 2, 2 : 8, 4 : 5, &c. "^^^17 With a rod, the sides of which are as 1 : 2, a parabolic curve may be produced, which will sometimes pass successively through the f<^wing phases, 2^.266. while others will present more complicated combinations of two unequal circnlar or elliptic motions. * Th« Bsm« tMta appMkn to prevail respeotiog tome of the grander ob- jeeta of mitiire, rinoe it baa reeently become the faahion to aimuarljr iUnmi- nale tbe FaPa of Bchaffhaqaen, aaa the Beiohenbaoh, the GiMbaeh, fto., ia Switcerknd. 200 DTKAMIOB. ^. S67. Bjrraflecting a rsjof h'ght from the Bhimng Bur&ce of a vibratiDg wire, Dr. YooDg was enabled to obeenre the curioQB corveB deacribed by its particles; some of these are repre- sented in Fig. 257, but their vanetj is endless. 376. Vibrations are performed either transyerselj or longitadi- nally with regard to the axis of the vibrating body. The former may be illustrated by fixing a wire to a proper support, ab, Fiff. 258, and drawing it at its middle out of its straight po- sition; the vibrations shoirn by the dotted lines are tran$ver$e to the axis of the wire. Fix a weight, d, to one end of a properly-suspended piece of ^.258. ^.258. f ^ brass wire, c d, Fig. 259, coiled into a loose helix. If the weight be raised towards o, and then allowed to fall, it will advance to, and recede from, d alternately, the wire performing a series of 2aii^iM7tna2 vibrations. 377. The longitndinal vibrations of a row of particles may, like the transverse vibrations, be either stationary or progressive, the stationary undulations resulting, as in the former case, from the reflection of progressive undulations. A progressive longitudinal wave is well illustrated in nature by the passa^ of a li^ht breeze over a corn-field. Here, taking a row of ears in the direction of the wind, each ear of com is successively deflected by the pressure of the air, and then returns to its former position : and the pro- gressive accumulation at one point, and recession at a succeeoing point, correspond to the elevation and depression of a transverse or normal wave. These longitudinal vibrations may be conveniently illustrated by an ingenious apparatus designed by Prof. Wheatstono for that purpose ; this consists of a long cylinder, about four inches in diameter, enclosed in a box, the axis passing ^roogh one *end of the box, that the cylinder may be rotated at pleasure by a small winch. A series or oblique rinn, about a quarter of an inch broad, are drawn on the surface of the cylinder, and a slit of the same width is made in the box, parallel to the axis of the cylinder, through which a small portion of each ring may be seen. If the obliquity of all the rings be equal, but the same phase of each ring be successively placed at equal axial and equal angular distances round the cylinaer, when this is rotated in the box, the appearance of a progressive longitudinal undulation will be producea. If any portion, as one-third, or one-fourtli of the length of another equal crHndar bs taken, and k traurarae ring be pUoed at Mah end of thu portian, and a leriee of obKqne rings between then gi«dnallj iTWTfiatiTig in obliquity, and agvn giadoalLj diminuhing, ibt tazue wiiea bein^ i«pe^«d oo either nde oT e*ch truiiverae ring in lb« refeiM paadoD, the ntatioa ef this cylinder in the box will produo* *' Bnnoe of a stationary loDgitudiiial Tibration of a row c Theeffect U moit itriking if the box be blackened, and the appeannoe of a stationary loDgitudiiial Tibration of a row of partidea. The effect i* moit itrikinR if the T ' " '----' ■-' wiat» ring! be drawn od a black cjSnder. Similar «ffi)ota, althoogb perhaps not eqaally perfect, may, bow- errar, bepndoced by meani within the reacbof anyof anr readan. For this pnipoae, a eeriei of eqindiBtant undnladng Knee are to be drawn on a iheet of paateboani, m in Fig. SCO, each t\ kad parallBl to itself; iwbind a . of pasteboard the appe grenirs wave trill be prodaced. If straight hnea I narTTTw slit in auother sheet of u . . .. — . — , „ ._ _,.^ratDS, tl width of the lines and of the slit should be the same ; and tt eBect will be most striking, if the liaes be leil white, aed the ground aa well as the screen l» blackened. 378. One nmarkable aDirersal law gonms all lb«sii vibratory morements, that no matter what theit magnitDdo, tbey are always meironons, that is, the excursion of each particle on either side 202 DTMAXICB. of its normal position is perfonned in ec^naX times. Thus, in the case of the cord vibrating in its entire length. Fig. 253, all pNortions reach the straight line (the position of rest) at the same time. It has been observed (290), that, generally, the amount of elastic force is proportional to the displacement ; therefore, in the case of vibrations, each particle will tend to retnm to its position of rest with a force proportional to its distance from that point. But it may very readily be proved by analysis, that if a particle be urged towards a given point by a force varying as its aistance from that point, it will reach the point in the same time from all distances. Hence vibrations will continue isochronous until the particles resume a state of rest ; their motions having been grada- ally overcome by imperfect elasticity, and by extemiu resistance.* On the subjects treated of in the five preoedmg chapters the student may consult with advantage any of the foflowing works : Peschel's Elements of Physics, translated by West; Moseley*s Illustrations of Mechanics ; Gregory's Mechanics ; and Ferguson's Mechanics, edited by Sir D. Brewster ; and the Monographs in Brewster's Encyclopedia, Lardner's Cabinet Cyclopaedia, tne En- cyclopndia Metropolitana, and the Library of Usetul Knowledge. Amon^ the Continental authors, the works of Pouillet, Poisson, Biot, Hauy, Qoetelet, and some others, will repay a careful studv. The laws of Statics and Dvnamics are treated mathematically in Wood's Mechanics, edited by Snowball ; Whewell'k Mechanics, Dynamics, and Mechanics of Engineering; Eamshaw's Statics and Dynamic^ ; Wilson's Dynamics ; and Moseley's Engineering and Architecture. In the Prmcipia of Newtoo, and Euler's Letters to the Princess of Anhalt-Dessau, many of the subjects are treated geometrically. * Ai thii ii s very ftincUmental inropositioii in Aoonttioi, the proof maj not be anwelcome to our more adrMioed reedert. Let • be ibe aiitasee or ear |>srticle from ito pontion of reat, a— « tbe •p«oe deeoiibed, aiid v the Tefoci^ ecqaired, ftt tbe end of tbe time t ; and sinoe/oc • by bypotbeos, letit=:|A*, tben ;&#&■— v.tf^v; integrating this, and coReeting, we obtain therefore —djt=v=i ^/it,, -/«»*— •*' wbenoe di Ctrfaiobs-i )=-i ^L,, integrating fbifl and eorreotiag, we obtain B(wriTia. chapter the conridsralfon of the propertiea pecnliar to (he eminentlj elutic, or gMeoDB fluids. SSI. Liqnidi, properlv to called, of vMch water miy be taken M the tjpe, are Got slightl]' comprtsBibls ; thia cbaracUr, indeed, wu Tor lome time doubted, as the celebrated eipariment, per- formed b; the Florentine academiciaoi, of sucIorinB water in a hollow ball of sold, and caonog the fluid to percolate Hf, m. the porei of the metal b; the pleasure of a screw, vai for a long time oonridered coucluBiTe on thia Canton, the compreaeibilit; of i preuure of our atmoepbere, equal to about fifteen . pounds on each aquere iuch^ was estimated at 0-OOO044 of iU bulk; while Mr. PerkiriB las since estimated the compreasion under the aame pressare at 0000048 ; and Profesaor Oenited, b; means of an extremely accurate set of eiperiments, has fixed on rather more Iban 46 milliontbe. or ^^ nearlj, as the dein«e of eompresdon experienced b7 a giren balk or water, for each addibonal pressure of one atmosphere. The appamtaa nsed by Profeasor Oenited, and to which he gave the name of pieaimeUr, consisted of a verr strong glass Tessel A B c D, ha Tine firmly cemented on to its apper part a abort iron cylinder e f, in which a piston o, capo- ' He of being moved bj the screw B, moTea air-tipht. A bottle K, into the neck of which ia firml; fixed a capillary tube I., fiimisbed with a acate grsdnated into fractions of as inch, ii plat^ in the glaaa vessel a n c d. By a previoas experiment, the contents of the tobe l, as compared with the bottle k, are ascertained. This consisted in first weighing carefully the empty bottle and tube, and Ellinf; both with mercury at a given tempe- ralore [32° F.), and weighing again; the difference of these two wei^hta would be that of toe contained mercniy at 82' F. A portion of the mercnry contwned In ihe tube was now expelled by heat, and the temperatnro again reduced to 32° F. ; the mercury will now be found to baie fallen in the tube, leaving n scale- divisions empty. The bottle is again weighed, and it is evident that the difference of the two last weights will be the weight of mercnry at 3!° F. contaiaed in n divisions of the tube. Bat the capacities of the bottle and tube must he proporlional to the weights of mercury at tlie tam» ttrnptrattire which tber contain ; if, uierefore, w be the weight of mercury Sllini; the bottle and tube, and ie the weightoftbat contained in n divisions of the tube, the value of each auile-division in parts of the whole volnme will be — . In aome of the tubes nsed, one inch in leogth held CX>1IP1IB8IIBIUTT OF FLUIOe. 206 80 mOIiouths of tbe contents of the bottie. The whole apparatuB, bottb and tube, being filled with water, or other fluid of wmch the compressibility is to be determined, the screw h is tamed, the piston o descends, and the pressure being communicated through the fluid in A B c D, the contents of the bottle k are compressedi the amount of compression being measured hj the descent of the fluid in L. The compression of the fluid is shown by the descent of a bubble of air in the tube, entangled in the upper part of l, belbre placing it in the larger vessel ▲ b c d. By means of this apparatus. Oersted determined the compressibility of the following fiiuds for each additional pressure of an atmospnere in millionth parts of the whole bulk to be for Mercury, 3; Alcohol, 21 ; Water, 46; Ether, 61. 382. In these experiments of Oersted^s an important source of error has been loet sight of, namely, the compression of the glass vessel itself; for the above results are manifestly the sums of the oompression of the bottle, and of its contents. To obviate this error, the following modification of the piezometer has been de- vised by M. Kegnadt. The stem of the bottle, instead of being entirely endosed in the outer vessel, passes air-tight through its cap, and a tube vnth a stop-cock, coming from a vessel oi com- pressed air, is attached to its open end ; and thero is a second tnbe, also furnished with a stop-cock, which connects the air-vessel with the outer yessel of the piezometer. By these means the pressure may be exerted either inside or outside the bottle, or on both conjointly ; and by comparing the results thus obtained, the error arisin^^ m>m the compression of the glass may be eliminated. The following more correct table of the compressions of various fluids has been deduced from the experiments of M. Grassi ; the compression is expressed in millionth parts of the bulk, and is that due to the pressure of one atmosphere. FlnM. Temp. (Cent.) Compr. Flnid. Temp. (Cent.) Compr. PreMUR ID Atmo- ■plierM. Mercury 00 2-96 Ether . 00 Ill 3-408 Water 00 50-3 It If 131 7-820 i« 1-6 51-6 1) 140 140 1-680 ,1 4-1 49-9 fi 13-8 153 8*362 n 10-8 480 Alcohol . 7-3 82-8 2-302 n 134 47-7 }i If 85-3 9-450 n 180 46-1 II 181 90-4 1-570 ft 260 45-6 11 II 991 8-970 If 34-5 45-3 Chlorofo rm 8-5 62-6 II II 430 44-2 11 12-0 64-8 1-309 >i 530 441 II 12-5 76-3 9-200 306 From thia Table it appeara that the compreuibilitj of £aidl il not congtaDt ; it varieB conaidenibl; nith tempAratura, hut not in the utme direction in all Quids, Tor wbila the compreBubilitj of vateT is fonnd to diminish with increase of temperatare, it ia aagmented by the same means in Ether, Alcohol, and Chloruform. It DiBj also be observed in the latter flaids that, >t the same tempeiature the amount of compi«ssion bean an mereaiing ratio to the angmented compreBaing force. 383. Johnion'i Deep^ta Pratvrt-gavg*. — Thiainttrnnenthaa Fit. MS. iiofio oonstructed for the pnrpose of measuring the depth to nhich it has been immersed in the sea by the amount of compreaaion sustained by the ' water in a cloaad cylinder, a. Fig. S63. This is furnished at the upper part with a tap, B, having an opening, c, for the admiselon of water, and another, d, for the eicape of air. The piston-rod, a, passes trough the ituffing-bax, r, and as it is forced into the cylinder, A, by the preunre of the water, it carries the index, i, np the scale, H, by meaoi of a projection at its lower end ; when lh« instrument is relieved (Wim pressure, the piston rod recedes, and leaves (he index, i, at tlie highest point to which it has been carried, and thus the amount of compresidDn snataiaed, and hence the depth of immersion, are determined. The piaton- rod and scale are protected by an external tube, with a door in the side of it, as ahown in the figure. It must be borae in mind that in order to obtain a correct reanlt the temperaturea both at the anrface, and at the point of groateat comprea- aion, mnat be ascertained, and the requisite correction applied. 3d4. Liqulda, on account of the eitrome mobility of their par- ticles, are capable i^ communicating pressure eierdoud on them equally in every direction, a properly conati- ffr- 2M. tnting Che most important characteristic of fj thia class of bodiua. Let abdc. Fig- 361, be a vessel oonlajaing a liquid destitute of weight, and therefore theoretically unacted , opon by the attraction of the earth ; and let ■ the shaded portion p be a solid piston, also r deatitulD of gravity, moving air-tight in xo, and exactly cove ring the auiface of the liquid. Now, as F IS without weight, it doea not press upon the fluid, and the sides of the veaael Ho may he pierced without ita escaping. But ir we place on f a weight of 100 pounds. It will attempt to descend, and would reach the bottom of the vessel were it not opposed by the liquid. Accordingly, the upper lajer of fluid X beooDM praaed bj tlie pitton, and woald fall, if not nip- ported bj tbe aattittceDt stnilam y, which tlios in tarn bacotnat pressed ; this mU oa the Ujer i, and this dd ihe subjacent hvjeis, trail ami tting the pressure eieiied b; the weight irith which the piston is loaded to the bottom of the Teasel. Also, from the mobilitj of the particles, those of any giTsn lajeT in contact with the sides of the Teasel would be farced out laterally, Boless resisted bj an eqoal pressure exerted b; the sides of the TBSsel, Ihey must, therefore, exert the same pressars against the •idea of the Teasel. And as the whole base, b p, supports the pressure of 100 ponuda, it follows that one half the bue rapports bnt SO, and 001 of the bass bat (hm poond, &c. From these considerations we ma.; safely infer that, A. Preaaure ia transmitted bj flnids in all directions: B. The transmitted pressure is equal in oTer; portion of the fluid: ' c. It is proportional to the area of the surface preaeed. These general laws joaj be proved eTperimentAlly by a closed TESsel filled with fluid, in the upper surface of which are two ^Krtmea, to which pistona are fiitad, haTine unequal areas, at 10: 1, fbrexample. Then if one pound weight be placed on the smaller pialon, ten pouads will be required to keep the larger one jnitsplsoe. If the larger piston be placed in the side of the TeaaeL Uie preasnra agaiuat it, ansiDg from the gravity of the fluid itael^ must firvt be oonntetacted, when the aame reaull will be obtained. Also, if an Drifioe be made iu any part of ihe veaael, the fluid will eticape in a jet, when any pressure is spplied to either piston. 385. Liqnids can never attain a perfect state of rest, and be in G0ii](4ete equilibrium, onJesa the particles in the upper and eipoeed layer form a surface perpeadicular to the direction of the forces acting upon it; and eTery molecule of Ihe mau of Suid eipe- riences eqnal and coutrarf presiures. To render the flrst condition inUlligible, let a e h/, Yig, 265, be a Tassel containing water, or olhorflnid; to attain aperfectequilibrinm, the snriaee of the fluid must be level and in a "'■ ■ plane perpendicular to the llnea g, repreaenting the dnections of the earth's attraction on the particles bed. If, instead of ronniiig a level aniface, the fluid be supposed to be bounded by s cnrre aAe(fe,asiiuiIlhoTiEontal layer, aathe , line bd, will be pressed by the weight of tbe molecnlea aboTe it; this preasura will be trans- mitted lalerally (398), and the molecules of flnid at b will be acted npon by this lateral jn'Cssnre, and pnahed ontwards, because there ^ u nothing to oppose tbia action ; immediately other paiticUs, acted npon in a Kmilar mauner, are pushed Oflt in 208 HTDROBTATIOS. their tuni; and this efllBCt continues nntil all that portion of fluid, standing above the horizontal line hd^iB depressed to one level surface, and then the our?e bed yanishes, and a horizontal surface, extending from atoe, perpendicular to the lines of pres- sure ^, is prodo(^. The fluid will then he in equilibrium, pro- vided the second condition obtains, that every molecule in the interior of the mass of fluid experiences eqoal and contrary pres- sures. That this is the case is evident, for everjr particle of fluid receiving the pressure of those above it tends, m consequence of the equality of pressure (374), to transmit the same pressure lateraUv ; and if the pressure on two sides of a particle be unequal, it will be acted upon by the stronger force, and continue to move until it has attained a situation where all the pressures acting upon it are eoual. The only exception to the law of the level surface of fluias at rest arises from the capillary attraction, or repulsion, exerted by the sides of the containing vessel (88). It may readily be shown bj precisely similar reasoning, that the common surface of two Uquids of unequal densities is horizontd, when the liquids are at rest. 386. The construction of the Spirit-level depends on the fact of liquids assuming a horizontal surface. This instrument con- sists of an hermetically-sealed ghiss tube, nearly filled witb alcohol, and enclosed in a case, leaving one side of tne tube exposed to view. The tube beine very slightly convex in the middle, the in- strument is so adjusted, that when it rests on a perfectly horizontal surface, the bubble of air shall occupy the middle point of the tube. Any inclination in a surface on which a spirit-level is placed, is indicated by a departure of the bubble from the middle point. 887. When two or more vessels, of any gnven dimensions, com- municate togetiier, the same conditions m equilibrium exist, as when a fluid is contained in a single FSg,2M, vessel. Let a, b, Fig. 266, be two diflerently si^ vessels connected by ^ the tube c; on pouring water into one of them up to the line 1 2, it will "^ be found to present a level surface in both ; ana the fluid in each will be at the same elevation ; for if the j-i-p ^**e^ ^^ ^t instead of being at i, p "tm — :ii±~|""r yf^YQ at m wf , it is obvious that the layer of fluid pp would be submitted to unequal pressure, being in b pressed by the long column Jo, and in a pressed only by the shorter column mjp, and consequently equilibrium could not exist (375). Therefore the narticles of fluid acted upon by the greater pressure will move, ana attain a state of rest only when the level of the fluid is the same in both vessels. If the diameter of the vessel n, be small enough to mantfest a sensible amount of capillaiy n- ^ Thia law i* equallT -nlid when the connected tmuU ptesent the ereatot Taiiet; id Boape or size. If the tabes i, d, c, ii, R, F, be filed ioto a common reBcrroir, L u. Fig. 267, and water be poared iotoD, itwillattuneiActlTthe aame elaTatioD in each of the fif. H7. tobea, notwithstanding the dif- t-nr s s r feieiKM !n the flgote and nze. The only ciicmrrtance intro- dncJDg the slightoat exception to this law is capillarit; (38), bywhich, if any of the tnbea or . TeaaeU in the abore GgnrM be ^vrj narrow, the water, or other fimd, will have a tcndent^ to riM to a higher elevation than in the wider ones ; and the eloTatioD above the ctnumon level will be exactJT what ii doe to capillaritr. 3S8. The hydroitatie Itstl acta on this principle ; it condete of two piecea of the tame kIsm tnbe conDecled bj a fleiiole tube, and when nearij filled with water, may be nted to ascertain two pointi in the ume horizontal plane, in litnationB not risible from oach other, aa in two diSerent parte of a mine. The two poinla at which the water reiti in the glaaa tubes will evidently be hotixontal, whatarer conna the flexible tnbe may take between If the gUa tnbes be oonnected by a rigid metallic tube, mounted at ita middle point on a tripod stand, the apparatna ii S89. The Mtne priadple oF "wat< nplain the oEt-obeerved phenomem which is merely a small hole bored, fre- miter, ti of claj or hnrd Blone, and c c, a permeable bed w of und or graiel between them. If now the porous stratum be tapped in a valley, as in the 6gpn, frota which the ground mes conri- derabl^, waler will continue to flow so loDg aa the source of water is higher than the mouth of the well. 890. The above law (387) appliea onl; when tbe connaunicfttine ^ ^^ veaiiela are filled wilh the »am« fluid; for if fluids of ' difierenl densities incapable of mixing, as water and i mercury, be used, the elevations acquired by each will be found to be in the inverse ratio of tbeir spe- cilic gravities (112). Let mercury be poarad into ihe tube acb until the bend □ is fillod, then pour water into n, and it will be found that to raise the mercury in a to the height of one inch, a column of water, rather more than 13} inches bigh, will be re- qalredin b: in coasequence of the relative gravity of mercury, aa compared with water, being as 13'6 : 1. 391. A beautifiil example ofthe truth of thin law of equilibrium of fiaids is presented in the figure of tho surface of oceans and seas in a calm state, by which the cause of their superficial curvature becomes immeiiiatcly apparent. It follows that, in common with everything belon^ng to our globe, the seas obey tbe farce of gravitation ; and ere also nibservient te centrifcgal force (330), the oceans end seas therefore necosaarilj assume the apheroidul furm, in common with the solid elements of the earth's crust, but not subjected to the superficial inequalities of the latter. On this account, where a standard place of obsen^atiou is required for very accurate barometric, or other meleorolc^cal observadons, so as to enable obscrvrrs in different paita of tbe world to compare the results of their observations, the level of the sea, or a given dis- tance above it, is always chosen. Among minor causes affixing the regular curved surface of the great mass of waters on our S;lobc, may be mentioned those which oriso from certain physical eatures of the earth itself; tbe mountainous elevations on its surface attracting, by lateral gravitation (60), the water of sees and oceans towards them. If the mountains of tbe CordJIIenu were about 100 times higher than they ore, the seas would, by tbeir attraction, be elevated into liquid mountains on both aides of the coasts of America, and the ports of France aud Japan be left dry. The peculiar directions of winds and currents are soureea of disturbnncc to an imporlant extent, caueini; elevations ia parti- culnr and isolated masses of water : thu^i the level of the Bed 8ea at hi^h water is more than thirtv-two feet higher than that of the Mediterranean. The level of the Pacific at Calloo is mare ele- vated than the accan at Cartbogena by twenty-three feet; whilst the ocean at Dunkirk, and the Mediterranean at Barceloua, are at the same eleratiou,* • PoaOlel, Fbjiique, p. lit. PKB8S0RE OV THE BABE OF A VESSEL. 211 -W J^' Q 392. The pressiire of a flaid on the hottom of the containing ▼eaael, is altogether independent of its shape, and is equal to t?ie weuffU of a cdumn of fluids of which the base is the same as that of the contauMig vessel, and the height equal to that of the oon- iainedfluid. The best mode of proving this ^' 270. * statement is bj means of the ap- paratus contrived by M. Haldat, Fig. 270, consisting of a bent tube, ABC, having at a a collar cemented on, into which vessels of different shapes, d, b, f, ma^ be screwed. Toe tnbe a b c is filled with mercury up to the level of the dotted line a c, and the tnbe ap fixed into c. The cylindrical vessel d is then screwed into A, and water poured in as far as h \ the base of the oolomn of water vnll of course be equal in area to that of the sur&ce of the mercury in the tube a. The mercury will then rise to a certain height in a, as p ; in consequence of the pressure of the water in d on the surface of the mercury in a. Then unscrew d, and fix on a the conical vessel, E, and pour in water until it has attained the same vertical height, as in D ; on examining the mercury in a, it will be found at the same point p as when the cylinder d was fixed on a. Be- move E and replace it by f, and on pouring in water to the same height, the mercuij in b will attain the same elevation as before : proving satisfactorily, that the pressure exerted by masses of fluid on a given base is quite independent of their quantity ; for the pressure was the same when either of the differently sized vessels, D, K, F, were used, each containing very different quantities of water ; in each, however, the actual base formed by the surface of the mercury, and the height of the column of water were the same, and the pressure, as above stated, varies solely with the vertical height, and area of the base, of the column of fluid. In the case of the funnel-Bhaped vessel, e, the inclined sides support part of the weight of the fluid: in that of f, the downward pres- sure on the base is counteracted by an upward pressure against the portions of internal surface, that incline inwards. It is easy to calculate the amount of fluid pressure on the bases of containmg vessels, by taking b for the area of the base of the column, II for its height, and d for the density of the fluid. The pressare upon the base b will be equal to b x h x d, for b x h will be equad to the volume of the fluid ; and to have the weight, this product must be multiplied by the density, d. 393. From this law (392), we are enabled, with a given bulk of p 2 flniti b . ... > icbmJ. For, witb » qDantitj of fiaid f^ certain Bmonnlof preware c«n be exerted on a Riren are*, when the vertical beigbt of (he fluid nh; ten timei thai preamra can be produced b; DarrowinK the capacit; of the TSsael, >o that tb« vertical 'height of the nuid maj be 10&. and conTeraelr ibe pressure may be leBSened to j^i bj eo inclining Ihe sides of the Teasel, tb«l the Yeriical height of the flnid maj be only ^ Bj BTaiiing oonelves of tbia law, a cask may be readilj' h irith , ., ^ into the bunghole. On ponring wMer into the tnbe, preitsnre n exerted, equal to the internal area of the vessel, multiplied by tlie height of tne column of water in the pipe, aud an amount of force sufficient to burst the cask with Tioleuce will be genersltd. The well-knowQ philosophic toy, called the hydrostatic bellows, or hydroetntio paradni (nbicb is no paradox], illustrates the same fact. This consists of two boards, connected loosely by strong leather; into the upper board is fixed a long tube, on pouring water into which, tbe bnarde are forced asunder, eien when previously pressed together by a conndeTable weight. In tbia manner, when tbe space between the boards is nearly filled vrith water, and a man stands on Ihe upper board, an ounce of water poured inlu tbe pipe will exert sutncient force to elevate him, notwithstanding (he weight which the fluid prenare ia required .. a constant rah'o between tlie extent oT BDrficei pressed upon by a continuoos mass of fluid, and tbe amount of the presBurea they sustain, explains the enormous pressure that Bramab's Hydraulic press is capable of exerting. This machine consists of two strong hollow cylinders a a, c d a, Tig. !T1, com- municating with each other by means of a pipe B D ; h, q, are two solid cy- " 'en, workine iu water-tight collars . and c. The cylinder v, the dik- er of which is large compared with that of 4, supports a platform f, on which the substance to be pressed ia placed, q is capable of being moved up and down by means of a lever m t^ having its fulcrum at H. D is a valve opening upwards, and n a valve openiur into the space a a ; e is a cistern BIIm with water ; and i is a cross piece fimlr secured to theuprigbtso.n. Toeiplain the action of this machine, suppose 9 to bo in its lowest positim, and tite space between the solid and ludlo* niTEBIUL FLUID PRiaSUBE. 218 cylinders to be filled with water ; then, on elevating q, the pressure of the ataiospheie acting on the surface of the water in e, forces it through D into the space previously occupied by q ; on depressing q, the valve d closes, and a portion of tne water in o d is forced through the valve n, which prevents the return of water into c d, and causes m to ascend ; and these actions are repeated with each soccessive stroke of the piston q, until the substance between i and F is sufficiently compreraed. The pressure may at any time be relaxed by unscrewing a ^lug at IK, which allows the water to escape from the cylinder ▲ b into the chamber b. Suppose the diameter of the small cylinder, or piston, to be half an incn, and that of the larger cylinder five inches, then the ratio of their areas would be as 1 : 100 ; and suppose the piston to be worked by a lever (110) by which an advantage of 5 : 1 is gained, then for every pressure of one pound on the lever, a pressure of 500 pounds would be exerted by the press. 395. Two ingenious applications of the principle of the hydraulic press to special purposes have been made by Messrs. Tangye, ot Birmingham. One of these is the hydravUc Ufting jaeky A, Fig. 272, in which the pump 18 enclosed in the head, a the solid ^' *"' piston being continuous with the stem which rests on the foot. The required resistance may be overcome by placing either the upper surface of the head, Aj or the toe, b, under it, as may be moet convenient. The second is the hydraulie punch- ing machine, d f, Fig. 272. In this the cylinder and pump are enclosed in the head of the machine, d, and worked by the handle, b. The punch, c, is continuous with the solid piston, and after having been pro- E oiled through the plateplaced beneath it, is withdrawn from the oie by the lever, F. The lower part of the machine is a solid iron casting, to sustain the pressure of the punch. Boiler-plates of any ordinary thickness may be readily punched by this machine. 396. Since the pressure against the internal surface of a vessel depends on the extent of the surface, and not on the capacity of the vessel, it follows that, as the sphere has the smallest surface compared with its capacity, a spherical vessel will be the strongest for resist- ing internal pressure. Consequently vessels made for the purpose of withstanding great pressures are usually either spheres, or cylinders with hemispherical ends, unless internal stays are employed. 397. In accordance with the general law of fluids exerting pressure equally in all directions, it follows that each layer of fluid presses as powerfully upon the superposed stratum, as it does SI4 tff. 173. upon the snbj&oent ooe. Thni it is srideiit thnt kll the particleB compoainf; any par- dcokr Btratnm of fluiti, ■* n^. Fig. 378, mnst be presHod npon hj all above then), in tbe Bamo mimner as if they supported a solid piston equal to tbo Suid mass n vp m. If then we regard a portion onlj of the layer mp, as a 6, we can readilj onderetand that tills is at once pressed jrom above dowDwards by the colnmn dabc, and from below opwoTda bj an exactly equal force, in such a manner that, if a solid cylinder were immened in the fluid with it< base resting on at, the upward pressure would tend to raise .it out of the fluid. These theoretical considerations ma; be readily reri- fied by means of an apparatus consisting of a lit. ^*- stout ^losa tube g, ¥ie. S74, the bottom of which is ground perfectlv flat, having a plate of brass, B, resting against its baset and re- ^ toined in situ by tbe striuK v. On immersing the whole in a Tessel filled with water to no, the plate will be pressed against the mouth d the tube b; the upward pressure of the fluid. L If water be then poured into jr until it nearly reaches the external level nn, tbe plate will obey tbe attraction of gTavitatioD, and wiU fall to the bottom of the vessel, as tbe iipuord pressure of the water below tbe plate b, be- comes neutralized by the doumaard pressure of the water in the tel>e g. On account of this upward pressure of fluids, if a hole be made in the bottom of a ship, the ^ water mshes in; to efibotnally oppose which, B force must be applied, equal to tbe weigfat of a column of wsler, of which the base is of tbe same area as that of the aperture in tbe vessel, and the length eqoat to the depth of the bole from the snrlace oftbewater. Hence in vessels of largedranght, the under surfaces should possess considerable strength lo enable them to oppose the upward treisure exerted by the water in which they , 398. As a consequence of tbe law of equal presBcre, evei^ portion of the sides of a con- taining vessel is exposed to pressure, corrS' ■ponding to tbe weight of the fluid pressing •gainst it. In tbe vessel of water a en. Tig. !T5, if a particle of fluid situated at b be prened %7 th« ccdnmn of iral«r xb, it will, for immdi atraadj stated, be at Ibe tame time pivnail upwards (397) bj an eqnal force, and thia pnssure will U canimDDicated laterally to the t£ of the same intensitj as that whicli acts contained in the correnponding horiunital 399. The lateral presaore is pmportioiuil to the depth of the fluid ; for in the lewiel B B, K^. 276, the fluid column A c transmits its pressure through the horizODtal lajer c D to D ; and the column n r jHesaing open the Isjer ra, has ita pretanre transmitted by F o to a ; then the pieMnre at a must be greater than that at a, in the same pro- portion as s P is longer than a o : and there- fore generally the pressure of a fiuid upon a eiTen small portion, or element, of surface, IB proportional to ita depth below the sor- i fiwe ta th^nid. 400. When the presanre upon the baas of a cubical water is knows, the lateral preMore can ^^ ^tt. be readily caicalaled, for (be pressure upon any one side of a cubical veBsel GUed with fluid, U one half of (he preasnre on the base. Let a e be the cubical vesael, bisected by the oblique plane cdoh, and let k, k, be corre- sponding elements of the side and sur- face ; then the pressure on it will be the weight of the vertical prism K if, and the same being troe for every other element, the whole pressure on the side DE will be the weight of the priam A B c i> a H, which is half the cul/e ; and each Bide 'pressure. But the base angtai a the ,«al to the whole weight of the flnid, since the sides of the rcBsel ai vertical, bence the total pressure against the surface of a full cubi- cal vessel is three limes the weigCl of the cnnlnined fluid, 401. CoUrt of Freuiere.— If a gir^n surface be oi posed to the presaare of a flaid, that point of the surface, about which the preaaores upon ita seieial partg are so balanced on all sides, that tbey may be aostained by a single presanre in the opposite direc- tion, is called the centre of pieiaure. The pressure of a fluid against any point of a surface must always act in the direction of a normal to that point, since otherwise motion of ibe particles of flnid mnat ensue, which is contrary to the hypothesis of the fluid !16 aCDtOMATtC*. being at r««t: but it will bs Bufficiaot to contider plaoe idi&om only, aguDst which the directioai of preuura are ■& panltel. — — LetiB, Fig.a78,be»pl«ne"nri«>« immersed id a Said, and let d ■ be the inlenection of the sariace of the fioid viththe plane a a produced to meet that surface. Take any point m io x ft, draw mc perpendliiilar to na, «ax Terlical, and ax horiioQlal; and let 9 U tbe angle tn c;i:. Tbrn the preaanra in B tmall element of the aurfaca, tm, .a the weigbt of a colnmn of fluid of which die base IB n and the beightmai; bat m K = c m . sin 6, and if u be ths weight of an unit of volnme of the fluid, then a.n.m^ or u . m . c n . sin 9 will be the presanre on m. The moment of this preHura round the aiiii d ■ (77) is cm.uj.n.am.iinO, or u.sin S.m.cm*; and conseqnentlj the inm of all similar moments is 10 . (dn e . 2 (m . c m«). But this ezpTesaion is precisely similar to that fnan which the centre of oscillation (347) orpercuaaioa (3&I) haa been determined ; and br pursuing tbe same steps, a trimiW resollwill be obtained; (he centre of pressnre of the surface ii is therefore found to co- incide with the centre of oscillation of a plate of the same form, and of uniform thickness, round the axis d a. If o be the centre of presanre, and o, the oenire of gravity, of the surfsce a a, it has been ahown (S49) that tbe product L'oxao ia a conatsnt quantity; when therefore a a ia Tery amall, CO must be Tery large, and oo Tanishes, when co is infinite, which is the case wlien ab is horiaontal: bence it appeara ihat the centre of pressure of a horizontal plane surface immeised in a tiniJ at any depth coincidea with tbe centre of mvity; and that if tbe iiDmersed plane be oblique, or vertical, the centre of pres- sure approaches the centre of ^vity aa the depth increaaes. If the surface be a tcuOuigle, one side of which coincidea with Ft« «7B Bo tm '*'* surface of tbe fluid, aa ac. Fig. 279, the centre of preaanre ~ D is found by binectiag ab, ci>, in a, F, joining ar, and taking K o = I K p, meoanring from ■. If the stirrsce be an isoaeelcB ■ triangle abc, Fig. 280, of which I the apex a coincides with tho I surface of the fluid, and the b«ae ac ia horiaoolal, biaect bo iD D, D and take aooJ a d, then o ia the centre of preoanre. BQUIUBSIUM OF FLOATIKO BODIES. 217 If the base bg coincide with the surface of the fluid, then DOs^DA. ^ The position of the centre of pressure in these and other par- ticular cases, such as those mentioned in reference to the centre of oscillation (347), may be determined experimentally by means of a Tessel containing water, a yalve in one side of which consists of a rigid plane of any proposed form, connected with the aperture in the vessel by some neziDle water-tight material, as India>rubber cloth. The point at which alone the pressure of the water on the Slane can be counterbalanced by a single pressure can then be etermined by trial. 402. The resultant of the pressure of a fluid on the several points of the surface of a solid, either wholly or partly immersed in it, may be determined by means of the following perfectly legi- timate hypothesis; that any portion of a fluid at rest may be supposed to become solid, without havine its equilibrium disturbed. Suppose then any portion v of a fluid at rest to become solid, therefore since its weight, and the pressure of the surrounding fluid, are the only forces acting on t, the resultant of the pressure of the fluid on tne surface of y is equal to the weight of y, and must neoessavly act upwards in a vertical through the centre of gravity of y (90). But Ihe fluid will exert the same pressure on the surface of any other solid, that occupies the same space which y occupied in the fluid : hence — The ruuUarU ofapresture ofafiuid on the surface of a solid immersed in it is equal to the weight of the fluid displaced, and acts upwards in a vertical line through the centre ^gravity of the fluid displaced. 403. Instead of sup]K>8ing v to become solid (402) we might have supposed the fluid surrounding y to become solid, without altering tne pressure at any point in y. In this case, the pressure at any point m the surface of y will be equal and opposite to the pressure at the same point in the former case ; consequently, the lesnltant of the pressure in the latter case will be equal and opposite to the resultant of the pressure in the former : hence — The resultant of the pressure of a fluid n the oolf forces that net on the solid ; therefore, since the nlid is at ~ ' '' wight, and tbe reenltant of lbs preunra of tbe flaid or vertical Ibroagh its centre of gravity; and the resultant of the pressure of the fluid is eq'ial to the weight of the fluid displao^, and acts upwards in a vertical threogli the centre of graritj' of the Snid dinplBced : therefore, tehoi a $olid, &c. 4US. If tbe eqoilibrinm of a floating solid be ib'gbtl; diiturbed b; making; it reiolve tbron^b a very nnall an^lein a vertical plane, without altering the mianlitj of the fluid diapUccd, the rennltant of the preBBure of tbe fluid on the solid in ils new position will stitl be eqnal to tbe wel);bt of tbe solid, and will therefore have no tendency to elevale or depress tbe centre of gravity of the solid : bot since the resultant acts in a vertical through the centre of gravity of the flnid displaced, it will tend to male the solid rotato round a horisontsl axis through its centre of gravity, unless theas two centres of gravity happen to be in tbe same vertical line. Whenever the pressure of Uic fluid acting upwardk Ibrongh the centre of gravity of tbe Qnid diaplsced tends to inertaie the anc'Ie through which the solid has moved, the eqnilibrinm of the solid will be tmtiabU ; whenever, on tbe contrary, the pressure of the fluid tends to iliminiik that angle, (be equilibrium will be itaUe. 406. The ifrtowBfif.— Let a n 6, Fig. S81, be a floating solid capable of being divided into two symmelHcal halves by a plane jLob, which coincides with the plan« Tff' !SI. of tbe psper; and let Q be its centre of gravity, snd a that of tbe fluid dia- plsced by A D B, the immersed portion of the solid, when floating in equili- brium in an upright porition. The plane a a, which cmncides with the surface of the Anid, is called (he plane ofjhntatiim. Since the solid is sym- metricat with regard lo ihe plana A D &, tbe line a h, joining the points □ and u, must be in that plnne. Sup- pose now that tbe solid be made to revolve through a small angle, S, in tbe plane adi, so that the quantity of fluid displaced may be the same as before; let ot br" be the new plane of floatation, a b and a b intersecting each other Id c. Draw h r, a vertical through r, the centre of gravity of the fluid displaced by the solid in its new position, and p r, nq, verti- cals ihroogh p, q, tbe centres of gravity of tbe wedges, i r y" a, BYj'b; also throogb H draw ur R parallel toab, meetiDg ce, k vertical throqgh c,1d b. The point m is called the (wfoceHfre. THB METACCHTBI. 219 I If a body be divided into any number of parta, the moment of Uie whole body with respect to a given plane is eqoal to the snm of the momenta of each part with respect to the same plane (86). Hence, since the density of the body is nniform, and therefore the mass is proportional to the volume (275), (volume of ai>&) EF+(wedge Aca)cr =3 moment of ao&d = (volume of A D b) E h— (wedge Bob) on; the negative sign being taken, because en is in the contrary di< lection to c r, and b h. But vol. of ▲ D B aa Tol. of 0 D 5 =: v, BUpposo ; then, (wedge Aca)cr+(wedge Bcb)cn= v.eh— v.bf =s V.HF = V.Hlf .0. . [a]. Now if m be a small part or element of the surface t a y\ and c m its distance from the line y tK, then the thickness of the wedge at the point m is c m . 0, and consequently the volume of the wedge ▲ cais S (m . c m . 9) = 9 . 2 (f» . cm) = 0 . t a y' . c r, similarly, vol. Qf wedge Bcb^d.Yhif .on. But since vol. of a d b = voL of aob, subtracting from these the common portion, a db, vol. of wedge a c a = vol. of wedge b c d, therefore YaY'.cr= t6y'.c»», and consequently c is the centre of gravity of the plane a y 6 t'. But since vol. of wedge Aca = O.y ai* .cr^ multiplying each aide by c r, we obtain, (wedge Aoa)cr = 9 .Yar* .cr^; similarly, (wedge Bo6)cn = ©.y6Y'.cn*; .-.(wedge A c a) c r + (wedge B c 6) c » = 0 (y a y'. c r* + y J y'.c »*) [6]. Now (wedge a c a) c r is thcr statical moment of the wedge round y y', and is the sum of the moments of all its elements ; but the element of the wedge has already been shown to be 0 . i» . c m, and the moment of this element round y y' is therefore 0 .m.c to', and the sum of these moments is 0.^{tn.om*); but this is the expression already found (346) for the moment of inertia of the plane y a y' round y y' ; therefore y a y' . c r* is the moment of inertia of the plane y a y' round y y' ; hence, YaY'.cr* + Y6Y'.on* is the moment of inertia of the whole plane round y y', and YaY'.cr'+TjY.cn' "= A.i*, wlure A 18 the tnt, of the plue of fliutation, tnd k ita r*din* of gyration (349) round T v'; therefon, bj equating \a] and \b\ and •nlMtitnting a., if for itd Talue in [&], we obtain l.i*.T.Hll. If Abe the beightof a c7liDdrTcalTeHel,oF which the base ia i, jnit capable of oootsining the.fiuid diiplaced, then t — a. A, and A.P.A.A.HH.ori'-A.HU; that Is : — the raditu of gyra^on of tht plane offioata^iXK about itf (mt o^ofeillaJton, u ameaufroportwnai b^iceenlhe htight qf a e^liniineal ti«M«I eap^de of oontaiitmg lAe ^luiij ditplaced, of tehvA A» bate U thtplaM offioaUaion, and IM dUttmet betiMM tA« MKfn oi^ gravity of the fluid diiplaeed and the raetaetutn, Thia eipreeiion hears a remarkable analog; to that relating to tbo centre of oscillation in 341, namelj, t.*=:ca.ao. 407. A pressure acting in the direction r m, Fig. 282, will tend Pig, 181. to diminish or increue the angle I OH F, according as u i* abore or below □ ; therelore the eqailihrinin of the floating solid vill he elable, aa A.ormutable.BSB, according as Mia above or belov o ; and the amount of stability will also eridentlj de- pend on the depth of a below ii. The two pressures at h and a being equal, and acting in parallel and opposite direct ion a, constitute a couple (SI). Therefore the stability of a sailing veuel, or its power of re- sisting the lateral pressure of the wiod on the Hits, depends on the depth of the centre of frraiity of the veinel below the met&- centre ; henco we perceive the necessity of accnmulating weight in the lowest part of the veasel, iu order to depress the cenbe of gravity : this is accomplished by means of ballast, when the veasel is not otherwise loaded. Rf . K3- '^^ conditioni of »qailibrinm of a floating light wood — for example, American pine — in the shape of a tcBnsverse section at a ship, 09 AB, Fig. 283, with an upright stem c, in the centre of the deck.Burface, a, on which slides a weight n, furnished with a clamping- screw. The keel, b, should be lo loodi^, that when the weight is at the bottom of the Btem, c, tho block when floating will right itself after being displaced laterally, bat that when the wei^t is at the top of the ~'~~1, it will npset. The changes in the QUANTITT OF FLUID DI8PLACr.D. 221 stAte of eqmlibriam, and the passage from stability to instabilitj may be examined hj gradoallj shifting the position of the sliding weight. 408. There is no Icind of Tessel afloat in which stability of equilibrium is of so much importance as in the life-boat, Fig. 284, in which stability is so fully realized, that if it be placed keel upwards in the water, it will, like the child's tumbling toy, in- stanUy right itself. This is effected by raising the bow and stem of the boat considerably, and enclosing at each end a water-tight air-chamber, and at the same time loading the keel heavily : by this arrangement the interval between m and o, (Fig. 282, ▲}, and consequently the stability, is rendered as great as possible. 409. When a solid is immersed in a finid, it displaces a quantity of the latter equal to its own bulk, a legitimate consequence of the impenetrability of matter (2). If this quantity of fluid be lighter than the solid, the latter will sink, but if heavier, it will swim : this has been already alluded to (61) as the result of gravitation. But if the flaid displaced be the same weight as the immersed solid, the latter yrill neither rise nor sink in the fluid, in whatever position it be placed ; a circumstance arising from the force of graritation acting equally upon the solid and the fluid displaced, the quantities of the matter in each being equal. Fishes appear to be in this state of equilibrium when immersed in their own element ; and for the purpose of enabling them to preserve this state at different depths they are prorided with an air- bladder, by compressing or expanding which, they are enabled to cause iheir bodies to acquire the same density as that of the water in which they live. At a very great depth, the air in this air- bladder becomes considerably condensed, and on suddenly rising Id the surface it expands ; and it occasionally happens that this takes place with sucn force, that the muscular efforts of the animal are unaUe to control it, and the or^an is ruptured, causing au extravasation of air into the surrounding tissues. The well-known hydrostatic toy in which a hollow glass figure, partly filled with water, floats or sinks in a vessel of water, by preasing a piece of caoutchouc with which the vessel is covered, u a popular illustration of these facts. Let ▲ b, Fig. 285, be a glan vessel filled with, water up to cd, havinjs; a little figure of uin g^ass, as a balloon, b, placed in it, in which a small opening •xista at the lower part of b, so as to allow water to enter or escape UXDB0STAT1C8. 1 it; preriouBlj allowiDg enough water to ir the baUoon lo raadsr it tienlj of the lame aierago density u the water in ad. Over the moDlb 1 is tied a piece of ibeet cooutehouc. If e 0 floate to □ D, and the caver a be preased inwards 1 into the jar, the air above c d wilf be compregeed. I the pressure wilt be convejed throngli the water to the air contained in i; this will coosequentlv be compressed into a smaller bulk, nnd enough water will enter e to render it heavier than the water, and it falls to b. On removing the band and tailing off the pressure, the air in B expand*, expels the water which had previously entered it. Fig. iga. is fundamental principle of Hydrostatics was linrt ob- served b^ Archimedes, who, as bisteiy informs us, was accidentally led to the conclusion that a bodj, when immersed in a fluid, loses a portion of its vroight equal to that of the displaced flgid. The truth of this may be shown experimental I r by suspending from one of the aroiB of ■ balance a hollow cylinder, o, having a cylindrical mass of any substance, i, capable of exactly fitting into it, banging from it by means of a thread. Place weights in the scale pan b until the solid cylinder a and the hollow one d are exactly coonterbslanced ; then pour water into the vessel c until A is completely immeTsed, and immediately the pan b will preponderate, the solid cylinder appearing to have lost a considerable por- tion of its weight; then poor water into the vessel d until it is quite fiUI, and as I soon as this is done, the } batani« will once more be in equilibtio. Now, as the cylinder D is of BUcb a size that tbe solid mass a vriU eucth' at into its in- terior, it iollows tiiot the ^ water with which D is tilled is precisely equal in bulk to the solid A ; proving most Batisfactorily that the appanint losn of weight saffcred by *, on being immersed in water, is precisely equal to tho weigbt of a mass of the fluid equal in balk to itaelf. The apparent loss of weight io the maas A, observed on immersing it in water, arises from the upward pressure (397) of the flnid partly supporting the immersed solid, and opposing, to a certain eitenl, the attraction of gmvitatiou. PHIICIPLB OF ASCHIMEDBS. 223 411. It may be shown as the ooBvene of this experiment, that the fluid appears to g pound both in air and water, and ascertain the loss of weight; then, knowing the weight lost by weighing the heavy body by itself in water, ascertain the difference of these losses, and by thii number divide the weight of the light body, the result will be its specific gravity. The rationale of this process is very plain, for the last loss s the weight of a quantity of water, equal in bulk to the heavy and light bodies together; and Uie first loss r= the weight of water, equal in bulk to the heavy body, and conse- quently their difference is equal to the weight of a mass of water of the same bulk as the light body. Ex. A substance weighed in air 600 grains, tied to a piece of copper, it weighed in air 2647 grains, and in water 2020 g^ns, suffering^ a loss of weight of 834 grains. The copper itself losing 230 grains when weighed in water, the body must have lost 834— 230 =» 604 grains ; then 600-^604B '993, the specific gravity of the substance. In taking the specific gravities of small solids, a frequent source of fallacy exists in the aidhesion of minute bubbles of air to the surface ; these sometimes adhere with so much tenacity, that no agitation of the solid in the water will dislodge them. When very great accuracjr is required, it is desirable to boil the solid in the vessel in which it is to be subsequently weighed, and to weigh it without removal from the vessel. 415. If the solid be soluble in water, it must be weighed whilst immersed in some fluid incapable of dissolving it, as alcohol, oil of turpentine, &c., and its specific g^vity as compared with the fluid ascertained. All that is required to determine its density with regard to water, is to multiply the specific gravity thus found by that of the fluid employed. £x. A substance soluble in water was weighed in oil; its specific gravity, as compared to oil, was found to be 3*7. The specific gravity of the oil was 0'9 and 3*7 x 0'9b3'33, the specific gravity of the substance as compared with water. 416. The specific gravity of a fluid may be discovered in several ways ; the readiest mode is to compare the weights of equal bulks of distilled water and of the fluia the density of which we are seeking. For this purpose take a phial of convenient sise and carefully counterpoise it. Ascertain first the weight of water re- auired to fill it, and then the weight of the same phial full of the nid under examination ; and, on subtracting from the latter the weight of the bottle, the weight of the fluid will be ascertained. Divide the weight of the fluid by that of the water, and the quotient will be the specific gravity. In order to obtain the greatest accuracy, the bottle should be stopped with a short piece of capillary tube, the bore of which may oe very readily filled exactly with the fluid in question. THE HTDROMXTBR. 235 Ex. A counterpoised bottle held 500 grains of water, and 412 gimins of alcohol; then 412h-500» 0*824^ the specific grayitj required. 417. Another and veiy convenient mode of finding the specific gravity of a fluid is founded directly on the fact of immersed Bolidfl displacing a bulk of fluid equal to their own (410). Forliiis purpose take a glass ball of which the loss when weighed in water IB known, then weigh it while immersed in any other fluid, and, subtracting this from its weight in air, ascertain this fresh loss in weight. Then its loss when weighed in the fluid, divided b^ its loas when weighed in water, will be the specific gravity reqmred. £z. A gUiss ball lost 30 grains when weighed in water, and 24 when weighed in alcohol ; and 24-^30=3 0*800, the specific gravity of the fluid required. 418. The hydrometer. The specific gravity of fluids is fre- quently very conveniently ascertained by meais of this instrameut, ttie action of which depends upon the fact that a floating bodv displaces a bulk, equal to itself in weight, of the fluid in which it floats (404), and consequently that a solid of a given weight sinks deeoer in a lighter than in a heavier fluid. Instruments of this Idna are made of various materials, usually metal or -^ ^ g^asa, according to the uses for which they are in- ^' tended. Their action is confined within a very Hmited range, unless they are of inconvenient length, and their indications are by no means ma- thematicaUy correct, still, for veiy many important , practical purposes they are extremely useiiu. For r~^ determining tne specific gravities of acids, and other chemical fluids, a glass hydrometer is used ; it has this advantage, that' it cannot be falsified by any change of form from external iigury. The construc- tion and mode of graduation is as follows : — ^Procure a thin glass tube blown into the shape of the figure A B, Fig. 287, and from four inches to a foot in length ; place in the narrow part of the tube ac a thin slip of paper, and pour in mercury until, when immersed in distilled water, the whole instrument will sink to within half an inch of its top or bottom, accordingly as the instrument is intended for fiuids heavier or lighter than water. Then thrust, by means of a wire, a fragment of cork and one of sealing-wax into the smaller tube, d : by holding it near the flame of a candle, melt the wax arouna the cork, 'and then idlow the whole to cool. In this manner the mercury will be kept in the ball b, without any danger of its falling out on inverting the instrument. Replace the tube in distilled water, and very care- folly mark with a file the point where the stem a is intersected by the surface of the fiuid : let this be a, then immerse it in a solu- tion of salt) of which tne specific gravity is known ; suppose this Q MLon toe lent poini musi m oaeerrea, sna laeir from 1, which vtll give the ipecifio ^vitr reqni Syket't hydrom^er ie ■ modificatian of thii i aaea in commerce for ascertuniug, b; meana of 33S U> he 1*030, and mark with a Ble ths point where the Item Ii inter- sected by the nufaca of the aolnlion; let thii be b. With a pair of compnsBei lake the distance ah, on a slip of paper of the same rize asthntprevionsl; p1u:adin a, anddiride this into thirty eqnal partB, and from the wme acale divide the vhole length of the paper nntil it has oxtj equal parts mailed upon it ; and nnmber those in fivei : diatinguishing every tenth diviKion with a darker or longer line than the others. Then introdnca this paper into the stem A, in place of the first piece, and push it down nntil the mark a eorresponds to zero, or 0 no (he paper acale ; when this is done, the latter may be retained in Its piaco by a little Tamlih or gam ; and the top being closed by the blowpipe, the instmment ia com' Sleted. To ascertain the specific grantj of any fluid, of greater engitrthan water, by this hydrometer, immerse it in the flnid, and when it floats at rest, note the pj the solid, veight of the solid- i—i ; uid iFeight of the not id - weight of the fluid diaplaced = a;ipamt weight of the solid in the fluid,a;i— i, tbereloTe might of the fluid diHplaced''(—i—(t—T)^Y—i; ... , ED. gr. of the solid z— i Bp. gr. of the huid V— X 8. 2^ compare tke tpeeifie gravM»t of tino Jliad*, a and B. Let ir be the weight of th8Dj^">'aBter: i the weight that mait be placed in c, to Buik the instraDient to h in the fluid a ; and t tlie coirespoDiliiig weight when in the fluid a; then, veight of fluid i. displaced "W + z, weight of fluid Bdi«pUced=w+T; bat the volnine oT fluid displaced it the same in botii cases ; sp. gr. offlgid A w + x sp. gr. of fluid b w + r ' 420. Hare't SydromtUr. — This instmineDt aflbrda a readj means of comparing the specific gravities of two fluids, a and B ; and conseqnently, when that nf either '\i known, the other maj be delermlned. b c, r i. Fig. 289, are two ^- *•*■ rertieal glass tnbea conunonicating at their upper extremities, a, p, with ■ cavity, o, supplied with a stopcock, through which the air may be withdiawn from it The lower extremities of the tubes, c, E, are immened in the fluids a and b, contaiued in two ir a portion of the ur be now withdrawn from o, the fluidB will be raised in the tubes b; the external pcennTeaf the atmosi>bere; and suppose the fluids A and B nse to the points p, q, respectivety, the sur- faces of the fluids in the Tessels being at c and a letpectiTel;. If the atmospheric preBsure = n, and the pressuie of the air in i> = m, then n-ii = (8p.gr.ofA).cp, also n-M=(»p.gr. ofB).B.); .. , tp.gr.of* nq Iherebn Hp.gr ofB^cp' In order to avoid errors dne to oapillaiT attraction (ST), a second obeerralion mntt be made at two other points, p*, ij', and the dis- tances, PF',<(q', CBrafnllrmeMored; then, ascaptllarity will aEfect the pant* f, r', alike, as well as the points q, tf, the colamiu p t', olelj b/ the vune diflarenM of preuares ; gp. gr. of i. qq' ■p. gr. of a F F 421. TTit SteraonuUr* — The object of this inBtnment ii to measure ibe volmaeB of small solids that cannot be immened in Alt KM), ^'t^''- ^°^ ^bis purpose the lower eitremitiei of two eari8on is changed, dry atmosphenc air being here assumed as unity, or,^ to avoid decimals, 1000. Let a copper or glass flask, furnished with * Tbe descriptions of this and the preceding initrament are plsced hare in connexion with the sobject of speoiflo gravities ; bat they wm be better onderatood after reading the chapter on Fnenmatacs. 230 HTDBOBTATICS. a stop-cock, be weighed when filled with air, and then again after being exhausted by means of an air-pump as perfectly as possible; the difference of these weights will give the weight of air con- tained by the flask. Then fill the flask with the gas under ex- amination, and carefully weigh it, this weight, tninui that of the flask, will give the weight of the gas. The weight of the ^as divided by that of the same bulk of air will give the specific gravity of the former as compared with the latter. Ex. A ^lasB flask, carefully counterpoised, held 5*7 grains of atmospheric air and 6*4 grains of defiant gas ; the specific gra- vity of the latter was therefore 5*4-t-6'7« 0*982. In examining the specific gravity of gases, they should be care- fully freed from moisture by being passed over recently ignited chloride of calcium ; and the results obtained corrected for tem- perature in the manner described in all chemical works. It is also necessary, in order to obtain very accurate results, to exhaust the flask two or three times successively, and refill it with the gas of which the specific gravitjr is required, in order that the residual atmospheric air may be so diluted, as not sensibly to afiect the result. 424. The following questions will illustrate some practical ap- plications of the knowledge of the specific gravities of the bodies. A. What is the weight of a cubic inch of copper? The specific gravity of copper being 8*9, or, more exactly, 8*879, we have to multiply this by the weight of a cubic inch of water, which, at 62° F., is 252*458 grains : therefore, by logarithms, — log. 252*458 » 2*40219 log. 8*879= "94836 log. 2241*5 » 3-35055. Ans. 2241*5 grains. B. A glass flask being filled with mercury at 0** C., the mercury appeared to weigh 3156*613 grammes, and the weight of the air contained in the flask was 0*281 grammes; therefore the true weight of the mercuir contained in the flask was 3156*894 grammes. When filled with pure water at 0° C, the water ap- peared to weigh 231*888 grammes; and the weight of air con- tained in the flask was 0*281 grammes ; therefore the true weight of the water was 232*167 grammes. The same volume of water at 4° C, when its density is a maximum, would have weighed 232*193 grammes: hence, sp. gr. mercury at 0® C. ^ 3156*894 ^ 13.50590 sp. gr. water at 4"'C." 232*193 " Two other observations gave for this ratio the values, 13*59578 and 13*59602 ; the mean of all three is 13*596, very nearly.* * Begnsolt, Aanales de dumie, t. 89, p. 296. TABLB OF SPECinO QRAY1T1E8 ; WATBB s 1, AT 4" G. 231 425. MeUds. Lithiom .... Potassium .... Sodium Msgnesium . . . Alnminiam . . . Anenic .... Tellnrinm .... Antunony . . . . Zinc Cast iron . . . . Tin Steel Manganese . . . Cobt3t Copper, cast . . . ' wire ... Nickel Bismuth . . . . Cadmium . . . . Silver Lead Palladium .... Thalfimn .... Tungsten .... Gold Platinum, forged laminated Mercurj Organie Bodies. Wood of ponlar . . . ■ cedar . . ■ lime . . . .' •"^■^■^^"^ Hall • • • • " UlHHSD • • • ' oak .... Ugnum-TitflB .... Cork White wax .... iTory 0-593 0-865 0-972 1-760 2-615 5*881 6-258 6-860 6-862 7 207 7-285 7-816 8-000 8-513 8-788 8-879 8-800 9-882 8-900 10-474 11-445 11-650 11-880 17-600 19-358 21-837 22-069 13*596 0-383 0-561 0-604 0-845 0-852 0-925 1-330 0-240 0-960 1-826 Inorgamc Non-MetalUe Bodies, Ice 0-865 Amber 1078 Sulphar 2086 Glass, crown flint . Rock crystal . Marble of Paros Diamonds . . Oriental rubies 2*488 . . 3-829 . . 2-653 . . 2838 3-501— 3-581 . . 4-283 Liquids, Ether Alcohol .... Bectified spirits . . Ammonia .... Sea-water .... Milk Oil of olives . . . turpentine . . cinnamon . . cloves . . . — bitter almonds Acetic acid . . . Nitric acid .... Sulphuric acid . . 0-715 0-792 0-837 0-960 1026 1-030 0-915 0-869 1-010 1036 1-043 1-063 1-451 1-841 0€ues. AiBs 1 ; Bab. at 30 in. Hydrogen carburetted Ammonia .... Nitrogen .... Oxygen ..... H^dro-8ul]^hnric acid Nitrous oxide . . . Carbonic acid . . oxide . . Cyanogen .... Sulphurous acid Chlorine .... 0-069 0-555 0-590 0-972 1-106 1191 1-527 1-529 0957 1-806 2-234 2-470 Weighis of given Bulks of Water and Air^ for oaleuUUing the absolute Weights from the Specific Oravities of Bodies. Bar. 30 in., therm. 62** F. loos. Cubic inch of dist water in grains . . . 252-458 . 2 '402 19 foot in ounces avoird. 997-13697 2-99875 in pounds ditto 62-32106 1-79463 Weight of 100 cubic inches of air, in grains 80*49 . . 148416 CHAPTER VIII.. In the preceding chkptar the conditiaoa of eqmlibrium uf the to- called non-elRBlic fluids have been considered; ia the present, some of the laws that govern the motions of tliese fluids vrill be investigated. 426. Fluids, escBping from orifices in vessels containing them, obsj, like solids, the law of grevitaticTi, and their motinii is acce- lerated in a corresponding manner. The eipro'sion of this fact ie known aa the theorem of Torricelli, snd ma; be thus 0 the diitanee o/iU rurface of the livid above the centre of the ori/iee. Floids obey this Ian without any relation Fig.Xil. to their density, their Telocity solely depending upon the depth of the orlSce, from which ihey escape, below !the level of the fluid. Thus, if a Tessel bo filled with water to the height of the dotted line, d, Fig. 291, and .1 three apertures be made in the aide of the ressel at i, B, c, the water will escape from each with very dif- ferent velocities. At A, it willposBCBB the same velocity caa if the patiicles of water had fallen in racuo from ii to A, whilst at B and c the eacapiiiK current will nos- suBB the same velocity as if the Bnid composing it had fallen from n to b, and from n to c. From this fact we learn that if two equal vessela be tilled with fluid, and allowed to diacharge their conteuta by equal orifices at e<|ual dejtthB, one of them being kept mite fu& bif the addition offieth finid, the quantlly of water discharged in the some time from the latter vesael, as compared wilh the qoantity escaping from that which vat allowed to empty itself, will be as 2 : 1. This result is analopius to that previonaly obtained (299), with regard lo the molion of a body acted on by a uniform acce- lerating force, namely, that tho space described from rest, in any l^ven time, is one half that which would have been described wi;h the last acquired velocity continued uniform. It followB, also, from (306), that V = Jig.h, h being the depth of the orifice ; or, in other wor]s, the velix:ity of a flnid issuing from an orifice varies as the squflra root of the depth of the orifice. Alao, since the ooantity of fluid paaung througfa an orifice in a given time must YKKJl OOKT&A.CTA. 233 be proportional to its Telocity, it follows that the qnantit j of fluid dischamd in a men time will be proportional to the square root of the depth of tne orifice : thus, for example, twice as much fluid will escane from an aperturo at the depth of 8 inches, or feet, as that discharged bj an equal orifice at the depth of 2 inches, or feet. 427. £aeh particle of a spouting fluid may be cousidered as a projectile, aua will therefore describe a parabola (307), and as it appears (309) that a bodj falling freely from the directrix of the parabola to toe point of projection will acquire the yelocity of pro- jection, it follows that a line coinciding with the surface will be the common directrix of all the parabolas described by spouting fluids. It may also be readily shown, that if a fluid spouts from apertures in the yertical side of a full yessel resting on a horiasontal plane, the horizontal range is greatest when the aperture is at one half the height of the yessel, and the ran^ is then equal to the height. AGo, the same range on the horizontal plane will be ob- tained from orifices at equal distances aboye and below the middle point. These results are precisely analogous to those preyiously obtained (313) respecting projectiles. If a circle be described on the yertical height of the nuid as a diameter, the horizontal range of the fluid spouting from any aperture will be the horizontal chord of the circle, drawn through the centre of the aperture. 428. When a fluid escapes from a circular onfioe having a yery thin edge, in the bottom of a yessel of suflBcient depth and capa- city— as, for example, a foot in width and depth, the following phenomena may be observed : — A. The particles of fluid descend vertically to yrithin about three inches of the bottom, and then move, in more or less curved paths, towards the orifice. This may be best seen by mixing with the fluid some particles of matter of visible magnitude, and, as nearly as mAybe convenient, of the same specific gravity as the fluid. B. The surface of the fluid gradually falls, remaining horizontal until within a certain distance of the bottom, when it forms a hollow cone, immediately above the centre of the oiiflce, the surface of which is convex mwards.* C. The cunnent of fluid havine escaped from the vessel, contracts in diameter to a distance from the orince equal to half its diameter : the diameter of the contracted portion of the vein being to that of the portion nearest the orifice as 5 : 8. p. Every fluid vein, moving vertically downwards from a circular orifice, is composed of two well-defined portions, which meet at the narrowest part, or vena eontraetOf as it is called. The portion nearest the orifice is perfectly transparent, like a rod of glass or crystal : its section is circular, and it gradually decreases in dia- * This Bnrfaoa is formed bj the rerolation abont its exis of a bjperbolio oorre of the fourth order, the eqaation of which in its simplest form is 334 HrDKODTaiHica. meter, until it jniDs the second portion of the carreni, which >■ Dearly onsque, and apparently much agitated, consisling of s mul- titude of drapH, each produced bj an annular dilatation of a portion of fluid at tbe orifice of the veear-], and undergoing, during the time of ita falling, it series of periodic vibrations^ bj vhich each drop alternately elongate* and contracts. A senea of pulutinitt thni ocean at the onGce of the vesael, their nnmber lieiag in the direct ratio of the rapidity of the cunent, and in the inTerae ratio of the diameter of the orifice; they are frequently ioffidantiy rapid to produce a distinct maaical sound. G. In consequence of the contraction of the fluid vein (C) liqaida escape with greater rapidity from a conical tube than IVom a cylindrical one of equal length, provided the truncated a^pex of tne rormer corresponds, in situation and MCiion, to the poJDt of gnaUtt eontraetum of the fluid currant. The following are the nnmerical results of some eiperimenta : — A *e«el with a nmple bole discharged . . 6! quart* U 100*1 „ with a pipe two diameters of hole in length 8! „ A vessel with tiie aame [npe inserted half way in the orifice, only 6! qouto in 100* : When the bottom nf the vessel was the para- bolic curve described by the particlea . . 92 „ With a beU-moQth added to this .... a moxwiiim. 429. It appears from the experiments of H. Lacontnre that not only the focm of the fluid issuiug from a fnnnel-ahaped vea>e1, bnt also the quanti^ delivered is mndified by receiving the fluid on a horizon tsl plane placed at various distances from ue orifice. If a ■mall quantity of lycopodium be suspended in the 6uid, the isaoing stream more readit; breaks np into globular beads, the number of which diminishes, and the size increases, as the oppoa- ing plane is brought nearer to the orifice, as a, 6, c, d^ Ttg. 293. In a, b, and e, the quantity delivered is sensibl;r the same as vben the stream is unimpeded. In d^ when only a single bead remsini, the Sow it considerably diminished, and in e the discharge is at a minimum. In the pention /, the fiow is mneh greater than wheo baskbr's mill. 235 JB9g,fg3. n unimpeded bj the opposed plane, and it reaches a maximam at the distance represented in g.* 430. In a vessel fall of water, the down- ward pressure of any column of fluid, as A B, Fig. 293, acting on the horizontal layer, c d, communicates an equal pressure on the opposite sides of the vessel (398) : if, then, an aperture be made at c, the pres- sure there becomes noil, and fluid escapes, whilst the pressure remains active at n. As the pressure at c against the side is removed, and that aeainst d continues in action, the vessel, if suitably suspended, will move as if repelled in a direction op- posed to that of the current escaping from c. Barker's Mill. — The movement, arising from this reaction against the sides of the vessel, is readily illustrated by means of the apparatus, ▲ b c. Fig. 294, consisting of a large glass tube, ▲, closea at both ends with corks ; two tubes, b, c, bent twice at ri^ht angle^ are fixed in the lower cork, their ends at e and r being bent in opposite directions. Fill a with water, place the f»rk, o, in its place, and p. ^. suspend the whole, b^ the *^' thread, h, from the ceiling. The apparatus will remain at rest, for no fluid can es- cape, as the pressure of the air against tne open ends, B F, exceeds the. gravitation of the fluid (427). Then remove the cork o ; the at- mospheric pressure will act on the water in a, which will now descend by its own gravity, and passingthrough the tubes^ b, c, and escap- ing at B, F, will produce a rapid rotation of the appa- ratus, in a direction contrary to that of the cunrent of escaping fluid. This motive power is known by the name of Barker's mill ; it is, however, of very little practical utility, as a mechanical agent. ^ 431. When a fluid passes through a tube, or channel, of which the section is greater at one part than another, the velocity of the liquid is necessarily greater in the narrow than in the wide parts, as the same quantity must pass through every section in • Les Hondes, Xay 10, 1868. 236 RTDSODTVAVICS. iV* SK. the same time. Thas, if in the tobe A b, Fig. 2d6, water be allowed to run throngh in a Btream, so as to keep it constantly full, ite Telocity at o or d will be much greater than when traversing tiie wide parts, E, F, in proportion as the section of s or f IS greater than that of c or d. The momentam of the fluid will be equal in every transverse section of the tube ; for as it is e^ual to the auantitv of matter multiplied by the velocity (276), although the quan- tity of fluid contained in c d, is less than in b f, yet its velocity is proportionably grater. For the same reason, when wat^r flows through a funnel, its velo- city is much greater when passing through the tube than when traversing the wider part of the instru- ment ; and hence also the current of riven is more rapid under the arches of bridges than at any other part. 432. Natural fountains are sometimes formed by the water escaping from some concealed reservoir through a channel, or fissure, in the strata containing the supply of fluid. On the water escaping from a point below the reservoir, it possesses a velocity regulated according to the theorem of Tomcelli (426), and therefore sufficient to project it upwards in the form of a jii tPeau, Artificial fountains are constructed on a similar FSff, 296. principle ; thus, if the tube a o, Fig. 296, be filled ^^ with water, it will escape from the aperture at o, \f in a jet risine to an elevation somewhat less than that of the cdumn of water in a; according to the experiments of Marriotte, attaining an elevation of 5 feet, if the column of water in the reservoir be 5 feet 1 inch high. The elevation of the jet d'eau would be equal to the height of fluid in the reser- voir, if all triction from angular bends or projec- tions, &c., as well as the resistance of the atmo- ^ sphere, were removed. The greatest elevation is \\ obtained when the fluid escapes through an aper- ture pierced in a thin plate of metal, avoiding all conical tenninations, or ajviageB, as they have been called. 433. The remarkable phenomena exhibited by the Geysers or thermal springs of Iceland, have been satisfactorily explained by Prof. iSpdidl. These consist of long vertical tubes or shafts, which become graduallv coated with a siliceous deposit from the water, and are supplied by some reservoir at the bottom ; the depth of the tube was in one instance ascertained to be 60 feet. The water at some considerable depth, perhaps 40 or 50 feet, is at a temperature above the boiling point, at the ordinary pressure of the atmosphere, but is maintained in the liquid state by the FBICTIOH OF FLUIDS. 237 preBsnie of the Boperincumbent column of water. When thii over-boOing water is, by a sudden accession o( pressure from below, raised above the point at which it is constrained by pres- sure to remain liquid, a portion of it immediatelr assumes the gaseous form of steam, and driyes up, in a magnificent jet, the column of water above it : and similar effects recur at uncertain periods. These phenomena may be artificiallj illustrated by a metallic tube seven or eight feet long, filled ¥rith water, placed Tertically, and surrounded by small charcoal fires contained in wire baskets, at the bottom, and about one-third of the length from the bottom, the lower fire being the larger of the two. If the orifice of the tube be surrounded by a broad and nearly flat fonnel-ahaped vessel, the water, after being ejected, will return into the tube, and the same result will be periodically repeated. 434. Friction is found to take place between solids and liquids, and eyen between the particles of fluids themseWes ; but is not susceptible of exact measurement, as is the case with solids (52 — 56). A stream of water is always more rapid in tbe centra than at the sides, as, being deeper there, the current flows on die sorfitoe of lower strata of fluid: whilst, in the shallow portions of the river, the water is exposed to the friction of the rough and miequal bottom. In the centre, also, the stream is somewhat more elevated than at the sides ; as, in its rapid course, it draws the water from the sides of the river after it, by the friction of its particles. M. de Buat has given the best practical rule for ascer- taining the yelocity of rivers, when the sectional area, and the fall in a given distance are known. Supposing the whole quantity of water to occupy a rectangular channel, the width of which is equal to that of the stream, from bank to bank, and the area of the transverse section equal to that of the whole transverse seo* tion of the stream, then the depth of water in this channel is called the hydrauUe mean depth. The velocity will be nearly proportional to the geometric mean between this depth, and the fall in a nven distance. If the course of the stream be very tortuous, tne yelocity will be considerably below the value thus obtained. The practical method of ascertaining the bulk of water dischaiged by any given stream, is to ascertain the approximate sectional area by soundings, and to observe the average time occu- pied by bodies of nearly the same specific g^ttvity as water, immersed in different parts of the stream, in passing a measmed space of 50 or 100 feet. The product of the sectional area in square feet by the velocity in feet per minute, will give the num- ber of cubic feet of water discharged per minute. Li the transmission of water through pipes, the friction against the inner surface of the pipes is so consKierable, that it is found necessary to allow one-third or one-fourth more diameter to the pipes, than would theoretically be requisite to transmit the pro- posed quantity <^ fiuid, provided it could traverse them without 238 HTDHODTKAMIOB. friction. And the same law is observed in the distribution of floids in the animal economy ; the sum of the sectional areas of the branches into which any large blood-vessel is subdivided, is always considerably greater than the area of the trunk from which they have beea derived. A sufficiently accurate estimate of the velocity will be obtained by supposing the height of the head of water from its Rurface to the dischaiging orifice to be diminished in the same proportion as the diameter of the pipe would be increased by adding to it ^th of its length, and then taking four-fit'ths of this height. Thus if the diameter of the pipe were 1 inch, and its length 100 inches, we must suppose the efiective height to be reduced to one* third by friction, ana the velocity must l^ calculated for a height of four-fifths of this, that is, a little more than a quarter of the actual height. If the pipe had been two inches, the head would have been supposed to be reduced only one-half by friction, and the latter pipe would discharge at least five times as much water as the former, although it has only four times the sectional area.* In the ajutage, or escape-pipe, of a foun- ^p. 8»7. ^jjj^ ^ similar fact is observea ; for if it be bent abruptly, and not with a regular and gradual curve, the passage of fluid is much obstructed. Thus,^ fluids escaping under equal pressures, will rise much higher if passing through the tube A, Fig. 297, than throu^ B. This may be most readily shown by in- serting two such pipes into two orifices in the same vessel, situated in the same horizontal plane ; and the larger the orifice of the jets, the more uneouafwill be the altitudes to which they are observed to rise : the prejudicial resistances in- creasing rapidly with the increase of velocity of the issuing fluid. There is a remarkable confirmation of this principle in the tortuous course ordinarily pursued by enlarged veins and arteries, the coats of which do not oecome thickened in proportion to their increased calibre; they are thus protected from the effects of sudden augmentations of pressure, which their comparatively attenuated coats would probably be otherwise unable to sustain. 435. The motion of nuids in conical tubes is illustrated by sn experiment of Bemouilli ; he found that water, in passing rapidly from the narrow to the wide end of a conical tube, a b, Fi^. 298, would empty the vessel, o, filled with water and communicating with AB, by a small lateral tube. Dr. Barry found that a similar effect was produced by a descending current ; for when water was * Idbrsiy of UseAil Knowledge— Art. HjdrMiliee. U This pbyaicalfact maTprob*b1j be best «ipliiiiieil tbag: — Each monsg particle bu acquired > certain amoont of energy, hj which it exerta apreMore in the directioD of the aiia of the labe, thiongh which it u paadng. If flowing lowardi the imaRtr end of a conical tnbe, A, Fig. 300, this pn»iit«, a h, maj be nooiied into rtg. Mo. a c perpendiijalar, and e b panllel to the naa of tbe tnbe; of these ae ii wholly efiectiTo againit the aide of [he tnbe, and if an apartnre, or lateral branch exiita, the fluid will eacspe thence. If, on the contraiy, ■he finid Sow tonardB tbe larger end, as in B, then c b, the portion of ihs preanire ab reMlved perpendi- cularly to the aide of the tube, acta enlirely Jtom its snr&ce, and if a Interal Invncb enter at that point, immersed in a small Tcaael of fluid, u c, Figa. Sgs, 299, atmoapheric preaaure on the floid in c, bei[ tnmBniitted throngb tbe brancb-tabe, and unoppoaed at ita point JQUclion, trill cause tbe fluid to enter the conical tube at that point. And it is eiident that the greater tbe value of e 6, that a, the greater the relocit; in tbe conical tube, the greater will b« tbe lateral infloi; this result ia conflrnied by eiperitDent, Ibraa the Telocity of the fluid in a increaaea, that in o maj be railed tbivagh a higher Tertical colman. In the circulating ayatem of animals, the arraDgementa of tbe bk>od-*easeli frequently exemplify these principles. Id the arterial syrt«m the blood, aa it is too well known, Bowa rapidly from an apertnre, or &om a divided branch, in accordsuce with wbat has been Mated respecting A, Fig. 300 ; and the branches are Ere- qoently given off obliquely, to facilitate tba onward current in ',5 240 HTDBODTHAMICS. them. In the venous system, on the contrary, in which the blood- corrent flows as in b, the branches usually enter the larger vessels more or less perpendicularly, so that a current of blo^ passing along one vessel, may assist m emptying a lateral branch ; or two currents entering a larger trunk at tne same point, may thus exhaust the contents of a small vessel entering between them. In the human bodv, the termination of the lefl spermatic vein in the renal vein, and that of the thoracic duct in the angle formed by the internal jugular and subclavian veins, afford remark- able examples of such hydraulic arrangements in animal structures. 436. The applications of the phvsical properties of fluids to the purposes of domestic economy, and the wants of civilized life, are extremely diversified, and afford some important objects of study to the mechanic and engineer. An outline of the construction of a verv few of these valuable contributions of science to art will not be misplaced in this chapter, as this will afford an opportunity of expl&inin^ to the student their modes of action on the principles al]^ady laid down. Among the various instruments used to elevate fluids above their former level, those termed pumps are the most important. Their theoretical construction is extremeljr simple : they mav be divided into two chief sections ; the first including the sucxing and lifting, the other the forcing pumps. The suckinff or suction pump, as it is incorrectly termed, con- sists essentia]^ of a hollow cylinder, a b. Fig. 301, having a valve, E, opening umoardB, fixed in its lower extremity. A piston, c, furnished witii a valve, also opening upwardSf moves in the in> terior of the cylinder. If the lower end of the pump terminate in a pipe immersed in water, and the piston be depressed to e, the air between c and b will escape bv the valve in c, and on elevating the piston, the capacity of the space below c being increased, tne pressure of the air con- tained in it will be diminished (499), and in consequence of the pressure of the air on the water at the bottom of the tube being thus diminished, the pressure of the atmosphere on the surrounding fluid causes it to rise in the tube, until equSibrium is restored. On again depressing and elevating the piston, a further diminution of internal pressure takes place, and a further portion of water is elevatea, and we may suppose this repeated until the water reaches the valve, s ; at the next elevation of the piston, a portion of the fluid rises through B ; and on once more depressing c, this water raises the valve in the piston, and passes through it, so that on again elevating c, a K^.801. 2f 1 3> colamn of water ii raised with it, which eTentiully ncapM through the sida tabe, or epont, o. Oa thai contJoaiDs kltenutely to ruae hhJ deprera the piston, witer ma; be raiaea from the reser* m the height of that pniot aboie the leTel of the water in well or reaerrair wei« leu than that of a cijlumn eqaa] in weight to the atmoaphers, which ii aboat 3S feet ; but aa the piston of an ordinary pump ii eapabte of producing only a vetj imperfect numnm, it followB that the height to whioh water may b« ruaed hj theas meana will be condderablT leM than 32 feat The action M the lifting-punip ia ao limilar, tnat a distinct account ofit i» DimeoeaBarj ; aa nanallj coiutriicted, it diSbr* chieflv, from the Emp jnit described, in the pistno entarine the cylinder fiom low, instead of from above. The following experimsnt will ahow (if indeed ■ demoaatralion can in the present d«7 be deemed necessary) that the elsTation of water by the commoD pump ii doe to stmospberic pressure alone, and not it) any hypothetical "^Dciple of snction," as was once supposed. FImo a (all re- oeiTcr over a vessel of water on un air-pnmp pUte, and let the Btem of a noatl modei-painp paw air-tight through the cover of tbe reoeiver. While the receiver is foil of air the pump wilt work madily, bat with difficulty when a partial vacunm is formed in tha noeiver; and if tbe edianation oan be carried so far, that the preacore of the air become* lesa than the weight of a column nachiogfromthevalTeoftheptitap to the surface of tbe water in die veaMl, the pump will not act at alL 437. Whenever it is required to raise water to a greater height than the lifting-pump oan efiecl, it becomes peceaaary to malie use of another construedon, Sl3.90t, called toe forcing-pump, which differs from the last in the position of its valves : the piston, B, Fig. 303, moves ur-tight in t}ie cylinder, fo, as In the sucking-pump, but it ' baa no valve. A valve opening upwards is filed in the lower part of Uie cylmder ; and at a, a lateral tabe, o a, is Sied, having a valve, D, opening outwards. On n being depresMd, the air is forced through the valve d ; ood if the pomp has its lower end plunged in water, OD raising a, the fluid will, when the air has bean expelled as before, rush in through c, in consequence of the dimioiahed pressnra on ita aorfaoe. And on depressing the piston, this portion of water will be forced through the valve p, ont of tbe nde tube, aa, as, in coneeqasuce of tbe valve c opening upwards, it cannot escape downwards at that point. B lUBODTa AHKM. The height of o abore tha r«Mrroir is limited, m in tbe pnoed- FIm SOS '"8 case, but there is do limit la the tteiglit to which the tube, a i, mKj wceiw), iinriaed CDDiidenble, the labour of working Che pump is much IncniwBd '"""'" Bisilv of oTercominK all at onoo 'the • • ■ ■ - - I br the ne I the ineiti r . the inertia of the wholn column ii each deaceot of the iiialan. This in euce m*7 be obviated by the uae ot an air- Teuel, DF, Fiff. 303, in which h is the lower extremity of the ascending tube. When (he surface of (he water in nt- HaeB above H, the preaaure of the air which is condensed iD r K, the upper part of d f, Ibroes the water ap H F in a continuous atream. 43S. That most'Tslnable acqniaition to modern medicine, the well-known stomach-pump, ia sq instriiment ot this deacriptioo; the tube introdooed into the atomach being alteroatel; cen- Dected with the lower end, or the side lube k, according as it is required to iqject fluid into, or lo emptj the conlenls oC, the ttuinach. 439. 2%« Oaiifornia Aimn.— This most useful and oomprehcD- UTe form of pump is due to the genius of oar transatlantic breth- ren. It is a double-acliue horiiontal pomp, and is tvpresented Hg 304 '^ ' 'E' ^^ altacbnd to the upper end of a ' verlicalboard : AB, isabehtleTer,bj which the sliding-bar, c. is carried backward and forward : the handle a ma; be inserted into a socket on either side m the piece, a, as may be most coovrnient; or two handli'S ~ua; be employed, if great force is required, IS when used for a Gre-engine. The piston- od connects a solid piston with the bar, c. In the chamber, k, abuve tbe barrel, are fmu valvea, two opening inwards connected with the inlet-pipe, H, and the other two opening outwards connected with an air- chamber, D a, which is clamped down od (he chamber e by two swing-bolts and nuts, E, F. D is tbe outlet [upe, and » a plug, which is screwed down when Iha pump IS required lo be used aa a forcing pump (437), and removed when a gentler flow ia required, aa in that cane the surface of water in the air-vessel is relieved from any pietsuln greater than the ordinary pressure of the atnio- aphsie. As tM water la received at one aide of the piston and delivered at the other, during its tnolion in boih directioos, the flow is nearly continuous, even without tho air«hamber: tbe parti an (oKd tad little likely to get oat pQlBi*e power is »ery much greater than that of the ordinary nd-ensiDe*. 441. In the pnmps already described, water U railed either by atmoopberio or machanical preianre; soma inetmnienta will now be described in which the momentom of one portion of fluid in motion is eSeclive in raising another portion. The ffadraulic Jtam. — A s, Fig. 305, is a pipe, descending obliquely from ■ reservoir of water, *, to the lower part of an air- Tenel,a,into the aide of which ii inaertsd the ascending pipa,fB. c is a imall air-vessel ; B, a Urge and light Talve opening down- wards ; D, a heavy bolt-Talre openiog npwaids; and B, a small valve opening sideways into o. Snppoae the Talves' k, b, closed by the pressure of the water in XB,a closed by its own weight, s and o filled with air, and r h filled with water up to the level of the water in a. r.>et the valve ■ be depressed and opened; then the water in abwiII move in the direction ±n, and flow oat at n, until the ctirrent becomes •officiently rapid to raise the valve a, and thus to close the orifice. Hm water in a b having its motion thus suddenly checked, will exert a very great pressure on the inner sur&ce of the chamber, a, and having raised the valve n, will msh into the air-vessel, a, and ■p the pips Fa, compressing at the same time the air ia a andc 244 HTDBODTMAlllOt. Aa KKin u tlie momentum of the water in l B is expended, and it becomes qiueiw«iit, Dcloaes, and the preieore of the air inccaiuei the water in i B to recoil Blightlj, nntil the air in c occnpiea » larger apace than it did under the pretsare of the atmotphei^ ; at ttjs instant, the internal preianre at B being lew than that of the atmoephere, b deicendii, and opens, and the action of the machine 19 renewed. In this manner the water ascBods in r a at each sdc- oeasive impulse, until it reachea the point to which it is desired to elevate it. A purtion of the air in a and o is taken np hj the water, wbich abaorbB a conaiderable qnanCity of air under a high pressure ; to snpplj the waste arising from this cause, the machine 18 prorided with the valve e, which opens and permits the sir to enter, during the recoil of the water ia a b. The hjdraulto or water ram maf be advantageously emploj^ed whenever the qaantitj of water reqnired to be r^aed la inconsiderable, and the expenditure of fluid in working the machine is of no consequence. The qnantitv raised at each atroke will obvionsl; be leas ai the height to which it is required to be raised incieaaet. The ram ma; be advantageousl; employed in raising water from a perpetual spring to a ciitem at a considerable height above it. 442. The Centrifugal Ptasp is another machine in which the molJTe power results from the momentum of a portion of fluid in motion. This will be understood b; supposing Fig. 2di to be in- verted, and made to rotate rapidly, the end o (now lowest) being immersed in water. During rotation, the fluid in the anus n, C will bj its centrifugal force tend to fl; outwards towards a and r, and to escape from these orifices, the pressnre of fluid in the tnbe l. will therc&re become less than that of the atmoephere, which vtill cause a fresh portion to enter the tube a at o. The heisht to which water may be thus raised is, as in tha oaw of the lifuoK pump, limited to less than 30 feet. Ther« it, however, a disalT vantageons expenditure of power in working thia maohine, and it is now rarelj if ever employed in practice. 443. AppoU'i Centrifugal ftanp. — An ingenione and very anccessfdl applicalion of ceaCrifngal force as a means of raidng Fia 306 water, was made by the late Mr. AppahT. * The essential part of this machioe is 1 represented in Fig. 806. A circular disc I of metal, c, is fixed transvenelT on an axis, I AB, and two equal discs, d, b, having large I apertures, as h i, in the middle, are al- I tached to c, by two series of onrved parti- I tions, f, o, &c This chambered wheel is I placed nearthe bottom of an upright ehaft, ^ ive recUngutar tube, between two il fnista, the edges of which approaoh ' ven near to the maniD, h a, and to a simi. lar margin on the other sicfe ; the reservoir from which the water is lo be raised to the t(^ of the shaft has access Ui these cones, and lam r nicaffnu THS 8TPR0V. 245 llherefore to the central epAce of tlie wheel BOTronndrng the axis, ▲ B. When a rapid rotation is communicated to this wheel, the water included between the nartitione passes outwards by its centrifugal force, and up the snaft, haying no other egress ; and ita place is continuously supplied through the cones from the re- servoir. Many readers wiU probably remember a considerable afaeet of water that was thus raised so as to form a cascade at the International Exhibitions of 1851 and 1862, by a wheel little more than one foot in diameter. The most advantageous application of Appold*s pump is in raising large quantities of water to small altitudes ; for example, it has been Tery successfully employed in draining fens, &c. 444. Tke Ciain and Bucket Pump is a simple application of power in raising water in a series of buckets, which are attached to an endless chain passing over two drams or pulleys, one of which is placed beneath the sur£ftoe of water in the reservoir ; the buckets, m passing over the upper dram, are tilted over, and •mpty their contents into some convenient receptacle. 445. Capillarity and adhesion have been employed in raising water by means of the rope jmmp, wbich consists of an endless hempen band passing over two pulleys, one of which, as in the preceding, is placed oelow the surface oif the water to be raised, and power is applied to rotate the upper pulley. The fluid absorbed by, and adhenng to, the band, is partly pressed out of it in passing over the upper pulley, and partly driven off by centrifugal force, when the motion is sufficiently rapid, and is received in an appro- Sriate vessel. The Quantity of water raised by this apparatus epends entirely on tne velocity of the band ; in one insUtnce it was found that when the pulley made 1000 revolutions per minute, 83 j^ons of water were raised 135 feet in the same space of time. This and the nreceding are now seldom employed. 446. The ayphon. — ^This well-known hy^ulic instrument, con- Bista, in its simplest form, of a bent tube, a b c. Fig. 307, having one of its branches longer than the otber. On immersing its shorter leg in a vessel of ^' ^* water, applying the mouth to c, and ex- hausting the air, the pressure of the atmo- sphere on the surface of the fluid, d b, i%ill force it to ascend in the tube : as soon as this has become filled with water, remove the end o from the moutb, and the water will continue to flow through the syphon, as long as the end a is immersed. The theorv of its action is simple : let « 6, Fig. 308, be the short, and $ d the long leg of the svphon filled with water. If the lag sd terminate at n, the pressure at h and n vrould be equal, and no fluid would escape : but f d being longer than hihj the distance nd, there must of necessity be greater 246 RTDS0DT1IAMIC8, 1^.809. Fig. SOS. pressure exerted at d than at 6, and hence the water escapes at d. If h is immersed in a vessel of water, the pressure of the atmosphere will cause the latter to rise in the tube, and thus 1>J this instru- ment the vessel is readily emptied. The length of the legs of a sjphon is calculated from the top^ # to a line corresponding to the level of the fluia in which the short leg is immersed. If the long leg of the syphon be immersed in the water instead of the short one, and it be filled with the fluid by exhausting it with the mouth, the upwardpressure of the air against the water in the shorter leg will be sufficient to drive it back into the vessel : consequently, no syphon will act, unless the leg outside the vessel be sufficiently long to reach below the level of the fluid. In order to prevent the entrance of any portion of the fluid into the mouth, the longer leg is usually provided with a small side tube, which opens into it near to d, Fig. 308, and, running up by the side of it for some distance, is then bent outwards for tne con- venience of applying the mouth. In order to exhaust the m>hon for the purpose of filling it, the end d must be stopped by the nnger, if not furnished with a stop-cock. 447. A tube, a b c. Fig. 309, with its extremities curved upwards, is a useful modification of the syphon ; its action is readily understood. jBeing filled with water, and one of its legs immersed in the vessel d, the column of fluid above ▲ will press upon the water in the extremity of the tube, and no cor- responding pressure being applied to the fluid in c, it overflows and escapes from the orifice, forming a little jet d'eau. This instrument is termed the Wirtemher^ tyfhcn. The common scientific toy, called Tantalus* cup, consists of a glass vessel. Fig. 310, in which the bent tube, a b c, is concealed. The long leg A passes out through the stem of the cup ; on pouring water into tnis glass, it will be retained as in any other vessel, until the hori- zontal branch, b, becomes filled, and then the water will escape through this syphon, until it falls below the orifice of the leg, c. The mouth of a little image is often fixed at b, to represent the fabled Tantalus ; and as soon as the fluid rises to his lips, it escapes through the syphon. 448. Another philosophic toy, illustrating Fig, 810. WATER-WHKELB. 247 flome of the principles already laid down, ^*9' 311. is known under the name of Hiero's foun- tain, and consists of three Tesrels, c, d, e, connected bv the tubes a, b ; the tube n, connecting the upper part of c with the upper part of d, whilst A passes air-ti^ht tnToagn d, connecting the reservoir e with the bottom of the vessel c : a jet tube f passes through the reservoir e, and extends to the lower part of n. To use this appa< ratus, the vessel n, and the reservoir e, are nearly filled with water. The water in E descends through the tube a into c, forcing the air contained in the latter up B into D, above the surface of the water, ^ on whicn it exerts a pressure eouivalent to the height of the column, A : thus the water in d is forced to rise through the tube r, in the form of a jet ePeau. The mode in which this apparatus acts is, consequently, analogous to that of the compressed-«ir fountain (511, c), dineiing only in the manner in which the com- pression of the included air is effected. 449. The obsolete hydraulic instruments, called the Persitm wheelf and the Screw of Arehimedee, were so constructed, that some portion of a curved or spiral canal occupied by water, al- though gradually elevated, remained lower than the acyacent portions on either side ; but the action of these machines is so dis- advantageous, that a detailed description of them is unnecessary. 450. Currents of water are frequently used as sources of power in moving machinery, by means of the well-known contrivances called wfiter^wheela ; these are of three different kinds, called re- spectively underahot-f breast-t and overahot-wheeU. A. The underahot wheel is furnished around its circumference with radial float-boards, and is immersed in a running stream to the depth of the float-boards. This kind of wheel is used where little or no difference of water-level can readily be obtained, or where the water is intended to act on it in either direction, as in a tidal stream. Wheels of this description are usually broad ; the breadth being sometimes e<^ual to, or even exceeding the diameter. When an undershot wheel is not required to work in both direc- tions, it appears from the experiments of De Parcieux and Bossnt that a decided advantage is gained by inclining the float-boards towarda the advancing stream, at an angle of 20° to the radius of the wheel produced. The water then becomes partially heaped up on the float-boards, and acts b^ its gravity as well as its momen- tam : also they leave the retiring stream with less resistance. It appears, as the result of experiment, that the effective power of the wheel is greatest, when the velocity of the float-boards is aboat one-half tuat of the stream. 248 BYDBOOTHAMIGS, B. The hreatt4ffheel differs from the former both in its con- stmction and mode of application. In this the float-boards are placed obliqnelj aronnd a continuous cylindrical surface, and are enclosed at each eiid bj a flange extending as far as their outer edges, so that the descending portion of the circumference of ^ Uid wheel consists of a series of buckets or wedge-shaped cavities capable of retaining a certain portion of fluid. A hreoMtwork of masonry is bnilt np to near the circumference of the wheel, from its lowest point, to about one-sixth of its circumference : and the water rushing down the breastwork, and fillin|^ the buckets, acts on the wheel both by its momentum, and by its gravity. This form of wheel is best suited to localities where a moderate supply of water, with a fall of six or eight feet, may be obtained. C. The overshot wheel differs from the preceding in the form of the buckets, and in the much smaller ratio that^ the width of the wheel usually bears to the diameter. It is available only in situations where the fall is not less than the diameter of the wheel, but may be driven by a much smaller quantity of water than either of the preceding forms. The water is received from a trough at the upper part of the wheel, and acts almost entirely by its ^avity. The circular rim that forms the base of the* buckets IS called the solSy and the lateral flanges, the shrouding. Each float-board consists of two, or sometimes three, distinct portions ; the inner portion is radial and is half the depth of the bucket ; the iBt« 4,4 middle portion is considerably in- ^' '"• clined to the radius^ as in Fig. 312 ; and the external still more so. The water is most advantageously em- ployed when only a little more than the radial portion of each bucket is filled : in tnat case it does not com- mence escaping until the bucket has reached the position a, about 35* from the vertical. Smeaton has in- ferred from experiment that in wheels of medium size, the velocity of the drcumferenoe should not exceed three feet per second, but that in large works it may be somewhat greater. It appears also that the power of an overshot wheel is more than double that of an undersnot, of equal magnitude. 451. I%e Turbine. — In some parts of the Continent, the em- ployment of horizontal water-wheels with vertical axes is much more frequent than that of the vertical wheels generally empk^ed in this country : to these the name of turbine is applied. Their general construction, subiect to various modifications, is that of a series of oblique radial float-boards, on which the descending current of water is made to impinge in the most advantageous THB BCBBW-PBOPBLLBB. 249 direcdon, and acting both hj its grayity, and its vis Tiva {340)i in driTing the wheel. 452. J%e PaddU^lieeL — ^Having briefly noticed the principal fonns of mechanism by means of which a cnrrent of water may be rendered available as a source of mechanical power, it remains to notice those in which the inertia of water is applied as a means of locomotion. Of these, the earlier in point of date is the paddl&- whedf the action of which is the converse of that of the nnder- shot water-wheel (450, A), while the constmction is nearly iden- tical. The power applied in rotating the ^ddle-wheel niaybe represented by a coaple (81), the arm of which is vertical. The lower pressure being counteracted by the resistance of the water, the upper one is wholly effective in producing progressive motion. In the paddle-wheels oif ordinary construction, the fixed float-boards encounter a prejudicial resistance both in entering and leaving the ^ter : for, in order that the float should enter or leave the water with the least possible resistance, it is manifest that it should be in the direction of a tangent to the point of the curve that the circumference of the wheel is at that instant describing. This is a cycloidal curve, not exactly what is generated by a ^int in the circumference of a circle roUing on a straight line as in 830, but ▼hat would be ^nerated by some point in a radius produced. As the direction of this curve is inclined from the radius towards the vertical, both at the points of entrance and exit, the resistance from this cause can be diminished only by moveable floats, the position of which is more frequently governed by an eccentric, but atiU better by a peculiar arrangement of link-work ; for the details of which the reader must be referred to the practical treatises on this subject. It may, however, be remarked, that the increased cost of production, and greater liability to derangement, are in practice found to be scarcely compensated by the motive power saved ; and, in consequence, fixed floats are generally employed. ^ 453. The ScrevypropdUr. — Another means of marine locomo- tion now very frequently employed is the BcrewpropeUer, The form of this instrument is that of -the sorew of Axohimedes, which is generated by a straight line intersecting perpendicularly at its middle point an indefinite stndgbt fine, along which the centre moves, while at the same time uie line rotates uniformly. The form of this may be more familiar, an being that of a spiral (or, as it 18 commonly called, geometrical) staircase. The direction in which the screw acts is at right angles to tiiat of the paddle- wheel : it is placed in a vertical rectangular cavity purposely 1^ for it, in the stem of the vessel, and being entirely submerged, is much less liable to injury from ooliision or impact, and to the in- equality of action to wmch fte paddle-wheel is HaUe, when the vessel rolls heavily. The appropriate pikih of the sorew, or angle at which the edge of the blade is inchned to the axis, depends upon the H ; D ia a vessel, called the condenser, into which a tittle ctid water tnay be injected ; B a is a tnbe which connects X B with tbe boiler, and with the condenser, d. At ■ and s ara placed valvea, ao connected with 1. p, that when h cornea to A, a com monicatiou is open- ed between a h, tbe chamber abore the piston, and the bmler, which ia closed when u has deaceifded abont one-third of AB ; alao between ub, the chamber below the piston, and the condenier. When u comea to b, aimilar commnnications are opened betweoD MB and the boiler, and between am and tbe condenser. Sappoae K to ascend from b to A, the space below m being filled with steam from the boiler; as aooD as m arrivea at A, the commu- nication ia opened between h b and d, throngh which the steam paaaea, and b«comet condensed, leaving a vacuum in h b : at the same time a conmDnication being opened between ah and the boiler, steam msbea into a m, and m ig forced downward* by tbe _1J 252 HTDBODTHAMICB. fnU prMsnre of the steun during one-third of its descont, and after the commanication between a. if and the boiler is cut off, bj the diminished pressure of the steam in the cylinder. In the same manner, when m arri?es at b, a yacunm is produoed in am by the condensation of the steam, and m is pressed upwards hy the steam admitted into the lower chamber. The condensation of the steam in D is promoted by a jet of cold water, which is remo?ed as fast as it ooUects by a pump, p; by which, also, any air that may hare been mixed with tne steam is remoTed. In practice the steam is admitted to, and escapes from the cylinder, not by means of separate valyes, as represented, for the sake of cleamess, in the diagram at r and s, but by means of a slide-Talve ; for a detailed description of this, and for the relative position and dimensions of its ports or apertures, as well as for an account of the various and important accessory contrivances, such as the parallel motion by which the upper extremity of the piston- rod is made to describe a curve very nearlv coinciding with a straight line, and the various means of regulating the supplv of steam and water, &c., our readers must be referred to the standard treatises on the Steam-engine. 467. The HSghprBUwre JSUaa^-enpnB.-^Th.^ construction of the cvlinder, piston, and valves, in this engine, is the same as in Watt's engine ; but the steam in the boiler has a pressure many times greater than the pressure of the atmosphere, and, instead of being condensed after each stroke of the piston, it is permitted to escape into the open air. Biqypoee m (¥ig. 314) to amend from b to a, the space m b being filled with steam from the boiler ; as soon as m arrives at a, a oammonication is opened between m b and the air, at the same time that steam from the bailer flows into a m, aod m is forced down towards b by the excess of the pressure of the steam above the atmoei^ric pnsaure ; and the return stroke of the piston is effected in a similar mannec. 458. Stationairy en^^ses of large sise are usually constructed on the lano^pTeamure^ or oondensing principle, both on account of the increased danger of high-pressure steam, and also because it is found that fuel can thus be more economically employed. In the construction (X portable and heomotiw engmes the high* pressure principle is adopted, by which the weight and bulk of the condensing apparatus is saved. In these the weight of the beam is also avoided, and the pistons (of which there must be two) act directly on a right-angl^ crank (218, II.), in order to maintain uniformity of action. In order tnat a large quantity of steam may be generated in a small space, in locomotive boilers the fur- nace-heat is transmitted through a large number of parallel tubes, surrounded by the water, by means of which a great extent of heating surface is obtained. In Marine engines, since the stability of a floating vessel is in*. THE BTEAX-HAKMKH. 253 creaflod by depreasine tlie centre of gravity (407), the beam, and the heavier parts of ihe framework of the engine are nsnally placed hek>w. In screw-engines the action is generally direct, the pistons acting on cranks connected with the screw shaft. For this pnr- poee it is necessary that the j>iston8 and cylinders be placed transveraelj : and as the space is very much limited, the diameter of the cyhuders frequently exceeds their length. Also as the heads of the cylinders most necessarily be brought near to the screw-shaft, the piston-rod instead of being solid is a hollow cylin- der, with the bottom of which the crank rod is connected, as it would work disadvantageously when inclined at a large angle with the piston-rod. Engines of this* description are usually called tnink-engines. 459. HydrcttdiCf or Water-engine*. — ^In some oases, in which the demand for power is occasional onlj^, and for short or uncertain pmods, it would be inexpedient to maintain a constant supply of steam; and steam-pressure on the piston may then be advan- tageously replaced by water-pressure, if a due supply of water can be procured from a sufficient altitude to afford the required pres- sure. The admission of water into, and its exit from, the cyhnder is effected by means precisely analogous to those employed in the steam-engine. The jBydramic cranSy for shipping or unshipping heavy goods, and the 'Hydraulic Uftj for raismg weighti to the upper part of a hif^h buikling, are examples of machines worked in this manner. The power of these machines is to be estimated on the same principles as that of the Hydraulic press (394). 460. The Steam-hammer, — In the manufacture of heavy articles in wrought iron, such as anchors, large steam-ensine cranks, and armour-plates for ships, an immense advantage has been gained by the introduction oi Nasmyth*s Steam-hammer. This machine is, in fact, a direct-acting steam-engine, in which the cylinder is inverted, and the piston-rod connected with a ponderous mass of iron, haTinga steel face, which impinges on an anvil placed be- neath it. The steam-pressure, being sufficient to lift the hammer, will, when admitted above the piston, cause it to descend with at least double the accelerating force of g^vity ; and hence the powerful effect it. is capable of i^roducin^. So completely is the tremendous power of this machine within the control of the en- gineer, ^at uie writer has seen nuts cracked on the anvil, without bndsing the kemeb, and a few moments afterwards, a mass of timber of nearly a foot in sectional area on which the nuts were placed, reduced to spHnters by two or three blows. In order to aooompHsh the former feat, the hammer is coaxed into a gradually augmented oscillation on the elastic cushion of steam beneath the piston, by small successive admissions and emissions of steam ; the latter, by putting in action the full force of the machine. It has recentiv been proposed to invert in some degree the arraogements of Nasmyth's Steam-hammer, and while the end of tliepiilon-rodii itUched to the solid frkmeiroik of the nttchiiw, to make the ojlindere pert of the nuui coiutituliDg the hmnmBr; bat the writer ia unable to ea; whether the pnctical advantage, or otherwise, of this mode of constniedoD hw lieen determiQed by •xpeKence. 461. Siemem' gi/romtiric gimenior. — It is a well-knowo bet, and one capable ofeai; demonstration, thiit if a cjliodrical veaael, cootiiiiiing a fluid, be made to rotate oa its axis (being Terticatj the anrface of the fluid will assume the form of a paraboloid. A yerj ingeaioos application of this has been made by Mr. Siemeos in iho conatractian of a goternor. This "#■ »«■ ooEBiats of a cup, c, Fig. 315, of a i*t». bolic fonn, open at both top Knd bottom, the latter dipping ilightl/ be- low the SDrface of a liquid coDtaioM io an eiteinal casing, B. The cup it supported bj four radial featbera, whicb connect it to a hoes fixed upon a ceo- Iral spindle, the ipiudle pasting down throogh a tobniar support, a, fixed to the bottom of the casing containing the liaiiid. The spindle jnit mentioDed, which is funiialied at Its lower end with a pinion, is placed in the saise ver^cal line as a lertical shaft, u, situated beoealh it, and driTea from the main shaft of the engine b; suit- able gearing. At the top of this shatt i« fixed an annular wheel (176) >, having its teeth in the ume horiioatsl plane as tbe pinion at the lower end of the cnp spindle. Between the pinion an the cnp spindle and tbe internal leetb of th» wheel on the lower ahaft, and gearing into both, are placed two piniiins, as shown at x ; these pinions levoliing freely npon stade fiied to an arm, which can, in its torn, revolie npon the central spindle. Bj means of a lerer and connecting link, this arm is oonnected with the vertical Mm of a bell oisnk fixed upon tbe axis of ihs throttle valve, the other or honsoolal am of this bell crank carrviug a weJf^t. The whole apparatus is supported hj twu legs, e, a, suitably attacbed to the firameworfc of the engine. The aotion of this apparatus is as follows : Wben the engiae is in motion, the rotation of the lower vertical shaft would tend to make the two intermedlale pinions nvolve round it ; this laotion is, howevsr, resisted by (he vei^ht fixed on tbe throttle valve lever, and the intennediate pinions are consequently made to drive the pinion fixed on the cup spindle and thus cause the 8ZXMBSS' OTBOMBTBIC OOTBRXOK. 255 rotation of the cap. When the cnp w made to reTolye, the liquid rifles within it (its surface assuming a fonn approximating to that of the cup, as shown hy the dotted lines), and eventuflily over- flows the uj^per edge. The portion thus overflowing is caught, and its motion amsted, hy a set of radial vanes, u, fixed to the external casing, and from these it falls upon another set of vanes, L, cast upon the exterior of the revolving cup. The arrangement of these vanes is shown in the figore. The action jost mentioned, together with the power absorbed in setting in motion the fresh Ut^uid drawn in at the bottom of the cup, proiduces a resistance to the rotation of the latter, which is constant at a g^ven speed, an increase in the speed augmenting this resistance by increasing the overflow. It follows, therefore, that if a constant driving power be provided, the cup will continue to revolve at an uniform velo- city. A practically constant driving power is obtained bv the arrangement of differential gearing which we have alreaay de- scribed ; the " pull" which the intermediate pinions are capable of exerting upon that fixed upon the cup spindle being limited by the resistance afforded by the weight fixed on the lever of the throttle valve. So long as the speed of the engine is such, that the teeth of the internal wheel move at the same rate as that at which the teeth of the pinion on the cup spindle are driven by the pressure produced by the weight on the throttle valve lever, the mtermediate pinions merely revolve upon their studs ; if, how- ever, the speed of the en^ne be au^ented, the fact of the rate of rotation of the cup spindle remaining uniform will cause the intermediate pinions, and the arm carrying them, to revolve round the central spindle in the same direction as the internal wheel is driven by the engine ; and this direction is so arranged that the motion thus given to the arms carrying the intermediate pinions raises the weight on the throttle valve lever, and closes the throttle valve, thus diminishing the speed of the engine. If that speed falls below the proper rate, a series of movements, the reverse of those just descnbed, takes place. It will have been undentood from what has been already said, that the cup vrill not maintain an uniform velocity, unless this velocity is such as to cause a continuous overflow over the brim of continuous oveziiow may be found by the following equation : » = H'-'l^^^r') 6-2832 B In this equation n = the number of the rovolutions of the cup per second ; h =s the height of the brim of the cup above the 256 HTDBODTVAMZGB. level of tlie liquid at rest in the external casing ; r « the redins of the lower opening of the cup ; r = the radius of the brim ; and ^ s: the force of gpravitj. All the dimensions should be expressed in the same units of measurement. The level of the liquid can be seen by the glass ^uge affixed to the side of the external casing, as shown in Fi^. 315 ; the cock at the bo.ttomof the gauge affords the means of withdrawing some of the liquid, if requisite, or, on the other hand, an additional quantity can be put into the casine through a hole at the top, which is closed by a screwed plug. The dip of the cup, and the speed at which it will be dnven, can thus be adjusted to any required amount Radial feathers are formed around the lower part of the casing, in order to prevent the main body of the liquid from obtaining a rotaiy movement ; and loss from evaporation is obviated by making the casing air tight. Any liquid, such as water or paraffin oil, may be employed. The gyrometric governor has stood the test of practical applica- tion very successfully. One of them has been at work for some months at Mr. Siemens' telegraph works at Woolwich, and has answered exceedinglv woU. The rapidity with which it acts is very remarkable, and it has been found by experiments that, in the case of an engine fitted with this governor, two-thirds of the load could be suddenlv removed without causing any perceptible ^ change in the rate of revolution. The figure, which is drawn to *.a scale of one-twentieth, represents a eovemor having a cup 8 in. in diameter at the top, and 8 in. high alxyve the level of the liquid. The resistance which a governor of this kind opposes to a change of speed is very great, and will enable it to be employed for re- eulating the speed of engines by the link motion, or for working Uie gate of a waterwheel, or in other cases where considerable power is required in the eovemor. 462. Flmds are capable of assuming nndulatory movements analogous to the vibrations of solids (869— -378), differing, however, in some respects, in consequence of the different physical arrange- ment of their atoms. If a pebble be allowed to drop into a cum piece of water, a series of npples will be| generated, diffused con- centricallv from the point of impact, and becoming more and more shallow as they recede from that point. On a small scale, thesd are best observed bv dropping a glass ball on the surface of mercury contained in a shallow vessel. 463. At the point where die pebble touches the water, a de- pression will be produced : this will, from the ready transmission of an applied force in all directions (384), produce a circular eleva- tion of tne water round it. The particles of water thus elevated above their previous level wiD, in their turn, fall, producing an elevation of the next circular series of particles. Thus the initial motion vrill be gradually propagated from the point of impact, in a series of gradually extenaing circular ripples, until opposing causes allow the eqmHbrinm to be restored, c^ Fig. 816, wiU « (371), 257 Fig. 319, ripple Bur- rooDding it. ■, the adjoiDing circle of depreuioD, &c. Tbe wLite circle! repre- •eDt the elevations, SDd the ahwled oQeg the deprenioDi of Iheae circalar w»«b. The particles of oater thus diapUced j merelf moTO id iniall vertical circles, *nd ue Dot reall; arfted from the ceotre to the bulk of the pond or brook, althoDeh it is difBcnlt to bellere at first light that the irater does not moTe laterally. This will, howeveT, he admitted, on rafemnK tothe vibratioDiof a or after watchiog the motiona oipiecee of straw, &c., face of water; tbe; will move np and dawn with each ripple, hut acarcel; leave the place where Drat olMcrved. These wave-like nKrvementfl are not only propagated laterally, but in all other dire^ tiona, aa might indeed be eipecled irom the laws already aQ- noQDced, and aiteod downwards to a vertii^ depth equal to 350 ^mea the elevation of each undulatioa. An entire ondidation ^ „ ccuiat., M in the c«H ^' "'' of the vibratioQ of solids, of a phase of depreaiion mud one ot elevatiaa, and the analogy ma; be ren- dered more obvious bj cod- caiving a series of circular ondiilalioDs,diTided at ac b, F!g. 317, so M toprewDt > vertical HctioD. Tiie phases irf elevation and depression will preaenl the series of cDrvea shown bj the line A'tftf, In non-elastio fiaids, vitcctity, or cobenve force, is the prin- cipal agent in bringing the undu- lations to rest; whilst, as it haa been alreadj stated, m the case of •olida and elastic fluids imperfbct alasticinr produces the same result. 464. UndulationB, wben imiuDg' ' ing against a salid, are reflected back in accordance with the ordi- nary laws of reflected motion: a I senea of nndulaticD^ propagated ftom a centre, c. Fig. 318, and reacbii^ a plane* obttocle, aa, will Rg. SIS. 258 be reflected Irom it in the Bsme Ibnn and muiDer u if tbe; had been propagated from * point, », placed at the name distance aio from the opposite side of the Sied plane. In this way, nndola- tioni geDsrated ID the centre of a circular voaitel may reach the boandaricB of the Qnid, and, 74. SIS. on impingiDgagainit the walla of the vessel be reflected back to the centre, and ao on. 465. In conaequcnce of the nndy reflexion of nndula- tions. thej may be prnpa- I gated in any direction by meaoe of properly-arranKM concave anrfaces. In UiiB way nndnlatioDB gpnenited In one of the foci, i, of on eUipae, Fig. 319, mny have tbair conjoint effects propagated to the other, b, as here Bhown. 466. If two undnlationa meet, their reanlting movement trill Tary accordine to the circum stances nnder which they come in contact, "xaoa, if two ondnladona meet in the lame pkiue, the resulting wave will be eqnal yij-SM. ,(, the sum of the two separate ones; bnt if in epoMile phatet, to their diflbrence. Hence it is qnits ' posuble for two wajei of equal in- tensity, tratelling in opposite diieo- tions, to meet, and completely de- itroy each other's motioo. This is lermed the interference of loava. The two equal aeries of undnlationa, prapagatea from the points a and n. Fig. 3S0, will, at the points when they meet ID oppoute phMes, intei^ ^■»1- fere and loae tbeir motion, whilst, at the points of inter- section of the cresta. the agita- tion of the water will be iolen- 467. When a series of nnda- btions impin^s upon an ob- stacle io which an apeitoiv eiiati, those which reach the opening will pss^ through it, the rest being reflected (464). Those which pass through, nn- deigo a peculiar change in their T7XDULAT10HB OF ELASTIC FLUIDS. 259 carve, in consequence of atrildng against the edges of the opening. Thus a series of undulations, propagated from c, Fig. 321, and reaching the opening, ▲ b, in a fixed obstacle, will be propagated throush it, so as to nil the space abed. The curye of tne con- centric waves will be altered at f, f ; g, o, &c., from the influence of the edges of the opening a b, becoming deflected in the direction F K and o L, in the direction of the arcs of circles drawn from a and B respectiTclj as centres. An analogous phenomenon, known as inflectum, is obeeired to take place when a raj of light is partiaQy intercepted by a solid witn a sharply-defined edge. See 468. It may readily be observed by experiment in a cistern or other large yessel with vertical sides, that if a wave impinge very obliquely on a side of the vessel, a portion only of the motion is reflected ; and a peculiar heaping up of the particles of fluid ap- pears to move along the side of the vessel. To this phenomenon Mr. Scott Bussell has applied the term lateral aceumulatum. It is by this kind of action that a sonorous wave runs along the curved surface of a building, as in the well-known example of the whispering gallery of St. Paul's Cathedral, so as. to afiect the ear at a remote point ; and not by a series of successiye reflexions at very obtuse angles, as has sometimes been supposed. 469. When elastic fluids or gases, as atmospheric air, are sub- mitted to mechanical force, they are capable of assuming certain alternating movements, analogous to the vibrations of solids (376) and the undulations of water (462), and other non-elastic fluids. These motions. of gases difier, however, in some particulars from those assumed by water, in consequence of their physical con- dition, their component particles being held together with a very weak attractive force (9). Suppose a certain amount of force, of momentary duration, be applied to a portion of air at a, Fig. 322 ,* under its influence, the adjacent particles recede equally in all directions, so as to fill ^^* 322. a larger space, as b. Now in thas expand^ ing from A to B, it follows that the air pre- viously contained in the space a b, most be driven off; but its inertia (278) opposes an obstacle to this taking place, it accordingly becomes momentarily condensed, the atoms approximating under the influence of the expanding force at a. The particles at ▲ then collapse, but their elasticity again causes them to en>and, and these futemations continue until the efiects of the applied force are lost, and the dis- turbed portion at a regains its state of rest. The concentric por- tion of air, B, compressed under the influence of a, in its turn dilates and acts on a shell of air external to it ; this, in its turn, on another, and so on ; thus the initial force acting on a exerts its 8 2 260 HrhRODTKUfics. influence on concentric portions of air, its eiTects gradaally dimi- nishing with each, until they become too feeble to produce any influence on more distant portions, as in the case of the ripples of water (462). 470. In the case of these o$eiUation», undukUianSf or pulses of air, it is obvious that we must regard them as extending equally in all directions in the free air, and limited only by the shape of the containing vessel when the air is confined in small spaces. Therefore the effects of the united oscillations or pulses extend equally in the course of radii from a centre to every point of the surface of a sphere. 471. The remarks made on the reflexion, transmission, and in- terference of undulations of non-elastic fluids, equally apply to the elastic fluids, or gases : it being borne in mind, nowever, that the vibrations of elastic fluids are commonly lonaiiudinalf that is, the motion of the individual particles is in the direction of the motion of the wave. Two waves of air concurring in the same phase will exert an influence on surrounding particles of air eqoM to their sum, and if in opposite phases, to their difference. This subject will, however, be again reverted to when treating of sonorous un« dulations, and of tne oscillations of ether, in explanation of the dj-namical theory of light and heat. Theory op Tides.* 472. The present chapter would be incomplete without some notice of a very important class of natural phenomena; — the Tides of the Ocean. In the calmest weather the vast body of the waters that wash our coasts, advances on the shores, inundating all the flat sands, and then as gradually retires to its former level ; and twice every day is this vast ucean wave observed alternately to advance and retire, independently of all casual disturbing causes. In searching for the cause of this remarkable phenomenon, phi- losophers readily conceived that since the Sun ana Moon each cross the meridian twice in the twenty-four hours, these bodies might by their attraction influence the waters of the ocean. Accordingly various theories have been adopted for the calculation of the tides on this hypothesis of solar and lunar attraction, of which the most noted have been those of Bernoulli i and Laplace. Universal gravi- tation being admitted, there can be but one universal and correct theory based upon it for calculating the oscillations of the ocean ; but, in consequence of the difficulties of the analysis, which have hitherto been insurmountable, other hypotheses must be resorted to, in addition to that of gravitation, in order to obtain an approxi- mate solution of the problem. The irregularity of the depth of the ocean, the manner in which it is spread over the earto, the * Fntft Meohaniesl Philosophy, p. 663 •< ttqq. THEORY OP TIDES. 261 position and decUvitj of the shoTes, and their connexions with adjoining coasts, cannot possibly be subjected to rigorous calcula- tion, although these and similar causes greatly modify the more- ments of the great tidal waves. All we can accomplish is to suuilyse the geDend phenomena which must result from the attraction of tne sun and moon, and to deduce from observations such data as are indispensable in completing for each port the theory of the ebb and now of the tides : these data are arbitrary quantities, dependent on local circumstances. 473. The theory of Bemouilli, which has been termed by the late Dr. Whewell the EquiUbrium theory^ sssumes that the attraction of the moon causes the ocean to assume at every instant the form it would have, if the earth and moon were stationair. It is foand hj calculating the tides on this hypothesis, supposing the pole of the prolate spheroid, which is nearly the form of equilibrium, to lag behiod the moon, that results are obtained which accord very well with observation, in some of the more ordinary phenomena of the tides. Laplace, however, has taken a different course ; he has calcu- lated the attractive forces of the Sun and Moon upon the ocean, and the results are found to contain some constant, and some periodic, terms. He ^ assumes that in consequence of the friction and resistances to which the particles are subjected, the waters would soon have assumed a form of equilibrium under the forces which are represented by the constant terms ; and then, taking it as a general dvnamical principle, that the state of a system of bodies in which the primitive conditions of motion have disap- neared under the influence of resistances, is periodic, when the mrces themselves are ^riodic, he obtains an expression for the height of the tide, which is the same as that obtained by the Equilibrium theory of Bernouilii. But there are so many assump- tions in Laplace*s theory, that we may, as far as we know, d prior i^ as readily adopt the Equilibrium theory ; the accuracy of the theory must in either case be tested by a comparison of the theo- retical results with observation. This laborious task has been in a great measure accomplished by the researches, and under the auspices of Dr. Whewell and others, and maps of co-tidal lines have been laid down with considerable accuracy. 474. The highest, or Bpring-Hdea^ as they are called, are ob- served to oocur at a certain interval after the new and full moon, at which periods the attractions of the Sun and Moon conspire to elongate tne fluid spheroid. The lowest, or neap-tideSf occur at the same interval* after the moon has attained the first and third quarters, at which periods the attractions of the Sun and Moon are the most opposed to each other, and therefore jointly produce the least elevation of the tide-wave. 475. The interval after new or full moon at which the spring- tide occurs is called the Establishment of a Port. In the port of 2 62 H ITDEODTN AMICS. London, calcolation and observation yery nearly coincide in de- termining the interval to be two and a half days. 476. If two tide-waves reach any given place by different routes, there will always be more or less interference between them, according to the interval between the similar phases of the two waves (466) ; if they meet in opposite pbases, and are of eonal depth, they will exactly neutralize each other, and there wouloi be no tide ; but if, as must almost necessarily be the case, the depth of one tide-wave be a little greater than that of the other, there will be only one small ebb and flow in the twenty-four hours. This singular fact has been observed at Batsham, a port of Tonquin, lat. 20** 5(y N. The waves seem to come by two channels, one of which runs irom the China seas between the continent and the island of Luconia, the other from the Indian sea, between the continent and the island of Borneo.* If there be a small interval between the similar phases, there will be two high and two low tides, separated by a corresponding small interval of time. This phenomenon has been observed in the Frith of Forth, in Scotland. References, — For further information on the contenta of the last two chapters the student is referred to the monographs in the several Oyclopsedias already mentioned, and to the works of Gh^g^ry, Youn^, Pla\'fair, Pouillet, Biot, &o. The whole subject of fluid mechanics will be found to be treated mathematically with great conoiseness and eleffance in Professor Miller's Hydrostatics and Hydrodynamics, to wnich the Authors are indebted for several paragraphs, as well as illustrations. The advanced reader may also consult with advantage Moseley's Hydrostatics, and Pratt's Mechanical Philosophy. * KewtOD, Prinoipia» torn. iii. prop. 24. mm^^ 263 CHAPTER IX. PVEUlLiTICS; OB TBS FBOPEBTIE8 OF ELASTIC FLUIIM. 477. The great mass of gaseona matter, sarrounding oar earth, and extending to a conHiderable distance from it, is termed the atmotphere, or attmaepherio air. This, like the denser fluids, obeTs laws similar to those treated of in the preceding chapters, witn snch modificadons as its eminently elastic character pro- dnces. Like the less elastic liquids, ^ases obey the attraction of CTATitation, and the conditions of equilibrium and equal pressure (374), explained in Chapter VII. Atmospheric air freea from moisture cousists, in 100 parts^ of Kitrogen, by volume 79 by toeighi 76*9 ; Oxygen, „ 21 „ 231. A variable, but small proportion of carbonic acid, and likewise of aqueous vapour, is always present in the atmosphere. As an average. It may be assumed that 1000 parts of air consist of Nitrogen, 788; Oxygen, 197 ; Aqueous vapour, 14; Carbonic acid, 1. 478. In consequence of the atmosphere being retained at the earth's surface by gravitation, and at eveij point sustaining the pressure of the superincumbent stratum, it is much denser near the level of the sea than at some distance above it : thus, at an elevation of 3 miles it is 4 the density of the air at the sea-level ; at 6 miles it is J ; at 9 miles, | ; and at 15 miles, ^ of that density. The greatest part of the atmosphere is thus evidently always within 15 miles of the surface of the globe, although, from certam astronomical phenomena, it is supposed to extend to a distance of 40 or 45 miles ; and here is, in all probability, its utmost limit. Dr. WoUaston* has shown that, at this elevation, the attraction of the earth upon any one particle is equal to the resistance arising from the molecular repulsive power of the medium. Another proof of the finite extent otthe atmosphere is found in the fact of the sun, and the planets, being destitute of any similar media sur- rounding them ; for if it were supposed to pervade infinite space, such large masses of matter as the planets must surely nave caused a considerable poition to gravitate towards them. Other philoBophersf have supposed that the extreme cold of the upper • FhiL TrvM. 1828, p. 90. t Phil. Trvis. 1826. 264 PNEUMATICS. regioDs is sufficient to prevent tbe unlimited expansion of the atmosphere. Dalton,* reasoning on one of Newton's propositions,f adopted the opinion of WoUaston. 479. Tbe extreme elasticity of gaseous fluids arises from the intensity of the molecular repulsioni which, instead of being nearly equally oalanced, or exceeded, by the intensity of molecular at- traction, as in solids and liquids (9), tends continually to separate the atoms still further from each other, and to press against the Kidos of a vessel containing them with sufficient force to rapture it, if sufficiently weak, were this effect not checked by external pressure. Unlike the far less elastic liquids, gases never present a level surface free from pressure, for they tend continually to expand themselves into space until repulsion is balanced by gravitation. 480. The weight of 100 cubic inches of atmospheric air, at 60** F., the height of the barometer being 30 inches, has been coQiputed at 30*9 grains, by Kirwan ; at 31*1, by Davy; at 30*5, by Sir G. 8huckburgh ; and at 30'2, by Mr. Brande. 481. The atmosphere exerts upon all bodies immersed therein a very considerable pressure,^ which would be sufficient to crush animal structures, ir in obedience to the laws of equal and con- trary pressure, tbis effect were not prevented. Let a piece of bladder be firmly tied over the brim A of a strong glass vessel a b, Fig. 323 ; it remains perfectly flat, and gives no evidence of any 2~ g23 pressure upon it, the pressures on ltd '^' opposite sides being equal. Then place the vessel on the plate of an air-pump (502), and exhaust the air from beneath the bladder; the upward pressure which prevented the weight of the atmosphere irom exertine its effect being removed, the bladder curves inwards under its influence, and at last dves way with a loud report. If the bladder should Srove strong enough to sustain the pressure of the atmo8j)here. roppine a small marble, bullet, or round stone upon it will generally induce its rupture. If a plate of glass were placed on a, instead of the bladder, it would, if sufficiently thin, be broken by the pressure of the atmo- sphere. This pressure is, in round numbers, equal to fifteen pounds upon each square inch of surface. 482. Atmospheric pressure is exerted upon everything on the surface of our globe ; nothing is naturally exempt from its in- fluence, any more than from gravitation, to which force this pressure is indebted for its origin (478). • Phil. Trsiiff. 1828. t Principia, Book Ji. prop. S, p. 202. 2SS If • vmmI be filled wilb floii], snd invGrted, the orifice, if Ui^ being covered with aajtbing that will keep the surToce of the fluid Fig.Sii. eotira, the preuure of the air will prefenl the escape of the flnid, pro- vided it be greater than the presanre of the fluid oa the cOTerjag of the TeaaeL Thia maj be illustrated by filling B gl&B3 Combler, A, with water, placing a piece of writing paper, BB, OTer ita mouth, ftnd careTully invert- ing it, as in fig, 334. It wiU be found that the fluid will nut escape, for the upward presaure of the Btmosphere will exceed the irravit^ of the water, and accordingly the veHBel will remain fall. Thi> Ui weci»ely onali^iu to the upward pressure of water, aa explained m397. «3. If » wide glaaa lube, a b, Kg. B25, be partly filled with water, and inverted in the veasel c, filled also with water, the floid will not fall in the tnbe, but remain anspended jrig. ju. at a higher level than th^l of the exlernal portion, In appearoDce contrary to the law of gravitation, of which it is, however, the simple effect. For ths atmosphere, presaing upon the surface de of the water in C, acta upon that ia a B, and keeps it elevated in the tube ; for the opposing pressare of the BurTounding atmosphere on the fluid wUhia the tube is cut ofi' by the end i. being closed. But if we perforate the upper extremity of the tnbe, the presmre of tho air la eqnalty exerted on the water m A and c, and accordiriglv in each it acquires the same level. If the tube a a be filled with water, Mid he of any length under about thirty-three feet, the preaaare of the ntmoBphere upon the surface of the fluid io which its opeu end la imineised will be sufficient to keep it full of water. If, instead of filling and inverting the tube, the upper end be connected with a good exhausting pump or syringe, and the air in its interior removed, the pressure of the atmosphere upon the water in tbe cistern, in which ila lower end is immnned, will force that liquid into ita interior, up to a certain elevation, averaging about thirty-three feet.* At tbis elevation the weight of Ihs column of water is balanced by tbe preaaare of the atmoephere ; and, of course, any cbange in the pressure of the latter will be attended by a corresponding change in tbe elevation of the water in the tube, farming a bOTo- iHtier, or measurer of aerial pressure. An inetiiiment constructed * Bojla'tWoili*; Dr. Bhan'B. edition, lT£S,TaLii. p. Ua. 266 PHEUMATXC8« .D Ftg. 326. in this manner was erected in the hall of the apart- ments of the Rojal Society, at Somerset House; but water barometers, in consequence of their leneth, and of the constant changes in the tension of the aqueous vapour in the upper part of the tube, due to changes of temperature, are useless as instruments of observation, and accordingly the mercurial barometer is universally employ^. 484. The mercurial barometer is constructed on the same principles as the water barometer, but the tube being filled with a fluid 13*58 times heavier than water, is required to be but -^ih. as long as that of the water barometer. A column of mercurv thirty inches in height, counter- balances tne average pressure of a column of atmospheric air of the same diameter. To construct a mercurial barometer, let a glass tube, AB, Fig. 326, about thirty-two inches in length, be carefnUy filled with pure mercury ; then, closing the end e with the nnger, immerso it in a vessel of mercnry, c. On removing the finger, the mercnry in a b will fall to a certain distance, leaving a column in the tube, of a height corresponding with the atmospiieric pressure at the time. It may here be remarked that, in practice, small quantities of air and moisture are found to adhere to the interior of the tube with so much tenacity, that in order to completely expel them, it is found necessary to boil the mercury in the tube itself; this plan is always adopted in well-made barometers, as the pressure of any air or vapour, however small the quantity ma^ be, in the chamber above the mercury, would falsify the indications of the instrument. The space above d emptied of mercury has been, until quite recently, the nearest approach to a perfect vacuum which could be procured by art ; for on depressing the end b deeper in the mercury, the whole tube becomes completely filled; the fiuid metal again falling on elevating the tuoe. The space above d necessarily contains a small quantity of mercurial vapour, and is termed the Torricellian vacuum, from the experiment naving first been made in 1043 by Torricelli, a pupil of Galileo. The height of the mercnry in the tube is always measured from the suriace of that in the cistern c ; and this elevation is the measure of atmospheric pressure at the time. The elevation usually assumed as the standard in this country is thirty inches, and to this all measurements and weights of gaseous bodies are referred. 485. Several modifications of the barometer are in use : of these the most common, and at the same time the least trustworthy, is the wheel or syphon barometer. In this, a portion of the lower end of the tube, five or di inches Iodk. i» bent upwards, and in this portion of the tnbe the morcurj fallj, u it rises in the npper portion, and met vtrtS, the actual height oftheoolamnbeiastnat of the upper garface above a horiiODtal plane passing throagh the lower auiface. A pleoe of glass attached to a string passing aver * pnllej, floats on the mercury in the lower bend, arid as the ibing is kept in a state of tensioa by a small weight or count«r- poise, a morement of the pulley correspondi with that of the •orface of mercury, and is indicated by a hand or index attached to the pulley. ^Vhen the areas of the upper and lower inifoces of the mercnry are equal, the movement of either will be exactly one half thn Tariaboa of the height of the coliunn ; also the apparent height will be independsnt of capillary depression {*l), aiuoe both Bur- bces will be similarly affected from that cause. 4S6. When the barometer consists of a tube immersed in b dstem, as in Fig. 326, it is evident that the surface of mercnrv in tbn cistern will be ruaed by a small quantity, as the npper sarface falls, and nice vertd; therefore an obserration of the variations of tbe npper suriiwe only, although sufficient for the ordinarv pur- poses of a weather gl/ui, is not sufficient when accurate results are requited. Several methods have been adopted in order to avoid this ■onrce of error, of which three onlv require to b« mentioned. I. A pointed cone, a. Fig. 32T, is attached by its base ^. „ to tbe upper snrface of the cistern, and the bottom of ' the cistern consists of some tieiible material, as leather, which is capable of being raised by a screw, c : before making an observatiou, the sarfaco of the mercury in the dstem must be nused or lowered by means of the screw, v, so as JDBt to touch the point of the cone, which ct incides with the zero point ol tbe scale. The exact col tact is readily effected, by making the point and its image seen by reSectioii from the surface of tbe mercury to coincide. For this purpose the cistern i — ' """ "' gJaes. II. The scale, d, is sometimes attached to the point B by a strip of brass, and both are raised or lowered by means of a screw (not seen in Fig. 327), in order tt obtain, as before, an exact contact of tbe point and sur lace. This arrangement possesses an important advan tage over the former, namely, that tbe temperature cor lection (487) is very nearly effected by the metallit connexion of the scale with the sero point. Initm- menta thiu carefully constructed are commonly called tlandard baromettn. m. In some portable, mountain, or marine barometers, M they •re sometimes called, the cislem consists of a piece of similar tuba, connected with the barometer ttibe by a shmt bend of stoat S6S tube, hiving a ranch sm&Uer bore, as in Fig. 328, th« object «f which ia to check violent oscilUtion of the meKaiT in the tobe, n, g{g_ hy which the upper closed end of the tube, a., mty b« reodil; broken. The scale (of bnus) is moveable on the tube, and the zero point, a horizonla] edge, in brought to coincide honzontalij irilh the euHiice of the mercury in the ciHlem c, which baa a email apeiinre near the top, to allow acceu to the Bur- rounding air. A horiEonta] edge attached to the vernier u then made to coincide with the surface of the mercurr in A, and the abBolute height of the column ii thuB reod'oCT. la order to render the in- aa compact as poaaible, and also to bring the centre of gravity of the whole tube to coincide with the axis of the item produced, the lower part of the tube is bent twice at the aame angle, as aeen 'n the fignre between a and n. In order to prevent an^ small sir-bubblcB, that may happen to get past the bend, from risine to the top of the tube, an oir-lrap is frequently employed : for this purpoBe the lower end at the tube, t, is drawn out to a fine point, and the conical end is hermetically sealed into a larger tnbe, B, lo the upper part of which the supposed air-bubble will rise, and the vacuum above the mercury will not be vitiated. As an additional security, the fine point of A is aometimes bent np in the form of a hook. In order to inaure a vertical position, the mountain barometer is saapendeii from a tripod stand ; the case itself ia Bometimes divided longitudinally into three equal portions, to form the tripod. This instrument is always inverted for safety in transport In making accurate barometric obBervations, great caremnetbe taken in placing the tnbe exactly vertical, becaase, siiice the pres- tore depends on the height of the column alone (484), the appa- rent height, or length of the column, will be in eiceis of the Kal height, whenever the tube is placed obliquely. 487. When it is required to make very accurate observations on die pressnre of the atmosphere as indicated hy the length of the column of mercDiy in the barometer, care moat be taken to mnko certain corrections for the temperature of the air aa infloencmg the expansion of the mercury. On tlus account, all aocarately reported barometric observations are reduced to a fixed tem- perature, which is generally that of freezing water, 3!° F,, b; suh- from the apparent height of the cunmn a small quantity, '' panrion of the column v ' ' ' ' ' ' "' uivalent 'ery nearly mtn, part of its hulk for each degree of Fahrenheit's scale, and the diminnlion of its density will be in the same propor- tion. Consequently, the height of the colnmn, which increases in the same proportion aa the density of ihe mercury diminishes. THE OOnCAL BABOMSTEB. 269 miut be reduced in that proportion. If Ms the obserTed height of the mercniy at the temperature S2*^ + t° F., then the reduced height will be A (1 - 00001 X t) ; If, then, we subtract the ten-thonsandth part of the observed height of the column of mercury for each degree of temperature above 32** F. at the time of observation, we shall obtain verjr nearlj the equivalent height of the column at the freezing point. 488. Capillary repulsion, by depressing the surface of the mer- car^, is another source of error, and must be allowed for in the estunation of the height of the barometer. This increases with the decrease in the diameter of the tube : its amount is shown in the table already given (41). 489. The Conical Barometer*— It has been shown (345) that the pressure on the base of a vessel depends only on the depth of flaic^ and the area of the base, and not on the form of the vessel ; a g^ven quantity of mercury will, therefore, if iotroduced into a conical tube, constitute a column of varying altitude, according to the portion of the tube it occupies, the column evidently becoming elongated as it approaches the smaller end, and vice verad. If,' then, a slightly conical tube of small size be sealed at its smaller end, and filled with mercury to the depth of 31 inches, and then inverted, it is clear that, the pressure of the atmosphere being unequal to sustain a column of 31 inches of mercury, the column will descend in the tube until the height becomes such as will be sustained bj the existing pressure of the air ; and the space through which the column will descend, corresponding with a g^ven change of height, or in other words the openness of the scale^ will depend on the acuteness of the anffle of the cone. It may be, for example, that the column may descend five inches in order to become one inch shorter : in that case an actual rise or &11 of one- tenth will be represented by half an inch on the scale. As, how- ever, it is practically impossible to obtain glass tubes of uniformly increasing bore, and four or five feet in length, the only available mode of constructing a barometer of this kind, as it was stated hj Sir J. Leslie^t is attained by joining together two tubes having uniform but unequal bores, the sealed end bein^ that of the longer and narrower tupe. If, for example, the sectional areas of the tubes were as 4 : 5, the mercury must descend five inches in the smaller tube to fall four inches in the larger, and it will then be shortened one inch, and the augmentation of the scale will be the same as in the former supposeacase. This form of instrument is recommended by its simplicity, and its ample range ; but the wider bore being necessarily small, probably less than ^ of an inch, in order that the mercury may not^ fiow out on any slight concus- sion, the column moves very sluggishly. A much larger bore may, * Invented bv Amontons in 1605. t Encyclopttdia Britaonio^ 7tli ad. 1842. 270 FHEUMAT1CB. however, be employed, if a loose piston be introduced beneatb the colamn, as proposed by Mr. Whiting. This consists of a steel disc, loosely fitting the tnbe, to the centre of which a bnbble of glass is attached, which, floating up in the mercury, keeps the disc in close contact with its lower surface.* 490. The height of the column of mercury undergoes several regular variations iji the course of the day; they are termed horary vcsriathns, 11 appears from the observations made at the equator by Humboldt, that the maximum elevation takes place at nine o*clock in the morning ; past this hour it becomes less, until four, or half-past four in the afternoon, when it attains its minimum ; it again ascends until eleven at nieht, when it reaches its second maximum ; and once more descend to four o'clock in the morning, after which it reascends until nine. Thus, every day, the mercurial column is at its lowest elevation at four in the morning and afternoon, and at its greatest at nine in the morning and eleven in the evening. The amplitude of these variations is but small, being calculated b^ Humboldt at only 0*07874 inch. In £urope, these horary vanations are marked by changes of atmospheric pressure, depending upon accidental causes, which, at the equator, are nearly without action on the barometer. As far as these horary variations have been observed in our northern latitudes, the maximum in winter appears to be at nine in the morning, the minimum at three in the afternoon, and the second maximum at nine in the evening. In the summer the maximum elevations are at eight in the morning, and eleven at night ; the minimum being at four in the afternoon. In spring and autumn, the times of these variations are intermediate between those of summer and winter. The difference between the greatest and least of these daily pressures, or the diurnal osdUationf as it is usually called, is equivalent to the pressure of a column of mercury, the height, hf of which is expressed by the following formula : — ^f A = 0*1193 (cos lat.) ^- 00149. 491. To obtain luxmrately the mean diurnal height of the baro- meter, it is necessaiy to observe the height of the column of mercury at several intervals during twenty-four hours, and to take the mean of these observations : but this tedious process may, to a great extent, be avoided ; for M. Du Bois Reymond has shown that at noon the elevation of the mercury corresponds almost exactly with the mean diurnal height. * This instrument, altbongb fbDj described in a work of large circulation more than twenty years ago, has lately been |>ut forward (perhapa igno- rantly) as a new Inrention : it wonld form a carioas chapter ra the natural history of icience to record in how many instances obsolete and not yery practical oontrifmnoes bare . been again and again reproduced as new dia* coreriee. t Prof. Forbes' Report on Meteorology. Height of the babouetex at great ALTrnTPxa. 271 492. The mean pressaie of the atmosphere is also subject to an aDnnal oscillation, the amount of whicn, except for some parti- cular places has not jet been ascertained. Within a zone, that extenos probably to the parallel of 40** on either side of ihe equa- tor, the ii^atest and least atmospheric pressures appear to corre- spond with the greatest and least zenith distances of the sun. Thns at Madras (lat. 13* 4' N.), the mean height of the baro- meter in January is 0-21 inches greater than in July. At Calcutta (Lfct. 22^** N.), the difference amounts to 0-62 inches. At the Gape of Good Hope (lat. 34*" S.) the height is 0-29 greater in July than in January. 493. The mean pressure of the atmosphere at the level of the sea appears to vary with the latitude. The comparative heights of the columns of mercury at 32** F. which are supported in Affe- rent latitudes, expressed in English inches, are, according to the moat trustworthy observations, as follows : — Lat. Height. L»t. Height. Lat. Height. 0' 10 20 30 29-930 29-976 30-064 30-108 40" 45 49 6li 30-019 30-000 29-978 29-951 64J" 60 64 67 29-926 29-803 29-606 29-673 494. Amon^ the many important uses of the barometer, must be mentioned its application to the purpose of measuring heights. As we ascend above the sea level the column of atmosphere pressing on the mercuiy becomes lighter by the removal of the subjacent stratum, and consequently the fluid metal falls in the tube. The increased rarity of the air, on ascending above the surface of the earth, has been already mentioned (478) ; the following is a table of the corresponding heights of the mercury in the barometer at several elevations : — Height abore aea level. Height of barometer. Height above sea lereL Height of barometer. Ofeet 6000 „ 10000 „ 15000 „ 300 24-797 19-000 16-941 3 miles. 6 „ 9 » 16 „ 15-00 7-60 375 100 Hence the subsidence of mercury in the barometer, on ascending mountains or other elevations, affords valuable data for calculating their vertical height. 495. 8elf-regUtering Barometer, — ^A large portion of the time expended in making and recording observations on the barometer 272 ■tad other mcteorolo^cal instrameTita, hoB been EitTed hj Bppft- retuB 80 constructed kb to recnrd tbeir TSriatioas bj some ftativ matic process. Varioiig mechanical arraneemBiita haw been derisea bj Dollond, Krei), and others, in which the grsvily of the displaced column of mercury is made to act upon a pencil, vhich marlia a sheet of paper, moving uniformly in its own plana 2* clock-work. The morementA of the pencil, correspanding with Me of the column of mercury, aro in a direction perpeadiciilaT to that of the paper ; conseqaently, by the combined moremenls of the pencil and paper, an irregular lin&or curve is traced, of which the abscissfB represent time, and the ordinates, the corresponding variations. The delicacy of tbe indications will, however, evi- dently depend an the smallnesB of the amoimt of friction in the apparatus itself, whicb, in all arrangemeata of pencil-tracing, must necessarily be considerable. The photographio method of registration, which was first aac- cessliilly applied bv the present ecutor of this treatise te the mag- netic Lnstrumen ta, has been convenientlyeitended to the barometeT, especially since the arti&:ial illummation and photugraphio apparatus necessarr for the registration of the balanced magneto- meter (see Magnetism), sec^e equally for the registration of the baromeler. XA, Fig. 3S9, is the BeK-regiBlering barometer; IV-3^ BB,tbe upper and lower ends of a cyphon baro' f the mercniy, irns; this has and RB this is e movement of OTercome, the Tom that caoie. cing for a few lent to perhaps the Tjjth or inch of mer- cury, has fre- qoentlfbeen recorded. SELr-REOISTBftINO BABOMKTEB. 273 with a small aDerture, through which a pencil of li^ht passes. By the length of ieTsrage, the indications are four times the actual variation of the column. o is a plate on which the tube rests, which is raised or lowered by a screw, in order to bring the arm into its mean or horizontal position when the apparatus is daily set to work. B, a stand supporting a gas-burner. I, the register line described on photographic paper by the pencil of light transmitted by the screen, f ; which will rise and fall with the column of mercury. K is a tube, with a plano-convex prismatic lens at each end of it, placed at the back of the burner ; tnrough this a pencil of light is conducted in the direction indicated by the dotted line, and de- scribes the base-line, l. By this arrangement two pencils are derived from the name source of light, which fall perpendicularly on two remote points of the paper. M N is a stand supporting a cylindrical lenn, through which the two pencils of light pass, and are brought to a focus. 9 IS a brass frame which supports a turn-table on three hori- zontal and three vertical rollers : a pin projects vertically from the centre of the turn-table, which enters a hole in the centre of the cap of t, the cylinder resting on the turn-table, round which the photographio paper is placed. The turn-table is carried roond by the hour hand of a chronometer, placed concentrically beneath it. The paper is covered by a second cylinder concentric with the first, in oraer to prevent its becoming dry (which greatly impairs its sensibility), during the twenty-four hours that the apparatus is designed to remain in action. A blackened zinc case is placed over the cylinders when in actual operation, to prevent any li^ht from falling on the paper, except tne two pencils that descnDe the register and the base line, from which the variations of the register are measuied. In order to avoid confusion, this is omitted in the figure, as well as another case of the same material, which covers the whole of the apparatus, to protect it from dust, and the sensitive paper from any stray rays of light. 496. The Aneroid Barometer, — A compendious and portable inatrument, capable of showing approximately the barometric changes, had long been a desideratum, until the invention of the aneroid barometer. The original instrument, invented by M. Vedy, consists of an exhausted eUstic metallic chamber, the expansiou and contraction of which, due to changes of atmo^^pheric pressure, are multiplied by a combination of levers, and indicated on a dial. The vacuam-chamber a, Fig. 330, is flat and circular, havine its top and bottom corrugated in concentric circles, to render them more elastic. In the best constructed aneroids the top of the chamber is, in a certain degree, heldnip in opposition to the pressure of the atmosphere by the elasticity of a folded lamina of spring- T whicli is raacbed fnim Fif.3K. an npertnre in tbe lottom of the e*ae, the indei-erroT may be corrected whenever such IB fonnd to exist : sod it maj here be re- ninrked that amall in- dei-errorB nilt occiai- ooally anw, ontil hj A little time and use the numerous nioieable parts of tbe inatrument hare aaaumed their pennanent bearingi; wheu, hoireTer, it is duly reasoned, it ma;, if originallf veil coii- struclcd, be carried about with ordinary care in travelling, without unde^^MDg aoy eoaaible changp. The folded spring, a, is fimilj connected with a atud on tha centre of the TBcuajn-cbBmber(which has bern carefully exhaurted b; an air-pomp, and the aperture soldered up), and rises and falls irilh it in obedience to atmospheric presaurs. An arm. d, is at- tached lo tha Bpriug, at the further extremity orvbich the aclunl morementa of B are considerablT amplified. The end of D is con- nected by a link (15T) wilh a abort arm proceeding from B lran». verse bar, f, which is moveable on its anis. Along aim, proceeding upwards from F, ia attached by its ezlremitv, o, to the ead of h Kteel chain (similar to the fusee-chain of an LDglish watch), which is wound round a small pulley on the aiis of the hand or index. A spiral balance-apring, attached by one end to the pnllej, and by the Other to the frame-work, opposes the pull on the chain at it, and cause* the index to retreat when the chain is relaxed. Since the elasticity of metals is diminished by elevation of tem- perature, Ihatchangeof lemperatnrowill toaamall extent pn>dac« the same change in tho indications of the ioBtninient aa increased preaaure; this source of error mny, however, be obviated by attach- ing by numerous rivets a slip of brass, ■, to the steel arm, d, which thus compenaale iho change ofelaalicity of tba vacoum-ch amber, ariaing trom the same cause. The dimensions of the slip of braas must be determined by actual trial. 275 Mr, J. Browning (by vhom prolulily the most •ccanlle inalni- inents of tbia kind bive b««n constructed) bu detennined bj' eipeiimeal tbat tc render the moTementB of the top of thti vacuum- chamber aiuform, doe proportiona muet exist IietKeen tbc diameter oT the chamber, Hud lbs widtb and deplh or tba ramigations. This ma ascertained by filing an exhauited chamber and a micnscope on the aame stand, and having substituted a cord and weight for the apring, n, examining by ' WBISnT or tHE AT1103PBEU. 277 pnmp, pravioaalj to being put in conneiion with tlis tuba. When placed tan vertical poaition, let D be the point kt which the BUrfacs of the mercury rests. If (he etop-cock between the tabe and it be opened, the mercury wi)l remnia at n, since the preiBiue of the air in nia the same asthatorthaatmo- '^' ^^■ sphere; if the stop-cock of n be now cloBed, aai Ih&t of n opened, the meronry will fall conriderablj-, »i, for iDEtanci', to E, since ihe pre^anre of tbe air in tn has been much reduced b; eihaustion : the column db there'.ore reprenonta the difference of prcsmrea in the two receivera. Let both the stotHMckB be now opened, and tbe preiauro eqoaliied in the two receiTera, when it will be foanil that (he mercury will riae to a point, p, midway between n aod E, provided the capacity of the commnnicationa, &c., be amall, compared with that of [he receivers. Hence it appears that the denaity in either receiver being the mean of the farmer densities, the pressure is the mean of the former pressures ; and thua the truth of the law is eatsblished. This experimeatal proof may be varied by partially exbaostiiig both receiven, hut in conri- dersbly diBerent degrees, when it will always be found tbat, when the prMaore is equalized, tbe point p will bisect the interval db. 500. Uegnault basahowo, that under great nmiaare airceasea to conform to Boyle's law. but that its compreBsibility increases with increasing preaanre. The compresaibility of nitrogen U also aug- mented by increasing preasure, b;it not to the same extent an nir. The value of the ratio of presaure to denaity for ilry atmonpheric air does not, hoirever, perceptibly change under the preaaure of a column of niercnij nearly 90 feet high. It has also been ahonn (478) that the expansibility of gases and vapoura is not unlimited. Carbnnic acid and other gasea cnnfarm more closely to the eeneral law as their temperature is raised. It appears probable, IraiD the Rxperimenta of Faraday, tbat every gas may he mode to Hsnme Ihe form of a liquid when eufBcientl; compreaeeil ; eape- cially when at a very law temperature. When the condensation of a gas is carried on nearly tu the point at which it- begins to liqoefr, the ra^o of ila preaaure to its density at a given tempera- tare IS no longer constant. 601. In consequence of the atmosphere, in avenes atatea, being capable of supporting thirty inches of mercury, it la eaay to calcu- latis the pressure upon each aquace inch of aurface expoaed to its action by ascertaining the weight of a column of mercurj thirty inches high, and one square inch in sectional area. Thia will be found to De nearly equal to fiFtoen pounds, which is therefore assunied as Ihe amount of preasnre on every square inch of surface etpoicd to the atmosphere. This pressure corresponds very nearly 278 with that of a cotnmn oTitnioipheTic air five and > qnuter milM in height, if of nnilbrm density equal to the me>a deositj >t tb« t*»- tevel ; but, aa the densit; actually diminishei in progiortioD to tbe height abore the level of the wo, the air reoUj eitenda to ■ much greater eleTation (478). If the anrfoce of an adolt be coBsidered as eqaal to SOOO Kiaat* inches, the preE«ure exerted on hie bod; hy the atmonphere, in equal to the enonnooB amount of 30,000 pounds, or nearly 14 tnit, a fonw more than EuGGcient to cmBh him, were it not oppooed bj il und contrary presauro of the oerironD and other floidi g the caritie* and tiosuea of bii frame. CtUX. The Fremira-aaugt. — Theamountofcompreaionofanen- cloeed rolame of air boa (Vequently been emplojed aa a meaanra of the compreaaing force; an iaitrnnient aSbnliaK thia indication ia callad a preBaure-gauge. The tube repreKntea in Rg. 833 will aoairer this pnrpoae veiy well for moderate pMwanroB, if it be filled with air, and tbe mercury be then made to stand at the same leTel ats and in the bulb. If then thetnbebe gradnated in aliqoot part* of A B, as ), ^, I, Ac., the mercury will be raised to theaa diriHiona by the presauro of 2, 3, i, &c., atmoapherea. At high pranuraa, howerer, the scale becomes ineonveniantly oontrmoted for reoord- ing amsll variations of preeapre. To remedy this in- jtj. 39*. ojnvenienoe, Mr. Allan tuta proposed to employ m conical tube, to which such a curved outlioe may b« given, as in Fig, 334, that equal increments of presMira maybe represented br equal apace* on the scale. The pamcolor inslrument here represented ii designed for a ateom-gaoge, the presaure of the aleam being eiertsd on cold water contuned i[i a D shaped prUongatioD of the tube beneath the gauge. The figures 10, 30, &c., repreaent pounds of pressure per square inch pheTio pressure, an eihausting s^nge, or an air-pump, b»- comes a oeceasary apparatus. These instruments are coostnwted on the same principlsa : the fonner cousiats of a barrel, b c, Fig. 335, of metal, funuahed with a acrew at c, for the purpose c^ con- nectinK it vith any appantiu required ; at * i* ■ Talve, opcDine upward*. Tbe pistoD, e d, maret air-tight in iLe Uarrel, perforata at E, and there fumiihed with a valve, also opeDiDg apvudB. Thii ijHnge beins coonected, b; ineana of the ^,_ jgj^^ ■crew c, with any clowd cavity, let E be drawn up to B bj raining the handle D, and then depre^ud ; the air encloaed between k and a will eacape through ihe Talve a: on again eleTatiog the piatoD E, the presiure on the valre, t, ia consider- ablj dimiiiiihed, (hen the eUatic pressure of the sir beneath a opeui it, aad the air panea inlu the space between A and ■ , and on again da- prrsamg the piston, this escapes thmagh the Talve K, and ao on; tbe air in the vessel con- nected with c hecoiuing each time more rarefied, until the eiceas of preaaure of tbe air below A, bejond that abore it, ia nn longer able to raise the TaiTe, when tbe action ceaaea. S04. As this process is eitremelf t«dioui, and in proportion as the air becomes more mreSed, the external atmospbere, pressing ou the piston, ren- ders It more laboriauitn elevate it, lliia ijringeb^is given way to the air-pomp, conalructed with two sioiilar harreln conoecled by a tube with a perforation in the centre of a perfectly datptale of brasa, on which strong glass vesae Is. called r^cnum, are fitted air-tight, by applying a little Kieoso to tbeir rima previouslj gronnd tmly flat. By working the pistons by means of a cog-vheel and two racks, tbe labour of eihnustion it much diminished, be- cause tbe preasare of air on one piaton is counlcrbalHnced by that on the other, since (he; move iii opposite directions. A, n, '~ — ' ) two barrels comma ui eating by a lube with ibu T% - ., ir-pump plate: this modiScation of Ihe air-pnmp is due to Hawkabee. In the eariier machines, the ImrTela were connected directly with a Urge globe, in which the ■nbatiuice to be ex perimented npon was In order that the vacuQni once obtained ■nay be mnintainei any required length of • BajUr, Wotki, n 280 PNEUMATICS. time, without any risk of leakage through an^ parts of tlie pumps, it is desirable to possess the means of isolating the receiver from the pomps : for this purpose the plate is generally raised from the wooden oase, and supported by a large and well-made stop-cock, as D, Fig. 336. 505. Smeaton's air-pump consists of a single barrel, similar to Fig. 336, except that the piston-rod works air-tight through a stuffing box in the cap of the cylinder, b, which is likewise sup- plied with a valve opening outwards; consequently, on raising the piston, the air above it is driven out through the valve in b, Fig. 335, but, on depressing the piston, a partial vacuum is formed, which relieves the valve at e from pressure, and allows the passage of air from the chamber below to that above the piston, when considerably rarefied ; consequently, the exhaustion can be carried much further. Also, the piston s being relieved from the pressure of the atmosphere, there is very little labour required in working the pump. 506. It has already been stated (503) that the limit of action of an ordinary air-pump is the power of the exhausted air to open a valve between the receiver and the cylinder. This difficulty was overcome in Cuthbcrt*s air-pump, in which, instead of a valve at the l)Ottom of the cylinder, there were apertures of communi- cation with the receiver, which the piuton just passed on reaching the bottom of the cylinder, and with this instrument a better vacuum can be obtained. The limit of action is now the capacity of the residual space above the piston, into which the bulk of rare- fied air that filled the cylinder must be compressed ; and unless its pressure is then sufficiently ixbove that oi the atmosphere to open the valve, none will escape, and the action ceases: this residual space should consequently be reduced as much as possible. Both these latter points of construction have been carefully at- tended to in the air-pump of Mr. Grove, by which the most perfect vacuum at present attainable by means of an air-pump may be procured. In this instrument the solid piston is a truncated cone, made to fit accurately a conical cavity at the end of the cylinder, the aperture at the end of which is just large enough to be closed by a valve which is reached by the end of the piston. If the end of the cylinder be imniertied m a vessel of oil, and the valve be a conical plug opened by the piston at itn extreme point of descent, the smallest bubble will escape that is capable of rising spon- taneously in oil. According to the original plan of Mr. Groye, the valve is an ordinary silk valve, which is a little strip of oiled silk, or thin gutta-percha, wider than the aperture, and tied tightly over it Grove's pump is not a convenient instrument for com- mencing the exhaustion, especially of a lai^ receiver, because the upper surface of the piston is subject to the full pressure of tlie air in the receiver; the most convenient form of apparatus, both for ease in working, and for jjerfect exhaustion, is one in which Orora'* and Hawksbee'e prineiplea an combined, a.a in Fig. 336, in which OroTe'a pump, r, ii pliced obliquelj at tbe aide, and is not intended to be used until the preraare of air in the receirer ia reduceii to leas than lliat o{ one inch of niercor;. 507. Aa, bj meanii of these inBtrnmenlii, a coDstanC aliquot part M1I7 of tbe residual sir ia abstracted bj eiwh atmke ol the piston, tho air, iu a connected vesse!, is only eitremelj rarefied, never becoming a perfect vacoam, it ia (requenllj doHrabte to measure the degree of rarefaction of the included air ; for this purpose, ths open top of a barometer tube ia consected with the eihanated Teasel, its lower end being plunged in mercniy. On eihnnating the air, Ihe mercury is fnrced up inio the tube by tbe pressure of tbe atmosphere on the mercury at its lower end: and the nearer its heiglit corresponila to that of the barometAr at the time of tbe experiment, the nearer the air in the rcL-eiver approaches to b •late of perfect eihaurtion. 608. In place of a tube immersed in a vessel of mercury, tho •«)AonAni«|l<'ig.337,iBmorecommon1yemplayed: this conaiats of a small stout glass tube, a d, bent twice on ^' '''■ its«lf at B and 0, the end n being cemented into a •crewed cap, by which it is attached ia the air-pump, mnd connected with the caTity of the receixer : for this piirpose a second smaller plaie is Ireqaently placed be- nind the larger one. The tnbe is closed at a, and the portion a b filled with mercury. When the pressure of air in the r ceiver beenmes less than that due to the column A 1 tbe mercury descends in a h and rises in b c ; and tt two surfdoes approach the same level in the tv branchea a b, B c, in proportion aa the vacDum beoom< more perfect. 509. When the density of ilie sir is required Pig, S3e. Ia be increased, ths condensing syringe, the con- Terse of the eihsustlng syringe (303), is employed. This consist* of a brass barrel, (Qmished at a with a valve opening downwards ; a perforation ia made | in the side of the barrel at A, just low enough to ■Low the piaton to passaboTB ' " lyringe on a strong metallic Teasel, ond raising n aboTB the openine at a, all the space between b and s becomes filled with ur, and, on depressing the piston, this ia forced through the toItb b, into tbe Teasel screwed on 0. On again raising b, air esanot escape through e, because the valve opens downwards; and on depressing the piston, a ^v'-h portion is forced through e into the vessel, and thus the condensation of several volumes of air into » small balk may be effected. 282 PNEUMATICS. Fiff.93». The limit of action of this instrument is the amoant of pressure that the hand is capable of exerting on the handle of the piston. Since the pressure of the compressed air upon the piston is propor- tional to its area, it is evident that the conaensation may be carried further with a piston of small diameter than with a larger one. 510. The air-gun affords an example of the practical application of the condenser, by which several atmospheres are condensed into a spherical ball, or cylindrical vessel, wnich is attached to the barrel. Those uf the beat construction are furnished with two condensers, the smaller of which may be used when further con- densation by the larger is impracticable. 511. By means of the preceding machines, many highly interest- ing experiments, illustrating the general properties of the gaseoos flmds, may be performed. The following are examples of these : Illustrating Atmospheric Pressure. A. Place in close contact the two brass hemi- spheres, A, B, the edges of which have been accu- rately ground together, and connect them, by means of the screw c, with the hole in the centre of tho air-pump plate (504) ; exhaust the air from their interior, close the stop-cock b, remove them from the air-pump, and screw on the stand f, or more conveniently for the purpose of forcible traction, or suspending a scale to be loaded with weights, another ring similar to the upper one. On then attempting to forcibly separate a from b, it will be found nearly impossible, by any moderate exer- tion of the strength of the arms, to effect this : r^ T-1 for they will be pressed together by as manv times js'U ) I fifteen pounds as there are square inches in the area "^k pL^^ of the section. This apparatus is well known as the *^Cy ^^ Magdeburg hemispheres, from its having been in- vented by Otto de Guericke, burgomaster of that town. B. Pour some mercuiy into the .cup a, excavated in the substance of a piece of wood screwed on to the top of the receiver b, and place the whole on the air-pump plate. On exhausting the air from b, the mercury will be forced through the pores of the wood into the receiver b, in the form of a metallic shower, by the pressure of the external atmosphere. On this principle, the minute capillary vessels of animal structures, and especially the absorbents, and the tubuli of the testicle, may sometii^es be iinected with mercury : for this purpose a glass tube drawn out to a fine point must be passed through the cover of the receiver and the bottom of h'ig. StlO. BE818TAXCE OF THE ATMOSPHERE. 283 ^.341. tbe cap of mercuiy, and the fine poiot inflerted into one of the larger Tessela, and suitably secored. lUuitrating the Elastieiiy of Air. C. Remove the jet b from the Teasel l. Fig. 341, and screw on the condensinff syringe (509), having preri- oasly hatf-fillea a with water ; on forcing air into this vessel, it will babble np throagh the water and rise on its sorfaoe, dd. After working the piston for a few minates, close the stop-cock, c, remove the syringe, and screw on tbe jet, B. The condensed air will press upon the surface of the water in a ; and on opening the stop-cock, will force it oat in a jet, forming a fbontain. D. If the same vesiiel, without any con- densation of air into it, be placed under a tall, narrow receiver on the smaller plate of the aiF-pomp, or on a separate plate, connected by a tube and stop-cock with the receiver, and the latter be exhausted, as soon as the two receivers are connected by opening tiie stop-cock, the water in the tabe b, being relieved from the pressure of the atmosphere, will be raised in the form of a jet, by the un- opposed pressure of the air in d. £. Press together the sides of a bladder, so as to nearly empty it of air, and tie it tightly at the neck ; place it under a receiver on the air-pump plate, and exhaust the air: as soon as the pres- sure of the air is removed from the surface of the bladder, the elasticity of the small quantity left in it comes into pla;^, and the air expanding distends the bladder. On ro-admitting air into the receiver, the small quantity left in the bladder is compressed to its fbrmer bulk, and the bladder appears as empty as at first. F. Place a vessel of spring water under tne receiver of the air- pomp, and exhaust the air ; as soon as the pressure of the atmo- sphere is removed, the air dissolved in the water expands by its elasticity, fonns large bubbles, and escapes from the water, thus producing in the latter a state of effervescence. G. On placing baked apples, raisins, or shrivelled fruit, under the receiver of an air-pump, and removing tbe pressure of the atmosphere, the air they contain expands, and dilating the integu- ments of the fruit, gives them the appearance of ripe plumpness. On re-admitting air into the receiver, this artificial and delusive appearance vanishes, and the frait again becomes as shrivelled as before the experiment. H. Place a glass vessel half fall of hot water under the air-pump receiver ; as soon as the air is exhausted, the water will begin to 284 PNEUMATICS. Fig, 842. boil Tiolently ; l)ecau8e the temperature at which water boils i» coDsiderablj reduced by diminishing the pressure of the atmosphere upon its surface. (See Chap. XXV.) 512. Benttance of the Atmosphere. — ^The slow and irregular descent of a light body, as a leaf, or piece of paper, compared with the rapid descent of a dense body, as a stone, is due to the gi'eater resistance that the atmosphere oflers to the extended surface of the light body ; this may oe shown by means of a thin lamina of heavy matter, as a piece of tin-foil or gold-leaf, which, when rolled up into a compact ball, will descend as rupidly as a stone. The same may be shown by removing the atmosphere, without altering the form of the light body. Let a coin and a feather be placed on two small brass shelves, a, h^ attached to the cover of a tall glass receiver, Fig. 342 ; these shelves move on hinges, and are kept in a horizontal position by means of a brass key, c ; on turning this key the shelves are released, and the coin and feather fall, the former reaching the plate d sooner than the latter, owing to the resistance of the air. Let them be replaced, and the air exhausted by an air-pump; when the bodies are now released, they will be found to reach the plate d at the same instant, thus showing that gravitation acts alike on both light and heavy bodies. This apparatus acts better when the descent of the shelves, a, &, is aided bv a light spring : and if the shelves be placed one above the other, and a coin and feather be placed on each, they may be released in succession, and the experiment may thus be repeated in the same vacuum. This experiment may likewise be shown by means of a long and large glass tube, closed at one end, and ground at the other, to fit a small receiver plate. The bodies will fall from one end to the other, on suddenly inverting the tube, when exhausted. 513. Mareet^s Apparattu ^or Artificial Betpiration. — ^A modi- fication of the air-pump, devised by Dr. Marcet, affords the most convenient means of producing artificial respiration. This instru- ment, like the air-pump, consists of two cylindera a, v, the pistons of which are simultaneously moved in opposite directions by means of racks, and a wheel turned by the double handle b c. At the bottom of each cylinder are two pipes, d, e, and f, o, in which are valves opening in the directions of the arrows, d and f are both connected with a pipe, through which the artificial re- spiration is to be effected. The valve in f is kept closed by a spring sufficiently strong to overcome atmospheric pressure, and is opened by the rising piston in v coming in contact with an adjustable stop on the roa h, which passes air-tight through tho pialon. This atop limiti tbe range of nmtion of both pistoni, and conBcquenllf [he unoont of sir injected nt eitth atmkc. Wh«a ihe pUtOD ID A is dvprened, and ^, gU, that ia V raiaed, the air, which had preriouslj entered a throueh t, pasaes throagh d into the re- apirstion tube, and the riaing Qneath it. But vhen the latter fhlun reaches tho stop, Ihs vaUe m r in opened, and that in d doaing, tbe already reapired air enlcrs ihrongh P, and filli Ibe lacuum in v. On roTerain|t the action, that is, raising tho piston in A. and depnming that in v, frei'h air panes into a. throngh b, and the expired air in v is dia- chirged throagh a, until the pii- tonfi reach tho top of A, and the botlom of V, when the aboxe . &U. It hu Wn .howd (498,9) that lh( . . . ic preisure of the air at a given temperature Tariea as ita denaity; hence, if p„ be thodentity of the air at 0° C. nnder the preutirc II, then Ilnfip,, when ft is coastsnt. If A be the altitude of tho column of u]crcui7 aupporteil k tlie preanure of tho air, o, its denailj at 0* C, and g Hie force of gratitj, then n = {r. a,. A,- hence, g.a,.k = ^.p, (a) it. 46°, the air being free Irom m constant preasare, and p„pi, its densities at the ' cantigTside, aa indicated by a mercurial ther- iccording to the eiperiment* of Magnna and u, = (l + 0'00366ox()ti„ 286 PKBUMATICB. provided the temperatare lies between 0* and 100" C, or does flot much exceed thoee limits. Since the quantity of air is constant, po • % = P< - ^«i hence ^, = (1 + 0003666 x«)Pf I and hence n=f4 . po=M (1 +0 003665 x t) p^ It is the result of observation, that at the level of the sea, in lat. I, ^=32-17237 (1 - 000256 x cos 2 Q feet ; hence, substituting these values, and that of fi in (a), we obtain the density of mercury at 0" C divided by the density of dry air at t"* C. under the pressure of a column of mercury at 0' C, h inches high, at the level of the sea in lat. {, 314688 1+0 003^65 x« X h 1— 000256 X cos 2 Z 516. If two vessels, of which the capacities are u and v, are filled with the ffases a and b, at the same temperature and pres- sure, and whicn do not act chemically on each other, and a com- munication be opened between them, it will be found that in the oourse of a short time a mixtiire of the gases will be equally dif- fused through both vessels (51), and the temperature remaining the same, the pressure will remain unaltered. If a volume u of A, at the pressure h, be mixed with a volume V of B, at the pressure n, then what is the volume to of the mixture at a pressure p, the temperature remaining the same throughout? M N Under the pressure r, the volumes of a, b, will be — tt,-t7,re8pec- f p tively ; but if the gases, after being mixed, occupy a space equal to the sum of their volumes before mixture, their pressure will still be p ; tborefore, under the pressure p, their volume to will be - tt + - 1? : therefore, p«7=Mtt + N». If tt = o = 10, that is, if the original volumes were equal, and the mixture be compressed into the same volume, then p=ii + n; or thepreMiure of the mixture = the aum of the original preB9ures. 517. When a volatile liquid is introduced into a vessel contain- ing air, precisely the san^e effects are produced as in vacuo, except that the vapour is formed more slowly ; the quantity of liquid finally converted into vapour is the same as if the vessel contained no air. Let m be the pressure of the air before the introduction of the liquid, and p the pressure that the same quantity of vapour would exert if the vessel contained no air. The volumes of the air, of the vapour, and of the mixture are the same ; therefore (516), the pressure of the mixture = m +p. PRBflBUnS OF VAPOUR. 287 518. If a small quantitj of any liquid capable of affording vapoQT be introdncea into an exhausted vessel, it will be almost instantly filled with vapour, the pressure and density of which are found to depend only on its temperature, provided the whole of the liquid be not converted into va|>our. If the space in which the vapour exists be increased, a frebh portion of the liquid will take the form of vapour : and if it be diminished, a portion of the vapour will return to the liquid state; but the pressure and density of the vapour will remain the same in either case, pro- vided the temperature undergoes no change. If the temperature be increased, a fresh portion of the liquid will be converted into vapour, of which the pressure and densify will consequent] v be increased ; and if the temperature be diminished, a portion of the vapour will return to the liquid state, and its density and pressure will be diminished. If the space be suflSciently increased, the whole of the liquid will assume the form of vapour : under these circumstances, the relations between the pressure, tem- perature, and density of vapours are very nearly the same as for air. The pressures exerted by the vapours of varioos fluids in contact with the fluids from which they nave been produced, have been determined experimentally, and empirical formulsB have been con- structed, whicn, within a certain range of temperature, express the results of these experiments with considerable accuracy : yet hitherto no law has been discovered by which the pressure at any given temperature can be determined. 519. The pressure of the vapour of water at any temperature from — 5° to 110** C. in millimetres of mercury at 0% as ODserved by Magnus, is very accurately represented by the formula, 7'44ff6i P = (4-525) 10 or log P = log 4525 + 2^69 +t. The following table gives the corresponding values of t and Pat various points of the centigrade scale : t. P. t. P. *. P. t. P. -5* ... 8115 25' ... 23-582 55" ...117-378 85«» ... 432-295 0 ... 4-525 30 ...31-602 60 ... 148-579 90 .. 524-775 5 ... 6-471 35 ...41-893 65 ... 186-601 95 ... 633*305 10 ... 9126 40 ...54-969 70 . 232-606 100 ... 760-000 15 ..12-677 45 ...71-427 75 ... 287-898 105 ... 907-157 20 ...17-396 50 ...91-965 80 ...353-926 110 ...1077-261 In DaIton*s table, the degrees are those of Fahrcnheit^s scale, as follows, the pressure at 80"" F. being the unit : — 288 FNEUMATICB. t. P. t. P. t. P. t P. 32r.. 0-200 60'... 0-378 70'... 0-721 90 ..• 1-36 35 ... 0221 55 ... 0-443 75 ... 0851 93 #.« 148 40... 0-263 60 ... 0-524 80 ... 1-00 96 ••• 1-63 45 ... 0-316 65 ... . 0-616 85 ... 117 99 •>. 1-80 520. When the pressure of a flnid is expressed in " atmospheres/* an atmosphere denotes, in the metrical system, the pressure of a column of mercury at 0** C. which is 76 centimetres, or 29*9218 inches high, at the mean level of the sea in lat. 45° ; this, in round numbers, is taken to be 15 lbs. upon each 8<^uare inch of surface. If T be the temperature of steam, and p its pressure in atmo- spheres, it is found that up to 224'' C, and probably much higher, T = 100 + 64-29512logp+13-89479(logp)« + 2-909769 (log p)> + 0-1742634 (log p)<. log 64*29512 = 1-8081780, log 1389479 = 1-1428520, log 2-909769 = 0*4638586, log0-1742634= 12412062. The following table, calculated from the preceding formula, shows the temperature, by a mercurial thermometer with centigrade divi- sions, or steam at various pressuras from 1 to 45 atmospheres. p. T. p. T. P. T. p. T. 1 . ..100 0** 5-5 ... 156-8° 12 ... 190-0° 21 .. 217-3' 1-5 ... 112 2 6 ... 160-2 13 ... 193-7 22 ... 219-6 2 .. 121-4 6-5 ... 168-5 14 ... 197-2 23 ... 221-9 2-5 ... 128-8 7 ... 166-5 15 ... 200-5 24 ... 224-2 3 .. 1351 75 ... 169-4 16 ... 203-6 25 ... 226-3 3-5 ... 140-6 8 ... 1721 17 ... 206-6 30 ... 236-2 4 . ... 145-4 9 ... 177-1 18 ... 209-4 35 ... 244-8 4-5 ... 1491 10 .. 1816 19 ... 212-1 40 ... 252-6 5 . .. 1531 11 ... 186-0 20 ... 214-7 45 ... 259*5 Fig. 344. 521. Elastic fluids, or gases, in escaping from lateral orifices, produce a similar reac- tion against the opposite side, and correspond- ing tendency to motion, as in the case of denser fluids (430). lliis may be illustrated by a very common toy, now made by all glass- blowers, consisting of a globular vessel, b, Fig. 344, of thin glass, resting on a pivot at From the opposite sides of the vessel A. proceed two tubes, bent at right angles to a radius near their terminations. When a little water is placed in the vessel, and heat applied by means of a spirit-lamp, it will become converted into steam, ana give to VELOCITT OF 18901X0 GAB. 289 the apparatus, on escaping from the Literal tahes, a rapid rotatoty motion. Elastic flaids also appear to obey the conditions analogous to the th^jorem of Torricelli (426), when escaping under the influence of pressure* from orifices, unless the difference between the external and internal pressure be verj considerable, in which case they offer some exception to this law. It is also extremely probable that, like denser fluids, gases undergo, when escaping from apertures, a contraction in the dia- meter of the current ; the area of the section of this contraction appears to be equal to that of the orifice through which the gas is escaping multiplied by the decimal 0*61 or 0*62. 522. One veiy remarkable phenomenon, connected with the escape of a current of air under considerable pressure, must not be passed over silently. M. Clement Desormesf has obseryed, that when an opening, about an inch in diameter, is made in the side of a reservoir of compressed air, the latter rushes out vio- lently ; and if a plate of metal or wood, 7 inches in diameter, be pressed towards the opening, it will, after the first repulsive action of the current of air is overcome, be apparently attracted, rapidly oscillating within a short distance of tne opening, out of which the air continues to be emitted with considerable force. This curious circumstance was explained on the supposition that the current of air, on escaping through the opening, expands itself into a thin disc, to escape between the plate of wood, or metal, and side of the reservoir; and that on issuing from the circumference of the plate, this current carries off with it radially the adjacent particles of air, and thus an external current towards the centre of the plate is produced, which keeps it in its position. It is not improbable that a slight pressure against the outer surface of the plate may be thus produced, but the real ex- planation of the fact is founded on what has been already shown (432) respecting the motion of a fluid in a divergent tube : for the space between the disc and side of the reservoir may be sup- posed to be divided radially into an indefinite number of diver- gent tubes, to any particle in either of which the same resolution of its pressure may be applied. This fact may be reaoil^ demonstrated by attaching a flat cir- cular brass plate about 2 inches in diameter, with a nolo in the centre, to the end of a piece of tube, about half an inch in dia- * The fonowing formula is Bemomlli's expreseion for the veloci^ of an MOftpiBg gM, where V is the relocity of the gM ; j», the internal, and p', the external preMore, and 2ife ie a ooeflOcient eqoal to 166610 for gases at the temperature «f 3r F. . _ t Annalee de Chim. et de Fhys. xzzvi. p. 69. U 290 FHBDMATICB. meter, through which a current of either air or ^ter may be discharged. On this plate place another of equal size, with a projecting pin in the centre, to enter the hole in the former plate, ana thus to prevent the latter sliding off laterallpr. It will t^en be found not only that no amount of current will displace the loose plate, but also that if the loose plate be placed downwards, its weight will be sustained by the diverging current; and an additional weight likewise, if the current be sufficiently strong. A circular plate of the thickness of a shilling may be sustained by the force of the breath alone. 523. When the air is put in motion, the currents produced are denominated winds, and are tolerably uniform for a given space. The following table* gives a view of the rapidity of currents pro- ducing winoB of various forces ; the numbers representing the velocities reckoned in feet per second : — . 1*64, scarcely perceptible wind; 3' 18, sensible breeze; 6*56, moderate wind ; 18*04, brisk wind ; 32*80, strong wind ; 65*70,. violent wind; 73*80, tempest; 88*56, violent tempest ; 11808, hurricane; I 147*60, violent hurricane ; the latter sufficiently powerful to tear up trees, and to produce the most violent mechanical effects. Marriotte has shown that a wind moving at the rate of 12*78 feet per second, impinges against a surface of 395*67 square inchea with a pressure equal to 2696 grains, or more than 5^ ounces. 524. Anemometer$. — Instrnments designed to indicate the pressure or velocity of the wind are called anemometers. One of the oldest of these is Lindas anemometer. This instrument con- sists of two vertical glass tubes about six inches long and half an inch or more in diameter, connected by a bend at the bottom, and one of the open ends bent down into a horizontal position. This tube is partly filled with water, and so attached to a vane, that the horizontal open mouth may always be turned towards the wind. The pressure of the wind acting on the surface of the water in the tube raises a corresponding column, the height of which is measured by an attached scale. By making a hole in that tube in which the water a«eefu2f, jnst above its surface when at rest, the instrument will be rendered self-registering of the maximum force or velocity between the periods of observation : for it is evident that all that would have been raised will have flowed out at the hole, and therefore that the height of the column due to the greatest pressure will be twice the interval between the surface of the fluid when at rest, and the hole. Dr. Robinson's anemometer consists of a vertical revolving shaft, * Ann. de Bnreaa det LoDgitudet pour 18S8. AXEUOXETERB. 291 vith four horizontal arms, canring hemispherical cups at their extremities, Fig. 345, soplaced that the diametral planes may be radial and Tertical. These cops are found to revolve with one-third ^' ^^' the velocity of the tpind. A train of wheel-work actuated by an end- less screw (203) at the bottom of the revolviiig shaft indicates on a dial the niunber of revolutions, and consequently the aggregate motion of the wind during a given time, firom which the mean or average velocity may readily be found. 525. Self-registering Anemometers. — Various apparatus for re- eistering automatically the force and direction of the wind have neen devised by Whewell, Ostler, Dollond, Ereil, and others, ill all of which the changes are recorded by two pencils, the points of which rest perpendicularly against a sheet of paper moving uni- formly by clockwork, the motion of the pencils being at right angles to that of the paper. One pencil is suitably connected with the vane, indicating the direction of the wind ; and the other with a moveable disc subject to the pressure of the wind, and reacted on by a spring, showing its force, or velocity, either of these quan« lities being a measure of the other. A very simple and ingenioas form of self-registering anemometer baa recently been devised by Mr. Casella. In this instrument the shaft of a Bobinson's anemometer (524) passes through a hollow shaft on which a vane is placed, consisting of two flat plates placed at a small angle with each other. Tbe vane-shaft is in gear with a revolving steel die, having an arrow on its surface. A strip of paper psasing between rollers is impressed with flgures repre- senting tne velocity, as i^hown by the rotations of the cup-shaft ; and a spring-hammer, actuated by a clock, periodically impresses on the paper the arrow in its existing position, and thus tbe direc- tion of the wind at the time is recorded. The whole apparatus IB simple and compact.* 526. It would be unjust to the memory of a sincere and earnest labourer in the field of science not to notice very briefly the remarkable system of forecasting the changes of wind and iveatfaer instituted by the late Admiral Fitzroy. He has stated, in an account of his researches, that broad and shallow currents gene- rally prevail, and that these are constantly in more or less circuitous, but mutually opposed, progress; sometimes side by • It is SDgKested to the inventor that the regiiter should be read on the raised nde of the paper, as the pofif ion of the anew is then more sharplj defined : also, that tne arrow shoold be »nrronnded by a fixed rins showing the fonr cardinal and four intermediate points of the compass, to oe simul- t«i>eoasly embossed on the paper ; this would render tbe reading the direc- tion of the wind more easy taa certain.— Ssitob. U 2 292 FVEUlfATlCS. side, bat in contrary directions, sometimes superposed, and always having lateral as well as direct prog^ssion. It appears to be well established that there is a general lateral translation of the mass of atmosphere towards the east in the north temperate zone, while northerly, southerly, or other currents are in very various movement, the actual movement at any given point being there- fore of a composite character. It appearSi also, (as was the opinion of Espy, confirmed by those of Dove and Herschel,) that winds always set from places of higher to those of lower barometric pressure, and that the meeting of such winds produces a circuitous or cyclonic effect. Hence it appears that by the approximate know- ledge now possessed of the progression of atmospheric currents, of their relative breadth, ana oi the revolving eddies frequently existing between their edges or boundaries, and by a compariaon of the pressure, temperature, and other characteristics of the atmosphere at each of numerous stations more or less remote from each other, the conditions of atmospheric change may be known over a considerable area, (within probably a radial dintance of 500 miles round London,) and a highly nrobable conjecture may be formed as to what changes are impenaing. In some cases the pressure of aeriform fluids is employed in doing^ mechanical work, aa in the steam-engine (455— -458) the principle of which might perhaps have been more appropriately explained in the present chapter. Of these applications of atmo- spheric pressure, a few illustrations may here oe given. 527. The Pneumatic Lever. — ^In the present system of organ* building, all the heavy work of the performer in opening the valves of large pipes, and moving the large parts of the machmery, is ao- complishea by the intervention of the pneumatic lever. This contrivance consists of a small rectangular moveable board, which is flexibly connected with another fixed board of the same size (like the sides of a common pair of bellows), and communicating^ with the wind-chest by a small aperture, which is closed by a valve. In large organ pipes, such as the pedal pipes, the aperture in the wind-chest that supplies the pipe is of considerable size, and a fatiguing effort of the nand is required to open it, in conse- quence of the necessary internal pressure of air on the valve. But if the valve be connected with the moveable board of the lever, the effort of the finger is required to overcome only the resistance of the small valve of the lever, which itself immediately opens the large valve of the pipe. Some other internal movements of the instrument are similarly facilitated which it is needless to de- scribe in detail. In referring to the construction of organs, it may here be men- tioned that the water-engine (459) is now frequently employed to work the bellows, the opening and shutting of the valves being effected b^ the moveable board of the ¥rind-ch68t, when it has nearly arrived at its extreme positions. i^ i^rm JLIB AKD GAS BNGIKE8. 293 528. The Compre89ed Air Engine.— li has been proposed to work an engine, constracted similarly to the non-condensing steam- engine (457), by means of compressed air instead of steam : but inaamucb as it would require a greater amount of work to com- press the air, than that rendered oj the machine, by the amount of loss by friction, &c., the proceediop^ can scarcely ever be expe- dient. It has also been proposed to impart expansive force to the air by means of heat, but tnis has not hitherto been economically achieved. 629. Lenoir'9 Oas Engine. — The vacuum produced in the cylinder of the condensing steam-en^ne, by the condensation of the steam, is in this ingenious contrivance produced by the com- bustion of an explosive mixture of air^ and ordinary coal-gas, ignited by an electric shock from an induction-coil apparatus (Ch. XV.). A horiasontal engine working on this principle is shown in Fig. 346, in which a is the electric apparatus, b, the communicator of electricity at the proper moment, and c, c, the terminals of the coil, between which the exploding discharge takes place. The air is admitted to the slide-valve chamber at d, and the gas at E ; f is the exhaust pipe, for removing the residue after each explosion, and a is the inlet, and h the outlet pipe for cold water, to prevent the cylinder from becoming over-heated by the . successive explosions ; i is an indiarrubber pouch, intervening in the gas supply-pipe, to equalize the pressure, and therefore the Jinantity of gas delivered at each stroke. This machine has been ound very serviceable, whenever from any cause the use of a furnace and boiler is inexpedient, and where at the same time a supply of gas is available. It is especially conveui(fnt where the moQve power is required only at uncertain periods. 294 CHAPTER X. AOOOSTICS; THE PBODUCTION, TKAV83fISSION| AND PEBCBPTION OF BOUND. 530. When the air, or any other elastic bodj, is made to assume a vibratory motion, consisting either of a single pulsation, or of a series of oscillations or undulations (469) repeated with sufficient frequency, a sound is produced. During the existence of such motions, the molecular arrangement of the vibrating body becomes altered, but acquires its normal state on their cessation. Thus, if a copper ribbon, 9 feet long, 0'4 inch wide, and 0*04 thick, be vibrated, its length will appear unaffected. Let a weight of 90 lbs. be fixed to its lower extremity, and still no change occurs, but if again made to vibrate. Its molecular arrangement will become per- manently affected, as shown by its length becoming increased 6 or? inches. When these vibrations take place in an uniform and regular manner, as when a harp-string is struck by the finger, a perfect sound or tone is produced ; but if the vibrations take place irregularly, and are not isochronous, or if a single impulsive disturbance of the air take place, as in the explosion of a pistol, or the crack of a whip, a noise alone ensues. 1 ne transmission of a single pulse through the atmosphere may be thus shown experi> mentally. Place norizontally a tube about 10 feet long and two or three inches in diameter, with a conical termination at one end, tapering down to half an inch, and near the mouth of the oone place the flame of a lighted candle. If now an impulsive move- ment of the air be produced at the open end of the pipe, as by- striking together two pieces of board, or the covers of two bound books, a sudden displacement of the flame will immediately after- wards be perceived, and if the flame be rightly placed, it will be extinguished ; or if a little smoke be produced m the mouth of the 'tube, as by a bit of smouldering brown paper, it will be forcibly- ejected. 531. When isochronous f378) vibrations are excited with suffi- cient rapidity in an elastic ood^, not less than 16, or according to some, than 30, in a second of time, the resulting tone or note ia transmitted by the excitation of fresh and similar movements in surrounding bodies, and in the air, extending on every side, like the gradually widening circular ripples surrounding the spot where a falling drop of rain disturbs the surface of a pool of water (463). THE PBODDOnOX OF SOUND. 295 These eventually impingpo upon the membrane of the tympanum or dram of the ear ; wmch then assumes a vibratory movement. From this membrane tremulons motions are excited in the fluid -with which the lahfrinth of the ear is filled, through the medium of the air included in the tympanic cavity, and of the delicate chain of bones connecting the tympanum with a membrane cover- ing an orifice in the complex cavity of the internal ear ; and which, actinj^ on the auditory nerve, produce that sensation of sound, vhicn we reoognise as a definite tone or note. 532. The inferior limit of the number of isochronous vibrations capable of blending into a definite tone may be determined by ex- periment. A ver^ convenient apparatus for this purpose consists of a mandrel carrying four flat wooden rays at right angles to each other, and in the same plane, so as to pass successively through a parallel slit in a piece of wood placed radially to the mandrel, a pulley on which is driven by a multiplying wheel, and band. The entrance of each ray into the slit is marked by a peculiar loud impulse ou the air. Some difference of opinion will, however, be found to exist between different observers, as to the prebise velo- city of revolution at which the impression of a continuous tone is produced. This the writer has found to depend in a ereat measure on the sharpness and distinctness of the individual impulses : for example, if the slit be set exactly parallel to the edge of the enter- ing ray, so that eveiy part of it may enter the slit simultaneonslv, a sncoession of sharply defined rounds will be produced, which ao not so readily blend into a low note, as when the slit is set a little obKouely to the entering ray, so that it may enter the slit, so to speM, more gradoally ; in which case the separate impulses lose much of their sharpness, and the intervals between them are less defined. dSS. Whenever no material substance intervenes between the vibrating body and the ear, no sound is heard. If a bell be placed imder the receiver of an air-pump (502), and the apparatus be shaken, the sound excited by the clapper striking the sides of the- bell is distinctly heard. Let the air be exhausted from within the receiver, and the bell again agitated, the clamper will be seen to strike its sides, but no sound will be audible ; in consequence of no elastic medium existing of sufficient density to convey tne sonorous vibrations to the sides of the receiver. A convenient apparatus for this experiment is a bell with a lever escape- ^' ^*' • ment (258) within it, to the anchor of which the clapper "^^^ 18 attached, Fig. 347. A pulley on the arbor of the scape-wheel carries a string, one end of which is attached to tne end of a rod working air-tight through the brass cap of a tall receiver, and the ouer end to the under sioe of the brass cap. On raising and lowering the rod, the escapement will drive the olapper ; and as the bell is connected by the string alone with the rigid materials of the 296 A0OUBTXC8. lur-pnmp, yeir little vibration will be tbus contacted, and in a tolerably gooa Tacunm scarcelj any sound is audible. 634. Trayellers, on ascending loflj mountains, have noticed the extraordinary diminution of the intensity of sound, in consequence of the rarefied st^te of the atmosphere at considerable elevations above the level of the surface of tne earth (478) : Saussure found that on the summit of Mont Blanc, the explosion of a pistol ap- peared no louder than the ordinary sound of a cracker. And con- versely the intensity of sound increases, on increasing the density of the air surrounding the sonorous body ; thus sounds which are of ordinary pitch in the free air,acQuire a painful degree of intensity, if heard in a reservoir of condensed air, or in descending in a diving- bell, in which the air is condensed by the upward pressure of the water (397). 535. The intensity of sound, like that of attraction (31), dimi- nishes in the inverse ratio of the square of the distance of the sounding body. This law, however, applies with its fiiil force only when opposing currents of air, or other obstacles, do not interfere ; for the sound of a church-bell is inaudible, during a contrary wind, at the distance of a few yards, while the sound of the cannonading at Waterloo is said to have been heard at Dover; and the noise of a sea-fight between the English and Dutch, in 1672, was heard at Shrewsbury, a distance of 200 miles. In these cases the intensity of the sound was no doubt preserved through these distances, by the presence of aerial currents, moving in the directions in which the sounds were heard. 536. From the researches of Dr. Derham, the intensity of sound is modified by — A. the direction and velocity of the wind ; B. varieties in barometric pressure ; c. chsnges in the temperature of the air ; D. its hygrometric state ; E. the original direction of the sound ; F. the nature of the surface over which the sound passes. Sound is heard with great distinctness over a considerable space, in a frosty air undisturbed by winds or aerial currents. Lieutenant Foster, in the third Polar Expedition of Captain Parry, held a conversation with a man across the harbour of Port Bowen, a distance of one mile and a quarter. . 537. Resonance. — The intensity of sound is found to be consi- derably anemented, if the vibrations be confined in tubes or cavities of any kind : of this we have a familiar illustration in the speak- ing-tube, by which the voice is conveyed from one part of a build- ing to another, freouently to a considerable distance, and by a circuitous route. Tne stethoecope, an invaluable means of ascer- taining the physical signs of pulmonary and other diseases, is another application of the same principle. Biot found that the ■ligbtest vliUper vss haard thioDgh an iron pipe 3120 feet long. If ibe handle ofa vibrating tunine-fork (Fig. 3A1) bereiteda«aiiut the head, and one earbeclogedbjthe pBlmofthe liaQd,imm«diatetj after Ihe umnd of the tDning-fork ceues to be heard, it* vibration will immediately be perceived by the closed ear, even althonph the fork real on a portion of the ikull coiitignoDB to Ihe oppoaite ear. In this experiroent the vibrations transmitted through the Bolid ilniclureB of the akull feebly affect the sentient o^an, nntil they are amplified by reverberation in the closed cavity of the ei- temal ear, and thus affect the tympBDom. The experiment farther ebows that sonorous impreasions are transmitted te the sentient organs principally, if not entirely, by the atmosphere, and Dot by the boneaof the head, as some phy Biologists have snppoeed. 638. This lact of small sonnds beiog ampHfied by closing the external cavity of the ear, and thus augmeDtin^ il« resonance, is the principle of Wheatatone's mierophons, which consista oif a Y ibaped metallic rod, the two upper ends of which are bent in lowarda each other, and terminated by small fiat cironlar plates, when these are placed over the two Burs, any feeble —^ ^^ ■omid, tranamitted tbrangb the stem, wilt be more Wadilj perceived, than if simply conveyed to the i •ar throDgh the medium of the atmoophere. 539. The Jietonator of MelmhoUz.—Ttiii is a transmitted throngh the atmospber partdallj closed cavity (in this case, cylindrical) i, Fig. S48, connected by a flexible tube with a small rennded ivory tube, b, to be applied to Ihe ear. Any sound, to which the cavity of a reciprocates, will by its uae be considerably angmented, and thus more readily perceived by the ear. 640. Sedpmcation of Soimd. — When the air is in ■ state of ■onoroas vibration, it excites similar movements in bodies with which it is in contact, if they are susceptible of isochronoDS vibratory movements. This may be shown by tuning two harp, violin, or guitar-strings in unison : on causing one to sonnd, the •ir Borrounding it assamea a vibratory movement, and, this being propagated to the second string, cansea it to vibrate, and emit a sound or tone, because each aerial pulse communicates motion to the second string, and as the movements of both are by the snp- podlioD isocbronooB, each aucceeding impnlss augments the effect of the preceding one; tbis phenomenon is termed the recipromfion of found. If an ordinary tuning-fork be held over the mouth of a tube about 20 inches long, and turnisbed with a piston, it will be found that in some position of the piston the tube will yield the aame note as the tnniug fork, while if moved an inch m eitbsr direction the tnbe will remain perfectly mute. Id this case, when the tnbe reciprocates, each puliation of the air prodaced by a vibia- 998 AOOCBTICB. tion of the fork must trayel down the tuhe, and being reflected from the bottom, reach the fork just in time to be reinforced hy its next vibration. In this experiment the resonance of the tnbe is much louder if the open mouth be partially closed bj a cap having an orifice in its centre. Instances have occurred of persons who, bj modulating their voices, have excited vibration in glassee, BO powerful as to overcome the cohesive attraction that held the particles together, and consequently, to break them in pieces. 541. Waves on the surface of water, unless they differ very freatly in sizej are capable of passing over each other without eiug destroyed. And in a similar manner, in the case of the waves of sound, or sonorous vibrations, excited by a crowded orchestra, an attentive ear can readily distinguish the sound of each particular instrument. These are individual applications of the principle of the fuperposition ofimaU motions, which may be thus enunciated generally : — If the partidea of which a body is compoied are actuated hy several small disturbing foreeSf thev will obey each u» the same manner as if it existed alone ; and the motion of a partide in any given direction is the algetiraic sum of the motions that would result from the disturbing forces acting separaUly. 642. AU sounds, in traversing given distances, are propagated with equal rapidity, passing through spaces proportional to the times : this is evident from the fact that the music of a band is correctly heard at anv distance at which it is audible, thus show- ing that all the sounds reach the ear in their proper place, that is, at equal intervals of time, whatever may be the length of their undulations. Sir John Herschel* has shown that, in round numbers, sounds of every intensity travel at the temperature of 62* F. at the rate of 1125 feet per second, equal to 9000 feet in 8 seconds, 12) miles per minute, or 765 miles in an hour. At a freezing temperature and in perfectly dr^ air, the rapidity of the propagation of sound is diminished; as it traverses 1092 feet, or 364yards in a second. Tne velocity of sound obtained by theory is about 175 feet per second less than that obtained by observation; this difference depends on the effect of heat disengaged by compression of the air by its own vibrations. The familiar contrivance for lighting a bit of tinder, or amadou^ hj suddenly forcing a piston to the bottom of a closed cvlinder, is a conspicuous example of the dis- engagement of heat by the sudden compression of air. It must not^ however, be supposed that the temperature of the body of air is elevated by the passage of sound, for there is as much 1030 i> 1040 II 1092 11 41640 24 3976 20 . 4218 II 4768 Sabetanoe. Biver water II II Lead . . Gold . . Copper Steel wire Iron . . 11 Temp. 15' C. 60 18 II II II II 200 Vel. 4714 5657 4030 5717 11666 15470 16822 15483 « Miller's HydroaUtict, p. 00. t C. denotes the oentignde scale. 300 ACOUSTICS. It ma^ here be observed that while the velocity of sound is in- creased m water, it is decreased in iron by increase of heat ; this might have been anticipated, from the well-kuown diminution of elasticity in metals, by elevation of temperature. It may also be remarked that in gases at the same tension, but of different densities, sound travels more rapidly as the specific gravity becomes less ; thus a diminishing scale of velocities is met with in hydrogen, air, and carbonic acio. Similarly if the tension in both cases be equal, sound will travel more rapidly in a warm atmosphere than in a cold one. It is equally a law established by observation, that in gaseous fluids of tne same density, but of different tension, the Telocity of sound increases with the tension. This may be readily ascer- tained, by measuring the velocity of sound in air contained in a closed cavity when heated : the Telocity will be found to increase with the temperature. 646. The Telocity of sound in wood has been observed to be Tery different in three directions ; in the longitudinal it is more than double that in any other direction ; and of the two transverse directions — Tiz., radial, or euross the layers, and tangential, or parallel to the layers, that in the radial cUrection is the greater of the two. This has been ascertained in seTeral kinds of wood : — Long. Bad. Tang. Pine . . . 10900 . . . 4611 . . . 2605 Oak . . . 12622 . . . . 6036 . . . . 4229 Elm . . . 13516 . . . . 4665 . . . 3324 Poplar . . 14060 . . . 4600 . . . 3444 Acacia . . 16467 . . . 4840 . . . 4436 It has been observed by Prof. T^ndall that the law of transmis- sion of heat in wood corresponds m a great measure with that of sound. 647. Sound is not transmitted with equal facility through all media: thus, various gaseous mixtures assume sonorous vibra- tions with extreme difficulty. The sound of a bell under a re- ceiver full of hydroeen gas is, according to the experiments of Dr. Priestley and Sir John Leslie, scarcely louder than when placed under an exhausted receiver (604). When hydrogen is respired, the voice of the person undergpes a curious change, being rendered extremely feeble and raised in pitch, as might be expected, from the lungs and windpipe being filled with a rarefied medium. The fiEkcilit^ of transmission of sounds is, like their velocity, ereater in fluids than in gases, and still mater in elastic solids. If a musical box be attached to one end of a series of firmly united deal rods, 100 feet or more in length, the sound will be distinctly heard by an ear placed close to, or in contact with the other end, when it would be <|uite inaudible without the intervention of the rods. If the sounding-board of a Tiolin or guitar be now placed in lOOXD. . 301 eantact with the other end, and perpendicnlar to the direction of (he rod, the musical KMiDdswill be greatly dereloped, aad the tones are a singalar mixture of those at the boi and iriHtruiaaDt. This eiperiment viU aacceed beat at loog distances, if the rod be ana- pended bj threads or strings, so that the looeitudinal Tibratiuns (3IS) a( the rod majr not be airesced br the contact of soUd matter. A fina cooneiion of tbe consecutiTe piccea of the rod is essential to the sQccen of this eiperimenl, la otherwise (he vibra- tioDs are considerably weakened by their tranamiasion from one piece to the other, and become imperceptible at a comparatiTely short diatince. Similarly the intenention of any portiooa of eUstic or yielding matter between two adjacent pieces of rigid matter is fonnd materially to interfere viUi tbe traDsmiasion of 648. Sounds generated in air are indistinctlT hsard by a person immeraed in water; bat if excited in that fluid, the/ are conveyed to a coDuderable distance with facility. M. Colladon heard Ibe aonnd of a bell Mmck under vat«r acroai the whole breadth of tbe Lake of Geneva, a distance of nine miles ; thia aound ap- peued to pass through the water with a trelocity of 4708 feet per 549. Inierferenix of Sound. — Two sets of aonorous ribrations of equal intensity, encountering each other in oppoiite phases of TibrAtion, will mterfirt, and become inotuBJly checked ; and thus aiknce will be produced by the conflict of two sounds. To under- stand this intarl'etence of Bon'>rous vibrations, let us suppose tbat two aeries of vibnitioDa, occurring simattaneonsly, are superposed on eacb other (Ml] aa a, b. Fig. 349, so related that some gireo number of nhrations iu the series a, 1! for example, may coincide iu dmation with one more, or one lesa, aa 13, inn; aJaolet the two aeriea be in opposite phases at the points \ and n, then after the pninosed nnmbera of vibrations have taken place, they will again be in opposite phaaea (369) at the same point, as at □. But at the poiut D, midway between a and a, one aeriea is half ■ vibra- tion ID advance of the other, and they will therefore be at that point, HI tAe tame phatt; consequently, if the two series be of equal intensity, they will neutralize each other at A and c, and grestly inteDsify each other at n (496), and a compound aeries of undulstioDS, B, periodically increasing and dimilliBhing in in- 302 . ACOUSTICS. tensity will result. For the sake of illastration, the vibrations are here supposed to be transverse (376) ; but it must be borne in mind that sonorous vibrations in the atmosphere are, for the most Eart, longitudinal (376). This result may be readily exhibited y opening at the same time any two ac^acent notes in the bass of the organ, when a curious pulsating sound will be heard, to which the term " heat '' has been appropriately applied. When the beats recur at sufficiently short mtervals to produce on the ear the impression of a continuous sound, as in f (Fig. 349), a new note is heard which is necessarily lower than either of those which conspire to produce it ; this is known as the Orave Har- monic. A curious experiment by Biot illustrates this point: — If an ob- stacle be so placed in the way of a vibrating string, that it shall be struck by the middle point of the string after each semi-vibra- tion, the note thus produced will be a fifth below the fundamental note of the string, whioh is the note that will result from its entire and uninterrupted vibration. 550. Another kind of pulsating or intermittent sonnd (not however to be confounded with the " beat " resulting from inter- ference) will be produced, if sonorous undulations be successively accelerated and retarded in batches : this may be effected by the apparatus of M. Mach, which consists of a hollow arm attached radially to a hollow rotating spindle, through which it can receive a constant current of air, to actuate a free reed (666) placed at its extremity. The rotating arm must be counteipoised. When this apparatus is rotated, if the ear be placed anywhere in the axis of rotation, a continuous note will be heard ; but if the ear be placed in the plane of rotation, the vibrations of the reed will be accelerated on its approaching, and retarded on its receding from the ear, and a Kyand of alternately higher and lower pitch will be perceived. 551. Flumographi.-^'ilLaiy varieties of compound, or resaltant, vibrations have been automaticallv delineated by means of an in- genious apparatus designed by MM. Scott and Koonig. This may be briefly aescribed as a larpe conical drum, one head being much smaller than the other, when two or more different sets of vibrations impinge on the larger drum-head, the resultant series is transmittea b^ the intervening air to the smaller, which actuates by mesns of a simple and appropriate mechanism, a tracing point that rests on the surface of a cylinder, so that the motion of the tracing-point may be parallel to the axis of the cylinder. The cylinder rotates hy clockwork, and is surrounded by paper, the surface of which is covered by finely levigated lamp-biacK. An extremely small amount of force is required to remove the lamp- black sufficiently to render the trace visible ; this is subsequently fixed by damping the- pnper, when a sufficient quantity of the lamp-black adheres to the size with which the paper has been COMPOUND ▲GOnsnC CUHVE8. 303 prepared ; the paper is Bubsequentlj vamigfaed, to preserve the Imce. As the direction of the continaous rotation of the cylinder is at right angles to that of the alternate motion of the tracer, when both motioDS coincide, an undulating line is traced on the paper, yerj similar to those represented in Fig. 349. The re- sultant vibrations arising from the consonance of notes at the various mnsical intervals are extremely interesting. 552. Another equally ingenious form of phonograph has been de- ▼ised by MM. Lissajous and Desains. In this the vibrations of one or more large diapasons are commnoicated to a lever carrying at its extremity a fine tracing-point, moving, as in the preceding, parallel to the axis of the rotating cylinder, similarly prepared. If two or more independent vibratory movements be simulta- neonsly communicated to the tracing-point during the rotation of the cylinder, it is evident that the resultant curve, representing the combined motions, will be traced out. Some very curious resnltant corves have also been traced in which the movements were at right angles to each other. A very copious and interest- ing series of tracings was exhibited by M. Koenig, at the Inter- national Exhibition of 1862: amongst these were the actual vibrations of the human tympanum (or drum of the ear), and even those of the membrane of the fenestra ovaUs were found to have been delineated. 553. Instruments have likewise been constructed for the optical . demonstration of these acoustic curves. For this purpose a small plane metallic speculum is attached to the end of one branch of each diapason, and a counterpoise to the other. A small bright pencil of light, as that transmitted through a small hole in a copper chimney covering a naphtha-lamp, failing on the speculum 18 reflected on to a screen; or still better, a small pencil of electric li^ht is employed. If the diapason be vertical, when made to vibrate, the spot of light on the screen becomes a short vertical line : when this is received on a mirror capable of rotating on a vertical axis, and thence thrown on to the screen, the rota- tion of the mirror will resolve the line into a horizontal series of imdnlations. If the pencil of light from the first diapason be received on the mirror of a second placed horizontally, and thence reflected, fall on the screen, when both are thrown into vibration, very beautiful and ever-changing resultant curves will be deli- neated. The simplest of these are produced when the two periods of vibratioTi are as 2 : 1 ; when either differs very slightly from this ratio, the series of curves represented in Fig. 256 will be Eiodnoed. When the ratio of vibrations is that of larger num- ers, as 2:8, 4:5, &c., more complicated figures wfll result. When the dissonance is a little greater than that just mentioned (which can be readily effected by a slight alteration of one of the weights appended to the diapasons) a very carious undulating dhange of the figures takes place. 304 ACOUSTICS. Various acoustic apparatus have been constructed, in which electro-maguets have been employed to actuate of control the vibrations of diapasons : but want of space forbids the detailed description of these and many other objects of great interest to the earnest investigator of physical truth. 554. The result of intenerence may be shown by vibrating a common tuning-fork or diapason, and ^'^' holding it over the mouth of a cylindrical vessel, a, Fig. 350, of a suitable length, that the air con- tained in it may assume synchronous vibrations, and produce the same note. Then hold a second similar cylinder in the direction of b, at nght angles to a, as shown in the figure, and immediately the musical tone previously heara will cease; withdraw b, the tone reappears ; replace it, and it again disap- pears, and so on. These curious phenomena arise from the mutual interference of the sonorous vibrations excited in the air contained in the two glass vessels. The following experiment by Prof. Wheatstone presents a re- markable example of interference. Let the handle of a vibrating tuning-fork, held obliquely, rest on the surface of a table : as long as it remains at rest, a loud resonance of the table is audible ; but if the tuning-fork be moved parallel to itself along the surface of the table, the resonance of the table immediately ceases, from the perpetual interference of the planes of vibration with each other* The instant the tuning-fork stops, the resonance bursts out again in a very striking manner. If the tuning-fork be held vertically, the planes of vibration coincide, and the resonance is not inter- rupted bv moving it. 555. Again, when a tuning-fork vibrates, its branches alter- nately recede from and approach each other, as shown ^.361. ]yy tijQ dotted lines in Fig. 351, both communicating their ms movements to the air, and producing a musical sound. \| // Let a fork, whilst vibrating, be held upright about a foot \ / from the ear, and slowly turned round. It will be found that when both branches are equidistant from the ear, or in the same direction from it, a distinct tone is heard, whilst in all intermediate positions scarcely any sound I can be detected. This is explained by the fact, that when J the branches coincide, or are equidistant from the ear, the A waves of sound combine their effects, whilst in all inter- H mediate positions, as they reach the ear in different phases, they interfere, and produce total or partial silence. A similar result of interference is obtained by attaching a tuning-fork to any rotating mandrel, so that the length of the fork IZA1CPLB8 OF IHTSRrERENCB. 305 may coincide with the axis of motion : if the fork he made to vibrate, no sound will be heard, so long as it continnes to rotate, bat will become andible the instant tbat the rotation ceases. This result is best shown b^ placing a reciprocating cavity, as ▲, Fig. 350, beneath the rotatmg tnning-fork. 556. The passage of sound through heterogeneous media com- posed of substances of different degrees of elasticity, is effected with difficulty ; for in passing from a less to a more elastic por- tion, sonorous waves of different intensities are excited, which, partly being reflected (464), and partly from mutual interference (466), become broken up, as it were, into numerous secondary vibrations ; and thus the sound, which eventually reaches the ear, will be not only of less intensity, but of a different quality from the true one. If some portion of a mixed medium be capable of conducting sound more rapidly than others, some vibrations will reach the ear before the others, and a confused false sound will alone be heard. We have an example of these facts in a glass vessel filled with carbonic acid ; this, when struck, instead of emitting the full tone proper to it, will merely produce an irregular flat sound : here the medium in which the vessel is immersed, the air, is of very different density and conducting power from that with which the glass is filled, and accordingly, vibrations of different intensities are excited, which, probably, by their interference deaden the proper tone of the giass yessel. Humboldt explains the fact of sounds being more readily audible at night than in the day, by the greater homogeneity of the atmosphere at that time : in the day- time its density is constantly changing by partial variations of temperature. 557. The comparatiye conducting power of different media for sound was well iuustrated by an experiment made by Biot. This philosopher fixed a bell at the end of a long iron tube ; on striking It, two consecutive sounds were heard by an observer at the oppo- site end, one conducted by the iron itself, the other by the air in its interior. The well-known double report of a fowling-piece, fired at a distance, probably arises from a similar cause, the sound of the explosion bemg condncted to the ear, unequally by the air, and the masses of vapour floating in it. iKmilarly, if the ear be placed near the surface of a rock which is beine blasted at a considerable distance, a distinct double re- port is heard, the first transmitted through the substance of the to^ the second, through the atmosphere. A curious phenomenon of this kind was once observed by the writer, at the Boyal Observatory. Greenwich, during the firine of the Tower guns, at a time when the atmosphere was loaded with a dense stratum of vapour. Each report was deadened, but preceded by four or five smaUer reports at equal intervals, and then a longer interval} thus : - - - - z 806 AcouanoB. 658. The BOond-wtTes in their traDemission throngh aiij me* diuiD, or from one medimn to another, will alwaja maintain the same direction : thoe if a thin disc of wood be fixed transrerBeljr at the end of a rod through which Tibrations are travelling loon- tudinally, the eonod transmitted throngh the air to the ear will be greatly augmented, because the Tibrations maintaining their direction become normal in the disc, and therefore act upon the air by a much extended moving Burface.* If one end of a vibrating rod be fixed perpendicularly in the Bide of a vessel in the form of a rectangular parallelopiped full of water, and the rod be made to vibrate first vertically, and then longitudinally, corresponding movements will be observed on the surface of the fluid in contact with the agitated side of the vessel ; and if a glass plate strewed with sand be freely suspended by threads in the water, the movemente of the particles will indi- cfkto vibrations in the fluid agreeing in direction with those of the rod. If a thin lamina of deal be placed horizontally between two parallel portions of the 'V* ^**« ^ same chord under equal tension, Fig. 852, and strewed with sand, the particles will indicate either normal or tan- gential vibrations in the lamina, according to the direction in which the chords have been excited by a viulin-bow. Again, if several small horizontal lamine of wood be separated, and also firmly connected, J^. 8«8. by small blocks of light / / vrood at their centres, and — — a vibrating chord be a^ tached to one of the series, Fig. 853, similar vibra- tions in all will be indi- cated by sand strewed on their surfaces. 559. In obedience to this law of continuity of direction in the propagation of sound, sonorous undulations must reach in their original directions the complex recipient and percipient structurea of the internal ear. Now it is a remarkable fact, that in all orders of the vertebrate kingdom one portion of these structures is met with in much the same perfection of development, even though other complex auditory structures, met witn in all the higher orders, are either wholly absent, or represented by less complex organs ; this is the system of semicircular canals, consisting of * Thia prindple hM been siiooenfblly applied by the preeeiit editor totba deteetion of nnaU Teaieal oaloali or fregmento, in ladiTlaiiftlB salTering front their presenoe \ eepedally wibeeqoent to the pnetioe of ttlhotiity. RBFLICTIOS OP 80UHD. 307 three curved tabes, more or leas exactly Bemicireiilar, Ijing tn- tHMriaUjf in three planes exactly perpendicular to each other, filled with a conttnuouB fluid, and opening into a common cavity ; the memfarane lining these tubes oeing freely supplied with branches of the auditory nerve. It scaroely admits of a doubt that when a •oond-wave is propagated in its original direction to these canals, each is influenoea by a portion of it resolved in the direction of its own plane, and the relative intensity of the resolved portions will depend on the direction of the undulation ; and thus oy means of the relative force of the impressions made on the nerves of the three canals, an impression of direction is instinctively conveyed to the sensorium, or common recipient of sensuous impressions. The mechanism of the auditory apparatus is most simple in those orders that are destitute of vocal organs, the fish-tnoe for example ; but for these a perception of the direction of impending danger is as important as for the higher orders, and hence the perfect development of their semicircular canals. 560. £e/e(ium of Sound. — Sonorous vibrations, on impinging Qpon a pliuie surface, are reflected from it in such a manner, that the angles of incidence and reflection are equal, in the same manner as in the case of the collision of an elastic body against a plane surfiice (296) : the velocity and intensity of the sound- con- tinuing the same aSfter as before reflection (see, also, 464). 561. When a sound is reflected, and reaches the ear altera certain interval, an echo is produced ; for this to be perfect, the observer must be at a certain distance from the reflecting sprface; and the syllable will be repeated once or several times, according to the number of reflecting surfaces presented by the body against which the sound impinges. The reflecting plane must be at a greater distance to affora polysyllabic echoes. ' At Woodstock is oue of this kind, repeating from seventeen to twenty syllables. A striking and beautiful effect of echo is producea in certain localities by the Swiss mountaineers, who contrive to sing their Banz des Yaches in such time, that the reflected notes form an agreeable accompaniment to the air itself. When sound is reflected between parallel planes, at a propei' distance from each other, multiplied echoes are produced, repeat- ingsyllables an almost indefinite number of times. The blow of a stick or hammer aeainst one side of a parallel fissure in a rock is sometimes found to produce the sound of a beU :* in this case the repetition of the first sound, by successive reflections, is sufficiently rapid to produce the impression of a con- tinuous and definite tone. It appears frx)m the exj^riments of M. Colladon, that if sonorous undulations excited within a fluid impinge very obliquely on its sur&oe, they do not emerge, but are tnterwiUy refUctedf as wiU sabseqnently appear to be the case with regard to fight. * The B«Opro«k a» Tnnlnndge WeUi le a weU>known example. Z 2 rti. IM. v/v -/V 1/ \il 1 ^ 1 1 &G3. Sound ia reflected by corred nufuMi in of aiif bard polinhed mb- ■tsDce, ind at r in tbe focoa (Ch. XIX.) of A, lei a low •oimd aa a whitper, be Qtterod. llie loiianHH vi- bntiniu that excited wUL in reaching a, be reBcclad n the direction of a nriea of liiiei parallel to thoae clrawc in (he Ggnm to n, from the concaira surface of which thej will coDvei]^ to & faeni at f', and be dii- tinctl? aodible lo an obeerrer ntuated there. IT a «klch bo plai^d at I, and the ear at r', the ticking will be distinctlj besnl, although inaudible at anj' other point id the Ticinitj of b. In a eimilar manner, any ■ound in an elliptic chamber, uttered in oob of tbe foci of the eUipie, will be audible to aa ebaerver plaenl in tbe other rocua, whilet penoni placed miilwa; will not be able to hear h (465). If the lubaUnce againet which the lound impingea be eoft and jieldiog, it will be much diminiehed in iutennly; tfaiu, wbilat Toicei are beard iu a remarkublj aoDorona muasr in loftj aptrt* menta with large polished walla, they almoat ceaae to be audibk in chambera bung with tapeatry, from the aouoroua ribratioaa becoming checked or abeorbed, on impinging againit thia aoft and jielding mWerial. 5«3. Rtfraciion of Sound.— \t will nbrnquenthr be abowo (Ch. XJX.) that when a ra^ of light reachra obliquely the oommcu aurftce of two media of different deumliei, it ii n^atMd at bent out of ita original course ; preciael; the aune efiect ii prodnced with regard to aonoraua undulationa, placed under aimilar ciRnmi- stanoei. Moreorer, the ratio of the ainea of the angtei of inci- dence and refraction ii found to be the aame ai that c^the Tcloci- tiea of aound in the respectife media, Theae (acta mar be readilr demonstrated li; means of the apparatua of H. HiTech. Thu Km uc conaista of a rectanaolar boi i » c. Fig, S55, "'' in which is encloaea a source of Bflund oif ani- I form pitch, conaiating of a diapason, or tnnii^- fork, Biruck at will bj a Bpring.hamoier, v\ front of this is a cyhndnul chunbcr dkfo, of which the external larfaoe, ef, is ■ •nr- tical plane oblique to ibe axis of tlie chamber, both ends of which are cloand by a thin mem- brane : it is rnmisbsd with two atopcocka fbr the admissioa and exit of any gaaeoua or other fluid, to be eiperimsnted on. A of Helmholta (539), in uniaou wiUi th< " •^ — ■^y' ■BFRACnOV OP 80UVD. M tacbed to an aim moving on an axia perpendicolar to the plane of the membnine, b f, ao as to move parallel to, and acitwa the centre of, iu sorface. The tube df, and resonator are enoioeed in a padded case, through a hole in the side of which the flexible tube passes, in order to isolate the refracted sound, and the resonator is moved by a handle projecting externally, by which its position is shown ; and it is thus moved from side to side, until the position is ascertained, in which the refracted sound is heard most distinctly. Let ab coincide with the axis of the chamber, and 6 e be the direction of the refracted undulations, then if the cbaoaber be filled with a gas denser than air, ( e will be deflected Uncardi the base of the prism, fo; but if with a gas of lest demdty, as hydrogen, the deflection will be in the contrary direo- tion, towards d e. 564. The Aooustie Lens of Shalf times its radius of curvature from the surface, and the ear be carried along the axis on the contrair side of the lens, some point will be found, at which the tick wiu be distinctlv audible ; but if the lens be re^ moved, not the faintest sound will be heard, until it is replaced. A much simpler form of apparatus may be extemporised, Fig. 356, which shows this experiment exceedingly well. This consbts Fig. 3S6. of one of the thin caoutchouc globes, used as children's toys, in* flated with carbonic acid. If the globe be inflated with hydrogen, no focus can be dift* covered ; in fact, it then becomes analogous to the concave lens in optics (Ch. XIX.), and the divergence of the incident rays is increased, instead of their converging to the ear. It most here be remarked that these facts present a forcible confirmation of the undulatory or dynamical theory of light and heat, to be hereafter investigated. 565. Injlexion of Sound, — Sounds excited in air are distinctly audible to persons cut off from rectilinear communication with the sonorons body by any obstacle, as a projecting wall, although with some diminution of intensity. This is precisely analogous to thd TMnlt obterred vhsii luidnlationa on the inrfaco of water en- ooiint«r Ui AMrturt (4ST), after psBsiag through which they •pread Utenll;. In wntar, however, M. CoIUdon foand that tfao piMenoe of a wtll or nick projecting between the eu- and the BOanding bod;, nearly rendered the sound inaudible, M thoogh * kind of " aeotulie thadou" bid been produced by the vaU. In thii case, owing to the phjsical properties nf the medium, niDch less lateral eiteniion M the nndalationi takes place. It will snbseqne at); appear (ChBp.XX.)_ thatintheTibralionsof the hypothetical medium, ether, producing the impreaaion of light, •nalogous plienomena of inflexion areobserred ; aa alsothose of in- terference (549—555), reflection (560, 1, 2), and refraction (663, 4). 566. The aama tone or note is always produced by the same number of vibrationa in a pven time, no matter what may be the means by which, or the medium in whioh, the Tibralinns may hare been Kenemled. The relatione between the tune and the nnmberof equalsuccesidve impulses producing it are well illuMrated by the BirenofCaiguanldeLatDnr, Fi^. 357. This Ifg.KT. inaCnunenC consists of a rotatiDg metallic plate. A, pierced obliquely in a concentric rin^ of equidistant holes, which stand over a circle of the same number of equidistant holes made obliqnely in th£ contrary direc- tion, through a plate in ibe base, B, reiy near to which the plate i rotalea. A cBvily beneath Ibis piste receives either air or ' ir under pressure, from h euitabie vessel which [he inetrommt ii inserted by the projecting piece, e. The spindle, c, on which is Gied, terminates above iu an endiesa ^rew (203). which may, by means of the ud, D, be (brown into or out nf gear with n wheel, on the axis of which the index, r, isplaced. Thiswhsel, ateachcompletc revolution, carries forwanl one tooth'of a second wheel, on the aiia of which the index a is plaoad. Bv means of these wheels, when in gear, the number of rotations of ^ may he counted. The apertures, a, in a, and b in B, being pierced obliquely thni— j« > the atteam of fluid iwaiug from the aperture b impinging on the side of a, will tend to pmdnce rotation in a, and a thas passing on, tho flow from b will be ■topped until the next apertare comes opposite to it, when another Ettle jet will issue fh>m a, and another rotator; impulse will be given. The apertures being equidistant, a constantly accelerated BDCoesfinn of impiiloes at ench coincidence of the apertures, and % aound rising gradually from a low drone to one of mtenae shriU- neia will be produced. If any given note is required to be main- tained for a ehort lime, for the purpose of counting the number of impulses producing it, the wheels most be put in gear, and tlw MUnOAL VOTM. 811 pmmiTe of the cnrrent of flaid regnlsted bj a stop-cock, so as just to overcome the resbtances of the apparatus itself, when the velo- city of rotation will remain constant. The number of rotations of the disc, multiplied hj the number of apertures, will give the number of impulses or vibrations in a given time, producing the note in question. The name of *' Siren was eiven to this instru- ment because it is capable of uttering melodious sounds either in air or in water ; bat^ except for the sake of demonstrating this fact, a current of air is always employed for purposes of expe- riment. Several modifications of this apparatus have been constructed : in the Siren of Seebeck a large aisc rotates by clockwork, in this are many series of concentric and equidistant apertures, correspond- ing numerically to the several notes of the gamut, also several double series, the numbers being in the ratio of the harmonious intervals. This is actuated by a current of air from a tube, or several tubes, placed in front of anv required series of holes. The Siren of Helmholtz is a reanplication of that of Gaignard de Latour ; there being two superposed, and the two discs at op> posite ends of the same axis. There are means of slowly rotating the upper chamber b, by means of which a beat (549) is produce^ the coincidences of the upper series of apertures being slightly decelerated or retarded, according to the direction of the slow rota- tion. There are also four series of apertures in each rotating disc in the numerical proportion of the notes of the common chord in music (574), namely, 4 : 5 : 6 : 8 ; to any or all of which the current of air may be admitted at will by means of stops. 567. Sounds of the same pUeh — that is, produced by the same number of ribrations in a given time — ^may differ materially in their character, so far as tiie timbre^ or quality of tone, is con- cerned. Quite independently of the number of ribrations producing them. Thus it is notorious that two players, on drawing the same bow across the same string, will produce tones of very different cha- racter, although of the same pitch. . It seem^ probable, from the researches of Dr. Young, that the timbre depends on the manner in which the string ribrates, and the curve which it describes. By reflecting a ray of light from the shining surface of a ribrating string. Dr. Young was enabled to observe some of these curves. Vide Fig. 257, p. 200. 568. When a sound is produced bv ribrations sufficiently re- Silar to constitute a musical tone (531 ;, it is termed a note; and to stinguish one note from another, a series of terms is applied to them. These, in this country, are taken from the alphabet, the first seven letters being used to designate particular notes. On the Continent, the seven syllables, tft, re, mi, /a, sol, la^ st, are usually preferred. These notes constitute what is termed, the DiaUmic scale, or gamut. A note is said to be sharper than another when it is produced by a larger number, and to be graver or flatter than another, when by a smaller number of vibrations 312 ▲C0DST1C8. in a given time. The gravest audible muneal sound is produced by about twenty, and the sharpest by about 12,000 vibrations in « second. This, however, is subject to great latitude, for, as Dr. Wollaston long since showed, many sounds at either extreme of the scale, utterly inaudible to some persons, are distinctly per- ceived by others. The chirp of the cricket, and also that of the grasshopper, are produced by such a rapid succession of vibrations, that to many persons they can scarcely be appreciated as musical sounds, and to some they are totally inaudible. A fine ear is able to recognise as a distinct sound, a peculiar hissing noise made by a body completing 24,000 distinct vibrations in a second. M. Savart has, bv means of a series of very interesting experiments, shown the high probability of there scarcelv being any definite limit to the audibility of sounds, provided tney are sufficiently loud. By means of a rapidly rotatory coeged wheel so arranged that each tooth should strike a piece of cara, or quill, he found that 12,000 strokes per second on the card produced a sound perfectly audible as a musical sound of high pi ten. 569. M. Biot * has calculated toe lengths of sonorous waves produced by different numbers of vibrations in a given time. The results of his observations are shown in the following table, in which the first column represents the number of vibrations in one second, and the second, the corresponding approximate length of the wave in French feet. These sounds are identical with those produced bv an organ-pipe open at bfith ends, and of the same length as that of the sonorous wave, given in this column. This is probably the utmost range of sounds audible by the human ear; it com- prises eleven octaves. It will be seen from this table that M. Biot assumes the velocity of sound to be 1024 French feet per second; a velocity less than that previously assumed (542). 570. An assemblage of eight consecutive notes is termed an octavO) 16 64 ft. 32 32 „ 64 16 „ 128 8„ 256 4„ 512 2 „ 1024 1 » 2048 6 in. 4096 8 „ 8192 14,1 12288 1 M 24576 in thus:— C D E F G A B C •^ m and one octave is said to be higher or lower than another, accord- ing as the notes it contains are produced by a greater or smaller number of vibrations in a given time. A note of any octave is produced by a certain number of vibra- tions, which are twice as numerous as in the corresponding note of the next lower, and are half as numerous as in the correspond- ing note of the next higher octave. * PrMB de Physique, i. 367. TABUTIORS OF PITCH. 813 The following table shows the Continental names of the notes, their English synonyms, the relative lengths of the wares, and numbera of vibrations producing them, expressed in fractions and Continental BngUik Lengtiuof Nomben of Yibrations namea. nMnes. WATflS. Tibntiont. in a second. ut C 1 or 180 lor 24 261 re D t„ 160 1 „ 27 294 mi £ i u 144 t„ 30 ' 326 fa F i » 135 *» 32 348 sol G i « 120 i» 36 391 la A *,, 108 J„ 40 435 • 81 B Ai, »6 Vn 45 489 Ut Ci i„ 90 2 „ 48 522 in the lowest integers, as well as the relative numbers of vibrations in a second, taking the French btandard, 435, as concert-pitch. The octave is that which occupies the lower lines of the treble in ordinary music, and is represented above. 571. In the various cities and countries of Europe, in which music has been much cultivated, and even in the same locality at diflfereot epochs, there has been, and is, a considerable difference in the pitch, or diapason, as it is frequently called, that is, in the oomber of vibrations per second that constitute some given note, as, for example, the A or 2a on the second space of the treble. The assumed tone or note in any particular locality is there called the concert-pitch. The following tables (from the report of the French commission, appointed in 1858 to aetermine and establish in France a uniform diapason) show the numerical relation of the diapasons in various places in Europe, and thoir differences from the then existing concert-pitch in Paris : and the variations in Paris, Berlin, and St. Petersburg, at different epochs, according to the most trustworthy observers. looattty. Vibrs. Di&. Locality. Vibw. Dxflb. Brussels . . London, c* . 455-5 455-2 452-5 4520 451-8 451-5 449-7 4481 448-0 + 7-5 + 7-2 + 4-5 + 40 + 3-8 + 3-5 + 1-7 + 0-1 Marseilles Pesth . . . Turin . . . Brunswick . Stuttgardt . Toulouse, of . h . Carlsruhe . . London, a 447-0 446-0 444-8 443-5 4430 442-5 437 0 435-0 434-0 - 10 — 2-0 — 3-2 - 4-6 — 50 - 5-5 -110 -130 -140 Lille '. '. . Berlin , . . St. Petersburg Prague . . . Munich . . Paris . . . ^ -^ . _ ■ I _L * ▲ u Meeers. Broadwood's pitoh« considered as beet suited to the Toioej 1, tbeir eoocert-pitch ; and c, Uke Philharmonic concert-pitch, t a n the pitoh at the Theatre, and 6, at the Conservatoire. 814 JkOOUSTlOS. Obterven. Bate. Tibn. ObMrren. ' Date. Vibn. PIXIS. Sauveur . . 1700 1713 1810 1823 1830 1839 1858 404-0 406-8 423*0 431-3 435*7 4410 448*0 BEBLIN. Marbure . . Nieprecnt . . • • 1762 1806 1830 1868 1796: 1858 421-8 430*5 440-0 451-8 436-0 4515 Drouet . . FiBcher . . Drouet . . . Delazenne Lissajous . . ST. PETKKflBURQ. Sarti . • . Lissajoua . . 572. In consequence of the practical ioconyeniences to ma- Bicians that arise from this eztensiye diveraity of diapaw^ns, and especially to vocalists, from the high pitch recently adopted in many places, the commission recommended that the number 4S5 be adopted in France as that of the normal diapaaoUf and this recommendation has since been carried into effect by the French government. It is much to be desired that other European nations should adopt the same uniform diapason. It may here be remarked that the meaning of the term " vibra- tion ** is different in France from what it is in this country and in Germany. What has been previously (369) represented as^ one complete vibration or undulation, the French consider to consist of two vibrations: French acoustic numbers must therefore be di- vided by two, to reduce them to English or German measure, and vice versA. 573. The Tonometer ofSeheibler. — ^This apparatus is extremely useful in precise determinations of the pitcn of musical sounds. It consists of a series of 65 diapasons arranged in rows, from C to C^ each of which differs from the preceding by four vibrations ; A practised ear will not only assign to any given note its place between two consecutive diapasons, but also give by estimation a near approach to its position in the interval : and thus the num- ber of vibrations in the note in question may be inferred : this number may also be accurately determined by the frequency of the recurrence of beats, each of which shows a difference of one vibration. 574. The perception of a simple^ musical tone has been aptly compared by Euler* to the visual impression of a series of dots equidistant nom each other, thus, If the intervals between these dots be greater or smaller, tlie tone produced will be lower or higher (568). It can scarcely be doubted that the perception of a smgle tone by the ear is analo- Sous to the appreciation by vision of such a set of equidistant ots ; thos enabling us to represent to the eye, in a certain degree, what the ear perceives on hearing sound. If the distances between the dots be not equal, or if they be irregularly scattered, thej * Letters to a Gennaa Prinoste, voL L let. 4» HUMEBIOAL KATI08 OP YIBIUTIOHB. 815 vonld represent a confoned noiBe, inconsistent with harmony. When two tones, each produced by the same number of yibrationsi strike the ear simultaneously, they appear to blend, forming a tmiaon; which may be represented by two lines of equidistant dots, thus, ::::::::: When the di£ferenoe between the number of yibrations pro* dndng any two notes is in a simple ratio, so that the ear readily diacoTers the relation existing between them, a concord is pro- duced. Bnt i^ from the absence of this simple ratio, this relation cannot be detected, a ditcord is said to result. The following are some of the most important concords. I. The octave represented by 2, because the higher note is gene- rated b^ twice as many vibrations as the graver one, corresponding to the interval of the two Cs or ut% : this concord is termed an octave, because in the musical succession of notes (570)^ C, is the eighth note from G, and the vibrations of C and C, are in tne pro- portion of 1 : 2. II. The>Sfroduc6 a certain number of vibrations ; with a tension of four, it will pro- duce twice as many ; and with one of nine, three times as many, in the same snace of time. This may be shown by an apparatus, Fig. 360, similar to the preceding, except that the chord, after passing round the pulley at B, is attached ^^ ^.880. to a block containing ^^^ two sheaves (1S4); there is also a pulley running on a pin at the end a. Another piece of the same chord attached to the fixed stud at a passes suc- cessively over one of the sheaves at n, the fixed pulley at a, the other sheaf at n, and the adjusting pin at a. It is manifest from the constniction that the tensions of the two portions of the chord will be always as 4 : 1. By the bridges c, d, e, any lengths may be intercepted ; and it will be found that the length of that portion of the ^hord, which is under quadruple tension, must be just half the corresponding length of the other portion, in order to produce the same note. •It may here be remarked, that an analytical investigation of the motion of a vibrating chord firat gave rise to the solution of a partial differential equation ; from which it appears, that if a chord, of which the length is l, the semidiameter or radius, r, and the density, <2, be stretched by a weight w, the time of an oscillation, .v^= and if K be the nnnberof *il>i*tianain* gireD time, tlMU titm which cxprtMon the Uwt a, a, c^ d maj be immertiately deJDced. If tbe weight wconiut or> Iflogth lofthe Btme chord, then •nd mbatitDtiiig this valiw in (a), we obtaio . .'-^'■^' .. which is the fbrm in which the reiult was orieintllj obtuned. llie troth dF this rorninU was tested by ^Veber, b? meiJia of a cotton thread 51 feet 2 inchrs long, whicli weighed 864 graio* : the fDllowiug timei of vibration were detenained both b; olcnl*- tion, and by acconle obsemtion : — ObKrred time . . 46-00" I CaknUted time . 46011"' „ „ . . 84-72 , a5S4« „ . . 16-25 I „ „ . . 17-48S It maj likewise b« demonstrated that the intenntT of a toand is proporlioDal to the square of the amplitode of the Titiration proouciDg it; thns, if a chord prodnce ■ certain sound with a Kiren bmadth of eicnrsioo, when the excaroras are twica as broad, tbe sound will be four times louder than it was before. 5TT. M. iUelde baa isgeiuausly illustrated the laws of Tibratine chords, by producing inaudible but virible vibrations of considerab^ amplltnda. For this puipose a chord is attached to one eitremitT td a fixed diapaaon cl laif^ size, a. Fig. 361, and paadng hori- K».sm. ^.Honne. B19 ■ootelly over » pnllcT. a, in ilrctcbed br & veight pUceil id th« Kale, c, ftttacbM to tbe end of the cbora. The fivme fapporting the palle; B mny be placed at tnj required disUnce fnnn a. Ths ribrktioDB of toe cliapaMti are exdtea bj drawing a baat-viol-bov aetiiee tbe side of ihe bnQcbet, in th$ direction of the choni If, for example, it be deaired to d(iiTHiiiBtrat« the lav, D |A76), let a thin chord, aa a. piece of ailk, be atretched bj a suitable weight, and let the diitance of tbe eiippart, b, be >o adjusted, that the chord will vibnte io ita entire length, aa a,b; then let (he etretch- ing' weight be redaced to one-fbnrtb, when it will be found that tbe choni will nbrate with one no-le at ita middle point, e : or (he pnltej, b, mnat be made to coincide with the point, c, in order that the inlerrening chord mar vi bra(e in ita entire length. If the wpjght be redooed to one-ninth, the chord will tibrate with 3 nodal points, and w on. In thii eiperiment it ia desirable to oonnleipoise Uie acale by a imall weight attached to a thread paaeing over the pulley. In order to demOBitrate the law, B, let the diatsnca, a B, Elg. 362, be ascertaiDed at which the cboid will reciprocate; then attach to B a qnadmple piece of the ume choni, iatretched by the aame weight, and let the pnlleybe placed al c, Bc being one half of A B ; it will now be (bund that the coropoand chord will vibrate with one nodal point, not however in its middle hnt at b ; thiu ptOTing that AS and bc vibrate synch rononaly. If the added diord, B F, he double instead of qnadrnple, then tbe length of e r most be equal to the side ofaaqoBre of which D B is the diagonal, and the node will now be found at K. The law, A, may be readily domonstrated by employing two diapeaons, one of which is an octave abore the other, end there- lore vibrates in half tbe lime. If the chord when attached to the lower, vibrates in its whole length, then when it in nttaohed to the higher, with the same tension, it will vibrate in half the length, with a node at e. Fig. 361. When the chord is placed in the plane of vibration of the dia- paaon, »■ in Pig. 361, one vibration of the chord carreapoiids in time with two of the diapason. For suppoee the diapason to he excited by withdrawing some bard anhstance, as a piece of wood, (a little thicker than the interval,) from between its branches ; before its removal, the branch » will have been presBed towards b, andtlnu relaxed the chord towards b. The first movement of the 820 ACOUBTIGS. brancb, a, will pull the chord up to the straight line between a and B, and the acquired energy of its particles will canj them op towards a, daring the return towards b, or second semi-vibration, of A. The second negative motion of a (from right tolefl, vide note^ p. 45) will again pull the chord straight, and the energy of its particles will carry them down towai^s b, during the second poixitiye motion of a, when one oscillation of tlie chord will have been completed. This may be proved by turning the diapason round through 90", so as to bring the chord perpendicular to the plane of vibration of the diapason : it will now reciprocate with a nodo at its middle point, or its length must be reduced by one half; one vibration of the chord now corresponding with each one of the diapason. To the double ratio of vibrations here described there is some analogy in the reduplication of motion by link-work (264). Illustrations of these interesting physical laws might be almost indefinitely multiplied, but enough nave been detailed to complete their practical demonstration. 578. The Vibratians of Bods, — These may be either transverse, or longitudinal ; and the rods may be either fixed, or merely restiup, or free, at one or both ends : their motions have been investigated by Chladni, but the analysis is difficult, and the results not altogether satisfactory. When rods of any elastic material fixed at one end (370), are made to vibrate, they produce sonorous vibrations varying in number in the inverse ratio of the sqnares of their lengths, and in the direct ratio of their diameters. These rods, like strings, may vibrate entire, or in nodal subdivisions. Another particular case affords a curious result : when a rod, resting at both ends, is made to vibrate in two or more nodal sub- divisions, the number of vibrations in a given time will bo as the sqpaare of the number of subdivisions ; that is, when vibrating in two or three parts, the number of vibrations will be four or nine times those of the entire rod. This result shows the fallacy of assuming any ^'^' ^ d»nV>ri foundation 01 the elementary principles of har- mony trom the laws of governing the vibrations of a chord. Fig. 363 repre- sents convement forms of apparatus for exhibiting the effects of vibrating rods, either resting at one or both ends,^ or clamped at any nodal points. The standards, A, b, o, are ac(ju8- tible, and fixed by a wedge, passing through a mortice. In the A ▼IBKATX0H8 OF TUBES. 821 standards b, c, the rod is clamped by a wedge in the angle of a triangular aperture. A musical instrument has been oonBtmcted of a series of thin wooden rods fixed vertically into a base, and of such lengths that their longitudinal vibrations produce the series of musical notes. They are excited by drawing them through the fingers previously rubbed with powdered resin. Beyond being a Scientific curiosity, the instrument is of no practical value. 579. When sonorous vibrations are excited by blowing into tubes, the higher notes are, ccgteris paribttSf produced by the shorter tabes. Sounds thus excited are produced by the alter- nate condensations and expansions of the successive layers of the column of air contained in the tube.^ The following are some of the more important facts connected with the relation between the sound evolved, the length, and the open or closed state of the ex- tremities of the tubes employed. A. In parallel sided tubes, dosed or open alxke^ the number of vi- brations IS, as in chords, in the inverse ratio of the length of the tube. B. In a cylindrical or prismatic tube, onea at both ende^ the sound is the same as that produced by a cylindrical tube closed at one end, and one half its length. C. In a cylindrical or prismatic tube, closed at hoik ends, the sound is the same as in a tube open at both ends. D. Nodes, or points at rest, in the included column of air, are observed in the case of the vibrations of tubes as in vibrating chords (373), or rods (375). 580. In the simplest mode of vibration of a tube open at both ends, there is a node in the middle point of the length of the tube, to and from which the equidistant layers of air in the ends of the tube approach and recede simultaneously. This may be demonstrated by an apparatus ^* ***• due to rrof. Wheatstone, consisting of an annular tube mounted on a stand, the two halves of which are jointed together at A. If the comer of a square vibrating^ plate of glass, to which the column of air m the tube is capable of reciprocating (540), be placed between the open ends of the tube (which are separated by an interval of half an inch) no resonance is produced, the im- pulses being in the same direction at both ends of the tube, and thus mutually destroy- ^ ing each other. If, now, the moutns of the tube be separated from each other by a distance equal to the side of the glass plate, and the plate he made to vibrate in its first mode (a. Fig. 367), if the adjacent comers (which are always in opposite phases of^ vibration) be placed over the months of the tttbe^ the impulses being now in contrary directions at the ends^ Y oFthe tabs, reKt on ewh other ti the noda in the middle, uid a loud resonance immedist«lf reinlti. If a tube be stoppad at botb endi, the oitremitieB are DOdal points, and the greatest Tibratoir motioa ii in the centre, like the vibrating Wring, Fig. 263. If the length of the slopped tobe be the ume as that of a tube open at both endi, the length of the wave is evidentlj the etuae, but ita holTei are joined together in a reTersedpoeition . 681. Ine conditioas of Tibrations of the air in tabee hare been ingeniously demonatrsted by anparatne deeigned by M. R. Kcenip.* One of these conaiatB of a wooden oi^n pipe, A c. Fig. 36&, banag apertores at one aide, at the half and quertera of its length. These apertures are covered by tbin latnime of coontchonc, over which are placed saucer-shaped Hj. 3M. metallic chambers, a, b, c. Each of these chambers is supplied vitb gaa from a common aonrce, and has a email tube proceeding front the centre, carrying a burner with avety noBll nperture. This, being a pipe open at bnth ends, will, when sound- ing its lowest note, have a node at its centre b, whero eonseqnenlly iuc- cessive condensation b aiid rarefac- tions will take place. If the jets be lighted, the pressure of gas in the cbsmbers being redaced to a loir point by a stop-cock, directly the pipe is sounded, Ihe jot at a will be extinguished, and a slight tremulous movement will be perceived at a and a. This happsDS in oonsequence of the diminished internal preseore on the mem- brane at B, during the phaae of rarebction ; atmoepberic preaaare on the orifice of the jet then stopping the escape of gas. The changes of pressure at a and c l^ing veiy much less than at B, are insufficient to canse the extinction of those jets, and merelj ^e slight tremor ia perceived. If bj a greater pressure on the bellows, the pipe is made to speak the ocCace above its ftmda- mental note, the wave-length will be reduced one half, and there will be two nodes at a and c, the lamina of air beneaUi B having now only a backward and forward motion, withont any change of density ; consequently the jets at a and c will now b« extin- gnishsd, and that at b wilt remain motiooteas. The other spparitna consists of two pipes having similarljr arranged ga»-jets at their middle points, d, b, only. The jets F, a, are furnished with longer tubes, so that they may be placed one under the other, and in front of a mirror capable Ol revolving on its veiiica] stem, H. For the purpose of vatying the expen- *SMnts these pipes are closed at the lop, and have lateral oriBoBs, * Foffgendo ff, Annai^B, eixU. VIBRATIOXB OF PLATES. 323 capable of being more or less closed bj sliding doors k, l, by wbich the pitch of each may be regulated. When these pipes are in exact unison, it will be found (contrary to what might nave been anticipated) that when both are made to speak, the sound pro- duced is much less loud than when either is made to speak alone. The reason of this apparent paradox is, that the columns of air are always simultaneously in opposite phases of vibration in the two pipes ; (hat being the mode of vibration in which the pressure of the air in the neighbourhood of the two embouchures is ren- dered most uniform. This fact may be readily proved by lighting the two jets, and leaving the flames a little too large for extinc- tion, when the pipes speak. A considerable fluttering of both flames will now oe perceived, and if the mirror be now made to rotate on its axis, h, the images of the two flames will be resolved into serrated lines of light, in which the phases of eleva tion of one will correspond vertically with the phases of depression of the other ; thus proving that the phase of condensation at the middle of either pipe is 8>*nchronous with the phase of rarefaction in the other. By varying the pitch of either pipe, so as to pro- duce a beat, also by employing two pipes, having intervals of a third, fourth, fifth, or octave, and further by making the tubes from D and e to unite in feeding one jet, a number of curious and interesting results may be obtained, for which the reader must be referred to the original memoir. 582. The vibrations of the column of air in tubes may be ex- cited in various different ways, and the quality of the tone will depend partly on the material of which the pipe is composed, and partly on the mode of excitation. 1. By blowing obliquely into the open end of the tuBe, as in the Pandean pipe. 2. By directing a current of air into an embouchure, or aperture, at or near the closed end, as in the flute, and in organ-pipes not fumished with reeds. 3. By a small flame of hydrogen gas. 4. By the vibration of the lips placed against a small cup-shaped cavity, at the smaller end of an open conical tube, as in all kinds of horns and trumpets. 5. By thin vibrating laminae of wood or metal, called reeds : these are of two kinds, one of which covers a small aperture like a valve, and vibrates against the edges of it, the others vibrate in an aperture which they nearly fill, but do not touch ; the latter are called fre^ reeds. Tne brass reeds of all varieties of reed organ- S'pes, and the wooden reeds of the clarionet and hautboy, are of e former class, while those of all kinds of harmoniums, concer- tinas, and accordions belong to the latter. 683. VUbratums of Plates. — ^Vibrations are readily excited in elastic plates by friction, or by striking them, and sounds are eyolved ; the plates dividing themselves into vibrating portions, separated by nodal points of rest, arranged in lines. The position y 2 324 ACOUSTICS. of these lines of rest is beautifully shown b^ scattering sand on the plates, and vibrating them ; the sand will assume a carious rapid movement, and be thrown off the vibrating portions, upon the nodai lines^ or lines of rest. If a square or rectang^ar plate _ of glass be grasped in the cen- ^. 8M. ^^ ^j^. ^ gjjj^jj hand-vice, Fig. 366, sand scattered over its surface, and the bow of a violin drawn rapidly across its edge close to one of its angles, the sand will be thrown into the position shown in a, Fig. 367. If the bow be applied to the middle of 1^.867. KO one of the sides, the sand will be arranged as in b. If the plate be held near one of its angles, and the bow applied as before, the sand will be arranged as in c. Prof. Wheatstone, in a paper on this subject, published in the Fhilos3phical Transactions, has calculated a large number of these acoustical figures, by the principle of the super-position of small motions (541), a great many of which have oeen obtained experimentally by himself and others. 684. From a series of highly interesting experiments* on this subject by Faraday, it appears evident that while the accumu- lation of sand or any other coarse and heavy powder, on the nodal lines arises from its being, as it were, jerked off from the vibrating portions, the vibrations excite currenta of air over the agitated portions, which entangle any light powder scattered on the plate : if it be a very light one, as lyeopodium, it will be caught up by the aerial currents, and will collect chiefiy on the most agitated portions of the plate, instead of on the quiescent portions, and appear animated with a curious vortex-tike motion. If the plate be vibrated in highly rarefied air, the lycopodium will lie collected on the nodal lines, like the sand when vibrated in ordinary states of atmo- spheric pressure ; and if the plate be covered with sand, and made to vibrate in a much denser medium, as water, the sand wiU be under the PhiL Tnuw. 1831. Fig, 968, ftr-«-=<^W VIBRATIOHS OF MBlfBBANES. 326 same conditions, reladvelj to the medium, as the iycopodium in air, and will be collected chieflj on the most agitated portions of the plate. Thus, the lines a, b, Fig. 368, represent the position of the sand when the plate is yibrated in air, and of the lycopodium, when in vacuo ; and the triangles, c, e, d, f, the parts or inter- nodal spaces where the sand is collected when the plate is vibrated in water, and the lyoopodium, when in air. 585. The vibrations of a membrane may be well exhibited by stretching a piece of bladder over the mouth of a funnel, and passing a horse-hair, retained by a knot, through its centre; by drawinff the hair through the fingers, previously nibbed over with resin, the membrane whI be made to vibrate, and if sand or lyoo- podium be scattered on its surface, a symmetrical arrangement of the heavy particles at the nodal lines, as well as the accumula- tion of the light particles at the centres of vibration may be observed. If a thin membrane be stretched on a triangular, square, or circular wooden frame, and strewed with sand, its vibrations will be readily excited by holding a tuning-fork, bell, or other vibrating body near it, and they will be indicated by the motion of the particles of sand. French tracing-paper, or still better, thin parchment-paper (prepared by immersion in strong sulphuric acid), damped a little, and attached by paste to the edges of the frame, will answer very well for these experi- .. „^ d86. A very delicate mode of detecting acous- tic vibration lias been described by Strehlke : * be scatters some lycopodium on water, so as to cover its surface with the thinnest possible layer, which is best effected by agitating the fluid in a box, the inside of which has^ been mbbed over with the powder. On placing a drop of this on a vibrating plate, the particles of lycopodium begin to revolve in the water, dividing into two or more currents, if the sono- rous vibrations be intense, as shown at A b, Fig. O- 369. If a drop be placed on each side of a nodal line, or line of rest (583), c d, these intes- tine motions occur, but in opposite directions. 587. The evolution of musical sounds during the cooling of heated metals, observed by Mr. Trevelyan and others, is extremely curious. These phenomena are best observed by using the th&rmo' phone. This consists of a bar of copper five inches long, and about naif an inch thick, grooved in such a manner that its transverse section resembles c. Fig. 370. A piece of thick iron wire, about eight inches long, is fixed in one end for a handle. On heating the copper bar, and resting its convex surface on the edge of * Poggendorff, Aanalen, xl. p. 146. 326 ACOUSTICS. a block of lead, as at b, it will begin to vibrate strongly, and soon afterwards evolve musical sounds, usuallv be^nning like the drone of the bagpipes, and rising to a loud plaintive swell, like that of the ^olian narp, and then falling in the most fitful manner. These wild and irregular "*^»870. sounds continue until the y— ^. — ^^ temperature of the block of ( ] C lead and copper-bar are nearly Ly^VJ eoualized. They are evolved with the greatest shrillness when a small channel is filed out in the back of the bar, as shown in c, or a similar chan- nel excavated in the surface of the leaden block on which it rests. It is necessary that the surfaces of the metals employed should be quite clean ; and that their powers of conducting heat should be as different as possible ; hence, copper and lead succeed the best, as the conducting power of the former for heat, according to Despretz, is 398, and that of the latter 179-6. PRODUCnON OF VOCAL BOUNDS. 588. The sounds emitted by the lower orders of the animal kingdom are not strictly vogoL : the hum of insects, and of the humming-bird arises from the successive impulses of the wings on the atmoRphere being sufficiently rspid to produce the impression of a continuous tone ; the hiss of tne serpent is but the sudden expulsion of air from the sacculated lungs through a narrow fissure ; and the acute chirp of the cricket and grasshopper is produced by the friction of the legs against the rough integument, just as an elevated tone is produced by passing a stick rapidly idong a row of railins^s. True vocal sounds are produced only By mammals and biras ; the vocal organ being at the upper end of the wind- pipe in the former, and at the lower end in the latter order. The vocal organs are most fully developed in the higher classes of mammals, in which the essential part of the organ couHists of two parallel folds of elastic mucous membrane, with a highly elastic chorQ extending through, and supporting, their free mar- p;ins. These parts, called the vocal chords, when suitably placed in apposition and stretched by the muscular apparatus of the larynXf emit a sound when air is driven between them by an eflbrt of expiration. * This may be readily demonstrated by at> taching the iresh larynx with a portion of the windpipe of an ox or sheep to a small pair of organ-oellows, when, by a little easy manipulation, the peculiar intonation of the animal may be readily produced. The mode in which vibration arises will be best understood bv a reference to the diagram, Fig. 371, in which a is a narrow slit PBODUCnOK OF VOCAL 80UND8. 327 in the wind-cbest of the or^an bellows, and b, c, two small wooden frames comprising three sides of a rectangle, to which pieces of yerj thin leather are attached. When these frames are placed m a converging position, as at a, resting on the sides of the slit, the issuing current of air will cause «. j... the free edges of the membrane to *^' ' become convex outwards, as at b, c ; but if they be placed in a divergent position, as at d, the issuing cur- rent of air acts as in a divergent tube (435), and ^Bspecially if the roace between me ends of the frames be closed by the finder and thumb) the membranes will become convex inward». If, now, the firames be placed in a nearly parallel position, the free maigina will have an equal tendency to become convex, or con- caye towards each other, and will consequently assume both posi- tions alternately, and be thrown into yibration. The actual conditions of yibration of the vocal chords may be more aptly illustrated by the following simple apparatus. Let ▲ B c be a small transversely-oval piece of wood, coming up to a thin narrow ed^ at c, having an aperture through it, and a tubular stem for insertion into an aperture in the wind-chest.* A thin bit of leather is bound on to this at ab; having two free margins at c d ; and two small pieces of cork are attached to the corners at d, for the pur- pose of regulating, by the fin^r and thumb of each Sand, the position and tension of these artificial vocal chords, which may be readily made to emit a sound when placed in a parallel position, and a current of air forced between tbem : and the pitch of the sound will be found to be regulated by the tension. If the upper edges of the bits of cork at d be turned outwaros, so as to separate the edaee of the membranes, no sound is produced when lower parts of their surface are brought into apposition ; it is thus that the actual glottis is closed whenever the production of sound is not in- tended. This and many other interesting phenomena relating to vocalisation may be readily studied by inspection, bv means of the laryngoscope, an instrument for the ocular examination of the lanmx, by means of reflected light. J n the production of the notes of the human voice, the length of the reciprocating tubular cavity, that surmounts the larynx, constitutes an element : and it may be readily observed that the larynx is raised when high, and depressed when low notes are produced. In singing, two distinct qualities of tone are recog- * A very oonvenienfe form of bellowt for tbit and other aoonrtical ozperi* ziMiits may be obtained firom Menrs. Elliott, Stnmd, London. 1»V. 372. ■»•_ V 828 Acousncs. niaed — the {oil, or chest-voice, and the faUetto^ or head-Toice : and mftny sineers can produce some notes in either quality of tone. The differeqce of these is, that in the chest-yoice the vocal chords are thrown into vihration, while in the head-voice vibra- tions are excited only in the reciprocating cavity, as in organ- pipes having an embonchare. 689. Vowel-Sounds. — Professor WilHs has shown, in a paper published in the Cambridge Philosophical Transactions, that vowel-sounds may be produced either by partially closing a conical cavity, excited bv a reed placed at its apex, or by a column of air in a tube excited by a reed at its closed end, the particular vowel- sound depending on the length of the tube. As tne reciprocating cavity is flpradually lengthened, the vowel sounds may do recog- nised in tne following order: — 55 (n), 6, l^ e, i. As the pipe is further lengthened, a point is reached at which the discord be- tween the notes of the reed and pipe is such that, neither being able to coerce the vibrations of the other, no definite tone, bnt only a harsh grating sound is produced. After a little further elongation, the same series of sounds is reproduced in an inverted order, bnt with somewhat less distinctness; and still further elongation will reproduce the first series of vowel sounds. In human articulation, the vowel-sound depends on the form and configuration of the oral cavity. It has been advanced by Helmholtz that the production of a vowel-sound depends on the superposition of some high harmonic on the fundamental sound. 590. The last-mentioned phenomena are illustrations of the theory of forced vibrations ; which assumes that, if$uffieient time has eiapiedfrom the commeneemerU of motion to oUow the iniHal periodic disturbances to have been destroyed byfriction, imp&rfect eUasticity^ and other causes^ the resultant motion^ if any^ wiu be vibratory and isochronous. This theory is applicaUe to luminous as well as to sonorous vibrations : it is likewise the foundation of Laplace's theory of the tides (503). Refebbncbs. To no single work on the subject of acoustics can the student refer with so much advantage, as to Sir John HerschePs mono- graph on Sound, in the Encyclopaedia Metropolitana, which embraces all the leading points of this subject. The writings of Young, Chladni, Savart, Weber, Seebeck, Helmholtz, Koenig, Lissajous, and others will also supply much valuable information. The subject is more geometrically treated by Newton, in the Principia, torn. ii. § 8. 829 CHAPTER XI. XAGNETISM. 591. The property of attracting pieces of iron, possessed by certain ferraginons ores, has been long known ; and the ores them- selves have been termed moffneta, from Magnesia, a town of Lvdia, near which they were stated by the ancients to abomid. Pliny states that these ores were in his time termed ferrum vivunif or quick-iron. In England the term loadstone has long been ap- Eiied to the magnetic oxide of iron. All the phenomena exhibited J such magnets, including their action on iron, cobalt, and nickel, and other metals which appear to obey their attractive influence, have been collated, and the important science of Magnetism foanded upon them. Not only do ores of iron possess magnetic properties, bat masses of that metal which have been placed in contact with them, or have been submitted to the effects of certain mechanical actions, generaUy present the phenomena of magnetism. The magnetic ores constituting what are termed natural — and the latter, arti- ficial magnets : but the phenomena presented by both kinds are of precisely the same nature. Nor must the great natural magnet, the mass of the earth, be overlooked, which has been shown to act on the magnetic needle precisely in the same manner as a com- pound artificial magnet would do, composed of two bars placed at an angle with each other, and suitably arranged as to magnitude, position, and distance. The investigation of the magnetic pheno- mena manifested by the earth, their magnitude, direction, and changes, constitutes the object of the science of terrestrial mag- netism. Magnetism will subsequently be shown to be inseparably con- nected with other forms or phases of potential energy, viz., elec- tricity, light, and heat; it must therefore be a cosmical, and not merely a terrestrial pr(»perty of matter : and this view is strongly confirmed by the recent researches of General Sabine, for it wiU appear in the sequel of this chapter, that certain periodic changes in terrestrial magnetism may be respectively identified with cor- responding periodic cotimical phenomena. Li the examination of magnetic phenomena, magnetized bars of steel are ^nerally employed: if straight, they are called bar- magnets; if smafi and tapered towards the points, magnetic needles ; and if bent into the shape of a letter U, horse-shoe magnets. 592. If a magnet be dipped m iron filings, it will attract them, caiuing them to ftilliere to its snriaoe, but nnrqnall]' in different parta; being collected in sbonduice at the ends, and nearljr abiient from the intermediate portiona. This is beHt seeo by placing & aheet of cardboard over "!'■ "■ tbe two polea of a horae-aboo magnot, FiE, ZT6, scattering; iron fllJD^ on its suriiLce, and then ' ta^piBg the paatebnard lijihtlj , witn the nail : the iilingB will ar- ' range themnetres in linea diverg- ^ ing from the poles of the m^net J in cnr»es, whilst the outline of ' both ends, n, i, of the bar will bo well defined by the iron filings, as ahonn in the fignre. K the card- board be now laid on the aide of the magnet, the direction of the magnetic curves, in a plane perpondicular to the fomer, latj be observed. The eilremitiea of the magnet, in which the nMgnetio action appeara thna to be concentrated, are tensed polf. The grenteat inlenmtj of action ia not found to be eiacttf at the ends of the magnet, but at pointa a little dialant from them, represent- ing centrea Iram which the magnetic force appeara to radiate. The ourrea formed hj the iron filing* may be conveniently re- garded aa pointing out the existence of mmnetic Una o/Jbree, Bod the apace, a, between the two polea has been termed tbe nag- nelicjield, or space where the two polar foreea mutually react. The inHuence of the lines of force traTeraing the magnetic Geld on certain Iradies, will preaentlj fall onder our notioe. 693. Let ■ magnetic bar be sospended by a thread attached to ita centre, or supported on a Sv. S7*. pi,ot_ jg K a, Fig. 374, so aa to be free to move in a hori- EOotal plane ; it will be fonnd (o asaumoi after a few oacitlations, a conatant po- sition, K it be moved from this portion, the bar icill return to it as noon as the diaturbing force is removed. One of the poles (592) of the bar will be found to point V ' — J constantlytowBrdetbenorth, "~— '—'^ and the other towards th« south. The forioer, h, in common language called the north, and the latter, s, the south pole, of the magnetic bar. 53i. Let the loulh pole of a bar-magnet held in the hand be brought Interally towards the north pole of a magnetic needle, placed on a pivot ; immediately the needle will more toward* tho POLES OP A MAGNET. 331 bar, being attracted by it. If the north pole of the magnet presented to the needle be now substituted for the aotUh^ the north pole of the moTeable magnet will fly ronnd to attain the greatest possible distance from it, repnlsion having taken place ; and the Boath pole will now be attracted. Henoe it appears that poles of the same name repel, and those of opposite names attrcict each other. That the attraction or repulsion is mutual may be proved by using two magnets on pivots, mstead of one. 595. n hen a piece of iron is in proximity to a magnet, it as- snmes magnetic properties. Present a piece of soft iron, b, Fig. 375, towards (he south pole of a bar-magnet, h s ; it instantly becomes at- tracted. And if a second bar, c, be presented to B, it will attract c, although less, strongly than it is ttee(^attracted by the magnetic bar ; proving that b assumes magnetic properties nnder the influence of the bar h s. Gradually slide Ns ofi*B, and instantly the magnetic pro- perties of the latter will vanish, and the bar c will fall from it. The influence exerted by H 8 on B, is termed induetionf because it induces magnetic pro< perties in the bar ; retaining them in it, whilst they remain in approximation. If the end of b be dipped in iron filings whilst in contact with h s, thej will adhere to it, and arrange themselves in curved lines. And m the experiment before mentioned (592), in which iron filings were arranged in curved lines, under tne influ- ence of a magnet placed beneath them, the filings became mag- netic by induction^ each single particle acting on its neighbour like a little magnet on a pivot (593), attracting or repelling it according to circumstances. 596. Whenever the pole of a magnet induces magnetism in a bar of iron, the end of the latter nearest either pole will acquire ^' ^?* properties of the opposite kind Fig, 876. y -S" Jf c If to it. Thus, if the iron bar, a b. Fie. 376, be brought near n s, it will become magnetic by induction (595), the end a becoming the north, and b the south pole, provided the v^^ 3^^^ end 8 of the magnet were a south, and n a ' * north, pole. If the magnet n s be brought in I contact with the middle of a bar of iron, a b, '* Fig. 377, the centre, c, will become a north pole, and the ends, a, b, both south poles. And if the pole of a magnet be placed in the centre of a circular piece of sheet-iron, the whole cir jr cumference will assume magnetic properties of the same kind as that of the pole of the magnet, whilst the centre with which it is in contact will assume an opposite polarity. 332 UAONETlflM. Fig. 379. C K I i 1 697. If a magnet, irs, Fig. 878, be broken in half in the centre, the half 8 will not be foand to possess all sonthern, and n all northern, polarity, as might be expected, bnt both portions will become perfect magnets, each rig, 378. ^^ ^Yi% fractured ends exhibiting a polar state, as perfect as the entire magnet. The fractured end, /, be- coming a south, and n' a north pole ; although at this middle point, where a' and n' join, no magnetism could, before breaking it, be detected, nor if the broken ends be again placed in close apposition. A strin of spring-steel, hardened and magnetised, answers very well for tnis expenment. 598. If either of the pieces n tl^ or n' s, be afirain subdivided, the same phenomena will occur : and the same will be repeated as far as the subdivision may be carried. This shows that me ma^etic energy, chiefly manifested near the poles of a magnet, is an aggregate effect of the energy inherent in each particle. A bar- magnet, then, AB, Fig. 379, may be considered to consist of an agg^gate of molecular ma^ets, e, <2, e, &c., all of r which have their axes of fK>- larity similarly arranged ; in the middle of the bar, c,^ tho polar enerey of the particles will be controlled and neutralized by equal and opposite energies on either side of them ; but on receding from the centre towards either end, the polar energy of each particle is less and less neutralized by the polarity of the particles beyond it ; and thus the agercgate of molecular energy will be manifested at each end of the bar. 599. An extension of this reasoning will explain why a steel ring may be converted into a magnet by passing it over the pole of a powerful magnet, without its exerting any attractive influence on iron, or exhibiting any other phenomenon charao- teristic of free magnetism ; for here every portion of the ring being oontinuovB^ the energy of one pole of each molecule is held dii- guised by the energy of the opposite kind, on the opposed side of the next molecule of steel in tne series. On breaking such a ring in half, the terminations of the fractured portions will be found to present energetic magnetic polarity, the portions which disguised their polar state having been removed. And thus ever^ fragment of the fractured ring will be a perfect magnet, a fact so interesting and extraordinary that the Abbe Haiiy wittily termed magnets let polypes du rigne mineral. 600. /The phenomena of induction and consequent attraction may be explained on the hypothesis that the permanent polarity of the molecules of a magnet is capable of inducing a similar y^ J poUritr in tbe moleculea Id b bar of mimagnetjBed steel, or soft iron, placed in close proiimilj with it. Thus, if the unmagnetiaed bar be placed parallel to the tnagnet, the polar arrangement of their molecules u represented b; the parallel rowe in Fig. 379, but if placed end to end, that armngemeut will be tjpified Gy the two halTeB formed bj a transverse diTJBioD of tbe same figure. Tbe only diflereiice betweeu tbe Bleel and soft-iroD bars is, that in the former the induced magnetism is more or less permanent, and in tbe latter, Iranaitory. It IB not improbable that the phenomena of dunaaffnetiim (to ha inbaequentlj considered) may be sirnilarlj eipUired bj the hypo- thesis tbBl a magnet is capable of inducing oppotite polarity, and consequent repidaon (394), in the moleculea of the diamngnelic 601. The ilaria^'t Corapaa. — A macnetic needle properly balanced upon a pivot (593), conelittiles the active agent in the well-known mariner's compass. This invaluable instrument was used in Euro^ in 1180, according to a sntiricnl poem of Gay of Provence, entitled "La Bible," in which it was minutely described. It is tolerably certain that it was known to the Chinese in a rude and imperTect form, nnder the name of Tchi-tian, or chariot of the aoQtb, about 2600 years before the Christian era, Miirco Faolo was the first European navigator who applied the compass-needle to tbe practical and important purposes for which it is now con- stantly used, in bis return to Europe from the East Indies in I26tl. Tbis important property of a magnetic needle pointing always in a constant direction has Wen variously accaonted for ; thus Cardan baa supposed that a star lodged in tbe coneleilation of Ursa Major attracts the needle, whilst otbers with more probability have sup- posed the earth to be, or to contain an enormous magnet, the poles ofwbicb nearly correspond with the geographical poles of tbe globe. 602. Tbe mariner's compass, as now con- gtmcted, consists of a poised needle at- tached to a card, on which the cardinal Eints [as they are called) of the compass, _ W, N, and 8, and the intermediate points are marked. This is enclosed in a case resting on a pedestal called a " bin- nacle-'' These are canstructed in a variety of forms; Fig. 380 is a design of one of the best kind, made in brass by Mr. Browning. The compass is contained in the vase A, and viewed tbrough a glazed window, a. Two lamps, o and d, are placed ahove for the purpose of illuminating the card at night. It has been aBcertained (as will subsequently be pointed out) that by using two needles parallel to. And at a certain distance froDl, 331 UAOKKTISH. tho N. S. line, instend of a aingla nna cobciding with it, an important source of error may be obviated : for this purpOM they muBt bo to placed, aB to intereect the cirouinferaiica of the card at a distance of 30° on either aide of the N. 8. line. In ths firsl-class compasBfls made hj Mr. Browning, the two needles are called dippiag-ntedlet, being sopported on a trans- verse aiia passing through their oantres of gravity, and trealy n «,, moving verticslly in sHls in tho "S- ™'- card, which arrangement is sop- I posed to dimiuish some of the a to vhlch the compase IB e. The distance B A, Kg. 381, hich one of the needles iutcr- .thecircumrerenoeisaU". The rests as usual by a small cup- ,.ed catity in a Bmnll piece of agate on a ateol point, c, but the agate-cup instead of being in the p)Bne of the card, is raised consida- Mb.SW, rablj above it by means of a bridge, b, I and thus the tendency of ihe card to oBcillaCion in a vertical plans is much diminished. This form of compass has been much approved of by competent authority. In the Admiralty standard compaiefonr parallel fixed needles are employed, as shown in Fig. 382 ; these are so placed th^t the distance h a, may be 15°, and x s, 45* ; the two are therefore at a moan distance of 30° from the N. S. line, 603. J)eviation of the Cornet. — From what has been alieady stated (595) respecting the induction of magnetism on ban of iron, it will readily be uaderslood that the masses of iron osed in the construction even of wooden ships most always have been 8 source of disturbance to the compass-needle, by innnencing it« podtioD due to the action of the earth's magnetism alone, and therefore falsifying its indication of the geographical direction in which the ship is moving. It must also be evident that this error of position, called the decialioa of ihe compaii, is immeasurably increased m vessels built wholly of iron, and especially in those that are also armour-plated. A knowledge of the properties of the compass, which has ex- isted in China for probably more than 4000 years, appears not to have penetrated into Europe more than fire or sii centuries ago, and little was dooe towards perfecting the theory of the compass until the commencement of the present century. In the voyage of Captain Flinders to Australia in IBOl, he observed, as omera had done before him, that the ditectiou of the compass-needle fnt- quently deviated cnnsidonbly from the known variation doe to DEVIATIOH OP THE COMPASS. 335 the geograpbical position of the ship ; bat not satisfied with ascribing this apparentlv capricious change to errors of construc- tion of the compass, as had previously been done, he proceeded to investigate the causes of the phenomenon, and soon observed that the error was most considerable when his ship's head pointed about east or west, and that it entirely disappeared wnen the line of the keel coincided with the magnetic meridian ; it ap- peared, therefore, that the north end of the needle was drawn towards the ship's bows by some unknown force, which he natu- rally supposed to be the south pole of some unknown magnet between tne biDuacIe and the bows. But Flinders found that in Bass' Straits the phenomena were entirely reversed ; the sotUh end of the needle was now drawn towards the bows, as the north end had been in the northern hemisphere. From these facts he readily inferred that the disturbing cause was magnetism induced by the earth in the stanchions and bolts in the ship's hull ; and that the disturbing intiuence might be counteracted by upright stanchions placed abaft the binnacle ; and for this particular error no better remedy has been devised. The phenomena of deviation in wooden ships wera further eluci- dated by the observations of Captains Scoresby and Sabine, during their voyages of Arctic discovery, but to the present Astronomer Royal, and to Mr. Archibald Smith, the elaboration of the theory of compass-deviation in its present complete state is almost en- tirely due. 604. The extensive introduction of iron in ship-building has introduced sources of error not only vastly greater in degree, but also differing totally in kind, from those previously observed. While the errors detected and corrected b^ Capt. Flinders rarely exceeded 2** or 3^ in some iron ships a deviation of 50° or 60° has been observed ; and the existing errors are alwavs largely in- creased, whenever the ship Keehf or rolls from the action of the wind or waves. The variation in the nature of the disturbing causes depends on the materials of which, and the direction in which, an iron ship has been built. This result may be thus illustrated : a bar of veiy soft iron placed vertically may be freely magnetized by induction from the earth, and if reversed in position may be demagnetized, and its polarity reversed in a few seconds ; while a bar of hardened steel is scarcely at all susceptible of the earth's induction. But a bar of hard iron partakes of both these quali- ties (of soft iron and steel); and although not very susceptible of spontaneous induction, a lar^e amount of induced magnetism may be hammered into it, which it requires an equal amount of ham- mering to subdue, or to reverse ; and this is precisely analogous to what takes place in iron ships, and in proportion as the iron partakes of the quality of steel, the induced magnetism once ham- mered in, cannot by any change of position, or by concussion, be entirely eradicated. That portion of the induced magnetism 336 MAOKETISll. which no subsequent mechanical violence will destroy has been called the permanent magnetism of a ship ; while that portion which, althou);h not susceptible of remoyal by merely reversing the position of the hull, may nevertheless be beaten or shaken out of it, has been called wh^oermanent magnetism, both differing in their effects on the needle from the induced, or soft-iron mi^« netism, which varies with the position of the ship on the earth b surface, and with the direction of her course. In the year 1839 an extensive Hcries of experiments was made by Mr. Airy on two small iron vessels, from which he was led to con- clude that the source of disturbance was ftlmost entirely the perma- nent and sub-permanent magnetism of the vessel (which of course concur in the direction of theirdisturbinginfluence), and thatif these were compensated, the temporary magnetism of position might be neglected. This compensation he effected by two permanent magnets placed in the neighbourhood of the compass, one fora ana aft, the other in a transverse position, the magnitude and position of which must in each case be determined by experiment, guided by the results of analytical investigation. But the diffi- culties of compass-adjustment are increased by another cause not vet alluded to. Liarge horizontal masses of iron, such as deck- beams, engine- shafts, &c., are introduced, and these disturb the compass in a manner totally different from the upright stanchions, &c., previously alluded to. There are, therefore, three distinct disturbing influences to be combated : — 1. Vertical induction ; 2. Horizontal induction ; 3. Permanent and sub-permanent magnetism. Theory and experiment concur in showing that the influence of horizontal induction vanishes when the ship is placed in either direction in the magnetic meridian, or perpendicular to it, and that it is a maximum at the four intermediate points ; this dis- turbance has therefore been called quadrantaL Vertical induction will cease to affect the needle only when the keel is iu the magnetic meridian, and the maximum effect will be produced when the keel is across that line : permanent magnetism vrill cease to act onlv when the needle is parallel to the magnetic axis of the ship, which may or may not coincide with its longitu- dinal section ; and the same influence will be a maximum when the needle is perpendicular to the ship*s magnetic axis : the devia- tions arising from these causes are hence caUed aemieircuiar. 605. The qnadrantal may always be readily discriminated from the semicircular errors, and both horizontal and vertical in- duction may be compensated by corresponding^ elon^ted masses of soft iron suitably disposed ; the latter especiallv m some ships 18 partially compensated by the iron masts, if the compass be suitably pUced. As, however, some difficulty and inconvenience OOMPBHBATIOH BT MAGHBTS. 337 attends the correction of qnadrantal deviation by mames of soft- iron, it occurred to Mr. JByans, and has been demonstrated in a paper by Mr. A. Smith and himself,* that the correction might De made by the reciprocal action of two compasses, placed at a distance of from 18 to 24 inches from each other, as in the ordinary double binnacle. For this purpose, the two needles must be of equal power, and as their correcting influence bears an inTcrse ratio to the earth's horizontal force, it is necessary, for accurate correction in high latitudes, that the interval between the two needles should be capable of adjustment. The semicircular error, arising from permanent and sub-perma- nent magnetism, may be compensated by magnets, after Mr. Airy*8 pum, but it is not always easy to riu^htly apportion the semicircular error between the vertical induction, and the perma- nent magnetism; and, moreover, any discrimination between permanent and sub-permanent magnetism is absolutely impossible. It must, therefore, be borne in mind that, supposing all semi- circular deviations to be accurately and completely corrected by permanent magnets, after Mr. Airy's plan, still the residual ▼ertical-induction-error will be doubled m a southern latitude, and that arising from sub-permanent maffnetism (frequently veiy considerable) will be doubled as soon as that sub-permanent mag- ne tism is beaten out of the ship by the impact of the waves, or still more rapidly and effectually knocked out of her by collision with a pier-head, another vessel, or a sunken rock. In fact, the efficient correction of the compass by permanent ma^ets would be utterly hopeless, were it not the result of ex- perience that, after a certain amount of buffeting, say after the ordinaiy casualties of a twelve months* voyage, sub-permanent magnetism entirely disappears, and the vessel appears to assume its permanent magnetic condition. In a new ship, therefore, magnet-compensation is a sadly broken reed to rest on, as experience has unfortunately shown. A new iron ship, the TayZeur, of 2000 tons burden, sailed from Liver- pool with emigrants early in 1854. She had, as usual, been gwung^f and evinced very large compass errors, amounting in one position to 60**. Like all very large errors, this was undoubt- edly due to the inherent— or transient — ^magnetism of the ship. A compensation by magnets was applied in the usual manner, and the compass-readings were fairly correct. She, however, experienced severe weather in going down Channel, and within two days after leaving port, was wrecked, with groat loss of life, • Phil. TnoB. leOB. t Swinging a Bhip is brioging her head round to all points of the oompass in soooeflsioiK for the purpose of ob«erTin|( the errors of her oompaasee. It maj here be remarked that this process is mudi faoilitated by the use of the " Feloms" of Ur, Browoing : which oonsista of a oompass-oard with a sight attached to it, but without a needle, and moving in asimath with saffljientlj stiff firiction. z SS8 MAexEnsM. on the coast of Ireland. No reasonable donbt can now be enter- tained that in her first encounter ¥dth the waves, she had parted with much of her snb-permanent magnetism, and that the applied correction had become worse than useless, — a delusion and a snare. It was hardly believed at the time that so rapid a magnetic change could have taken place, but the sad catastrophe led to careral observation on the loss of magnetism in ships. The ill-fated BoycU Charter sailed on her first voyage with an error of 20** in her standard compass (which was uncorrected). All but about 3* of this error disappeared in her first voyage, and the steerage- compass, which had been compensated, came home with an error of 22^, due entirely to the over-action of the compensating mafi;net. On the contrary, a striking example of the magnetic stability which a ship acquires after some years of service, was afforded by the Adventure. She once struck on a rock with so much force as to tear awa^ a portion of her outer iron skin ; yet, on careful examination, it was found that this violence had produced scarcely^ any sensible effect on her permanent magnetism. The inherent difiSculties of mecnauical compensation have led Mr. Archibald Smith and some others to prefer a careful observa- tion and tabulation of a ship's compass-errors, to their mechanical compensation :^^oubtle88 both plans have their advantages and disadvantages, the balance of which it must be left to practical mariners to detennine. Analysis and experiment have disclosed another source of error due to the proximity of the compensating magnet, to which the name of eexttrntal deviation has oeen applied, on account of its occurring periodically at the ^th parts of the circumference ; this error may however oe entirely obviated by the arrangement of two or four compass needles, already described (60^ : and another, termed octantal deviation, due to the proximity oi a soft- iron coinpensator, is by the same means eliminated. 606. The effects of horizontal and vertical induction may per- haps be better apprehended by the aid of a diagram. Let the transverse bar ab, Fig. 383, placed transversely beneath the Fig. 9S3. binnacle, represent the aggregate of transverse masses of iron, and either the single bar c d, or the two c e, f d, that of lonnta- dinal masses. The qnadrantal deviation would be produced by cither of these types, but there is this important difference be- w^ BRSOBS IN AHMOUB-PLATED 8HIPfl, 339 tween tbem, that the continuous bar, c d, would always diminish the dirvctive force, while the separated bars c b, f d, would in crease it, if their combined inflaence were greater than that of a b. If the effect due to vertical iron be that of a bar o h, its in- flnence on the heeling error due to the combined effects of a b and 6 H will be readily understood. If o be beneath a b, then g, and the end of a b that is raised by heeling, will consmre in pro- ducing a heeling error to windwara, because they wul then be both on the windward side of a vertical plane passing through the compass ; but if o be above a b, then in heeling they will be on omorite sides of the same vertical, and the heeling error will be the difference of the actions of a b and g h ; and if the influence of g H predominate, the heeling error will be to leeward. Compasses on the upper-decks of iron ships, especially if built head to N., are of the type a, and there is a large heeling error to windward, but the main-deck compasses, and particularly those of armour-plated ahipe, are generally of the type b, and their heeling error is fire* qnently to leeward. 607. The more recent investigations by Messrs. A. Smith and Evans of the magnetic conditions of the armour-plated ships of the Boyal Navy,* have shown that the introduction of armour-plating, and tiie great increase in the amount and thickness of iron used m the construction of modem ships of war, have greatly increased the amount of the deviations previously considered, and have given importance to two sources of error not hitherto regarded, viz., the cUmintUion of directive force, and the heeling error. The observations made confirm the conclasion that the semicircular deviation in an iron ship is chiefly due to the attraction of the north pole of the needle to that part of the ship which was south in building, this direction in armour-plated ships being modified by the direction in which the ship was plated. The following is an approximate value of the semicircular deviations in British waters in the Warrior^ Blatk Prince, and Defence, and of the proportions due respectively to vertical inductiqu, and to perma- nent magnetism : — S0miciro. deT. Vert. ind. Perm. mag. Warrior . . . Black Prince . Defence . . . -244° + 23 + 26i + 12'* + 23 + 14i -36r 0 + 11J The great difference in the last values between the Warrior and Blade Prince depends on the fact of the former having been built head to N., and the latter, head to S. In the iron-built armour-plated ships the quadrantal deviation * Phil. Trans. 1866. z 2 340 IfAONETISU. becomes very laree, greatly exceeding what has been fonnd in' other vessels. This, however, is not to be attributed to the armour in all cases, as it has been determined both by theory and observation, that in plated wooden ships, with the compass in a central position, the effect of the armonr is to diminish tlie qnad- rantal deviation. The following table shows the larg^ amoont of qnadrantal de- viation in four armour-plated iron ships : — Compua. Wurior. BUe. PriDo«. Defcnoe. BaosUaee. Standard • Steering - Main-deck 8'*2r U 66 11 43 7'* 38' 10 32 13 06 7*00' 10 16 14 35 6M7' 8 28 14 00 In the following armour-plated wooden ships the ouadrantal deviation of the standard compass was diminished to tne respeo* tive amounts : — Royal Oak, 3' 0^ ; Caledonia, 2* 67' ; Ocean, 2*31'; Prince Consort, 2* IS*. The diminution of direction force, producing sluggishness of the needle, is also remarkable ; in the main-deck comnasses of some of the armour-plated iron ships the mean direction force scarcely exceeds 0'7 of that exerted on the same needle on shore. In the same vessels the amount of heeling error is also very considerable, averaging about l** for each degree of heel, or lateral inclination ; but greater in those that have ueen built head to N. Thus, in the Warrior ^ it amounted to 1** 49' for each degree of heel. This error may be corrected by means of a vertical magnet. On the contrary, in the armour-plated wooden ships, the heeling error is very small, and generally to leeward ; thus, for each degree of heel the amount is — Royal Oak, 7' to windward ; Prince Consort, 8' to leeward ; Ocean, 15' to leeward. The more important practical conclusions drawn by Messrs. A. Smith and Evans are, that the best position for building an iron ship is head to 8.; that if armour-plated, the plating should be laid on in a position the reverse of that in which the hull was built ; that there should be as little iron as possible within the space of a cone formed by the revolution of a line passing through the needle, and forming an angle of 64'' 46' with the vertical ; and that it is very hazaraous to compensate the compass of a nevf ship by permanent magnets. It also appears that the effect of iron masts is to increase the qnadrantal error. The scope of this treatise forbids a full analytical investigation of this all-important subject, but it is hoped that enough has been written to render its leading features intelligible. The more ad- vanced student, and the naval officer, will find the subject fully •^^■^K ■ - V . — »^*- ■ - ■ - . ■■'-.•-».■-_ ,iif TEBRE8TBIAL UAOKETI8U. 341 treated in all its bearings in the last edition of the " Admiralty Manual on Compass Deviation." 608. It appears that, admitting the existence of bat one mag- netic pole in either hemisphere, it is difficult to explain the pheno- mena noticed bj different observers. In the northern hemisphere, two poles or centres of attraction have been distinctly made out, one m Siberia at 102** E. long., and to the north of 60** N. lat. ; the other, and apparently far the more important, is situated about 96"* 40^ W. long., and 73** 14' N. lat. ; these two poles are about 200^ of long, apart, measured across Qreenland and Norway. The two southern poles are supposed to be located, one near Cape' Horn, and the other to the south of Australia. Frof. Hansteen supports this notion of the existence of two magnetic poles in each hemi- sphere ; he however places them rather differently. On the other hand, a high authoritT, iVof. Gauss, from more recent researches, is induced to conteua for the existence of a single pole in each hemisphere. Faraday has, howeyer, expressed an opinion, that the hypothesis of the existence of magnetic poles at the geo- graphical poles is unsatisfactory, and that the phenomena of the dipping needle lead to one of two things ; either that the mag- netism of the earth is simply the result of the induction of electric cmrcnts — or, if a terrestrial magnet really exist (which is highly improbable), its poles must be close together, near the earth's centre. 609. The compass-needle does not point exactly north and soath, a circumstance generally supposed to have been first ob- served by Columbus iu his earliest voyage of discoyery in 1492 ; and consequently, the magnetic meridian, or plane bisecting the earth in the direction of the needle, does not coincide with the geographic meridian. The magnetic meridian is not constant, sometimes bein^ on the east, and sometimes on the west of the geographic meridian; this difference is i^. 38i. termedthe magnetic declination. Thus, 1 if AB, Fig. 384, represent the geo^phic ^^ — I — -v^^ meridian, v s will represent the direction /^ \ x. ines \ \ y 683, ^^^J^ lagnetism, first paper on the isogenic tines, or lines of equal declination, in the year 1683, and a general map, comprising all that was then known on the sul^ject, in 1701. He supposed the exist- ence of four magnetic poles (a conjecture whicn has been con- firmed by subsequent observation), one in each hemisphere sta- tionary ; the other two, the northern to the east, and the southern to the west, subject to a periodic revolution in about 700 years. On certain portions ot the earth's surface the magnetic and 842 MAGNETISM. geograpbic meridians appear to coiDcide, as in some parts of North America, the nortb-eastem point of South America, the western part of Austrah'a, &c. These places are connected by an imaginary irregular cnrred line, termea the line of no variaHon. This line appears to move proffressively over the surface of the globe ; it passed through London in 1660, in which ^ear the needle there pointed exactly to the north, and in 1663 it passed through Pans. In its westward course it has lately traversed Amenca. These have been termed by Prof. August, agonic lines, and two of them are supposed to exist, one in the western hemisphere termed the American agoiMy and another in the eastern, or Asiatic cigone. They both intersect the geographic meridians at different angles. Prof. Gauss is induced to believe that there exists a greater and lesser agone ; the greater em- bracing the globe like a meridian, passing through the magnetic pole, and dividing the earth into an eastern and western magnetic nemisphere. Of these the former will embrace Australia, Arabia, Persia, and Russia ; the latter including the eastern parts of North and South America. The lesser agone of Gauss forms an oval, and runs through Eastern Siberia and China. The mean decli- nation in Europe is about 17^ W., increasing towards the west, and decreasing towards the east. The following table shows the amount of declination in London and Paris at different epochs. Year. Beolia. Year. Beelin. YAUS. 1 1580 1634 1660 1670 1690 1720 1740 1750 1770 1780 IP 16' B. 4 6 1. 0 8 — 2 30w. 6 Ow. I 14 17 w. 17 Ow.| 17 48 w. 21 9w. 28 17 w. 1780 1800 1810 1818 1820 1830 1841 1850 1860 1865 23''39'w. 24 8 w. 24 11 w. 24 30w. 24 22w. 24 2w. 23 16 w. 22 23w. 21 14 w. 20 82 w. Year. Deolin. Year. BecIin. 1680 1618 1663 1678 1700 1767 1785 ir86'i. 8 Ox. 0 0- 1 SOW. 8 10 w. 19 16 w. 22 Ow. 1805 1813 1817 1822 1826 1830 1866 22** 6'w. 22 28 w. 22 19 w. 22 Uw. 22 12 w. 22 «w. 18 44 W. 610. Prof. Ben wick found the declination to amount to 5" 28^ W. at New York in 1837. At London the needle at present points about 204** west of the true north pole, the maximum variation having been attained in 1318, when it amounted to 24** SO'. Largo variations have been observed by the Chevalier de Langle be- tween Greenland and Labrador, amounting to 45° W.: and by Captain Cook, in lat. 60'' S. and long. 92'' 66' E., where the variation amounted to 43** 6', east of the geographic meridian. 611. A magnetic needle, if movable on a horizontal axis pass- ing through its centre of gravity, does not remain horizontal ; its north pole io our hemisphere dipping considerably; and in the southern hemisphere the opposite pole inclines ; this is termed the dip or indinatton of the needle, and a needle thus suspended i|i termed a dipping-needle. The inclination of the magnetic needle nrcusATiov. 843 WM discovered by Robert Nonnan, FIff, 885. in the 16th centary, who found it to ^f"^ ""^v. smoont to 72". Let a b. Fig. 386, /\ | >. be a needle balanced on its hori- ^ \ '• \ Bontal axis, o, and placed in the / \ | \ magnetic meridian; in England, ^/ \ J.^ then, instead of remaining horizon- ^\ tally, as d s, it dips or inclines to- \ wards the north, its north pole V forming an angle, bob, of nearly x,^ 68 J* with the horizontal line d e. ^ ^ 612. A line traced over the earth's surface through the various points at which the dip becomes evanescent is called the mag- netic equator. It does not coincide at more than two points with the geographical equator, from which it diflbrs as the magnetic do from the geographical meridians. The magnetic eouator is tolerably regular for a part onlv of its course, and may oe repre- sented by a part of a great circle inclined at an angle of from 12^ to 13** to the geograpnic etjuator, which it intersects in at least two points ; one near the island of St Thomas in long. 8* £., another in the PaciBc in long. 142*^ £. In the southern hemi- g»here, however, especially between the Sandwich and Friendly lands, this line presents numerous irregular and sinuous curves Hke the magnetic meridian. The magnetic equator is an irregular doable curve to which the term of adinie line has been applied ; it, like the agonie lines (609), appears to be undergoing a pro- greuive motion, which, as far as observations have been made, is in a direction from east to west. Lines connecting places where the inclinations correspond are called iaodinie, or isoclinal. These have during the last twenty years become more nearly parallel to the meridians. The greatest inclinations of the needle ever observed, were by Captain Cook, who, in lat. 60°40' S. observed it to be TSMa'; Captain Phipps, in 1773, in lat. 79" 44' N. found it to be as great as 82* 9' ; and Sir James Roes, in 1831, in the vicinity of Hudson's Bay, in lat. 70** 5' 17" N.. found the dipping needle to be within one minute of being perrectly vertical. 613. Prof. Krafit, of St, Petersburg, announced in 1809, a veiy simple law governing the amount of the dip, at different parts of toe earth s surface, which has been confirmed by the later researches of M. Biot, viz., if we measure the latitude of any place from the magnetic equator, and calculate its tangent, it wul be found exactly equal to half the tangent of the dip at that par- ticular locality. 614. The inclination or dip of the needle undergoes a secular change, but bv no means to so great an extent as the declination, as shown by the following table : — 344 MA0SSTI8M. Tear. Inolin. Tear. Indin. TAMia. 1680 1723 1773 1786 1790 1800 1818 73*30' 74 42 72 19 72 8 71 53 71 25 70 34 1828 1830 1840 1850 1860 1865 69*47' 69 38 69 12 68 51 68 21 68 2 Yaar. Inelin. Tear. Inelin. 1798 1810 1818 1824 1826 69*61' 68 50 68 35 68 7 68 0 1829 1831 1835 1840 1865 67*41' 67 40 67 24 67 7 65 58 The diminution of the magnetic dip has heen going on in London for the last half centniy with great regularity, at the rate of about 2*81' annually. From the observations of M. Quetelet, it appears that the angles of inclination and declination seem in Europe to be undeigoing a tolerably constant gradual diminution ; these angles at Brussels were found by this philosopher to be of the following values : — Tear. Inelin. DecUn. Tear. Inolin. Deolin. 1827 68* 56' 5" 22* 28' 8" 1838 68*26' 1" 22* 3' 7" 1830 68 51 7 22 25 8 1839 68 22 4 21 53 6 1832 68 49 1 22 19 0 1841 68 16 2 21 38 3 1834 68 38 4 22 15 2 1860 67 30 8 19 23 5 1836 68 32 2 22 7 6 1865 67 19 9 18 50 6 615.^ Besides these gradual changes, which are termed aecular varitUionaf of two of the magnetic elements, the declination and the dip or inclination, various other periodic variations have been detected by the careful reduction of large series of observations, which Gen. Sabine has clearly shown to be of cosmical origin, that is, arising from causes external to the earth itself.* These magnetic variations may be arranged in two classes : one comprising those that are uniibrmly periodic, continuous, and comparatively small in extent ; the other, those that occur at un- certain intervals, and are equally uncertain both in magnitude and duration, but yet manifesting certain periodic characters. To the latter class the term disturbear entirely ; and on the south of that line they re-appear in an inverted order. Science has been greatly indebted to the ingenious researches of Faraday, for a nighly probable explanation of the pheno- mena of solar-diumal magnetic variation. This acute phi- losopher having observed that oxygen gas exhibited magnetic Properties, thence inferred that the diurnal variations might be ue to the varying intensity of this foive. It has long been known that an artificial magnet loses a portion of its force by elevation of temperature, which it regains, either partially or entirely, according to circumstances, as the temperature is again reduced. And the same changes take place in the magnetic intensity of the atmosphere, whioh is due to the oxygen it contains. In our latitude, atmospheric ma^etism will evidently be weakened east- ward of the meridian dunng the momine hours, by the solar rays, and consequently, as it is observed to be, the deviation is then towards the west ; and the contrary must for the same reasons happen during the afternoon : also, as the atmosphere does not immediately part with its absorbed heat, the heated mass of air mnst lag somewhat behind the sun, hence the change of deviation from west to east does not occur exactly at noon, but at some short period afterwards. The observed average quiescence of the de- clination maenet during the nocturnal hours, is an evident con- sequence of the same hypothesis. The observed absence of diurnal variation in the neighbourhood of the magnetic equator is equally day, an tifmify different periocU of time. The h ^x^n of an attronomical (in •ootndisunotioii to ft eimi) daj are nambered eonsecvtively from d^, it* oom- it at noon } thus 6 A.if. in dvil reokoning will be, aatronomii^Uy, 16^. 346 IfAOMBTIBK. a necesBaTy result ; for the atmoflphere will be eqaallj affected by the sun's rajs north and south of a magnet there sitoated : con- Bequentlj, two equal deflecting forces, in opposite directions, will neutralize each otner ; while in the southern hemisphere, the sontli pole of the magnet will be similarlj influenced with the north pole u our hemisphere ; and consequentlj, the diurnal movements will be there exactly contrary to ours. If two bar-magnets be laid on a table, with their opposite poles towards, and at a small distance from, each other, and a very pmall magnet be placed anywhere in the magnetic fleld (554), the whole being covered with a sheet of card-board, and strewed with iron-filings, the distortion of the magnetic curves by the small magnet will rouffhl^ illustrate the distortion of the terrestrial curves by atmospneno magnetism. 616. The solar-diurnal variation of declination has been found by Gen. Sabine to be subject to a verv remarkable semi-annual in- equality. The means of the diurnal variations at each solar hoar have been taken from April to September, and from October to Mareh, and tabulated in the form of curves. In the summer curve a maximum, but in the winter curve a minimum occurs at from 19*^ to 20^; and in the summer curve a minimum, but in the winter one a maximum, at from 1^ to 2^. At seven magnetic stations from which the observations have been reduced, the contour of the curves is extremely similar : at two stations, namely, Kew and Toronto, a small secondary maximum and minimum occurs be- tween 5^ and 7^. These semi-annual curves are at each station bo remarkably similar to each other, that if one were turned over on the other about the line of mean position, they would almoet exactly coincide ; one curve may in fact be said to be the reflected image of the other. The extreme amount of this inequality does not exceed 4'. 617. Lunar-ditamat Variation of Dedi7iation.-—'Bjf a Judicious exclusion of " disturbed" observations, and by an elimination of the Bolar-diumal change. Gen. Sabioe has succeeded in establishing the reality of lunar influence on magnetic declination ; an influence not less remarkable for its extreme regularity than for its minute* ness, its amount not exceeding 20". The curve presents a re* markably qrmmetrical double progression in each lunar day, having two easterly and two westerly maxima at very nearly equal alternate intervals of the hour-cirole ;* and in this respect it closely resembles the great tide-wave of the ocean : may it not be due to the atmospheric tide-wavcj which must at the same periods alternately increase and dimimsh the amount of atmospheric magnetism on opposite sides of the meridian? At Pekin, some degrees nearer to the equator, this variation is zero 84^ earlier than at Kew. In the southern hemisphere, at the Cape of Good Hope, which is nearer to the equator tnan Hobarton by about the • FULTrMM.1868. DIBTUBBJUICB TABIATXOVS. 347 same amoant, it is also 2\^ earlier ; and at St. Helena, which is still nearer the equator, it is 3i^ earlier than at Hobarton.^ There is no trace of a decennial period in this ▼ariation. A similar pro- gression was snhseqnentljr discoTered, by the same indefatigable observer, in the lunar-diurnal yariation of the horizontal and ver- ^taX components of the earth's magnetic force.* 618. Annual Variation of Total Force»—Then is a Pinall an- Bual variation both of the total magnetic force and of the dip ; both have their greatest value at the winter, and their least at the Bummer solstice. As this variation is alike in both hemispheres, in which the seasons are opposite, it must necessarily depend on the sun*s distance from the earth, and not upon changes of temperature. 619. The force by which the north pole of the dipping-needle is directed obliquely downwards, may be conceived to be compounded of two forces (284), one acting horizontally, and the other verti- cally ; by the former of which acting alone, the needle would as- some a horizontal, and by the latter, a vertical position. In this conntry, the proportion of the vertical to the horizontal force is nearly as 2 : 1. As the instrumental means of measuring small variations of these two components are more available than those for measuring directly the aip and total force, the values of these magnetic elements are frequently inferred from a comparison of the components mentioned. 620. disturbance Variations, — Some remarkable facts have been developed by a separate investigation of the second class of magnetic pnenomena Mfore alluded to. It appears from the re- duction of the observations ou declination made at Toronto and Hobarton in the years 1843-4-5, by Gen. Sabine,f that both an annual and a diurnal law may be discovered in the larger mag- netic disturbances, called shocks and storms. There appears to be a maximum in summer, and a minimum in winter, and to a certain extent there is a correspondence between easterly distur- bances at Toronto, and westerly at Hobarton. Easterly distur- bances predominate in l^orth America, and westerly disturbances in Nortnem Asia. The aggregate amount of disturbance is small in the Tropics, it is augmented in mean latitudes, but by no means in the ratio of the increase of latitude, as there is a large dispro- portion in different meridians ; for example, the hourly observa- tions made at Point Barrow during 17 months in 1852-4, show an amount of disturbance unparalleled elsewhere, even in the highest latitudes. Here, as elsewhere, a correspondence has been observed between the occurrences of Aurora Borealis, and mag- netic disturbance : it is recorded that Aurora was seen during at least one-third of the hourly observations then made. It has since appeared that the mean diurnal disturbance-variation of declination is remarkably similar at all magnetic stations, the • FhlL Truu. 1866. t Fkil. Trans. 1851. 548 MAONBTI8M. distarbed obBer^ations of which have been reduced. It may here be remarked that the "disturbed*' observations have been taken to be those that show a variation from the mean position exceed- iuff a certain fixed amount, which depends on the amount of local solar diurnal variation. It was then (in 1861) stated to be pro- bable that if the larp^r disturbances were eliminated, the residual diurnal variation might prQbablj appear as a single progression with but one maximum and one minimum in uie twenty-four hours; and this anticipation has subsequently been verified. When in the disturbed observations made at Kew and Hobar- ton (separated from each other by nearly half the circumference of the earth), the easterly and westerly deflexions are separated, and curves laid down representing the local-hourly means, a very near approximation is observed between both pairs of curves. They all, and especially those showing the easterly deflexions, present but little variation during the morning and mid-day nours, from 18^ to 3^ ; there is then a steady advance towards a mirUmum in westerly, and towards a maximum in easterly deflexions, from 3^ to 1 1^ and then an equally steady retreat during the night to 18''. At Nertchiusk in Siberia the curve of westerly deflexions corresponds very closely with that of easterly deflexions at Kew and Hobarton, but the minimum occurs at 9^ and the maximum at 21^, just twelve hours later. May not this depend upon the providential presence of Aurora during the long and dreary nights of that inhospitable region? 621. One of the most singular and unexpected results of the reduction of the disturbance-variations of declination has been the discovery of a periodical change in the annual amount of disturb- ance ; and a v^ry remarkable coincidence of natural phenomena, between which there is no apparent connexion, has been revealed by the independent researches of Gen. Sabine, and M. Schwabe : the former naving reduced the lar^r magnetic disturbances ob- served at Toronto, and other colonial observatories, during a con- aiderable period, found that their frequency evinced a gradual increase, and subsequent diminution, during a cycle of nearly eleven years ; and exactly the same cvcle, having simultaneous maxima and minima, has been assigned by the latter to the vary- ing frequencv of the observed occurrence of spots on the sun's disc. Prof. Lament has assigned a duration of 10*43 years, and Prof. Wolf one of U'll vears, to these solar periods. These wholly independent investigations were published at nearly the same time. 622. The magnetic changes that occur in any given locality may be comprised under six different heads, independently of the sulidivision already made, into ordinary and extraordinary varia- tions, namely, those which deflect the declinometer to the east, and those which deflect it to the west ; those which increase, and those which decrease the inclination, or dip ; and those which in- increase, or which decrease the intensity of magnetic force. The OBSBBTATIOH OF MAaHBTIC YARIATIOKB. 84S^ remits of the researches above mentioned appear in some measure tb confirm the anticipations of M. Gauss, one of the ablest pioneers in opening out the path of magnetic investigation, that the phe- nomena arranged under each of the above heads would be found to be governed b^ independent laws. M. Gauss has truly re- marked that it will be a triumph of science should we at some future time succeed in unfolding the intricacies of the phenomena of magnetic variation, in separating the individual forces of which thej are the component result, and in assigning the source and the measure of each. The instruments by which the changes of the magnetic ele- ments are observed are the declinometer; the bifilar, or horizontal force, magnetometer ; and the balanced, or vertical force, magne* tometer. The declinometer consists of a bar-magnet freely sus- pended by a long bundle of untwisted silk fibres : the variations of the position of this magnet correspond with those of the vertical plane in which the earth's force is exerted. The bifilar is a similar bar-magnet, suspended by two nearly Srallel bundles of fibres, separated by a small interval. The nble point of suspension is twisted round until the bar assumes a position exactly perpendicular to the magnetic meridian, in which it will then be retained by the opposition of two equal forces — the gravity of the bar and its appendages tending to un- twist the suspension skeins, while the horizontiO component of the earth's force tends equally to turn the bar in the opposite direc- tion, and to increase the twist. As the former of these forces re- mains constant, it is clear that any variation of the latter will produce corresponding changes in the position of equilibrium of the magnet : and it is by the observation of these changes of position that the variations of horizontal magnetic force are determined. The balanced magnetometer is a bar-magnet, very delicately poised on knife-edges, resting usually on planes of agate, so as to move in a vertical plane like the beam ofa balance (113). And Uke the balance, this instnunent is most perfect, when a single knife^dge rests on a single plane. To dimmish the influence of the twisting tendency of the magnetic force, it is better that the middle portion of the knife-edge be cut away. This instrument is placed at right angles to the magnetic meridian, and is main^ tained in a horizontal position by a weight, or, more correctly speaking, bv a portion of its own gravity, which coimteracts the tendency of the earth's vertical force to place the magnet in a vertic4i^l position. As the counterpoise remains constant, it follows that any changes in the amonnt of vertical force will be indicated by corresponding changes in the position of the magnet ; which latter have been made a subject of observation. 623. The method formerly adopted for observing the indications of these instruments has been that of viewing, through a fixed telescope, the divisions of a fixed scale reflected by a plane mirror attached to each magnet: or by viewing a finely-divided scale 360 IfAOHBTlSM. on glass, placed at the further end of the bar, in the focoa of a lens placed at the nearer end. But by this system of obsef> vation an imperfect knowledge of the nature of magnetic changes has been obtained; and as it has been deemed necessary, in magnetic observatories, that the observations of the various in- struments should be made at intervals of at furthest two hours, by night as well as by day (many important changes being even then lost sight of), this laborious duty has devmved upon the assistants ; hence some means of enabling these instruments to record their own changes was long an acknowledged desideratum in physical science. With the aid of photography, this much- desired object has been attained bv means of instruments the construction of which will presently be described.* By these instruments, an unerring and almost uninterrupted record of all magnetic changes is now maintained at the Koydl Observatory, Greenwich. These results could not have been obtained by personal observation ; for even if every telescope were oonstantly watched by the eye of an assistant ^which would require a very numerous staff), the results would still be liable to errors of observation ; and occadonallv the magnetic variations are too rapid and transient to be contmuously recorded by an observer. It may further be remarked, that since the employment of this apparatus at Qreenwich, the number of assistants in the magnetic department has been reduced, and the fatigue of night duty has been dispensed with entirel;^. 624. Magnetic registration is undoubtedly the most useful application hitherto made of the beautiful art of photography. The method suitably applied to each of the ma^etic instruments may be thus described : — A concave metallic mirror, three inches in diameter, is attached to each magnet by a frame possessing all requisite adjustments : the rays of hght from a lamp or ^as-bumer, placed at a distance of about two feet from the mirror, pass through a small aperture in a metallic plate and fall on the mirror, whence they are reflected to a focus at a distance of about nine feet. The reflected pencil should pass as near as convenient to the source of light, m order to reduce, as much as possible, the * The merit of these instramenta wm acknowledged by the aw»rd of • council medal bj the jurors of the Qroat Exhibition of 1861, and of a pre- mium previously offered by the OoTernment, to their inrentor, the present editor of this treatise. It is desirable that self*re){isteriog magnetic instruments should be pro- Tided with the means of making eye obsenrations, in order that the photo- graphic results should be from time to time compared with direct obaerra- tions on the same instruments. In the set of instruments designed by the writer^ and erected under his superintendence at the Imperial Obserratory at Pans in 1856, the three bar-magnets are hollow cyhnders about eight inches long, and one inch in diameter, having a collimator scale flnelr nued on glass at one end, and ao achromatio lens at the other, and the ooUimator •cafe is viewed by the lens through the tube. This tubular fbrm is probaUlj the best adapted fur the purpose. ADTOMATIC BSQOTBATIOH BT PHOTOOBAPHT. 361 distortion of the image fiom oblique reflexion. The source of light bein^ fixed, it is clear that the moyements of the focal point of li^ht will correspond with those of the magnet : but the angular deTiation of the luminous image is evidentlj double that oT the mirror ; for each of the angles of incidence and reflexion is in* creased or diminished bj the same quantitj. A cylinder covered with photographic iiaper is so placed that the point of light m^y fall OD it, the axis of tne cylinder beins^ parallel to the motion of the local point. The cylinder is camea round on its axis by clock- work, and, by the combined movements of the point of light, and of the cyunder, the magnetic curve is self-traced upon the sensi- tive paper. The photographic process has also been applied to the barometer, and to the wet and dry bulb thermometers ; but the mode of application is di£brent from the preceding, the light not hcing reflected from a mirror. The description of the figure will render further explanation unnecessary. Fig. 886 represents the bifilar self-registering apparatus, which is supported by a framework of brass tubes, springing firom the four comers of a black marble slab (which, when in actual opera- tion, would be cemented on the top of a stone pillar firmly fixed in the ground, and insulated from the floor of the observatoy) : these tabes, about four feet long, converge alternately to four points of the torsion plate ; thus they compose a framework possessing ffreat stiffiiess.* To the suspension-frame of the magnet, a plane glass mirror, and a concave metallic speculum are attached. The plane mirror is for the purpose of making eye- observations with the telescope in the usual manner. A gas-light or lamp is so placed, at a distance of about two feet in front of ecu:h speculum, that an image of a small slit in the copper chimney surrounding the burner may fall on the sensitive paper attached to the registering apparatus. This consists of a stand supporting horizontaUy on fnction rollers two concentric glass cylinders, round the inner of which is wrapped a sheet of prepared photographio Saper: the outer or covermg cylinder keeps the paper moist arine the twenty-four hours it remains in action. A bent arm, attached to the axis of these cylinders, is carried round by a fork at the end of a hour-hand of a timepiece specially constructed for the purpose (230, note). The horizontal motion of the tracing point of light, combined with the vertical motion of the paper, traces out the magnetic curve. A light is attached to the reg^teriog apparatus, for the purpose of drawing a standard- or hue-line on tne paper ; by the varying distance of any point of the magnetic curve from this line, the magnetic variation is de- termined. At the distance at which these instniments have been placed, an angle of 1^ is Represented by two inches on the • In iiutmmenta more recently construoted, a triple has been preferred to a qaadmple lopporCh I«per;but tb« MBlevtlm maj be enlarged at pleMtiTe,bf placing tliem liirther apart. B la a conoave (pMulam attacbed to the magnet. c, ft plane glass mirrar also attached to the maenet, for maJdng oleerratioiiB b; a telescdpe. id the old method, when reqaired. p, the toreion plate, readini; to minates bj two Temiera. B, a frame atanding upon the torsion plate. A poliey, capabla of being raised or lowered bj a screw, is attached to this frame ; the mafpiet is anspended bj a skein of ontwisted silk fibres paeaing over this pnlle;. I, a gas-burner eDcloaed in a copper chimnc;, from which no light can escape, except a small pencil which pasaea tbrongh a uannw slit k, capable of being a^jnated by a screw; on the breadth of Ibis alit, the breadth of the register line depends. L L, a frame supporting a combination of two planoHjMTaz cylindrical lenaes. The pencil of light paaaine throngh K, fidli on the mirror a, and ia refiected to the cjlindrical leaaes; by Ibeae, the image of the slit is condenaed to a point of light on the surf"ce of "f- ***- MH, the regislcrine appaiata ' '" * two concentric cjlindera, betwt photographic papvr ia plaoed. e, the maccelic curve traoed light o, a gas-bnmer, fixed to the i the cjlindera mat. r, a plaao-conTBZ prismatio h the lop of qtt, an opaque boi (ben repi line), which prut«cta the pholo« from extraneoua light. A pencil paaaea thrtingh r, and ia brought to ■ tbcus on the nirboe of the paper. b, the base line, deacribed by this point of light. M u, the bifihir, or hurizontal force magnetometer. T T, the apparalUB for producing an automatic temperature oom- pensalion, cuUBJating nf two zinc lubes, which are clamped t<> a glass rod by two ad.jiitible clamps, w; the auspenslon-sliein pMMS over ■ pulley attached to e, and the enda are attached to MAOirSTlC flTOBMS AMD D18TUBB1.1ICS8. 953 two hooks, w w ; as ihe temperatare rises, these hooks are ap- proximated to each other bj a quantity equal to the difference of the expansion of the ghaa rod and the zinc tubes, between the damps, T y, and thus we torsion force is diminished ; the position of the clamps is so adjusted, that the diminution of the torsion force shall be equivalent to the loss of power in the magnet, as the temperature rises (588), and vice versd, when the temperature decreases. The bifilar and its appendages are enclosed in a plate-glass box as a protection from currents of air, as well as from sudden changes of temperature ; and the suspension'skein is enclosed in a glass tube which passes through a stuffijig-box in the Ud of the former; these are omitted in the figure, in order to avoid con- idsion. The declination magnet, with its suspension-skein, &c., similarly sapported and enclosed, is placed at an equal distance on the op- poeiie side of the registermg apparatus, m m,^ and its reflected pencil traces the register-line, a. The register-lines a, e, are traced pa opposite sides of the base-Hne, &, in ofder to avoid confusion. A blackened zinc case is placed over the registering apparatus, when in actual operation, to prevent any light from falling on the paper, except the two pencils which describe the magnetic curves, and another which passes through a prism on the top of the inner case, q q, and draws the base line : in order to avoid con- fofiion, this also is omitted in the drawing. 625. The magnetic observations that nave been for some years past assiduously conducted in various parts of the globe, have re- pealed the occasional occurrence of what have been termed moff- netic itorma; during these, the magnetic elements are subjected to great and violent changes, and a comparison of observations has frequently shown that these disturbances are experienced simultaneously over large tracts of the earth^s surface. A small, but well-marked disturbance occurriog in a photographic register. kept by Lt.-Gen. Lefroy, RA., at Toronto, m Canada, was found to agree precisely in time, and very nearly in amount, with a similar disturbance indicated by the Greenwich register. The disturbances of the dechnation, and of the horizontal force, are usually found to ag^e very nearly both in time and ioi amount, bat the same amount of agreement between the disturbances of ^e vertical force, and either of the former, has not hitherto been observed to exist. The occurrence of Aurora Borealis has invariably been found, both at Greenwich and elsewhere, to be accompanied by consider- able magnetic disturbance ; and especially when brilliant corus- cations are observed to shoot up towards the zenith, large deflec- tions of the declination and bifilar magnets occur simultaueouidy, but discharges of atmospheric electricity do not seem to have any jnmilar e£Eect on the magnetic instruments, for the precise time of A ▲ 854 VAORKTIBM. near and WyTd flashes has been freqnentl/ noticed at Greenwiob^ and no corresponding disturbance is indicated by the register. Flashes of lightning have, howeTcr, frequently been found to destroy, and sometimes to reverse the polari^ of the electric tele- ^ph-needles ; this will be subsequently shown to be due to an intense current nassing through the ceils of wire by which they are surrounded, but it has no reference to terrestrial magnetism. 626. Earth-currenti of electricity have recently been the sub- ject of observation and photographic record at the Royal Obser- vatory, Qreenwich. For this purpose, two insulated telegraph wires of some miles in length are employed, one being nearly in the direction of the magnetic meridian, and the other nearly perpendicular to it One of the terminals of a galvanometer is connected with each of these wires, and the other two terminals with the earth ; the line-wires are also connected with the earth at their further extremities. Whenever derived earth-currents past through either of these wires, the needle is correspondingly affected^ and its movements are traced by a pencil of light reflect^ from an attached mirror, as in the magnetometers. It is fre- quently the case that any considprable earth-currents are found to beaccoinpaniedbycorresjpondingdistuibancesoftheinagnetometers. 627. The intensity of^the action exerted on a magnetic needle by the earth varies remarkabl v in different parts of its surface. As a general rule, that action is less at the equator than at the poles, and is weaker in the warmer than the colder parts of the earth. Professor Hansteen has applied tbe term uchdynamie lines to lines connecting the different parts of the worid which act upon the magnetic needle with equal force. In their position tliey approach the isoclinal lines ^569) already described, although they still more closely correspcna to the lines of equal temperature or i$o4hemud lines. The ma^etic mtensity is greater in the western and northern, than m the eastern and southern hemi- spheres. Hansteen has given the foUowmg values of the terrea- trial magnetic foroe in several localkies. St. Petersburg 1-403 Berlin . . . 1*364 Stockholm . 1342 Paris . » 1*838 London . 1*330 Yienna . 1*325 Madrid . 1*294 Florence . 1*278 Borne . . 1*264 628. The action exercised upon the earth by a magnetic needle is not strictly an attractive, but rather a directive force ; for if a magnetic bar be placed on a cork, and allowed to float on the Bunace of water, it will not traverse the surface so as to reach its northern side, but will remain where it was placed, a line joining its poles becoming parallel to the magnetic meridian. The bar will thus point towards both poles of the earth without evincing any tendency to move towards either. Hence the influence of the earth's polarity on a needle is directivef not aUractive, and may MAOVSnC mTALB. 355 ^.887. ,.--^ be represented bj two eqiud and opposite pAnJlel forces. If a magnetic needle at rest in the magnetic meridian, ab, Fig. 387, be made toaasome the direction oh, the resultant of the forces parallel to ab, wbich act on o, to move it towards ▲, maj be represented b7^ lo, parallel to 1.0. Bat ^18 force maj be resolved f 69) into two others, one, i p, parallel, and another, p o, perpen- dicular to o c : the line p g will therefore represent that part of the force, ig, which is effective in moving o towards a. At the other end, h, of the needle a similar resolution of force will also apply ; the forces acting on the opposite ends of the needle in opposed directions will constitute a eoupU ^81), which tends only to direct the needle o h into the line of tne magnetic meridiai^ ▲ B. This directive action on the needle is alwavs proportional to o p, tAe fine ^ the angle g i p, which the needle makes with the magnetic mendian. 629. If a bar be irregularly magnetised, maffnetio proper- ties may be developed, not onl^ at its poles, but in certain intermediate positions; this anses from an irregular distri- bution of its magnetism, and is generally conuectea with some peculiarity in the structure of the bar, if not in the mode m which it has been magnetised. In such a bar, if placed be- neath a sheet of pastebMurd, and iron filings sifted over it, the existence of its several JPig,SBi, K>les will be demonstrated St the manner in which toe iron filings become ananged. Instead of a single series of curves as in 554, as many additional series are developed as there are intermediate p<^s in the bar ; pointing out the position of what are called consecutive poles. Thus, in Mg. 388, c, (^ are tlie terminal, and a, b^ the consecutive poles. 630. In the foregoing remarks, the only substance mentioned as capable of assuming and presenting maguetic phenomena, is iron. It has, however, been long known that two other metals at least nickel and cobalt, possess a similar property, although in a much less degree than iron. From some researches of Coulomb, however, it appeared probable that some organic sub- stances were obedient to the influence of magnetism. The whole subject has received a vast and unexpected development in the hands of Faraday. This distinguished philosopher foond that when a powerful electro-magnet was employed, the A A 2 350 . KAaSBTISlC. following bodies were acted upon with yrpng Iniennij, and hence they moBt be added to the category of the magnetic metak, iron, nickel, and cobalt. Manganese. | Cerinm. Chromlnm. ! Titaninm. Osmium. Palladinm. Platinum. It was, moreoTor, discovered that the salts of these bodies were^ as well as those of iron, nickel, and cobalt, obedient to the power- ful electro-magnet, when made into bars b^ filling thin glass tubes with them: and even their solutions were similiarT^ acted on. Green bottle-glass, crown-glass, and even a roll of writing-pajper, are at- tracted by the magnet in consequence of their containing iron. ^ 631. tron has oeen shown to be always susceptible of in- duced magnetism, which may be readilv excited by various processes. A bar of soft iron placed in tne magnetic meridian (609), almost instantly, under the inductive influence of the earth acting like an artificial magnet (595), lacquires a low degree of polarity ; if the iron be too close and compact to allow this ready disturbance of the magnetic equilibrium of the bar, a few blows applied at one extremity, to cause it 'to vibrate will, generally, very considerably aid the inductive influence of the earth. A bar of iron heated red hot, and allowed to cool in the direction of the magnetic dip (611), will generally be found to be magnetic, and bare of iron left for some time in this position, or one approaching to it, will acquire a low degree of magnetism: hence pokers, tongs, iron hooks, or other ferruginous bodies, long kept in the magnetic meridian, and especially if at an in- clination of about 70 degrees with the horizon, are always found to be more or less magnetic. A thin rod of iron, as a piece of wire^ may be rendered magnetic, by forcibly twisting it until it breaks. A strong electric discharge will produce a similar effect on a needle, and even, according to some observers, exposure to the violet rays of the prismatic spectrum. 632. A steel bar ma^ be more readily rendered magnetic by various processes, technically termed touche$j all depenaing upon inductive action (595). The simplest mode is to pass one pole of a magnet several times over the whole length of a bar of iron or steel, of course always in the same direction ; the end of the bar last touched by either pole of the magnet becoming the opposite pole. This is usually termed the process of the nngle touch. According to Dr. Scoresby, a largo Fig, 888* amount of magnetism is thus commu- nicated by placing a piece of thin sheet-iron or hoop-iron on the end of the magnet ; he states that a maxi- mum effect may be produced by one: pass alon^ each side of the bar. Another and convenient mode is to jom the opposite poles of two ^ Jf I.I 1 1 I TABIOUB MODSB OF MAOXXTIBJLTIOS, 357 magnets, a, b. Fig. 889| to place them oyer the centre of the bar of Bteel, c, and then to separate ▲ and b from each other, drawine them in contrary directions over o. They are then remoyec^ again placed together, reapplied to c, and once more separated ; and by repeated application on both sides the bar c nltimately acqnires a consideraole degree of magnetic energy. The process of the aeparalU tatieh is somewhat similar to the last, except that the ends of the bar, c, rut upon the opposite poles of two sets of magnetic bars made by fastening three or four together, with their pdes in the same airection. a aod b are, instead of simple bars, similar compound magnets, not lying on the bar c, but eleyated at an angle of about twenty-fiye or thirty d^irees ; they are united, and then separated by drawing them to the opposite ends of the bar o, as in the last described nrocess. 633. In the process of (Epinus, or the double Umekj the bars are similarly placed, as in the $epar(xU touch last described, but the magnetising bars are inclined at an angle of fifteen or twenty degrees, and not separated ; but moved from the middle to the ends of the bar of steel backwards and forwards, commencing and ending the friction in the middle. In Fig. 390, a b is the bar to be magnetised, n « « qaa and fC$\ the fixed ^'^^ magnets on which it rests, and bs, h^s^ the moveable magnets , ^ kept asunder at s h* . ■ "^T — . ■ by a smaU piece of ' *' --^^ 1 I ^ wood: by this process,^' '* ». * rraeaied on both sides, very thick bars may be readily magnetised. The magnets employed in these processes do not give up any portion of their magnetism to the oars, they are used merely to eaoeUe by induction, m the manner already explained (557). 634. An excellent mode of exciting magnetism in bent steel bars is the following, the merit of which is due to Jacobi of Ctesden. Let A B, Fig. 391, be the bar to be magnetised, place it on the table in contact with the poles of a horse-shoe magnet, bs, then place a bar of soft iron on the poles of b s, and elide it over AB, m tne direction ot ine arrow ; then lift it ofij replace it, again ^de it, and so on. After repeating this half adossen times, the friction should be applied to the opposite sides, and the bar will be found powerfully magnetised. Feschel succeeded, by stroking a horse-shoe of steel of one pound weight six times in this manner, in rendering it so powerfully magnetic, that it lifted with eaje twenty-siz pounds and a half. 358 HAOKETX8M. 635. Several ma^ets are not anfrequentlj fastened tpgether, lia 901 ^^^^ ^^^^'^ similar polea in the same direction, '^' * constitutinff a compound magnet, or bcMery of magnet$. In this case they are pecnliarlj fitted for lifting heavy weights, as, hy applying a bar of soft iron, ▲, Fig. 392, commonly called a keeper, to their poles, it becomes, by indoctrye action (595), a magnet, and will adnere to the poles with a veiy considerable force. In con- structing magnets, it is usual to draw, with a file, a line on that end of the bar which it is in- tended to convert into a north pole, or that which, if freely suspended, would point towards the north pole of the earth. 636. The capacity of steel bars, to receive by induction and to retain magnetism, appears to depend on several cir- cumstances. First, the quality of the Aeel has a considerable influence; this depends either on the pxecise quantity of carbon combined with the iron, or on the presence oif some other ele- ments not well ascertained, in very minute quantities ; but it is known that the most powerful magnets may be made from the best Swedish iron' converted into steel. The power of retaining magnetism with undiminiBhed intensity appears to depend prin- cipally upon the uniform hardness- of a bar : and as a thin bar can be more perfectly hardened than a thick one, a thin magnet may, ccBtens paribus^ be made more powerful for its weight tnan a thick one. When a bar approaches to saturation, any concus- sion or even fiiction against a hard substance will diminish its power ; and any elevation of temperature, above the temperature to whieh it hat previoudy been raieed eubeemieiUly to ite mag- netieationj will have the same effect. If the temperature be raised to that of a red heat, the magnetism will be entirely dft* stroyed, and at a white heat, iron and steel become wholly insus- ceptible of magnetic induction. 637. Whenever a steel bar magnet is raised to any tempera- ture not exceeding 100° F. and a little less than that to which it had previously been raised, it is found to suffer a temporary dimi- nution of its power, which it regains when its temperature is again diminished ; and this temporary loss of power is nearly, and has generally been assumed exactly, proportional to the elevation of temperature. It difien considerably in different magnets, but generally bears some inverse proportion to the pennanent intensitj of the magnet, if originally magnetised to saturation. If / be the force of a magnet at 32'' F., then, at any tempera- ture, 32* +0 the force will be /(l-JL.«-B.<«-0.«'-&C.) where the ooef&cienta a, b, &c., must be determined in each par- DSmtlllirATIOV OF MAOHETIC FOBCZ. 859 ticokr case, a has a cle8 round its point of suspension, and took up ita position at right angles to a nne connecting the poles. The position of the piece of ^lass was uninfluenced by revenung the magnetism of the bars, being always repelled by both poles imder all cir- oumstances, so that it might be regarded as a magnet pointing east and west, in relation to the north and south poles of the electro- magnet. If but one pole of the magnet be employed, the sama repulsive action is exerted, although of course with less energy. > 644. To produce the effect of pointing across the Hues of mag- netic force, the form of any homogeneous dia-magnetie body must be elongated. A cube or sphere will not thus point, but two or three {Maced side b^ side in a paper tray win act as a single elon- gated mass. Portions of any shape are, however, repelled ; thus, if two firagments be suspended between .the poles parallel to each other, they appear to attract eadi otheri in consequence of being aimultaneonsiy repelled by both poles. 645. Flint-dass .is similarly acted upon by the magnet, but not so powerfully as the heavy glass. Cylinders of phosphorus, sulphur, and caoutchouc are readily affected by the magnet. A large number of cirstalline bodies as well as ether, alcohol, oils, water, and blood, when enclosed in tubes, were all found to be dia- magnetic, and to be repelled. Animal flesh is thus acted upon ; hence, as Faraday has observed, if a man were suspended nori- zontaUy over the poles of a sufficiently laree magnet,^ ne would be lepeUed, and point across the magnetic field. 862 VA0NBTI8M. 646. Among the metals, the following were found to be most energetically diamagnetie in the order in which they are placed. Bismnth. Antimony. Zino. Tin. Gadmimn. Mercury. Silver. Copper. Bismuth is very readily thus acted upon, and a small har of it^ two inches long, and half an inch wide, is peculiarly fitted for th« exhibition of the phenomena now described. , 647. The fact of salts of the magnetic metals obeying the littractive action of a powerful electro- magnet has been already alluded to (581). In the case of iron, some curious and highly interesting anomalies were observed, evidently connected with the constitution of the salt. Thus the chlondes, iodides, sul- phates, phosphates, chromates of iron, and even Prussian blue, all obeyed the attraction of the maenet, whilst the yellow and red ferro-prussiates of potash, in which the iron does not play the part of a Vase, were repeUed and appeared dia4nagneUe : a fine illus- tration of the rektion between the foroe of magnetism, and the molecular constitution of a salt. Faraday placed solutions of protosulphate of iron in thin glass tubes, and so suspended them that they oould be immersed in glass vessels placed between the poles of a venr powerful electro- magnet. He thus discovered, that when a tube was filled with the solution of iron, and immersed in a solution of iron of the same strength, it was utterly indifferent to the action of the magnet. When immersed in a much stronger solution, it was repelled like a dUtrmafj^neiief and when in a much weaker solution attracted like a magneiU body. Water being dia-magnetic, and sulphate of iron magnetic, a solution can be preparea of such strength as wheo suspended in the air to be abeblutely indi£ferent to the action of a magnet 648. The following list has been given by Faraday as showing a Magnetic . Iron. Nickel. Cobalt Manganese. Chromium. Cerium. Titanium. Palladium. Crown glass. Platinum. Osmium. Oxygen. Azote. Arsenic. Ether. Alcohol. Gold. Water. Mercury. Flint fU Cadmium. Heavy glass. Tin. Zinc. Antimony. Phosphorus. Bismuth. dia^magnetie. SFFBOTB or MAOVETIC POLABITT. 868 gradation of the intensities with which different bodies exhibited magnetic and dia-magnetic phenomena; the bodies at the ex- tremes of the list exhibiting their respectiye properties with greatest intensity. ThaUinm has oeen stated to be strongly dia-magnetic, bnt its Sreciae position in the scale of dia-magnetism has not yet been etermined. It may here be remarked that Prof. Tyndall has obserred that dia-magnetic bodies exhibit dia-magnetism by induction, just ae magnetic bodies exhibit magnetism, when surrounded by a ooil of insulated wire, through which a galyanic current is jpassmg. 649. If any strongly magnetic or dia-ma^etic miid be placed in a shallow yessel, as in a watch-glass, m the magnetic field (554) of a powerful magnet, its properties will be -. ^^ immediately manifested oy the form of the surface. "^ If magnetic, the fluid will be concaye in the centre, and more or less heaped up towards the poles, as A, Fig. 394 ; if dia-magnetic, the fluid will be re- peUed from the maigins next the poles, and raised m the middle point between them, as b. 650. It is really difficult to guess at the limit which may exist to the power of magnetism in controlling or influencing molecular forces. The elaborate inyestigations of Faraday haye opened out a field of rich promise. A force which a few years ago was sup- posed to influence masses of iron only, has been by these researches shown to act upon almost eyery form of ponderable matter. It is perfectly true that Le Baillif some years ago ascertained that pieces of bismuth and antimony acted on the magnetic needle, aiKl that Coulomb made a similar statement regarding many organic substances; but neither of these philosophers followea up their obeeryations, and to our own distinguished countryman is due all the merit of the important discoyeries of which an outline has here been giyen. 651. There are some few remarks on record respecting the in- fluence of magnetic polarity on the reduction of metals, and on crystallization, hitherto regarded as but of little importance, but the discoyeries of Faraday make all such statements now mattera of interest, and render a further inyestigation of them necessary. Berzelius states, on the authority of Hansteen and Maschmann, that when the centre of a U-shaped tube is filled with meroury, and a solution of nitrate of silyer poured into either leg, the re- duction of the silyer and growth ofthe Arbor Diana takes place equally in either leg when they are placed respectiyely east and west. When, howeyer, they are placed parallel to the magnetic meridian, the silyer is reduced in greater abundance in the northern leg. Murray has stated that when iron wires are placed in weak solutions of nitrate of silyer, no change takes place, but the silyer is reduced immediately the wires are rendered magnetic by toringing'near them the poles of a powerful magnet. 36i VAGHXTIBX, Another cnrioQB statement hui been made by Lndecke, tbmt when a glaaa Tessel containing a concentrated solution of salt is allowed to rest on the poles of a powerful horse-shoe magnet, the crystals which form will be collected at the bottom of the glass in every part, except a space corresponding to tbe two poles and the magnetic field between them. Ludecke mentions solutions of acetate of lead and sal ammoniac as readily exhibiting thitf Shenomenon. This might be explained by regarding them as ia-magnetic, had he not also stated that sulphate of iron pr&> sented the same effect, which salt^ being magnetic, would not permit of the same explanation. A somewhat contrary phenomenon has been observed by the writer. A large bar-magnet was suspended for three weeks in a water-bath, and a long cylindrical bulb of a thermometer was placed in the same bath, and very near to one extremity of the bar ; a ring of oxide of iron was so firmly deposited on that part of the bulb which was opposite the extremity of the bar, as not to be capable of being wiped off by a cloth. 652. Several phenomena have been observed in cr^tallized bodies, afpareiuLy contradictory to the general magnetic, or di»- magnetic character of their elements ; these were ascribed hj Pllicker to a repulsive power inherent in the optic axes of the crystals ; and by Faraday, to a modifying influence of crystalliza- tion on the direction of tne mimetic axis, to which he has applied the term magne-crystallic axis. These observations have, now- ever, been brought within the scope of a eeneral law deduced from the investigations of Prof. Tyndall and M. Knoblauch on this subject. 653. The general law is this : — That if ike parijdea of which a moM contUU are more doeeL^ aggregated in one direction than in any other ^ that line of directum vnu, when free to do so^ tcAe an aanal or trantverte position in the magnetic jidd^ according as the tody ie magnetic or dia-magnetic, whether the line of greatest density corresponds with the longest dimension of the mass, or otherwise. Tnis very important law may be elucidlated by experi- ment. The method pursued by Prof. Tvndall has b^n to reduce various substances to powder, to make them into a stiff paste with gum-water, or other adhesive matter, and having compressed the paste into the form of a thin flat calce, to diy it under continued pressure. In a mass thus artificially prepared it is manifest that the lines of greatest density must be all perpendicular to the plane of the cake. Brick-shaped masses should new be cut from these cakes, of the relative dimensions 3, 4, and 10, for example, the greatest density being in the direction of the least dimension. If these be successively suspended in the centre of the magnetic field, with the direction of maximum density vertical, and there- fore perpendicular to the lines of force alike in all positions, then the long dimension of the mass will take an axial position, if it be DlBBCnOH OP 9B&iTBST XBEBOY. 865 magnetic, as, for instance, if made of carbonate of iron, and a transverse position, if it be dia>magnetic, as one of bismuth. But if the masses be suspended with their greatest and least dimensions both in the horisontal plane, then the superior inductive action in the line of greatest density will overcome the leverage of the lazger dimension of the solid, and the position taken up will be the leverse^of what it was in the former experiment, and (mparently in opposition to its magnetic or diarmagnetic property. Ii the len^h of the mass be considerable compared with its other dimensions, as, 3, 4, and 30 or 40 for example, the length of Veterage will then sensibly oppose the influence ot greatest density and the mass will take an intermediate position, wmch is, in fact, a jesultant of two conflicting forces. If a rhombohedron (24, V) be cut from the carbonate of iron mass in such direction that tne axis of the rhombohedron coincide with the line of maximum density, the artificial solid will comport itself in the ma^etic field exactly as the similar natural crystal^ from the pulverisation of which it may have been derived. The above results afibrd a beautiful illustration of the manner in which, the simplification of first principles invariably follows the advance* meat of scientific knowledge. 36$ CHAPTER Xn. Fig. 996. FRAHKLnrio* ELBcrnucmr. 654. If a large glass tube, previoasly made dir and wann, ho briskly nibbed, tor a few seconds, with a piece of silk or woollen cloth, also dry and warm, and then held near small pieces of jMiper, pith, or cork, placed on the table, these light substances will be attracted by the excited tube, and leap towards it. After adher- ing to its surface for a short time, they will be repelled towards the table, after touching {which, they will be again attracted by the tube ; and these phenomena will be repeated, until the properties excited by the previous friction on the surface of the glass disappear. A piece of amber, sulphur, or sealing-wax, after exdtation oy a woollen cloth, will exhibit the phenomena of attracting light bodies, like the ^lass tube. 655. Suspend a light ball of pith of elder by a long silken thread from the ceiling, or any con- venient support. Fig. 395v and anproacb towards it an excitea glass tube; the ball will be attracted, and, after adhering for a short time to the tube, will be repelled to a considerable distance, nor will it be again attractea until it has touched some substance connected with the earth, and has thus lost the peculiar properties it had acquired by contact with the tube. Then bring towards the pith ball thus repelled by the tube, a piece of sealine-wax excited by briskly rubbing with a piece of diy flannel, the ball will instantly be attracted, soon however becom- ing repelled, when it wiU rush ^ward the glass tube, if held suf- ficiently near. It will thus vibrate like a pendulum between the excitea glass and sealing-wax, being alternately attracted and re- pelled by each. 656. From these simple experiments it appears that oertaio bodies acquire by friction properties which they did not previously exhibit, but which properties are readily manifested by the attrao- • Thit term wsa first applied by FundAj, in contradistinction to Toltaio, and in commemoration or the illostrions Franklin, who was one of tiie earliest experimenters in electrical science. ooin>vonov ahd ihbulatiov. ^67 tlm kad. repolniDii of light bodies. As these phenomena werer fint obBenred hy Thales, b.c. 600, in pieces of amber (^Xv), the term eUetrieUy has been applied to the properties thus excited^ It appears also, from the observations jnst made, that the elec- tricity excited bj friction on the sorface of glass is communicated to pieoee of paper, or pith balls, placed in contact with the glass, ana that the hodies thus acquiring electricifj are repell^ by the tube until they have changed their electrical condition by contact with some other body ; and as, when thus repelled by ex- cited gUss, the ball is attracted by excited resins, there is valid reason for concluding that the electricity developed on these sub- stances by friction exists in opposite states, or conditions. That which is acquired by excited glass is termed the vitreous, or posi- Hve electricity, and that excited on amber, and resins, the retinofUf or negative electricity. It appears, moreover, that' hodies in one electriecd Hate are attracted hy thoee in the oppo- site, and repelled hy those in the same sUOe, A substance ex- Ubiting electricity in an active state, or as it is now commonly called^ j^otential electricity, is said to heeUetrified positivdy, if its electricity be positive ; and negatively , if it be negative. 657. In consequence of the sealing-wax, glass, &c.. in the pre- ceding experiments, acquiring electricity bv friction, tney are said to be idiodeebriCj whilst those not ordinanhr manifesting this pro- perty, as metals, are termed anelectrics, from the general law of JFV.896. TT I Dodios similarly electrified repelling each other, arises a very convenient mode of de- tecting the presence of free electricity. For this purpose, instead of a single pith ball (665), two are attached to the ends of a piece of thread, and suspended by the middle across a fit support, cut off from all ekc^cal communication with the earth, by means of a pillar of glass or resin. Fie. 396. On touching this little apparatus with the excited tube or sealing- wax, electricity will be communicated to it, and the balls, being similariy electrified, will repel each other, and separate to a con- siderabfe Stance, forming^ the simplest kind of electroscope, or indicator of potential electricity. 658. Insert into either end of a hollow metallic cylinder c, Fig. 397, supported by a glass pillar, a wire or rod of some metal, as brass, B, and one of glass, shell-lac, or sealing- wax, A ; and suspend from each a pair of pith balls, attached to thread or cotton. Then touch the middle of the cylinder, o, with an excited glass tube ; immediately the pith balls suspended fit>m the brass rod b, will separate from f- Fig.ZVr. n 368 FHAlfflfLTlfflO KLBCTBICITT. each other, whilst those stispended from the glass, jil, will retbam un- affected. This arises from the fact of certain bodies, as metals, cotton, thread, &c., possessing the property of conehuting elec- tricity^; whilst others, as sealing-wax, glass, silk, &c., are incapable of being freely traversed by it. On this account, bodies nave been divided into two great groups ; conductors and nonrconduo- tors of electricity f the former Ming in general identical with aneileetrieSf and the latter with idioelectrics. The line of de- marcation between these two great classes is h^ no means strictly defined, as a large nomber of substances exist which conduct electricity when presenting greskt energy, and insulate it when feeble ; or the conducting powers of which vary with their tempe- rature. Electricity is not recognised on the surfeoe of metaUio bodies submitted to friction unless carefully insulated, in conse* quence of their so readily transmitting electric force, that the BurfisMse-ezcitement is diffused through the substance of the metal when continuous with any conductor, as fast as it is generated. 659. Among conducting bodies may be ranked all metab, char- ^al, water, steam, all animal and vegetable substances containing water, and manj other substances : whilst glass, and all vitrifica- tions, gems, resins, sulphur, organic substances perfectly free from water, and ice, are all more or less perfect non-conouctors and idio-electiics. A substance supported by a non-conductor, as when placed u^on a stool with glass legs, is said to be insulated^ fit>m its electric communication with the earth being intercepted. 660. The capability of electrical excitation appears to be an universal attribute of matter. Electricity may be aeveloped either by friction, or by many other mechanical and chemical means : but whenever one body, in consequence of either of these means being applied, manifests the presence of electricity, some oUier body simultaneously shows the presence of the opposite kind of electricity ; if the first becomes positive, the secona becomes nega- tive, or vice versd : thus in the experiments previously mentioned, when the glass tube is positive, the silk muber is equally nega- tive ; and when the stick of sealing-wax is negative, the flannel rubber is equally positive. It will be found better to abandon the terms vitreous and resinous, inasmuch as the electricity of glass depends on the nature of its surface : if rough, as by grinSng, the electricity developed is of the kind called resirumSf and there- fore, that teim is not distinctive. The two forms of electricity, although possessing some disUne- tive characters, produce generally the same physical effects, the amount of effect produced depending on the relative difference of electrical condition, or potential energy^ as it has been termed, in the agent and the body acted on. 661. Electroscopes, — Instruments designed to exhibit the presence and kina of electricity, without reference to its potential energy, are called electroscopes; these are constantly called i|i requisition, in prosecuting the study of electrical science. ELEOTBO0OOPE8. 369 Hie pidr of pith balls already described ^» 398. (657) is finqoentlj called bj this name, and employed to detect the presence of electric potential. As the currents of air always m motion render the indications of the pith balls obscure, they are frequently eitspended by linen threads, or fine wires, from a metallic rod fixed by a resinous cement in the neck of a glass bottle or cylinder, a, Fig. 398, and surmounted by a metalfic plate, b. ^ On touching the top, b, of the apparatus with an excited piece of glass or resin, the electricity is difliued along be metallic rod, c, in consequence of its being a good condactor, and reaching the pith balls, they, becom- ing similarly electrified, repel each other (656], and by their mntual repulsion the presence of electricity is mdicated. The electricity does not escape from the rod, c, to the earth, in conse- qaenoe of the glass jar supporting it being a non-conauctor, and If the outside of the glass vessel, in which the pith balls are sus- pended, be moist, they will still more rapidly lose their electric state, in consequence of their potential energy being conducted by the film of moisture to the earth. For this reason it is absolutely necessary to carefully dry the exterior of the glass vessel, in order to ensure the success of an experiment. To prevent the deposition of moisture on this as well as on all other electric apparatus, it is usual to cover the upper ^art of the glass externally witiii a solution of shell-lac in alcohol ; this, on drying, leaves a nearly transparent covering of an excellent insulating substance, which is much less liable to attract moisture from the air than the nncoated glass. 662. The best electroscopes are generally furnished with a con- trivance for rendering the insulation more per- ibct. In this arrangement the metallic rod to which the pith balls are attached, passes through a glass tube, a, Fig. 399, covered both externally and internally with lac var- nish ; this rod is retained in ite place at b by a plug of silk, lac, or other non-conducting sabstance ; the advantages of this contrivance are sufiiciently obvious, for it is evident that any electricity communicated to the plate o, cannot be dissipated excepting through the unless the whole of the interior of the Jl^. 300. C air, tube. A, and the outeide of the apparatus, be- come covered with moisture. The late author c J B B 370 FRANKLXVIO ELSCTRIOITT. repeatedly found such an instrament perfectly sensitiTe to mera traces of electricitVi after having remained nnnsed, and even coyered with dust^ during six montns. When it is required to detect minute qoantities of electricity, the weight of the pith balls in the first described electroscope in- terferes with the delicacy of the instrument ; on this account two slender slips of leaf-gold, hangine parallel to each other, are with great advantage substituted for the pith balls. Two slips of tin-foil, d, d, are usually fixed alon^ the inside of the glass case of the instrument, so as to touch its base, which must be of metal, or some good conductor. On communicating electricity to such an electroscope, the gold leaves separate, and, if the electric charge be too powerful for tne tenacity of the slender laminae, by approaching or touching the slips of tin-foil, they become readily unelectrified. 663. An ingenious mode of determining the quality of very feeble charges of electricity has been devised by Dr. Radcliffe. For this purpose two similar gold-leaf electroscopes are mounted on glass stems 10 or 12 inches long, one of which is thoroughly coated with a solution of shell-lac. If these stems be slightly excited by friction, and the caps be placed in connexion witn the earth, the two pairs of ^old-leaves will become charged by induction (676), with opposite kinds of electricity: if now a feebly electrified body be placed in contact with each cap in succession, the divergence of the ^old-leaves will be sli^tly increased in one instrument, and dtminished in the other, and thus the quality of the charge is determined. By these instru- ments manifestations of electricity have been detected in the living body, sometimes positive and sometimes negative: and likewise in fresh blood, as from an animal just slaughtered. 664. JSlectromet&rs. — The instruments above described, merely indicate the presence^ and not the precise qwaWtUy^ of electricity present in any substance in an active state. Tor a mode of gaining an approximation to the knowledge of the Quantity of electricity we are indebted to the torsion balance of M. Coulomb. It con- sists of a slender bar, b. Fig. 400, formed of melted shell-lac, fur- nished with a gilt pilh b^ill at one end, and a little vane of gilt paper at the other. This is suspended by a fine metaUic wire, c, or still better, by a filament ot spun glass, in the middle of a cylindrical cage of glass. The upper end of this wire, or glass thread, terminates in a key, d, furnished with an index, and capa- ble of moving in the centre of a circle, o, graduated into 360^. Through a hole, e, at the top of the glass cage, a rod of lac, f, terminating in a gilt ball, is inserted ; being prevented falling in by a stop at e. This ball is generally termed the carrieritdl^ on account of its being used to convey the electricity of an ex- cited body, to the electrometer, so that its potential may be deter- mined. To use this instrument for measuring the amount of olectricity, the rod r » nmiorad, and iM b«H bronght in contact with tlMiubgUucs to be exniniDed ; the ball srajuires >oma actiie electricitj, aod on being placed in the glaai cage, it shares its electricit; with the ball terminating the horisont^ needle, b : the two being similarij electri- fied, then repel each other, and as p i« fixed, ■ necesBsrilT mores, and describes a certain angle, wbich it ret^u antil it low* iU eleetridt;. To measnre the amoant of energj thus acquired bv tha b*lla, tbe ke; i>, to which the glass thread c is factaned, is tamed ronnd, until, by tbe tonioD, or twisting of the thread, tbe ball of B is compelled to come fn contact with that of r : then tbe nomber of de- grees described by tha index fixed to the leTolnng ke1. 9 on tbe tame principle as the preceding, namely, that the amount of lension is delennined by the amount of repnlBion of two bo^es similarly electriSed : but the constnictioa in somewhat difierenl. A central metallic stem terminated abore by the ball P, Hg. 401, ia eSectnally inaulnted by the vul- canite haae to which it is attached. Ttii* stem is perftirated at a, to allow the paewge of a bent wire c D, to the centra of which a small maenetised Deedle is attached, and bou are poised on a fine »lael point beneAth e: thus od acquires a ■mall direclive force. Two rods with balls, 1, B, at their extremities, ' are fixed parallel to saoh other into tbe lower part of tha stenL so that tbe ends □, d, may be both nearly in oontacl with a and b respectively. The instrument is so placed for use, that OD may be in the magnetio meridian, and also in contact with ab. It is sometimes found de- sirable to place cj> in cloee prox' BB 2 imity to A and b, bnt nnl in actual cootact. id aiiti U> prercnt adhedon. If anj charged bod; b« now brought into contact with P, a cbai^ will be aimultaneonBl; cominanicated to A ■ and o d, and tb« antonntof rapnlsion will be a meamreof ita teoiion. Thia instrnment it highl; Mnritint, and ver; conTcniant. 666. Tlotnaon'f Eledrom^er. — Thii inatnulient ia cotutmcted on the principle that if two indefinite panllel pianos be un- eanaliv electrified, the rapuliinn of n email portion of one fran Ibe otber will be ioTerael; as the diatance betwOen them, and not iiiTeraelj ae the aqnare ol' that diitanoe, which ia atrictl; the caaa odIt when the extent of the electrified inrfacei ia amall ccanpared with their dUtattce : thia may be readiij prored bj analfiU. JVd tnt '*' "' ^^' ^^' "^ ^' **° eepantel? inn- Uted plane*, of which a maj be reached throogti the coTcied apertnra c, bj removing ila cap, and A ii in metallio conneiion with a central pillar, on which the op, d, alide*. When the cap ia cIom down, it ia in contact with the ciQler braas caae of the inatrnnwnt, ■nd thna the plate is placed in conneiion with the earth. When the cap J* raiaed, it i« in- ■nlated from all except tfae cap, a. In the middle of a ia an aperture neariy filled b; a plate E, which ia in one piece with a amall ■creen r ; and the pieco aria balanced im a atrettbed wire placed beneath b, the airection of which hum* throogh (he centre of gravity of the piece ; and it is so balaDoed a finewire Bird in front of it._ In order that the plale_ .__, keep its charge, the interior air ia kept dr; b; some pieoea of pnmice moiataned with atrong aulpbnric acid, contained in a leaden box in the npper part of the inatmment: Ihia is not ahown in the figure, which must be considered not aa an exact rcpreaent*- tion of the inilniinent, bnt mere!; aa a diagnun to explain ita conEtructton. The plate a ia raiasd or lowered b; a micromoter screw bj mrana of a dinded plate o, placed above the cover of ■he inatmment. When both plates are charged, and the index r ia brongbt into crate pap«n of Faraday. In the PhikMophioal TnoMotiou for 18S8, should be oonaoltcd, espeeial]|y % Utt-Ttl. IHDUCnON TNFLTJSNCEfl ALL IKTBRTEHIRO MATTEB. 381 electricitj of which was affected by its action ; bat it mast not be aasamed from this, that the disturbance of the natural electric state of the conductor arose from an action at a distance ; for most satisfactoiy evidence has been adduced by Faraday that the intervening dielectric air has its particles acted on in a manner analogous to those of the conductor c d, Fig. 405, by the inductive influence of the charged globe. The theory of induction depending upon an action between contiguous molecules is supported by the fiict, which would be otherwise totally inexplicable, that a slender rod of glass or resin, when excited by friction and placed in con- tact with an insulated sphere of metal, is capable of influencing the latter b^ induction most completely, even at that point of the ball which is most distant from the roa, and, conRequently, inca- pable of being connected with it by a right line not passing thmugh the ball. Faraday excited negatively a cylinder of shelMac an inch in diameter, by ^' ^^* rubbing it with a piece of warm flannel ; and @) placed on its top, which was cut concave for the •"'^^^s. • pmrpofle, a lai^ge brass ball, a, Fi^. 406. It is <^f \ ohvioas that a molecular perturbation of this ball ^^1 ] most be created by the inductive influence of the ^-^ V J excited lac, as its lower half becomes positive, ^y p^- — ^ and the upper half, negative. If, then, a be tOQched with the finger, the negative electricity /^ is discharged, and the ball remains positive, like V> the cover of an electropborus (686). If the canier-baU (664^ of Coulomb's torsion electro- meter be placed m any of the various positions shown by the figured circles in Fig. 406, and then returned to the balance, the force of torsion required to re- store the horizontal beam of the instrument to its proper position, will give the inductive force exerted by the lac-cylinaer. Wher- ever the carrier^ball is placed, both it and a must be first uninsu- lated, and then insulated, before removing^ it to the electrometer. The numbers in the cut snow the comparative amount of inductive influence exerted by the cylinder in different positions. Thus, at the top of the ball, a, the carrier-ball received a charge of positive eleotricity of 130** by induction from the cylinder. So tnat we must either consider that induction is exerted in curved lines, or propagated through the intervention of contiguous particles. New, as DO sinffle force can act in curved lines, excepting under the coercing influence of a second force, we are compelled to adopt the view of induction actingthrough the medium of contiguousparticles. 682. This inductive action appears to be manifested in every electric phenomenon : thus, in the simple experiment of attracting fight bodies by an excited tube (654), the positive electricity on the tube acts hy induction on the jsieces of oaper, rendering their surfaces opposed to its action negative, and tnus they are attracted 382 FBAMXLINIC BliBCTRXOITT. J^. 407. b^ the tube, in obedience to the law of motual attraction between differently electrified bodies. The following experiment illnstratea in an interesting manner the development of electricity by indno- tion. Let a pane of dry. and warm window-glass be supported about an inch from the tame by means of two books or blocks of wood, B, B, Fig. 407 ; and let several pieces of piper or pith-balls be placed oeneath it. On exciting the upper surface by friction with a silk hsiid- kerchief, this acts by induction on the lower surface of the glass, the intervening dielectric becoming pola- rized in the manner alreadjr expiauied. The lower surface of the glass, thus becoming electrified by in- duction through its substance, attracts and repela alternately the light bodies placed beneath it in a sunilar manner as the excited tube (664--656). 683. All cases of electrical repulsion are in reality referable to attraction under inductive influence. Thus apparently the two slips of gold leaf, similarly electrified, repel each other; thia repulsion, however, is really the effect of the attraction of sor- roundiuK bodies of which the electric equilibrium is disturbed by their inductive influence : their inner and opposed surfaces do not manifest any free electricity. 684. Induction takes place through a thin plate of a perfect con- ductor, as readily as through a non-conducting dielectric. A thin piece of gold leaf may, by the inductive power of an excited electric, become intensely positive on one side, and as powerfully negative on the other, as long as it is within the influence of the inouctive body. 685. Tfie lUlectrophonu, — ^Into a circular tray of tinned iron or zinc, a, Fig. 408, about eight or ten inches m diameter and one inch deep, pour a mixture of two parts of shell-lac and one of Venice turpentine, until it is rather more than half filled, and let it cool graaually. A circular plate of stout tinned iron or brass, c, about two inches less in diameter than a, is furnished with a glass handle, b, fixed into its centre. Remove the metallic plate from the resinous cake, ▲, and excite the latter by friction with a warm and dry piece of fiannel; then place on it the plate c: under these circumatancee the negatively electrified cake rendere the under side of the plate, c, positive, and the upper side ne^tive by induction. If then c be lifted off by its glass handle, it will be found destitute of tree electricity. Keplace c on a, touch the former with Fig.4M. THB BLE0TBOFH0BU8. 383 the finger, aod its negative electricity, excited by the indoctiye influence of ▲, will ^ transmitted to the earth ; then let o be raised, by the handle, b, and it will be fonnd to exhibit a charge of positive electricity, which will be discharged, on the ap- proach of any conductor, in the form of a yivid spark, the plate resuming its naturally neutral state. Again, jplace o on a, touch it with the fin|B;er, negative electricity a^n escapes to the earth ; lift off c, bring any conductor towards it, and another spark of poeitiye electricity occurs. This process may be repeated an almost indefinite number of times, the cake ▲ losing none of ita electricity by the operation, as it acts solely bv its inductive in- fluence on the metallic plate d. Indeed, alter being once excited, a spark may be obtained from this inHtrument, during many weeks, without any fresh excitation, and on this account it haa been used as an electrifying machine, and was by its inventor, the celebrated Volta, termed eUdbrofcro perpetwy. This deetro- phoTus is a most valuable instrument, not only from its affording a beautiful illustration of inductive action, but from its yielding a targe supply of electricity. 686. A small electrophoms, about 2} or 3 inches in diameter, ia a veiy convenient instrument for charging various experimental ap- paratus, such, for example, as Profl Thomson's Electrometer (666). A disc of vulcanite, or ebonite, is an exceedingly good material for the induction plate, as being both durable and highly excitable. If the surface of the vulcanite plate be connected by a pin with the metallic cell into which it is inserted, the trouble of touching the insulated plate at each induction is saved, as the negative electricity passes through the pin to the earth. 687. A veij useful modification of the electrophoms is made by coating a thin pane of glass on one side with tin-foil to within about two inches of the edge. Placing it with the coated side on the table, excite the other surface by friction with a piece of silk covered with amalgam (693), then carefully lifting the glass br one comer, place it on a badly-conducting surface, as a smooth table or the cover of a book, with the unooated aide dotontoarda. Touch the tin-foil with the finger, then carefully elevate the plate by one comer, and a vivid spark will fiy from the^ coating to any conducting body near it ; replace the plate, touch it, again elevate it, and a second spark will be produced. An electric jar may be charged, in a few minutes, with an apparatus of this kind only four inches square. This modification of the electrophoms is a most convenient instmment in the laboratory where electricity is required for eudiometric purposes, and where the introduction of an electric machine is inconvenient. 688. If a given amount of electric potential be communicated to a surface exposing sixteen square inches, and a similar amount be communicated to another of but four square inches of surface, it is obvions that each square inch of the former will contain but ^Si psAHKiJinc BLBOTRicrrr. one«fonrth of that present in eyery square inch of the latter; hence, although the amounts of potential are alike in both, yet BSf in the former, that energy is distributed over four times as much surface as in the latter, there will he found so much less power of producing the phenomena of attraction and repulsion,, induction, or light. The potential of the smaller sur&ce, is con-* sequently said to be gp^ater than that of the larger. 689. A rounded surface, as a brass knob, on being held near to an electrified bodf , allows induction to take place with much lesv facility than a pomted wire similarly situated, on account of the inductive action being concentrated on a smaller surface, causing thereby a greater electric energy on the surface pf the point, than on that of the knob ; for this reason, whilst a rounded surface may be brought within an inch of an excited tube without abstracting much of its free electricity, the point of a sharp needle, held at four times that distance, will almost immediately effect the transmission of all the electricity present on the tube. For this reason, all kinds of apparatus destined to retain electricity, are terminated by knobs or rounded surfaces ; and those intended to facilitate its free and rapid transmission are furnished with points. Similarly it is eyident that an electrified sphere has its electricity equally diffused oyer its surface, whilst, in the case of a prolate spheroid, the greater quantity is found at the ter- mination of its long diameter, and of a cube, at the apices of its solid angles. 690. With the exception of the electrophorus (685), no in- strument for furnishing large (Quantities of electricity has yet been described. The first machine constructed for this purpose was contrived by Otto de Guericke, of Magdeburg ; it consisted of a globe of sulphur, turned by a winch, and submitted to the friction of the hand. Improvements were yery gradually intro- duced into its construction : first, a globe or cylinder of glass was substituted for the sulphur, and then the silk rubber was used, in lieu of the hand ; the last great addition consisted in the adapti^ tion of a metallic conductor, so as to expose a large surface to the inductive influence of the excited glass. The revolving glass electric was used by Hawksbee in 1708, the rubber and conductor being introduced in 1741 ; Boze, of Wirtemberg, contriving the latter, and Winkler the former; thus rendering the electrical machine nearly complete. 691. Two forms of the electrical machine are used in this country, differing firom each other in the shape of the revolving electric, which in one is a cylinder, and in the other a circular plate of glass ; each varying in diameter from eight or ten inches to two feet, beyond which size it is inconvenient to use a cylinder, but plate machines are made of three feet, or more, in diameter. The best form of the cylinder machine consists of a cylinder of glass, levolving by means of a winch, between two upright pieoes 385 «f itoatuid well-dried wood, a, i, rig.tca. Vig. 409 : thU ii aubmiCted to tha fiictiDD of B rubber, fanned of u olilaiig piece of wood, p, about tbrei or four iaches (barter thari the Cjlioder, covered witb leather, fbrnuhed wilh a (Up of gilt, b, tendiiig over oesrlj' half the circ ference of the glue. The rubber caa be placed at any distance from the cylinder, supported by a Btroug S'ua pillar, and connected with a diog foot of wood, filed bj means of B screw. On the side opposite to the rubber is a cylinder, t, of hollow tiiiDed iron, or, what is MTsred with tin-foit, and about three or four in . this is termed thepriTM condtictor; it is, like tbe rubber, insulated on BgtasBleg. Tbe aide of the conductor neit to theglssec;liDder b fumiahed with a row of pointed pieceH of wire, to allow of its mora ripidlj aojuiring an electric state from the reToliing indue- tire glass. This piece of the apparatus baa a number of holes, of variooB diameters, bored in it, to permit the insertion of wirea of various aizea ; the moutha of these holea, as well as eTer; other part of the condnctar, except the poiots already mentioned, must be carefnlly freed from all sharp edges or prominences, which cause a rapid diuipatiou of electricity (669}. 69!. Tbe plate machine consists of a circular pbte of thick ^lass, revolving vertically, by means of a winch, between two upnghit, A, 4, Fig.410; two pairs of rub- J^.iio. ben, formed of slips of elastic wood eorered with leather, and fhrnisbed wilh silk flaps, are placed at two equidiatanC portions, b, b, of the plate, their preuiiTe upon which may be increased or diminished by means of brass screws. Tbe prime conductor consists of two curved arms of hollow brass, supported horizontally by a glass pillar from one of the uprights t. ; its anna, | where they appnHch the plate at c, c, are funuBhed with pomfs, for the same reason as in the cylinder machine. Great advantage is gained by causing a row of metallic points, ootinected with the prime condnclor, to be presented to both sur- fitces of the revolving plate, instead of to one only, as in Ute ■ "■- if theii « machines. 886 FRANKLIMIO BLBCTBICITT. It 18 very difficult to give an opinion of the oomparative merits of these two machines, — for an equal surface of glass, however, the plate appears to be the most powerful ; but it has one ^reat inconvenience, viz., the difficulty ot obtaining ne^tive electricity from it, in consequence of the uninsulated state of Us rubbers: some plate-machines are, however, specially constructed for thiH purpose. 693. When an electrical machine is required for use, it should be placed within the influence of a good nre, so that its several parts may become dry and warm. The rubber and conductor are to be removed, and the plate or cylinder rubbed with a piece of flannel, dipped in oil, until it becomes quite clean and bright ; the layer of oil thus left, bein^ removed with a linen cloth. The rubbers are then to be made quite dry, and their silk flaps wiped clean ; a little amalgam made into a soft paste with lard, to be spread over the surface of the cushions of the rubbers, unless there happens to be plentv left on from a previous experiment, in which caae the suiiace is to be cleaned bj[ rubbing it with a piece of rough brown paper, or by scraping it with a knife. The rubber, or rubbers, are to be then applied, and by means of the a<^u8tinK screws, made to press with moderate force against the surface of the cylinder or ntate. On then turning the winch, and holding the hand towaras the revolving glass near the lower surface of the silk flap, the electric discharges will be felt between the hand and glass, like a brisk wind, attended by a crackling sound, and in tne dark, by a lambent blue flame, 'rhe prime conductor is next placed in such a manner that its points stand about one-eighth of an inch from the glass : on holding the hand towards it, whilst the winch is being turned, vivid sparks, often some inches in length, oppear ; these are attended by a loud snapping noise, and on striking the hand, produce a pungent pricking sensation, some- times causing a papular eruption on the skin. These sparks, and all similar visible manifestations of the existence of electric potential, are produced by the induction of the electrified on the approaching body, through the medium of the intervening atmo- sphere. Whenever the transmitting medium is, like the air, a bad conductor, that is, incapable of freely transmitting the electric form of molecular action, a portion of that action will be manifested in other forms, namely, those of light and heat. Whenever the amount of potential in the excited body is larse, induction on the atmosphere alone will take place, accompanied by a more diffixsed luminosity, in the shape of a brush. 694. During the excitation of electricity by the machine, and indeed in other cases in which luminous discharge (619) takes place, a peculiar odour like that of phosphorus is evolved. This odour has been traced by Professor Schonbein, of Bale, to the formation of a substance termed by him (wone, and which is now known to be an allotrapie form of oxygen, possessing some moet peculiar and characteristic properties. ACTIOS OF AMALGAM. 887 695. The deTelopment of potential electricity apon the prime (K>nductor is so intimatelj connected with the theory of induction already explained f677), that the remarks there made will he suf- ficient to remove all ohscnrity as to the mode in which it is effected. On rotating the glass plate or cylinder, a molecular disturhanoe takes place at the points of friction between the rubber and the flass, m consequence of which the surface of the glass is rendered ighly posit iye, and the rubber equally negative. The excited suHaoe of the glass is covered with silk (which is frequently var- nished) to prevent its potential energy from being dissipated by induction on the surrounding atmosphere, until it reaches the row of points already mentioned, when the chief part of that energy is expended in polarising, by induction on the points, the molecules of the prime conductor, which becomes strongly positive, especially at those parts farthest from the glass, whilst the metallic comb is negative, so long as it is under the influence of induction. The prime conductor being insulated, it soon acquires so high a degree of potential energy, that it is incapable of acquiring more, until a portion of that energy is expendea in induction on neighbouring Dodies, or in transmission through a conductor in contact with it. Similarly, the rubber, if insulated, soon acquires such a degree of negative energy, that its action on the glass ceases, but if con- nected by a conductor with the earth, or with any large mass of conducting matter, the acquired energy is constantly expended on the conductor, and the action of the machine continues. Just so. if a body be exposed to a continual source of heat, as a ball of metal anspended over a gas-burner, it will become more and more heated until a point is reached, at which the heat is dissipated by radiation as fast as it is acquired, when no further elevation of temperature can take place. But if a good conductor of heat be now Drought into sufficient contact with the heated ball, its temperature will immediately be lowered, and cannot again be raised to the same point, by the same accession of heat from the supposed source. From what has been stated respecting the nibber, it is evidently necessary that it be connected by a good conductor with the earth ; for this purpose it is best connected by a wire or chain with the water- or gas main of the house. 696. Much discrepancy of opinion has existed concerning the modus cigendi of the amalgam applied to the rubber ; it certainly acts yeiy powerfully in increasing the excitation of electricity. The best combination for this purpose consists of two parts of zinc and one of tin, melted together, and added to six parts of mercury, previously heated in a crucible : the mixture bemg stirred until cold, is readily reduced to a fine powder, which requires merely to he formed into a paste with lard, to be ready for use. It has been, with Kood reason, supposed that the oxydation of the amalgam, by the friction employed, aids at least the increased excitation; for #in>RJgaTnii of gold, and other difficultly oxydisable metals, do not cc2 388 FKAHKUSflC BLECTBICITT. appear to increase the development of eleotricitr. In accordance with this view, Dr. Wollaston found that an electrical machine, when worked in an atmosphere of carhonic acid, gave no evidence of electricitv : the accuracy of this statement has however been questioned by later observers. One mode in which the amalgam acts is certainlv by affording a soft cushion of good conducting matter, which thus presents an excellent surface for inducing elec- tricity on the revolving glass. Instead of an amalgam, the bisulphide of tin, or aurum musivum, as it is often called, may be rubbed upon the cushions of the machine, and with similar results. This latter substance acts probably like the amalgam, by undergoing oxydation, as bv fric- tion it absorbs oxygen, and is partiaUy converted into bisulphate of tin. In a similar manner also iron pyrites, by friction, is partly converted into sulphate of iron. The chemical influence of fric- tion, indeed, is more energetic than is usually supposed; even siliceous minerals, as mesotype, basalt, and feldspar, oecome, ac- cording to Becquerel, partly decomposed, giving up, when long triturated in a mortar, a portion of their alkali in a free state. When the prime conductor is connected with the earth, and the rubber of the machine insulated and connected with a second prime conductor, sparks are seen on approaching the hand, or other conductor, towards it ; these are termed sparks of negative electricity, and as in the case of sparks from the former prime conductor, they arise from the opposite polar induction of the rubber on the neighbouring conducting body. 697. Ebonite or vulcanite, which is a mixture of sulphur and caoutchouc submitted for some hours to a much higher tem|>era- ture than that required to form the ordinary elastic vulcanised caoutchouc, is an excellent material for the disc of a plate-machine ; being, however, soil, compared with glass, it requires a much softer form of amalgam, than that recommended for the glass plate. A verjr efficient form of prime^onductor is a large ring aboat two feet in diameter, placed in a vertical plane above the machine, in which situation it is much more out of the way of losing energy by induction on neighbouring bodies. This form was proposed and adopted by Dr. Winter of Vienna. In one particular case, in which sparks onlv seven inches long could be obtained from an ordinary prime-conductor, sparks of twenty inches might be ob- tained from this. 698. Some years ago, a workman on the Newcastle and Carlisle railway observed an electric spark to issue from the boiler of a steam-engine on the approach of his hand. This curious pheno- menon induced Sir W. Armstrong to investigate the subject, and his researches, with the later ones of Faraday, have developed a mode of exciting electricity to an almost indefinite extent. It appears that whenever a current of steam escapes from a boiler THE HTDBO-BLECTRIC MACHINE. 389 Fig, 411. with sufficient Tiolence to cany off mecbanically particles of water, it will, in its course tbrough a proper escape-pipOi excite by the eviction of the water agaiust the ndes of tne pipe an enormous amoant of electricity. 699. Upon this principle is founded the constraction of the hydro-electric macoine of Sir W. Arm- strong, Fig. 411 : this consists of a sphe- rical or cyundrical boiler of wrought iron, at least eighteen or twenty inches in dia- meter, of sufficient strength to bear a nressure of sixt^ or seventy pounds on the Square inch. This boiler, ▲, rests on a small furnace of sheet iron, b, and furnished with a bent chimney, c. The whole is care- fully supported on four stout legs of glass. The boiler is provided with a proper safety- valve, D. From its upper part, a tube an inch or more in diameter rises, furnished with a stop-cock at e. To the end of this tube is fixed a spherical vessel of brass, f, about six inches in diameter; into the upper part of this a tube, furnished with a stop-cock and a peculiar jet, is fastened. The construction of the jet is shown in Fig. 412, in which the whole is seen in section, ¥ being the spherical vessel, a the stop-cock furnished with a stout brass cap, H, into which is firmly screwed the jet, 8. This represents the section of a conical plug of box-wood, terminated by a brass month-piece. The shaded parts represent the metallic portion. Having filled the boiler about half full of water, and placed burning charcoal in the furnace, in a short time the water will boil, and after the air has been first expelled, the stop-cock e should be closed, and the globe p and its escape-pipe screwed on. When the quantity of steam generated is equal to a pressure of fifty or sixty pounds to the inch, open the stop-cocks e and g, some of the effluent steam will be condensed in f, and the particles of water violently driven forward with the vapour through the wooden mouth-piece of the mg. 412. and it is necessary to obtain an efficient discharge of its electricity, for which purpose a coil of thick copper wire connected with the earth may be so placed, a few inches from the escape-pipe, that the current of steam may traverse it. 390 With Buch a bydro-elsctrio machine, sn larKS a qnnntitj of ele- tricity maj be obUiaed as to enable it (o replooe with adTantags the ordiDarj electric machinea. Tba onlr Dejection to its geneml adoption is, that unloaa the boiler be anfficielitlj large, the iteam quickly aesumea too hieh B atata of teneion, and an explosioD may be not impowible. Sucb an Bccidoot baa in fact actnally occurred. TOO. It ie remarkable, that, 80 long aa the globe p containa merely a little pure water coadensed Irom the ateam, the eioita- tion of electricity ia abuudaat; but if a little autpliuric acid or common aalt be placed in it, all generation of electricity ceaaea, apparently in conaeiiuence of the water being rendered too good a condnctor, and thus allowing of the difiuaioii of electricity, aa aooij* aa it ia develripcd by fiiction. If ■ little oil be dropped in, the eicitatioD of electricity continuea, but ia changed in coancter, the boiler being poeitive, and tho aieom negative. There can acaroely be a quaatioQ of the accui«cy of the DpioioQ of Faraday," (hat fnction ia really the exciting cauae of electrici^ in this mBchine ; for if the Btaam be allowed to escape eTen in torrents, and under high pressure trom the opem'ng of the aaietj- valve, no electric excitation oocura. Hence the neceadly of wi ar- ranging the opening of the escape-pipe, aato preaent aome impedi- ment to the paaaage of the ateam, in order to augment the friclioD. 701. A now form of electrical machine has been produced by H. Holtz, of Berlin, the general arrangement of which ia shown in Fig. 413. Into a wooden stand are inserted four npright glaaa _ ,. bars, i, which are con- '*■ «*• ii«cted above and belc™ by four boriionlal and paraJlel bant, B ; and the front and ' back uprights are con- , nect«d by two paralJel I wooden ban, c, which anp- / port at their middle paints I the aiia of a rotating glass plate. A small pulley placed near the end of the same axis ia coDnected bj a band with a much lai^r puliev placed beneath it, its axis; ibia lattersmalt pulley _, cond laree pulley on a separate axis at the side, to which a winch ia attached. By turning the winch a very rapid rotation may be communicated to the plate, by means of the multiplying pnlliea. A second glass plate, about two inches larger in diameter than the former, ia placed behind it, having a hole in the centre, LhruuKli which tbe aiia passes freely. The brger pUte is supported by foor wooden damps, h, sliding on the * PUL Tiana. IMS, p. 17. M. BOLTZ' MACHINE* 391 glasB bars, b, and ib thus completely insnlated. This plate has two lar^ apertures opposite each other, each bounded by two radii containing an angle of 43° or dO*", and by arcs of two concentric circles. At the correspoDding radial sides of these apertures two strips of paper are attached, and perpendicularly to the middle of these a second strip of paper, cut to an obtuse point and projecting over to near the middle of the aperture. The fixed plate may be adjusted to any required dintance from the rotating plate, by means of the sliding clamps ; and both plates are coated with a solution of sheil-lac, to prevent the dissipation of electricity by moisture adhering to their surfaces. A vertical glass rod passes through the middle of the front wooden bar, c, terminated by knobs through which pass two horizontal brass rods, terminated by " combs" or rows otpoints, placed radially in front of the rotating disc. Across the front ends of these brass rods are two stout wires terminated by knobs, and furnished with glass handles by which the knobs may be placed at any required distance from each other. The fixed plate is placed about half an inch from the rotating one, and it is so placed that the radial paper slips may be near^ but not quite behind the combs. If the disc be now rotated by means of ine winch, no signs of electricity appear, but if one of the slips of paper be charged by an excited glass tube or by a stick of sealing- wax (or still letter, by a glass tube, or a rod of baked wood thickly ▼amished with shell-lac), and the movable plate bo put in rapid rotation, a copious stream of sparks, sometimes four or five inches in length, will pass between tne knobs ; and this extraordinarily large evolution of electricity continues until the charge of the paper is dissipated by the moisture in the air. It is a singular tact, that so long as the paper remains unelectrified, the plate rotates freely with very little force, provided the various bearing points be sufficiently lubricated, but the instant the paper is eleC' trified, a considerable resistance is experienced to the rotation of the plate ; and this resistance increases with increiu»ed rapidity of rotation, and the consequently increased potential evolved. 702. The action of this curious machine has been to many quite a scientific riddle, but it appears to be capable of a simple expuna- tion. When the molecular disturbance due to electrical induction has been excited in any body, iome time, although probably an exceedingly small interval, is required for the subsidence of the disturbance, after the excited is removed from the inductive bod v ; but the removal must be effected very rapidly, in order that the disturbance may survive it. Now a portion of the rotating plate in front of the excited paper undergoes a disturbance by induction, but in consequence of the rapid rotation, this portion of the surface reaches the points before the induced disturbance has subsided, and acts on tnem inductively, and this process bein^ repeated by each succeeding portion of the plate, the comb and its conducting rod acquire a high degree of potential by the continuous accumu^ 392 FRAVKLIKIO BLEOTBICITT. Mlg.41i. lation of Bmall inductionfl. It is probable that the continual attraction existing between the inductive portion of the plate and the opposed comb constitutes a perpetual drag on the rotation, like a friction-break, and produces the resistance ezperienoed. To this presumed explanation of the phenomena there is in some degree a parallel case in Optics. As it will subseqnentlj appear, phosphorescent bodies are those which are capable of re- taining for a short period the light impressed upon them, and again emitting a portion of it : that is to saj, a portion of the luminiferous molecular action is imparted to the phosphorescent body, which again transmits that action to surrounding matter. But in some substances this influence of light is so transient, that if they be enclosed in a glass tube capable of rotating oo it^ axis, and placed behind a slit in an opaque screen, and then strongly illuminated from behind, no light will be given ofi* through the slit, unless the tube be put in rapid rotation ; otherwise the phos- phorescence subsides before the tube has made half a revolution. And in this case, also, the amount of light radiated is up to a certain point increased hj greater rapidity of rotation, because a greater amount of ene}]gy is accumulated at the points of radiation. 703. If a pointed wire be held towards the insulated rubber of an electric machine in action, it will by induction become highly positive ; the electric tension at the point soon becomes so hi^h as to produce dis- charge through the dielectric air, in the form of a brush or pencil of rays, as at the point of ▲, Fig. 414. When, on the other hand, a similar Soint is held towards the positive prime con- uctor, it acquires a high state oi negative tension, and luminous discharge occurs, not in the form of a brush or pencil ; but the end of the wire becomes illuminated with a minute but brilliant star of light, as at the point of b. By using similar wires, the electric state of a con- ductor may be ascertained by the character of the luminous discharge occurring at the point of a wire held towards it. 704. If the conductor and rubber of the electric machine be connected with each other, or with the earth, by means of a con- tinuous conductor, as a piece of wire, the electric discharge will take place alon^ it invisibly, unless the machine be extremely energetic, in which case the wire will appi^ar surrounded with a lambent flame. But if the conductor be interrupted, then vivid sparks will appear at each rupture of continuity, arising from in- ductive action taking place at every one of these points. £xp. A. Connect the prime conductor and rubber with each other, by means of a brass chain ; on working the machinoi vivid sparks will appear at every link. ISTEBRUPTEO DIBCHARGE. 893 2. Fig. 415. B. On a plate of glass, Fi^, 415, paste some stripft of foil, haTing portions cat out, so that the spaces represent letters. On connecting the first piece of foil wiih. the condnctor, and the last with the ground, the letters will appear in characters of fire, in con- sequence of luminous discharges in the form of sparks occurring at each division of the foil. C. Draw, on a pane of glass, a serpentine line witn varnish, and place on it, before it dries, metallic^ spangles, about one-tenth of an inch apart; on connecting the first of the series with the machine, and the last with the ground, a serpentine line of fire will be represented^ D. I ( in a similar manner, the Ro 4ia spangles are placed on a glass ^' tube, Yig. 416, in a spiral direc- tion, a spiral line of sparks will be produced. 705. In all these experiments, it is better to allow the electri- city, before passing through the tin-foil, chain, or luminous condnctor, to acquire some degree of tension ; this is conve- niently effected by means of an instrument called Lane's eUetro- QK/sAA.^^jQ ^.417. meter J or more properly, discharger. This apparatus consists of a curved arm of varnished glass, b, fixed by a brass stem into the prime con- ductor, A. Fig. 417, and terminating in a ball, c, through which passes a rod furnished with two brass knobs, D, B, capable of being placed at any required distance from the conductor. If any of the above- descnbed pieces of apparatus be connected with the ball d, elec- tric discharges will take place through them, as soon as the electricity has acquired a sufficient potential to efifect an inductive discharge through the air between ▲ and k. 706. Induction takes place through a greater space in an air- pump vacuum than under ordinary atmospheric pressures, a cir- cumstance arising from the resisting dielectric medium being diminished in density. This led to the error of oonsidering a partial vacuum as a conductor of electricity, which is not the case, polarization of the particles of rarefied air being transmitted through it readily, providing the two conducting surfaces be suf- ficiently near to permit induction to take place : this will occuf at a distance of five feet or more, in a very good vacuum. If a glass tube, a, Fig. 418, two or three feet in length, be fiir- 394 FIUNKLIKIC ELECTBICITT. nisbed at either end with a brass hall projecting into its interior, and carefollj exhausted of its air bj means of a good air-pump, on connecting its upper end, n, with the prime con- ductor of a machine in action, and its lower end, c, with the earth, b becomes positive, and induces a contrary state on the ball at c ; the induction taking place with facility, in consequence of the atmospheric pressure being removed, is accompanied by a beauti- ful blue light, filling the whole tube, and closelj re- sembling the aurora borealis. This luminous dis- charge undergoes some verv interesting changes: when the rarefaction of the air is considerable, the tube is filled with a purplish lambent flame ; if a little air be then admittea, the continuous column of light is replaced by distinct flames repeated several times in a second, and darting from one ball to the other ; and if more air be allowed to enter, the discharge takes place in beantiful zig-zag lines of brilliaut light, like flashes of lightning, occurring, however, at consider- able intervals. 707. Since electric induction takes place with very great faci- Jltf 410. ^^^y through highly-rarefiea air, it is easy to under- ^ ' stand the rationale of the Leyden vacuum. This con- sists merely of an electric jar coated as usual exter- nally, its interior being[ exhausted of air, by means of the air-pump, and having a point projecting into its ■interior, ana connected externally with a knob. This apparatus. Fig. 419, may be used like the common electric jar, induction readily taking place from the point over ito whole internal surface. On charging and discharging it in a dark room, the point of the wire in its inside becomes beautifully illuminated with a star or pencil of rays (647), according as the electricitv in the interior of the jar happens to be of the positive or negative cha- racter. To this the term reciprocating dieeharge has been applied in contradistinction to the discharge taking place in a vacuum between two electric terminals. 708. Every conducting substance, insulated and connected with the prime conductor, or rubber, may be considered as part of either, so far as their electric state is concerned : thus if a man standing on a btool, furnished with iubulating glass le^, touch the prime conductor, he virtually becomes part of it, being simi- larly electrified, and all the phenomena proper to the prime con- ductor may be observed at any part of his surface. 709. The electric spark does not impart to the finger a sensa- tion of sensible heat, on account of the impression being too transient, although it is capable of exciting sufficient caloric to produce the combustion of iufiommable substances. S95 Exp. a. Coaaect > Hhallow matallio cap with tbe prime con- dactiir, and pour ether into il ; on bolding the finger, or a knob of bra« over it, the electric indactioD taking place thnmgh it will evolve BuXdent heat to inflame the ether. B. Pat iuto a bottle giaDolated sac, and some dilate ml- phoric acid ; Si !□ ile neck a, cork famished with a tube, ti natioriii " '■— ■ '---' .-.i ....... . .. «^haT^ {mm it ma* strike the ranee, he little apparatus ml] begin to revoWe fith great rapiditj. Tbecarrentof airthii.i set in motion bj discharges frompoiutod virea, is sufficient to react npon them, and caose them to move in in oppoHte direction to the cnrrent, pru- jn^, ks. -ided the; be moveable on an axis. -^ — k- B. PUca the cap of the electrical flj, ijrniflhed with four pointed wires b*nt lear their terminatjons at right angles, in a pivot fixed in one of the boles of he prime conilnctor, Fig. 425. On tarn- ue the wincb, tbe wire will rapidlr tv- roT™ in a direction oppoaed to the points, 13 nhown by the arrows, eibibiting in the lark a complete circle of light. 713. The mechanical force of an electric discharge is very c< •iderable. pronded its effects be concentrated in a Ma ^1 reiT small space. Fill a phi«l, i. Fig. 42S, with oil, or other ni :finilucting tluid, pass thrangh tlie cork a copper cire bent near its lowor end at right angles, so that its point may press Hgainat tbe inside of the glass, snd suspend it by the apper end of the wire from ths primo conductor, 'ibe point of the wire in the phial will assume a high state of posi- tive electric potential (689). On bringing towards it a brass knob, or a knuckle of the hand, induo- Liiin and consequeal discharge will take place ihrough the glass, which will become perforated with a h media diSeriiu; from .... Thas, in ranibd air, ;s light is blue and less vivid, than when under ordinary atmo- spheric pressure. Faraday found that, in nitrogen, ic was veiy brilliant, bluish, and aonorons ; in oxygen, less brilliant, and white ; in hjdrc^n, crimson, and accompanied by little or no siiuod ; in carbonio acid ita tint was rather more green than in air; in coal-gas it waagreon or red,«oiqetimo8 both, with frequent inlermptions by black spots ; and In hydrochloric acid gas, white 398 FBAMK.LIN1C ELECTSICTTY. without any of the dark spots so frequently present in the case of the other gases. Occasionally the spark appears interrapted in its centre oy a non-luminous spot, owing to induction taking place at that point in a more diffiised manner than nearer the inducting surfaces. In common air, the luminous electric dischaige or spark, heoomes modified in tint according to the surface at which it takes place ; thus, from a lai^ brass oall, it is white and bril- liantly luminous, whilst on diminishing the size of the ball, it becomes bluer and more scattered, assuming the form of a brush, which itself depends upon a series of intermitting discharges taking place with considerable rapidity. From the surface of ivory, the discharge is crimson-coloured ; from silvered leather it is ^en ; from powdered charcoal, yellow ; and purplish, when taking place on the surface of most imperfect conauctors of elec- tricity. The li^ht of the electric discharge is capable of under- going decomposition by a glass prism, ana polarization by reflec- tion or absorption, like ordinary light. 715. Several varieties of electric discharges have been pointed out, and are readily distinguished by their attendant phenomena. A. Conductive IHseharge. — ^This takes place when bodies dif- ferently electrified are connected by means of a good conductor. It is unaccompanied necessarily by any mechanical e£G9ct| or dis- placement of portions of the conductor. B. DUrvptive Ducharge. — Under this term is indoded all the varieties of electric discharge, accompanied by lights from the faint lambent gleam at the extremity of a wire, to the vivid flames and sparks accompanying the transmission of potential electricity between good conductors. In all cases of this discharge, an actual displacement of particles through which it occurs, takes place. We have a go63 example of it in the frequent rupture of electric jars by spontaneous discharge taking place through them ; the perforation of a glass bottle iiill of oil (660), is also a case of this C. Convective DUeharge. — A form of discharge in which, under the influence of electric currents, ponderable matter is set in motion. Thus, the aerial currents from points (712), are examples of the convective discharge. Another series of cases in which ponderable matter is transferred by the electric current, is found in almost all instances of discharge between metallic sur- faces, or charcoal points; minute portions of the material of which the conductor is composed being conveyed from one surface to the other, so as to cover it with a superficial coating of vola- tilised matter. The transfer of solid matter, in these cases of convective discharge, always takes place in the direction of the positive current. 716. When two insulated conducting bodies are differently electrified, and approximated towards each other, so as to lie within the influence of their mutual induction, but not saffi- TBB C0XDEH8ER. 899 1.^ Kpir n cf 2i- ] cientl J near to pepuit of lominotifl dischar^, no signB of eleo- tricity wiU be conunonicated by either to pith-ball electroscones connected with them, until the bodies are separated to a consider- able distance from each other. The opposite electricities are then said to be diagttised or paralysed^ by their matoal inductive action. Let two plates of metal, ^ ^^ A, B, Fig. 427, Mven or '* eight inches in diameter, be insulated on varnished glass legs, c, d, fixed into pieces of wood moving in a groove in the boara b. To the back of each of these plates is attached a brass wire, furnished with a binding screw; these hold wires, o, h, irom each of which is suspended a pith-ball electroscope. Separate a and b from each other, and touch one with an excited piece of glass, the other with excited resin, the pith balls connected with each plate will diverge, one with negative, the other with ^itive, electricity. Gradually approximate the plates, and as their mutual distance diminishes, the pith balls will by degrees collapse, until ▲ and b are very near to each other, when they will appear totally unelectrified. The apparatus being in this state, gradually separate a and b, and, m proportion as this is done, the pith baits will diverge as before, proving that the potential electricity of the plates hi^ not been destroyed during the course of the experiment : that of either plate having been held in abeyance by the inductive influence of thitpposed plate. Next, remove by the contact of any conductor all potential electricity from both a and b. brin^ them vdthin one-sixth of an inch of each other, and toucn a with an excited glass tube ; it thus becoming positively electrified, acts by induction on b, the opposed surface^ of which ^ becoming negative, its pith balls diverge with positive electricity. If b be now touched by the finger, or any other conductor, all the potential electricity not held induc- tively on the surface of the plate, will escape, and the pith balls will collapse. The plates are now in the same condition, as in the former part of the experiment, when they were oppositelv electrified, and on again separating them, both pairs of balls will diverge as before. If Tefl to themselves the plates will retain their potential for a period of time varying with the dryness of the atmosphere : if, as in Prof. W. Thomson's electrometer (666), a special provision is made for the removal of aqueous vapour by absorption, the potential will be retained for a considerable period of time, amountiiig perhaps to several days. 400 FKAHKLIKIC ELECTBICITT. 717. Any other dielectric may be substituted for air in these experiments : and if a plate of gutta-percba or sheU-Iac be used, the electricities accumulated in the two surfaces may be increased to a very considerable extent (687). £xp. A. Place a large pane of glass, about fourteen inches square, between the two plates of the apparatus Fig. 427, and bring A and B so near to each other as to be in contact with the pane. Connect a with the prime conductor of the electric machine, and work the latter so as to render the plate powerfully positive : this will act by induction through the pane of glass on b, as before (664), which, on approaching the hand to the back of b, will produce a series of sparks, or discharges. After a certain time these will cease ; then remove the wire connecting a with the prime con- ductor, and leave it insulated ; the plate a. will then be chained with positive, and b with negative electricity, both in a state of high tension. Connect the two plates by means of a curved wire, and ditruptive discharge results, attended with a vivid flash of light, and a loud snap. If, instead of using a curved wire, the plates be connected by the fingers of both hands, the same di»- charge ensues, accompanied by an exceedingly disagreeable and painful sensation, extending across the arms and chest of the experimenter, well known as the electric shock. ' B. Instead of placing a pane of glass between the two metallic plates, coat it on each side with a piece of tin-foil, leaving about one inch and a half all around uncovered. On connecting one piece of tin-foil with the conductor of the machine, and the other with the earth, the glass dielectric will become chai^ged as before, the side connected with the conductor acquiring a powerfully positive, and the other an equally energetic negative chai^ge. 718. The ehargCf thus communicated to the pUte of glass, penetrates its substance to a certain small distance, as was first pointed out by Mr. Henley. Exp. a. Coat two thin pieces of window-glass on one side only with a piece of tin-foil, considerably smaller than the glasaea ; place them toeether, with their uncoated sides in contact. Charge this double pmte as before, and then attempt to separate them, they will be found to adhere veiy firmly together; on pulling them asunder, the naked side of that plate which had been con- nected with the conductor will be found to be positively, and that of the other plate negatively electrified. £xp. B. This may be still more readily shown, in the manner proposed by Faraday, by charging in the same manner two plates of spermaceti covered on one side with tin-toil. The im- perfectly insulating character of this substance enables us to detect this penetration of the charge more readily than when glass plates are used. At the instant the discharge takes place, the two electricitieB, accumulated in a stete of mgh tension on the coated surfiMMs LEYDEH JIB. 401 of the glftM, pass from a state of constraint into one of rapid motion, constatnting the eUetrie current. In all cases of disruptive dis- chaige, the current is bat of momentary duration, and ceases the instant the electric equilibrium of the dielectric is restored. 719* Induction, and subsequent charge, do not appear to be materially modified by the figure of the glass, its thickness only influencing these actions ; easteris paribus^ the thinner the glass tile more powerftil charge will it hold. As the plate is a very inconvenient form of apparatus, on account of its being readily injured, ^lass jars or bottles coated with some conductor, are almost universally substituted for it This, indeed, was the first arrangement used, forming the celebrated electric or Leyden phial, so called from the place of its discoyery, by Guneus, or Mnschen- broek, in 1770. White and green glass answer almost equally well for the construction of electric jars ; wide-mouthed glass jars are very convenient, but on account of their expense, common wide-mouthed green bottles may be substituted, provided they are free from air bubbles, and specks of unvitrified matter. Cylin- drical glass vessels are frequently employed in the construction of electric batteries. 720. The ordinary Leyden phial, or jar, consists of a glass jar of any convenient size, coated internally f^id externally with tin- foil to about three inches from its mouth. The jar is closed by a dry and varnished cork, or ^' *^* by a wooden disc, a. Fig. 428. A stout brass wire, furnished with a ball of the same metal, passes through the cover, a, and has several thin pieces of wire, or a chain fixed to its end, B, so as to touch the inside coating in several places. The knob thns corresponds with the internal coating. When narrow-mouthed jars or bottles, as the common sixteen-ounce phials of white glass (which, from their thinness, form excellent electric jars) are used, it is better to coat them internally with brass filings, instead of tin-foil, on account of the difficult of its application to their inte- rior. For this purpose some thin glue should be poured into them, and the botlle turned slowly round, until its inner surface is covered to about three inches from the mouth. Brass filings are then put in, and the bottle well shaken, so that they may be diffused equally over its surface ; on inverting it, those which are in excess will fall out, and the bottle will be left coated internally sufficiently well for its intended purposes. Some jars should always be provided with hooks, instead of knobs, as it IS requisite frequently to suspend them from the prime conductor. To preyent the too rapid deposition of moisture on the uocoated part of the glass, and the consequent escape of the charge, it is a D D 402 rRAKKLnno slsctbicitt. good plan to TarDiBh the jar aboTe the external coating, with m solution of shell-lac in alcohol, or with the common spirit-TarniBh of the shops : taking care to warm the jars before, and after its application. 721. If the knob of a Lejden jar be held about half an inch from the prime conductor, whilst its outside communicatea with the earth, a rapid snccession of sparks will pass between the knob and conductor, which will continue for some time, and tiben cease. The jar will then be charged^ its inside becoming positively, and its outside coating negatively, electrified; neutnuization being prevented by the interposed glass, unless the tension of the elec- tricity be considerable, in which case, discharge often ensaea either by passing through the glass, which is then perforated, and the jar rendered useless, or else by passing over the surface of the uncoated shoulder of the bottle m the ibrm of a bluish lambent brush of flame, constituting the spontaneous dischai^. If the potential be not sufBcient to produce these phenomena, and the cMttle be set aside, its electricity becomes gradually dissipated by the conducting action of the surrounding atmosphere. 722. When an electric jar is^ charged, its discharge may be effected by connecting its outside coating with the knob, by means of a thick curved wire, which is generally furnished with a brass ball at each end. This instrument, the discharging-rod^ Pig^ 489. is usually attached to a glass handle, and has a p cradle-joint, like a pair ci T ^^""^Vs^ compasses, so as to allow ' ^Ni,. the metallic arms to be r~r^ ^< placed at different dis- tances from each other, Fig. 429. The jar may be also dischaiged by graap> ing the external coating with one hand, and touch- ing the knob with the other, in which case the person who performs the experiment experiences the peculiar and painful sensation, termed tne shock. in nis arms, and, if the jars be large, through his shoulders ana chest. A charged jar, the outside of which is negative, and the inside positive, is said to be positively electrified ; and to be negatively electrified when the electricity of its internal coating is of that kind. 723. In accordance with the conditions of the induction and disguise of electricity (716), it is obvious that an insulated jar cannot be charged. £xp. A. Place a jar on any insulating support, as a stool with glass legs,- with its knob in connexion with the prime conductor ; on workipg the machine for some time, and examining the j^, XUOTUOAL BATTBBT. 403 it wQl be found to be almost destitute of any electric charge. For on connecting its outside and inside coating, by means of the discharging rod (722), a minate discham takes place, a faint spark onljr appearinjg between the knob of the discharging rod, and the jar. £rp. B. Place the jar in the same position, and while the machine is in action, bring the finger near to the outside coating, yivid sparks will pass towards it, arising from the discharge ot indnoed electricitj from the outside of the jar. After a certain time these sparks will ceane, and on applying the discharging rod to the jar, the flash of light and loud snap mat ensue, prove that die jar has received a considerable charge. If the knob of a second iar be substituted for the finger, it will become charged b^ ^e electricity proceeding from the outside of the first jar; this mode of charing is termed, by the French, '* charger en cascade.'' And in this manner a series of jars, Fig. 430| can be readily charged, representing a polar arrangement, in FSg. 4A1. which the knobs of the jars are all positive and the outside coat- ings all negative. 724. The charge of an electric jar varies, coBterU paribus^ with the extent of coated surfietce ; and on this account, veiy large jars have been constructed. These, however, have several inconve- niences, and amone them may bo mentioned, the necessary thick- neee of the glass when the jars are Tery large, preventing induction to any great mtensity taking place throQgh them. On this account, several small iars coated in the usual manner (720), are placed in a box lined with tin-foil, or other good conductor, so as to connect their ontsides, whilst their knobs, and consequently their insides, are connected by brass rods : the whole oonstitnting the eSfctric battery^ Fig. 431. As the interiors of all the jars communicate, they may be charaed as a single jar, their exteriors being connected with the earth. A hook, a, is fixed in the side of the box in contact with the metallic lining, so as to allow of readily connecting a chain or wire with the outside of the jars. dd2 404 fhakklinic electricity. 725. In charging a battery, its interior is connected bj means of a wire or chain with the prime condnctori and its exterior con- nected with the earth ; and for the purpose of tracing the progress of the charge, the quadrant electrometer (710) is fixed in one of the holes of the pnme conductor. On taming the machine, the potential of the prime conductor, being now shared bj a largely extended conducting surface, is augmented much more slowly; but by degrees it is accumulated on the conductor, and acting on the electrometer raises its index, which, when the battenr has at- tained its utmost charge, seldom rises above 40** or 50 : as the tension of a batteir charge never equals that of a single jar, pro- bably on account of the larger surfied with platinum, passes Terticallv through a raised piece of brass, b, under- neath tne point of which is a brass stud, c. Two wires pass through upright studs, d, b, so that their points, f, o, may stand opposite each other on fhe surface of a raised block, b, k, are two brass clamps, by which a piece of gold-leaf may be clamped between two pieces oif glass, ana a metallio connexion maintained, a has a metallic con- nexion underneath with b, c with b, d with n, and k with l, and L with one binding tifblly demonstrated hy means of the fignres of Leichtenberg. To show these, make the resinoas cake of an electropbonis (685) dry and warm : draw lines on it with the knob of a positively charged jar, and siit over these places a mixture of sulphur and red-lead ; on inclining the plate, to allow the excess of the powders to fall off, every hne marked by the knob of the jar will b«s observed covered with the sulphur, whilst the minium will he dispersed. On wiping the plate, and drawing figures with the outside of the jar, the stuphur will he dispersed, and the minium collected in a very elegant manner on the lines described by the outside of the jar. The rationale of this experiment is very obvious ; the sulphur becomes negatively and the red-lead poeitivelv electrified by the friction to which they are necessarilv exposed, and on allowing the mixture to fall on surfaces to which one or the other kind of electricity has been imparted, the sulphur will be collected on the positive, and the minium on the negative portions of the plate, according to the ordinary law of elecmc attraction. 736. The fact that the intensity of a chaige has no necessary relation to the quantity accumulated must never be forgotten in experiments witn charged surfaces. Thus, let an ounce phial be coated like an electric jar, and charged in the usual manner, a vivid although minute spark and distinct snap will accompany its discharge. If the finger and thumb of one nand be usea to con- nect the outside and inside coatings, an electric shock will be dis- tinctly felt Then recharge this phial, and connect its interior with the kaob of a coated jar holding a quart, and unite their out- side coatings by means of a wire. Separate the two jars, and it wiU be found that scarcely the trace of a spark, snap, or shock, ma 4S7 ^^^^ accompany the discharge of either jar, al- ^' though the actual quantity of electricity must be ) the same as in the fonner experiment. The real 9 change undergone being a diminution of potential «A^ energy in the charge from its diSusiou over a com- 1^ parativelv large surface. CXD 737. The unit-jar, contrived by Sir W. S. Harris, enables us to measure with considerable accuracy , the comparative quantity of electricity accumulated in a jar. This consists of a small coated phial, in- sulated on a glass support, Fig. 437, the charge of which is assumed as the unit of measufe. A smiJl coated jar, a, (generally made of a piece of glass tube,) is inverted on an insulating support ; a wire furnished with a knob at each end, capable (^ moving through the ball, b, is connected with the THB C01IDB1I8KB. 411 onteide coating of tlie jar : the wire and hall, c, are connected with the inside of the jar. Let the outside of the iar, a, be con- nected with the prime conductor of the machine m action, and the end of the wire, c, with the knob of a larger jar. It is obvious that the jar, a, will be positively charged externally, and that the interior of the larger jar will be charged oulj bv induction through the glass, until the potential of the prime conductor, and therefore of D is sufficiently exalted to polarize the mass of air intervening between j> and c, when a spark will pass between those points, which will be repeated as soon as the potential of the prime con- ductor is raised to the same degree, when another portion of positire electricity enters the larger jar, and so on. Thus, as- suming the electno potential required to charge and dischaige the small jar as unity, toe number of luminous discharges occurring between d and c will be an approximate measure of the elec- tricity communicated to the larger jar. 738. The Condenser. — In consequence of the action of indue tion causing the dUguited etate (716) of electricity, very minute traces of potential electricitv may be detected with facility by accumulation; instruments designed for this purpose are called eond&isers. To illustrate their use, touch the prime conductor of an electric machine in weak action, with a disc of metal fur- nished with a glass handle, as the cover of the electrophorus (685), and on bringing it towards the cap of an electroscope, the gold leaves will be scarcely affected. Then touch the conductor once more with the disc, holding beneath and parallel to it, at the distance of about a quarter of an inch, a second disc of metal, but unhuuUUed. Bemove them in position from the conductor, and touch the cap of the electroscope with the insulated plate, quickly remove the other plate, and immediately the gold leaves will diverge to a considerable distance from each other. In this experiment, the conductor being weakly charged, the plate of the electrophorus employed can only remove a portion ot electricity equal to its own surface, a quantity far too small to act upon the electroscope. But on repeating the experiment, with a second plate held parallel to the firs^ induction comes into play, the electricity which first enters the insulated plate becomes Tot^nf or dUguisedf a fresh portion enters, and so on, until the plate of air confined between tne two discs of metal becomes charged (664). On then separating them, the coercing force is removed, and the released electricity readily acts on the electroscope. The most ooQTenient form of tne condenser is furnished by the apparatus previoariy made use of to illustrate the phenomena of induction (716). ui order to apply this as a conoenser, remove the cork- oall electroscopes, connect one of the plates, as a, with a gold- leaf electroscope (662\ by means of a wire, and let the other plate communicate witn the earth by means of a piece of chain or wire ; then bring the two plates as near as possible to each other. 412 FBAHKLINIC ELEGTBICITT. bnt witboQt allowing them to tonch. Bj means of a wire, or hj absolttte contact, connect the body of which electricity is to he examined, for a few seconds, with the plate a, then remove it, and quickly separate b from ▲ : instantly tne electricity, left free in a, will canse the gold leaves of the electroscope to diverge. In this manner, minute traces of potential electricity can be readily detected. 739. To explain the principle of the condenser, let the plates be called p, N, the fonner oeing connected with the earth, the latter being iuKuIated. Now, on placing an electrified body in contact with N, a certain charge e enters it. This reacts by induction on p, and the potentials of x and p mutually constraining each other, a further charge enters n, which is again constrained by a further induction on p *, and the fresh quantity of electricity in p then reacts on n as before, ad infinitum. To determine the measure of the influence of a condenser in in- creasing a charge of electricity, let the potential imparted to x by contact with the electrified body be taken as the umt : it will in- duce on p a potential 0, which must always be less than the unit, unless absolute contact took place between the plates. The eflfect of e on X will be to develop oy induction a second charge of elec- tricity, and hence the quantity in this plate will be equal to e x «, or «*. The influence of this on p will necessarily set free a quantity of electricity equal to e' x e, or e*, and so on. Hence the result of this series of actions will be a converging geometrical series, since e is less than unity ; and the accumulation of poten- tial will be in X, and in p, 1— c* c+«*+e"+«' + e' + &c.= l-e« 740. In the condensers usually made in this country, the unin sulated plate, p, Fig. 438, is made to move back on a hinge, ai shown in the figure, when the electricity of the insulated plate, x has to be examined. JV-438. ^.489. f ▲PPUOATIOn OF TRB OOHDBSSEB. 418 As it 18 difficult to place the plates of the condenser as close as neoesaaiy, without their accidental contact often ensoing, it is usual to cover their opposed surfaces with a thin layer of resinous varnish, as a sohition of gum-lac in alcohol. When plates thus prepared are used, the layer of resin hecomes the charged dielectric^ instead of the thin plate of air. Thej are then most conveniently arranged horizontally, as in Fig. 439, and this is the form in which they are generally used on the Continent. 741. On a principle analogous to that of the condenser, in- struments have heen devised for the pur]^ose of accumulating potential electricity hv successive inauction. The earliest on record is by the JEtev. A. Bennett,* a description of which would be sunerfluous, as a more complete instrument on the same prin- ciple has been constructed by Mr. C. F. Yarley, which might be called a multiplying inductor. It consists of an axis on which are fixed two opposite rows of equal and parallel segments of brass a, b, c, &o., a', b', o', &c Of these it will be convenient to consider the action of one row only. As the axis revolves, these vanes simultaneously enter two rows of insulated brass shells, which closely envelop, without any contact, their outer edges, and their sides nearly up to the axis : let these be called a, 6, e, &c. ; a', b\ €f, &c. These shells, or envelopes, are thus coupled : — & to e, ble, with one end in cootact with the (mtmde coating, a pieoe of bru* chain. Diuharge the jar by meanB of Ihedia^arginerod, and the instant the diichjuve oGcnra, the chain, altboDgb uotforming any part of the dicoit, will be illnminated by a ipuit appearilig before each link. B. Let an ininlatM cofidDCter, q. Pig. 441, be placed aboat three inchei from tbe end of the prime cwtdnctM', a, of an electric macbiDe. A condnctor, d, connected with the earth by ^- **i- means of ■ cbun, is placed ■bont a qnartcT of an inch jj f from o. Then i, being pon- tively electrified, acts iiutno- tivel}- on c ; and the indaced chai^ of c acta on i>, utd polansing tbe tbin stntlom of •ir between c and d, a apark D, on □, BO that c is left in a negative itale. On dis- y Faraday,* admirably illnt- kop of copper wire, abo, is insnlsted by nu- penooD, haTing a Wl at One end, 0, the other end, 1, being in coniieiion with the earth. Two portions of the wire near the ends are brought •ufGciently near to each other at e, that when » charged Leyden jar is discharged of the wire adjacent to B be now connected by attached wires, f, a, with the inner and onler CAatinnof a fnll'Sised Leydenjar. The poten- tial of the charge will be so moified by tlw Indnctive action of these coating that it will no longer be able to orercome tbe reeiatacce of the inlervening air at b ; which epace, when that potential is nndiminiahed, oSers less resistance to its puBtge than the entire circait of the wire. • Lntnm at Hay Instil. Ju. 1) 416 FBAXKIilinC BLVCTRICITT. 746. Hitherto, it has been presumed that positive and negative electricity possess the same properties with regard to conductioD and insulation ; differing only in the appearance of their luminooa discharge ; the one being accompanied 07 a star, and the other bj a pencil of light (703). A remarkable circumstance has been observed, which tends to indicate the probability of the existence of some more important difference between them, instanced in certain bodies being capable of conducting one kind, and insulat- ing the other, when they are in a state of ^stremely toeaib potential energy. These bodies are termed «mjN>2ar; among them the flames of alcohol, coal-gas, and sulphur appear to conduct podtiva electricity, whilst the name of phosphorus, dry albumen, ivory, and dry soap, conduct negative electricity. Of an approach to this curious class of bodies we have an instance in atmospheric air, which would appear to allow the discharge of positive, to take place more readily than that of negative, electricity (730, G), although Prof. Belli has stated the contrarv to be the fact* 746. Conductors, and nonconductors, pass into each other bj insensible grades, and indeed rather di£fer from each other, in one insulating better or worse than another, as they all offer more or less opposition to induction and resulting dischanpe taking plaoe through them ; and at length, such a point of inmfference to the discharge of electricity is met with, that bodies are known which allow discharge to take place through them in one direction, and prevent it in another, as in the so-called unipolar bodies discovered oy Ermann. Many non-oonductors insulate when cold, and con- duct when heated red-hot, as glass. Others do not acquire their conducting power until they are fused, as in the case of resinons electrics, which allow discharge to take place through them when they are fused, a circumstance first, it is believed, mentioned by Cavallo,t and shown to hold good even with electric currents of weak tension, by the elaborate researches of Faraday. 747. The atmospheric medium, by which we are surrounded, contains, like eveiy other form of matter, a considerable quantity of potential electricity ; sometimes of one kind, sometimes of the other ; but as a general rule it is always of an opposite kind to that of the earth. Different layers, or strata of the atmosphere, placed only at small distances from each other, are frequently found to be in opposite electric states. various kinds of apparatus have been contrived to facilitate an examination of the electric state of the atmosphere. These consist in general of poles elevated about thirty feet into the air, provided with a metallic point at their upper, and insulated at their lower ends. The most perfect mode of insulation hitherto devised con- sists in attaching the atmospheric wire to the apex of a hollow cone of glass, under the cavity of which a small lamp is kept con- * PofTgendorif, Annalen, t. xl. p. 73. t Treatise oo Blectrioilj, p. 906. London, 1777. BLECTUCITV. 4 1 7 ■buitly burnintc; b; thii the temperature of the glaag tupport is maintalDed Bufficiently ubare that of the snironading atmoephere, to preveat the depoaitlon of moisture, and consequent escape of electricity, orer the surface of the glass. The electric bells (711, C), have been suspended from a coitdiictcr in contact with such apparatus, bo that by their ringing, they may indicate the presence of electricity iu the conductor.* A long Sshinc-rod, raised aboTB ibs highest part of the housa, and proiided with au insulated conducting wire, furnishes a very conTenient apparatus for occamonal obseryations.f Tlie apparatus used by Saussure in his researches whs merely a well.insulaled electroscope, provided itith a poirited conducting wire about three feet in length, to take up the electricity from the atmospbere. For the purpose of aacertainiog the kind of "" "" atmosphenc electricity, an instrument called a dittinffaitking electroscope, fig. 443, ban been employed : this consists of a small tubu lar Lejnlen jar inserted in the neck of a gold- leaf eleclroBcope, the inner coating of which is connecled with the wire carrying the gold leaves. This is doily charged with negative electricity, and if carefully iosulaled with shcll- lac varnish, will retain the charge with little diminution for twenty-four hours. The leaves. conae<|uenlly, are constantly divergent with negative electricity, and their increased or diminished- divergence will show (679) the kind of electricity, if any, present in the atmosphere. Tbe same result may on oblainoil by means of the podtivs and negative eleclroiKopea of Dr. Eadclifle ((j(j3), and more conve- niently, if the poteudal be very feeble. 746. By means of some of theBo apparatus, a knowledge of the electric state of thosii portions uf the atmosphere nearest the earth « may readily be obtained. Iu clear weather, indications of positive electricity are always to bo met with in the atmotphere ; this is weak before sunrise, becoming stronger as tho sun passes the horizon, and soon afterwards gains its greatest stale of iutensit; ; it then rapidly dimini-hes, and regains i[8 mininiiini state some bouTB before sunset, alter wbich it once more iucrcasex. and gains its second moxintum state ; and then decreases until the following morning, t M. Schnbler of Stnttgard, to whom tbe above observations are due, has remarked that the atmospheric electricity increikses from July to January, and then decreases. It is also much more in- tense in winter than in summer, and appears to increase as the t Canllo, p. Sao. 418 PKAVKLIHIG BLBCnUClTT. cold increases. According to the obsenrations of M. Qaetelet, atmospheric electricity exhibits a nuunmum intensity in Jannary, and a minimum in June. From a series of upwards of 10,000 observations made at the Kew Obserratory in the years 1844-8,* it appears that negadve electricity was observed only once in 81*4 times. In summer, the hours of maximum intensity appeared to be 10 ▲.!!. and 10 p.m. ; and of minimum intensity 2 a.m. and noon. In winter, the mcucima were sit 10 a m. and 8 p.m., and the minima at 4 a.m. and 4 P.M. The greatest potential was observed in the most humid months. The manifestations of negative electricity were usually accompanied either by rain, frequently heavy, or by the occur- rence of clouds of the cirrfhstreUuB, or eumuli-HrcUus variety in the zenith. 749. Among the causes modifying the electric condition of the atmosphere must be ranked its hymmetric state, as well as, pro- bably, the nature of the effluvia which may be volatilized in anj given locality. Thus, Sanssure has observed that its intensity is much more considerable in elevated and isolated places, than in narrow and confined situations; it is nearly absent in houses, under lofty trees, in narrow courts and alleys, and in indoeed places. In crowded cities it is most intense in the squares, and upon the bridges. In some places the most intensely electric state of the atmosphere appears to be that, in which large clouds, or dense fogs, are suspended in the air at short distances above the surface of the earth ; these appear to act as bodies charged in- ductively by the earth. 750. Cavallo, from a set of experiments performed at Islington in 1776, ascertained that the air always manifests po$iHve elec- tricity, except when influenced by heavy clouds near the zenith. This electricity he found to be strongest in fogs and during frosty weather, being weakest in hot weather, and just previous to a shower of rain ; and to increase in proportion as the instrument used in its investigation is raised to a greater elevation. This indeed necesoarily happens, for the earth's surface is always nega- tively electrified, and acting inductively on the atmosphere, no positive electricity can be detected withm four feet of the soifaoe of the earth. Mr. Crosse, of Bromfield, collected and examined the atmo- spheric electricity by means of wires, insulated and supported by poles and by the trees in his park. When these conductors were about one-third of a mile in length, he frequently succeeded in collecting sufficient electricity, to charge and discharge a battery of fifty jars, containing seventy-thrae square feet of coated surface, twenty times in a minute, accompanied by reports as loud as those of a cannon.f • Bep. Brit. Aaioe. 1850. t Sturgeon's Jovirnal. Tol. i. p. 139. ATlfOSPHBBIO BLIOTRiaTT. 419 751. The first satisCM^toiy attempt to oolleot the electricity of the upper regions of the air, was made by Dr. Franklin in North Amenca, in 1752, although it must be observed that a short time previously, Dalibard, in France, had, by means of a lon^-pointed conductor, raised in Mary-la-Ville, succeeded in obtaining vivid sparks of atmoepheric electricity. Dr. Franklin raised into the atmosphere a kite, formed by stretching a silk handkerchief across two rods of light wood, and with thb, when the string had been rendered sofficiently moist by the falling rain to conduct elec- tricity, he obtained a copious succession of sparks, from a key, fiutened to the end of the string. Subsequently, M. Romas, in France, h^ increasing the length of the string, obtained flashes of electric light from his apparatus, ten feet in leneth, accompanied by a report as load as that of a* pistol. Sbort^ afkerwaros Professor liichman, of St. Petersburg,' was struck dead by a discharge from an apparatus, similar to that - of M. Dalibard, with which he was experimenting. Cayallo, in 1777, raised an electric kite repeatedly in the neigh- bourhood of London, and obtained an enormous quantity of elec- tricity; he found that the electricity frequently changed its character, as the kite passed through different aerial layers, or strata. 752. Perhaps the most in^nious mode of investigating the electric state of the upper regions, is by means of the apparatus used by MM. Becquerel and Breschet, on the Great St. Bernard.* These physicists placed one end of a cord, coverea with tinsel, about ninety yards in ^* length, on the cap of an electroscope, and, / tying the other to an arrow, fig. 444, they projected it, with the aid of a bow, into the air, and they found that the -gold leaves divereed in proportion as the arrow ascended into the atmosphere. In this experiment, the effect would probably have been aug- mented by surrounding the head of the arrow with a small bit of cotton- wool mois- tened with alcohol, and igniting it, previous to projection. 753. The existence of tree electricity in the air has been referred to various sources; the phenomena of animal and vegetable life, as well as chemical action, haye been called in to explain its origin. Among others, the evaporation of water, and other fluids, constantly taking place on the earth's surface, may certainly be regarded as one of the sources of atmospheric electricity. The eyolution of electricity by evaporation, may be readily proved by placing on the cap of a ^old-leaf electroscope a small metallic cup containing water, in which some common salt has been disBolvcJ. • Traits de rSIeotricit^ et da Magn^tisme, t. iv. p. 110. E K 2 420 FBAKKUiriO ELECTRICITT. On dropping into it a piece of hot cinder, the vapour will ariae copiously and carry off positive electricity, leaving the cup nega- tively electrified, with which electricity the gold-leaves will di- verge. If water, containing a minute portion of an acid, be substituted for the weak brine, the reverse will occur, the gold- leaves diverging with positive electricity, and the vapour being negatively electrified. The potential electricity evolved in these experiments has been ascribea by Faraday to friction ; but it appears more probable that the true cause is evaporation. 754. The clouds, consisting of immense masses of aqueona vapour, are tolerably good conductors of electricity, and conae- quently manifest a considerable potential energy. There can be but little doubt that a cloud consists of an aggregation of minute vesicles of aqueons vapour. These when similarly electrified do not repel each other, and fly apart, unless they are quite beyond the inauctive influence of the earth, or of any nearer body. Thus, a glass feather fixed in one of the holes of the prime conductor of an electric machine will appear animated, all the fibres mutually repelling each other. But if the hand, or a large brass ball be held near it, then the fibres will fall together, and losing their appearance of repulsion, will bend towards the hand or ball under the inductive, and consequently attractive influence, exerted by it. 765. Two clouds, being in different electric states, act upon each other through the particles of the intervening dielectric, the air, like the inductive surfaces, or metallic coating of a charged jar ; and when sulficiently near to each other, dtaeharge occurs, pro- ducing the vivid flash well-known as lightning, generally accom- paniea by the loud reverberating sound of thunder. When, on the other hand, induction takes place through the air, between an electrified cloud and the earth, an explosion or disdtarge ensaes, when the intervening particles of the dielectric are so arranged as to admit of its occurring ; producing a second, and much dreaded form of lightning. This mode of establishing an equilibrium be- tween the oppositely electrified bodies, often ensues through the medium of the nearest prominent conductor, which, if a tree, is often riven in sunder ; if a building, is frequently dashed in pieces ; and if an animal, severely injured, or even killed. These natural events present examples of the commutability of physical forces ; when the intensely exalted potential manifested in a flash of lightning meets with a good conductor of sufficient magnitude, that is a body havnug sufficient capacity to receive and trans- mit the force, it is transmitted harmlessly to the earth : but when that force is impressed on bad conductors, that is, on bodies not sufficiently capable of receiving and transmitting it, as the atmo- sphere, and non-metallic bodies on the earth's surtace, a portion of tnat force is converted into, or is manifested in the form of, light, heat, or dynamical force ; and thus the gazing rustic is killed or LIGRTXIXO CONDUCTOBS. 421 JF^.MS. blinded, the stack is fired, the oak is rent, or the towor is shivered to pieces. 756. Several instances have occurred of the fatal efiects of a tempest having been exerted on animals at a considerable dis- tance from the spot where the most serioas results have taken place, and where the violence of the storm appeared to have been chiefly^ exerted. This will readily admit of explanation, on the supposition of a lateral explosion or returning i^ock (743) having occurred. Thus, if a b be a large cloud, positivelv electrified, ap- proaching at its end, a, Fig. 445, within striking distance of the church-steeple, o, the ex- tremity, B, will, oyits inductive action, excite and retain a large amount of potential energy in any object at d, as a traveller, for example, leaving him in a negative state. When a has approached sufficiently near to c, an explosion will occur, and electric equilibrium will ensue, b being thus left unelectrified, no longer exerts a coercing force on the electricity in d, which now rushes back with violence to the earth, producing discharqe^ and a restoration of electric equilibrium, witn such mechanical force, however, as to even kill the unfortunate individual situated at d \* an event which is stated to have actually occurred. 757. Science, and mankind generally, must ever remain debtors to the ingenuity of Dr. Franklin, for proposing at least a partial protection against these dreaded effects of the tempest, in the in- vention of the j^aJtonnerrea, or lightning-conductors. These consist of metallic conductors, of sufficient thickness, usually fixed against the side of the building they are destined to protect ; their upper extremities extending some feet above it, ana terminating in a point, which is best constructed of some metal not liable to oxidation : the lower end is buried in the earth, to the depth of a few feet. For ships, ^flexible paratonnerres, composed of copper chain, or slips of that metal, are fixed to the masts, and extend from their highest points to the outside of the keel of the vessel, so as to conduct the electricity harmlessly to the water in which the vessel floats. Whatever form is used, one general pre- caution is necessary, that aU and every portion of the paraxon- nerre should be as perfectly continttous as possible^ for wherever a break or interruption occurs, the potential energy in being trans- ferred from one portion to another, is liable to produce the very danger which these instruments are intended to avert. * See Tnit4 El^mentaire de Fhysiqixe, par M. 1* Abb^ Hauy, p. 434. Paris, 1806. > 422 FR1.HKL1NIC ELECTRICrrr. 758. To illustrate some of these positions, the thunder-honse, as it is termed, was inTented ^•^' by Dr. Franklin, ab, Fig. 446, is a piece of hard drf wood, cut into the shape w the gable end of a honse, with a brass rod, terminat- ing in a ball at c, fixed against its side, and termi- nating at D in a hook. At ■ this coqductor is intermpted by a sauare block of wood, fitting loosely into a cavity _ made to receive it, having a J wire fixed across it ; so that when B is fitted in its place, as in the figure, the conductor, o d, is perfect ; but when placed in the opposite direction, as shown by the dotted line, the para- tonnerre, c d, is interrupted in its centre. £xp. A. Charge the jar f ; connect its outside with the hook at the end of d, and its knob with the pointed wire supported on its inndatinq stand, h, and bearing on its apex the brass rod k, terminating in balls, and moving on it in any direction, as on a pivot. Phice the window e in its place, so that the brass conductor may be continuous, and cause k to revolve, so that one of the balls terminating it may pass within half an inch of c. The jar will be discharged, and the window b remain unmoved. B. Repeat the last experiment, with the window b placed so that its wire may be at nght angles to the direction of the wire CD. On discharging the jar as before (A), the effects of the ex- plosion will be exerted on b ; and it will be projected with violence from the cavity into which it fits. C. Let the apparatus be arranged as in (B), remove the knob on c, and leave the paratonnerre pointed : on allowing k to re- volve, the jar will be tUently dischnrged. The electric current during this gradual discharge by the point, never acquiring suf- ficient tension to act energetically on s, although it was displaced with violence, when D terminated in a knob. D. The protecting infiuence of pointed conductors is more strikingly shown by the electrical toy, called the powder roaga- xine, in which the interrupted portion of the conductor reposes in a mass of gunpowder, placed in a wooden model of a house. If the jar be dincharged whilst the paratonnerre terminates in a Soint, the powder is unaffected ; but if a knob be screwed on, the ischarge explodes the powder, and blows the model to pieces. In repeating this experiment, a piece of wet string phould be used to connect the jar with the baiBe of the paratonnerre, for reasons already mentioned (780, D). AURORA, AND M LIBORS. 423 759. When lightnme strikes a sandj soil with sofficient force, it often penetrates to the depth of seyeral feet, fonoing a kind of tube, known as afuk/uritey by the fusion of the a4J<^<^ii^ calcareoas and sificeoQS particles ; and which, in almost every instance, has been found to terminate in a subterranean reservoir of water. The lambent lightning ho common in the sultry autumnal evenings is unattended with the sound of explosion, and often a,pjpe&rs in the most opposite regions of the sky. It has been in many cases traced to the restoration of electric equilibrium dis- turbed by storms actually below the horizon. 760. The well-known meteoric appearances so frequent on the Sointed masts of shipping, known as Castor and Pollux, the feu e St. Elm of the French, and Elmsfeuer of the Germans, appear to depend on the gradual discharge of atmospheric electricity by thepointed masts of the vessel. The beautiful aurora borealis, so frequent in the north of Europe, and of late years not of unfrequent occurrence in the neighbourhood of the metropolis, depends, in all probability, on the passage of electricity through a highly rarefied meaium. From the calculations of Mr. Cavendish, it is probable that the aurora usually appears at an elevation of about seventy-one English miles above the earth's surface ; at which elevation the density of the atmosphere must be but the ttt^^ P^^ ^^ ^^^^ ^^ the earth's surface, a degree of rarefaction far above that or- dinarily afforded by good air-pumps. As electricity is difiiised in a quantity nearly proportionate to the elevation above the earth's surface, it appears very probable that, under favourable circumstances, an inductive transmission of electricity would ap- pear luminous to us, in the vast regions of rarefied air terminating oar atmosphere, in a manner analogous to that in which it appears on an infinitely smaller scale in an air-pump vacuum. When the discharge of a large jar is e£fected through a tube filled with rarefied air, it appears limiinous, not in flashes, like the artificial aurora <706), but in a condensed form, like a beill of fire, falling through the tube ; resembling in appearance another class of meteors known Asftdling or shooting stars. 424 \ \ CHAPTER XIII. VOLTAIC ELECTRICITY. 761. It has been already mentioned, tbat even two plates of glass when pressed* together, and suddenly separated, assume op- posite electnc states : but the same thine occurs more manifestly when two discs of difi'ereut metals are similarly treated. To de- monstrate this, tak^ a plate of copper and one of zinc, each about four inches in diameter, and furnished with a glass handle in its centre; connect a gold-leaf electroscope with the plate n of the condenser (738), allowing p to be connected with the earth. Press the copper and zinc plates together, holding them by their insu* lating bandies ; suddenly separate them, and apply one to the plate N of the condenser ; again press them togetlier, having pre- viouslv touched them with the finger to restore their electric equilibrium, and re-apply the same plate to the condonser. Re- peat this about six times, then draw back the uninsulated plate p, and the gold leaves of the electroscope will diverge with poti- tive electricity if the zinc, and with negative^ if the copper plate has been applied to the condenser. 762. The development of positive electricity in the zinc, and of negative electricity in the copper plate, was attributed by the illustrious discoverer of the fact, Prof. Volta of Pavia, to a pecu- liar electromotive force, under which metals, by simple contact, tend to assume opposite electric states. This theory has now but few supporters, in consequence of the mass of evidence that has been opposed to it by Fabroni, Do la Hive, and our illustiious countryman, Faradav, to whom this branch of science is so largely indebted. Tliese philosophers have very satisfactorily proved, that whenever electricity is developed during metallic contact, it is owing to some chemical action undergone by the more readily oxidizable metaL So rigorously has this been demonstrated, that it may be stated as a general law, thcU no cJtemteal action oceurSf unaccompanied hy disturbance of electric equiUbriumt and eon- eequewt development of. potential eUctridty^ although it is fully possible for such to occur without our being able to detect it ; for unless the electricity evolved is in sufficient quantity to circulate as a current, or of sufficient tension to be collected by a condensing plate, and to act on the leaves of an electroscope, it may escape the evidence of our senses. EI.£CTBO-P08inTB AND HEOATITB BUSHEKTS. 425 763. In every chemical combination, whether saline, haloid, or of still more complex nature, the force by which the elements, both proximate and ultimate, are held together, appears to bear a dose relation to their electric state, and their separation is ^eno- ntlly accompanied by the evolution of a weak current of electncit j. So genera] is this fact, that the discoveries of Faraday have cer- tainly very clearly pointed out the probability of chemical affinity be- ing merefy a modification of electric attraction ; an opinion previ- ouslv adopted, with some limitation, by Davy, Berzelius, and others, not less deservedly celebrated in this branch of experimental science^ 764. Among the ultimate elements with which chemistry has made us acquainted, there are twenty-four which are characterized by their electro-negative, and thirty-nine by their electro-positive state in relation to each other : with these are given their chemical symbols, some of which are derived from their Latin names. I. ELBCTBO-NEOATrVB ElBMEHTS. Oxygen 0 H^'drogen...H Nitrogen ...N Sulphur S Phosphorus..? Chlorine .,.Cl Bromine ...Br Iodine I Fluorine ...F Carbon C Boron B Silicon Si Selenium ...Se Arsenic ...A« Chromium ...Cr MoIybdenumM Tuuj^sten ...W Antimony ...S5 Tellurium..Te Titanium ..Tt Tantalium To Vanadium. V Niobium. ..Nt Pelopium ..Pe n. Electbo-positivb Elements. Gold An Platinum. .Pt Iridium ...Ir RutheniumBtt Osmium ...0« PalUdium..P(i Rhodium .. JRA Silver A^ Meroui7...H^ Copper ...Ctt Uranium ...U Bismuth ...Bi Tin 8» Lead P6 Thallium...TA Cadmiom...CJ Zinc Z Nickel Nik Cobalt Co Iron F0 Manganese Mn Lantanium La Cerium Ce Didymium D Zirconium 2^ Yttrium ...Y CsBsium ...Co; Rubidium... Ri Erbium E Terbium ...Tr Glucinium G Aluminium Al MagnesiumM^ Calcium ...Ca Strontium.. Sr Barium ...Ba Lithium ...L Sodium ...Na Potassium K These substances are, it must be remembered, negative or posi- tive only in relation to each other, and their mutual chemical afiinities appear to be in the ratio of the intensity of the diflference of their comparative electric states. Thus potassium has a greater affinity for oxygen than any other substance in nature, and ao- cordinely we find that, whilst the former is in its combinations powerrally positive, the latter is as energetically negative. In 426 VOLTAIC ELECTRICITY. the list of uegative bodies every element is to be remrded as negative to all below, and positiye to all above it in the list ; tbns hydrogen is negative with regard to nitrogen, bot positive with regara to oxygen : a similar observation applies to the list of electro-positive elements. The electrical relations of many of these bodies must not, however, be regarded as absolutely correct in this arrangement ; many of them being arranged from their chemical analogies only. ^ 765. Let a piece of zinc be amalgiamated by immersing it in a little dilute Bulp>horic acid, and rubbing a few globules of mercury over it with a piece of cork. Fill a ^ass with a mixture of one part of hydrochloric acid and six of water, and place the amal- gamated zinc in it. The brilliant surface of the zinc almost im- mediately assumes a greyish tint from its becoming covered with myriads of excessively minute bubbles of gas. These consist of hydrogen, arising from the decomposition of the acid, its chlorine uniting with the zinc, and the hydro^n, for which the metal has no affinity, mechanically adheres to its surface, and thus by a gaseous covering shields it from the further action of the ncid. Then immerse in the fluid a rod of any metal standing above zinc in the list (764), as a piece of copper or silver : no obvious action will occur until it touches the surface of the zinc, when in an in- stant a torrent of bubbles of gas is evolved from the copper, as though it were undeming solution, no evolution of gas from the sine taking place. Tne copper, however, remains chemicallv un- acted upon, and the zinc is alone dissolved^ and consequently mere chemistry is incapable of affording a satisfactory solution to the curious phenomena just described. From the facts already stated, it is seen that the copper and zinc, being placed in contact, assume opposite electric states, from the chemical action of the fluid on the more oxidizable metal. The origin of the action itself must be referred to an exalted attraction of the zinc for the chlorine, which becomes at last so intense as to enable it to take the latter irom the hydrogen with which it was previously combined. But the hydrogen is evolved at a distant part of the fluid, viz. from the surface of the copper, which may be even several feet from the zinc plate, and the inter- mediate portion of fluid undergoes no visible cnange of any kind during this transfer of hydrogen from the zinc to the copper plate. This IS explained hy the fact that at the moment the atom of hydrochloric acid is decomposed at the zinc surface, and the chlo- rine combined with the latter, a current of positive electricity leaves the zinc, and by a kind of convective force carries with it the atom of hydrogen which was deserted by the chlorine. This atom, instead of being itself carried onwards, decomposes the first atom of hydrochloric acid in its path, uniting with the chlorine ; this second atom of hjdro^n still uiged onwards by the convec- tive force of the current in its turn seizes the chlorine of another HATUSS OF A TOLTAIO KLEWSITT. Ail 427 atom of hydrochloric acid, caiuiiig its hydrogen to he eyolyed, and this action continues nntil the electric cnirent reaches the copper plate where it leaves the last atom of hydrogen, which, hecoming paasiTe, is here set free. As these changes occur instantaneously and inTisibljr, they altogether escape detoction by our senses. The following diasram, Fig. 447, will perhaps render these changes more intolligible, in which c is the copper, and s the zinc plate, ^.447. ^.418. connected by a wire, d ; and h and cA, respectively represent the atoms of hydrogen, and chlorine, the arrow showing the direction of the positive current through the fluid. 766. The metals employed need not be in actoal contact in the flaid, for if connected by a conductor out of the fluid, the effects above described take place. This conductor may be a wire, as in fig. 447, or be constituted by the plates themselves, by so iDclin- ing them that they may lean against each other as in rig. 448, where c is the copper and z the zinc plate. The arrows represent the direction of the electric current /rom the positive to- werrdi the negative element voithin the cell, and in the contrary direction, toiihoiU it. The pointe at which the active metallic plates are connected with any conducting matter are called jx)2m, or eUetrodee; and as the current peases externally from the copper to the zinc plate, a piece of metial at- tached to the copper plate is the pomtive electrode: and uiother attached to the zinc plate, the negOtioe electrode : of this fact, the existence of the letter (p] in copper, and of (n) in zinc, will serve as a " memoria technica." It must also be remembered that the positive ^ate is connected with the nM;ative polCt and vice vers&. That such a current really existe will presently be shown to be beyond a doubt. As a tolerably satisfactory proof, however, the well known calorific effecte of electricity may be observed bv sepa- reting the plates c, z, at the upper pairt and connecting them by 428 VOLTAIC ELECnUCITT. a piece of very fine pintinnm wire, half an inch in length. This, if the plates be about four inches long and two broad, will become brilliantly ignited, from the resistance presented to the electric current passing through it, so long as chemical action continues. In repeating these experiments, onlinarj rolled sine may be sub- stituted for the amalgamated metal, but the phenomena described will be masked by chemical action ensuing at the zinc surface, independently of that due to the current : this is usually termed local action. 767. The electricity thus evolved, although weak in intensity, is considerable in quantity ; and for many important experiments a pair of zinc and copper plates, excited by dilute sulphuric acid, constitute a valuable source of electricity. These eusctroTnotort as they are termed, are readily made by placing a piece of sheet copi)er, a foot long, and six inches wide, having a copper wire for an electrode, soldered to it, in the inside of an earthen jar ; a piece of sheet zinc, nine inches long and six wide, furnished with a similar electrode, is bent into a cylindrical form, amalgamated (765), and covered loosely with a fold of linen, so that, when placed in a jar, metallic contact between it and the copper may be prevented. The jar being nearly filled with dilute sulphuric acid, containing one part of acid to six or eight of water, the Slates are immersed, and the current of electricity evolved is irected by the electrodes to any point the onerator pleases. 76tt. In all cases in which electricity is evolved by the chemical action of a fluid on one of two metals in metallic connexion, and ex- posed to its influence, it is necessary, as already stated, that one of the metals should be more oxidizable than the other, or, in other words, more positive in its electric relations. We may thus conveniently separate the metallic elements of a voltaic circle into a generating^ and a conducting plate ; the former being alone active in determining the evolution of electricity, the latter acting chiefly as a BUi*face on which the convective energy of the current may be impressed. Unless the fluid in which the metals are im- mersed, is decomposable by an electric current, it has not the power of exciting one ; hence it must be a compound, consisting of at least two elements. Thus, water acidulated by any of the mineral acids, or in which an alkaline salt is dissolved, is power- fully active in these circumstances in evolving an electric current. A second precisely similar zinc plate can never act as a conduct- ing plate, necause it will itself teml to generate an equal current whicn will oppose the first in direction. 769. If, instead of immersing the zinc and copper plates in dilute acid (765), they had been placed in water only, chemical action and the evolution of electricity would have ensued, but with much less energy : electricity of very small potential being evolved, in consequence of the very low intensity of the chemical action of water on the zinc. In a solution of common salt, the BBLATXYK BBS OF POSITIYE AND KXOATIVE PLATES. 429 effects are more obvious^ the chloride of sodium being decomposed, and chloride of zinc fonned, the chlorine being the negative, and Bodinm the positive element (764); and electricity is evolved from the decomposition of the salt, in the same manner as it was from that of the water, b^ hydrochloric acid. The quantity of electricity evolved increases with the snrface exported to the chemical action of the fluid in which it is im- mersed ; and hence gigantic plates have been constructed for the puipose of obtaining an inmiense quantity of electricity. Mr. Pepys Dad an electromotor made for the London Institution, consisting of a copper and zinc plate, each fifty feet long, and two feet wide, rolled into a coil, witn horse-hair ropes between them to prevent their tooclung each other. About fifty gallons of dilute acid were required to act upon these plates, and the amount of electricity evolved was truly immense. 770. Having ascertained that the excitation of electricity bears a direct relation to the amount of chemical action exerted on the more positive metal employed, and that it increases with the ex- tent of surface acted upon, the evolution of electricity may be increased to a considerable amount by a proper arrangement of apparatus. It is found from experiment that a considerable ad- vantage is eained by causing the conducting or negative element to surround the generating or positive, so as to present a surface opposed to both or all sides of the latter, a fact depending^in all pro- bability upon the greater extent of the conducting surface ensuring the whole of the evulved electricity assuming the form of a cur- rent. For it is fully possible for an enormous quantity of elec- tricity to be excited, and yet but little to appear m the form of a current, either from excessive local action (766), or from a defective arrangement of apparatus. On this account, in well-constructed electromotors, the zinc or exciting element is generally placed in the centra with regard to the copper. It has been stated that an increase in the quantity of the evolved electricity ensues when either the zinc or copper exceed each other in size, and that the quantity of excited electricity is a minimimi when the metals expose an equal extent of surface. If the fine plate be the lai*gest, the maximum efiect is said to be obtained when it is seven times larger than the copper ; and if the latter be the largest plate, that the maximum evolution of elec- tricity occurs when it is sixteen times latter than the zinc plate. In the former case the quantity of electricity is three, and in the latter four and a half times greater than when the plates of copper and zinc are of e(^ual size. Tlie late Prof. Dauiell, however, proved that if the diameter of the mean section of the active fluid remains the same, and all interfering causes arising from depohition on the conducting plate be removed^ it mattera but little, so &r as the resulting current is concerned, whether the generating or the conducting element be of laiger dimensions. 430 VOL' 771. Smt^i Battery. — A coDTsnieot and oerUinlj^ poweiAil smngement Lai been proposed bj Ur. A. Smee, coniiitiiig of two pUtM of anulgoTUftted (765} nnc, ei, Fis. 449, clumped to > piece of wood, B, bj mflaiiB of ft bent piece of brau, c, '«■ **"- liimitbed with a binding screw ftt i.. Between \*. the pUtes oF dnc is fixed > thin plate of uItot I connected at its upper end witb snotber binding I screw. This plato ofBilverii coTpred witbathin lajer of platinum, \iy immersing it Ibr a sbort time in a soiution of cbloride of plAtinnm whilst '■ connected with the negati-re eloctrodo (766) of B TOititio batterj. The platinum is depodted oo the plate in tbe form of a fine powder, and from the myriads of conducting points thus formed b; tbe inconceivably minute particles of reduced metal, the evolutiuii of the hydrogen goi is greatlj facilitated. An arraiiEement of this lei nd, placed in a pint jar of dilate salpburic aci^ becomes an excellent and efficient soarce of electridtr- 772. In tbe arrangements of apparatas abore described, a con- siderable loss of electricitj occurs during; the evolution of the hydrogen. To prevent this, certaio means nave been had recoorae to, for the purpose of absorbing the bydrc^en, bj employing it to reduce metallic oiides, or by combining with the oijgen of any highly oxidized fluid, as nitric acid. If the plates of sine and copper, instead of being acted upon by a dilute acid, be immereed in a solution of sulphate of copper, cbemiual decompoaitinn and consequant evolotion of electricity will occur. No gas is in this case evolved, as the snlphate of copper is alone decomposed ; the sulphuric acid and oxygen acting on the lino forming the sulphate of that metai, which ii dissolved by the water ; the copper being deposited, in a metallic stale, on the surface of the oopper plate used. Thus the battery, or alectiomotor, may be advantageoosly excited with a solution of sulphate of copper instead of dilute add. 773. In all these arrangements, both plates are inunetved in the same exciting fiuid ; but considerable advantage is gained by employing two different fluids. This mode is founded on facts longknowD but first applied to tbe conatruction of electn>motors by Daniel!.* The theoretical action of those arranecments is readily explicable: let a, Fi^. 460, be a vessel filled with a solu- tion of common salt {chloride of sodium] ; b, a glass tube im- mersed therein, fiuniahed at its lower part with a diaphragm farmed of a piece of bladder, and filled with a solution of sulphate of copper ; a plate of copper, c, and one of sine, i, connected by the wire, d, are immersed in the two flaids. The geDoikting or positive element, i, decomposes the chloride of sodium, uniting with the negative chlorine, forming chloride of liuo, and teleaung ^1 FSg,4B0. £i I the positiye Boditim, vLich pMses through the bladder-diaphragm under the convective influence of the excited current, to reach the ne^tive plate, c; here it enters the eolation of sulphate of copper, which it decomposeR, uniting with the sul- phuric acid and oxygen to form sulphate of soda, and setting free copper, which ia deposited on the plate o, and the positive current which accompanies the chemical action passing along the wire d to z, de- composition goes on as before : the atoms of Bodiam and copper first set free, are not thoee which are ultimately active m effect- ing decomposition, or in being deposited on the conducting plate ; the same series " of molecular changes occur as in the case of the decomposition of hydrochloric acid already described (766). In this appa- ■'^ ^ ratus, after the current has continued passing for a sufficient time, the fluid in a will be found cunverted partly into chloride of zinc, and that in b into sulphate of soda ; whilst the beautiful crystals of copper deposited on c, will be found to bear that rela- tion to the quantity of zinc dissolved to form the chloride, which the atomic weight of copper does to that of zinc. If the wire d were cut across in the middle, chemical decomposition and the evo- lution of electricity would cease, until they were united by being placed in contact, or connected by means of a pood conductor. 774. As in this apparatus the inductive action of the two plates on each other is limited by the area of the base of the tube b, through which alone a current can pass from the ^nerating to the conducting plate throogh the flmd, the evolution of electricity will be increased by replacing the tube b by a porous reservoir of animal membrane, as bladder ; and this constitutes a form of ap- paratus frequently employed. A piece of sheet copper is bent into a cylindrical form, and placed in a bladder fastened round its upper part by a piece of stnng ; the whole being placed in a jar, containing a concentric cylindrical roll of sheet zinc ; a metallic wire, or electrode, is soldered to each plate. A solution of sul- phate of copper is poured into the bladder, and one of common salt, or sulphate of soda, is placed in the jar, exterior to the bladder, so as to act upon the zinc plate. DanieU^H Battery.— ihe inconvenience of this arrangement arises from the zinc being placed on the outside of the copper, which necessarily produces, as Daniell has shown, a certain loss of power ;* accordmgly the arrangement which he proposed, con- sists of a cylinder m amalgamated zinc, z. Fig. 451, placed in the centre of a hollow cylinder of copper, o ; the former being Phil. Trans. 1838, p. 41, et Mq. Ifg. «L aorronnded by a luW of porous earthen ware, cloKd at the bottom, or, which aOBwera the pur- pon exceedingly well, a cylindricul bag of oom- pact aail-cloth, preriouilj soaked in water. The exciting fluid acting on the zinc, ia a mixture ef one part Bulpharic acid and eight of water, the copper cylinder being filled with the same mixture saturated with sulphate of copper. On connecting the two platoa, by meani of a wire, the zinc ptate decompoaes the water, ilihydn^en, influenced by the convective force of the posi- tive current, passes tlirouiih the membranoua bag, towards the copper plate, where it is not evolved, hut aids the decompoijition of the sul- phate of copper ; uniting with the oxygen of the oxide to form water, and setting free the copper to be deposited in beautiful crj-stals, on the surface uf the copper element. 775. The cnpper deposited in these eiprimenta upon the nega- tive pUte Is found, irthe electric action be not !<» mtense, to be compact, firm, Hiid even malleable ; nnd on sepamiiug it from the surface on which it has been deposited, it will be found to present a perfect fac-siiuile of every mark and scratch exiiting on the sur- face of the negative plMa._ This hna led to the discovery of the beaatifid art of electrotyping, by which exact copies of almoet anything of which the surface is capable of being rendered a tolerably good conductor, may be made in copper. Many con- trivances hafe been made fur the purpose of ■*%■ «>• &cililating the deposition of copi»r from its solutions, and will be found described in the numerous popular treatises on the subject. I I I I I The siDiplest apparatus consists of an I il I JL^ I earthen or vsminlied wooden vessel, ^ n ^1 ' I (3) I* Kg. 452, divided vertically by means of » I I — I I ^^ I poniusdiapbrngm,c,ofwoodurearlhenware, ^^^^^^^^J thus fiimiing two cells ; one of these, as a, is filled with a vei; weak solution of common nit, the other, a, with a solution of sulphate of cupper. In the generating cell, a, is immersed a plate of zinc, i, connected by a wire with the medal, &e., to be copied, which is placed in h. lliig tnedal should he coveted with a resinou" varnish or some noii- conduclor, except on the surface to be copied. An electric cuit^ol is soon set up, and l>oth solutions are ducumposed (773), miitalljc copper being deposited freely on the face of the medal ; and when the deposit has attained aufhcient thickness, it will, if adruilly removed from the surface of the metal, prevent a moat accurate ■nd beautiful copy of the original. It is scarcely necessary to say that the cell, b, should be supplied with fresh crystals of sol- VAXIOira FOBm of SLBlCSHTt. 433 pbate of copper, in proportion as the flnid loses its colour by depo- siting its copper. In this manner, by careful manipulation, most accurate copies of engraved copper plates can be readily made, and those beau- tiful products of art DO multiplied to an almost unlimited extent. Even the inconceivably delicate tracings of Daguerre's exquisite pictures can be copied by the electrotype. Where the object to be copied is not metallic, it may be rendered a sufficiently good conductor by covering it with a thin layer of finely powdered plumbago, and thus casts made of wax or sulphur can be readily copied in copper. 776. Orove't Battery. — By far the most energetic voltaic ai^ rangement, in which the hydrogen is absorbed, is that proposed by Mr. Grove. ^. 458, Various constructions of this excellent contrivance are met with. They consist essentially of a slip of platinum-foil, p, Vig. 453, furnished with an electrode, a, immersed in a cylinder of porous earthenware, c, filled with strong nitric acid (sp. gr. 1'33). This cj'linder is surrounded by a roll of amalgamated sine, having an electrode, s, soldered to it, and placed in an earthen or glass jar, B, containing dilute sulphuric acid (1 acid to 6 water). The hydrogen separated from the water decomposed, when ▲ and s are connected, is not evolved as g^, but combines with some of the oxygen of the nitric acid, reducing it to deutoxide of nitroeen, which partly dissolves in the acid, giving it a green or blue colour ; the rest escapes, and produces red fumes, by combining with the oxygen of the air to form nitrous acid. According to Jacobi, with equal surfaces of platinum and copper, the apparatus of Mr. Grove is about seventeen times more powerful as a source of electricity than that of Daniell (774). With a nitric acid element capable of oeing contained in a two-ounce jar, fine platinum wire may be brilliantly ignited. The superiority of Mr. Grove*s arrangenient is owing, not only to the SMorption of hydrogen, but to the excellent conducting nature of the fluid employed, and to the remarkable facility with which nitric acid undergoes decomposition, and parts with a portion of its oxygen. 777. IhuiseiCs Battery, — ^The expense of platinum is a serious drawback to the use of Grove's battery; to obviate this, Prof. Bunsen has proposed substituting cylinders or plates of carbon for the platinum* He made these, by strongly and repeatedly heating a mixture of pulverised coal and coke, and thus obtained a porous mass capable of being easily worked into any required form. The porous mass was subsequently consolidatea by oeing F F 484 YCLTAIO ELBOTBIdTT. immened in strong syrnp, and dried, and the mggr then cb^ bonized by exposure to a white heat in a closed TesseT. These car- bon-batteries are said to be equally powerful with thoae of platinum. According to the experiments of MM. Liais and Flenry, the internal resistance of the cell may be oonsiderably diminished, and oonsequently the power of the battery increased, by the omission of the diaphragm, proyided the carbon be kept saturated with nitric acid. For this purpose the carbon cylinder must be hollow, and cemented into the bottom of a glass vessel a little larger than itself, the interrening space being filled with nitric acid. This form of nitric-acid battery is much used on the Continent, but has -not found favour in this country. A carbon-battery may be constructed by means of the best black-lead crucibles, after strongly igniting them for a short time. For this pur]^ose a cylinder of amalgamated zino, ^' ***• z. Fig. 464, is placed in a porous cylinder con- taining dilute sulnhnric acid, and immersed in the crucible, c, filled with nitric acid ; a wire coiled tightly round o acting as a conductor. Such an arrangement, although powerful, is, however, certainly far inferior to Mr. Grove's apparatus, probably on account of the earthy matter which is always present in these cru- cibles, rendering them imperfect conductors. ' 778. Schlhibein^t Battery. — Prof. Schonbein has suggested an eflSective combination, in which the platinum of Grove's, and the carbon of Bunsen's battery, are replaced hj panive iKSk, This is a peculiar state assumed by iron under several circumstances, especially after momentary immersion in a mixture of strong nitric and sulpnuric acids. It then retains its metallic lustre, but has .lost its power of being readily oxidized by exposure to air, and of .being dissolved in strong nitnc acid. Schonbein places in a vessel of passive iron, a mixture of three parts of concentrated nitric and one of sulphuric acid. In this is immersed a porous earthenware jar, filled with dilated sulphuric acid, and containing a plate of amalgamated zinc. This forms an economical and powerful apparatus. • 779. The MaynootK BaJttery. — ^The arrangement to which this term hcM been applied was devised by Dr. Callan :* it consists of a water-tight cast-iron cell, containing a porous cell, within which is a plate of amalgamated zinc. The iron cell is charged with a mixture of nearly equal parts of strong nitric and sulphuric acids, and the porous cell with a mixture of two parts of sulphuric acid, one of nitric acid, and eighteen parts ot water. This form of battery is stated by Dr. Callan to be nearly one and a half times as powerful as Grovels, when of equal dimensions. 780. RcherWi Battery. — A simple and efiective modification • Phil. Mftg. Tol. XTTiii. TAJUC^B F0&1I8 OF ELEXENT8. 435 of the zinc-iron batter/ has been introduced by Mr. Boberts :* this consistg of an alternate series of plates of passive (778) iron, and amalgamated sine, placed in a wooden frame, and kept in equidistant and parallel positions hy slips of wood. The connexion of the plates is peculiar : let a, b, c. &c., represent the iron, and a, b, c, &c., the zinc plates, then in tne series A a, B &, c e, D d^ &c., A is connected with 6, a with c, b with e, b with d, and so on. lu this arrangement the intervention of two plates between each pair in metallic connexion prevents the loss of electricity by conduction through the excited fluid, and supersedes the use of ])artitions ; the whole is immersed in dilute sulphuric acid contained in a wooden box with water-tight joints. Mr. J. Watson recommends the iron plates to be prepared by immersion in dilute hydrochloric acid ; and the zinc pUtes to be amalgamated in M. Bizot's bath, which is thus prepared : — One oz. of mercury is dissolved in a mixture of one oz. of nitric and three of hydrochloric acids, and three oz. more of hydrochloric acid are subsequently added. He states the relative electromotive forces to be, if clean copper be used, 7 ; if sheet iron, 9 ; and if iron thus prepared, 13. 781. Leewn^g Battery. — In this batteiy pairs of zinc plates, one of which is a little longer than the other, are grooved into the sides of a trough, and are connected by resting on pieces of zinc at the bottom. Within these zinc cells, as they may be called, is placed a porous cell containing a plate of copper, bent over at the top and clamped to the higher side of the next zinc cell. The porous cells are charged witn a solution of one part of bichromate of potash in ten of water, and the trough with dilute sulphuric acid. In this form of battery, as in the preceding, water-tight partitions are omitted, as being useless. 782. Platinum and potassium being at the opposite extremes of the electro-positive series of metals (764), constitute a most ener- getic voltaic arrangement. The decomposition of acidulated water, and the divergence of a gold-leaf electroscope, have been effected by the energv of a single element : but the expense of the materials precludes tne practical application of this powerful com- bination. A convenient mode of employing it has been proposed by Mr. Goodman.f 783. A verv efEec^ve, but rather costly form of the zino-carbon battery may oe constructed by charging the siuj^le cell with a saturated solution of sulphate of mercury^ contaimng some of the nndisBolved salt at the bottom. When this salt is decomposed, the disengaged mercury adheres to the zinc plates and keeps them fully amaJgamated, thereby effectually preventing any local actioiL • Proc. Elect. 8oc.jp. 357. t Mem. ManokeMer lit. and Phil. 8oo. toI. Tiii. P F 2 436 VOLTAIC BLECTRICITir. Fy.465. This form of battery is especiallj convenient wlien considerable electromotive foroe is reqmred, and when the battery is also re- 3 aired to remain charged and ready, but out of action, for coofi* erable periods of time. 784. It is not absolntely necessary to use two different metals to obtain an electric current, for if two portions of the same metal be employed, the surfaces of which are so constituted as to be unequally acted upon by the fluids in which they are immersed, electricity will be evolved ; the portion of the metal most acted upon becoming the positive element. Thus, a plate of rolled, and one of cast zinc, constitute an actual but feeble voltaic arrange- ment ; as does also a plate of new clean zinc, with one which has b^en previously corroded by an acid. A new and a corroded plate of copper acted upon by nitiic acid, will also evolve electricity. 785. If e(|ual surfaces of one metal be used, no electricity will be evolved, unless acted upon by fluids exerting different chomical actions upon them. Thus, a plate of smooth inin acted on, on one side by dilute sulphuric acid, and on the other by water, sulphate of copper, &c., deve- lops a voltaic current. Let a plate of copper, A B, Fig. 455, be placed in a glass vessel, and a saturated so- lution of sulphate of copper poured in up to the line c d, so tliat about one- third of the plate may be immersed. On the surface of this fluid slowly pour some very dilute sulphuric acid, or weak salt and water; takine care that the fluids do not mix. Under these cir- cumstances the upper part of the plate, a, will be slowly acted ujpon by the sulphuric acid ; the lower end, b, becoming the nega- tive element, decomposition of the sulphate of copper smwly takes place, and the metal becomes deposited in a crj^stalUne form, on that part of the copper plate whicn is immersed in the sulphate of copper. 786. If the electrodes of a single pair of plates be famished with platinum terminations, and instead of bemg in metallic con- nexion, be immersed in the same solu- tion as the plates themselves, no current will pass, llie electricity excited in the cell, A, Fig. 456, will not be able to pass from p to p in the cell b, because the current is too weak to overcome the affinities of the elements of the liquid in B fur each other, and it cannot traverse the fluid save by effecting molecular changes in the elements of the com- pound present. Tlie current may, how- Fig, 469, QUJLITITY ASD FOTBVTIAL. 487 eretf be induced to pass, eitber by replacing tbe fluid in b bj one wbicb ie more readily decomposable, or bj calling in the aid of the afifinitj of the positive conducting wire for one of the elements of the liquid in b. To illustrate the first case, let a and b be both filled with dilute sulphuric acid, when the current will not pass through b. Beplace the contents of b by a solution of iodide of potassium, a salt of Ipeady decomposition ; the current will now readily pass, decom- posing the iodide, evolving iodine at the surface of the platinum plate connected with the copper in ▲, and if a little starch be added to b, the evolution or the iodine will readily be detected by the formation of a splendid blue precipitate of iodide of amidine. The second case may be illustrated by filling ▲ and b with dilute sulphuric acid, and letting the conducting wires be of copper, with their naked terminations immersed in b. The current wul now pass, and bubbles of hydrogen gas will be evolved at the end of the wire connected with the plate z. Here, although the corrent per Be could not effect a separation between the elements of the water in b, yet when aided b^ the affinity of the copper composing the positive conducting wire for oxygen, it succeeded in decomposing water, and traversing the fluid. 787. In investigations on voltaic electricity, it is necessary al- ways to bear in mind a distinction between the quatUity ^'nA. inten- ftity or potential of the electric current ; the former bearing, caUeris pmhuMf a relation to the size of the plates, or to the number of plates combined, and the latter to the number of alternations. A pile or other voltaic arrangement of fifty pairs, excited by pump- water only, will readily cause the gold leaves of the electroscope to diverge, and will produce a sensible shock ; but will scarcely decompose even a small portion of water in a space of time sufficient, when the battery is excited by an acid, to rapidly resolve a much larger quantity into its gaseous elements (754). The following facts will place the effects of the combinations of voltaic elements in a ^' ^' ' clearer light. If in two elements the conduct- ing wires of the sine, and those of the cop- fer plates, be respectively joined together, ig. 457, the current excited by the action of the acid in a on z is opposed in direc- tion to that similarly excited in b. Tbe consequence is, that they mutually inter- fere, and no circulating force is developed, imtil the connecting wires be themselves connected by fo, which will transmit the currents due to the electromotive forces of both elements, as shown by the arrows. But if, instead of allowing the currents in a and b to oppose each 488 VOLTAIC BLBCTRICirr. Other, we canse them to pass in the same direction, we greatlj increase the potential of the erolved elec- tricity, and enable it to overcome a much greater external resistance. Thus, in Fig. 458, the currents in d and e travel in the same direction, and, as it were, urge on each other, so that by their com- bined inflaence they can traverse a fluid which wonld insulate the current of d or E separatelv. 788. Volta^sPiie. — A considerable quantity of electricity may be evolved by the various electromotors now ((escribed, but unless the number of elements be considerable, the current is of small potential energy. To Prof. Volta of Pavia science is indebted for the discovery of the means of indefinitely augmenting the poten* tial of the current, by increasing the numbler of elementa employed ; he thus placed in the hands of philosophers an instrument of analvsis and investigation, greatly exceeding, in its effects, anv of the means of experimental research previously discovered. Omitting the earlier experiments of Volta, or the mode of reason- ing by which he was led to this discovery, as out of place in a work of this description, it will be sufficient to observe, that, by combining the action of several pairs of plates, a great increase of energy and power is gained. The following is the construction of the voltaic pile : place a plate of copper, a, Fig. 459, on the table, and on this one of zinc, z ; a piece of thick flannel, f, moistened with a dilute acid, brine, or even water, la placed on the zioc ; a plate of copper on this, and so on ; copper, zinc, wet flannel — copper, zinc, &c., until any reouired number of alterna- tions is employed. Place the whole pile on an imulating stand, and connect the lower plate, c, with the condenser (738), connected with an electroscope ; the gold leaves will divei^e with negative electricity. Then connect the upper plate, z, with the condenser, and the leaves will diverge with positive electricity. In an insulated pile of anv number of alternations the potential of each form of electricity u observed to increase from the centre to the extremities. The direction of the current between the terminal plates of the voltaic pile is here apparently at variance with that previously stated (766) ; but, in point of fact, in the arrangement just de- scribed, the terminal plates are merely electrodes, and not eleo- tromntors ; the lowont zinc plate z, and the hic^hest copper plate, c; are the terminal active plates in the pile. The arrangement here described was based on the contact theory: namely, that the evolution of a current resulted from the contact of different metals. If a pile or batteiy be constructed like the one originally Iig.U9. PIJLTBBHAGHBB*8 OHAHI FILE. 439 eontriYed by Yolto, but comprising at least thirty alternations, and the top and bottom of it be touched at the same instant with the moistened hands, the electricity accumulated at each end of the pile will discharge itself throagh the arms, producing an dectric thoek. If a piece of well-burnt charcoal be placed QjKin the uppermost plate of the pile, and a wire communicating with the lowest be brought in contact with it, a series of faint sparks will be visible on drawing the wire over the surface of the charcoal. * 789. The source of electricity in the ToUatc pile may be easily traced to chemical action, for in the lowest pair of plates in Fig. 459, the zinc is attacked by the flaid in tne wet flannel, and a current is determined through the flannel from the sine to the second copper disc, and the lowest disc, c, is in a negative state. In the second couple, the positive state of the copper plate neu- tralizes the negative state of the zinc plate, arising from the current determined upwards through the second flannel ; and this series of actions is repeated to the top of the pile, no greater fuanHty of eketrieity being obtained from a piUf than from a nnple pttir of plaUef* the potential of the eUctrie cvrrent cdon4 hetng inereaeea: for the chemical action, and disturbance of electric equilibrium, in the intermediate plates of the pile or battery, are exerted onlpr in urging on the electricity to the ter- minal plate, and thus increasing the electromotive force of the current evolved. 790. An ingenious modification of Volta's pile has been made by M. Pulvermacher. In this, pieces of gilded copper and of zinc wires, arranged side by side, but not in contact, are wound on a piece of porous wood, each wire terminating in little hooks. This constitutes one element of the chain (as it is called), and is con- nected with a second by means of these terminal hooks ; this with a third, and so on. Tuis apparatus is excited by immersing it fbr a moment in distilled vinegar. Enough of the acid adheres to the pieces of wood in each link to excite a current of electricity by acting on the zinc wire. The whole forms a most convenient source of electricity, a chain of 100 links giving a most painlul shock, and producing the ordinary chemical phenomena. 791. A still more in^nious and effective apparatus has been contrived by Mr. Stnngfellow, of Chard. Each el«^ment of this apparatus consists of a plate of zinc 2'5 inches long, and 0'3 inch wide, on which are wound, in a spiral manner, 30 coils of flattened copper wire, as close as possible to the zinc, but separated irom it by a non-conducting medium. Four of these alternations, merely moistened with a sponge, dipped in common water, pro- duce a current sufficiently powerful to decompose distilled water, evolving a copious stream of minute bubbles of oxygen and hy> drogen from the platinum points immersed in the water. With twenty-two alternations (which after being moistened with dis- • Farsdty, Fhfl. Tnuui. 1894. Exp. Bwetxohei, dth Series, 991. • 440 TOLTAIG BLBOTRIOlTt. tilled Tinegar, are placed m a caae the mn of a common card- case), a carrent of electricity is evoWed, capable of producing distinct shocks, and rapidly aeoomposing water ; and it remains scarcely diminished in mtensity after half an hour's action. For physiological purposes, this is certainly the most useful apparatus which has been hitherto contrived. It owes its remai^bb power to the iii^nious manner in which all resistance to the pas- sage of electricity is removed, by the soldering together of the metallic elements, and to the very small bulk of fluid required to excite them. Hence, neariy all the electricity evolved is thrown into current, instead of being partly lost from imperfect conduction. 792. Marie Davy^e Pile. — ^This yery energetic and eflfective arrangement, for many experimental purposes, consists of a series of ciroular iron dishes, to the bottom of each of which a plate of zinc is soldered. In each dish is a layer of salphate or chloride of lead moistened with water: of these salts the chloride is much more active, but it is likewise more costly. 83 parts of zinc will reduce 144 of sulphate of lead, and will yield 104 parts of lead. A pile of 40 of these elements has been in use at the cen- tral telegraph office. 793. The power of the yoltaic pile decreases, and finally ceases, with the neutralization and evaporation of the fluid moistening the piece of flannel, and with the oxidation of the plates. These constitute sources of considerable inconvenience in experimental inyestigations ; to diminish which yarious means have been pro- —^ ^^ posed, as b^ fixing the pairs of nnc ^' ' and copper lu a trough of wood, Fig. ^^^ 460, and replacing the wet flannel by ^^ a fluid poured into the cells thus ^ I formed : constituting Craikshank*s ar> V I rangemenU This is not inconvenient, ^ sgj^^aggg ^ especially when a solution of sulphate of copper is used for the ezcitine fluid ; which, as Dr. Fyfe has shown, increases the electromotive rorce of the current, as compared with that evolved by dilute sulphuric acid, in the proportion of nine to two. The positive electrode, whether of a single element, or of a series constituting a voltaic battery, is always that which is con- nected with the last active copper or platinum plate, and the nega- tive, that connected with the last active zinc pUte. Much un- necessary confusion, with regard to the expression of the negatiye or positive side of a battery, has been introduced in many works^ from the want of a role like that ^ven by Faraday, of connecting their sides with a g^ven direction of the current. Thus, in Oruikshank's battery, the positive electrode is that which is con- nected to the last zinc, and the negative, to the last copper plate. This difference is only apparent, as will be evident by referring to the original yoItaic pile (788). Remove the terminal plates, and then all obscurity will vanish, for the positive electrode YAUOUS FOSM8 OF BATTBBIES. 441 J^.46L wiU be in actual contact with the last copper plate, when the Bnperfluous and truuking plate is removed. In a Graikshank trough, excited by an acid or saline solution, the positive elec- trode will be that which is fixed to the end towards which aU the zme plates look : and the negative, that fixed to the end towards which aU the copper pUUes look. A great improvement in the construction of these batteries was effected by Dr. Wilkinson, who fixed the zinc and copper plates to a wooden beam, and immersed them, when required for use, in an earthenware trough, furnished with partitions of the same sub- stance, and filled with the exciting fiuid. This arrangement i» rendered still more effisctive by causing each zinc puite to be completely surrounded by the copper plate of the next pair, as sogiested by Dr. Wollaston. Earaday nas proposed an excellent arrangement,* in which the metals are brougnt as close to each other as possible, the alter* nate zinc and copper plates being separated, not by partitions of earthenware, but oy pieces of stout cartridge paper, or card. 794. A series of elements constructed on Daniell's principle (774), aflfords a most valuable source of potential electricity, and has, moreover, the advantage of being constant in its action for several hours ; whereas, the others above mentioned, although very eneigetic on the first immersion of the plates, become rapidly weak- ened bv the continual action of the fluid employed, an eflect but partially preventea by amalga- mating the zinc plates (^765). Ten pairs on Professor Daniell's ar- langement, the zinc cylinder of one being connected with the copper of the next, and so on, con- stitute a most valuable and poweitnl voltaic battery. Fig. 461. A very efficient arrangement is made by connecting in a similar manner, a dozen pairs of zinc and copper cylinders, sepa- rated by means of bladder di^hraipnsy Fig. 462, the *^- ^' zinc bemg acted on by common salt, and the cop- per bv sulphate of copper ; this has the advants«e of cheapness, and of being readily constructed. The zinc and copper plates are most conveniently con- nected by copper wires, • FUL Trans. 1833, lOth Scries, Bzp. Beiearchea, 1123. 442 VOLTAIC ELBCTRICTTT. fixed bj a binding-Bcrew soldered to each plate, and tfie electrodes can be readily attached to the screws of tne terminal plates. 795. As bladders and other membranons diaphni|^8 have the disadvantage of becoming rapidly corroded, and pierced, by the action of the exciting fluids, and of being torn by tne sharp edges of the crystals of metallic copper deposited on the copper plate ; various attempts have been made to substitute for tbem cvlin- drical vessels of porous earth. Vessels of this kind have been nsed by Daniel], and are now made sufficiently thin to prevent their opposing much obstruction to the transit of the electric ourrenl^ so that their use has become very generaL As already stated, bags of firm sail-cloth well sewn, or still better, pieces of the tubular woven hose used for garden engines, form excellent diaphragms, and withstand for a long time the action of acids. 796. The most poweiful battery is made bv an alternate series on Mr. Grove's arrangement (776). Six of these elements, each having a platinum puite three inches wide, placed in thin rectan- g|ular cells of porous porcelain, so as to bring them^ as near the zinc as possible, constitute a most powerful and efficient arrange* ment. The largest hitherto constructed is that made by Professor Jacobi of St. Petersburg; it contains platinum plates, each having a superficies of 36 square inches. Even with very small pirates, a powerful battery may be made with very little expense. For this puroose, procure the'bowls of six tobacco pipes, and stop up with seaun^-wax the holes left by breaking off the pipes. Place on the teble six small glass tumblers. Fig. 463, each an inch and a half or two inches high, like those used by children as toys, plaoe in each a piece of amalgamated zinc, bent so as to form a hollow cylinder. In each of these cylinders let a pipe-bowl be placed, and id each of the latter immerse a piece of thin platinum foil 1^ inch long and half an inch wide, connected with the next zinc cylinder by platinum wire. Fill the pipe-bowls with nitrio acid and the tumblers with dilute sulphuric acid, and an eneigetio current of electricity will be set free, capable of rapidly decom- posing water (821), igniting wire (815), charcoal pointo (808), &c. 797. It must not be supposed thfit all the electricity which is excited by the chemical action of an acid, or other fluid, on the generating or positive metal, even in the best arrangements, ohm's thbort. 443 appears in the fonn of a carrent. Various causes, modifying in a - renuuicable manner the quantity of electricity which appears in the current, exist in the best constructed apparatus. These liavo been mathematically investigated by Prof. Ohm of Nuremburg, and the results are developed in what is known as his formula. The accuracy of this has been submitted by Wheatstone, Daniell, and othersi and in a most successful manner, to the test of expe- riment. The following is a brief explanation of the more simple results of Ohm B investigations.* Let E be the electromotive force, equivalent to the affinity of the exciting liquid for the generating metal, and corresponding with the amount of electricity which would appear in current, if all opposing causes were removed ; i?, the internal resistance, or that opposed to ^ b^ the contents of the cell, ariiong for the most part (rom the affimty of the ele- ments of the exciting liquid for each other ; r, the external resistance, arising chiefly from the imperfectly conducting nature of the wires used to convey the current : and C. the current force, or the amount of potential which actually reaches the end of the conducting wire ; then E The theoretical value of ^is diminished materially in practice by the affinity of the conducting plate for the ingreUienc of the ex- citing fluid which tends to combine with the generating plate ; this affinity, however weak, is still seldom absolutely nuU. The mutual affinity of the separated elements of the fluid, evolved at the surfaces of the plates, also diminishes the intensity of E, The internal resistance, R^ varies directly with the distance D, between the two plates, and is inversely as the area of the section, 8f of the exciting liquid, or n ^ ri-i r, or the external resistance, so far as it is dependent upon the conducting wire, varies inver$ely as the section oi' the wire, #, and directly as its length Z, or I r^i 8 798. If the circuit be closed without any external resistance, then rso, and n ^ ^^ hence a single voltaic element produces the same effect as a * For tho furtbar darelopment of this theory, and its Tuioos importmnt ■ppUofttionSr the alodent is referred to the eU borate" Chemicsl Fbiiosuphy** oi the lata Frof. Dwuell — % work that ought to be iu the bands of every •todent; also to Fntf. Obm'e original work, *' Die GalvanlBcbe Kette mathe- matiech bearlwitet," a digest of whiou baa appe«red in the 2ud vol. of Tajlor'a ooientifio Memoirs ; and to a p^per by Frof . Wbeatstoue, in the PlttJ. Traoa., Part IL for 1043. 444 VOLTAIC BUBcniciTr. l>atteTT oonnstiDg of an}[ number of preciMlj similar domenta, provided no external reeittanee be interpoeed in the dretni (789). Also a thermoelectric element (Ch. aVL), and a voltaic ele- ment will prodace the same effect, when the greatly inferior eleo- tromotive force of the former is compensated by a correapending decrease in its resistance ; in a thermoelectric arrao^ement the resistance is in general small, because the circnit is entirely nwtal^ lie, while in a voltaic element^ the resistance of the liqind is al- wavs considerable. It appears from [a] that when r has any value, it will diminish that of C: that is, any interposed extenui resistance will weaken the force of the current, bat less so as it is smaller in proporcioa to the other internal resistances in the circuit. If n elements be united together, then B becomes - , and JS nE , — 1 nr ^'=-5— :=3rF - +r n but if the n elements be arranged in series, then B, J?, become m E, n 5, respectively, and ^ _ nE The value of C^ will evidently increase rapidly as « ii when r is veiy small compared with M; this explains the advan- tage of employing several small elements combined, or else lam elements, when uie resistance to be overcome is small: and it is equally evident that the value of (7, will increase with «, when r is large compared with B ; this again explains the neceeaity of emploving a series of voltaic elements, in order to ovcreume con- siderable external resistances. The same remarks will apply to the comparison of a voltaic with a thermo-electric circuit. 799. Suppose that r^m B^ and that jc of the a elemenia be ar- ranged in series and - of these series united, then by snbatitiiting these values in [a] we obtain _ __ nE ^-T^) The value of C. will be a maximum, when the value of x-l- — X is a mtntmum, and this is the case when 1 — -y =0, whence «= v m n ;* • BytheDiffeNotial Csloalus, il. /(«)BO,wbeB/(#) is»: <«.(«+V)-»-7' wumiitTon'i BaiDos. 4411 I preMDts the moat adnata^na mode of Riranpn^ a •.T of alemeDts, when the nno of the eitenuJ and m- itiEea u known : it Bppeara that the niunber to ba BoiieH ahoald be the neareit integer bi a mean ptt^• :ween the aamber of elrmenta, and the ratio of ei- itcrnal reiiatances, tliat is a diTisor of the number of rhns, sappoae it were reqaired to ascertain bow » H'b Utter)' (794) of 12 cells should be arranged in d the strongest cnirent throngb a given quantity of (coiled round an electro-nugnet [877] for example), le or which has been ascertained to be dnuble that of he batlerT ; hem x would be a mean propoiiiooal be- 12, or the equaiv root of 24. which is 48 nearlj: ' the greatest eRect will be produced hj miiling three consisting of four elementi. er important deductions nuT be obtained, aa corol- Ohm's formula ; but its application to the solution of liooB relating to electromotive force has. It is hoped, :nt to facilitate its further apphcation to anj otbar loy be required. ■jiUtone't Briftne.—ln all the Tariooa and importatit plications of roltaic currents a correct estimate of the ulancea of Tarinos bodies (or, an the conrenie of r»- Htmelimes called, their condDctiTities") is india- icewarj, in cnler that the abore and many other lulting from Ohm's law may be made uae of The ly which these reaiaCancei arc determined ii Wktot- igt, the principle of which is this : — a Toltaic current between two conducCoia m arranged that the partial .ypasa in opposite directions through a galTanometer t IB evident that if the two currents are exactly equal, nil remain at rest. If then the resistance to be eati- nlerposed in one of the circuits, and in the other a nouni of known resistance to bring the needle to tero, icd resiHtancea must be equal, and the value of the UO- ■epresenfs this inBtromeaC in ita original and riuplest 446 TOLTAIC ELECTBICITT. tance from esch other, in the middle of the ndee a xt* d ■, Me placed two other pairs (^binding-ecrews, b, r ; o, h ; the conneiioni between the binding-scTews shown in the figure are made with copper wire, namely, a-c, on, Art, f-d, d-o, h-b. When an ezneri- ment is to be made, a and d are connected with the tonmnaJs of a battery, and b, o, with those of a galvanometer, m, whidi for the sake of explanation is represented in the diagram, aa being interposed between c and d. In order to adjust tne bridge two equal small resistances, as two equal short lengths of the same copper wire are interposed at b, r, and a, h ; and the diObreotial current in the galvanometer is then reduced to aero, by means of the joined arms d k, which being of laige section compared with the wire connecting the binding-screws, will take off auch a por- tion as may be required of the resistance of either fd, or do. The required resistance is now interposed between e and r, and a known resistance between o and h, which is varied nntil ^e differential current in the galvanometer is again reduced to The course of the currents over the bridge is rather oomi ~~ but by a little care may be readily traced out. 8np]foae the tive voltaic current to enter at a, it will then be divided bet^ A c, and A E F D ; the portion arriving at o will be a^ain sobdivided between c b, and c m d, and that arriving at d will be aimilariy subdivided. The current will therefore have four distinct oomaea between a and n, vis. a-o-b, a-e — p-d-q — ^h-b, a-om-d-o — b-b^ and A-E — F-D-M-G-B ; the first two of these wiU dearly have no eflect on the galvanometer, and of the last two, the portions and F-D-M-oB, also a-e and h-b are by cons^nctioo e^nal in ■ ■ the ■ resistance ; if therefore the remainders, the interpoaed B — F and G — ^H, are equal, the whole must be equsl, and the diffe- rential current, which alone influences the galvanometer, most « 0^ and the needle will remain unaffected ; henoe the amount of known resistance a — ^h will be a measure of b — ^f, the resistance sought. This form of bridge is convenient for estimating small resist- ances, but it is not suitable for large ones ; for it IbUowa from Ohm^s law, that if a current be divided between two channels, the quantities passing through them will be inversely propor- tional to their resistances ; suppose then that the resistanoe ■ — f were 10,000 times that of the wire ac, it follows that obIv nrirv^^ part of the current will traverse the galvanometer, and the aifferential current being again a smaU fraction of this^ is liable to become imperceptible. To remedy thia inoonvenieooe; two more pain of bmding-screws must be interposed between A, c, and c, b, between which it will be most advantageona to interpose equal resistances, and also neariv equal tc thoae at b, f, and o, h; as in that case nearly one-fourth of the whole cnrrent will pass in each direction through the galvanometer, and the differential current will then have its maximum value. 801. There is, however, another fonn of the bridge now fre- quently employed, which, besides doing all that the form above rAHDABD wot OF BLICTBIOAL BBBUTillCB. 447 capable of, has alao the advantage of ihoiving approzi- ratio of the interposed resistances, when their aiifer> Qsiderable. This instrument consists of a stent oard, about forty inches long, on which is a scale of a d into millimetres, a 6, Fig. 465. Parallel with the scale is stretched a piece of German silver wire, be* ds of two flat copper oars e, d^ fixed to the ends of the J^. 466. laving binding*i«crews at their proximate ends. Be- ids of c, df are three equal copper bars, e, /, g, each nding-acrew in the middle, and one at each end : the g ones are marked with the same letters as in the pre- "am. The points k, l, h, o, correnpond with the pro- als in the sides, a o, o b, of Fig. 464. ▲ is a blocic of ict with the stretched wire, furnished with a binding- doveable along the scale a b. llie battery is inter- en ▲ and B, and the multiplier or galvanometer, m, id D, as shown in the figure. The counter-resistanoea g always equal, the ratio of the resistances s — f : a — h uximately that of the portions of the scale, xb: AC, resistance of the wire is very much greater than that ' the apparatus. dard unit of Electrical BeiUtance, — Some definite aparing resistances being indispensably necessary for ion of electromotive forces, and the amounts of current became necessaiy to adopt some unit, like the units e, and weight, in terms of which anv given resistance (pressed, and for this purpose arbitrary units have ed. Wheatstone proposed a given length of pure of a given weight ; this is not, however, quite satii«- 3ils of such wire have been found to undergo consi> taneous changes of resistance. A column ofdistilled ^ven dimensians was proposed by Dr. Siemens: this d is more free from spontaneous change, and more irodncible, but it is subject to considerable variation from change of temperature. Many electricians have k more, desirable to establish an €U>Jiolute instead of an ait, that is, one depending on abstract considerations ,ce, and force, or velocity. A determination of this it made by Weber,* which it is needless here to de- has been snperseded by a method devised by Sir W. * Poggsndorff, Annslsn, Izzxii. p. 83. 448 VOLTAIC BLSCTOcrnr. Thomson, and carried out by a committee appointed by the British Association for the determination of electrical constants. The investigations of this committee have led to very satisfactonr results, of which only a bare outline can here be given ; bat aU requisite information on the subject may be obtained from the various reports of this committeci published in the ** fieports of the British Association." Ohm's law, 0-=-^ (798), establishes a relation between elec- tromotive force, resistance, and the amount of current, which may be thiis expressed in words: — An unit current i$ produced by an unit electromotive force in a circuit of unit retietance : and a relation between TFthe work done, and current, resistance, and time <, namely W=C*Bt, has been experimentally demonstrated by Joule ; which may be thus expressed — an unit ofioork is done hy an unit current pasS' ingfor an unit of time through a circuit of uniX reeistance. A third relation, involving electro-magnetic force, may be thus established : — ^Lot/be the resultant electro-magnetic force exerted by a current, C, at the centre of an annular coil, through which it is passing, and of which the radius is k, and the length, L ; then it IS evident that CL and if a short magnet, having a magnetic moment, m, be sus- pended in the centre of the coil (which must now be supposed to be placed in the plane of the ma^etic meridian), the deflecting force upon the magnet in a direction peipendicular to the plane of the coil will be CLm and if the axis of the magpiet be deflected to an angle B with the plane of the coil, the deflecting force will then be CLm ^ • . , cos©. But if ^be the earth's horizontal magnetic force, the force acting on the magnet, in the direction of the magnetic meridian, wiU be Hm sin 9, and if these forces counterbalance each other, then -_— cos 9 = Jim sin 0, whence C = — r ^ = — ^ tan B : L COS0 L from which it appears that in a given coil, provided the earth's horizontal force remain constant, the current is measured by the tangent of the angle of deflexion. This, it may be remarked, is the principle of the tangent galvanameteTf to be described here- BTAVDABD UXIT OP ELBCTBICAL RESISTANCES. 449 after. This formula is absolutely true only for a coil of no sensible thickness, acting on an indefinitely short magnet : and approxi- mately true, in proportion as the len^h of the magnet, and the transverBO width of the coil, are botn small compared with its diameter. It may be deduced from the precedine formuln that when the coil rotates on a vertical axis passing through the centre of the suspended magnet with a linear Telocity v, and the currents generated in the coil, bv its several turns being moved across the lines of force (592) in the earth's magnetic field, deflect the mag- net to an angle 0, the couple (81) exerted on the magnet will be j^lTmcos^, and the opposing couple due to the earth's magnetism will be Hm sin 0 : equating those values, we obtain 4i;5=tan0, whence -^Tp ^ot^; from which expression the magnetic moments, both of the sus- pended magnet and the earth, have been eliminated, and the resistance of the coil is expressed in terms of its dimensions and velocity, and the resulting deflexion onlv ; and thus an absolute value of resistance may be determined. For a detailed description of the apparatus by means of which the numerical determinations have been made, and the ingenious means devised for obviating very various sources of error, the reader must be referred to the reports before mentioned. The nature of the electrical action of the rotation mav, however, be thus explained : — suppose direct motion of the coil to commence, then the north side of the coil is moving from west to east, and experiences an electromotive force tending to produce an vpicard current ; but the south side of the coil is moving from east to west, and in that portion a doumward current is generated ; and if the circuit be closed, these currents will recur at each coincidenoe of the plane of the coil widi the magnetic meridian.^ This intermittent deflecting force produces minute oscillations in the suspended magnet, but they are of quite insensible magnitude. If one metre per second be taken as the unit value of v, the metre-second unit of resistance is a verv minute quantity ; it has been determined to construct material standard resistance-coils each containing, or being equivalent to, 10,000,000, or 10^ metre- second units of resistance, oy a careful comparison of the actual resistance of the rotated coil with that of the proposed standard ooils, by means of a suitable modification ol Wheatstone's 450 VOLTAIC BLECTBICITY. bridge (800). It is desirable that these should possess two re- qaisites, — ^^ermanency of resistance, and the least attainable variation, due to change of temperature : these desirable objects appear to have been best attained by the copper alloy known as ''German silver," and by some alloys of the precious metals. These standards may now be obtained from Mr. rleeming Jenkin, the secretary of the committee. As Messrs. Siemens, and some other electricians, appear to prefer the mercury standard of resistance, it is very desirable, for the sake of uniformity, that there should be no " break of gauee," but that they should adopt such dimensions as would make their standard commensurable with that adopted by the British Asso- ciation, and now very extensively employed in practice.* The best means of deducing from that of the resistance the values of the other electrical constants have scarcelv yet been fully determined, but little uncertainty or error is likely to arise, when the value of any one of a series of dependent constants has been satisfactorily established. On this subject also much in- formation may be obtained from the " fieport " for 1863. 803. Besistanee CoUt. — It has already been shown (800), that an tmknoum may be measured by comparison with a knoum re- sistance, by means of Wheatstone s bridge. The known resistance consists of a series of coils of insulated wire, wound round bobbins, and for convenience arranged on a stand. The first of these may be assumed to be the B. A. standard, and the best means by 'which any multiple may be made up out of the smallest number of coils is to have die three succeedmg ones multiples of the unit coil by 2, 2, and 5 respectively, then the next four, multiples by 10 of 1, 1,2, and 5, and so on. Thus with a series of twelve, any multiple of the unit coil up to 1000 may be obtained; vrith 16 coils, up to 10,000, and so on. The whole of these are generally joined up in series, that is, say the lower end of the first coil is connected with the upper end of the second, and so on ; and any coil is excluded from tne circuit, by joining its upper end to that of the succeeding coil by a conductor of ample magnitude, which the apparatus is furnished with ready means of effecting. 804. The Rheoetat. — Whenever large resistances have to be measured, such as those of a line of telegraph-wire, or of a snb> marine cable, and in which minute accuracy is not required, the resistance coils suffice for the purpose ; but if it be required to measure more accurately any smaller resistances, the object is most readily attained by the use of the rheostat, whicn, with luanjr other highly convenient electrical devices, is due to the in- genuity of Mr. wheatstone. This simple but effective instrument consists of two parallel cylinders, of equal diameter, which rotate * If meroory be employed^ it 10 sofrratad Uiat re-distillation mifht ooatri- bate matcriAlly to it« aniformitjr; t£« writer having found tlut tba pQii^ of water it notably aogmented oj sooocMiTe dialiUataon. COXDUCTIVITr OF METAM. 451 on their axes ; one of brass, the other of wood, having the thread of a screw cut over its snrrace. Each cylinder has a brass plate at the front end of it, against the edge of which rents a spring connected with a binding-screw ; and a thin wire attached to the plate on the wooden cylinder, after being wound in the groove of the screw, is attached to the contrary end of the brass cylinder, and may be unwound from one and wound on to the other at will, by means of a small winch. It is evident that all that portion of the wire, which is wound on to the brass cylinder, is taken out of the resisting circuit connected with the binding-screws ; and if the Talne of the resistance of the unit coil in turns and parts of a turn of the wire be known, the comparative value of any smaller amount of resistance may be readily ascertained. 805. The conducting power of metallic substances differs re- markably, but the worst condueting metal is many hundred times more powerful in this respect than the best conducting liquid. The following table shows the conducting powers of different Metals. Beo. qoerel. Ohm. Leu at 0°C. Leniat 100°. Lenzat 200°. Copper . . . 1000 1000 100-00 7300 64-82 Gold . . 93-6 57-4 79-79 65-20 54-49 Silver 73-6 35-6 136-25 94-45 68-72 Zinc . . 28-5 33-3 — — — Platinum 16*4 171 1416 10-93 900 Iron . . 15-8 174 17-74 10-87 700 Tin . . 16-6 16-8 30-84 20-44 14-78 Lead . . . 8-3 9-7 14-62 9-61 6-76 Mercuiy 3-46 — — Potassium . 1-83 — — — — metals according to Becquerel, Ohm, and Lenz ; it likewise shows that the conductivity is inversely proportional to the resistance, as determined by Sir W. 8. Harris, from the amount of heat deve- loped by the electric discharge (733). The conductivity of metals is considerably diminished by elevation of temperature ; this is shown by the observations of M. Lenz at the temperatures of 0^, 100**. and 200° C, in the pre- ceding table, from which it appears that at a temperature of 200* U., metals lose about half of their conducting po^ver. The following conductivities of several alkaline and earthy metallic bases have been determined by Mr. Matthiessen, that of silver being taken a#100 : — Sodium, 37-43 ; Magnesium, 25*47 ; Calcium, 22*14 ; Potassium, 20*85 ; Lithium, 1900; Strontium, 6'71. 806. Having a battery of sufficient power, which if of Crnik- o o 2 452 VOLTAIC ELBGTBICITY. shank's or WoUaston's arrangement (793) should oonsist of at least 40 pairs of four-inch plates, or of 10 or 12 cells of Smee*8 (771), orDanielPs (774) battery, orof 6 or 6 cells of Grove's battery (7 96), let the electrodes be connected with the two moveable rods ▲, b, of the universal discharger (729), and having unscrewed the knobs, tie on each rod by means of thin copper wire, a pencil of well-burnt boxwood charcoal, or still better, of the plumoago-like substance found lining the interior of lonff-used coal-gas retorts. On movinf? the rods of the discharger, so that the pieces of char- coal may lightly touch each other, a vivid light will appear be- tween them, igniting their extremities, and heating the air so intensely that on allowing the charcoal points to be withdrawn a little distance from each other, the discharge will continue with a most dazzling light through the intermediate space. If the battery be of smaller extent, as a single trough of Wol- laston's construction, of ten pairs of pUites, a piece of the charcoal should be attached to one of the electrodes, and a piece of plati* num wire to the other, which should be brought in contact with the carbon ; at the point of contact a vivid dazzling light will be evolved, the platinum wire will be ignited, and if tmn, melted into globules. 807. The discharge of the voltaic batteiy and consequent evolu- tion of light, either when charcoal or metallic surfaces are em- ployed, does not take "phcti at . first without absolute contact. Jacobi* carefully approximated two metallic points terminating the conducting wires of a battery of 12 pairs of zinc and platinum plates, excited by dilute sulphuric acid, until they were within 0*00005 inch from each other, and not the sUghtest evidence of the passage of electricity was observed; the discharge beinar checked by the small interval of air. Prof. Daniellf repeated this experiment with his large battery of 70 cells, and found that no discharge ensued even on heating the closely approximated electrodes to whiteness. On transmitting the chai^ of an electrio jar through these electrodes, so that the dischiu'ge might take place at the point of separation, the battery current became esta- olished, and luminous discharge ensued. It is evident that the discharge of the jar, by producing a transfer of particles of matter from one electrode to the other, thus formed a conducting medium for the battery-current ; for an intense luminous discham of a bat- tery is always accompanied by the transfer of some kindof matter. 808. The evolution of light does not depend upon the combuB- tion of charcoal terminating the conducting wires, for it will take place with equal splendour m a vacuum. This may be shown by allowing the wire nolding one of the pieces* of charcoal, to slide air-tight through the brass neck of a glass globe. Fig. 466, a second piece being attached to a wire, fastened to the lower part, and connected with a brass cup, z. On exhausting the globe of • Pog. Axmalen, xliv. 635. t Phil. Trans. 1839, p. 93. -»*" rf LUMINOUS DIBCHABOE. 453 air, connecting the electrodes of the batterj with the brass cups, c, z, and approximating the charcoal points sufficiently, an eyolu- tion of intense and dazzling light will ensue. These experiments are of the most brilliant ^' *^* kind of any in experimental science, especially ^f^ when performed by the aid of a large battery, W as one consisting of 30 or 40 of Grove's ele- JL ments ; or of the powerfal batteiy of 70 elements ^3^ constructed by Prof. Daniell. In this case a /liN very curious transfer of carbon from the positive f ^&. \ to the negative electrode is observed, the piece I ^^ / of charcoal constituting the former presenting \JLx a conical cavity from this loss of substance. This 3— C. is beat seen bv throwing on a screen an image z V-r^ of the carbon electrodes of an electric lamp, when TJtC^ the transference of particles of incandescent car- ^-"^-^ ^ bon from the positive to the negative pole be- comes quite evident. The light thus evolved between charcoal points has been proposed as a means of artificial illumination. Indeed, some experiments lately performed speak well for the ultimately ■uocessful application of tbis mode of lighting the streets of large towns. Several trials made at Manchester have been very satisfac- tory ; the intensity of the light is so remarkable that the burning gaa-Iamps in the streets are hardly visible in its splendour : but the expense of maintaining a sufficient current has hitherto been found too great to admit of an extensive practical application of the electric li^t. 809. Prof. Daniell* has observed that when the nenitive elec- trode, or the wire connected with the last zinc plate of the battery, is furnished with a termination of platinum, and the positive elec- trode with one of charcoal, and the discharge of a powerful battery, aa one of 70 elements, is transmitted, an abundance of intense light and heat is evolved, and the carbon is carried from the posi- tive electrode and deposited on the platinum point, which becomes beantifrilly moulded in its extremity. When the current is reversed, particles of platinum are transferred to the carbon negative elec- trode, and are deposited on its surface in the form of fused globules. 810. J3elf^egtu€tting Electric Lampa. — The voltaic discharge between carbon electrodes having been of late years extensively employed as a source of brilliant fight, not only tor the purposes of experimental demonstration, but for the more important practical purpose of illuminating light-houses, it became necessary to devise some means by which uniformity, not only in the intensity of the light, but also in its position, might be maintained. The heated carbon continually undergoes a slow corabastion, besides which there is necessarily (808) a continual transfer of carbon particles from the positive to the negative electrode, the consequence of * Phn. Tr»nf . 1839, p. OS. <54 V0I.1 which is that m practice the oonaoniptinti of the pogiti™ electrode » about twice u ntpid hb that of the negHtivo : it is neceasarr, therefore, that bj some mechaniam the eJectroJes should be lunde to approach each other at a rate prupurticinal to their conioniption, i.e„ an 2 ^ I. This is gonerall; effected by two rncki and wheela, or chorda and pullejg coonected with a train of wheels, the laat of which ia held b; a detent controlled h; an eleclro-magaet, actu- ated b^ the current : the train is released, and allotted to run, and BO to approximate the electrodes, whenever the currcot is weakened by their being at l^io great a dialance from each other ; and when the foil current ia re establlahed hy lh« mulaal approach of the electrodes, the detent acta, and Blops the train. Varioua plans have beeu devised hy Hart, Ueiach (Murray' and Heath), and Holmes in this countrv, by Uubosq and Serrin in France, by Jasper of Liege, Gresaler of Berlin, and others ; of theae that of M. V. Serrin will alone be described, aa it poaaesses the important adranlage of being ablu to be lighted at a distance or extinguished, bj merely turning on or off the current. SeTcral of the others require manual interference, on the cessation of the current, lo prevent, in the absence of control, the approximating mechanism from jamming together the carbon points to their own desiructiou, and also to adjust them at the commenceDiont of action. IHiis in- eenionsly contriredspparatua iarepreaented in Fig. 467, in which ii.. — I ;..._ — -Hmped vertically ovei each other lo two llie positive electrode, pr, slides, witb liGcitnt friction to su]jport the weight of ]■, in a tube, kl, which ia jointed lo two lual and parallel hoHaDDtarhnlis, ab, ed, and therefore capable of moving verticajlj ; 'ts movement being limited bj a stod on he ourside, placed between the points of BO adjusting screws, u, o. The negative electrode, hh, slides treaty in a tubular support, c u, and is leminated below bj a ack, which oiWr gearing with a wheel, r, inters a socket, e, Id keep it steady. On the same axis with r ia a pulley of doable its dianiolcr, auil a still larger wheel iii h a pinion, o, which has a wheel xis in gear wilh the pinion of a click-wheel, h, whicli kst is held hy a detent, o, attached to the socket, k l. A o, aud descends lo be attached t bottom of p. Tlin end e of a lever, eg, lurniii|; on a fulcrum, / is connected wiih a soft-iron cure, v, placed inside a bobbiu irrRATIFICATIOXS XM ELECTRICAL DIBCHAEGBS. 455 of insulated wire, b ; the other end is connected bj a link, gh^ with a stud projecting from the socket, k l, and the ▼ertical motion of the core, m, is ifurther secured by a link, 2, parallel to the lever, eq. The core, ic, just balances p p and its socket k l, to which is aaded, if required, a little heavy matter in a saucer-shaped cavity placed at K to receive any proceeds of combustion that may fall from the carbon points. The current enters the apparatus at p, whence an insulated wire wound round the bobbin, b, proceeds to a fixed stud connected by a chain, ^ with the bottom of p p, whence it passes up through the carbon electrodes + and—, then down through H]pand away by the wire, n, attached at d. In order to follow tne action of the apparatus, first suppose the carbon points separated, and the current not on ; n H wiU descend by its own weight, and the rack, e, jiutting the train of wheels in motion , will draw up pp (and with it the balanced socket, kl, as far as the screw, v, permits) at double the rate, as required, because the pulley is double the size of the wheel, v. As soon as the points come in contact, the slightest further pull on the chain pulls down the detent, o, and stops the train. Suppose now the current put on ; it pursues the course already described, and m being drawn up into B, the carbon points are slightly separated and the light developed. As the points wear away, the current is weakened by increased resistance, and m descending by its own ^vity raises kl and its attached detent, o, and releases the train, which ap- proximates the points until the current is sufficiently reinforced to raise m, which aepresses k l and o, and thus stops the train, it will here be seen that on the cessation of the current the carbon points are left in apposition, and therefore ready for its renewal. Thus the lamp may be with ease and certainty extinguished and relighted at a distance as often as may be required, without further manual interference than that necessary to replenish the carbon points, when worn away. In the lamp of Mr. Heisch the current is further regulated by ihe diversion of a portion of it into a second circuit, the resistance of which is controlled by a rheostat (804) ; this is a convenient addition. 811. Stratifications in Electrical Disclwrges. — The striated condition of the electrical discharge in vacuo when two wires, in- serted into a well>exhausted tube, are connected with the ter- minals of a powerful induction coil, were first observed by Mr. Grove,* when the vacuum was rendered still more perfect by the absorption of oxygen by a bit of phosphorus placed in the ex- hausted vessel. These curious phenomena have been made the subject of an extensive series of investigations by Mr. Gassior : he has obtained very satisfactory results with Torricellian vacua (484), rendered still more perfect by a method devised by the lato Mr. Welshjf which consists in attaching a small supplementary * Phil. Trans. 1862. t Phil. Trans. 1S56. pta. «s. ijrphonto thenppnrendof thetnbt, into which anjrandiulbobUe of Mr or gas may be tlirown bj inclining the tabe. In a Tacnrno thna obt«iii«d, tliii Htjatiti«l appearance of ad electrical ttiachargv taking place between two platinum wiren, hemietiRaUj ttt£d into the tube at diatant poinu, maj In TSTj well obeervod, and is repreacnted in ^g.468. The stralificationa an ob«n«d e coDCtTe towarde tbe poaitire wire to be larger in proportiuo aa the dia- meter or th« inbe i> increased, aa ia tbe figore. Thej appear to proved &i>D tbt 'live term inaf towatdB tbe negating I which thej are aepantod bj a dark band, or space. The negalive tennioal i« Burroonded bj a brilliaat glow of light. takes place. The lauM efiecti msj be produced, when tbe wirts are reapec- tivel]' connected with the rnbber aird prime condacloraf an ordinaij electrical machine, or wh«n the diechorge of a Leyden jar ia efiected throogfa a wet string, in order to modiij its intensitj. The Bame observer has obtained similar results with a water- battery containing 8620 cells, also with a series of 400 calli of Qrove's batteT7. More recently Mr. Oassiot has emplajed in hi* rmearcbex a batterf of 4000 nno-carbon elementa, chargod with inlphate of mercniy (TS3], and carefiiU; insulated, from which a cnrrent of yery great potential, ar -~" -- "' '•■' — " nencr, has been obtained. 613. JnjtutMea/JiatUlaiKXOJH has obtained several verj curious results, bj introducing a , . . ,.. ., .=_.... .1. ,. , ^ ^^ u of oooiideiable u duated reeistance in the circuit; this couiiita of a V-aha«i tabe. the lege of which are 16 or IS inches toog, filled with d^ tillaa water, in which two ptatinam wires are iiisertad, famg UiToogh corki in the mouthe of the tab«>, so that bv maing or lowenng one or both of the wires, anv retioired length of watei^ miitaiice maj be iDterpoaed in the circuit. When a cnn«nt (i«m 1200 of the elements wm tmianiittad throagh one of the vacnam-tubes, with a (ew inches onlj of wala> resistance, a series of 12 to 14 well-^leflned Inminona diaci ap- peared : SB tbe water-retiatanoo was gradnallj increaeed, thrnu IB layerv appeared to be abeorbed one bj one into the ricrw '' '-'- ' QDlil all had diaameared ; bi2 oa „ , „ e resistance, the bands appnaml Bucceasivel; to flow out from the positive pole. With another tube a still more Bingutar resolt waa obtained, which is represented in £1g, 469. With a certain amount of nsia- nrsuLATios bt ax absolotb tacuux. 457 ) a series of 19 well-defined lonated disos, concsTe towardfi the [ye pole were produced, as in a ; bat when the resistance was (((((((((((((((UU tly diminished, the discs became snccessiTelj doubled, as in cy being again successively resolved into single discs, on in- ling the resistance. The negative termination of the tube is ted in the figure. another of the vacuum-tubes, the luminoas discs appeared to e each other in batches from the positive to the negative pole : xpUination has yet been offered of these anomalous and pecu- phenomena. 3. Innilation by an AbtohOe Vaeuum. — ^The facility with th an electric discharge of sufficient potential is transmitted agh a to-eaUed vacuum, by induction on the particles of ter intervening between the electric poles or terminals, ap- -s to increase with the tenuity of the matter, of whatever 1 it may be. But recent investigations have shown that trical conduction requires the presence of $07ne matter, how- it may be attenuated, as in tiie carefally-prepared Torricel- vacuum above described, in which nothing probably remains a minute quantity of mercurial vapour. By the following pro- an ahtchOe vacuum has been produced.* large glass tube, in which towards its extremities two pla- m wires are hermetically sealed, has a smaller tube, six or it inches in length, attached to one end of it, in which two or e pieces of fus^ caustic potash are placed, and the open ends be compound tube are drawn oat. It is then filled with dry onic acid gas, exhausted by an air-pump, and refilled several ^8, sufficiently to replace the whole of the air contained in tho ; by carbonic acid. One end is then sealed, and the other end g immersed in a cup of mercury under a receiver, the carbonic is exhausted to the utmost extent, and the tube immediately >d. The smaller portion of the tube containing the potash is I heated to the pomt of fasion of the potash, and when the ;r is fused, the tube is turned round, so that its interior may »me coated with the alkali. In a few days it will be found the residue of carbonic acid has been absorbed by the potash, thus an absolute vacuum is obtained. On connectine the inum wires, as before, with two electromotive terminals, no age of electricity takes place, nntil by heating with a spirit > the tube containing the potash, an attenuated atmospnere * G«dot, Phil. Trans. 1859. 458 VOLTAIC ELECTRICITY. either of the vaponr of that inbstance, or of carbonic acid, is dis- engaged ; the stratified discharge now takes place, and will ooo- tinoe to do so, until the disengaged matter is again absorbed by the potash. 814. Diseharae arrested by Mofftietie Force. — ^Mr. Gassiot has remarked that tne stratifications are very powerfully affected by a magnet when the discharge takes place from wire to wire, as in ▲, Fig. 468. If the poles of a horse-shoe magnet be passed conse- cutively along the tube, the discharge will assume the form of ^^^ , in consequence of its tendency to rotate round the poles in opposite directions. He also observed that when a carbonic-acid ▼acnum is placed across the magnetic field (592) of a powerful electro- magnet, the discharge through it of the water- and Grovels bat- teries, preyionsly mentioned, is entirely arrested.* 815. If the electrodes of a voltaic batterr be connected by means of a fine platinum wire, and the current ue sufficiently powerful, it becomes heated to redness, and even melted. A small battery will heat a considerable quantity of wire of ^A^ inch in diameter, a single pair of small plates, igniting an incu ; and a battery con- sisting of ten alternations will neat to redness about eight inches. The best mode of showing this experiment, is to roll about eighteen inches of wire into a long spiral, and place it in the interior of a ^lass tube ; its ends passing through corks, so as to be readily twisted round the electrodes of a batteiy. If the cur- rent be too weak to ignite the wire, it will heat it sufficiently to communicate a very high temperature to the glass tube in which it is placed, so that phosphorus may be infiamed by bringing it in contact with its exterior ; and by immersing this tube in a nnall quantity of water, the latter may be speedily raised to the boiling point. The heat evolved by the passage of a current increases with the resistance opposed by the wire ; hence with difierent metals the heating power of a current traversing them will be in- versely as their conducting power (805^. When thin metallic wires forming the electrodes of a voltaic oattery are placed across each other, the wire terminating the positive electrode becomes ignited and melted, whilst that connected with the negative re- mains comparatively cool ; a fact which as yet has received no satisfactory explanation. If thin metallic leaves be subjected to the action of the current of the battery, they infiame and bum with considerable brilliancy. This experiment is best performed by attaching a plate of tinned iron to the negative electrode of the battery, and having taken up a leaf of any metal on the point of the positive electrode, bringmg it in contact with the tin plate. In this manner, gold bums with a vivid white li^ht, silver with an emerald g^reen, copper and tin with a pale bluish, lead with a purple, and zinc with a daszling white muue. • Phil. Traoa. I860. THE OALYARIC KKIFE, AHD CADTERT. 459 816. The Oatvanic Knife^ and Cautery. — ^The heat developed bj the passage of a current of large potential through an insuf- ficient conductor has in several wajs been applied to the purposes of operative sui^iy. One of these is the galvanic knife, Fig. 470. This consists of a sliding platinum bbde, which is sepa- Flg, 470. rated down the middle, nearly to the point, in order that it maj constitute the heated conductor. The handle is also divided down the middle like the blade, and having on each side an ample mass of metal in contact with the blade and also with one electrode of the batterj, the protruded portion only of the blade constitutes the acting resistance, and tne heat will evidently bear an inverse proportion to the length in action. The blade is graduated in numbers, so that with a given amount of battery power, the tem- perature wiU ran^e from 600' up to 1500' C. it is stated that at 600° tbe combustion of the tissues is so gradual that hnmorrhage 18 completely arrested, which is in many cases of vast importance ; but that at 1500** the combustion is so rapid, that the action of the edfCB very much resembles that of an ordinary steel knife. in the galvanic cautery a piece of thin platinum wire is wound round the end of a rod of some ^ood insulating material, as ebonite, and beyond the point at which the heat i.p of water pre- viously cooled nearly to 32° be placed therein, on the current passing, it will become rapidly frozen.* In this instance it must be concluded, that in consequence of the peculiar thermo-electric relations of these metals (Ch. XVI.) a jK)rtion of their heat {thermic potential) is inductively convertea into electric potential, and therefore disappears as heat. 818. Dry Piles. — ^A curious modification of the voltaic battery is found in those arrangements termed drypUes; these consist of a large number of alternations of some metal in a state of extreme tenuity, as silver, combined with one more oxidizable, as tin, and alternated with pieces of writing paper ; the moisture in which substance appears to act as the excitmg fluid on the more oxidiz- able metal. Thus, a pile composed of pieces of tin-foil and silvered paper, if containing about 200 alternations, will act power- fally on the gold-leaf electroscope by aid of the condenser. The piles of Zamboni are the most convenient : these are constnicted by pasting on one side of a sheet of paper, finely laminated nnc, and covering the other side with finely powdered black oxide of manganese. On cutting discs out of this prepared paper, and piling them upon each other, to the number of 1000, takmff care to press them together, a little pile will be obtained capable of diverging the gold-leaves of the electroscope to the extent of half an inch, on touching its cap with one ena of the apparatus, the other being connectea with the earth. With the aid of acondenfler, a pile of but 300 alternations will readilv act on the electrosoope. These dry piles continue in action dunng several yean, and are capable of yielding a spark by means of the condenser, although not the famtest shock, nor the slightest evidence of chemical action, has yet been obtained from them. The electricity they yield appears to be of high potential, bnt extremely minute in quantity, and disappears altogether when the paper discs have lost all their humidity oy gradual evaporation. 819. A very remarkable form of apparatus for the excitation of electric cnrrents has been invented by Mr. Grove. It is termed the gas battery, and consists of a series of platinum plates covered alternately with jars of oxygen and of hydrogen in the proportion to form water. It has been long since shown by Faraday that plates ofplatinum will greatly accelerate the oombmation of these Kases. By connecting the consecutive plates in pairs, Mr. Grove aiscovored that in proportion as slow combination of the incloded gases went on, an extremely weak but very distinct current cir- culated through the apparatus, and which he succeeded in increas- ing in tension, until it afforded a minute spark, and gave distinct * B. Lens. PoggendoriT, Annal. zIIt. p. 848. 6£0VE 8 QA8 BATTEBY. 461 evidenco of being able to effect chemical deoompoeition. A series of ten cells is stmcient to exhibit minute sparksi and even slowly to decompose water. 820. The foUovriog mode of constracting this cnrioos battery is recommended by Mr. Grove, as being the most convenient : — ^a. c, Fig. 471, is a glass tube with a series of tubular legs attached to, Fig, 471. * and opening into it ; it terminates at a in an opening closed by a glass btopper, and at c, in a ^nnel-shaped opening. Into each of a series of glasses b, two platinum plates are fixed, one long and narrow, the other shorter and wider, the former being placed lower than the latter ; the wide plate of one cell is connected with the narrow one of the next by means of a platinum wire. The glasses are then filled up to the top of the narrow plates with acidulated water, and in the vessel z, filled with dilute sulphuric acid, is placed a piece of zinc supported on a little tripod. The stopper Doing removed from the tube, a c, the legs are immersed in the cells so that each narrow platinum plate may be inclosed in a leg, the wide ones being excluded and half exposed to the air : the hydrogen evolved in the vessel z will rise and fill a c, expelling the atmospheric air. The glass stopper is then to be inserted into A, and the generation of hydrogen will continue until the piece of zinc becomes uncovered with acid ; then the narrow slips of plati- num will be exposed to an atmosphere of hydrogen in the legs of the tube, the wide ones being exposed to the oxvgen of the air.* A current of electricity will thus oe generated, the electrode con- nected with the terminal narrow plate being negative, and that connected with the terminal wide plate, positive. 821. Having learnt that an electric current excited \}y chemical action may be made to circulate through conducting wires, and its force thus brought to act upon any intervening compound body that it is capable of traversing, it becomes necessary to investigate • Piul. Tnne. 1813. 462 VOLTAIC ELECTRICITY. Fig, 472. ,0 more in detail the peculiarities of the changes effected in cam- pound bodies thus traversed bv the current, and to study the phenomena of electro-chemical decomposition, or electrvlyM,* as Faraday has termed it. Let tne electrodes of a batteiy, consisting of at least ei^ht or ten elements, in good action, be placed in the cups, ▲ b. Fig. 472, containing a few drops of mercury, and communicating with the platinum plates, p, p. The tubes, o, h, are filled with water, rendered conducting by the addition of a little sulphuric acid, and in- verted in the vessel e, filled with tne same fluid, over the platinum plates, p, p. Directly connexion i.s made with the battery, the plati- num plates will become coyered with bubbles of gas, which being disengaged, will rise in the tubes 0, H, in unequal proportion, rather more than twice as much gas being collected, in a given time, in one tabe, as in the other. These gases consist of oxygen and hydrogen, the former being evoWed at the surface of the platinum plate, where the current of electricity enters the fluid in e, and the hydrogen, at that surface where it leaves the fluid. As these gases are eyolved from the deoom- * posed water, their volumes ought to be to each other as two to one ; the reason why they are not precisely in this proportion, is to be found in the partial solubihty of oxygen in water; and hence, its real volume is rather less than it would be, if this source of fallacy were absent. In this experiment, the gases are evolved from both plates simultaneously ; and, although at each instant, but a single atom of water is decomposed, the hydrogen being evolved from one, and its oxygen from the other plate, the gases are not observed to pass from p to p, the fluid between these electrodes being free from bubbles. This circumstance may be explained in a similar manner to the electrolysis of hydrochloric acid (765) : let the two platinum plates be represented by the letters P, N, the former b«ing that by which the current is sup- posed to enter, and n that by which it leaves the acidulated water ; a, b, c, d, are supposed to be four atoms of water lying between the plates, p, n, each consisting of an atom of oxygen, o, and one of hydrogen, h : thus A B O D ^^A^ ^^A^ ^A^^ ^A>^\ P . . . OH, OH, OH, OH, ... IT The positive electricity entering the fluid at p, decomposes the atom of water a, with the evolution of oxygen, and causes the hydrogen to pass towards n ; and this being carried forward by • *UkiKTpw, and XvM, soIto. FOSMATION OF OZOKE. 463 the inflaence of the current, decompoBes the atom, b, uniting with its ozjgen, and repelKng its hydrogen, which in its turn aecom- poees the atom c, and so on ; at last, the hydrogen of the atom d ia set free, and is evolved at the surface of the plate h, as the electricity, by influence of which the decomposition of the atoms, A, B, c, D, was effected, leaves the fluid at this point. A similar explanation is applicable to other cases in wbieh eledrdyteB (826) being decomposed, the elements are evolved at distant portions of the fluid traversed by the current 822. If, instead of platinum electrodes being employed, the copper wires themselves be plunged into the dilute sulphuric acid (821), water is, as before, decomposed, hydrogen being evolved at the negative electrode ; whilst at the positive, the oxygen com- bines with the metal of which the wire is composed, forming an oxide which is dissolved in the acid present. 823. During the decomposition of water by the voltaic current, a ])owerful phosphorus-like odour of ozone will be evolved. The evolution of this matter, now recognised as au allotropic form of oxygen, has been already noticed cuiring the action of the common electrical machine (691, 2). The odour of this ozone has been long recognised, but its cause was first traced to the formation of this peculiar bodv by Professor Schonbein of Bale. The same substance is evolved under many other circumstances, as when a stick of phosphorus is allowed to remain for a short time in a laree glass bottle fiill of moist air ; or, still better, bv placing a litue ether in a large glass bottle, and then holding in it a previously heated glass rod, so as to reach nearly to the surface of the ether. Ozone is a most ener^tic oxidizing agent, a piece of silver leaf on beinff exposed to its influence, crumbles almost immediately into oxiae : it is also a most remarkable deodorizer, almost in- stantly removing the offensive smell evolved by a piece of tainted meat. Ozone frequently exists in the atmosphere, especially in the air blowing from the sea, and, in all probability, plays a most important part in the laboratory of nature. It acts on iodide of potassium, like chlorine, setting free the iodine : hence a piece of paper, moistened with a mixed solution of iodide of potassium and starch, turns blue when exposed to its influence, and thus becomes a delicate test of its presence in the atmosphere. 824. Ozone, on account of its powerful antiseptic properties, might perhaps be advantageously employed as a remedial agent in medicine and surgery : but for this purpose some simple and effective means of prtnlucing it in large quantities become neces- sarv ; these are provided in a simple little apparatus represented in Fig, 473. This consists of a glass tube about two inches in dia- meter, and 10 or 12 long, terminated at one end by a much smaller tube, d. Into the other end of this a rather smaller tube, widi a closed end reaching nearly to the end of the large portion, is hermetically sealed, the mouth of the inner tube being left open. Near the point of anion another (nece of emftll tiib«, o, is joinsd latarsUvinto tbe lu^er one, opening ioto the epaee between the tnbec. The intide of tbe inner tnbe receives a metallic coating hy being moistened with gnm- "S-*n. ^g^tet, aad then haTJng I some gnaular metal scat- tared orer it ; and the out- lide of tbe outer tube ii ooated with tin-foiL Tio apparatus is damned on a Btsad bj two blnding- BcrewB, A, b; ofvhicb a. is in metallio connexion with the outer tin-foil, anil B with the lining of the inner tuba. When a and b ara respectivBlj oonnucted with the iiaulftted rubber and prime crnductor of a macblne in action, s powerful iuductin discharge will take place between the opposed sorfacea of the two tubes, attended bj a copious evolution of ozone, which will issna from c, if the noude of a pair of bellows be applied to d. The same result will beproduced, if the terminaie of a poweifol ss- condar? coil (Ch. XIV.) be connected wiih a and a.* 82d. If several pieces of apparatus for the deoompodtion of waler (621) be arranged, so that the cnrrcot of a battery may paa thmugh each in succcssian, the quantity of gases evolved in each will tie found to be precisely equal. And if the current, beudea passing through one of these apparatus be also made to traverse a metallic solution, as sulphate of conper, the quanti^ of copper procipilaled in a metallic state, will iwar tbe same relation to the qiiantily of oxygen and hydrogen collected, as their atomic weif^la. Thus, a current of electricity capable of decomposing 9'01 graioi of water will decompose 5878 of chloride of sodium, I63'!8 ot acetate of lead, Td'HS of aalphateof copper, &c This anses fiom tha definite nature of tUetro-chemieal or tUOroli/tie thcompontioit, a fart first demonstrated by Faradaj.f 826. Compound bediee, capable of being decomposed by Ibo agency of electric currents, are convenient^ termaa ebdrolytet. Before an electrolyte can be decomposed, it is necessary that it shoald be capable of allowing induction, and consequent con- duction to take place thrDneb it ; as the latter cannot occur, in the great majority of cases, whilst tbe electrolyte is in a solid state, It must be dusolved in water or fused, in which state it generally readily conducts the current. Thus, the chlorides of tin, silver, and lesd, nre readily decomposed when the cnirent is transmiltad throoeh them, whilsl tbev are in a state of fusion. Some com- pound fluids exist which refiiae tooondnct the currant, and therefore • Tbli appantni wu HinstTDCtrd b; Ur. W. Iddd. t FhikMophicd Iruuctioni, 183^ fth Suin, Mvlion 7. 465 ft few othon conduct It readily, and yet can BcaroelT be said to yield lo electro- lytic force ; of this cIbu solphuric acid is *.n eiaoiple. B27. Wlien varioui electrolytes sre Bnbmitted in a diasolved, or fiued state, to the action of the current from the voltaic battery, the tUciro-titgalivt elements ore in variably set free at the positive plate, vhere the current is suppoeed to eutei the fluid; and' the ~'~~'n>w(ilti'e' elements, at the negati re plate. Thus, if cblo- of sodium, iodide of potassium, hydrochloric acid, sulphate IV-*'*' of copper, nitrate of lead, or fused chloride of lead, be submitted to the action of the current simultaneously, by placing them in Teasels connected by platinDin wires dipping mtosach, the chlorine, iodine, mlphuric, and nitrio acida will be set free at that point where the positive current enters the solation, or fused maaa ; whilst at the electrode where it leaves them, the soda, potassa, hydrogen, copper, and lead, will be developed in an isoUted Btat« : the evolution of the elements of the electrolyte bearing a conabuit relation to the direction of the cnrrent traversing it. 82B. Ae the only true teat of the smooDt of electricity in circuit ii its dedTolytie power, the volta- iN«t«r or Tolla-elwrtrometer, as it 11 termed by Faraday,* becomes K valuable instnunent in giving an approximate measure of the power of a battery or pile. This consists of an apparatus, in which water is submitted to the action of the cur- rant, so that the gases into which .it is resolved may be measured. — | 1 j r 1 1 i j i. A convenient form of this instro- ^ iTZ^r ' *■»... nwnt ooniiats of a glaM Tesiel, a, ' £1g. 474, cemented into a wooden base, having two plalea of lilatinnm passing into its interior, connected by wires with mercury cups, or binding Rg-tn. screws, B. The glass ressel being filled wi£ dilute BQlphnric add, has a bent glass tube passing through a cork fixed in its mouth, BO as to convey the gases evolved into a graduated receiver, standing in a pmumatio trough. Avolta^lectrometermay beteodilr constmcted by fixing two pieces of thick 0 the .foil into a good cork, so as to dip of a small wide-moathed bottle, Fig. 472: peces will enabli with any apparatus, and a with any apparatus, and a bent tube past- ing through the cork will carry off Uie ~ Thil. Tnu. ISH, 740, 741. 466 VOLTAIC BLBOTRICITT. gaaefi to be measared. The charge of these volta-electrometers should be one part of salphuric acid diluted with eight of water. 829. The platinum electrodes employed to effect the decompo- sition of water assume a peculiar electro-polar condition, by which, on being disconnected from the battery, they develop a secondary current, passing in a direction contrary to that of the battery current. This may be detected by connecting the cups b, Fig. 474, of a voltameter with a delicate galvanometer (855), after re> moving the battery electrodes ; when the needle will immediately traverse, from the action of this secondary current. The electrodes do not entirely lose this property by pouring out the acidulated water in which they are immersed, and replacing it by fresh, or even by washing them with hot water. If a rod of amalgamated zinc be plangnd into the acidulated water contained in a volta- electrometer, the platinum plates of which have been previously connected with a voltaic bifittery for a few minutes, and wires twisted round its upper end be connected with the two cups b, decomposition of water will, of course, ensae, and hydrogen will be evolved from both platinum plates, but in unequal volumes, nearly twice as much being evolved from one, as from the other, as has been elsewhere shown.* This curious polarized condition of the electrodes in all probability arises from the fixation of small portions of oxygen and hydrogen on their surface ; a view counte- nanced by the experiments of Schonbein,f who has found similar propeKies to be assumed by platinum plates, after immersion in oxygen, chlorine, bromine-vapour, &c. 830. The secondary current here mentioned is produced by the affinity, or reuniting tendency, of the atoms of oxygen and hydro- gen adhering to the platinum plates, and is identical with the action of the gas battery (820) : and a similar contrary electro- motive force is always generated by the affinity of any chemical elements disunited by the force of a voltaic current. The exist- ence of this contrary force may be readily shown by connecting three or four decomposing cells, or voltameters, arranged in series, with a battery of moderate power, consisting, for example, of 6 or 8 of Smee's (771), or Daniell's (774) elements, when it will be found that the contrary electro-motive force of the platinum plates will considerably retard, if not entirelv arrest the decom- position of the intervening water ; but if the voltameters be united, and the electrodes of the same battery be connected with one plate of each voltameter, an immediate disengagement of the gaseous elements of water will ensue. 831. It is necessary that all parts of the circuit should be formed of as good conductors as possible, in order that the whole electrolytic force of a voltaic current may be effectually exercised, as the amount of decomposition bears a ratio to the facility with • Phil. M»Kume, 1839. t Poggen jor^ Annalen, zlvii. p. lOA. ELECTB0LT8IS B7 1. SINGLE ELBIfEMT. 467 Fig. 476. which the cmrent passes. Hence, a flaid not readilj acted upon by a current in consequence of its resistance, often yields reaaily to the current, when made to conduct it more freely : thus, pure water conducts badly and is decomposed with extreme slowness ; on the addition of sulphuric acid it becomes an excellent conductor, and is decomposed with I'acility. This is an example of the man- ner in which the value of G in Ohm's formula (7^7) is increased by diminishing that of Ji, 832. Although compound batteries have been referred to in the above remarks, as necessaiy to produce chemical decomposition, yet it must not be supposed that they alone are efficacious ; for a single pair of plates properly constructed, is capable of effecting, by the current evolved, most important decomposing actions in bodies the elements of which are held together with the greatest force. Faraday decomposed iodide of potassium (a salt capable of very ready decomposition by a small force,) alkaline chlorides, and sulpbates, hydrochloric acid, and even water, by means of a single pair of plates. M. Becquerel,* by availing himself of weak cnrrents, aided by " well chosen affinities," succeeded in effecting the reduction not only of the more readily reducible oxides of copper, lead, or tin, but even of the refractory earths glncina, alumina, and silica. This phi- losopher obtained these interesting results by means of a single pair of plates, placing the solution of the metallic salt in a glass tube. A, Fig. 476, closed at one end by means of a plug of moistened clay, and immersed in a weak solution of common salt: on placing a com- pound metallic arc formed of zinc and pla- tinum in the solutions, in such a manner tnat the platinum plate p may be immersed in the tube containing the metallic solution (to which M. Becquerel applies the ^neral term of " ne- gative tube"), whilst the zmc is placed in tbe solution of salt, de- composition ensues, and after a lapse of time, varying from a few nours to some weeks, the metal in solution is generally de- posited on the platinum plate in a more or less crystalline form. 6ecquerel did not attribute the reduction of the metal to the elec- tric current alone, but conceived that three distinct causes, at least) concurred in producing this effect. The decomposition of the water and of the common salt by the electric current set in motion, and the transferrence of hydrogen and soda through the clay diaphra^ to the negative tulie, where the alkali unites with the acid holding the metal in solution, causing the deposition of its oxide, which, while in its nascent state, is reduced by the hydrogen, and precipitated in its metallic form on the negative plate ; thus regarding the hydrogen funiished by the decomposi- • Traits de rEUoiriolt^ et da Magn^tUme, vol. iii. p. 228, et uq, 1836. H H 2 tion oF the water bb the Bctaal TsdncinK agent. la wine catea, a Toartli cause it Bupposed to be aiiperuHded to these, aa vben » bodj IB lued for the oegiitiTa pjate, for which the metal in aola- tion has a certain degree of aiSnitr; a well known example of vhich is fonnd in the redaction of potaaiium from a solution of pat»ssa,whea sabmittedtocomparatiTelyweakToltaic action whit« m contact with mercnry. Mercury ia not the only metal applicable to this porpoae, Becqnorcl having frequently osed iron with suc- ceBS. He found that the Bolutions of the pure chlorides of air- coninm, glucinum, titanium, silicon, &c., rat'uacd to yield to the reducing action of weak electric currentu, nnlil after the addition of a BDiall quantity of chloride of iron : this the cnrreDt readily decompoeed, precipitating the iron in a crystalline form on the platioam plate, which deposit speedily inducMthecommencemeut of the decompoailion of the more refrsctory salts. This circmm- stance he attributeit to the affinity of the iroa for the odier metal tending to the formadou of an alloy, a:id eipressly statei, that when perftctlu pure the ahoTe mentioned chloiidea diit nit in- der/fo the tlighiat dMoiapoiition. 833. From a series of experiments on this snligect, it appeared that the quantity of electricity was not so essential as a contiDuoiM weak current, and the late Author was induced to prefer the follow- ing apparatus (which howercr is out a slight modification of Daniell's), in cooaequenoe of its aSbrdiag a constant and ragnlsr currvnl of electricity of feiy weak tension, continuing (brie- Teral weeks or even longer, without any fresh addition of ex- citingfluid, Aglaaaoyliiider,D, '=- 477, 4 inches in length, diameter, was closed xit-tm. Fig. : audi' at one end by means of a ping of planter of Paris O'T inch in thicknesa :* this cylinder wm fixed by means of corks inside » cylindrical glaaa vosmI, a, abont 5 inches deep and 4 inches in diameter. A piece of sheet copper, 6 inches long end 3 inches wide, haTinga copperconducting wiie, F, soldered lo it, wng loosely coileil qp. and placed in the small cylinder, with the pUstar bottom; a piece of abeel anc,!, of equal size, was also loosely coiled up, and pUced in the larger external cylinder, being famished like the copperplate with a condacting wire, a. The larger cylindrical glass Deing then nearly filled with weak brine, and the smaller with a gnturaterl solution of sulphate rf copper, the two fluids being prevented from mixing by the plailer of Taiia diaphragm, the appaiatui is complete i and if cms • Phil. Trui. 1S37. ■- »t-i^w«tf^ - jj- -kar « BECQUSBSL's BJITTBBT. 469 be taken that the fluids in the two cylinden be at the same level, it will continue to afford a continuous current of electricity for some weeks, the sulphate of copper being very slowly decomposed. 834. If the ends of the conaucting wires of this apparatus be immersed in a solution of nitrate, or acetate of lead, no immediate action ensues, but in about fijfteen minutes, or even less, some elegant and delicate feathers of metallic lead, which rapidly increase in sixt, appear at the negative electrode. This effect does not occur when both conducting wires are of platinum; but when the negative electrode only was composed of that metal, the re- duction of the lead continuod with apparently increased energy. From these experiments, as well as many others of a similar kind wluch it is unneoessaiy to detail, it appears that to render effective the reducing agency of a feeble current, or at least of that elicited by a single pair of plates, it is necessary that the positive electrode should be a readily ozidizable metal : thus using a kind of battery of tioo cells, in which the wires forming the electrodes, and the fluid submitted to experiment, constitute the elements of the second cell. 835. But few metallic solutions yield so readily as thoee of lead to the reducing agency of weak currents ; and where a longer time and continuance of action is required to effect the reduction, the decomposing apparatus of M. Becquerel will be found a neces- sary addition to the little battery, with the substitution of a plug of the plaster of Paris for one of clay. This apparatus is, in met, a counterpart of the battery itself, and is represented in Fig. 477, connected with the wires f, o; it consists, like the former, of two glass cylinders, one within the other, the smaller one having a bottom or floor of plaster of Paris fixed into it : this smaller tube may be about half an inch wide and three inches in length, and is intended to hold the metallic solution submitted to experiment, the external tube, in which it is immersed, being filled with a weak solution of common salt. In the latter solution a slip of amalgamated zinc is immersed, for the positive electrode, soldered to the wire coming from the copper plate of the battery ; whilst for the negative electrode a slip of platinum-foil, fixed to the wire from the sine plate of the battery, passes through a cork fixed in the mouth of the smaller tube, and dips into the metallic solution which it contains. 836. When a solution of the chloride or nitrate of iron, copper, tin, zinc, bismuth, antimony, lead, or silver, is placed in the smaller tube, and connexion made with the apparatus in the manner already described, action is almost instantly apparent, water is decompoeed, and torrents of minute bubbles of hvdrogeh are evolved at the surlace of the platinum plate (negative elec- trode), which generally continue for a short time, sometimes, in- deed, lasting for hours; a circumstance depending apparently upon the degree of facility with which the metal under expen- f^^mr^^^gtam-^ _ m^^} ■ "w^.* .<> . ■» 470 .YOLTUO ELECTRIdTr; ment is reduced. Thus with Bolations of copper, scarcely a' bubble appears, the metal being almost immediately redaced, all the hydrogen being probably employed for that purpose from the instant ot completing the circuit : with solutions of lead, tin, or silver, the evolution of hydrogen continues for a short time only,' and ceases as soon as the minutest portion of reduced metal ap- pears on the platinum plate ; bnt with solutions of iron and man- ganese, the evolution of gas frequently continues for six, -eight, or ten hours, or even longer ; the evolution of hydrogen thus seem- ing to bear something uke an inverse ratio to the ease with which metal is reduced. After the hydrogen has ceased to appear at the negative electrode, striaa of the reduced metal, which rapidly increase, are deposited on the surface of the platinum. The metals tnus reduced generally, but not invariably, possess a perfectly metallic lustre, are always more or leas crystalline, and often very beautifully so, affording a considerable contrast to the imegnlar soft spongy masses obtained from the same solutions by means of currents from compound batteries. The crystals of copper obtained by the process just detailed, rival in hardness and malleability the finest specimens of native copper, which they much resemble in appearance. The crystallization of bismuth, lead, and silver by these means, is veiy beautiful, that of the former being lamellar, of a lustre approacning to that of iron, bnt with the reddish tint peculiar to this metal. Silver may be thus obtained of a snowy and indeed dazzling whiteness, usually under the form of needles, or cicicular cr3rBta1s. 837. The metallic solutions hitherto mentioned as yielding to the action of weak currents, are, as is well known, equally acted on by voltaic batteries, consisting of a considerable number of alternations, the metal being reduced in a spongy form, often des- titute of a metallic appearance. But there are some metals which are deposited from their solutions as oxides only, when acted on by currents from large batteries, and yet are deposited in a brilliant metallic form, if submitted to the action of toe currents from the little apparatus already described. Of these, nickel is an example : a solution of its chloride or sulphate, when placed in the smaller tube of the decomposing apparatus, yielding after some hours a crust of metallic nickel on the negative electrode, often of a sil- very lustre on the surface immediately applied to the platinum, that portion of the crust more in contact with the fluid being generally black, and frequently covered with a layer of hydrat^ and gelatinous green oxide. 838. For the reduction of silicon, let a solution oF fluoride of silicon in alcohol be prepared, by passing a current of the gaseous fluoride into strong alconol. On filling the decomposing tube with this solution, and making the connexion with the battery in the manner already described, bubbles of hydrogen were copiously evolved at the surface of the platinum plate (negative electrode), ^*-_ ;;^»> ■iw" REDUCTIOX OF ALKALIHE METALS. 4?! oantinning from eight to ten Lours, when the platinnm appeared to be tarnished, and in twenty-four hours a copious deposit of sili- con had taken place on the platinum, to the surface of which it firmly adhered. Around the reduced silicon, and suspended in the fluid, was a dense gelatinous cloud of silicic acid. On quickly withdrawing the slip of platinum, dipping it in water, and then pressing it between folds of bibulous paper it was dried, and freed from any adhering solution. The silicon was nearly black and granular, under a ^ns, exhibiting a tendency to a ciystalline form. It was not deposited on the platinum in a confused and irregular manner, but in longitudinal striae, which appeared to follow the direction of certain lines of minute eminences on the surface of the piece of platinum, produced apparently by scour- ing it with fine sand and a piece of cork before being used for the construction of the negative electrode. 839. Potassium and sodium may be readily reduced by these weak currents, and obtained as amalgams by using a modification of the decomposing apparatus before described. Let the smaller tube containing the metallic solution be replaced by a small glass funnel, A, Fig. 478, the beak of which has been ^^ ^^g^ carefvdly filled up with plaster of Paris : &x on this plaster floor a piece of glass tube closed at one end, about 0*5 inch in length, and 0*2 inch in diameter, and half filled with pure mercury ; this tube should not be placed vertically, but inclined so as to form an angle of about 40** with the plaster floor of the funneL The external cylinder communicates as before with the copper plate of the battery, by mesns of a slip of amal^mated sine, z, dipping into the brine it contains : a solution of chloride of potassium is to be poured into a, and a piece of platinum wire connected with the zinc plate of the battery being twisted into a flat spiral at one end so as to present a larger surface, immersed in the mercury contained in the little tube submerged in the saline con- tents of the funnel. The circuit being thus completed, electric action soon becomes apparent, bubbles of hydrogen being evolved from the surface of the mercury (which now formed the negative electrode) in a very curious manner, not in confused and rapid streams, but in large and distinct bubbles, which very slowly appear, and perform several gyratory movements on the surface of the fluid metal before they are detached. In about eight or ten hours the mercury will have swollen to double its former bulk, and if it be removed from the little tube as quickly as possible, and poured into distilled water, an evolution of hydrogen gas takes place from its whole surface, and the water becomes alkaline from the formation and solution of the oxide of potassium or potassa. The film of mercury adhering to the platinum wire remains on I l/t m- 472 YOLTAIC ELBCTBIGITT. • it for Bome days, giving it the appearanoe of haring been amal- gamated. 840. Of all the saline solationa that the late Author sabmitted to experiment, none afforded soch conclusive and interesting re- sults as those of ammonia. The compound ammonium being reduced with almost as much ease as copper or tin, when a solu- tion of the chloride (hydrochlorate of ammonia) is submitted to the action of the voltaic current in contact with mercury, in tho same manner as chloride of potassium or sodium, the same adhe- sion and creeping up of the mercuty along the wire is observed, and after a few hours the fluid metal swells to five or six times its former bulk. On removing it quickly and drying it, b^ allowing it to fall on bibulous paper, the amalgam of ammonium is obtained of a buttery consistence, possessing a dull silvery colour, and yielding a peculiar crackling, or (if it be allowed to use the expres- sion) an emphysematous sensation to the finger on pressing it : on being immersed in water it very slowly gives off hydrogen, and yields a solution of ammonia. 841. By far the most satisfactory method of obtaining this amalgam is by using for the negative electrode a piece of platinum wire coiled up at one end, after it has been amalgamated by dip- ping it into the aromoniacal amalgam obtained by the last de- scribed process (840). A minute quantity of mercury is thus made to adhere to the wire, which being connected with uie zinc side of the battery, is dipped into a solution of hydrochlorate of ammonia contained in the smaller tube of the apparatus used in effecting the reduction of silicon (838). The circmt being completed, a few bubbles of hydrogen are disengaged from the amalgamated wire, which soon cease, and in an hour or two, a leaden grey spongy mass is observed adhering to the wire, which is sometimes suf- ficiently bulky to fill the tube, and putting on much of the external appearance of a mass of cellular galena. This mass consists of a spongy amalgam of ammonium, containing a very minute proi>or- tion of mercury; it is lighter than the solution in which it is im^ mersed, for on adroitly separating a portion of it, it rises to the surface and rapidly decomposes water, hydrogen being evolved and ammonia formed. It is a very curious and interesting fact,' that although this spongy ammoniacal amalgam cannot be kept immersed in water even for a few instants without the formation of ammonia, yet as long as it is connected with the negative electrode of the battery, it may be preserved without change for days and weeks. The instant the connexion with the battery is broken, a mass of this amalgam, as large as a walnut, appears to vanish in a few seconds, torrents of minute oubbles being given off, and a scarcely appre- ciable quantity of mercury being left on the wire. On again closing the connexion with the battery, decomposition recom- mences, and the amalgam is reproduced. SLIOTBOLTBD BT A XACBIHE-CUBBBHT. 473 JV-479. 842. The deoompomtioii of seyeral electrolytes, as sulphate of soda, iodide of potassiam, &c^ may be effected by means of a cmTent of franklinic electricity, from the electrical machine. For this pnrpoee, place upon the table of the unixersal discharger a piece of bibmoiu paoer, soaked in a solution of some alkaline combination, as iodide of potassium ; fix to each of the sliding rods of the apparatus a piece of fine platinum wire, to serve as electrodes, which must rest lighily upon the paper, about an inch from each other. Con- nect one of the rods, n, Fig. 479, with the rubberof the machine, or with the earth, by means of m chain, and the other, p, with the prime conductor by a wire, or, still better, by a |»iece of wet string: on workmg the machine, the salt will oe decomposed, iodine being set free at that wire which is connected with the conductor, or at the point where the current of electricity enters the compound ; and the alkaline base at that which is connected with the rubber, or where the current escapes. The alkaline element may be detected by placing a piece of turmeric paper, moistened with the solution employed, on the table of the discharger, in place of the ordinary bibulous paper. 843. It is not necessary to use metallic conductors to effect electrolysis by franklinic electricity. To show this, take two tri- angular pieces of paper, a, b, Fig. 480, B being coloured with litmus, and a with turmeric, place them base to base on a glass plate, and moisten them with a solution of sulphate of soda ; let a pointed wire, p, proceeding from the prime conductor of an electrical machine in action be placed a few inches from b, the sulphate of soda will be decomposed, the acid will be set free at B, where the electricity enters the paper, and will turn its blue colour to red, whilst the soda will be set free at a, staining it brown. This elegant experiment of Faraday is conclusive against the old notions of the electrodes inducing decomposition by acting as attracting surfaces, or poles. 844. Electricity is evolved not only during chemical decompo- sition, but has been supposed to attend chemical combinatum / a statement first made by BecquereL The truth of this opinion has been, by many, either aJto^ther denied, or limited to the case of the combination of nitnc acid with alkalies. That an electric current, certainly of extremely low tension, is really evolved during the combination of sulphuric, hydrochloric, nitric, Fig.iSO, 474 VOLTAIC ELECTKICITT. phoBphoric, and acetic acids, with the fixed alkalies, and even with ammonia, is readilj demonstrable, bnt what the immediate cause of this evolution of electricity may be, is (questionable. In the case of electricity evolved during the combination of nitric acid and potassa, or Becquerel's battery, as it has been termed, Daniel] *8 view of the composition of salts enables a tolerably ready explanation to be proposed. The npparatus consitita of a tube closed by a plug of pipe-clay filled with a solution of potassa, and immersed in a vessel of nitric acid. Plates of platinum fur- nished with conducting wires are immersed in the acid and alkali. As soon as these conducting wires are twisted together an electric current takes place, oxygen rising in bubbles from the plate im- mersed in the alkali, whilst hydrogen is evolved in the acid and immediately acts on it, tinging it yellow from the formation of nitrous acid, the hydrogen abstracting a portion of oxygen from the nitric acid. Meanwhile combination of the acid and alkali occurs through the clay diaphragm, and nitrate of potassa is slowly formed. . On Daniell's hypothesis, nitrate of potassa, considered in its electric relations, is a compound of N O^ + E, and not of N 0^ + K 0, and hence was termed oxynitrion of poteusium. Similarly aqueous nitric acid would be oxynitrion of hydrogen consisting of N Oe + H, instead of N 0^ + H 0. In BecquerePs apparatus, the following elements are therefore arranged on each side the porous diaphragm, represented below by the double vertical line || : K0|1N0, + H= I NO« + k| +H0. Thus an atom of oxygen is set nree in the alkaline solution, and one of hydrogen in the acid, so that in this case the evolution of electricity may be really traced to chemical decomposition ; con- sequently Becquerel's arrangement does not present any exception to the general rule. 845. The statement, that in cases of electro-chemical decomposi- tion, the changes which take place in the electrolyte are continuous through a line of molecules, and not limited to those in contact with the electrodes (765), meets with an interesting illustration in the well-known experiment in which an alkali appears to traverse an acid without combining with it ; and which has been erron^usly regarded as a case of suspension of the laws of chemical affinity. Let three cups, a, s, b, Fig. ■^* ^^' 48 J , be placed side by side, and connected by means of pieces of lamp-cotton moist- ened with a solution of sul- phate of soda. Let a and b oe^ filled with a solution of this salt, and the central cup, TRAX8FERRENCB OP CHEMICAL ELKHENTB. 475 By with dilute salphnric acid. Let a pomtiTe platiniim electrode, c, dip Into A, and a negative electrode, z, dip into b. The voltaic current will now enter the fluid in A, and escape from b through z, traversing s in its course. Electrolysis of the sulphate of soda will take place, its acid with oxygen heing set free in a, and the sodium witl ]^ass through the sulphuric acid in s, and reach b, so that a quantity of free soda irill soon be found in b ; the sodium being oxidized at the expense of the water. It is evident that this alkaline body must have traversed the acid in s, with which, indeed, it for an instant combined, and the resulting sulphate of soda being decomposed by the current, the soda ultimately appears in b. 846. That in experiments of this kind, the base really combines with the acid it is made to traverse, is proved by using a salt with the base of which the acid forms an insoluble combination. Under these circumstances it is removed from the influence of tbe current, and does not reach the third cup. Place in a and b, solutions of chloride of barium, and in a, dilute sulphuric acid ; on the current Dassing, the contents of a are decomposed, chlorine is evolved, and oarium set free ; this is conveyed in the manner before described to the middle cup, and here it is arrested in its course by the acid which, in combining with it, forms an absolutely insoluble salt, the solphate of barytes, which falls to the bottom of the vessel, and then neither barium nor its oxide reaches the cnp b. Hence the salt chosen for experiment must be one of which the base fonns a soluble combination with the acid in the middle cup 8 (Fig. 481). 847. When water containing a very minute proportion of saline matter is subjected, in two cups connectoil by threads of moistened lamp cotton, to the action of the current, not only are the elements of tbe water set free, but the traces of saline matter are decom- posed into their constituents, so that the acid will appear in one cup and the base in the other. It has been observed by Daniell, that if a solution of sulphate of soda be thus treated, a voltameter being included in the circuit, not only is the Quantity of mixed gases collected in the voltameter the same in bulk as that set free in the solphate of suda solution, as might be expected (825}, but a quantity of the sulphate is itself decomposed, equivalent to the gaseous elements evolved from the decomposition of water in the voltameter and in the solution of the sulphate. Thus, the current which decomposed an atom of water in the voltameter at the same time decomposed an atom of water and one of sulphate of soda in the apparatus connected with it; forming an apparent exception to the general law (825). To meet this difiBculty, Daniell has sug- gested that the elements of the water in which the salt is de- posited, are separated by a secondary action. According to this view, sulphate of soda consists of S 0^ + Na, instead of S 0^ + Na 0, being in the prooosed nomenclature an oxysulphion of sodium. Then, when a solution of this salt is decomposed by an electric current, S O4 is set free, and immediately acts on the water, taking 476 YOLTAIO ELECTBICTTT. ftn atom of hydrogen to form the aqueo-acid, and thus an atom of oxygen is evolved from the water. The sodium then acts on an- other atom of water to form soda with oxygen, and sets free its hydrogen ; and thus the decomposition of an atom of water and one 01 sulphate of soda by a current, which is alone capable of decompobinff one atom of water when the salt is absent, is attri> butable to the secondary action of the assumed elements of the salt on the water. The same ingenious explanation applies to the electrolysis of all solutions of oxy-salts. 848. It has been already observed that salts materially differ in the facility with which their elements aro evolved uniier the in- fluence of the voltaic current. This difference is attributable to the varying amount of intensity with which these elements are united. Thus, as has already been shown, the current from a single pair of platinum and zinc plates is capable of decomposing a solution of iodide of potassium ; chloride of sil ver kept fused in a glass capsule is readily resolved into chlorine and metallic silver by the same weak current. On the other hand, a solution of sul- phate of soda, and nitrate of potass in a state of fusion, resist the action of this current, but if its intensity be exalted by the addi- tion of a little nitric acid to the exciting liquid, it is then capable of overcoming the force which binds the elements of these salts together, and they are readily evolved at the surface of the respec- tive electrodes. In the following list of electrolytes, the firet three are decomposed by the current from a single pair excited by dilute sulphuric acid, while the last four bodies do not yield until after the addition of nitric acid to the exciting liquor. Chloride of lead, fused. Iodide of lead, fused. Hvdrochloric acid. Dilute sulphuric acid. Iodide of potassium, dissolved in water. Chloride of silver, fused. Frotochloride of tin, fused. 849. The only difference between franklinic and voltaic eleo> tricity consists in the low potential or intensity of the latter, as compared with the former, which it vastly exceeds in quantity (767) ; their identity has already been demonstrated (732). By availing himself of the law of the definite nature of electro-chemicid decomposition, Faraday has, by a series of very ingenious experi- ments, succeeded in demonntrating the enormous quantity of elec- tricity naturally associated with the elements of a grain of water. He found that when two wires of platinum and zinc -^ inch in diameter were immersed to the depth of {■ of an inch in a mixture of one drop of sulphuric acid and four ounces of water, as much electricity was set free by this miniature battery in about three seconds of time, as was yielded by an electric battery (724) having 3500 square inches of coated surface, and charged by thirty revo- lutions of a plate machine 50 inches in diameter. The quantity of potential electricity yielded by the machine, and sufficient to FBAHKLIHIG AJID TOLTAIC CUBSBKTB COMPJLBED. 477 kill a small animal, was thos evolved bj the solution of an almost inappreciable portion of zinc wire. By an extension of this reason- ing, it would appear that 800,000 charges of the electric battery would be required to decompose a grain of water, a quantity capable of being supplied at an infinitely lower potential by a pair of platinum and zinc plates, sufficientljr excited by an acid to keep Ignited during rather less than four minutes, a platinum wire y}^ inch in diameter. In a voltaic battery, containing any given area of exciting sur- face, it is found that, in proportion as the number of elements is increased, and their size diminished, the current will become more assimilated to that evolved by friction, and the discharge between the two electrodes will be more disruptive. It may be remarked that in a battery containing a large number of elements, 400 for example, the divergence of the gold leaves of an electroscope in connexion with one electrode, may always bo observed ; and that divergence will be doubled when the other electrode is connected with the earth. Rbferbhces. To the no less excellent than laborious Traite de TElectricit^ et dn Magn^tisme, of Becquerel, the student is referred for an elaborate account of all that is valuable in electrical science. The papers of Faraday, in the Philosophical Transactions, now fortu- nately collected into a separate work, cannot be too attentively studied by those who wish to acquire a thorough acquaintance with this beautiful science. Nor ought the writings of Pouillet, Coulomb, Poisflon, De la Bive, and many other Continental philo- sophers, as well as those of our talented countryman, Daiiiell, to be overlooked by the student. Noad's Manual of Electricity is an elaborate treatise, from which much useful information may be ob- tained ; but it is unfortunate that the old " fluid " notions are still retained. Ferguson's electricity (a volume of " Chambers' Edu- cational Course'') is an elementary work of great merit, and Inrought up to the knowledge of the present time. 478 CHAPTER XIV. ELEGTR0-DTNAMIC8. 850. The direct influence of the discharge of franklinic e]ec- tricit,v on magnetic needles, was studied long ago by Franklin, Beccaria, Wilson, Cavallo, and others ; the power it exerted of communicating, destroying, or reversing polarity was also pointed out. But it was reserved for Prof. Oersted, of Copenhagen, to announce to the world the existence of a new and peculiar force reciprocaUy exerted between magnetic needles and the connecting wires of a voltaic battery ; a fact, to a certain extent, theoretically anticipated in a work, b^ the same philosopher, published twenty years before his great discovery, which was made in 1820. 851. Let a copper wire, connected with the two poles of a ▼ol- taic arrangement, be stretched parallel to a magnetic needle, sup- ported on a pivot, and free to move in a horizontal ^lane. The magnet will instantly leave its position in the magnetic meridian, and after a few osciiiations will ^' assume, and retain, a position at, or approaching to, right angles to the wire, so long as the cur- rent continues to pass. To show this, let a thick brass wire be supported by two pillars, ▲, b, Fig. 482, passing through their long axes, and soldered to the binding screws, c, z. The mag- netic needle, n s, is supported by a pointed wire, w, fixed in a hollow stem, i), in which it may to placed at any required height by means of a screw, n is the north, and 8 the south pole of the needle (593). A. Screw the positive electrode of an electromotor (767^ into c, and the negative into z, then the current will pass in the direc- tion A B, as shown by the arrows ; and the needle n a, placed in the magnetic meridian, will move from its previous position; its end, M, moving towards the voest. B. Ix)wer the wire w into the socket d, so that the needle irs may be beneath the conducting wire. On making c. aod let A and u be the north pole* of the two needles. Then (ntfqndcg them to be suspended perpendicularly them to be suspended perpendicukriy to the plane of Che papei^ tbe earlh'n foree will act on them in the direc- I tions of the arrows. ■ suppoMug the msgne the needles to U unequal, let that of a a be In that rf c » a. cu-OA- then the resultant of Ihe parallel momenta of < and c wiU be a moment equal to Iheir sum acting in the aame direction at o (761 Join k, the interaoction of a a and c u, witli o, and draw KP biaecting, and also perpendicnkr to, a c. Then tl>e mi effoct of the moments at A and C wil! be equal to that of a .mgle moment actioR on the short, half-mspnet k ... «.d the p<«.t»n of equilibrium of the system ip ■'■-• ■" "'"■■'■ -"» >"«■»* t mi- isition E y ; that is, th" i-aEwilhlhe niaBn«l''= n....-.— .. are equal, then to vvill coi.icide with . r, and the s rest exactly across the meridian. IPthe momentaare _ . ,_ . tKe nrKTlo A E D decreasBs, E 0 will approach and would nlUmalely ■ -X -.;.l, „r- \wr,ee if the moments of the needlea are on- in iW matnictic meridiun. If ihe needles bo quite puaUel, and th«r moments also equal, then « r wiU b«oino cT^ac«it ;_ then, and then only, the system will be ab»luMly ortrt.^*™ m fixed posilion of eoutlibnum, and the n«dle. if deflected by ■ cuncutTiill remain when ths deflecting fon-e ccaaes to act, aad Tenieut. In practice tbe nt if Dot very nnt-qual, will n the Btrongi>r, but will have s Tsir ai >r sensiliilily; na they :,C; [1 quite equal, nliich they gcnerully ai in iagtrumeiils of the greatest delicituy, ihey will rest exHClly |jer- peodicular to the mrriiliau : aail tlie length of the virtual mo^el ■ FbeiQg very Biuall, the oscillation uf the Bystetn will be very alun. 869. Du LfoiK-IleymoDd, whose t-laburate rexeitrchee on the cur- renli of electricit; exisUng lu aniiuul stniclurea have attracted bu much iotereltj baa carried Iha pcrfecUun of galvBDuniEteni to an almost incredible sxlent. One of bis ioitrumenta, nsed to detect the musuular currents, has a coil of line ineuhiled copper wire. 3360 feet long, and -0067 inch ia diameter, wound 4650 ti roond the frame. The other, the sensibility of which ' that it detects the electricity floniug through the i wire 16,760 feet, or more than three miles long, wound 34,1 1 tiniee round the ^me. The Epnce in which the lower needle u ■uspeaded is but ODe-leDthofna inch in height. Tlietwo needles, which are 1'5 inch long, with llitir cuiinecting piece (made of tor- toise-sliell), weigh only 4'9 grains, and are bu equally magnetised, that they perform a single libralion in 33 beconds, A minute correcting maguet was applied to the astatic needle in this inatru- ment, but its employment is unnecessary. lusLruitieats of equal, if not of greater ecmtibilily, have been constructed hy Mr. Becker, in Londuii, in wbicli tbe subetituiion uf aluminium tor turtoisS'Sbell saves a small portion of tbe weight. 839. TItomion'i Stfiteting Oahianojaeter.^Tim peculiar fea- tures of this itistniment, designed by Sir W. Thocnsoii for tele- graphic purposes, are that the galvanometer o, Fig. 487, consists of a circular coil. In w .„ the centre of which ^*- **'- a very small magnet, attached to the back of a small circular pended. A small ^Qcil of light pass- ing tlirougb a tiole in the chimney uf u lump, t, fulls upon is theuce reflected on to a scale, s, on which the deviationB of the magnet are read, with the advantage of the angular dis- placeoient of the reHected pencil of light being doohle that of the *^.«». 484 Ftf.taa. magnet itself. An a^uBline magnet, H, >!iile« I up and down on the Tertical st&ia, and moves horiKint»llj_by_ the tangent rerew.T. Thi« is designod principnlly for telegraphic porposea, and la at) excreuingly naeful instrument. The actual size of the magnet, lit, and mirror em- ployed is represented in Fig. 48B ; being made of inioroecopio glass, the mirror weighs only a few grains. 860. Thonuon'i Marine O^mmomeler.—Sh W. Thomson has ingeniously adapted bis preceding inatrumcnt to manne ponioses : in fact, the signals constantly transmitted to tbe Ortat Ea»tem during her recent Bucccasfulpragresa in iayiag the cable across the Atlantic, were received by means of this ingtrument. Aa tbe un- certain and incessant motions in all diractiona render the use of on ordinaiy galvanometer impracticable on board ahip, tho mirror and magnet, instead of being freelv sngponded, «re attached to Ma sliding frame, a, Fig. 489, by meana of a slender Bloment III' stretched along it, in a line pasH- "" ing Ihraugh tho centre of graiily of the magnet and mirror \ the poattiou of the miTTOr is therefore Dever oltered by its own gravity. The coil, e e, is surromided by ft stout aolt-iron cylinder i t, which conaidemblv diminiahea the in- fluence of the carth'a magnetlam on tho auspended magnet; and this is furtbU' modified by a soft-iron box, oonHiatingcd the pieces i., B, C, D, in which the ^vanometer is enclosed. The snapended .magiiet ia adjuati:d by meana of a aemicircular magnet, ir, placed ontaide the aoft-iron cylinder, and capable of being moved hori- lOntaliy by the tangent-screw^ t. This instrument ia admirably contriviid, and perfectly etScacioua. 8S1. Oaugmn't Tangent Otdeanom^tr. — It has already been shown (802) that if a cireular coil be placed in the veiticaf plane of the magnetic meridian, and a needle be placed at ibo centre of it, the length of which is small comparetl with the diameter of the coil, then tlie needle will be deflected by a ct ing through the coil, and the potential of the cum proportional to the tangent of the angle of deflexion, nient constructed on this principle is called a tangent goXnano- mfttr. In Gaugaiu'a inatmment, Fig. 490, instead of a single coil in a plaoe passing through the needle, two coils, D, B, are employed, both of which He on the surface of a donbls cone of I2\y, the common apex of which is at the centre of the needle. t wifl^ Thrae are three Isjers in each coil, whi< and the termiDals are hrousht to four b inther one, two, or all threelayen may be brought into cireuit at pleasure. ■''■ *"■ There are bIbo tno single coils of rery thick wire, nnited i>f e. transveraa portion becealh, vhich terminate in two binding-BcrewB, x,b; these are designed for the meaaurBment of cur- rente of large polential. 862. If the ma^eti be fixed, «id the conducting wires nioreable, thus reTereine the coodilionBof tbegalvano- meter, the wires will be acted upon bj the magneta, and assume a constant position with regard to the direction of the current, and the position of the magnetic poles. 8(i3. Let a thic^ curved wire be connected with an electromotor M that the current maj traveis« it ; divide it iu the middle, leav- ing ahont an inch between the divided ponions, and re-connect them by means of a piece of fine copper wire. On dipping this thin wire, whilst the current ig passing through it, into iron filings, Ihej will be attracted and adhere to it as if it had suddenly ac- quired magnetic pro^rties. The filings will he attached to the wire in the form of nuge, about one-twentieth of an inch apart, and will drop oS the instant the cmrent ceases to be transmitted. 864. Wires conducting electric cnrrents aitraet taeh Other akat the currtsU are moving in the laiae, and reptt each other, trhen they more m contrary directiom. To show this, let a frame of 491, be fixed to a piece * of light wood, D, moving on a jiivot, the ends of the wire dipping ioiolwD . cnncentric annular cells, <■ filled with mercury, and connected by wires pau- ing through the item e totheacrewa, p,a. These •civws are connected by wires with the innerior (854), which by tho wires, tf, z, is itself con- nected with the two plates of an electromotor. A current thai trareraea the frame, A e c, in a diroclion varying with the position of the bars of the inversor; and let the current move in the 486 ELECTRO-DYNAMICS. direction shown by the ritowb, and let a thick bent wire, m l y, be placed in communication, by means of cups of mercury, with the two plates z", c^', of a small electromotor. Lei this wire ap- proach towards c ; the positive currents will be descending both m c, and in l m, and thus moving in the game direction, the frame of ABC will move on its centre to meo^ h m , mutual attraction ensuing. Then move the bars of the inversor. so that the positive current will ascend in c, instead of descending, and immediate repulsion will be observed to occur. If two flat coils, each consisting of a single spiral layer of in- sulated wire, be suspended parallel and near to each other, and a current be transmitted through each, they will be strongly attracted mutually when the currents are in the same direction, and equally repelled, when the currents are opposed. 865. By means of Roget's electrical spiral, the mutual attrac- tion of conducting wires conveying currents moving in the same direction can be easily demonstrated. This consists of a loose coil of thin copper wire, a b, Fig. 492, suspended from a metallic support, z, connected with one electrode of a battery : the end b just touches the surface of some mercury commu- nicating by the wire c with the other elcc trode. On establishing connexion with the battery, the wire coil will contract longitiidi- nally, the successive coils attracting each other, and the lower end being raised out of the mercury, the connexion with the battery is thus broken : the weight of the wire then causes it to fall into the mercury again, and the passage of the current iH restored ; and these actions being repeated succes- sively, a rapid longitudinal vibration (376) of the wire is produced. 866. The action exerted by a conducting wire on a magnet (851), is obviously not a single force, but a couple (81), by which the opposite poles of the magnet tend to recede from the con- ducting wire in opposite directions, and assume a position of equilibrinm when the opposite actions of the wire on both poles become equally balancea by the earth's directive force. Reason- ing on this fact, Faraday concluded, that if the action of the current could be confined to one pole only of the needle, a rotary motion might bo produced, provided no opjyosing forces interfered. After a series of experiments on this subject, lie succeeded per-, fectly, and thus developed one of the most interesting and extra- ordinary phenomena in electrical science. The most convenient apparatus for illustrating the rotation of magnets round a conducting wire, consists of two slender magnets, N s, N a. Fig 493, fixed vertically and equidistant from each other, with their poles in the same directioni in the piece of wood, a, H Fig. 402. |2 "^ B ^ — e c BLECTRO-MAOKETIO BOTITIOV. 487 supported hj a pointed wire, b, bo as to rotate freely on its centre. Tne middle of the piece of wood, a, is excayated, and contains a Fig.4Sa, drop of mercury, which communicates by means of a curved wire dippins" into it, with the external circular trou^ of mer- cury, E. A pointed copper wire, supported by a screw at o, dips into the mercury in A ; and is fumisheci at its upper end with a cup containing mercuiy, so as to be readily connected with an electromotor, by means of the inversor (854). llie cup, c, and trough, s, are then connected, the former with the copper, the latter with the zinc, plate of tne electromotor. So that the current descends from c to a, and then reaching e through the bent wire, escapes to z. It thus acts only on the poles n, k, of the magnets, and the forces acting on these poles being e<|ual, and in opposite horizontal directions, constitute a couple, which will cause the connected magnets to rotate round the conducting wire c, from left to ri^ht, or in a direction like that of the hands of a watch. By shiftmg the bars of the inversor, or otherwise changing the direction of the current, the direction of the rotation will immediately be reversed : the same thing also occurs, when the position of the poles of the magnet is reyersed. Let the mag- nets or currents be arranged as they may, the direction of the rotation always corre^'ponus with the formula of Ampere (852). It may here be remarked, that in this, as in all other experiments in electro-magnetism, where wires dip into mercury, tneir ends should be cleaned and amalgamated, by being dipped into a solu- tion of nitrate of mercury, to ensure perfect contact. If a fiat bar-magnet be substituted for the pair of magnets and conducting-wire in the above experiment, the same results will ensue, and the magnet will rotate round its own axis. 867. If the magnets be fixed, and the conducting wires move- able, the preceding conditions will only be reversed, and the con- ductors will now rotate round the fixed magnets. U his may be readily shown by means of a horse-shoe magnet, n s. Fig. 494, placed in a vertical position, with circular troughs, a, b, clamped upon its legs ; a light wire frame, supported by a fine steel point from each pole of the magnet, is so arranged that its vertical branches just touch the surface of the mercury in a and b. Each of the wire frames terminates in a cup containing a drop of mercury, into which the ends of the cross wire from b dip. Connect the cup of mer- cury, B, by means of a wire, with the positive electrode of an electromotor, either directly, or by means of the inversor, and let the virea, c, t. coming from tb« dninlar troneh*, a, b, be belli connecteil witb ibe negative electrode. Uoder theae circnm- — ^jj_ BtaiiceB, a cnrrent of electricity will enter the cup E, nnd there, being divided into -'' twn portions, will deacend the Tertteil brancheB of the wire fnuoea, and retch- ing the trongbi A B, witl leave the *pp*- ratua bj the wiree o, t Directly the cur- rent IB in action, the wire frame roapended from the north pule of tbe magnet besini to rotate rapidly in a direction from leU to right, and that ronnd ibe sonlb pole, in a Contrary direction, from the action of tho filed magnet on the corrent in the moveable conducting wiren. If the direc- tion of the current M reversed, either by altering the craineiione with Uie electro- motor, or by abiRing the bara of the iorer«or, the diicction of the rotations niU alao be revaraed. If the electric current be transmitted tbroogh the wires c, t, from B to A, or vice vertd, it will travarsa the vertical bara of the two wire ca^s in oppotite directions, and consequently they will both rotate in the lamt diraetinn. fiimilur results may bt obtained, bh was Gi«t shown by Ampere, when the annular troughs a, b, are converted into clectromotora. For this par[>oee tbe wire cages are double, tlie outer ones resting by needle points in little mercury cups at the top of tbe inner ojies. Short cjUndert of eheet zinc are aoldered to the ends of the wirea of the inner cages, and of copper lo those of the outer onea. The tron^bs must be Riled wilb dilate sulpbnric acid, or still better, with a saturated solution of sulphate of copper, ■ little acidulated (TT2), and be lar^ enoo^h to admit of the immeivoa of the nnc and copper cylinders without contact either at tlio aides or bottom of the trough. While the cylinders are immersed in acid, curreote will travel tip tbe wire« of the outer cage, and dovm those of the inner one, and they nitl ho found to rotate in opposite directions. 868. The rotation of a conducting wire may be also conve- niently shown, by bending two wires into helical ouila like cork- screws, and allowing each to rest by one extremity on the depi«t- aion on each pole of the horse shoe magnet. Fig. 494, the other end dipping into the mercury in tbe circular tmughi A, B. On coonecIinE one of tbe latter witb the positivs, and Uie other with the neffstive electrode of the electromotor, the current will ascend through one belii, descend the pole of tbe magnet which supports it and ascend the other pole, and reaching the second helix will deacend alonfi il, and thus by the mercunal trough into which it dips, reach the sine plate of the eici^g apparato*. In thia ROTATIVO DUCa. 489 Fig. 405. ▼ariation of the experiment, the helical coils of wire will rotate round their reepective poles in the tame directUmy because whilst the current ascends in one, it descends in the other. 869. It; instead of submitting a conducting wire to the action of one magnetic pole only, it be so arranged as to be exposed to the influence of both poles, it tends to move in a plane equi- distant from both, and if it be smtabW attached, a vibrating, insteadof a rotatory, motion maj ensue. Let a light wire, w, Fig. 495i, be suspended from a brass rod connected with the cup of mercury, c, so that its lower end just dips into a cavity cut out in the base of the in- strument, filled with mercury » and connected by a wire with the cup E ; and let a horse-shoe magnet be placed, as shown in the figure, so that the end of the wire, w, may be midway between the poles of the magnet. Connect c with the copper, and z with the zinc plate of an electromotor ; the current of electricity will descend w, and being acted upon by both poles of the magnet, the wire will tend to rotate to the right, round the pole, m, and to the left round the pole, s. As it cannot at once obey both these forces, opposed in direction, it takes an intermediate course, as wonld be expected, from the law of composition of forces (284V and is thrown forwards out of the mercury, in the direction indi- cated by the arrow. Connexion being thus broken with the battery, the wire by its gravity falls into the mercury, and, thus completing the circuit, is again thrown oat, keeping up this oscilJating motion as long as a sufficient current traverses it. Let the direction of the current, or the position of the magnet be reversed, and a vibrating motion of the wire, in an opposite direction, or backwards, will ensue. 870. If the electric current be made to pass through a spur ^g* 406. wheel, w. Fig. 496| instead of a wire, a rotary move- ment between the poles of the magnet ensues. Thus, if the current passes from the cup c, to the axis of the wheel w, it descends through that spoke which happens to dip into the mercury, and passes from thence to z, and to the zinc plate of the elec- tromotor. As soon as the current descends the radius of the 490 BLBCTBO-DTirAMICS. wheel, tbe portion dipping into the mercnrjr ib thrown onf, as in the Tihrating wire; another spoke of the wheel dips into the mercuiy, and is thrown out in its turn, and so on, a continued rotary motion ensuing. If the position of the poles of the magnet, or the direction of the electric current, he reversed, the wheel will rotate in an opposite direction. The wheel w may he replaced hy an entire disc of metal with advantage, as the motion is then more uniform and continuous. 871. If a horse-shoe magnet he hronght near to a suspended rectangle of wire, a c, Fip. 491, through which an electric current is passing, it will he forcibly attr:\cte(^ whilst the current is pass- ing, and the poles of the magnet placed, in one direction ; and repelled, if either of these positions he reversed. This apparent attraction is really owing to the same cause which determmes the vibration of a wire suspended freely between the poles of a magnet (869). The rectangle having a tendency to rotate, in common with all conducting wires (867), round the poles of the ma^et, in opposite directions, it is compelled, by the law of com- position of forties, to advance between, or move from, these poles, according to tbe position's in which they are respectivelv placed. 872. If the freely suspended rectangle before aescribed, through which an electric current is moving, be left to itself, uninflnenoed by any opposing cause, it will be acted upon by the magnetism of the earth, and will assume a definite position ; which it will, if suffi- ciently mobile, regain, when disturbed from it by any apj^lied force. That /oee of the rectangle through which the positive current is moving in the direction of ue hands of a watch, aiwavB turning towards the south, whilst the other, or that in whicn the current of electricity appears to move from right to lefl, or in a retrograde direction, will assume the properties of a north pole, and will consequently face the north. u1ius in Fip. 491, that face of the rectangle ac, which is there represented, will regard the south pole of the earth, the current of electricity moving in it, having a direct (p. 122, note) motion. If the conduct- ing wire be bent into a circular or other figure, it will present the same phenomena as the rectangle ; tbe shape not influencing its properties. 873. If, instead of a single loop of wire, a coil of several con- volutions be employed, its polar phenomena will be proportionately lig. 497. increased, lliis may be very satisfac- torily shown by means of the little ap- paratus contrived by De la Rive, con- sisting of a plate of zinc, z, Fig. 497, about an inch square, placed between the folds of a bent plate of copper of the same size, and separated from it by bits of cork, or wood. A piece of copper wire, covered with silk, is soldered to tbe 491 ecmper pTiite. and after being twiited into aboat twaoty circular ooil»,B,kept close together by means of thread, ia filed by its other eitramity to the zinc plate. This apparatus ia placeit in a >faaIlon wooden cnp, A, filled with dilute anlpbunc acid, and, on alloning it to float in a veaael of water, the coil will, after a few oscilUtiona, arraDge itaelf acroaa the magnttio meriilian ; the action of the ftcid on the plates, c, i, deTeloping aufficient electricity to cants the coil B to present magnetic phenomena : that face in which the current ie moving from lelt to right, regarding the loutherD betniiphere of llie earih. On presenting a magnet towarda the coil of wire b, whilst the apparatus is in action, attraction and repulsion will enaue, as if the wire iteolf had really became a nwgnet. If otie of the ends of a bar magnet (according to the direction of the cntrent) be introduced into tbe ring, b, it will tTOTel slowly to the extremity of the magnet, and then turning inond, will again embrace it ; this ia a curious and interesting experiment. 874. The peculiar polar properties of this coil of wire may be well illustntfld by Giing it oti a piiot, in the centre of a ehallow circular trough of mercury, diiided into two portions by a little wooden partition, aa shown at A i>, Fig. 498. Tbe ends of the wire coil are pointed, and so long as just _^ ^^^ to touch the surface of the mercory in the dirided box, a u, as it, by capillary repul- rion (41), rises above the level of the pa^ tition without overflowing. On connecting the two cella of niercaiy, bj meaua of the wires, c e, with the two plates of an electro- motor, and placing the whole between the poles ofa horse-shoe magnet, tbe wire coil, B, will rotate rapidly, from the two faces uf the coil being idlemately attracted and re- pelled by tbe magnetic poles, k, 8, and tbe direction of the current traveraing it being reverseil at each half revolution. 'Iba^ diaphragm must be so placed that tbe poliirity of the coil may be reversed just after it has faced Iht attracliag poles. 875. Ibe coil of wire used in the preceding eiperiments may be regarded, aa long aa the current traveraea it, oa sjiat mugnet | but il tbe convolutions, instead of being nearly in the same plane, be drawn out, ao as to represent a long helix, aa A R, Fig. 4^9, ila apparent maenctic properties become much more distinct. Let a wire, covered with cotton or sillc, be coiled on a bIrbs tube, in a direction froio hit lo right, forming a right-handed helix {Wi), and be supiwrted on a pivot, aa at c, ill two ends, D B, hanging down, and just dipping into two concentric troughs of mcrcnry, connected with tbe screws, i, t, aa in the support of the rectan- gular cohdnclor before described (6641- Cm connecling these 492 BLBCTRO-DTHAM1C8. ■crevB Trith the two plates of an electromotor, tbe electricitj will traverse the helical conducting wire, which, after a few He 499 oscillations, will arrange itself in the '^' ' magnetic meridian; that end in which the current moves from left to right, pointing towards the south pole of the earth. The two extremities of this helix are respectively attracted or repelled bj the poles of a magnet, as long as the electric current traverses it, as completely as if it were a permanent steel magnet. If the extremities of this helix be attached to the plates of a small floating electro- motive element, as in the case of the flat coil (873), it will assume the direction of the magnetic meridian, and will comport itself in all respects as a floating magnet. 876. Ampere, to whom we are indebted for the knowledge of the properties of this and other helical conductors, has termed it the eleetro-dynamic cylinder. The most important pro^rtyof this helical conductor, is its power of inducing magnetism in aoar of soft iron, placed in its interior. Thus, if a bar of soft iron, in which magnetism is readily excited, be plaoed in the helix, ▲ b, Fig. 499, and a current of electricity be made to pass through the latter, by connecting its two extremities with the poles of an electromotor, the bar of iron will instantly acquire the power of attracting another piece of iron, and indeed present all the pn>- Eerties of a powerful magnet These magnetic properties are, owever, transient, and are manifested on^ whilst tne electric current is traversing the helix, vanishing altogether on the elec- tricity ceasing to pass through the wire. As in this experiment the current of electricity does not aUer the iron, but merely passes round it in the coil of wire, we learn that an electric current traversing a wire possesses the property of inducing magnetism in iron bars brought within its influence, and placed with their axes at ri^ht angles to the direction of the current. If they be not plaoed m this position, the induced mag- netism is proportionably weaker. 877. If a bar of soft iron be bent in the shape of the letter U, and be covered vrith several series of coils of copper wire, insu- lated bv being covered with silk or cotton, and a current of eleo> tricity be transmitted through the wire, by connecting its two ends with the electrodes of a voltaic battery, the intensity of the induced magnetism will become very obvious. On placing a smooth bar of soft iron opposite to the poles of this eleetro-magnfet^ it will be attracted, and remain flrmly adherent ; and an immense weight may be suspended to the bar without separating it from the poles of the magnet. In this manner, iUdro-tnagneU^ capable of mppOTtiDg WTeral bnnilTedireigliti, and evva tooB, hara been constructed. It is remarkable, that if tbe contact with the eleo- tcotnotor be broken, whilst the poles of the electro-magnet ere nn- connected vith each other, the induced mscnttiun will, if tbe iron lie veiy soft, almost entirety ranish : but ifthe poles be counected by a bar of sort iron, before communic-ation with the source of electricily be interropted, ■ conriderable magnetic inleoBity U left in the cnrred iron bar, and ia penaBDent So long as its poles ara connected, disappearing only ou the remoTal ot the piece of iron adhering to them. 878. If a bar of hard iron, or steel, be mbstitnled for soft iron, little 01 no magnetism is developed, so long ai tbe electricitj tro- Ternng tbe belli, in which they are placed, is of low notentlal. But ir a current from a powerful Toltoic battery, or tbe discbarge of a Leyden jar, be transmitted throngb tbe coil of wire, the in- claded bar becomes permaneBtty magnetic, ill polar properties Dot disappearing, as in the case of soft iron, on the cessatioD ofthe inducing corrfuit. In every case, the dirtetion of the poles of the indoced eieclro-magnet Iiears a conatant telatioo to the cootm taken by the electric current, and is the same as that in the eleo- tnwljnomio cylinder (876). 879. Tbe phenomena of the electric indoclion of monietism may be well illoatrated by means of a contnTonce of the late Dr. Sitchie, consistine of a bar of soil iron, supported by a pi*ot, and covered with a coil of insulated copper wire, the two eitremiliea of which just (ouch the aurikce of the mercury contained in acir- calor trongb, divided into two cells by a transverse slip of wood. In Fig. 600, H B is on nprigbt horse-ehoe magnet, bavii^ the bar of iron, x, covered with a coil of insnlated copper wire, supported hy ita [uvot over the tw»celled vessel of mercory, b. On c, in a second cup, connected with the other plate ; on suddenly withdrawing one of them, as d, the secondary current thus excited rushes through the arms of the person who grasping a and a forms a short circuit between them, and a severe electric shock is produced. If the hands be moistened, to render them better conductors, and connexion be made and broken with the electromotor, by connecting c with one plate, and drawing d over the surface of a file connected with the other r891 B) a rapid succession of very painful electric shocks will pass through the arms and chest of the operator. By placing in the hollow axis of the reel a bar of soft iron, or, still better, a bundle of insulated soft iron wires, e f, the intensity of the in- duced current, the vividity of the sparks, and strength of the shocks, will become remarkably increased. These shocks have been by some persons erroneously regarded as directly produced by the electromotor, whereas they really arise fipom a secondary induced current, quite independent of (except that it is excited by it), and far exceeding in intensity, the current originally generated. The electricity of the wire appears to be constrained by the inductive force of the battery current, and to be kept in a state of coercion so long as the current continues to pass : but when the coercing force is removed by the cessation COSREVT BVOLVISD BY ROTATIOV. 601 of the current, the electricity accnmulated at one end of the coil rashes back partly through the wire itself, and partly through any external conductor intervening between a and b, and the re- lative quantities of electricity traversing the external and internal circuits, will be inversely as their resistances. Hence it follows that the severity of the shock will, eceterU paribus^ be augmented by increasing the length of the secondary coil. The induction of one coil on another may be readily demon- strated by the suspended flat coils already mentioned (864) if the terminals of one be connected with an electromotor, and those of the other with a galvanometer. 894. In all electro-magnetic apparatus, in which the contact with the battery is suddenly broken, a vivid spark evinces the passage of the induced current excited by the action of the magnet on the conducting wire. This may be seen in the vibrating wire (869), where each time the moving wire leaves the mercury, a vivid spark is observed ; although the electromotor itself may be incapable of affording one, without the aid of induction. The existence _ ^' ^^' of these currents may be readily S roved by means of the revolving isc. It has already been shown (870), that the passage of a radial current through a disc placed be- ^^ tween the poles of a magnet pro- >^^ duces rotation : and the converse ^^ of this is equally true, namely, ^^ that, if a copper disc be made to rotate between the poles of a permanent maenet by means of a handle, as in Fig. 506, and two wires, one of which is in contact with the axis of the disc, and the other with the mercury in a trough in which the edge of the wheel is immersed, be connected with the binding screws of a galvano- meter (856), the needle will be deflected by the currents perpe- tually induced in a radial direction, by the poles of the magnet. If two discs of tolerably thick sheet copper about nine inches in diameter be placed vertically one above tne other in a frame, their edges being Kept in contact by the gravity of the upper disc, and a powerful compound ma^et be placed horizontally, so that the point of contact of the discs may be midway between its poles, the axes of tlie two discs being in metallic connexion with a gal- vanometer, it will be found by the deflection of the needles on rotating the discs by a handle attached to the lower one, that actually a larger quantity of electricity will thus be evolved by induction, than from a four-feet plate machine in full action ; a result that appears at first sight scarcely credible : it must, how- ever, be remarked, that this induced current is one of compara- tively small potential. 895. The currents thus excited (887—894) are available for all the experiments in which ordinary voltaic electricity is applied, 502 ELECTRO-DYKAMICB. and yarious kinds of apparatus, termed magnetihelectric and electro-magnetic machines, have been contrived for the purpose of exciting them with ntpidity. These may be divided into three prin- cipal kinds, in two of which an electric current is employed aa the pri- mary exciting agent; and, in the other, a permanent magnet is used. 896. The simplest and most convenient form of electro-magnetic machine is founded on an experiment already described (887), and may be constructed by winding on a wooden reel, five or six inches in length, with a hollow axis, sixty feet of insulateJ capper wire of about the bixteenth of an inch in diameter, its termina- tions being soldered to binding screws : this is termed the primary coU. Over this, wind about 1400 or 1500 foet of insulated copper wire, about the sixtieth of an inch, or even less, in diameter, and solder its terminations to other binding screws : this con>titute8 the secondary coil. If, then, the primary coil be connected with an electromotor, whilst the ends ot the external or secondary coil be held in the hands, espcciallv if tin or copper cylinders be used to increase the extent of sur&ce for contact with the hands, on interrupting the primary circuit, all the electricity under con> straint in the exterior coil by the inductive influence of the primary current is released, and passes through the body of the operator, producing a severe shocK. If the terminals of the long wire dip in acidulated water, or rest on paper moistened with a salt, as iodide of potassium, electrolytic action results, and the proximate elements are separated. 897. It is obvious that some means of breaking contact with the battery with sufficient frequency is necessary to ensure a rapid succession of electric currents ; and for this puipose various plans have b?en proposed. Ratchet- and toothed-wheels (265— -267) have been employed for this purpose ; but as they involve the necessity of being turned by the hand, they are very troublesome. If any apparatus of this kind be employed, instead of a toothed wheel, a cvunder of wood having two bars of metal inlaid, connected with the electromotor through the primary coH should be used. A brass spring, connected with the other electrode of the batteiy, presses upon the cylinder, and on causing the latt«r to revolve by means of a multiplying wheel, the contact with the battery may be rapidly made and broken. Connecting the primary coil with the electromotor through the medium of the vibrating wire (869), stellated wheel apparatus (870), or still better, of the roiatine coil (874), or magnet (879), will answer very well, as contact wifi be effectually broken several times in a second by their action. The late Author preferred, however, a little apparatus which has been described elsewhere,* consisting of a light iron beam vibint- ing between two fixed magnets ; this produces a break of contact about 400 times in a minute, and consequently affords a rapid succession of currents of induced electricity. * Phil. MBgMine. horember, 1837. COIL-MACHINES. 603 898. The most convenient form of the electro-magnetio machiDO is, however, the foUowing; it is far superior to that contrived by the late Author, on account of its certainty of action, and its dispensing Fig.Wl, with the use of mercury.* It consists of a wooden bobbin, a, Fig. 507, on which the two coils of wire already described (896) are woiud, the ends of the long and fine coil being soldered to the binding screws b, u. One end of the short and thick (primary) coil is soldered to the beginning of the copper wire surrounding the two little vertical bars of soft iron, its other end being con- nected with the screw o. The other extremity of the short coil is soldered to the base of the brass column d. This column sup- ports a slip of elastic brass, bearing at its end a disc of soft iron, placed over the vertical iron bars. A slender screw k, furnished with a platinum point, passes through the top of a bent support of brass, and gently presses on a pLate of the same metal fixea on the slip of brass below it ; the foot of this support is connected with the binding screw f : all these connexions are made under the base of the instrument. On connecting the electrodes of a single element, s, with f, o, the iron bars become magnetic by induction (877), and attract the disc above them. This being drawn down, Dreaxs the contact between the end of the screw, k, and the brass spring, and of course the magnetism in the bars ceases. The elasticity of the spring raises ue iron disc, and at the same time causes it to touch the end of K ; contact is thus made, the bars again become magnetic, and break the circuit, and so on. The course of the current from the plates b to the primary coil on ▲ bein^ thus interrupted and renewed many hundreds of times in a minute, a loud humming sound is produced by the vibrations of the brass spring, which, when they are sufficiently rapid, assumes the character of a defi- nite tone. Of course at each of these renewals and interruptions of the primary current, induced currents traverse the secondary ooil, which become remarkably increased on placing a bundle of insulated soft iron wires in the hollow axis of the bobbin, a. On then grasping a pair of conductors connected with b, c, in the hand, a rapid succession of severe shocks will be experienced. • thoM particular form of apparatna, wbioh ia peonliaxiy adapted to medical pnrpoaes, ia extennrely mannfactmed by Mr. Neeree, tondon. 504 BLBCTSO-DTXAiaCB. J^,80B, U. 899. From wbat htm been already remarked (886), it is obTitms that the induced, or secondary currents thus excited will be alter- nately in opposite directions. Those excited when contact ia broken with ue batteij being much more energetic than those excited when contact is m&dn. The following experiments will be found instructive. A. Place on a plate of glass a slip of bibulous paper, moistened with a mixed solution of starcn, and iodide of potassium ; let the points of two platinum wires fixed to the screws, b, c, rest on this paper, the blue iodide of amidine will appear at both wires, a much larger quantity being developed at one, than at the other. B. Let two platinum wires b be thrust through a cork fixed in the end of a glass tube, a, Fig. 608, filled with dilute sulphuric acid. On con- necting the wires with the screws b, c, a torrent of minute bubbles of mixed oxygen and hydro- gen gases will be evolved from both wires ; one giving of^ how- ever, much more than the other. 900. The apparatus just described may be conveniently called the electro-magnetic machine with alternating currents. It is, however, sometimes important to be able to obtain the induced currents in one direction only, hence the contrivance of the electro- magnetic machine with a single current. A very convenient arrangement of this kind is represented in Fig. 509, in which the required contacts are made and broken by a contrivance frequently introduced in electro-magnetic machines, namely, a metallic spring resting on the circumference of a wheel or cylinder, the surface of which consists of metal, and wood or ivory, in alternate cughp,F. Whichof the electrodesF, f, ispoaitive, and whichnega- tive, will depend on the connexions of the electromotor with d and b. The same obiect may, howeyer, be attained by a simple ad- dition to the coil-machine already described (Fig. 507) ; this con- gists in placing two other brass standards bent over at right angles on the opposite sides of the brass spring that carries the iron keeper, having^ platinum-pointed screws, which may be brought into contact with a bit of platijj^um on the upper surface of the brass spring, simultaneously with the point of k. If the ends of the secondary coil be connected with these last standards under- neath, it is evident that the current induced on making contact will pass through these standards, as the shortest circuit from one end of the fine wire to the other,* while that induced on breaking contact will traverse any conductor interposed between b and c. If the experiments made with the apparatus with a double current (899) be repeated with either of these last, the iodine and potassium in the one case, and oxygen and hydrogen iu the other, -will each be set free at one wire, but not at both. 901. Bukmkorff't Induction' Ajaparatus. — M. Ruhmkorfif of Paris, brought the induction coil, in the year 1851, to a greater degree of perfection than it had hitherto attained, by paying great attention to the insulation of the secondary wire, each layer of which he covered with a laver of shell-lac varnish. The energy of this apparatus was considerably increased by the application to it of the condemer of M. Fizeau ; which consisted of two strips of tin-foil, each containing four or five square feet of surface, placed alternately between three wider strips of oiled silk^ and the whole folded up : the pieces of tin-foil are respectively in metallic con- * Tins ptooeM is teohnioally termed ahfrt-drcmiiHff a cozrent. 506 ELECTB0-D7NAMIC8. nezion with the Btandards that support the contact-breaker. The condenser now generally employed consists .of pieces of tin-foil laid between larger pieces of oiled silk or thin gutta-percha, and connected alternately with each other. The function of the con- denser seems to be in forming a temporary reserroir for the poten- tial accumulated in the extremities of the primary coil, b^ the inductive action of the current on the electricity in the coil itaelf. The disruptive discharge that takes place between the ends of the primaiT coil, at the moment of breaking contact^ is consider- ably diminished by the application of the condenser, just as it has been already shown (736) that the discharge is much enfeebled, when the charge of a small Leyden jar is transferred to a much larger one. The inductive charge of the primary coil acts preju- dicially on the inductive charge of the secondary ; and conae- Quently it is found that the potential of the inductive charge of tne secondary coil is greatly augmented by the condenser, and the disruptive discharge becomes more violent. In this appa- ratus, the discharge took place through about an inch of air. In the coil of Buhmkorff the vibrating hammer acts against one ex- tremity of the core. It is also furnished with an inversor and contact-breaker: this consists of an ivoiy cylinder, resting bv two disconnected brass pivots in two brass standards, at which the primary circuit is interrupted. Two pieces of brass are at- tached to opposite sides of the cylinder, each of which is in con- nexion with one of the pivots, and two brass springs in connexion with the electrodes of the battery, are so placed as to rest against the opposite sides of the cylinder* When these rest on the ivory the circuit is interrupted ; and it is completed in either direction by bringing the corresponding metallic portions of the surface of the cylinder into contact with the springs. 902. Hearder'g Induction CoiZ.— -Subsequently a more effective arrangement of this apparatus has been earned out by Mr. Hoarder, of Plymouth : the principal features of this are, that the primary and secondary coils are distinct from each other, and consequently the length and thickness of the primary coil may be adapted to the battery employed. A short primary coil of thick wire, actuated by a battery containing a small number of large ele- ments was found the most effective. The secondary coil con- tained 3000 yards of insulated wire, and the condenser about thirty square feet of surface. 903. Liodd's Induction Apparatvs. — Some of the most power- ful induction coils hitherto constructed are those bv Mr. W. Liadd, of London. The core is 13 inches long, and 1*6 m diameter; it consists of a bundle of rather fine iron wire (No. 22), carefully annealed and insulated. The primary coil contains three layers of thick copper wire, and the secondary coil is three milea in length. The utmost care is bestowed on the perfect insulation of the secondary coil : the ends of the bobbin on which it is wound FABADAT^S OBIOIKAL IXDUCTION APPARATUS. 507 are thick platos of gutta percha, and several layers of a tliin lamina of the same most efficient insalator are placed between the suc- cessive layers of the coil, and hermeticanj sealed to the ends of the bobbin. The wire is evenly laid in a spiral, so that no turn of the coil may overlap a previous one, and an inch of thin gutta percha is left at each end of the coil, which, like the uncoated margin of a Leyden jar, prevents the disruptive discharge taking place between contiguous layers of the coil. The condenser con- sists of fifty sheets of tin- foil, each containing about a souare foot of surface, laid alternately between sheets of gutta percna. The vibrating sprine is placed vertically, and the hammer oscillates between the end of tho core and that of an adjustible screw tip- ped with platinum. The pressure of the spring for maintaining contact is regulated by a screw that presses against its middle }K>int, and by tightening which the primary current is interrupted ess fre^^uently, a greater amount of induced magnetism in the core being rei^uired to overcome the spring, and thus the energy of the inductive charge is increased. With this apparatus, ac- tuated by a Grove's battery of five elements, a spark of four or five inches in length in air may be obtained. The discharge of this machine through a vacuum of several feet in length produces a torrent of electric light that is truly astonish- ing ; and all the beautiful phenomena of the stratified discharge (811), variously coloured by the nature of the attenuated medium in which it takes place, may be most successfully exhibited. One of the most striking experiments that has been devised is a lipped goblet of uranium-glass, placed under an air-pum^ receiver, and resting on a small metallic plate in connexion with one of the terminals of the secondary coil. The other terminal is conducted through a glass tube to a small brass plate placed in the bottom of the goblet. When the positive current is directed to this, a stream of electricity flows over the lip (being the shortest way) to the plate beneath, and the whole vase is Fig. 510. brilliantly illuminated with fluorescent ^*=^ light. (Vide Ch. XIX.) 904. The simplest means of demonstrat- ing the existence of a current produced by the induction of a permanent magnet, is the original apparatus devised by Fara- day : this consists of about ten yards of insalated copper ribbon wound round a soft iron bar a b, Fig. 510, in contact with the poles of a magnet n b. Let one end of this coil be soldered to a plate of amalga- mated copper, c, upon which the other end, sharply pointed, is madie'to press with elas- ticity, to effect which, it is bent into a loop, d e. The bar a b becomes magnetic by induction, and on suddenly jerking off one the electric current dsTeloped in the coil U shown bys Tind spark occnning at the point where b pressea on c, aait beoomea ilightlj rttiaed rrom the piste b/ the sudden Jerk cominnnicat«d to a ■. 905. Of mogDela-fllectric mschineB, in which a pennuiciit raaefnet ia the exciting caiue of the cmrentg, there are many VKneticB. Of these, Suton'g and Clark's arraQgement are nipe- rior to those of Fiiii and others ; that of Mr. Clark being upon tho whole more conrenient than Saxton's from its small bulk, il tensity of action, and its dispensing with the use of meionrj. '. coDiists of an upright componoa horsa-Bhoe magnet, clan against a board, d, Fig. fill, by tlie cros^-piece, c. By raeana of a maltiplying wheel, B, the ■^ ■ onniiture, ABOF, isBiade to re- ToWe rapidly before the polea of the fixed mafnet. This arma- ture consists oT two pieeei of aoft I iron, coDBectedatrightangle* to f the bar of iron, aB, byacrewi; round the legs or branches of which are wound about 1500 J, One end of the w . . connected with a collar of brass, against which the spring B presses, the other end being soldered to an insulated brass collar, I, part of the cifcnmls- rence of which has been remored, as shown on a larger scale in the side figure. A thick copper wire I, presses against i, and is conneclcd by a brasa pilur, r, with A metallic strap, L, fixed on one side of the wooden block, ■, whilst a similar piece of metal, n, with which l may be conueclsd by a bent wiie^tf , is on the opposite side, and supports the spring m. When v, o, and consequently their iron axes, are opposite lo the poles of the magnet, the latter, by indoction, couTerts the included iron into ■ temporary magnet ; at the instant this action occurs, a cnmnt of electricity is induced in the coil. If the armature be turned half roand, the ma^etism of the iron piece becomes reversed, and a second current in an oppotUt direction is excited ; and as at the moment this takes place, the wire a comes in contact with the intermpted portion of the collar i, a brif^ht spark passes between them. On rotating the armature with rapidity, a succession of ri lid sparks ensues ; and if wires attached to the braai pieces, i., u, be immersed in acidulated water, de- oemporitiDn of that fluid will occur, (he oxygen and hydrogen gases being evolved alternately from each wire; for of the sue- MAaNBTO-BLECTSIO lCA0HIlfB8. 509 oeasiye induced cvrrents, each is alwa3r8 oppodte in direction to the preceding, the alternate ones only moving in the same direction. 906. If a copper cylinder be grasped in each hand, whilst wires connected with them commtmicate, one with the piece l, and the other with a cavity excavated in the end of the revolving arma- tare, on turning the wheel b, a rapid succession of currents is sent through the body of the person grasping the cylinders, pro- ducing a series of severe and almost intolerable shocks; the muscles becoming so spasmodically contracted, that he is generally unable to drop vie conductors. If tne wires, instead of terminating in copper cylinders, be furnished with platinum points, electrolytic decomposition of any conducting fluia in which they are immersed will ensue, as in the case of the induced current of the previously described apparatus. 907. If an armature, having a ahart helix of thick msulated copper wire, be substituted for the armature a b, in the machine just described, the intensity of the evolved electric currents will be diminished and no shock will result from them. The vividity of the spark at i will be, however, increased, and pieces of platinum wire may be readily ignited by allowing the electricity to pass through them ; also a feeble chemical action may be detected. The ordinary phenomena of electro-magnetic rotation may be pro- duced b^ passmg these currents from the short helix through the appropriate apparatus (866, &c.) ; this helix is commonly called the quantity armature^ because the quantity of electricity put in circuit is proportional to the sectional area of the wire which constitutes the helix. Some important practical applications of the magneto-electric current have been made : one ofthese is to the purpose of electro- plating by Mr. Woolrich,* in whose machine four powerful com- pound norse-shoe magnets are placed edgewise in the form of a cross, their similar poles being in two horizontal planes, between which a wheel, carrying at its circumference four armatures, rotates on a vertical axis. By an appropriate arrangement of commutators for transmitting currents in one direction only (which it is not necessary to detail), at the moment that each armature passes the poles of either magnet, the induced current is directed to the decomposing cell. B^ some of these machines as much as two and a-half ounces of silver have been deposited per hour upon articles properl;^ prepared for electro-plating. Another useful apnbcation is to the development of a sufficient amount of current lorce to produce the electric light (808) for illuminating lighthouses. This mode of illumination has been employed at the South Foreland lighthouse, and may probably prove one of not the least important contributions of science to the wel&re of mankind. 908. A very energetic kind of apparatus for ^nerating magneto- currents has been constructed by Messrs. Siemens and ^dske. * Mechanics' Mag., toI. zzxriii. p. 146. :r of honc-ahoe mugnelE, o, <3, Fig. 613, or af bar-macitcla ted at their further eii(bi with an Iron pUte, and hiiTing imilar polaa a^acent, are fixed parallel l« each other, but not in coniAcl, on a ilaud. Tho Hrmutiire e is rotated by a palley and band f, which paaess over a larger pulley l, driven by a winch H, to gain velocity. The coil passes leiiKlbnise over Ivo opposite sides uf the armature e, huiI is encloBed in a caae kept together by two rinfta shown in the figure One end of the coil IB connected with tlie axis f, of the armature, which pauea through the metallic suppnrt, v ; and in thia is a binding-screw, w, for ono electrode ; the other end is cnnnected with a collar, b, insulated friim the aita, r, and a projectinn from this comes in cimtact with one of the springa, s (of which the upper one onlj ia Hoen in the figure), nt the oionient v/hea each induced current ia released ; the other electrode is attached to the support of tbeM springs. It ia evident from the description that the saccesdve currents will be eignal in intensity, and opposite in direclion, since tliu induced uuirenti are in cnntrarj directions on the upper and vniirr udes of the coil, from which tho current proceedi altemalely. 909. As in tticte cases the electricity evolved bears a ratio lo the magnetism induced in the iron nucleus of the annatuiea. it Ibllows, that by increasing the intensity of this mngnetiaro, the electric cuirent becomes proportion ably increased in energy and quantity ; and, as by means of a current of electricity of low potential powerful mi^tnetiam may be excited in an iron bar, the application of this as the iaducing agent, lias been used !d ibe construction of these machines: indeed, it was by a contrivuice of this kind, Ibnt Faraday firat discovered these currents. The moat powerful electro-macnetic machines are conslructed on this principle; the following is a description of one of them. Two ban or verj eoft iron, ■, 8, Pig. 513, ftboul fourteen incboa Ion «nd an inch in diameter, are connected bj a croaa piece of iroi Ajfirml; wrerfedlo (hem. These _ ,,„ bare are covered with a coil of insutattd thick copper vire, abonC 300 feet in leogtb, the «nda of which are coanecled with the •crews, D,E. Oier this are wound aboot 1600 feet of verj thin in- ndaleil and vamtthed copper wire, its enda being connected with the screws, u, u. Un connecting n, e with a bat- tery of about ten elements, tbe iron bars become snlEcieatlj map-- D lift aboQt silt; ponnd ; and, if the copper cj'lin [i tbe moistened bands, an almost insupportable shock i ensue, on breaking connexion with the battci7. To oSect this rupture of contact with fncilitj, a contrivance umilar to that used bj Mr. M'Oaalcj* will be found veij Dseliil : this consists of a beam of brasa sup^rted by a horizontal axis at k, having at one end a ball of soil iron, l, suspended, and at tbe other a forlt of thick copper wire, so arransed that by its own weight it will fall into two cupa of mercuiy Sied at k, and thus connect them with each other. One of these cops is connected by a wire witb a screw d, whilst tbe other is by a wire z, connected with one electrode of tbe batterr, the screw e being in communication with the other electrode. As soon aa these connexions ai« completed, tbe bar s, becoming mague^c, attracts tbe ball i, which by de- scending raises the fork h from the cups, thus breaking conlact with the battery, and prodnci[ig a vivid spark attended n4tb a loud snap, and combustion of the meri:ury. Tbe ban losing their magnetism, the fork p falls by its own weight, and re-establishes connexion witb tbe battery ; l is again attracted, and so ou, the beam rapidly vibrating amid a complete shower of sparks from tbe mercury, producing a most brilliant spectacle in a dark room. 910, As a rapid succeasion of powerful alternating currenta tir- culfttes through the long coil at each rupture of contact, the shock felt at the screws, o, H, or at the cylinders connected with them, becomes intensely painful, com pie lely paralysing (he arms of (be person grsaping the conductors. With these currents evolved at o, H, the chemical decompoaitions already described (S2I), mny be performed and other effects produced, as with a voltaic bAttery. If a piece of charcoal be placed ou a, and a platinum wire connected with H be drawn ligbtly over it, whilst tbe machine is in action, a aeries of minute aparka from tbe induced currents will be observed. 512 ELEOTRO-DTKAMIOS. 911. WUde?8 Magneto-eUctrie Machine. — A machine of enor- mouB and unprecedented power, arising from a happy comUnatioQ of known facts and principles, has been constnictea dy Mr. Wilde for the purposes of illumination. In 1838 MM. Moigno and Baillard* showed that bj using an induced current from a mag- net, capable of sustaining only a few grammes, to excite an electro- magnet, the latter could be made to support 600 kilogrammes ; but it remained for Mr. Wilde to apply an induced current from this electro-magnet either to purposes of illumination, or to the excitation of a second electro-ma^et, weighing three tons, the current induced by which, in a coil weighing 232 pounds, melted 7 feet of No. 16 iron wire, and made 21 feet of the same wire red-hot: and produced a Kght that, at a distance of a quarter of a mile, cast a shadow of the gcu-flamei on the adjacent houses-f It should also be mentioned that a steam-engine of seven-horse power is requisite for the development of the full power of this vast machine. The construction adopted in this machine is precisely that of Siemens and Halske's inductor (908), except that the arma- tures are partially enveloped by masses of soft iron bolted to the poles of tne magnets whether electro- or permanent, and by the suitable arrangement of a commutator attached to each rotating spindle, the transmitted currents are all in the Bctme direction. And further, the magnets are placed vertically, with their poles and armatures downwards, instead of horizontally, as in Fig. 512, and the set of permanent magnets, sixteen in number, is placed on the top of the electro-magnet. The facts just described present a conspicuous example of the interehangeability of physical forces : first, heat becomes dyna- mical force in toe steam-engine ; secondly, this force becomes electricity in the magneto-inductor ; and thirdly, this latter force becomes neat and light in ite impeded passage through the di- electric air. 912. As electric currents are induced by other currents passing near the conductora in which they are excited, the theory of Ampere (883), receives considerable support from the facts enu- merated in this chapter. Granting with him that a magnet is full of perpetually moving currents of electricity, it induces mag- netism in a bar of iron, by exciting similar currents, as in the case already mentioned (883), and then the remarkable fact of magnets exciting electric currente in wires moved near them, wilfbe resolved into a similar case of currents exciting currents ; we are thus enabled to generalise the phenomena of magne- tism and electro-dynamics, in a very important and satis&ctory manner. 913. The phenomena of induced rotation produced by rotating * Hoigno, Tdl^grmphie Eleotriqne. p. 15. t Quarterly Joam. of Science, October, 18d0. M AOKETO-INDUCTIYB CAPACITIES OF METALS. 513 a plate of metal ander a suspended magnet, may be referred to a similar explanation ; the currents in the magnet exciting Fig. 61^ similar currents in the revolving plate, which hy their reaction on the magnet, cause it to re- volve. Fig. 614 exhibits a suitable apparatus for exhibiting these, and the converse experiments in which the rotation of a suspended disc is induced hy the rotation of a mag- net placed beneath it. In order to make it evident that the effect is not in any degree due to mere disturbance of the atmosphere, it is de- sirable to place a glass diaphragm between the rotating disc and the magnet. 914. The amount of current force induced by the same magnet in different metals varies considerably, as may be showu by the mutual action of the induced and inducing currents. A convenient apparatus for this purpose was contrived by tbe late Mr. Sturgeon : this consists of a series of circular discs of different metals of the same size and weight, capable of being supported on an axis, so as to rotate between the poles of a horneshoe magnet placed hori* aontally. If small equal weights be attached to the circumference of each disc, they will ordinarily oscillate in equal times, if they receive equal impulses, as by raising the weiffbt in each case to a level with the centre, and then releasing it : out when thus made to oscillate between the poles of the magnet, the times of oscilla- tion will differ consideraoly ; and as the degree in which the oscil- lations are retarded depends on the force of the induced current, the amount of retardation will be a measure of the inductive caracity of the metal. With a very powerful electro-magnet, such as that used at the Boyal Institution by Faraday in his experiments on light, and dia-magnetism, this retardation is so considerable, that the power of the arm is insuflQcient to draw a piece of thick sheet copper rapidly between its poles. The sensation produced by this unseAi resisting force, which increases with the effort made to overcome it, is very peculiar. The same facts may be illustrated by a variety of striking experiments, one of which is the following : — Let a cube of copper, measuring about an inch each way, be sus- pended between the poles of a powerful electro-magnet, and made to rotate rapidly by twisting its suspension ; the moment the magnet is excited, the rotating mass stops dead, but re-commences its rotation as soon as the circuit is interrupted. LL 514 CHAPTER XV. ELECTSO-TELEGRAPHT. The principles of electrodynamics have met with their most extensive development in that most important recent contribution of physical science to the comfort and conveuience of mankind, the electric telegraph : — a practical application of the principles of ahstract science, that ought to be received as a conclusive answer to the cui bono question, with which the trulj philooophic inquirer is not unfrequentlv assailed. As time -signalling, whether for the purpose of merely recording its passaee, as in eUctrie cU>eka, or for the purpose of observing rerj small intervals, such as that occupied by a projectile in tra- versing a space of 50 or 100 yards (which is the chief function of ckronoecopes and chr, are two binding; acrewa, by which 917. Tbe 617 aide b; tide beneath the needlei, and Ihs metallic conneiions nre so armneed, that when either handle ia moved «tdewa;B a bntterv ia brooghc into the cinniit, and bj meana of a commutator attached to the ails on which either liondle ia fixed, (he current is sent in aqch a direction through the coila, a, n, that the needle B a mmj mave in ihe aame direction aa the handle beneath it. The airange- ment of the commutator will lie readiij under- ■tood from the diiigmm Fig. 516. Itoouainta Fy.aio. of a disc of some iuanlaiinK material, a onitsaiis by theeiteraalhanille, H, inti. . . circumference of vtbich are inaerted the jiiecea of braaa, a,b, e,d, t,f, g; of which a, c, am' / are connected, also b and e, d and g. Fun flpringe rest on the circmnferenceof the com matator, of which E goes tn earth, c and z an the terminalB of the local butter the line Blrument in handle vertical. In this position the local balteiy ia out of circuit, aa there ia no metallic connexion between o and x, and tbe circuit from the distant station is cloaed tbrough L^a— c— /— i, so that aignala uaj be received from thence. If the handle, h, tie moved to the rigAi, e comea into contact with z, d with c, and g with k, and a ia alwaya in contact with i. ; the conrae of the current will then be 0— d— y— e — distant indicator— line -f"— »— l— a— e— ». If moved to the Uft. then b cnmos into contact with i, o with c, and E with e ; and the course of the current now ia c—e — a — L— H — m" — line — distant indicator — b— « — 6— », or the reieree way through ihe cortesponding needle coils, and the defleiions of the needles will therefore correspond with those of the handle h. The signals consist of movements of either or both needles, in the same or opposilo directions ; and one, two, or three tDOremeota are found to afford a sufficient variety of higoala, which consist of the letters of the alphabet, the numereia, yea, do, wait, go on, imderstand, not anderstond, and eomo few other conven- tions. It is, however, to bo regretted that the signals representing the alphabet were not originally so arranged by Mr. Cooke, that the letleia of most freqnent occurrence abould invariably be re- presented by the simplest signals, whereby much nnneeeaaaiT manual movement might have been saved, as is done in the drdi- i^aTy arrangement of typea in a compoeiLor^s caae; in which the letters moet in reqaeat require the least movement of the hand to tEach them. This inconvenience was felt in tbe earlier daya of tbe needle-telegraph, and the Morse code of signals (to he de- scribed presently) ia now ver; mnch employed. »18. The EUclrk -llonim.— Unle&s the traasmiision of a aigDol 618 BLBOTBO-TELBQBAPHT. be rendered aodible, as well u Tisible, it would be necessaiy that the dial of the telegraph should be constantly watched by the eye of an attendant, by which the smonnt of personal labour would be greatly augmented. This desirable object is attained by the electiio alarum connected with each instrument, which, when the apparatus is unemployed, always forms a part of the circuit, so that the transmission of any signal is accompanied by the ringing of a bell ; and the practice at any station is to continue to ring the bell at any other station at which a signal is required to be received, until the return of a signal indicates the presence of the attendant, who fortunately has the powerofsilencing his clamorous monitor during the transmission of signals. The electric alarum consists of an ordinary clock train (228) with an anchor escape- ment (258), a small electro-magnet (877), and a bell. A hammer,- or clapper, occupies the place of the forked piece, k, Fig. 171, and strikes the bell at each extremity of its oscillation, consequently the bell keeps ringing as long as the train continues to run. To the contrary side of the train a small horse-shoe electro-maen^t is attached horizontally, and a small flat piece of iron is placea oppo- site, and very near to the poles of the electro-magnet. This iron keeper is connected by an arm with a moveable axis placed verti- cally beneath it, whicn sustains its weight, and consequently en- ables it to oscillate through a small angle by the application of an exceedingly small force. Whenever a current passes through the wire coating of the electro-magnet, the keeper is attracted, and when the current ceases, it is removed to a small distance by a light spring. In this latter position of the keeper, a pin rests against it, which is fixed transversely to the axis of one of the wueels prolonged, as s, Fig. 171 ; but when the electro-magnet attracts the keeper, the pm is released, by which the train is allowed to run, and consequently, the bell to ring. It has likewise been proposed to make use of tne electric alarum as a protection against fire, burglary, and other casualties ; for the first purpose a platinum wire, connected with one electrode of a battery, is inserted in the bulb of a thennometer, and another in- troduced into the stem from the top, and descending to a certain point, is connected with the remainder of the circuit, which in* eludes the coil of the electro-maffnet belonging to the alarum : whenever the heat 6f the surrounding atmosphere is sufficient to raise the column of mercury to this point, the circuit is completed, an^ the bell rings. The second object is attained by connecting wires or stringy, attached to the several outlets of a house, with a lever by the movement of which the circuit will be completed. 919. The letter-showing telegraph is an in^nious device of Prof. Wheatstone. In this the communicator and indicator are distinct instruments. The communicator, Fig. 517, consists of a revolv- ing wheel attached to a fixed support. The circumference of the wheel is divided into an even number of compartments, which LETTEB-SHOWnCO TELEOBAPH. 519 Tig. 517. Tig. 618. consist aUernately of metal, and wood or ivory : the face of the wheel is similarly divided, and a letter inscribed on each compartment; and a row of pins, cor- responding to the compartments, pro- ject from the circumference of the wheel. Two brass springs, each connected with an adjacent binding screw, rest against the wheel, one agamst the axis, or any other part entirely metallic, and the other against the rim, consisting of alternate portions of condacting and non-condnct- mg matter. It is clear that if the binding screws of this instmment be connected with the electrodes of a battery, the circuit will be alternately made and broken, as each letter passes a given fixed point. The indicator, like the alarum, consists of a cloclc train, with an anchor escapement and an electro-magnet, the terminals of the coil of which are attached to two binding screws ; the pro- longed axis of the scape-wheel carries an index that traverses a dial. Fig. 518, the circumference of which is divided into as many compartments as the communicator, and corresponding let- ters are inscribed on each. In this instru- ment the iron keeper is attached to the axis which carries the crutch or anchor, d^ Fig. 171; and the pallets, a 5, cd^ Fig. 197 ; consequently, one tooth of the wheel will escape, and the index will advance one step, at each movement of the keeper : but this movement takes place as the circuit is alternately made and broken by the com- municator; consequently, the movements of the communicator and indicator will exactly cori'espond, and the letter at which the rotation of the former ceases, will be shown on the latter. A somewhat greater degree of certainty in the indication of a signal may be obtained bv substituting for the index in Fig. 518, a disc, with letters inscribed round the circumference, which is placed behind the dial, through an aperture in which the required letter is shown. It should here be noticed that the construction of a small electro-magnet, which could be effectively excited by a current of moderate potential from a distant station, is entirely due to Prof. Wheatstone ; although it was first brought into extensive use in. the Morse-telegraph. 920. The most powerful arrangement, and that best adapted for the transmission of signals to great distances, on account of the high potential of ma^eto-currents, is the magneto-electrio telegraph, which is likewise due to the fertile genius of Prof. Bmt^tmmm'mm^i^^'^^^^^^^^^r^^^y^f'^^'^^ 520 ELBCIBO-TKLEORAPHT. Wheatstone. In the earlier instramenta of this kind, the elec- tromotor waa an armature similar to that of the magneto-electric machine (905), in which a current is set free hy the rapid move- ment of the armature either towards or from its position of maxi- mum induction. The magneto-electric telegraph possesses the advantage of perpetuity of action, without any renewal of a bat- tery, which is necessary in all other kinds ; this must be looked npon as a decided advantage. Some of the earliest forms of electric telegraph were on this principle; as that of MM. Gauss and Weber, of which an account was first published in 1835; and that of Steinheil, which was in operation in 1837. Henley's instrument, which has been frequently employed, is constructed on this principle. A powerful compound magnet is em- ployed, consisting of a number of fiat bar-magnets firmly bolted together. An armature, enveloped by two large coils of filne wire, is placed opposite each end of the compound mi4piet: these actuate two needles, placed side by side, as in the ordinary needle- telegraph. 921. An efiective instrument of this kind was many years since constructed by Prof. Wheatstone. The communicator is a rotatine disc with projecting spokes, similar to Fig. 617, but placed hon- zontalhr ; the indicator is a dial, as in Fig. 518. The armature, instead of rotating, is suddenly withdrawn a small distance from the permanent magnet, by means of a lever acted on by a series of cams placed round the circumference of a wheel, or cam-plate (255), and shaped something like the blunted teeth of a saw; by means of these the armature is suddenly withdrawn, in onler to nve full effect to the induced current in the armature, and gra- attaUy approximated, to diminish the induction of a current in the contrary direction. The current thus induced is one of very high potential, and therefore well calculated to overcome the resistance of a long cirouit : one of these instruments appeared almost to reouire the intervention of 600 or 800 miles of telegraph-wire, in order to work satisfactorily ; in fact the distance, through which signals might be convej^ed, exceeded the existing means of testing the capabilities of the instrument. The construction of the indi- cator is the same as in the preceding (919), except that the signals were only ten in number, the numerals and a cipher. The Ad- miralty code of numerical signals was intended to be employed in this instrument. 922. Siemens* Magneto-Teleffraph.— The difficnltjr of starting and stopping the heavy armature aboye described, with sufficient facility and rapidity for signalling, rendered the preceding instru- ments inconvenient in practice : this inconvenience is partially remedied in Siemens* communicator Fig. 519. In this, as in the inductor Fig. 512, an armature, e, coiled longitudinally, rotates between tne poles of a series of parallel horae-shoe mag- nets, o. Thecnaeortbi to the ImUer n[ which one terminal of the coil is altached. The coit is driTea by a wheel, L, gearinff into Tm); and the wheel ia atlacbed to the a'lle bj a cr^la-joinC, in onler that the rotation OUT be stopped at the Tight point, b; de- pressiog the handle into a notch in the •emted rim i beneath it. One notch cor- KBponds with each hall-tuni of the anna- ture, and coTi«equent- Ij, with each induced carrent released; and, as before described currents are in opposite directions. •erted into the cap* f, r". th« The indicator la n hand moTing round a dial which is fixed on scape-wheel, driven by a propelment (SOS), which ia _c .L.. .1 ,_ m .-n i^p scape- precisely the reverse of that shown in Fig. wheel. A, is driren by the OBcillnting apnng- palletA D, E, the moirameQtB of which are limited by aiMusting-acrews, to prevent "tripping" of the wheel, as are also the oscillaliona of the ■ofl-iron bar, a, by the aiJjnsting-BcrewB, r, a. The hiwer end ofs is indnctively magnetised by the coil c, and according to its polarity, is at- tncied by one and repelled by the other of the poles a, B, of two hone-shoe magnets placed on rither side of it ; and the site mate currents be- iiiK opposite, the bar a and its attached pallets wul oscillate and drive the scape wheel and its index in accordance with (he movements of the winch, n, Fi^. (519). In thie apparatua tha coil rotates with the least possible vis viva it has been frequently employed in practical teh>gTaphy. 923. irAeii(ftoiw'iifam«to-2WeffrapA.— In the practical apj plication of the eleotrio telegraph, rapidity of action is a point of Rg. Ml. "Ttl 52a great imponADce ; Rod the ftbuace of thii qoililj, in conaaqnaBca of the Til viviL of the rotating mui, for aame tinte conatitDled tlie cbi«f objection to nuigneUvtelegnipha. Thii objoction haa Wea entirelj obviated in aa eitremel; elegant and portable inatra- ment, Fiir. 521, coutnded hj Mr. WheatMone, in wiurk A ii the commnnicatoT, ud a the indicator. The eiccItcDce of thin iaitrament depeoda on two points of conalnictiiia — Gnl, the monng parti of the , indicator am rediiced to ibe I emaUeat pwsible dinmaMaa, I bolh as to bnlk and raogc o( ^ molion, and conaeqiwnlly tbe leant amonni of ^ re- quired from tbecnrreDt; asd aeeondlj, the loft iron keeper eiont rotaU* in the cannDnnicstar, and rotalea coD^Diiouelj; the induced cnrreota being intemaUr intercepted, when the^ are not wanted (□ be lent into the circtdt, — J .1- — I .-. 1... :„ overcoming and restariug the m. . . .._.7.^ ^j jjj^ ke«p«» ii ' the figure, And I in^l; iogeniouB contriTance the indnc^d cnireBta ai alternatelj in opposite direction!. 924. The inducing hon&ahoe n^net h. Fig. 52!, doe* nat cx- j. ,,_ ceed four iocbea ia bagdi. ^'" In front of the polea are fixed IfoureqaidiitaDtfoftiroDMna, tvo to each pole, lamMmdoi by coili of a cODtiuDOii* win wound in the lame direction □□ A and a, and in tbe roa- trarj direction on c awl a. It haa been ahovn (BBC) tk«l the currenta indoced in ap- proaching and receding Itobi coDlaot are in Miponte direction!; and in order lotnce tbe direclioaa of the inducted carranti in thia apparatag, let the keeper ba oppawte to B Hod D, and let the receding carrentofsbe •*-, theoMDcac n a similar pole, bnt its coil wonnd oppoiiieli/ to a, tbe appioacbing. current of O will al» be +, and will conaoqaentl; teinforee tbe former. The receding-onrrent of o will hence be ~, and aa c aad D are contrary polei, but their coila are wound tkt «^b« tmu, the approaching-current of i> will alio be - , and Ibeae again will co-operate. Similarly the d-a currenla will be both 4-. aad the A-B, both — ; and as the keeper is a little wider than the m- SZ3 t«ml b«twMn two aitJBceiit cores, the nmilnr curranU arc in eftch case oomplelelj' blended into one. Thus it np^an that n current in one directioD ii diicharged wheDeTsr the keeper is Tertical. and one in the opporits direction, vheaeTer It is horizontal. The vinble part ofthecommunicator consiataofadial a, Fig. 521, round which are placed the letters of the alphabet and aome sigiio, with an index pointing to them ; then are sairounded bv an equal number of studs at the ends of radial levers. When no stop is down, the index ia in gear with the mtating ails, and advances one step for eitch induced current; but when the index arrives at a stop put down, it stops, being pat out of gear with the rotating plate, and while the stop remains down, all currents are intercepted hj an internal short circuit. When onv lerer is depresBed, it re- mains down, until another is depressed which raises the former to its QonnBt position bv a rer; simple and ingenious mechanism. This consists of an endless chun, Ijing in a circular groove under the ends of the levers, with just enough of " slock" to allow one lever only to be depressed. As soon a.s the depresse d ke; ia raised, the index again travels, and corresponding Gorreals ars Bent into circuit. 926. The indicator isa dial, B, Fig. 523, sarronnded bj the same letters and signs, as that of the communicator, the index of which is actuated bjr the propelment (259), the wheel not being larj^r than tbe Bcnpe-wheelofasmall Geneva watch. The reciprocating piece. B, Fig. 198, is governed bj the alternating movemEUts of a small frame, a. Fig, 523, contwning -. ^^ two curved magnets, not larger than _ "' knitting-needles, placed sjmmetricall; I in rcvemed poeitioue. As the centre I of eravitj of this frame is mode to CO- ■ inctde with the axis of motion, its I movementi are not in an; position im- 1 peded bf gravity. Tbe pennaneat I magnets are placed between a pair of I smul cylindrical electro-magnets, b, I which are likewise placed in a pHmllei ' but ravened positioD. The magnetism of these is inverted by each succeeding corrent, consequentlj holh attractions and re- pulsions are bronght into pla; to produce the movement of the oscillating magnets, and there is no DeceBsit; for an; spring or other mechanicBl resistance to be overcome bjthe very minute electromotiTe force employed ; which is rendered efficient only by the extreme delicacy of the mechanism. The armature is oon- 524 ELECTBO-TELEORAPBT. municator in its previous position of rest. Conseqnentlj it is necessarr to ascertain the correspondence of the indicator and commnnicator, before the signalling commences. This, in fiust, is eBsential in every kind of dial-telegraph. This oompendions instrument has been extensively employed by the Universal Private TeleCTaph Com[>an^, for private use in the metropolis, and in several large provincial towns and cities.* Printing Telegraphs. — Various kinds of mechanism have been from time to time devised for the purpose of rendering the electric telegraph automatic; that is, that either letters, or some kind of conventional signs, should be impressed upon paper by the agency of the mechanism itself. Some of the earliest successful essavs in electro-telegraphy were in this direction. Steinheirs tele- graph, already mentioned, comprised some special mechanism for this purpose : and that of Prof. Morse merits notice on account of being still extensively in use in America and on the continent of Europe. Although the idea was conceived some years earlier, the actual construction cannot, it appears,t claim an earlier date than 1837. 926. The Morse Telegraph. — ^The transmitting instrument, or ^ Morse key " as it is commonly called, is a lever a b. Fig. 524, moving on an axis c, on the under ^•^**' side of which is fixed a stud, d, jost above another fixed stud b, from which the lever is raised by a spring, o, to a distance regelated by a screw at b. b is connected with one electrode of a battery, and F with the earth ; the other elec- trode being connected by ihe line- wire with the electro-magnet of the relay at the receiving station. l*hus it is evident that whenever the handle, a, of the key is de- pressed, the paper will be marked. A momentarr depression will produce a " dot,'* and one more prolon^d reqaal to the time of making two dots) a " dash," and the various letters and nume- rals are indicated by different arrangements of dots and dashes. The series of marks that constitute a letter, number, or conven- tional sign, are separated bv small spaces, consecutive letters by larger, and separate words by still longer intervals. 927. In the receiving instrument. Fig. 626, a b, is a train of wheels, wound up by the liandle o. Between the roller p, con- nected with the train, and another, q, in contact with it, a strip of paper v m is continually drawn when the machine is in action, * The writer has made oae of it Jbr Mversl ^een between his reeidenee in FiUroy Square and the Westminster Hospital, with great oonvenience and advantage. He has fonnd it perfectly easy to ose, and not Uable to derangement. t M. Hoigno, Traitfc de TOtgraphie Eleotriqae, p. 76. B2& oDad from s ctnl, n. A lerer i l mareabls «d a fnl- iBBt theendEapaintedBcrev, that isailjuBtediupreH OD the surface per, lehea the nf.BOi. I. is attracted t-o-magnot, t. of the leier i« a third arm contact vitb marked bv v. magnet d, and teminates between two a^usting screws, B, F, passing through ihe aims of the standard a, and of which e is insulated from a The binding screws a, %, connected with the aCandards, o,c, receive the terminals of the local cireuit, and the electro-magnet, those of the line circuit. Whenever the electro-magnet is excited, the armature d is attracted, and the end of the iever coming in contact with the point of r, completes the local circnit. It is evident that in this inatniment the line.current has no further work to do, than to eicite the electro-magnet to attract the armature, and thus to close the local circuit. 931. Sitmtm' l^larUed Belay. — This appsratos ncaHssea a magnetic arrangement of great merit, which has been largely em- ployed in diroct-acdng receiving instruments : and ajtbongfa specially designed to work with nearly equal reverse cnrrenls, it can be adjusttd so as to work with -(- or — currents alone of any strength, as well as with reverse currents of any required relative Btrenj-th. Fig. 527 represents a plan, and Fig. 628 a vertical sec- tion of this iaotrument. The electro-magnet, b, b, is composed of two cores of solt iron, united in the ordinary manner by the cmaa- bar A. The coils of this electro.magnet terminate in the binding *r. 627 •erem, I aod 2. Tbe bent pennanent maj^et, h, i, is scnwed upon the cnMB'b&r, and eommoiiictilea north-polarilj to it, and to the two coral and poUs of the electro-mapiet, B, An iron "»■ '^■ tongue, 0, is attached tn the toath pole, a, of the magnet voder the bracket a, and this receives ■onth-polarit}'. This tongae ia so placed that it ia free to move eaailj between the north potea, x and m', of tbe electro-magnet. Its extent of motion U regul&ted b; the Ecrews, D Bnd d'. The point of the Bcraw, D, is u>ed as the contact for cloaing the local cir- cuit, including the printinf; in- Mnunent, and local battery. The acrew, d', lisi an a^ale point, and, ^ aguDst it, the local circuit ia broki^ii. p ai ■creva of the local circuit. Hence it follow! that tbe aoutb-potariied ■ tongue, c, cannot be attracted to P either of ihe north.polarixed endn I of the electro-magnet, s, a', whilst I it is ilationed equidistant from I both. When this is not the case, ■ however, it will always be at- 1 tracted to the nearer pole. 'When the relay is naet circuit working with rever rents, it is so adjusteil that the timgue lies upon that side to which it waa last impelled. On lines, however, where currents in onl/ one direction are used, the tongue, a, must rest against the point, l/, which is insulated, when there is nn current in the circuit, i.e., while in a state of repose ; it should therefore be more powerfullj attracted by the pole, k'. This pole, tberefore, performs the fonctiona of the ^ring in ihe ordinary relay ; and, where in the onlinsTy relay, the spring is tightened for strong cuirenU, in this inslrument the ttmgne, c, is simply thrown out of the point of equilibrium between the poles, K and a', and made to rest on the side «', These changes are eSecled by means of tbe adjusting screw, k. 932. Bain's electro-chemical telcgnipli dt>es not diOer essen- tially in its constmctioQ from Moneys ; but, Instead of the style, which is of steel, being imprassed on llie paper, the latter ia moistened with a solutiou of cyanide of potassium, and passing over a metallic cylinder forms part of tbe conducting circuit ; and 528 ELECTKO-TELEQAAPHY. wherever a current passes^ the salt is decomposed and the paper Btained by ferro-cyanate of iron, or Prussian blue. 933. Two modifications of printing telegraphs due to the in- genuity of Prof. \\'heatbtone demand some special notice. One of these ranks amongst the earjiest important improvements in electro-telegraphy, although ita -complexity and consequent oosUi- ness may perhaps have interfered with i t s practical application. In this apparatus the communicator is the same as that of the letter-Miowing tele^ph (919) ; and the indicator is also similar, but with the addition of tne urinting apparatus. In place of the disc of letters there describea, is a revolving circular plate of thin sheet brass, which is cut radially into separate strips, and a raised metal type attached to each ; the types are chaii^ed with printing ink, by a roller attached to the machine. A shp of paper passes slowly but continuously over the surface of another roller, very near to the surface of which the required letter stops, and is then gently pressed or struck againbt the paper, by an appropriate action of the machine itself. In order to prevent damage, it is ingenioufily contrived that the printing action can take place only when the circle of types is quiescent. By these means any oom- niunication may be printed in very little more time than is other- wise required for its transmission. 934. The Automatic Priminq Telegraph. — ^Another form of printing telegraph has been devised by Prof. Wheatstone, which appears to possess manv important advantages over its prede- cessors : it might be not uaptly termed the " Jacquard tele^^ph'* from its analogy with the loom of that name described m 1^. The analogy consists in the message being previously prepared by punching small holes in a narrow strip of paper; this is effected by a small machine consisting of three nunches placed in a row, the middle one being smaller than the otner two : these are acta* ated by three levers having raised studs for the fingers to rest on. Q'he machine is provided with a ratchet and click (265^, by which the paper is carried forward a small space after eacn action of either of the levers : this in machinerv is termed ^feeder. The alphabet is represented by various combinations of the holes in the outer rows ; the middle row merelv serving the purpose of carrying forward the prepared paper in tne communicator, f^g. bt6 re- presents the appearance of the paper. fW. A29. For the purpose of transmitting the message, the end of this paper is placed in the communicator, and a similar plain strip is placed in the indicator ; both of these have a feeding action eqnal AUTOMATIC PBDITDrO TELBORAPH. 529 in amount to tbat of the punching machTne. On torninff a winch in the communicator, three metallic pina rise against the paper, one of which will neceaaarily enter a nole, and will close the cir- cnit by coming in contact with a plate of metal placed oyer the paper. When the contact takes place through a hole on either flioe, an electro-ma^et in the indicator becomes actiye, and a dot of ink is debited m a corresponding position on the strip of paper. If the circmt be completed tnrongh a central hole, the autograph in the indicator is merely carried forward one step, without being marked ; thus a space is secured between contiguous letters, and bj a larger number of central holes, a longer space between words : and a printed fac-simile of the outer rows of perforations is ob- tained. By a more recent arrangement, the indicator prints the "dots" and "dashes*' of the Morse code (928), now so generally employed and understood by tele^aph clerks. This apparatus is not impeded in its action by a motion sufficiently rapid to transmit 500 letters per minute. As the inconyenient delays, experienced by the public in the use of the electric telegraph, frequently arise from the length of time necessarily oocupiea in the transmission of signals on the systems now in general use, it is eyident that much important time might hereby be sayed, as any required number of hands might be employed in the preparation of messages. Also meoaces might at little trouble ana expense be prepared by priyate indiyiduals, in which any arbitrary signs might be employed. Another adyantage would be that long and important despatches might be simultaneously transmitted to different places, as the prepared paper might pass through seyeral communicators in suc^ cession, all moying at the same rate. It may be remarked that if the dots above and below the central line be supposed to cor- respond with the moyements of the needle right or left, the ordi- nary alphabet of the single-needle teleffranh may be employed. A double row of dots on each side might be effected by a little addition to the mechanism, and by employing five punches, which would pennit the employment of the code of the double-needle telegraph, which is in yery general use. 935. The copying telegraph, invented by Mr. F. C. Bakewell, is analogous in its operation to the electro-chemical telegraph already described (932). The communicator consists of a metallic cylinder, which is kept uniformly and slowly rotating b^ clockwork, rouna which is placed the message written on tin-foil with sealing-wax vamish. A metallic point rests with light pressure against the sorface of the tin-foil, and is moved gradually forwards by means of a screw placed parallel to the cylinder, and rotating with it, by the rolling contact of toothed wheels ; so that when the cylinder has made one revolution, the point has advanced the distance of one thread of the screw, and uerefore passes in suocessive parallel lines over the jpieoe of tin-foil. The cyunder and the resting point are in connexion with the opposite ends of the battery circuit, and M If fiSO HUtOTBO-TILMBArHT. it 19 eTident tbfti a cnrrsiit will pasa aioopt wtisn the point loti on onj part oftbe vamiab-letters. The udicator in thii appantiu is preciwlj nmilar to the com- muiiicAtor; but in place of the tin-fail ia a piece ot paper nxa*- tened with a solutioa of F^rroc/anate of potasR, and dilute h^n>- cblorio acid, the point or at^le retting on vbich ii oTateel. When- erer a cnrrent masea through the paper, it will be coloared by the fonnatioD of Pnuaian blue ; and conaeqneatl]', the uncoloured partioaa of the paper wiU exactly correapond with the writing on the tin-foil, aa in '*••*'■ Kg. 680, which i» ■ ifac-aimile of a written commanicatJon be- tween London and Bngbton. It ia eri- dentJj neceasarr that the rotatioua d the two c/lindera ahonld be Bynchranon* ; this is accompliahed by an electro-msgnelio regulator, the action of which depends on the force of a aeparala ourrant, which ia ai^usted by the amount of lurface of the nen- 036. In concluding o ctical branch of elecl i« of the difSoultieg that occur in yery long, and especially in auumarine, circuitg. Oftbeiie the mogt important ia the retention of the current in the condactor by induction through ita inanlating envelope on the aarreunding medinm. The conductor in fact be- comee aaaimilalad to an extremely elongated Leyden jar, in which the charge ia for a time retained by mutual induclion in tbe ooat- inga, and exhausted only by degrees. Thug, in the chemical pnnling telegraph (820), tbe depoait of Pmaaian blue would ter- minate abniptly on breaking oontact in any moderate aerial ^r- ciiit; but with a lubmarine circuit the cbeuiicat action aubudei gradually, and ceaxes only after a considerable interval, thui ren- dering each signal liable to become blended with the aucceedinr one. Reversal of the current, the employment of a current of high potential nbtained from an induction coil (SST), and varions other expedients, have been reaorted to. In illustration oftbe influence uf induction in retarding the trannnisvion of currents, a series of eiperitnents was made on the subteiraneous wires insulated with giitta percba, and enclosed in metallic tubea, Itid between London anil Manchester. When the ends of tbeae were alternately oon- nected. they presented a continuous circnit of more than 1500 miles in length. A period ot two aeoondj was required for an electric current, entering one end of the circuit, to reach a galva BUBMABIini CABLB8. 531 nometer placed at the other end ; and the electric wave appeared to flow on throngh the wire, after the contact was broken. It waa found practicablci by properly-timed contacts, to deflect the needle at the proximal end of the circuit by a second galvanic impulse, at the same instant that the needle at the distal end was deflected by the first current-wave. These effects are the result of lateral indueUonf and are necessary consequences of the relations of con- duction, insulation, and induction as laid down b^ Faraday. Another important difficulty is, that in consequence ot the loss of current-force by imperfect insulation, in long circuits the amount of force transmitted is not sufficient to actuate the mechanism of the indicator ; this has been obviated by the use of relays (930, 1). 937. Submarine telegraphy dates only from 1851 ; nearly 2500 miles were laid up to the end of the year 1857, and more than 15,000 before the end of 1863 : but the crowning triumph of iup ^nuity, skill, and perseverance was reserved for the year 1866, m which not only a new cable has been successfully laid across the Atlantic, but the lost cable of the preceding year has been recovered and completed. And so perfect is both their conduction and insulation, that when the ends of the ti*o were recently con- nected on the shores of Newfoundland, a single element of very small dimensions sufficed to send a signal from the shores ^ Ireland across the Atlantic and back again. It would be impossible here to enter into a detail of the various constructions of cables that have been successfully or unsuccessfully employed ; but as the last Atlantic cable may be looked upon as a model, it may not be uninteresting to give a detailed account of its construction : — The eonduetorf a strand of seven copper wires of No. 18 gauge ("048 inch in diameter), six being laid round one, imbedded in Chatterton*s compound (a mixture of shell-lac, and Stocldiolm tar, or some other similar material^. The inmiatorf four layers ot gutta percha, alternating with four thin layers of Chatterton's compound. The proteeiOTf ten wires of No. 13 gauge ('095 inch in dia- meter), drawn from Webster and UorsfalT's homogeneous iron, and galvanised. Five strands of white Manilla yam are laid round each wire, and hempen yarn round the gutta-percha cere, both being saturated witn a preservative mixture. The ten covered wires are then laid spirally round the covered core. The weight of the cable in air is 31 cwt per nautical mile, and 14} cwt in water, its sp. gr. is therefore r83. Its breaking strain is 8 tons 2 cwt. ; that of the cables of 1858 and 1865 having been respectively 3 tons 5 cwt., and 7 tons 15 cwt. 938. Siemens andJBalske's Cable. — One other form of telegraph cable, conspicuous for its lightness and tenacity, may here require notice. The conductor or core^ a, Fie. 531, consists of a strand of copper wires, thinly coated with Cnatterton's compound : the M m2 ■LKTBO-TILBOBIPHT. insulator ooariits of thin Utctb o( Monlcbooe, b, laid kaghadrndy «od thBir edges nnited by heavy premiue, the sMUns of ■OLti*mi Uf era being at right angles to etch other j these m by layer* i» gnlta percba and Chattvrton i oompoinid, e. The protector coneiBta of two layera of hempen itringa aatnnted will tar, if and e, laid ipirally in gppoidte ditMtiooa ; and over Af a ■pirallaTer,/, of stripe o( phoaplmietted copper, OTerlaptnug each other half war, but redaced tea level siiriiK«bf cotuideraUe pna- (are. TheactualdiRmetarof theseTeral parts is aliown in the fenre. 939. Sooper's Oore. — The iasnlating properties of caont^oDC being nolonouBly neatly superior to those of gnttapercha, a node of insulation has been devised by Mr. Hooper, which ia beKand, and has bitberto proved lo be, free from the liabiii^ to MAMtisK and consequent loss of insulation, Id which the inaalatCT ia ex- posed, when vulcanised caoutchouc' is in ooDtact with tlie cener conductor. This plan ooniists in surroDnding ths condnctar with a coating of pure caoatchonc, which is sepxrated from another of the mlcanisabls compound, by a thin layer ofauotber compooBd, which is impennesble by ihe mlphnr of the ouler layer. "Toe cote is then exposed for some houn to a lempeiatare of SBO* F. by which the outer layer is Tulcanised, and the whole modersd oooipact and inseparable. The dumbility of this core has been confiimed by Sr C. Bright, who foonJ that a length tested at T!>' F. in Hay, 1863, bad a n- NsUnceofeoOB. A. units per knot, and that the sum coil, vhsn again tested at the same temperatnre in December, 1S6& had acquired a resistance of over 800 anils. The resistaaoe of Hr. Hooper's core at a temperature of S12°F. has been faond to he doable that of the Ferwan Oulf core (insulated with gnttaperdia) ■t 100° F.; and the former sustained no ii^ory by uiat elentioa of temperalura. Under a preasare of two tons per square inch (equal t« that of a column of water two miles deep), the resistance ot^thia iMolalor was increased one-third in about 31 hours, and two-tUrdi is «ii days : and it appears from the eiperienoe of tbe Atlantic cable, tbAt other insaiators are similarly unproied by sabmuinaL It has been staled by Prof Wheatslone that a roatiag trode of a battery c z, the other electrode of which is pat to earth, B, or with one terminal of the coil of a nJTanometer o, tlie other terminal of which is put to earth, tf. The condenser bdsg mow charged by the potential of the battery, by making ooDtact at b, is immediately afterwards allowed to discharge itself throi^h the galvanometer, by making contact at k, and the deflection of the needle is obsenred. The cable a b. Fig. 534, is now joined to the key, p h, the (iirther end of which, k, makes contact with a resistance b, and also vi^ the galyanometer, q ; the further ends of both b and o beinf pot to earth, tf. The cable is now chaiged by the potentiid of the batteij (supposed to remain constant from the last ea^rimentX and discharged through the double circuit o and b ; and b ia ad- justed by trial, so that the deflection of the needle may be the same as m the former experiment. Let ^, r, be the resialancee of G and B respectively, then it is evident that the current now tra- versing o will be of the whole current, and henoe capacity of cable a*^ capadty of condenser. The object of determining the inductive capacity of a oaUe b its influence on the rapidity of signalling; it naviog been deter- mined both bjjT theory and experiment that the number of signals callable of being transmitted in a given time bears an inv«ne ratio to the inductive capacity of the cable. The soonduess of a joint may be tested hr the apparatos F%. 533, the electrode z bemg put to one end of the insulated cable, TBST8 TO DBTECT FAULT8. 537 and R to the irater of a tank in which the joint is immeraecL The condenser is now chai^ged with the leakage of current (if any) by maintaining the contact at h for two or three minutes, and then discharged as before through the galyanometer ; the deflection of the needle will indicate the amount of leakage. 946. Test8 to Detect Fatdts.—FtLvMe in cables may be thus classed: — 1. Bnptnre of the conductor within the insulator: 2. Rupture of conductor, ¥nth slight breach of insulator: 3. Rupture with considerable exposure of the conductor : 4. Conductor in contact with iron sheathing : 5. Slight breach of insulator only. The existence of the first kind of injury is known from the power of the cable to Tecei?e and retam a chargOi although it will not transmit a signal. Its distance from either end is ascer- tained by measuring the total resistance of the insulator, and dividing the known resistance of one knot by this quantity ; the quotient will be the distance of the fault in knots. It is much more difficult to localize the second kind of iigury, in which there is only a slight exposure of the conductor, for the resistance at the fault may stilT be considerable, and it is more- orer subject to great and capricious charges. The resistance-test (801) in this case merely snows that the fault cannot be beyond the distance corresponding to the least obseryed resistance : but if the same test can be applied at both ends, a very probable guess at the true locality may m made by splitting the difference be- tween the apparent results. Tlie third Kind of fault is that which most frequently occurs when a cable is broken with violence. In this case also there is a total cessation of the transmission of signals, but the resistance- test gives uniform results ; and the distance, which is proportional to the resistance, may be definitely measured, since the resist- ance of the ocean in the circuit is like that of the earth, absolutely zero. It was by this test that the operators at Valentia were able to ascertain that the Atlantic cable of 1865 had met with no further iiguTT, since its final rupture. The fourth kind of fanlt is very similar in its results to the preceding : if the conductor and sheathing are squeezed into con- tact bv a kink, there will be a frequent succession of feeble cur- rents, n-om the action of the salt water on the point of contact of the two metals ; if they be connected, as by a nail or bit of wire thrust through the insulator, the resistance at the fault will be slk^t and nearly constant. The fifth kind of fault may be easily detected ; there will be a considerable decrease in the insulation-resistance, and some dimi- nution of the apparent resistance of the conductor, but signals may still be transmitted, as a portion only of the whole current, inTenel; proportina*! la tb* reticUuiM of the hnh, MMp theUnk,orBeL Tbigkind ofr&nltiiia;slK>baad d. A eecoDd series, r, each of 200 anita nulj bj niiable oooUcti be Bubetilated for any two of the fonner, and the contw:), i, msj be made with an; one of thsse. If Rreater socormcj wen required, a third aeriea of 40-auit coilt mioht be nmilail; anper posed apon r. B; this Bmngement it ia endBnt that anj injiured partition of 10,000 inenlstion at soioe particular poM, aa a rnptore of Ihe win woaU be im mediately Tisibie. He joins Ihe fanltj with a boqkI viteat tiie distant BlatioD and takes the mealnml ra«i*lai>M of tbe whole, as the "denominator:" he then puts oM pole of the battoj to earth, and measures the difiHreooe of the resistances of the proxi- mal portion of the faulty wire, and its distal portioa plna ths sound wire (which is evidently double the reaiitaDoe of tin dlMal portion], for the " numerator.'' Thig Graction of the di«lsiini W tweeo the stations will be the distuoe of the &alt fim the further station. The writer was informed that in one inataBce a clerk was somewhat dislurbed at not being able to And any *>!« forthe "numerator;" the factheingthattbelaiilt w«b wilhia the office at the further station. M». JltiirUmee of a Batttrj. — Aa it ii often n ascertain the total redstanoe of aoircnit, it ma; he oa gire here a read; mode of dateimining the internal n rif. Ufl. P a batter;. For this purpose let ihe electrodes <^ the battety c^ i. Fig. &36, be coiuiected with the teiminais of the coil of a gain- THE ELBCTJUVMAOIIBTIG LOOK. 530 nometer o, tlie resistance of which is n imits, and let a juncfion A B be made between the terminals, the resistance of which is one miit : then rth part of the current will traverse the gal- vanometer, and let the deflection be observed. Next remove a b, and let a resistance b, Fig. 537, be interposed between c and a, and be adjusted to produce the same deflection of the needle as beforehand let m be the indicated resistance, the resistance of the battery will be — units, the resistances of the connexions a c, b z, being neglected. If the resistance of a b be a units instead of one, then battery-resistances— a units. 950. The Electro-moffnetic Loom, — A recent application of elec- tro-magnetism to the economy of manufactures by M. Bonelli, an eminent Italian enffineer, may perhaps become too important to be entirely omitted m even an elementary treatise. This consists in the substitution of magnetic induction for the ordinary mechan- ism of the Jacquard loom, in figure-weaving. In order to render this intelligible to many readers, it will m necessary briefly to describe the mechanism of the Jacquard loom, by which the pro- duction of designs in all kinds of textile fabrics has been nniver* saUy effected for nearly thirty years. The production of patterns in monochromatic fabncs depends on the alternating predominance of the loHffUwdinalf^ or warp4hreada, and of the transverBe, or weft; and this again depends on the selection of warp-threads under and over which the weft is to pass at each throw of the shuttle. Passing over antecedent contrivances, it suffices for the present purpose to sav that in the Jacquard loom, the warp- threads are respectively connected with a series of vertical wires arranged in six or eight rows, each terminating above in a hook. As many rods as rows of hooks, rest in a frame beneath them ; and the firame, on rising, raises all those threads the corresponding hooks of which have not been pushed out of its way. The selec- tion is thus effected : each vertical wire is linked to a horizontal wire, and the ends of all the horizontal wires present themselves in a vertical plane, placed equidistantly from each other. In the action of the loom, a rectangular box, with as many e<}uidistant holes in it as there are horizontal rods, now presents itself, but covered by a card in which holes have been punched corresponding to all those threads under which the shuttle is destined to pass. The card advancing pushes back the horizontal rods wherever it is not pierced to transmit them, and with these the corresponding vertical rods and their hooks ; the selected threads are then raised by the frame of rods, called the "grifE)'* and the shuttle passes under them« The displaced horizontal rods are then replaced by 640 ■pniigi, another card is presented on the face of the box, and ihtb same train of actioni is repeated. A great amount of labour and expense mnsi be bestowed upon the preparation of the series of cards required for an elaborate desi^ — a rich pattern for a damask cnrtun, or table-cloth, mar require from 20,000 to 50,000 cards, the production of which would occupy four, six, or eight months, at a cost ot, perhaps, 150L, or more. Nearly all this time, labour, and expense is saved by M. BonelIi*s ingenious contrivance, which, it may be said, extempo* rises each successive card from the original desien ; wluch is thus effected. The desi^ is traced in black varnish on an endless band of paper of suitable length and width, the suHace of which is covered with tinfoil. The pattern thus drawn is laid over a cylinder in the loom, above which stands a row of thin parallel metallic plates like the teeth of a fine comb, which aie isolated from each other by non-oonducting matter. The metallic plates are severally connected with one end of the helices (875) of as many small bar electro-magnets as there are threads in the waip; these are arranged horizontally with the extremities in the same vertical plane, and opposed to the ends of an equal number of soli iron rods similarly arranged in a frame, which piays the part of the Jacquard card previously described. The other end of each helix is connected with one electrode of a small voltaic battery, and the metallic surface of the pattern with the other electrode. The rods in the Jacquard box have each a small enlargement or button at the further end, which is opposed to one end of the rods with which the threads of the warn are connected as in the Jacquard loom. The several parts being tnus arranged, the series of plates desoeady and their pomts rest on tlie surfaoe of the pattern cylinder. By each plate that rests on the metallic surface the circuit is Dieted; its corresponding electro-magnet becomes active, and this Dv its induced magnetism withdraws its corresponding rod into the Jacquard box. By the plates that rest on the varnisn the cir- cuit is not completed, and their corresponding electro-magnets remain inactive. A sUght vertical movement m the front et, aad therefore independent of the Toriatioiia uf the carrent. It will Buffice for the objects of tbii treatiae to deacribe one plan of cea- ■truction, deTimd by M. Froment, and mmswhat rnDdified hj M. HanJj. The pendulum, p, fig, 639, n Buapended by a thin luruBa of B with of the ctnl irf an electm-niagnel at (he end of an arm r atlached to the pendulum cornea in contact, mt tbe ei- '.remity of its oacillatioDj witli a a| tremity of its oacillEtion, witli E apring H, the filed end of *liich,.BDd the DDper end of the coil a, are maiMcIei with the electrodes of a battetj. IV end of the apring a reata on s atad D on ■ vertical rod « ■>, which ia jainlml at A to the end of a Oat piece of kA iron, placed near the end of the elsclrv- magnet, and raised from it bj a ahort spnng B, the force of which ia rnnlaled ijy a acrew Egainst the point of whick it rests ; and A c being thus raised, raises the end of th« apring K. When the arm f cumes in contact with a the ciimit is i tiaiil. and the electro-magnet B, by attracting c depreaaea a ■>, irtirk thus releases a aoii allowa it to are h^ lu elasticity tha ra^lAai impulae to the pendulum, (he rod A n is kept in a Tertical pariila by ila lower end paasing through a Gied hole at a. Tba naMtf o( impulse on the pendulum evidently depends on tbe atraagAsf the spring, s, and not on the strength of the current. Many oditf ennlnvBni.-e9 Era much more complicated, without being kbit effectual. 956. Ii ices E series of electric docks, diatribated ii are all actuated by a single ragnlBtor, by :( effecled at each beat of tl and coDTnnicnt mods of dmng ibii hu been derited bj cault. The pendalnm, p, is connected bj» hoiiwwitJ ^- '*'■ Ih another link B eqoal aod 1 the upper part of the pen- ad the joncticm of these ia by a tbird link c with the igbt spring, ■, ■ Mnall itnd is tiTDUubt into coQiKt irith a similar spring t beneath moment that the pendalnm I, and the links B and c, an iilo a etraighl line. A< these ; nn the principle of the 30) the contact i> efected I pull of the pendulum, and l^heaUlinu'i ChriMaKopt. — a exceedingly minut t the . of its lentn designed to I H mm vKiy luiuuLo initrraia oi Lime have been termed iprt; vhile those that record the inlerial by means of a DiDt on paper or other malerisl ire called thTimographt. e important function of theie insTmments is that of re- the velocity of projectiles during any required portion of ht. A toIihIc current was first apjilied to this purpnee ^healstono in ibejear l)MO, but the instrDnient then de- I liim has since been conaidemMy modilied and improved, tent rr-cordin;! instrument cnnsisis Ibid. • Abhaad. der Aoad. t. Berlin, 1820, 1821. 7 phil. Trans., 1774 • Vermischte Sohriften, p. 272. Yienna, 1788. • Phil. Trans., 1839. lo Abhand. Aoad., Berlin, 1884. 1^ Handbuch der Physiologie des Menschens, i. p. 66, Cobleoai 1837] or Bailej's trandation, London. 1837. The Tetraodon is described br Paterson in Phil. Trans., 1766, p. 388. The Triohinms is flffored by Willonghbj, in his Ichthyolofu ; Appendix, t. 3, ilf . 3, and described bj Nienhof in " Zee on Lant Beise door Wast en Ost-IadicB," p. 870, Amsterdam, 1682. THE QTICHOTUS AHD 8ILUBUB. 553 gastric neryjes. The power of communicatiDg the shock depends upon the integrity of the nerres, for the heart may be cut oat, and the animal flayed, without its losing this faculty; but as soon as the nerves are divided, it vanishes entirely. The intensity of the shocks is increased by irritating the oripn of the electric nerves with the point of a knife. The electric discharge is directed from one surface of the fish to the other, the dorsal surface beine positiye, and the ventral, negative ; and no shock is experienced^ unless direct or indirect communication be made between the belly and the back of the animal. A complete polarization of the two sur&ces does not occur, as that portion of the animal nearer the electric organs is positive, or negative, according to the par- ticular surface, with respect to other parts nearer the tail. Dr. Davy socceeded in decomposing acidulated water, and iodide of potassium, as well as in heating but not igniting platinum wire, and in magnetising needles placed in a spiral coil of wire, by means of currents from the torpedo. 978. In the gymnotus, the electric organs are on each side, double, and extend from the head to the taiL They are each formed of longitudinal membranous structures, placed at a short distance from each other, provided with numerous tran»> verse septa, and filled, as in the torpedo, with a ^latinous fluid. These organs are supplied by spinal nerves, in which respect this differs from the last described fish ; these consist of 224 pairs of intercostal nerves. The gymnotus resembles an eel in appear- ance, and is often four or five feet in length ; its shock is ex- tremely powerful, and capable of paralysing horses and mules. Walsh and Ingenhouss, in 1776, observed a spark to pass between two pieces of tinfoil through which the discharge of this fish was transmitted. This was doubted until, in 1836, the power pos- sessed by electric fishes of yielding a spark was again assertea by linari ; and in 1839 this statement was placed beyond a doubt by the researches of Faraday, who, availing himself of the electric eel publicly exhibited at the Adelaide dallery, succeeded in ob- taining a current of sparks, and by the aid of an induction-coil (887), and once even by the direct current between the surfaces of two pieces of leaf-gold. 979. Faraday obtained the electricity from the gymnotus whilst immersed in water, by means of collectors formed of sheet copper bent into a saddle shape, so as to grasp gently the sides of the animal. The backs of these collectors were covered with sheet caoutchouc, so as to insulate them from the water. Conducting wires, also insulated by being covered with caoutchouc, were sol- dered to each collector. The shock was best obtained by placing one of the hands near the head and the other near the tail of the fish ; it was conveyed with facility to the moistened hands by the condnctors. "When the conducting wires were connected with a galvanometer, deflection of the needle to 30** or 40° took place. 554 OIOAHIO BLBCTSICITT. And was in sacb a direction as indicated a current firom the an- terior to the posterior extremity of the fish. When the current was allowed to trayerse a short helix, a steel needle placed within it became magnetic. In like manner, when the conductors wen furnished with platinum terminations, and allowed to rest upon paper moistenea with a solution of iodide of potassium, polar de- composition ensued, iodine being evoWed at the end of th« wire connected with the anterior part of the fish. 980. On whatever part of the animal the collectors were placed, the current of electricity was alwap found to pass from that nearer the head to that nearer the tail. So that if three collectors were placed on the animal, one near the head, the other on the middle, and the third near the tail, the first was found to be pon- tive with regard to the second ; which, although negative with regard to the first, was positive in relation to the third. It appears that the moment the gymnotus wills the shock, the lines or force dart ofi^ diverging from him in the water, and whatever is in their course receives the shock. Hence, if a person immerses one hand only in the water near the fish, when it wills a shock, he expe- riences its effects, although not so powerfully as when in contact with the animaL 981. The silurus is still less known than the gymnotns ; its electric oreans are double, and are separated by a tough aponeu- rotic membrane : the most external of these organs lies imme- diately under the skin, the deeper one beins imbedded in the muscles. They are both divided inte cells ; their nerves are, it is remarkable, the same as those of both the torpedo and gymnotus, one of the organs being supplied by the pneumogastric, the other by the intercostal nerves. 982. Among invertebrate animals, a few have been stated to have claims to be considered as electric, but this is extremely doubtful. Molina* relates that a certain Chilian spider possesses the property of benumbing the hand of the person who touches it. Kirby and Spencef mention a species of cimex, the redwnnt ierraius, as having the power of conununicating what have been regarded as electnc shocks. An account is on record sAso^ of one of the great marine annelidsB, loonice ^anteo,^ giving a powerful shock to the person who touched it. 983. Prof. Galvani, of Bologna, in 1791, published a com- mentary " de Yiribus Electricitatis in Motu Musculari," aod aa- Bounced those facts which laid the foundation of that scieiioe which bears his name. He then stated that a particular form c£ electricity, denominated by him animal eUdrtcUy^ existed in all animals : but he believed that he merely excited and rendered sensible this electricity by coating a nerve and muscle with * Natorgeaohiohttf tob Chili, p. 175. t Introduotion to Entomology, i. p. 110. ^ SiUimui'i Joomal, xr. 867. EZFEBDIIHTB OF OALYAIII JLHD TOLTA. 555 netaU, and failed to regard the latter as the real source of tht exciting current. This celebrated experiment, although well known, is one of xeally so marvellous and remarkable a character that, repeat it as often as we may, it can never be looked at without a feeling of wonder and delight. Prepare the legs of a frog by denuding them ef their skin, and removing them from the body, together with the portion of the spine from which the lumbar nerves arise ; and having laid the preparation on a glass plate, place a <^* Ml* piece of zinc, z, Fig. 551, ' * in contact with the nerves, and allow the feet to rest on a thin slip of silver, s. The limbs will remain at rest, and appear dead and powerless ; but there exists a power which can be caJled into action, capable of endowing these appa- rently dead muscles with vital power. The only spell required to er^ka this power is a piece of wire, w, one end of which must toQch the zinc, and the other the silver plate ; instantly the legs -violentlv contract, and kick away the silver plate. It has been stated by Prof. Matteucci, that this curious observation was not original with Galvani, but was made some time before by the celebrated Swammerdam : and that the experiment was exhibited by him in the presence of the Ghrand Duke of Tuscany. 984. Shortly after the announcement of this discovery. Prof. Volta, of Pa via, in repeating this and other analogous experiments, arrived at a different conclusion ; and he showed that the elec- tricity was reallv excited by the metals, and the contraction of the muscles of the frog was only an index of its existence, fle, however, supposed that the electricity was excited by the mere contact of the metals (762), as the necessaiy agency of chemical action was not then recognised. It is now almost universally admitted that in this experiment the zinc is acted upon by the chloride of sodium or other salts existing in the fluids with which the tissues of the frog are moistened. Although these and other discoveries of that great man obscured for a time the views and researches of the ifiustrious Galvani, attention was again drawn to them by the experiments of bis talented nephew, Prof. Aldini, of Bologna. He was inspired with so much zeal in defence of his uncle's theoiy, that he travelled through France and England for the purpose of demonstratiog the truth of his views ; and, in the presence of the medical officers and pupils of Guy's Hospital, he, in the year 1803, supported and defended a series of propositions 00 satisfactory and conclusive, that he was presented by his audi- tors with a gold medal commemorative of his labours. 985. Aldini's propositions and conclusions are so important and of such high interest, that a brief reference must now be made to U6 ora. «oma oTtheto, aa they appear to deiDOTiBtnite,iii»nip. pear tn all coDTemtnt witb this branch of phyaiologj, moat r»- markabl; anlicipate the later resaarchei of hii countrj'man, FmC, Matteucci. Pbuf. 1 . — MiiBciiIar contractiona are excited bj the dereli^ ment of electric potential in the animal machiiie, vhich la tranv mitted from the nervea to the mowlea without the concurrence or agency of metals.* EiF. A. In proof of this statement, Aldini procared the head „ „, of a recenttv killed oi, Fig- 532. Wilh ^'- "^ the one huid he held the denuded lea of ■ fro?, eo that the portioni of tCe spine alill connected irith its lumbar nerres toucbsd the tip of the tongue, vhich had been previously drawn out _of the mouth of the oi. The circuit WHS completed bj grasping wilh the other hand, well moistened wilb salt J and water, one of the e»i» : the frog's I legs instantly contracted ; the contrac- n tions ceasing the instant the circuit rl vas broken by removing the hand fitun M the ear. The intennt; oT these cnatT«ction( was much incressed by combining two ~ or three heads, so as to fonn a sort of batteiy ; just as Matlencci forty years later ibond to he the cae witb bis pigeon and rabbit batterv. Gip. a. Aldini, having aoaked one of bia hands in ealt and water, held a frog's leg by ita loe, and, allowing the ischistio nerves to be pendulous, ne brought them in contact with the tip of his own tongue. Contractions instantly ensued from a current of electricity traversing the frog'sleg in its route from tbeeitemml or cutaneous to the internal or mucous covering of the body. By this very interesting experiment Aldini demonstni led the eiiBlence of the mtiscuto.cutaneous current, and completely anticipated ill reJiacovery bj Donn6 some five-and-tbirty yeare afterwards. -, ... EiF. C. The proper electiicity '^■™' of the frog was found by Aldini to bo competent to the production of contractions. For ibia pnrpoae he prepared the lower ertremitiaa of a vigorous frog-and by bending up the Was in Fig. 553, brought the muscles of the thigh in conUct wilh the lumbar nerves, when con- * Aldini: AcoDimtoftiifllatflliDpiDVeiiintolaQaiTaoiiiii.Ma. Loodoi^lBOS. THE0BIE8 OP OALYAHI AKD YALLI. 557 tractions immediately ensued. This experiment is now a familiar one, and has been repeated and modified by Miiller and others. Exp. D. a ligature was loosely placed round the middle of the crural nerves, and one of the nerves applied to a corresponding muscle : contractions ensued ; but on tigntening the ligature, this convulsions ceased. d86. This last statement is very important, as upon its accuracy or error depends what has been regarded as one ot the tests of the identity or diversity of the electric and nervous agencies. It wa0 repeated soon after Aldini's announcement of the fact by an Italian pb^ician of celebrity, Signor Valli, who commenced his researches in 1792,* only a year alter the publication of Galvani's discovery ; and he found if the ligature were applied nearer tfie fttuade it did not allow the contraction to occur ^ but if nearer the 9pine^ it did not prevent it; and this was afterwards corroborated by Humboldt : but it has been since found by Matteucci, that if care be taken to insulate the nerve, a ligature applied to it will arrest the contraction, as well as the passage of a very weak artificial electric current. « 987. It must not here be omitted to notice the neuro- electric theory of Galvani. He assumed that all animals are en- dowed with an inherent electricity appropriate to their economy, which electricity, secreted by the bram, resides especially in the nerves, by which it is communicated to every part of the body. The principal reservoirs of this electricity he considered to be the fibres of muscles, each of which he regarded to have two sides in opposite electric conditions. He believed that when a limb was willed to move, the nerves, aided by the braiu, drew from the in- terior of the muscles some electricity ; discharging it upon their surface, they thus contracted and produced the required change of position. This theory was adopted and defended by Aldini. 988. Valli, whoseexperimeots nave beenreferredto(986), believed the neuro-electric "fluid '* to be secreted by the capillary arteries supplying the nerves, bv which it was conveyed to the muscles ; these he uelicved to be always in an electric condition, the interior being negative, the exterior positive. He also noticed the curious fact, that ill experiments on frogs, the nerves lose their irritability to the stimulus of electricity at their origin first, retaining it longest at their extremities ; and on this hazarded an opinion that probably the distal extremities are really the origin of these structures. Both these statements are of deep interest; the former from its bearing on the later researches of Matteucci, the latter fri)m its curious connexion with some views of Dr. Marshall Hall, regarding the peripheral origin of incident, or sen- sory nerves. 989. It may now be asked, what proof do we possess that the action on muscular fibre here alluded to, where no metals are em- * Willdiuon's QalT«iU8m. London, 18M. Vol. i. page 40. 558 OBOAHIC SLEOTBXCITT. ployed, 18 really prodnoed by electric ourrents? One gretX evi- dence in favour of this opinion is at once found in the tact, tliat contractions produced in frogs can only be excited wben connexion is made between a nerve and a muscle by a conductor of eleo- tricity, all insulators interfering with the production of this phe- nomenon. The only experiment amounting to positive proof before the researches of Matteucci is that of Valli, in whicn he formed a sort of battery of fourteen prepared frogs, and by the electricity thus accumulated succeeded in producing the pheno- mena of divergence in a delicate electroscope. It is to be regretted that no accurate account of this experiment has been left on record ; for if true, it must be regarded as most satisfactory in grovine the identity of the electricity of the fipog with that obtained t>m ouier sources. 990. The researches of Prof. Mattencci,* of Pisa, hare, how- ever, completely set this matter at rest. He has incontestably proved that currents of electricity are always circnlating in the animal frame, and not limited merely to cold-blooded reptileo^ but are common to fishes, birds, and mammals. From the re- searches of this philosopher it appears that the interior is always electrically positive to the extenor of a muscle; and that al- though the potential developed is exceedingly small, yet that by arranging a series of muscles having their exterior and inte- rior surfaces connected, he developed sufficient electricity to pro- duce enei^tic effects. By thus arranging a series of natf- _j thighs of frogs, Fip. ^" 654, he succeeded in decomposiog iodide of potassium, in deflecting the needle of the ga£ vanometer to 90°, and by the aid of a conden- ser, caused the gold leaves of an electroscope to diverge. When more delicate tests of the electric current were made use of, its existence was demonstrated in the muscles of all animals, and even of man himself. Dr. Wilkinsonf calculated that the irri- table muscles of a frog^s leg were no leps than 56,000 times mors delicate as a test of electricity than the most sensitive con- densing electroscope. I>r. Wilkinson found that two pieces of zinc and silver, each presenting a superficial area of yW inch, produced violent contractions in the leg of a prepared frog ; whilst two laiige circular plates of zinc and copper reonired to be broneht twenty times in contact with the condenser, before any sensible divergence of the gold leaves of an electroscope was produced. By comparing the area of these plates, multiplied by the number of contacts, with the superficial area of the minute pieces of zinc * Fhilosophioal TranMctioBS, 1845, p. S88. t BlemcnU of OslTmnism. 1846. 8to. Y ol. ii. p. S16. DIBSOnOH OF OUBBBVTB IH MUBCLBB. 559 tfid BilTereioployed to affoct the frog*B leg, lie smved at the eon^ elusion here stated. 991. Mattencci availed Mmaelf of this circumstanoe in his contrivaDco of theyro^rAeoseo^. This is made by skinning the hmd kg of a nog, and separating ^< (^* it from the trank, taking care to leaye as long a piece of sciatic nerve projecting as possible. The teg is then placed in a glass tube, the nerve bang- ing over, Fig. 555. In using this contrivance all that is necessary is to let the piece of nerve touch simultaneoDsI J in twoplaces tne part of which the electric condition is 'CSbe examined. If a current exist, the muscles of the leg will become convulsed at the moment of contact. In this way Mattencci detected a current in man ; by making a clean in- eirion into the muscles of a recently amputated limb, and bringing the nerve of a frog rheoscope in contact at once with the two lips of the wound, contraction instantly occurred. 992. In pigeons and fowls, as well as in eels and frogs, cur- rents were readily demonstrable ; indeed, by alternating a series of the former by approximating their sides, the ratr surface of the muscles of which had been exposed by a quickly made cut, Matteucci formed a sort of battery resembling that made of the thighs of frogs. The result of this experiment thus proved that energetic currents existed in hot as well as cold-blooded amimals : more intense, indeed, but very soon disappearing on the death of the animaL . 993. By means of the frt)g rheoscope (991), not only the exist- ence, but the direction of a current may be discovered ; for if the leg be kept for a short time before using it, so as to a little diminish its sensibility, the muscles will contract on making con- tact with the bodv under examination, if the electricity pass from the nerve to the leg, whilst it will contract on brecJeing con- tact, if the current move in the opposite direction. Using this delicate test of an electric current, Matteucci discovered that the intensity of such currents rises in proportion to the rank occupied by the animal in the scale of being, their duration after death being in the inverse ratio. He found that when a mass of muscle belonging to a living animal, or to one recently dead, was placed in contact with a piece of wire so that one end of it touched the tendon, and the other the body of the muscle, a current could always be detected circulating in the mass in the direction from the tendon to the external surface of the structure. He further demonstrated* the very important fact that everything which de- creases the vis vitcg of the animal diminishes the evidence of electricity immediately after death. Thus, when frogs were killed by asphyxia, aither by immersion in sulphuretted nydrogen, or MO OBOAVXC ELECTSICITT. in water freed from air, the electricity detected in their femoral mascles sunk to a minimum ; and the thighs of frogs whose hearts had been previously removed, gave less evidence of the existence of this important agent, than those which had not been thus injured. 994. It has been shown that certain fishes (976) possess a peculiar apparatus by which they are enabled to accumulate the electricity developed in their structui'es, and thus to produce the recoenised effects of potential, as shown in the Denumbing shocK felt on grasping the torpedo, or silurus. This endowment is, however, peculiar to very few creatures, and all the electricity developed in other organisms is only to ^be detected by com- paratively delicate tests. It is, however, very remarkable that in the batrachians generally, especially the frog, an electric current, denominated by Matteucci tne proper current, possessing some approach to tension, and capable of deflecting the needle of a galvanometer to 5**, can readily be detected; its direction is always definite from the feet towards the head. This remai^abk fsicX was probably first pointed out by Nobili, but accurately studied by the Pisan philosopher, whose researches have so often been referred to. 995. We are indebted to M. du Bois-Reymond for very oon- siderable additions to our knowledge of the existence and direc- tion of electric currents in the muscles and nerves of animals. Aided by the very delicate galvanometers already described (858), and by the peculiar arrangement of the electrodes employed, he succeeded in demonstrating the existence of electric currents in mere fragments of muscular and nervous tissue. We must refer the rea^r to the published account* of these very interesting researches, as they demand the most careful study : the author of which has taken extreme care to remove all possible sources of fallacy, and his mode of carrying on his investigations is very in- genious. The electrodes employed in these investigations con- sisted of two cushions of lint, dipping into, and overlapping the edges of two glass vessels filled with a saturated solution of salt. Slips of platinum of equal size, and carefully cleansed, are sup- Sorted by clamps, and immersed to equal depths in tne saline uid. The clamps are in metallic connexion with the terminals of the coil. Without the most scrupulous attention to the uni- formity of condition of the two electrodes, currents will inevitably be developed, so as entirely to vitiate these delicate experiments. The electrodes proposed by M. J . Begnault, consisting of plates of amalgamated zinc, immersed in a saturated solution of sul- phate of zinc, have more recently been preferred to the preceding. The more important results arrived at are the following : — A. The muscular and nervous structures are, while living, en- dowed with electromotive power. • Untersacbnngen fiber Tbierischa Elektrieitiit. Berlin, IMS-S. Animal JSlcctricity, by Dr. Bence Jones. London, 1861. RELATION OF EFFECTS TO BTBEKGTH OF CUBREHT. 561 B. The cnrrent is always developed in the same direction, in both nerve and muscle ; everj longitudinal surface being positive, and every tranwene section negative. And every fragment of muscle or nerve, however minute, obeys this general law. G. As a necessary result of this law, the exterior of every en- tire muscle will transmit a cnrrent through the coil of the galva- nometer to a clear transverse section. D. These currents, discovered in muscles and nerves, must be regarded as derived portions of greatly more intense currents cir* cuiating in their interior around their ultimate particles. B. In the contractile tissues, the electromotive power is always in proportion to their mechanical power. M. du Bois-Reymond has demonstrated the existence of the nerve-current in every species of nerve, as well as in the brain, spinal cord, aod other great nervous centres : he has also traced toe muscular current previously detected by Matteucci from the entire muscle, to the single fasciculus, and shown its existence in almost every department of the animal kingdom ; — in man, rabbits, guinea-pigs, and mice; in pigeons and sparrows; in lizards, snakes, toads and salamanders ; in tench, in fresh-water crabs, and in earth-worms. To him we are also indebted for the investigation of the changes occurring in the muscular and nerve- currents, in the interval between the death of the aanimalj and that of the tiatue; an iaterval the duration of which is generally in an inverse ratio to the normal activity of the circulation : — as well as of the changes occurring during ordinary muscular action, and nnder the influence of continuous voltaic currents, — changes which are of fundamental importance in clearing up much that is obscure in the physiology of muscular motion.* 996. Much tuat was unintelligible in the action of both con* tinuous and momentary currents, without the supposed existence of an " electro-tonic state" of the muscle, or some such arbitrary hypothesis, has been elucidated by the researches of M. Chau- ▼eao, of Lyons.f He has shown that if a momentary current (as from a coil machine) be passed through the body from one hand to the other, if powerful, it affects all that portion of the frame through which it passes ; if much weakened, it is felt in the hands only, and if sufficiently feeble, the shock is felt in the hand towards the negative terminal only; moreover if several persons joinine hands receive this feeble shock, it will be felt by each in the negative hand only. Also if the electrodes be placed on the facial nerves of a horse, a feeble current produces spasm on that side only the nerve of which is under the negative electrode : and if severed hor:C8 be similarly placed in circuit, the sides under the influence of the negative electrodes will alone be convulsed. It * Baddiffe, Bpileptie and other ConvaUiTe AiFeotioiis of the Iferroog System. Churchill. 1861. t BrowiiP^i^uard, Joumal de la Phynologie, July 1859 to Jolj 1800. O O 562 osaAviG blbgtricitt. bAs likewise been obeenred that the negative pole ramAining on the nenrey if the poatiTe pole be placed ei^er above or below it on the same nerre, or anywhere elsei the aame result enmiee ; ihe only neeeuary condition being that the nerve be under the influenoe of the iM^of ioe electrode. A precisely similar result ensues, if a sufficientlv feeble current be applied to a separated muscle, or to a senes of Bep«rate muscles, connected by metallic conductors: — contraction is visible only in the fibres ale voltaic current is transmitted ; passing up one nerve, across the spine, and dmon the other nerve. As in the former experiment on the horse, the limb in relation with the negative electrode is convulsed on closing the circuit, and that in relation with the positive electrode, on opening it. In the former case, the direction of the current in the nerve was " direct*' or " centrifugal," in accordance with the old theory ; but the fallacy of this hypothesis is shown by the progress of the experiment. If both the electrodes be now placea on the same nerve, convul- sion ensues on closing the circuit, indifferently whether the course of the continuous current be up or down the nerve. If now the sciatic nerve be isolated, and the lower part of the femur removed, lea vine the leg connected with the thigh by the sciatic nerve only, and the positive electrode be placed on the lumbar, and the negative on the sciatic nerve, the leg only is con- vulsed on closing the circuit, the muscles of the thigh giving do response to the " direct'' current through their nerves. But if the electrodes be reversed, both parts of the limb are convulsed on closing the circuit (by the influence of the negative electrode) in spite of the " inverse" current through the motor nerves of the thigh. ^■nai^nH EFFECTS OF COHTIHUOUB CUBEEKTB. 565 Bat another experiment placed the facts in a still clearer light. For this purpose tne sciatic nerve of an uninjured limb is isolated and raised from the limb on a wire, and another ^ire is laid on the muscles beneath the former. If the wire supporting the nerve be now made the positive electrode of a very weaK current, and that resting on the muscle, the negative, on closing the circuit the leg ou^ht according to the " direction" theory to be convulsed, but neither on closing nor on opening the circuit, does any such effect take place. If on the contrary the nerve rest on the negative electrode, then notwithstanding the inverse or " centripet'il" direction of the current, spasm ensues on closing the circuit, and then only. In this crucial experiment the potential of the current muBt be reduced below the point at which the inverse terminal impulse is capable of exciting any functional energy. 1000. The change of action that ensues when a musculo-motor nerve has been for some time traversed by a continuous voltaic current, may be conveniently observed by means of the rheoscopic limb (991). It appears that the effect of the continuous current is to exhaust the vitality of the nerve, from its free extremity towards the limb with which it is connected. While its vitalitv is unimpaired, the nerve responds to both exit-impulses at both points of contact ; when the nerve at the further point of contact 18 dead, it responds to the two exit-impulses at the nearer point of contact only, viz., those attending the closing of the direct, and the opening of the inverse circuit. When the vitality at this nearer point is impaired but not extinguished, the nerve ceases to obey the latter or weaker of these two impulses, but when quite dead it obeys neither. The existence, suspension, or subsidence of functional energy in the nerves must therefore in all experiments be taken into account, as an important element, and this has pro- bably been a fertile source of erroneous physiological conclusions. The following experiment of M. du Bois-Reymond is also very instructive in showing the relative influence of the positive and negative electrodes on the nerve-current. He removes the whole length of the sciatic nerve, and placing its extremities in position on two galvanometers (i,e. with the transverse section resting on «ne terminal, and the outer surface on the other), he finds that nearly the same amount of nerve-current ia indicated in both. The electrodes of a small element are now placed on the inter- mediate portion of the nerve, and the result is, that the nerve- current is augmented under the influence of the positive electrode, and diminished under that of the negative, as shown by the altered positions of the needles in the two instruments. 1001. It is the result of observation that the subsidence of the muscular and nerve currents is coincident with the subsidence of functional activity, and that the direction of these currents is liable to a change, or to a succession of changes, when they are verging on the point of extinction. Moreover, when thes^ cur- 566 OBOJLHIG SLBCTBlClTr. rents have entirely disappeared, functional activity is also extinct, and riffor mortiSt the state of universal muscular contraction, speedily supervenes. It is, moreover, a noteworthy fact, that causes inducing an extensive depression of the vititl powers, such as excessive haemorrhage, or strychnine, induce also a convulsive action, consisting of irregular and involuntary contractions of the muscles. An experiment of M. du Bois-Reymond* demonstrates that a diminution of electric potential always accompanies muscular contraction. To show this, the gastrocnemius muscle is removed from the limh of a frog, with a long portion of its nerve remaining attached. The muscle is now placed on the terminals of the galvanometer (858), the transverse section heing in contact with one terminal, and the external surface with the other ; and the de- flexion of the needle, due to the muscular current, is noted. A portion of the nerve is then laid across the terminals of an induction-coil (896), and the muscle throvm into a state of spasm by the rapid succession of shocks': the galvanometer-needle will instantly swing back, and subsequently take up a position of equilibrium much nearer to the zero of the instrument than before, thus indi- cating a considerable abatement of the muscular current. The same observer has also found a similar abatement of the nerve- current, whenever the muscle is thrown into a state of spasm ; this is best seen by placing the isolated ischiatic nerve in position (like the muscle), on the terminals of the galvanometer, and then poisoning the animal by the introduction of a few drops of solution of strychnia under the skin : as soon as the spasms are developed, the needle shows a diminished potential of the nerve-current^ which may probably be the immediate cause of the spasms. These, and many other similar experiments, tend to establish the conclusion that muscular contraction is always accompanied by, or attendant upon a diminution of electric potential ; and this appears to favour the views of the nature of muscular motion en- tertained by Dr. Badcliffe ; f namely, that contraction is due, not to the direct influence of any vital or other stimulus, but simply to the negation or abatement of that electrical condition, on the due maintenance of which the continuance of the state of relaxa- tion depends. 1002. Numerous experiments have been made by Prof. Elckhard of Qiessen,:!: in which the nerve of a rheoscopic limb was suh- mitted simultaneously to the action, at different points, of a con- tinuous current, ana of a succession of shocks ; firom these it appears that the susceptibility of the nerves to the influence of electric impulses is considerably modified by the action of con- tinuous currents. In other experiments the chemical stimulus of a strong solution of salt was substituted for the shocks. A rerj * UntennohvogeD, &o., rol. ii. pp. 60, 89. t Bpileptio and other ConvnlriTe Aiffeetioiis, &o. CharehUl, 168U X Beitr&ge lar Anatomi* und Phytiologie. Gieaaen, 185B. JIXTB OP TIUV81IIB8IOK OF IMPBBSSIOKS. 567 instructiTe experiment was loug since made by Bitter,* in which a pair of rheoscopic limbs were immersed in the water-electrodes of an electromotor, when it was funnd that the functional enerf;y of the nerves is weakened bj the continuous action of a direct current, but that it maj even be subsequentlj restored by the action of an inverse or centripetal current. These facts show that the power of a motor nerve to evoke the contraction of the muscle is suspended, or entirely annulled by the influence of a centrifugal or direct) and may be restored by that of an inverse, continuous cur- rent*: a result directly opposed to the theory hitherto generally received. lliat this is so may be farther inferred from the fact that the oonvulaions resulting from poisoning by strychnine may be. and those occurring in spontaneous tetanus are stated to have oeen, entirely arrested by the maintenance of a continuous voltaic cur- rent down the spinal cord. 1003. Bate of TraTumiaion through the Nerves. — ^Many elabo- rate series of experiments have recentlv been conducted for the purpose of ascertaining the rate at which the impressions of sen- sation and volition are transmitted through the brain and nervous system. The rate of transmission through the sciatic nerve of a irog has been determined by the myoffraphion of Ptof. Helmholtz. For this purpose the gastrocnemius muscle is removed from the leg with a small bit of the thigh-bone, and the whole length of the nerve attached to it : the bone is fixed in a clamp, and the tendon connected by a hook with a light lever, carrying at its -extremity a traciue pointwhich rests on the surface of a small plate of smoked glass. This plate is capable of being moved rapidly by a spring in a plane parallel to the plane of motion of the lever, and m a direction at right angles to that of the tracing point ; and it may, at will, be set in motion by the in- duced current that, acting on the nerve, induces the contraction of the muscle. By first causing^ the muscle to contract only, a vertical base line ▲ b, Fig. 556, is drawn by the tracing point on the plate at rest; secondly, by allowing the plate only to move, a horizontal base line a o is traced. If the terminals of the coil be now pjlaced on the muscle itself, and the plate be started by the electric impulse, the curve d will be traced, and a d will represent the time occupied by the muscular fibres in obeying the impulse. If the terminals be placed on two points of the nerve, near the * Beveis dsM «m telbtUtiiidifer OalTMiinniit, Ac. Weimar, 1786. 570 OBOASIC BLBCrrBICTTT. these mvat, like the carbon, by this Tery act become soaroes of electricity. Bat a more important sonrce of electric excitation is found in the series of decompositions which take place in the bodr, daring the action of the yarioas vital processes. It is impossible that any two elements can be rent asnnder without setting free a current of electricity, which insignificant as it might theoretically appear, is nevertheless competent to the prodoction of many important phenomena. As one amon^ many examples, the case of common salt may be cited, which pMys so important a part as an article of food, and for which perhaps alone, of all condiments, an universal appetite exists. In addition to the proportion of this substance which enters the blood unchanged, and becomes an element of all the secretions, a part is decomposed, and one ele- ment in unison with hydrogen appears as hydrochloric acid in the stomach ; another, in union witn oxygen, constitutes, as soda, an important element of the bile. What, it ma^ be inquired, can be the influence of these apparently infinitesimal developments of electricity, evolved thus from the resolution of a few grains of salt and water into its elements ? But it is easv to produce a mass of evidence to show that these small quantities of electricity are more so in appearance than in reality. A reference to the powerful electrolytic infiuence of weak currents (832, 3) will afford sufficient proof of this. 1009. It is a remarkable fact, that when an acid and an alkaline solution are so placed, that their union may be effected through the substance of an animal membrane, or indeed of any other porous diaphragm, a current of electricity is evolved, the causes of which have already been investigated (844). Now, with the exoeptioit of the stomach and ccecum, the whole extent of the mucona mem- brane is, in the human sulject, bathed with an alkaline mucous fluid, and the external covering of the body, the skin, is as constMitly exhaling an acid fluid, except in the axillary, and perhaps pnbic regions. The mass of the animal frame is thus placed between two great envelopes, the one alkaline, and the other acid, meeting only at the external outlets. This arrangement has been shown by Donn^* to be quite competent to the evolution of electricity, and accordingly he found that if a platinum plate connected with the galvanometer be held in the mouth, whilst a second be pressed against the moist perspiring surface of the body, the needles will instantly traverse, as tney did in the experiment just shown with an acid and an alkali. The current thus detected by Donn^ at once explains the cause and confirms the accuracy of the oe]e> brated experiment of Aldini, in which he excited convnlsionB in a fro^ by holding its foot in the moistened hand, and allowing the sciatic nerve to touch the tongue. His curious experiment with the head of an ox (985) admits of a similar explanation. • BeoqnareL Traits de TElectxioit^, voL iii. UBBIO'S BB8EARCHS8. 571 1010. The remits of some researches of Liebig* have rendered it very probable that a large proportion of the electricity of mascnlar structures isowingto the mutual reaction of an acid and alkaline fluid. The blood, in^ a healthy state, exerts a decided and weU-marked alkaline reaction on test-paper : now it is remarkable that although a piece of muscular flesh contains so larse a proportion of alkaline blood, still that when chopped up, and digested in water, the in- fusion thus obtained is actually acid to litmus paper. This curious circnmsti^noe is explained by the fact aunounced by Liebig, that although the blooa in the vessels of the muscle is alkaline from the tribasic pho^hate of soda, yet the pro^r fluid or secretion of the tissues exterior to the capillaries is acid from the presence of free phosphoric and lactic acids. Thus in every mass of muscle we iiave myriads of electric currents arising from the mutual reaction of an acid fluid exterior to the vessels on their alkaline contents. Whatever may be the ultimate destination of this large quantitT of electricitv, it is at least remarkable that a mus<3e Bnould be really an eiectro-genic apparatus. We have thus two flources of the electricity of muscles— tlie efiEbcts of themetamorphofliB of e£fete fibres on the one hand, and on the other the mutual reaction of two fluids in different chemical conditions. It is cer- tainly curious thus to find a muscle, an organ long regarded as the mere motor apparatus of the bony levers of our frame, invested with new and important properties. In the course of twenty-four hours, a considerable proportion of watery vapour is exhaled from the surface of the body : this has been variaoly estimated, and in all probability is liable to great Tariation, but from thirty to forty-eignt ounces of water may thus be got rid of from the system. It is more than probable that the evaporation of this amount of fluid is sufficient to disturb the electric equilibrium of the body, and to evolve electricity of much higher potential than that set free by chemical action. Evapora- tion may thus probably account for the traces of free electricity generalfy to be detected in the body by merely insulating a person, and plaong him in contact with a condensing electroscope. The causes of the variations in the character of the electric con- dition of the body admit of ready explanation in the varying composition of the perspired fluid. For if it contain, as it gene- rally does, some free acid, by its evaporation the body woiud be left positively electric (753) ; whilst, if it merely contain neutral salt^ an opposite condition would be induced. 1011. iaectroscopio indications of animid potential have been detected by several observers ; by Qardini and Hemmer, about the time of Galvani's great discovery; by Ahrens, in 1817; by Nasse, in 1834 ; and recently by Dr. Kadclifie. Pfaff and Ahrens generally found the electricity of the body thus ex- amined to be positive, especially when the circulation had * Oomptes Bendua de I'Aoad^mie, Jan. 18 and Feb. 8, 1817. 572 otOJ been excited bj partnVing of alcDboHc aldmiiUnts. HeBmer, ftnother abierrer, found that in 2422 expenment« on hiina*lf| ki< bodj' wBB positiielj electric in 1252, negatiire in 771, aod neutnJ in 399. B/meane of [hepairofpositiTeandnfgktiTc electnanijiei (663), Dr. RsdcliSe h&a frequeatl; obUbed trmna »f potaitul. •ometimog panitire and Borne Limei negative, in his ovn body, afid in that of othera. Ue bas alio found traces in fresh-dnwn blooj fram the shambles, generally negatire, somelimei very ■ligbtly Seitlve, but these indicatinns alwaj* diaitppearing In an hinr oc K. The Bpiua] cords of oieu mere rather ■trongly poBtiir, the cerebellum of a sheep neutml, and tba brain of a donkey □egaliTe. I^eces of muscular tissue gBTs more nncerluii iodiea- tioDS ofpotentitd. 1012. The potential quality of animal electricity vai demoo- ■trated by a remarkablo experiment of Humboldt. He prepared the leg of a very ligorous frog, and arranged it as aliowa in J, ^ Fig. 557. The leg ia laid ot a clean dry plate of glaas, aod tbe ' nerre being divided, tbe cni ends are laid at a imall diataocv from each other, and iLe pniii- I mal end of the nerrc on a amall plate of meta). The interval betneen tbe ends of tke nerri being about 2"~, when c«>- neiion vaa made between the body of the moacle and ihe pitir of metal by means of a pair of conipassea, contraction ensued, ahowirg that the potential of the nerve was then laScicnt w act by induction through that interval. In the cooiae of about ten minutes, however, contraction did not ensue, onlna the dividad portions of the nerve were brought inio actual con- tact, the vital energy of the nerve being even in that short time thns far impaired. 1013. Independently of combustion, chemical action, or evapo- ration, the mere contact of heterogeneous erg&nie matter* is cun- petent to produce indications of electricity. ThuB a pile orallemair slices of muscular tissue and brain, with pieces of wel I»tbet in- terposed, has been found by Lagrave to evolve a current: s>d Dr. Baconio, of Milan, has shown that a few alternations of Blk-va of beet-root and wood of the walnnt-tree were capable ofgrneratinE sufficient eltwtricity to eicite convuUinns in a (rog when couven^ to ita muscles by nieaus of a conductor formed of a leaf of ecorrV' grass. Matteucci has ibrown out the soggeslion, that the oij!»- nixation of a muscle is possibly Bucb as thus by heterogeneity of ■trmclure to account for the development of electricitjr ; be cod- ■iden the analogy between Ihe voltaic arrangements and the mi- ■titution of muscle to be complete, if we conceive the poaiiive plate u> be represented by tbe tme 6bra, the negative plate bj ths sarcolemma, and the exciting Said by the blood. HEBBOHEL^B HYTOTHBSiS. 573 . 1014. Secretion and nervons agency have always been the favoarite phenomena which electncity has been called in to ex- plain, and with some considerable appearance of probability. Dr. WoUaston, nearly forty years ago, first suggested from the resolu- tion of salts into their elements under the influence of feeble currents, that secretion depended essentially upon the electric state of the secreting glands ; he thus regarded the kidneys as constituting the positive, and the liver the negative electrodes of the electric apparatus of the body. A curious anecdote is related of Napoleon, who is said by Chaptal to have remarked, on seeing the voltaic battery of the French Academy in action, " VoiU, doctenr, Pimage de la vie ; la colonne vertebrale est le pile, la yessie le pole positif, et le foie le pole negatif." 1015. There is, in connexion with this hypothesis, a most inte- resting and important observation of Matteucci, to whose ingenuity and perseverance we are so largely indebted: this philosopher introduced a plate of platinum into the stomach uf a living rabbit, placed another on the liver, and connected both with a galvanometer ; the needle instantly traversed an arc of 20**, proviDg the existence of a powerful current between the liver and stomach. This, it maybe observed, shows the existence of a currenty but does not prove whether it is to be regarded as an effect or cause of the chemical changes alluded to, for it has been already shown, that when an acid and alkaline fluid are separated bjr permeable structures, they actually develope a current of elec- tricity : and as the stomach contains an acid, and the liver an alkaline secretion, this might afford an explanation of the current observed by Matteucci ; and had the experiment ended hero, this plausible objection would have been a fatal one. But the nerves and vessels passing into the abdomen were divided above the diaphraem, and in an instant the needle of the galvanometer was deflected to 3"* instead of 20** ; and on cutting off the head of the rabbit by a sudden blow, even this little deviation almost entirely vanished. Nothing could be more conclusive than this experiment in proving that the electric current was the cause, not the effect, of the chemical metamorphosis of the saline ingeata, the decomposition of which furnished acid to the stomach, and alkali to the liver. How this current is excited is unknown, although it can hardly be doubted that one of the causes which we have already examined is competent for this purpose ; but then there remains the difficulty of pointing out the route taken by the current to reach respectively the liver and stomach, for the pneumogastric nerves, at least in man, cannot, from their anato- mical distribution, explain this. 1016. Sir John Herschel has beautifully expressed the possible relation between galvanic electricity and the vis nervosOj and hinta at the brain being either the organ of secretion, or at least of the application of this agent ; adducing in illustration the dry piles, as they are termed, of De Luc and Zamboni (818), and 574 OROAvio xLBOTBicrrr. remarks, that " if the brain be an electric pile conatantlj in action, it may be conceived to discbarge itself at regular interTals, wben tbe tension of the electricitj reaches a certain point, along the nerves which communicate with the heart, and thus to excite the pulsation of that organ.'* Bj the " diy pile " a ball maj be kept m motion for many years, without any obvious waste of power, and some analogous arrangement would constitute the most con> stant and economic mrimum mobile of a moving oijnn which the resources of limited numan reason can suggest. Dr. Amott has also hinted at some such cause being the active asent which keeps up the regular pulsations of the heart. Aocoraing to Dr. Raaclifl^'s views, the periodic inaction of the heart is the intelli- gible and necessary result of tbe periodic stimulus of the supply of blood through the branches of the coronary arteries. 1017. The exercise of the vital functions of vegetables appears to be frequently attended by the excitation of electricity, sufficient to evolve even sparks, at least if we are to believe reports on this sul^ct. Pottillet has satisfactorily proved that electricity is evolved during germination, and Dr. Donne has shown that car- rents may be detected by means of a delicate galvanometer, in all ripe firuits, passing between their bases and apices. From a few observations made by the late Author on this sub- ject,* he arrived at the following conclusions : — 1. The great improbability of vegetables, on account of their feeble insuution, ever becoming so charged with electricity as to i^ord a spark ; and the probability of those luminous phenomena said to be exhibited bjr some plants, depending on other soaroes than on electric potential. 2. That verv feeble electric currents are always circulating in, and exerting their influence upphere, by the particles of air assuming undu latory movements, so any self-luminous body, as the sun, or a lamp, excites analogous undulatory movements in a surrounding medium,which, being conveyed by contiguous particles, eventually reach the eye, communicating the sensation of light to th it organ, in the same manner as scmorous vibrations convey tha sensation of sound to the ear : and the cessation of undulations. TELOCITY OF LIOHT. 579 or the repose of the transmitting medinm, resnlts in darkness, as the absence of similar movements in the air o(!casions silence. It has been objected to the undnlatory theory, that if true, light ought to bend round opaque objects, in the same manner as the waves of water (467} are propagated round fixed obstacles, and to be communicated through curved tubes, like sound, and con- sequently that no true shadow ought to exist. These objections, however, are more apparent than real ; for, taking the case of sono- rous vibrations, we hnd that they do not bend round obstacles with facility, and that an acoustic shadow does really exist : thus the sound of a rapidly moving carriage becomes less distinct as it turns the corner of a street ; and sounds passing through water are still more readily obstructed (565). The existence of an acoustic shadow may be better shown oy a vibrating tuning fork, held about six inches from the ear; on suddenly interposing a piece of card between the latter and the sounding.body, instantly the tone will disappear, and on withdrawing the card, it will again become audible. In the case of curved tubes, we know that whilst sonorous undulations are readily transmitted through them, those of light are completely obstructed ; for no one can see through a bent brass pipe. But, in this case, it must be recollected, that the sides of the tube, whilst they are sufficiently smooth to reflect sound, are infinitely too rou^h to reflect the undulations of light. There is no difficulty in seeing objects through a tube bent four times at right angles, provided __ ^ suitable means be employed, as ^.oa , in the well-known optical toy, Fig. 558, by which we are appa- rently made to see througn a book, or other opaque object ; but ordinarily, objects are not visible through bent tubes, because the substances of which they are composed absorb or disperse any luminous undulations (1019) that may enter them. Lastly, whilst sonorous undulations have been shown to pass round projecting obstacles, more or less freely ac- cording to the nature of the medium, so those of light are capa- ble off to a certain extent, passing round the edges of opaque bodies, and entering their shadow, as shown in the phenomena of inflection or diffraction (1120). 1023. Luminous undulations (or, in other words, light) are pro- pagated from the sun through space, and to the surface of our globe, with an enormous velocity, at the rate of about 191,515, or in round numbers, 192,000 miles per second ; and this motion is the same for light evolved from tne most distant fixed star, as for that from the nearest self-luminous body. This rate of propaga- tion of light was first diKcovered by Olof Boemer, a Danish astro- nomer, in the year 1676 when observing the occultation and emersion of the {- perty of intercepting the passage of light, and thus produce a shadow by obscuring the source from which the liuninous undu- lations proceed : these shadows in general present the same figure as the outlines of the intercepting bodies. Such bodies as permit light to pass frccl;^^ through tnem are termed transpareiU^ in oppo- sition to those which intercept it, constituting opaque substances; bodies that transmit light imperfectly ai*e termed trantlueent. LAW OF nrraxsiTT; photoxetzbs. 581 1025. Non-luminoTiB bodies become Inmiooiu in the presence of 8 sonrce of ligbt, either by reflecting the nndnlatoiy movements, or if phoephorescent, by having vibrations excited in the molecules of the boaj itself, which are thence communicated to the sarround- ing medinm. Thus, then, bodies are not rendered visible by any matter given off from a luminous source, and impinging upon them, but by the undulatory movements successively com- municated to contiguous particles, which reaching the illuminated body are dispeTsed in all directions from its irregular surface ; and thus the bodjr becomes itself a source of divergence of fresh luminous undulations. 1026. The intensity of the illumination of any body in the pre- sence of a given source of light depends upon its distance from Uiat source, and obe^s the general law of radiant forces, as attractions (31), the intennty of the light varying inveraely aa the Bquare of the dUtcmee of the^ luminous bodyjrom the source of light. Thus, if a single candle illuminate a boay to a certain extent at a dis- tance or a foot, it would recjuire the light of four candles at a dis- tance of two feet, and of nine at three feet, to produce equal illu- mination. This will be more readily understooa from the following experiment: — ^Having ruled a sheet of paper or pasteboard in squares of one inch, place a piece of card one inch square with a slender support, as a piece of wire, two feet from a screen with a small hole m it, and place a lamp or candle as close as possible behind the screen. If the ruled card be now held in the shadow of the small square, it will be found that at four feet from the screen, the shadow will occupy four squares, and at six feet, nine squares : and as the light received upon a surface of one square inch is thus shown to occupy four incnes in the first case, and nine in the second, it follows that each inch at the distance two, received only one-fourth of the li^ht, and at the distance three, one-ninth ; or, generally, the intensity of the light at any point is in- versely as the square of the distance of that point from its source. 1027. PhoUymeters. — ^It is often important to be able to compare the intensity of two sources of light, and for this purpose instru- ments termed photometers have been contrived. The instrument most frequently employed for this purpose is the photometer of Les- lie ; this consists of a rectangular treueh from six to ten feet long, at the open ends of which the two lights to be compared are placed. Two mirrors meeting at an edge, and each inclined at 45** to the axis of the trough, reflect tne two lights on to the a^fftcent portions of a translucent screen fas of thm white paper or ground glass), placed level with the surtace of the trough . The mirrors are moved along the trough, until die two portions of the screen are equally illuminated, when the ratio of the intensities of the two lights wul be found from that of the squares of their dis- tances from the middle of the screen. Another veiy convenient instrument is that contrived by Frof. Wheatstone, consisting of a 582 LIGHT. bead of Bilvered glass rapidly moving l>ackwards and forwards in a straight line, by means of a simpie and ingenious mechanical contrivance, — ^a wheel revolving within a fixed annular wheel (176) containing twice as manj teeth (184), and having a bright bead attached to its circumference : on the moving bead the two lights to be compared appear bj reflection as two luminous parallel lines. Then by altering the relative distances of the lights until the luminous lines appear to be of eoual intensity, and squaring these distances from the photometer, tne relative illuminating powers of the two sources of light may be readily discovered. Some approach to a comparative measurement may be obtained by ascertaining the distances at which any two sonrces of lights a-s two candles, require to be placed, to cast upon a wall shadows of a rod of wood or metal of equal intensity ; the squares of these numbers will be to each other in the ratio of the intensities of the light evolved from the two candles. The illuminating power of any source of light will of course not only depend upon tne inten- sity of its light, and its distance, but upon the extent or area of its luminous surface, thus, according to Dr. Wollaston, it would require 200,000 millions of such stars as Sinus, or 5563 wax candles at the distance of a foot^ to produce a light equal to that of the sun. 1028. If the Bur&ce or internal structure of a substance be snch as to be influenced alike by all the luminous undulations emanat* ing from a source of light, it will communicate to the eye the sensation of white light ; but if it be so constructed as to absorb all the luminous undulations which impinge upon it, it cannot become the source of a fresh set of analogous movements, and is said to be Hack. We know that in the .£olian harp the strings assume different states of vibration, and evolve corresponding sounds, when acted upon by a current of air, according to the diameter and tension of the chords (576); the more tense or thinner string evolving the higher, and less tense or thicker, the grayer note. In an analogous manner are the undulations arising from any source of light supposed to be affected by the physiau structures of bodies, by which some assume undulatory movements analogous to the tightly- stretched oord in the u£olian harp, and these communicate to the eye the sensation of violet or purple light ; whilst the particles of other substances under sinular in- fluence, oscillate with a less degree of velocity, and these vibra- tions convey the idea of retly on reaching the eye. The rapidity of the undulatory movements assumed and propa^ted by colonred bodies immensely exceeds that of sonorous vibrations; thus, whilst to evolve red light, it has been calculated that a body must communicate about 45i3 millions of millions, and to evolve violet, not less than 699 millions of millions of undulations in a second, the middle C (570) is produced by only 522 vibrations in a second of time. It has also oeen calculated that if a string of the proper LUM1K0U8 CNDULiLTlONd. . 583 length to produce a sound when 'vibrating, corresponding to this miridle C, wero bisected 40 times, it would, supposing it were possible to make it vibrate, evolve not a sound, but a yeUotOMh green light : the vibrations of a chord increasing in rapiditj in proportion to the diminution of its length (576). Colours conse- quently are no more innate or abstract properties of bodies than any particular sounds or notes which they emit; the latter varying with the teusion, length, and thickness of the subiitances, and the former with certain, possibly analogous, modifications of physical structure. 1029. Undulations radiate in all directions from every portion of a luminous body (1022), but vary in their rapidity with the colour, of the substance. If a small hole be made, or, still better, if a convex lens of suitable focus be fixed in one end of a wooden box, blackened internally, and it be presented towards any object or landscape, an inverted image will be painted upon a piece of white paper, placed at the opposite end, and presenting the very same hues as the object of which it is the image. 1030. A ray of light on the undulatory hypothesis, is a wave propagated in a ri^ht line from the luminous body, and the undu- lations producing it are transverse to the course of the ray, which therefore must be considered as merely expressing the direction of an effect, namely, the motion producing the impression of light. When a ray of light falls upon the surface of any substance, it may undergo one or more of the following modifications : — A, it may be reflected back into the medium in which it was moving (1033) ; B, it may pass into the substance, and herefraeted (1052), still retaining ita original characters ; or C, it may be divided into two portions, each possessing distinct physical properties (Ch. XXI.) ; D, a ray may become coloured by having some of the undula- tions producing it absorbed; or £, it may excite a fresh set of undulations, and consequent ra} s, in the substance, thus rendering it visible (1113); F, it may also, by meeting with a second ray, have its intensity modified by their mutual interference (1116) ; or G, it may during its refraction, or reflection, or partial absorp- tion, acquire new properiies, characteristic of polarized light (Ch. XXI.); and lastly, H, it may have the rapidity of the undulations producing it so affected as to give rise to the various phenomena of fluorescence. 1031. When luminous rays proceed from a very distant body, as the sun, they may be regarded as parallel; when they are given off from a point, extending as tney proceed, they are termed divergent; and when they gradually approach each other, as when acted upon by a concave mirror, or convex lens, they are said to be convergent. 584 OATOFTRIGS. 4» O A ff -y' f ^ y 1 ir 1 s R 1082. Wlien parallel rays fall upon a plane Borface, tbe illami- nation Tarics with tbe angle at which thej meet the surface, being greatest when they fall perpendicularly upon it : let tbe paralM rays, o, 6, c, d^, e,/, Fig. 660, fall perpenoicularly upon a surface, o p, then it is obvious tbey will all be effectual in illuminating it; but if the surface be in> clined, as pb, fewer rays will impinge upon it, and it will be proportionably less illuminated. Draw B 8 perpendicular to /p, then, since the illumination of the sur&ce is proportional to the number of rays falling on it, Illumination of p b : that of op:: B8:(ops)pr:: cos p b s : 1. The angle p bs is evidently equal to tbe angle of incidence (296) of the rays : hence for a given intensity of light, lUumination a cos angle of incidence; and it follows from this, and from 1026, that generally JU *«/rf • dbeolute intensity x cot angle of incidence (distance of source)* 1033. Whenever a ray of light falls upon a polished sur&oe capable of reflecting it, it obeys the same law as that of the oblique impact of a perfectly elastic body (296), the angles of inci- dence and reflection being equal. Thus, let a b. Fig. 561, be the jiy^, Ml. surface of a plane mirror, and d c the direction of a ray incidient upon it at the point c ; draw the normal to that point, c p, and o b, forming the angle p c s, equal to the angle PCD, then will the ray be reflected in the direction ce: pcd being the angle of incidence, and p c ■ that of reflection. If, instead of the ray being incident on a plane, it had encountered a curved surface, it would have obeyed tne same law, being reflected from a point in the surface, as from the plane, which is a tangent to the curve at that point. Thus, if the nj D c were incident upon tbe concave surface, a 6, or the convex one, A.' b', it would still DO reflected from c in the same manner as if it were incident upon a c b, a tangent to either curve at c. The lines, D c, p c, and e c, or the directions of the incident and re- flected rays, and the normal to the point of incidence, will always be in the same plane. 1034. A considerable proportion of the luminous undulations are absorbed or transmitted on impinging upon the reflecting sur&ces of transparent bodies, consequently the intensity of the reflected is never equal to that of the incident ray ; this loss increases as LAWS OF SEFLBCTIOH. 585 the obliquity of incidence is diminished. M. Bou^r has pven the following table of the number of rays reflected at difierent anzles from the surfaces of water, and of glass, the number of incident rajrs being supposed to be 1000 : — • Incidence. 85° 80 75 Water. Glau . Incidence. Water. Gkn. 501 333 211 549 412 299 40° 20 10 22 18 18 34 25 25 Even when reflected from the surfaces of the most perfectly polished metallic mirrorSj much light is lost ; thus, from the surface of mercury at an angle of incidence of 78" 5', only 754 rays out of 1000 are reflecte£ When the reflector is diaphanous, as a elass plate, more li^ht is reflected from the second than from the first surface, and this proportion is increased by coating the back with some resinous cement, or still better, with metallic amalgam ; the vividity of the reflection from the second surface then com- pletely echpses that frt>m the first: thus, in the common looking- glass, the bright images seen in it are reflections from the second or coated sunace. 1035. Any substance pomessing some regular form, and suffi- ciently polished to reflect light, is termed a tpecvlum or mirror. These are made of various materials, as of polished metal, or of glass, covered at the back with an amalgam of tin, or with silver precipitated in a metallic state from a solution. Mirrors are made in various forms, of which, the plane consists of a level reflecting surface ; the concave presents a hollow surface like the inside, and the convex, a projecting superficies like the exterior of a watch-glass. Besides these, mirrors have been constructed in the form of the curves called conic sections, the parabola, ellipse, and hyperbola. 1036. Bays of light incident upon the surface of a plane, mirror, as a looking-glass, always retain their relative rectilinear direc- tions after reflection. Let ab, Fig. 562, be the surface of a plane polished mirror, and cxj i>y, be parallel rays incident upon its snrface, thev will be re- flected in tne direction y df accord Fig. 682. xc, or ing to the law already mentioned (1033). Di- verging rays proceed- ing from E will, after incidence, continue to diverge in the directions e, e, 6, and converg- ing rays, as f, f, f, will continue to converge after being reflected Tram A B towanla ihs point a : the pninta orronverp>ncii orAirr- gence of tlie incidcDt ind reOecleil ravs lieiiig at equal and oft- ]>oait« distancea frum the mirror. In all thcM caae*. u obJKU itpp^ar to ihe eye Ui be aitualo in the ilireotiMi of (lie tavi wUch ovedtiially reach that organ, to npeclaton placed ai e o^ e < e, atid O, the rajTB C n, i, and err, vill appear lo haie come frooi bt- hind the mirror, ad, in the direction of the ilotled linea, c', d'; %' ; f", r', f". tU37. Ab all bodies became, nndrr certain cin:uiiiitaiic«c, lbs BOurce of luminouB tindulatioua proci'eiling from erer/ pnint of llieir Burfftce, it follows, that anj object [Isced at en. Fig. 3^3, will appear to a spectator at ed, to be in the direction etf, df', as the ra^B eTolred from the object will, afler reSectioD from a b. proceed in the iJireclione xe, yd, and conwtjuentl^ appear to tbe obnerror to haro been given otT from some object aitnatcd at c*, r>', us far behind A a ai c ii is before it. ThiB repnaeDtalion of ihr object BO vividly prpsenled to the eje ia tenued an imapr, and precisely reiembleB the real object, to which it owea ila origia. 103S. When two plane miiron are placed parallel to each other. and any object ia utuated between them, a long aeriea of imagei n-lll be Been in each mirror, from the object and ita image in one being reflected by the other, and so on, nntil then figurea appear BO remote aB to become inrisible. If the two reflecting maifaeri be inclined towards eacb other at any angle, the imagea of an oK ject placed between them will appear to lie in the cireiimfeniKv of a circle of which the mirrors reproent the radii. Tlia i* tlie S-inciple of the well-known kaleiduscope inrented by Sir DaTid rewster: in Ibis elegiknt iostrumsnt, the imagei of Ike otgcctt placed between the reBectura ara seen most beautifully airanf^ when the latter form an angle which is an aliquot pait et 180' ; the number of images formed, including the object, will tben be equal to 360° divided by that angle. Thiu, if tlie angle betwere the mirrors be 60°, the images of the object will appear arrangrd in a circle, and a heiagonal figure will be produced. 1039. Wheu an assemblage of rayi called a pencil of licht hit* j^^ B83_ on the surface of a mrred airrcr, _ each lay of ibe pencil ia relet ltd I from the point vf the miner ea I I whichitfallB,predaeIjaaitwnaU I have been from a tuig«nt pUnr. I or flat sni&ce looching tb* I mirror at that point (913)1 Ltl " "' diTcrging fhiBi 563, he incidFEt pberical anibn , A B, of which o i* tW t c^ the centre of the carratBra of ■, which ia called Uie axit of the t pencil of rays diTcrging fhiai ■be point p. Fig. 563, he ini' - in the concave apberical ai FOCUS OF A REFLECTED PENCIL. 587 pencil. The line o c joining the centre of the mirror and its centre of curvature is called the cucis of the mirror ; and when, a8 in this case, the axis of the incident pencil coincides with the axis of the mirror, the incident is said to he direct^ other- wise it is called oblique. Join a p, a c, and draw a q such, that the angle caq^scap; then, since ao is perpendicular to the mim)r at a, a q is the reflected ray corresponding to that incident on A from p. Take any other point, d near to o, and find as before the reflected ray d/; also take o p = } o c. Wherever d may be, between a and o, / is always nearer to c than q, and when d is indefinitely near to o, then / is called the GeometriccU focus of the pencil. Let p o=v, co=r, and/o«v; then, because the angles p a o, G A Q are equal (End., vi. 3), p a : a q : : p c : c q ; and, ultimately, when d moves up to o, p o : o/: : p c : o/, or u:t>: :»— r:r— 1?, whence tt(r—»)«»» (« — r) ; dividing this equation by ut7r, we obtain = , whence — + - = — ; [a] from which v may be found, when u and r are given. The same expression will be obtained if / be the focus of inci- dent, and p the geometrical focus of the reflected rays, conse<^uently the points p,/, are reciprocal, and are called conjugate foci. 1040. When the point p is removed to an infinite distance from o, or in other words, when the incident rays are parallel, then — =0, and [a] becomes — = — , or t? = — - : in this case, the point /'becomes the principal focus^ r ; and o f, which may be called /, is the focal ^ ^^ length of the mirror. Thus a pencil of ^- *^ parallel rays, d, «,/ ^, A, Fig. 664, will, after reflection, converge to the prin- cipal focus, f, midway between o and ■ : and, conversely, a diverging pencil incident on the mirror, from f, will, after reflection, form a parallel pencil d efg h, 12.. Since -t= — , substituting this value in [a] we obtain U V f that 18, ike 9um of the reciprocals of any pair of conmgaie focal distances is equal to the reciproad of the focal length of a mirror. It is obyious that as the luminous undulations constituting the T*^ d, t,f, g, \, will be raflected lowtrds r, Bad, kniriBS si tkat point will c&nae >d accmniiUtian of motion correspoodiiiK to tbe united force of bU the nndnlationi propagated from tbe Rflectne ■nrface. On tbii Bocount bII the light uid heat belonging to Ibf incident rsji will become concenlnlcd at p, and InmiaoeB and oalorific eSecla of oorreapoDding intenntj will be eiched ea bb* bod; placed at that ptnnt ; thii point wbb hence oTiginaDr tuiaid the foeui, at fatflaee of Ibe minor, a e b, for the puBlkl aoUr raye. IMI. If the radiBOt point be placed neanr the m ' — -"■ ^ orincipai fonu, the raja will be reflected, not pua feni, Bs tbough thej were eiolred from Kune point pUoe4 be- ind the mirror : and, oonveraely, ' ' ' principal fonu, the raja will be reflected, not pualU bat ^m- s thoUL' ■' _ . . - . ^ ■--_.. ... sraelj, when oDtnvTRing ts^ii ■ cident on a concave minor, Ihej will be reBccted to a (Wirer tbe mirror than the pnnoipal fbcni, r; the rerwae eequentlj of divetsing nj«. These raja mnat be aaiiiinii converge towards aoms point aitoated behind the mb tbej an acted open in a manner oppoaite to that in which tkej were bj a codcbts reOectiiiR Bsr- '*■'•*- face ; for whilit a coocave rdtector •i^r leMsoi the diTergencj, and iu- / I' creBee* tbe conTeigencj, of bH ji y „-^ incident reje, a convei ooe in- .■■\i ~^ " cTOBMi their dirergencj. Bad di- " A tniniahea their connrgencj. TliBa, "slreyi, a,i,e,d, a, be iB- — e if parallel n _rf cident on th ^^ of which c ii the eentie of tnm- tnre, the; will be reOected accrad- ingto the general law (1033), in the direction! r a" r f , r ^, r c', •« if tfaej had proceeded from s point, r, placed behind tfae mimr. which thni becomee the wrtaal, or m^w focai of the icBected _ nm. Tbe/oeoldutneee,/, Rr '^■'^ p^mOlel IB j» U ooe half of 4e and r ii alwaji ntnatad b^iad fledor, p ia'belrae it (1039V la tk caee of diTerging nj*, tbe focal distance will be leaa, and far c»- Terging rare greater, thu/. 1043. When a pencil of raj* i> incident npon a cnmd rcAectiv. thej, after reflection, mntnallj interaeet each other, and tbiK pointa of interaectiDn constitute a cnrred line, tetnted b tmmtic. FORMATION OF I1CA6B8. 689 ^.667. Let the rap p a, p b, &c., be incident from p on the mirror a o, and let A a, B 0, &c.| be the corresponding reflected rays ; it is evident to the eve that the reflected rays are accumulated in the neigh- bourhooo of the curved line, or caustic, in which their socces- sive intersections take place, which locality will therefore be more highly illuminated than the ad- jacent parts. To exhibit this caustic curve by reflection, nearly fill a glass tumbler with milk, or fit . a circular piece of card into it about half an inch from the top, and, exposing the con- cavitT of the glaiis to the sun or a candle, then a brilliant double curve, represented in Fig. 567, wiU be seen on the surface of the milk, or paper. A rim about an inch wide, cut from a cvlindrical glass shade six or eight incnes in diameter, silvered on the outside and laid on a sheet of white paper, answers exceedingly well for this experiment 1044. Images are formed by spherical mirrors in the same man- ner as by plane ones (1037), but difler from those produced by the latter instruments, in being of a different size Irom the object. Thus, if rays be supposed to emanate from a distant body, they will, on being incident on the concave mirror, a b, Fig. 668, of which c is the centre of curvature, be reflected to a focus at f, a little beyond the principal focus (1040), and there produce an image of the object E D, diminished in size, and inverted in position, because the axis of the pencil of rays from e being above the axis of the mirror, the axis of the reflected pencil will lie below it, and vice versa with regard to the rays from d. The image p will be extremely Tjvid from its being illuminated by all ihe luminous rays in- cident from this object on the mirror. The magnitude of the image p will be found to bear the same relation toED as the dis- tance of p from the mirror does to that of the object from it. If an object be placed at p, its image will be depicted on a screen placed at e d, diflused over a large space, and consequently mag- nified. 1045. In the case of convex mirrors, the images are in an erect position, much diminished in size, and behind the reflecting sur- face as in the plane mirrors. For if an object d b. Fig. 669, bo phiced before a convex mirror a b, of which the negative focus 18 at F, the luminous rays will, after incidence on a b, be reflected diverging ; and being seen by a spectator at h, they will appear Fiff. 668. inwpnKAe^gfram>nobi«et, dc,behiDd the mirror, and ooc- 'ablysiiullertbuiDB,of whicbit IB me:«]jft dimiaiHlml ima^. The ini«ge !n spheric*! mimn u ^- ^- always distorted ; that of a itnii^i boe beiDg one of the conic Kctiona. Jepead- ■ iog on iti distance from the mimr.* 1046. Tbea6erra(io«oratiyt«aect(d is the d tncal foctu of tlie pcDcil, and the piiiit wbere the reflected ray interaecta the aiisi thus in Fig. 563, q f ik the aber- ratiim of Ibe reSecled lay, a q : and the o&crraltoH of a pencQ ie hitherto contidered oolj direct reflection (1039), ^flection be ohllqoe, the axis of the pencil not coin- that of the mirror, the condition of the reflection ar« ifferaot from those alrevir deturmined; there is no cat point, bnt, in place of it, tva/o«oI iinet separated iterral, and at tight aogles to each other, to which rajB cODTerge. > eipUin the fonnation oT these Tocal IIdsb, letoQ, the axia of a pencil iacidrnt directly on a spherical face. If this pencil be made ap of n series oi^ conical aja having 04 as their commDn axis, sioce all the 1 surCice vill be similarlj reflected about OQ, the f the re- ^ i-ill rorm a Dical ■ 7,a,ii uca the 1:0 (1043).' If, instead of taking the whole pencil, we . portion ofit on]]' which is incident on an aanulos of Z sat-fBce that would be generated h; the revolntioD o Q, we must have, cortesponding to this, an annulot ic snKace, tlirough >ame point of which each ray of hell ofllie reflected rafs passeii. Ifuc lie small, this la oauatio surface may be considered a circle, q^ t, in «ndiciilar tooq, and to the plane of the paper. if the entire conical shell of light, if we now consider portioD of it, adjacent to H >, ne arrive at the case liqoje reflected pencil, of which the axis is a o, g,; and ra; will pass through SDme point in a Email circular . to q,, which maj be considered approximately a perpendicnlar to the plane of the paper ; this lice is imary focal iine, am) the paint j, the primary foeKt. :tion of the reflected pencil by a phme tbroiigh g, plane touching the SDriace of the mirror at x, though :ry elongaled li^nre of 6, resembling a. Fig, 6T1, may ai a straight line, and is called the lecondary focal le point, q^ in which the axis of the reSecU^d peneil alkd the leconJiiru fociu : also the plane <)oa, or the Faper, is calle.l the primari) plane. Hence a small after reflection conTergea lo, or diTorgas Iroiu, two al lines, one of which lies in the primary plane, and perpendicular to it. 593 Whan tho abeimtion of ddErect pi ._ , . potitivt, the primir; tocat of a small olitique pancil, froni the ume origEn, ii neaivr io tha iiarfiice than iha Bocondarj focus, as in Fig. 571 ; bnt the contrary, vrhen from the suriaca, or lugativt. 1049. If a aectioD of the reflected psDcil be mnd« b; a plan* parallel to thn tangent plane to the reflecting sorface at a, that ■action haa been explained to be a straight line perpendicular to the primary plana, when the plana paaaea through q^. If lbs CDe be new Boppoeed to move parallel to itnlf from q, to q^ tbs adth or the Heclion gradually increases in the primary plane, and decrvaaea in the perpeodicular direction, until at g, the sec- tion becomes a straight Ime in tho primary plane : at aome point, therefore, between q, and q„ the two ditnenBions of the section are eqnal, and the section very nearly circular ; this particular section of the reflected pencil ii called tho circU of leiat eon/uuxi, and exhibits tho amsUent spare through which all the rays of the pencil pass. It is fo called, because, when an im^e of an object IS formed by reflection from a spherical surftce (1IM4, 6), the reSscled pencils from two adjacent points of the object will at that point urerlap each other aa little aa poaaible, and will them- fore create the least posaible amount ofcoufuaion in the image. 1050. A glance at Fip. 566 will readily point ontthat there is a very largo amount of aberration in concave spherical mimra of large angular aperture; hence, when the amount of light required to be reflected is considerable, and consequently a lai^ apertara IS indispensable, it becomes necessary to alter the eamture, or figure, as it is termed, of the mirror, in order to diminiah the aberration. It is a wellknown property o( the conic acctiDns, that lines ioining the foci and any point of the curre, make eqnal angles with the tangent at that point: consequently, by the law of reflection ^1033^, if the surraca of a mirror be farmed by tha reTolution ofa conic section about its axis, a pencil of raya inci- dent upon its surface from either focus, will, after reflection, ooo- verge to, or diverge from, the other focus, aa the case may be. It follows from (lie ordinary pruperlics of ihe curve, that if tba form of tho mirror be a parabola, as p. Fig. 572, a pencil of parallel rays, a, b, e, &c., will converge to the focua y, aud coiktarsely, a OOBBEOnOV OF SPHERICAL 0UBYB8. 593 pencil incident from p will be reflected parallel. Mirrors of this form are made use of in reflecting telescopes, and in lightlionses, in the former the incident^ and in the latter the reflected, is the parallel pencil. If a large pencil of diverging rays be required to converee accn- rately to a focus, an elliptic mirror, b, is requisite, in which all the rays of a pencil incident from either focus on the mirror will be reflected to the other focus. Elliptic mirrors have been made nse of by Prof. Amici and others, in the construction of compound microscopes, and by the writer in his self-registering magnetic apparatus (624). If a^ hyperbolic figure, H, be given to the mirror, a pencil of rays, diverging from f, and incident upon the conyez surface of the branch a, or upon the concave surmce of 6, will, after reflec- tion, divei^e from Fy A concave hyperbolic mirror is usefiil for accumulating light m a divergent pencil, for the pencil diverging after reflection from 6, evidently contains the light due to a much larger angle, than if it had proceeded direct^ from the same source placed at f^ ; always excepting the amount of light lost by reflection n034). 1051. It either of these curves be compared with the circle of curvature at the centre of the surface, o, it will be found that the curve lies without the circle, except just at the point of contact ; hence a spherical mirror requires to oe flattened out towards its periphery, or else to be deepened towards its centre, in order to dimmish its aberration. This, in the construction of specula for optical instruments, is in practice accomplished bj a method purely tentative : namely, in grinding a speculum, which is usually composed of an exceedingly hard, brittle, and colourless alloy of copper and tin in atomic proportions, a lateral and circular motion of the hand are so combined as to abrade most at the centre, or at the peripbeiy, at the will of the operator. In grinding and polishine the specula for telescopes oi large size, such as those of the Larl of Kosse, Mr. Lasseli, and others, these movements are mechanically accomplished by a due acyustment of circular and eccentric motions. In order to giye an idea of the extreme accuracy requisite in the curvature of these specula, it may be stated that m a speculum large enough for a five or six feet tele- scope, the definition of the image may be sensibly altered by the polisher in a few minutes, the quantity ot metal removed from the whole surface during that time not Ming an appreciable fraction of a grain. Accormng to Sir J. Herschel the utmost variation of a speculum, of four feet focus, from a spherical curve is less than -00005 inch. 1 052. A few years ago it was proposed by M. L. Foucault to con- struct the specula for telescopes of glass, and to render the curved surface reflective, bj^ depositing on it from a solution a coatinff^ of metallic silver ; which, when perfecUy dry^ obtains a high polish 594 DIOPTRICS. by a little gentle friction with clean wash-leather and finely levi- gated rouge. If the reflecting surface be tarnished or otherwise damaged, it may very easily be renewed without any xisk of altering the curvature of any part of the mirror. 1053. The process of silvenng ^lass specula is as follows : — P^pare three solutions, A, B, and G ; A. Ciystals of nitrate of silver ... 90 grains, 4 fluid ounces ; 1 ounce, 25 fluid ounces ; 4 an ounce, 5 fluid ounces. Distilled water B. Potassa, very pure . . Distilled water . . . G. Sugar of milk (powdered) Distilled water . . . The solution G must slways be fresh. To prepare a quantity sufficient for sUyering an 8-indi speculum : — Four 2 ounces of A into a ^lass vessel capable of holding 36 ounces. Add drop by drop (stirring constantly with a glaas rod) as much liquid ammonia as is just sufficient to dissolve the grej precipitate first thrown down : then add 4 ounces of B. The orown-black precipitate now formed must be just re-dissolved by the gradual addition, as before, of liauid ammonia. Add dis- tilled water to make up 15 ounces, and tnen drop by drop a little of A, until a grey precipitate, which is not rehdissolved by stirring for three minutes, is obtained ; then add 15 ounces move of distilled water, and allow the precipitate to subside. When the mirror is ready for immersion, add to the above pre- pared solution 2 ounces of G, and mix them thoroughly wiui a glass rod. The glass speculum must be cemented by pitch to a drcular block of wood attached to a ring by tiiree eaual strinss. The adhesion of the ^lass to the warmed surface of the pitcn will be promoted by moistening the glass with oil of tuipentine. The speculum may^ then be suspended face downwards in the fluid. Before immersion the surface should be thoroughly cleansed wiUi strong nitric acid, by means of a smiJl pad of cotton wool tightly inserted in the end of a bit of glass tube ; it should then be rinsed in common water, and finally with distilled water, and then placed in a shallow vessel of alcohol, while the silvering solution is being prepared. The process of silvering will be completed in from fifty to seventy minutes according to the temperature of the atmosphere. When the speculum is removed from the solution, it must be immediaUijf rinsed in plenty of water (as by letting a tap run over it), then with a little distilled water; and lastly, placed in an oblique position to drain off the water, and left to dry. When, dr^, it may be polished by a piece of very soft wash-leather and a httle fine rouge, with a circular motion progressing spirally firom the circumference to the centre. THB LAW OP SINES. 595 1054. So long aa a ray of light traverses a imiform medium, it continues its rectilinear path, which it also preserves when it is incident on a homogeneous diaphanous substance in a direction perpendicular to its surface. But if the ray be incident in an oblique direction, it is then more or less bent, or refracted^ out of its original course : this bendine, or refracticm, not being the same in eveiy substance, as is the direction of reflection (1033), but varyine considerably in different kinds of matter. Let a b, Fi^. 573, DO the surface of a reflecting medium, as water, of Jfj^.BTO. greater density than another medium, as air, above it ; draw c B D peipendicular to a b, and let PE be a ray incident on ab at b; a certain portion will be re- flected, the remainder will enter the medium, but instead of fol- lowing its original direction, B o, will be^ refracted or bent to- wards ed in the direction bk. The line pb will, therefore, represent the incident, and ex, the refracted ray ; f e o will be the angle ofincidencef and d b k the angle of refraction. Take Bf=Khj and draw the lines /c, h d, perpendicular to o d ; the former will be the sine of the angle p b c, and the latter that of the angle d e k ; the law of retraction, or, as it is usually called, the law of HneSy is that the sines of the angles of inddmce and refraction loiU always he to each other in a constant ratio for each refracting stthstance : and it is^ another law of ordinary refraction (bo called, in contradis- tinction to extraordinary remiction, which will be subsequently considered), that the refracted ray always lies in the same plane with the incident ray, and a normal to the common surface of the two media, at the point of incidence : the incident and refracted rays are moreover always on the opposite sides of the normal c d, and of the sur&ce a b. When^ a ray is incident on a refracting surface, bounded by curved lines, the same law obtains as when incident on a plane. For if A B were replaced by a concave or convex surface, as a 6, or of b'f the ray p b will follow the same course as if it impinged on the plane which is a tangent to the curve at the point of incidence. 1055. As the visibility of any two points is mutual, it follows that a ray of light, x e, passing from a denser refracting medium, ADB, as water, will, on reaching the surface, ab, of a rarer medium, as air, be refracted in the direction e p. In this case, as s B is the incident, and f b the refracted ray, the line/c, which is QQ 2 596 now tk« lina of Tefraction, ii ipeater thin the line dk,or troe of incidence, the reverse of the former om ; alee the rsj ■ r is r»- frtciedfrom tha normal or pet^ndiculat c c, in place of torarda it, aa in the fbrmer case. 1066. The relative poBitions of the incident and refracted rsyi may bo convenientlj iCustraled bv means of a moveaUe diagram. On a board. Fig. 574, take any three points, a, b, b, in the sane strught line, and to tbewpointt "S- O'*- Mladi moteably the eqoal rodi I A a, b/, ■ p, ■ ■, uid let /b be prolonged to b, ao that /a : b6 may be the repaired ratio of the sioea of incidence and re- fraction. Connect a K, rf,hj links (154) respectively eqiul li) 1 K, E B, and connect a b, by a link, when a a and n h are both vertical. Then it is evi- dent from the cons true tioa, that the distances of b and / from a vertical throngh b, are in the given ratio, and are in opposite directiors ; bnt fe is parallel to /b, and ei to ao, and the di>- lancei of a and b fmm verticals through A and B are approxi- mately equal, coowqucntly re and Kt, the distances of w and i from a vertical through b, will bo veiy nearly in the required mtio^ that is, in all positions, rx, be, will represent corresponding in- cident and refracted rays. Let the hoara be now covered with a sheet of paper, on which draw LorJEontal and vertical lines thronah the point E, and a circle with centre b and rsdios e f. Let the pap^becut ihrougUin the vertical line, CD, so that F/and a% may past through the slil, and EP,Fe, eh, tk, may appear in front of the paper, the remainder of the links being unseen, as ivpresanted by [he dotted lines. 1057. Let the my p b be lupposed to pass tlirongh a highly attenuated attnoapheiv, and let the ratio of /e: iJit, Fig. 57^ b« represented by fi, that is, fc-.d ■■3 H a called tl then the quantity fi |g ciUled tUv injtx of refraetiim, or rtfraetiee potetr, of the medium in which e e is the direction of the cor- responding refracted ray. The index of refraction varies oon- siderably in difierent media, being for chromate of lead 2 974, and for air 1000294, between which limits varions intennediale de- groosof refraction exist. It was ascertained by Newton, that in- flammable bodies in general possessed a higher refractive power than other substances ; on which account he made the bold aog- gestion, that the diamond, of which the re&sclive index is aboat 2-439, consisted of a combustible substance {" qni ut probabile est, substantia est unctuoaa, coagulata ;"*) a statement of which * KcwtoD. Optin, liT* da i«ll«ioii^i, te.. Inns, III). 11. pan S. Lat. red. S. darlia, LosdoD, 1718. INDICES OF BEFBACTIOH. 597 the correctness has heen amifly demonstrated bj the diBOOTery of the true chemical nature of the diamond. As a general law, the greater the specific gravity of a body, the more it refracts light passing through it ; to which the chief exception is found in the case of inflammable bodies pointed out by Newton : and if the ratio of /t* — 1 to the specific gravity of the body be taken to renresent its ab»olute refractive power^^ this class of substances will be found to possess a greater ahiolfUe refracting power than any other bodies. In the following table the indices of refrac- tion of severed substances, when a ray is incident upon them from a highly rarified medium, are contrasted with their absolute refractive powers : — Sotetaaoes. Taenum . . Hjdrogen . . Oxjieii ... Common air . Kiirogen . . Ammonia . . OarbonioMid . Chlorine . . Tibasheer . . IC9 • • • • Wat«r . . . Bthor (anlphc.) Alcohol . . . Hjdrochlorio ) aoid . . / Nitrle acid . . Sulphariti acid Flaoripar . . Alum. . . . Olive oU . . Index AbBolnte' of refract. > reir. pow*r. 1-000000 0-0000 1000138 8-0063 1-00027S 0*3790 1-000294 0-4628 I'CiOOSOO 0^4734 1*000386 0*4734 1*000140 0-4537 1000772 0*4813 1*111 ? 1309 P 1*336 0-7846 1*358 2-56IH) 1*872 1*0121 1*410 0*6614 1*410 0*0240 1*434 0*6124 1*434 0*3414 1*4«7 0-6&70 1*470 1-2607 Index Absolute Sabitancea. of refract. refr. power. Oil tarpentine 1-476 1*3510 Cantor oil . . 1*490 1*1480 Oil of doves . 1-536 l-3('90 Crown glaas . to . 1-526) 1-534 f 0-6260 Plate glaas . . 1*614) 1*632 f p to . Amber • . . 1*547 1*3664 QnarU . . . Flint glaas . . to . 1*646 0-6416 1*585) i*e«oj 0*7086 Oilofoaaaia . 1*641 1-7634 Bisulphide ofl carl>on . j 1*768 1*4200 Sapphire . . 1-794 0*5666 Garnet . . . 1*816 0-6423 Zircon . . . 1*061 0*0064 Sulphur . . . 2*143 2*20(10 Phosphorus 2*224 2-8867 Diamond . . 2-430 1*4566 On looking at this table, it will be found that the absolute re- fractive power of hydroeen exceeds that of all other bodies, in consequence of its Terr low specific gravity. These absolute re- fractive powers are calculatea on the supposition of the ultimate particles of all bodies being equally heavy. 1058. When the refractive power of any medium, on any ray entering it from a very attenuated medium, is required, it will be found from the above table; but when the di- rection of a ray passing from one medium to another is sought for, it may be found by dividing the index of refraction of die second medium by that of the first, and the quotient will give the ratio of the sine of incidence in the first medium to that of refraction in the second, or the index of refraction of a ray pais- * Ibid., prop. 10. 598 DIOPTRICS. ing from the former medium to the latter. Thus, if the index of re&action for a ray passing from water into plate-glass were re- quired, the index of reiraction of the former being 1*336, and of tue latter 1*642, it is found bj dividiu^ the latter by the former number, or Ulii = ri54, the required index of refraction. It appears from the experiments of the Rev. T. P. Dale and Dr. Gladslone* that the refractive index is in all substances found to be diminished with increase of temperature. 1059. Luminous undulations are propagated through media with a velocity varying with their refractive power ; the higher the refractive power of the medium, the slower the ray of light moves through it, the velocities through any two media bein^ in the in- verse ratio of the sines of refniction ; consequently, if during a given time a series of luminous undulations are propagated through a tube filled with air, of 100 feet iu length, a similar series in the same period of time will traverse but 75 feet, when the tube contains water. ^ 1060. From an inspection of the moveable diagram fie. 574, ▲ Bc being a rarer, and abd a denser medium, we see that fo, the sine of the incident, is always greater than x d^ the sine of the refracted ray ; and if the ray p e be made incident at so great an obliquity that its sine would nearly correspond to radins, and, consequently, that the luminous ray could only graze the surface of the medium a e b d. still a considerable portion of the light would reaUy enter and be refracted. The converse of this propo- sition is extremely remarkable: for if ke be a ray paasing through the dense medium, a db, into a rare one, acb, the sine of retraction will exceed that of incidence (1055). When ke is incident on a b at a greater angle than that at which the sine of the refracted ray would be equal to radius, the refraction of the ray becomes impossible, and instead of entering the rarer medium, it is reflected back again from the internal surface of the denser, in obedience to the ordinary law of reflection (1033). This sudden substitution of reflection for refraction is consistent with analysis, and afibrds the only instance of totcU reflection with which we are acquainted ; for if the ray be incident in a dense medium on the suri'ace of a rarer one at a sufficient obliquity, it is totally re- flected, no light bein^ lost, except from a few undulations lieing absorbed bpr the medium itself. The angle of incidence at and beyond which this internal reflection occurs, is termed the limit- ing angle between refraction and reflection. This limiting an(de may be found by dividing unity by the index of refraction of uie substance ; and on looking for the quotient in a table of natural sines, the angle corresponding to it is the limiting angle. Thus, a ray cannot pass from water into a rare medium if the angle of inci- dence exceed 43** 27*, for , ^^,. =8ine of that angle: nor can a • Phil. Trans. 1858. UVUBUAL BEFKACnOX. 699 ray pus from flint glass into tlie same, if the angle exceed 88^ 41', for JL » 0*625, the sine of that angle. The briUiancj of the light thus reflected far exceeds that reflected from the best metaluc mirrors. This may he readily shown by nearly filling a wine-glass with water, and holding it^ np, so that the sorface of the fluid may be seen from beneath : it wiU appear like a sheet of bamished silyer, from the perfect reflection of the incident light, and no object held above it will be yisible if the position of the eye be beyond the limiting anele. 1061. When an object is yiewed throogh two or more strata of different refractive powers, very curions results follow. This may be often observed when an object, situated at or near the horizon, is so far distant, that, in consequence of the curvature of the earth, a right line could not connect it with the eye of the spec- tator: it will be invinble except under some remarkable states of the atmosphere, giving rise to the phenomena of unuautd re- fracHon, For tiie production of these e£kcts, it is necessary that the strata of atmosphere near the earth should differ considerably in refractive power, either by one portion being more loaded with vapours, or possessing a lower temperature than the other ; so that, by the great degree of refraction to which some rays passing from the distant object are submitted, they reach the eye in curved lines, and the spectator sees an image of the object in the air, in the direction of a tangent to these curved lines ; other rays from the olject may be reflected at the common surface of two strata of unequal density, and produce an inverted image. Phenomena of this xind, constituting the mirage, or fata moraana of the Italians, are occasionally seen in great splendour in the Straits of Messina. Lithe north of £urope, and in several parts of Great Britain, the mirage has been frequently observed, and is by no means of very rare occurrence on the English coast, in the evenings of hot autumnal days. Borne of the conditions for the production of the mirage may be obflnred by regarding a' small object through ^ ... the point of mixture of two fluids of different '^' densities, as syrup or alcohol, and water, when images will be seen on a plane higher, and in an inverted direction, with regard to the original object. The same effect may be ob- aerved by looking at an object across a red- hot iron, as in fig. 675, or over a charcoal chauffer ; or still better, on a cool day, by re- garding a distant wall, or tree, over the lioiler of a steam-carriase : tne wall or tree will ap- pear to be divided into several portions, and surmounted by inverted images visible for a considerable space above the source of heat. 600 DIOPTRICS. 1062. The transition from partial to total reflection may be beautifully seen in an experiment described by Newton.* Hold an equiangular prism, in the ^•*^*' position shown m Fig. 676, ^^ before an open window, m such ^S^^ ^x^*N^ a manner that a line drawn Nw A.y^^ ^\w» froni the eye may describe an angle of about 40' with the base of the prism. The base A B D o, Fig. 576, will appear to be traversed by a curvod iris, YT, of a bluish yiolet coloiy, the space between t t and A c appearing of a sombie hue, in which reflection is ex- -^j^ treraely imperfect; but beyond y T incloding the space y B D T, the whole will appear shining with a metallic splendour, the clouds and surrounding objects bein^ depicted upon it with great bril- liancy. The ins y y thus divides the space between partial mid total reflection. 1063. If a ray of light be incident perpendicularly upon tiie surface of a refracting medium, bounded by plane parallel sidesy as a plate of glass, it will undergo no disturbance ; if in any other direction, it will be Te> ^. 677. fracted according to the l&wi already detailed. Thus, if a b. Fig. 577, be incident on such a medium as a plate of glaaSi c n. it will undergo refraction, and emerge on the opposite side, in a direction paraUelto the incident ray; oecause it will be refracted exactly as much from the normal, on leaving the ghiss, as it was towarae that line, on entering i.^ • -J * ^1. .« i^ « **• If diverging rays, as EPo, be incident, they will, after refraction, emeree fiom cD pandlel to their former directions, their divergence being the same, but taking place fix)m a point nearer to the glass than before ; and if converpng rays, as k l m, be incident on c d, and converging to o. they will, after emerging from the medium, really converee to p. at a greater distance from the class than q. 1064. A Pritm is a wedge-shaped portion of a refracting ioe> dium, having two plane surfaces meeting at an edge. Prisms an usuaUy made of glass for optical purposes, with their sides At * Opkioe, Mpra otfa<. lib. ii exp. 16, p. l». REFRACnOH AT A BPHBRICAL SURFACE. 601 varioiis angles of inclination, arc, Fig. 578, represents one of which the sides are inclined to each other at angles of 60* ; c a, are termed the refracting sides, and a r, the hase, of the CR pnsm. If a ray of lieht, d e, he incident on the side c a, it will Die refracted towards toe base if the prism be denser, and towards its apex if rarer, than '/. the surrounding medium. ^' Let the prism be of glass, and draw gel perpen- dicular to Ao; nie ray DB, on entering the prism, will be refracted towards the perpendicu- lar OBL, and conse- quently towards its base, A B|^ in a direction e f : which at one particular angle of incidence will be parallel to the base A r, as in the figure. On emerging from the prism at f, the ray will be refracted from the normal to the point f, in a direction fh, and will conse- quently deviate still further from its original direction. Hence, in riewing ohjects through a prism, they always appear to be higher or lower than they really are : for, if an object be placed at D, it will appear^ to a person stationed at h to be at d, be- cause the ray h f, if produced, will reach d, and objecti attoays appear to he tUuaied in the direction of the ray a which eventuauy reach the we (1036). 1065. When refraction takes place at a curved surface, it is said to be direct, as in reflection (1039), when the axis of the pencil is a normal to the surface ; otherwise the refraction is said to be oblique. In order to find the geometrical focus of a pencil of rays after direct refraction at a spherical surfiMe, let p, Fig. 579, be the origin of a pencil of light m- j^ ^^ cident directly on a sphen- cal refracting surface, or, of which o is the centre, and OB the radius; then o p is the axis of the re- fracted pencil. Let p r be any ray incident on o r at B and reflected in a direction which cuts o p in 0 ; i reflection) be the geometrical focus, or the when R is indefinitely near to o. Let opi^tf, op=v, oc=r, lines being considered positive, when measured from o in a direc- tion contrary to that of the incident pencil ; ft, the index of re- fraction of the medium 0 R. and let f (as position of q 602 DIOFTBIOB. Now ii=-t , by the definition (1067), ^sinpRC , BinBC^ ^^^^ ^^^ ^^^ Rc^are identical. sinRCP Bin^BC PC B g } because two sides of a triangle are aa the "bp eg' I 8™" of the angles they subtend ; but ultimately b p, b g, c g become o p, o f, c p respectiTely, and therefore! in the limit, PC op_tt— r V '*""op cf"" u v—r whence M (l - ^) = 1 - ^. or M (J- ^) ■= — i : It 1 li— 1 r* t and by transposing, ^ "" « " r~ * '•"^ which determines the position of f. When the incident rays are parallel, o p is infinite, and conae- quently - = o, and calling/the focal length, as in reflection (1040), u we obtain fix)m [a], /= — ~ r, which eives the distance of the principal focus from o. It will sometimes be found convenient to express the relation of the foci of inddenoe and refraction in terms of their distances from the centre of curvature of the refracting surface : for this purpose let cp^p, and cw=q] lines being considered poriUve that are measured from o in a direction contrary to that of Uie incident pencil. We obtain, as before, _po ^ OF_ p '^~op 0F*~2?— r q ' and by proceeding as before we obtain q p r from which Hm dtetaaoe of f from o is detennined. Hie ipheiical aberration of the extreme refracted ray may be detennined by the same means as in reflection (1047), and may be shown to be propoitional to the square of the aperture of tbe r^ fracting surface : and the last circle of aberration has the same position and magnitude as in a reflected pencil (1048). 1066. The observations that have alraady been made (1049), concerning oblique reflection at a spherical surfitoe, and the fonna- tion and position of the two focal lines, will in all inspects ap^y, mutatis tnutandUt to the case of oblique refraction at a sphen<^ sur&ce : and the same values may be obtained for the magnitude FOBMS OF LBHSEB. 603 and position of the circle of least confagion (1049): it is situated midway between the two focal lines when the angle of the pencil iM smaU. 1067. Caustic carves are formed by the intersection of refracted rays, in the same manner as in reflection (1043). They may be seen by holding a glass sphere, or globe foil of water, near the candle, and allowing the refracted rays to fall, after passing throagh the sphere, on a sheet of paper held nearly parallel to the horizontal axis of the sphere ; a luminous figure, hounded by two sharp curres, will be obserred, meetiugatthe point corresponding to the focus of the sphere. These curves may be more distinctly seen by covering a cylindrical glass vessel with black paper to within about an mch of the top ; pour water into this vessel, until it rises half an inch above the level of the paper. Cut a piece of white card, so that when placed at the level of the blacK paper, and perpendicular to the axis of the vessel, it may half surround the glasis ; then hold the latter up to the sun, or before a candle, with the card away from the source of light. The luminous ravs passing through tne water will be refracted to a focus on tne card : and a triangular luminous figure, bounded by caustic curves, will be depicted upon it. The formation of a caustic curve bv one refraction may be ob- served in the same cylindrical vessel, by rendering the contained fluid very slightiy turbid by a few drops of milk : on allowing the li^ht to enter two or three inches of the depth of the fluid, and viewing it in a vertical direction, the caustic curve will be seen in the flmd, the light bein^ reflected by the diffused milk-globules. 1068. Lenses for optical purposes are generally constructed of glass, but certain transparent minerals, of various kinds, have occasionally been used for this purpose. Sections of the principal kinds of lenses are shown in Fig. 580 ; and, if these be supposed to FSg. 680. reTolve round the axis a a, each will describe the particular lens of ^ ^ ^ -J"^ J J^ which it is tiie section. /\ (\\7 \\\\ \\\\ The tpherical lens, c, is a simple \~/\Ji\\7/\ j/Jj sphere, as its name implies ; the v £-i^ /J double convex lene, d, is bounded by two convex surfaces, concave towards each other; the double eoncave, e, has both its surfaces concave, their convexities being opposed to each other ; these two lenses may have both their sur- faces of unequal, or of equal curvature. A plano-convex lens, f, is merely half a double convex, one surface being plane, the other curved, as in the latter. A plano-concavCf o, is a lens having one gnrCace plane, and the other concave. The lens h, termed a meniscus, has one surface concave, and the other convex, and these curved surfaces meet if continued, since the convex surface has a greater curvature than the concave ; whilst the concavo- 604 DIOPTRICS. convex lens, i, bas similar surfaces, but they do not meet if pro- duced, as the conyei bas a 2tf«Mr curvature than the concave sorfaoe. 1069. The course of a ray refracted through a spherical lens may be readily understood ; let ▲ b d c be a sphere, of which the jf. ^. index of refraction is ii, and let -^^ ***• the rays e, k, o, be incident upon it : the ray h, being inci- dent perpendicular to the sphe- rical surface, will pass throuch without refraction (1054). To find the course of the ray k, draw the normal at a, k a s, and draw the line a c such that si]iCA8:8inKAE::l:/c; the ray a o is thus bent towards the normal k s. On reaching c, the ray will emerge into a rarer medium, and will again suffer refraction, being now bent from a line k o s peipendicnlar to the surface at c, at such an angle that sin l c s : sin m cf : : 1 : ^. By a similar process, the course of the ray o may be found. The three rays will tnus meet at f, which is the joeus of the refracted pencil. 1070. In order to detennine the position of the geometrical focus of a pencil of light refracted through a sphere, let p be the distance of the focus of incident rays from the centre of a sphere, and o,, 9, the distances from the same point of the foci of refracted pencils after the first and second refractions respectively, and r the radius of the sphere : then as in (1065), 1 ift tt— 1 r , -C =-C — , [a] and from refr'action at the second surface, if the coarse of the pencil be supposed reversed, therefore[a]-r5], i!^-^=-.2-^, or 1-1= -2^5^^ whence the geometrical focus of the emergent pencil may be found. If the incident pencil consist of parflJlel rays, p is infinite, and q becomes/, the/oooZ length of the sphere ; then we have -. = .. 2 - — t And consequently = ->' If the sphere be of glass, ft may be taken to be nearly 1*6 (1057): con«Kine»tly, /= -^^f= "jiIfs'"' "''^ " •"• The principal focus of a glass sphere will consequently be at the distance of half the radius from its surface: ^e negative sign means that the focal distance must be measured from the FORMULA FOB FOCAL LBHOTH8. 605 centre of the sphere, in a direction opposite to that of tho focns of the incident pencil. The course of the refracted rays, and conseqnentlj the position of the focus F, will vary according to the refractive power of the substance of which the lens is constructed. Thus, Sir David Brewster* has shown, that in a sphere of Tabasheer, one inch in diameter, of which the refractive index is 1*11145, the focal dis- tance for parallel ra^ will be four feet from the lens ; in one of ^lass of a refractive index of 1*5, it will be but half an inch ; au'l in one of zircon, of which the refriu:tive index is 2*0, it will coincide with the surface of the sphere. The following rule results from the above formula : to find the focal distance of a sphere from its centre, divide the index of refrctction of the material of which it is eowitntcted, by twice its excess above unity, and the quotient will be the distance expressed in radii of the sphere, 1071. The course of a ray through a double convex lens may be found in the same manner as that already explained in the case of a sphere (1069). Let the ^, 582. lens AB, Fijj. 582, be of the ,fS. y^ same material as the sphere, ^^^o^o^ and B, H, Q, three rays entering v— — — a^<*^ it ; K will pass on and emerge without refraction. The ray, b, will, on entering the lens, be refracted towards the normal ^ ^ K o B : and on emerging from c " y^^Y^' into a rarer medium, it will be y^ \ again refracted, but in a contrary directiuo, or from tne line sou, a normal to the point of emergence. By a similar process, the course of the ra^ o may be ascertained ; b, k, o will thus be found to meet at f, which is the focus of the lens. Supposing the incident rays b, k, o, to be parallel, and there- fore F to be the principal focus of the lens a b, if the rays inci- dent on the lens oe converoentj the focus will be nearer the surface of the lens than f ; but it divergent from any point further from the lens than p, their focus will fall beyond that for parallel rays: if the incident pencil diverge from f, the refracted rays will be parallel, and if from a noint within f, the refrttcted rays will di- Terge. The coune of refracted rays through a plano-convex lens, as well as through convex lenses of unequal curvature, may be found by a similar process. 1072. In order to find the geometrical focus after direct refrac- tion through a lens, let q, Fig. 583, be the origin of a pencil of which the axis q a b passes perpendicularly through the centre of a lens ; let f, be the geometrical focus after one refraction, and F that of the emergent pencil. Let a q= v, bf=s9, and r, «, the radii of the surfaces a and b respectively ; lines being considered * Treatise on Optics, p. 37. London, 1831. potitiee when iDeasnrsd in ■ direction oMtraty to Uut of tlie in- cident pencil. After refraction at the fint mrUce (1065, a), ^■'^- n \ —1 i7;-i=V= [-1 Since v is the geometrical Tocug of the rays aAer the second refraction, coDveTaelra pencil converging to f woiud, after refraction at b, converge „_1 m If the thickneiB of the lena bo neglected, and it bo asnmied that i?, = BP„th6n[al-|6], from which the position of Fmaj be determined. The dtWancea »i and V being Teciprocd, tho pdnti p, Q, are caUed emJugaUfod. When the incident raja are parallel, u ii infinile, and ctnue- quently -=0; abo o then becomes/, the /tfcolfen^oftholens, and the point r the prineipal foau, and the preceding fomnlB becomea y = ^~^l\r'^~i)'' and consoqnentl]', e ~ w ~ ?' ^^ When / is poutive, the leni ia thinnest at it* axis, and when/ is neaative, the Iuiih is the thickest at its aiis; Ihns lenses him be divided into tno classes, dietin^shed by the sign of the focal length, or, in other words, the direction from the lens in which the focus lies. Those of which the focal length is rBsitive, are called concave lenses, and those in which it is negative, convex leaaea. Lenses may, however, hsive an infinite varietj of forms, bat still the same focal length. The reciprocal of the focal lengih ia aonie- times called the pmner of the lens. As the lenses of optical instmmenta am almost nnivsnally com- {losed of glass, it will suffice for the present to confine our atten- tion to these; and as the index of re&actioD in glass may be taken to be 1*5 in rontid nnmbeit (1057], the prect^ing formnla dien which ma; be applied to particnlar cases. BBFBACnOM THBOUOH COHCAYS LBK818. 607 Oonoex lemes, f negatiye. FormtUat for parallel rayt. A. Doable con rex lenBes; « negative, /= — — • B. If their cnnratare be equal, r =s *, ancl/= — r. C. Plano-convex lenses,— = o, and/= — 2 r. D. Meniscns lenses, /negative; and $ positive, f^ Formtdafor diverging rays. E. Doable convex lenses u and $ negative, v = —, r — - — ° tt(r+»)-2rf tf r F. If tbeir corvatare be eqaal, r = s, and v = tt— r 1 2 Uf G. Flano-convex lenses, — =0, and v = 9 ' u-2r H. Meniscns lenses, s positive, and v=^ ; p. The fommlsB for converging njs may be obtained from these last, by merely changing the sign of u. 1073. To find the coarse of ravs incident on a doable concave lens, let b, f, o, Fig. 584, be, as before, the rays, of which h will pass throagh withoat refraction, b, on reaching o, will enter the glass, ^' "^ and be bent towards xs, a normal to the surface at the point of inci- dence ; and on reaching c, the ray OG will emerge and nndergo a second refraction, being bent from the normal at the point c ; by which its divergence wul be increased: the coarse of the ray o may be 9\ found in a similar manner. Thus the rays b, n, o, if parallel, are made to diverge by refraction throagh a concave lens, instead of converging, as in a convex glass. The emei^ent rays b, s, t, will diverge in the same manner as they would, if thev had proceeded frt>m a radiant point at f, as shown by the dotted lines f c, f d ; this point is the focus of the lens, and is a rnrtuai, or negative focus, as in the case of reflection from convex mirrors (1042). If the incident pencil be convergent, as b, s, t, but to a point more distant than f, it will diverge after refraction ; if convergent to f, the refrtusted pencil will be parallel ; and if convergent to a point nearer than f, it will still converge after refraction, but to some point beyond f. 608 DIOPTBIC8. The oonne of refracted rajs through plaiKMsoncavei aad double concave lenses of unequal curyature, may be traced by a similar process. From an inspection of the last dia^m, it is clear, that if the incident rajs on anj concave lens be divergent, the negative focus of the refracted rajs will be nearer the lens than the prin- cipal focus F. 1074. The negative focal lengths, for parallel rajs, of all the varieties of concave lenses, maj be found bj means of ^e formnlis alreadj given for ponvex lenses (1072, a, b, c, d). Their foci for converging rajs maj be found bj means of the formulae for diveig- ing rajs and convex lenses (e, f, o, h), and vice versd, 1075. The action of menisci and concavo^onvex lenses is similar to that of convex and concave lenses of the same focal length ; the foci in the former being real or podtive, whilst in the latter thej are virtual or negative. The Tormuln for concavo- convex lenses are similar to those alreadj given .for menisci (1072, D, h). Both kinds are used in correcting spherical aberrations. 1076. Let anj number of lenses be placed so that their axes maj coincide, as in Fig. 604, of which the focal lengths are /*„ /^ &c., let tt be the focus of rajs incident on the first lens, v, that of the refracted pencil ; v, the focus of incident, and o, of refracted rajs in the second lens, and so on ; then (950, d), 1 _ 1. ^ J_ »l u /, l^ _ 1 1 »t^ ^l =7; &c. = &0. 1 1 _ 1 Vft »!,-, ft n and bj addition, =-?+>+ ...+7-» which determines the focal length of the combination, the thickness of each lens being neglected. As the reciprocal of the focal length has been called the power of a lens (1072), it is thus shown that the power of a eornhkuition is the mm of the powers of^ the eeparate tenses ; tnot is, the alge- braical sum, due regard being paid to the signs of all quantities emplojed in the several expressions. 1077. Images are fotmea bj lenses in the same manner as they are bj mirrors (1044). Let ▲ b be an object situated at a consider- able distance ; the rajs propagated from it will, on reaching the convex lens e f, sufier refraction, and after emergence will paint on a screen, placed near its principal focus (1072), the image o d of the object, out in an inverted position, in consequence of the crossing of the rays. If the screen be removed, and a piece of ground glass be placed at 0 d, the eje placed behind it, as at o, HlGHIFTHrO POWER OF CONVBZ LEK8E8. 609 will see the image vety distinctlj ; then let the glass "be remoTedi and if the eje has been placed within the limits of distinct Yision, ^.685. a picture of the object will be seen painted in the air, a little beyond the principal focus of the lens. 1078. If the object be within a moderate distance of the lens, its image will be formed on a screen as before ; and will be visible most distinctly when the object and the screen are placed in the conjugate foci (1072) of the lens. If the object be still nearer, and it be viewed through one of the modifications of the convex lens, it will appear larger, and if through a concave lens, smaller, than it really is. This curious property of lenses entirely depends upon the apparent angle under which the object is viewea. Taking first the case of the double convex lens, as a b (Fig. 582), let the rays b, h, e, be supposed to pass from an object placed near it, and the eye be placed between the lens and its focus f ; under these drcumstances, the object will appear to be larger than it really is; fvr if the rays fc, fd be produced, they will diverge at a considerable angle, ana, as bodies always appear to be placed in the direction pursued by the rays which ultimately reach the eye, the ra^s f c, f d, will appear to have passed from the object in right hues, and the object will appear to the eye to be sufficiently large to fill up the whole aperture of the angle. If, on the con- trary, an object be viewed through a concave lens (Fie. 584), it will appear to be diminished, because it is visible under a less apparent angle *, for if an object be placed so that its rays e, n, o, suffer re- fraction in the double concave lens, they will diverge, and the object will appear to be situated in the direction of the right lines r f, TF, ana included in the angle of convergence of those rays. 1079. The manner in which the eye judges of the size of an object, according to the appa- rent angle under which it is visible, may be readily shown. If the eye placed at e view an object AB placed at such a distance that the ri^ht lines A B, BE, subtending it at the eye, may form an angle of 20^ BR Fig. 689, 610 DI0PTBIC8. ' it will appear of a certain magnitade. Let a b approach to the position a 6, it is evident that it will appear under a greater appa- rent angle than before, as a line c b, passing through it to the eje, will, with b b, contain a larger ande, and, juasing of its size from this angle, it will appear to be larger than wnen at a b. If the object be placed at one half the distance, as €^b\it will then subtend an angle of about 40**, and will appear to be twke as large as when at A b. 1080. The magnifying power of a lens may be determined hj the limit of distinct vision for minute objects, which is generally about five inches, divided by the focal length of the lens. Thu refers to its linear ma^ifying power, its superficial power being obtained by squarine its linear, and represents the number of times the whole surtace of the object appears to be magnified. Thus the linear power of a lens of half an inch focus will be 5-T- i s 10, and its superficial power, lO**" 100. 1081. On referring to ^1047), it will be seen that the rays pass- ing nearer the axis of the lens will be refracted to a focus at a greater distance from the glass, than those which pass nearer the circumference. On holding a screen of ground glass near the focus of the central ra^s, a picture of an object will be seen on the other side, very vivid in its centre, but less distinctly defined at its edges ; on gradually withdrawing the screen, the maiginal ]^rtion of the picture will become more vivid as the centre loses its dis- tinctness. Hence, it is obvious, that no object can be seen with perfect distinctness in every part through a convex lens at the same moment, in consequence of this spkerieal aberratvm, as it is termed. In a plano-convex lens, with its convex side towards a distant object when used to form an image, or towards the eve when used as a magnifier, this aberr tween the prism and the screen, which, If sufficiently near the former, will bring all the rajs nearly to a focus, and repruJuce while light. It muit not, however, be supposed, Irrim the preceding obaer- Tations, that the separated rays of any one Tery small pencil ure reeombined, for, as the rajs refracted at diflerent angles on their incidence, ai« each equally refracted in a contrary direction on their ome^nre, it Tollows ihal each emergent very ^ ^^ smalt pencil will consist of parallel rajs of diETereut colours as TK, Pig. 588, but as the same separation of the coloared rays takes place with each aucccs- ■ive Tery bihbII portion of the incident pencil, the overlappiug of the successive parallel spectra re- produces white light. This may be seen to be the I case by observing the pencil of light (1082) en a I ■creen alter oblique refraction through a thick plate I of glass or a veaael of water with parallel (class sides, when Itie npper margin of the spectrum will be observed to lie tinged blue, and the lower mai^n red, while the inlennediate portiun coosists ef white light ; Ihis evidently results from there being no rays to combine with the extreme rays of the outermost spectra. For the same reason a peacil of light, transmitted through an ordinary lens, is observed lo be sarrounded bv a fringe of coloured rays. 1086. From a set of scciirnte admeasurcmentB made by New- ton,* the following table, showing Ihe length and rapidity of nn- dulationn producing the principal coloured rays of tSie spectrum, has been constructed (see Table, p. 6U). Thus red light is pre- sumed to lie canned by a little more than half as toanr osciilHtions or undulations as are necessarr to generate violet light, and henca the waves of the latter are a little. morv than half the length of those ol red light, or more nearly aa 63 : 100. 1087. Fromsome researcbes of Sir John Heischel, in connexion with the photographic powers of the spectrnm, it appears certain that a hand of coloared light of (till higher ic&angitiility than the • TreaMs* on Ufbt, io Sus. Uetoop., bf 8ii Jobs Haneb*!, S7G. 614 CHBOMJLTICS. ▼iolet exists just beyond the limits of that tint. This new band is barelj luminous, and has been denominated the lavender band by its discoverer. Colours ofrayi. £ztreme red Red . Intermediate Orange Intermediate Yellow . Intermediate Green . Intermediate Blue . Intermediate Indigo . Intermediate Violet . Extreme violet No. of waves in an inch. 37640 39180 40720 41610 42510 44000 45600 47460 49320 51110 52910 54070 55240 57490 59750 Lenffth of each wave. 00000266 0*0000256 00000246 00000240 0*0000235 00000227 00000219 00000211 00000203 0 0000196 0-0000189 00000185 0-0000181 0-0000174 0 0000167 No. of wares in a second. 458x10" 477 495 506 517 535 555 577 600 622 644 658 672 699 727 t» II II >i II II II II II II II II II II 1088. The seven colours of the solar spectrum are generally td- garded as simplef because they cannot be separated into otnen by a second reiraction through a prism, in which they differ from the tinted light obtained by passing the sun*s beams through most varieties of coloured glasses. When light passes through even the most ti'ansparent medium, as water or glass, some of its undula- tions are absorbed, and these vary in quality according to the nature of the substance ; the transmittea undulations which ulti- mately reach the eve, communicate the sensation of that colour which is produced oy the undulations of white light ininu$ those which msy have been checked or absorbed whilst passing through the given medium. Thus, on holding a piece of smalt>blue glass between the eye and the light, the transmitted rays will be of a line blue colour and consist of a mixture of all those undulations which have not been absorbed by the glass ; and if decomposed bj the prism, will exhibit a spectrum (1082) deficient in those rays which have been absorbed by the blue glass. 1089. On examining the solar spectrum through such a piece of glass, which is best done by placing it before a prism, through niiich the observer is regarding a hole m a window-shutter, Sir David Brewster found that the greater part of the red and orange rays had disappeared. The yellow band appeared greatly increased in breadth, encroaching on the spaces formerly covered by the orange on one side, and the green on the other. Hence, the coloured glass had absorbed those rays which, when mixed with the yellow, OOMPLBMSKTAJIT COLOUXS. 615 oonatitnte orange and g^en, and conseqaenti/ the green of tlie Bpectnim becomes decompoBed into blue and yellow, and the orange into yellow and red. This has been termed the simplifi- cation of the spectrum bj absorption, and greatly corroborates the views of those philosophers who have contended for the exis- tence of but three primary colours, as red, yellow, and blue. 1090. The solar spectrum has by some been re^rded as com- posed of three spectra of equal lengths oTerlappmg each other, the red having its greatest intensity in the middle of the red space ; the yellow, in the middle of the band of that colour, and tne maximum of the blue between the band of that colour and the indigo. Sir David Brewster has exhibited by means of three curves the intensities of tint of the three spectra, which he conceives to constitute the solar spectrum. ; Thus, if oh, I^.6». Fig. 589, represent this spec- trum, the red curve b com< mences abruptly at o, and gradually declines to h ; the yellow one t commences less abruptly ; and the blue one B begins with a very gradual curve ; — the heights of these curves, or lengths of their ordinates, represent the intensities of the tints of these fnimary spectra in every part of c h. Putting B for the primary red, b for the primary blue, and t for the primary yellow rays, the following will be a view of the pro- portions in which these rays have been considered to exist in the spectrum, and in white light : J* •l -^ ^ |*!/| * Cokmr. Proportions. White . 20R + 30Y + 50B Bed . . 8 R Orange. 7B + 7 Y Yellow . 8 Y Colour. Green Blue . Indigo. Violet . ProportioBB. 13Y + 10B 6 Y+12B 12 B 15B-t-5R Jn^m 690. 1091. Each of the prismatic colours has some other which is said to be complementary to it, and which, when combined with it produces white light. If we consider the indigo, not as a separate colour, but as a deeper shade of blue, the remaining six may be regarded as composed of three primary, ana three secondary colours. The complementary colours to eacn of the former will be the compound tint made by blending the other two, whilst the comple- mentary tint to each of the latter will be tnat primary colour which does not enter into its composition. This may be seen by a glance at toe diagram, Fig. 590, consisting of three 616 CHSOMATICS. intorseotiDg circles, each re]^reaeiitin^ a primary tint. In the centre, where they all overlap, white light is produced, and in the other spaces the complementary colours are exactly opposite each other. 1092. Oorham^a Colour-top. — ^The phenomena exhibited by the blending or intermixture of different colours, may be conTcni* ently studied by aid of Mr. Gorham's colour-top :* this condste of a short and broad spinning-top, the upper surface of which is quite flat. This is furnished with a series of circular discs of paper, which are white, black, blue, red, yellow, and green. Each has a hole in the centre by which it may be placed on the stem of the top, and a radial slit, by which they may be made to orerlap each other, so as to bring into view sectors of any required angular magnitude. The discs, when placed in any required podtioii, are retained by means of a screw. The blending of two or more colours, distributed on contigaons surfaces, by a rapid rotation, is analogous to the well-known ex- periment of whirling a hot coal, or otner luminous body, by the nand, when an unbroken luminous circle is peix^eived. As the luminous body can occupy only one point of its path at a time, it is evident that the impression on the retina of the eye must last for at least the period of an entire revolution. Ck)loared surfaces, when rotated, form, in the same manner, circular areas of coloor, the images of which being superposed on the retina^ the impres- sion of mixture is produced, and a compound colour results. The resultant colour is generally identical with that which would arise from a mixture of the pigments in the same proportions : but to this there is a remarkable exception in the production of greens. This, as is well known, is produced bpr the mixture of blue and yellow pigments in almost any proportion ; but there ate no known blue and yellow which, when combined in any propor- tion by rotation, will produce even a tolerable green. By cover> ing one disc by another with an aperture of a suitable form, the gradations of shade fh)m any given colour, to white or black, or to any other colour, may be beautifully illustrated. It may be remarked that no mixture of colours by rotation will produce absolute whiteness, but a gray, or neutral tint, such as would re- sult from some mixture of black and white, may be produced. 1093. Media of various colours absorb different primary rays ; thus, the piece of blue glass already referred to (lOiBS), absorbed the red and part of the yellow ; some pieces of red glass, or a com- bination of blue and red, absorb eyery ray except the homogeneoas red. A solution of the ammoniacal sulphate of copper transmits the violet, but absorbs all other undulations ; while the ammo- niacal oxalate of nickel absorbs the violet, and transmits the blue and red. This remarkable absorptive power of different substances becomes curiously modified by heat, as shown by the tints * l^orotoopioAl Jonmal, Jan. 1860. DISPER8ITE POWERS OP SUBSTANCES. 617 aesumed by yarious substances at different temperatures ; thns, the biniodide of mercury tarns yellow, bincxide of mercury black| and tbe salts of cobalt blue, or bluish green, on being heated. 1094. The absorption here spoken of occurs during the passage of the rays through a medium, but an analogous phoBomexion has been observed to attend the reflection of light from the polished surfaces of certain metals. The metals generally, except gold and copper, reflect nearij colourless light, but after repeated reflections from the sur&ces m the same metal, the reflected light becomaf coDodenXAj coloured : — iVom Copper, the colour is Scarieily „ Gold „ „ Ked, „ Silver „ „ Purs Yellow, „ Zinc „ „ Indigo Blue, „ Iron „ ,, Violet Light transmitted through a very thin lamina of any metal, is usuall^p^ of a colour complementary to that produced by repeated reflection from its surfac^. 1095. On examining the solar spectrum (1082), the green rays are observed to be placed very nearly in the centre, and are hence frequently termed the mean or medium rays of the spectrum. If, instead of using the prism referred to, one of the same kind of glass, but of greater refracting angle, be employed, the length of the spectrum, or distance of the mean rays from tbe extremities will be increased ; and diminished, if the refracting angle of the prism be lessened. But when the spectra produced by two prisms, one of flint- and the other of crown-glass of equal angles, are examined, that produced by the latter will be found to be shorter than that by tne former; hence flint-glass is said to have a greater disversive power than crown-glass, because it spreads or disperses tne spectrum over a greater space. A hollow prism of thin glass fiUea with oil of cassia, produces a spectrum of twice the length of one produced by a pnsm of solid glass, on account of the great dispersive power of that fluid. 1096. If the prism a b c. Fig. 587, be of flint-glass, and one of crown-glass, a f c, be applied to it, the angles a c b, c a f, being Buch that the deviation of the mean rays may be the same in both, the spectrum will disappear, and the spot of light w will be repro- duced, not colourless, as when the prisms were of the same kind of glass (963), but elongated a little vertically, and tinted above with purple, and below with green light. This arises from the unequal dispersive power of the two prisms, which prevents the latter from completely neutralizing the effects of the mrmer. Tne course of the rays will perhaps be better understood by a reference to Fig. 591, in which the rays are seen to converge less coloured ntji emei^ from the ctowuImi priam is the revene of vbat it would be if the rari n-ere rcfrxcted bj thM prinn ■Icbc, iIk red ray ■, b, being toward* the bue, kod tiie violet rnjg, v, towardi theapexofthmtpruo. Or if the nj were drawn inddeot poiModic*- larly on the firat larisce, u at i>, it wovU proceed Dnrafrscted lo iba amanum rarftoe of the two priimi, the mean nj would tbeoo pnnue its ori^nal conrae withoat re&accioB, but the extreme rayv would diverge >t an an- gle dependisg oo the difference of the dicper- liTo powers of the two pnama. and emei^ parallel to the mean ray, at the aurface x r. In this Utier case, chroniat" '' change ir 1097. The diepersi . _ to ita index of refrsctioa ; it waa fonnerlj determined bj dindiug the difference of the indices of relraction for the twl and nrlet rajB, hj the eiceas aboie nni^ of the index of refiactioD of (he mean njt. That, tlie disperaiTa power of crown-glaas ia CK)39, for (1084) rMee-i-5a6e=oi)2oe, Md^^^-oflsg. . turn Oilofcaaua . 0'139 Oilofcaraway 0-M9 Ether. . . . Fhoaphonig . . OlSB Flint-glsu . . 0048 Caator oil . . Bimi1ph.carbonO'U6 Oil of juniper 00*7 Water .... (MOS OilofcloTBB . 0-062 Oiloftarp. . 00*2 Flate-glMa . , 0-03i Oilafaaaaafraa OOGO Amber. . . . 0*041 Sulphuric acid 0031 Rock aalt . . . 0-053 Crown-glan . 0-039 Alcohol .... fyi>i9 aioflhjms . 0-050 {Diamond. . , 0-038 RockciTMal . A*« fh f*S f*K Water at) 18-76«»C.) Oiloftarp. Crown'glass Flint-glass . 1*88006 1-47040 1*62431 1-60204 1-88171 1-47163 1-62630 1-60380 1*88867 1*47443 1-62708 1*60848 1*88686 1*47836 1*68137 1*61463 1*88780 1*48174 1*68434 1*62004 1*84127 1*48820 1*63901 1*68077 1-3M17 1-40387 1*65468 1-64C87 The dispersive power of any substance is now taken to be measared by f^BZJtt but the resnltB thus obtained will not be /"n-l found to differ materially from those of Sir D. Brewster (1097). 1102. It appears from the experiments of Messrs. Gladstone and Dale,* that the index of refraction always decreases with increase of temperature ; but that the amount of this tempera> ture-change of refractive power varies considerably, being only 0*0002 per 5"* G. in water, and the highest observed, 0*0042 in phosphorus. The length of the spectrum also decreases with increase of temperature ; with highly dispersive bodies as bi- sulphide of carbon, and hydrate of phenyl, considerably; bat in water the decrease is scarcely appreciable. In some substances the dispersive power is diminisheo, in others it is augmented by increase of temperature : this depends upon whether the nume- rator or the denominator of the above expression for the dispersive power decreases most rapidly. The amount of the temperature - • PhiL Trans. 1868 and 1868. niTBXBXTT OF UOHT IH THE 80LAB BPBCTBUU. 621 change of refraction, appears to bear some relation to the change of density due to the same elevation of temperature. If the quantity tt — 1 be called the refractive energy ^ and the ratio of this to the density, the specific refractice energy, it appears that the specific refractive energy of several liquids observed is a constant, and not affected by 3uinge of temperature. It appears also that the specific refractive power of a mixture of liquids is a mean of those of its constituents. Much further information on the relations existing between refraction and chemical composition, as well as a copious table of the indices of many fluids for all the lines from a to h will be found in the latter of the two papers mentioned. An abstract of this table containing the temperatures of the observations and the indices of a, d, and B, of several characteristic fluids is here given: — Liquid. i«>C. /'a I'd Mh Water. . . . 160 1-3284 1-3324 1-3431 Ether .... 16-0 1-3629 1-3666 1-3683 Alcohol . . . 160 1-3600 1-3638 1-3761 Chloroform . . 10-0 1-4438 1-4490 1-4661 0. turpentine Bensole . . . 240 1-4596 1-4653 1-4846 10-6 1-4879 1-4976 1-6306 Aniline . . . 21-6 1-6644 1-6774 1-6297 Beet. 0. cassia . 28-0 1-6649 1-6801 1-6244 ( Bisulph. carbon . 110 1-6142 1-6333 1-7090 Phosphorus . . 350 2-0389 2-0746 2-2267 (/««) 1103. Sir D. Brewster and Dr. Gladstone* have given a very carefully drawn map of the solar spectrum, five feet in length : in this is recorded the position of many lines not found in Frann- hofer's map. Some lines observed only at low altitudes of the sun are supposed by the authors to be due to the atmosphere. 1 104. Tne intensity of licht in the solar spectrum appears to be S latest in the yellow band, and from that space it decreases to th extremities of the whole series of tints. Fraunhufer has exhibited these variations in the light of the different parts of the spectrum by the curve bkl, Fig. 593, the ordinates of which indicate the intensity of light in the difierent parts of the spectrum bv, in which the position of his lines has been marked. Taking the ordinate X If falling nearly in the boun- dary between the yellow and orange as unity, the following ^.683. * Fhn. Trans. 1860. 622 CHROMATICS. will represent the illmninating power of tlie different portions of the spectram in which Fraunhofer*s lines are seyerallj situated ; the red extremity heing indicated by r, and the violet by ▼ : — Parts of the ■peotrum. B B C D B F 6 o-osi H V Intenntie* of light. 0-0 0-082 O-OM 0-64 0-46 0-17 0-036 0-0 1105. The calorific powers of the spectmm increase from the ▼iolet to the red extremity, and extend considerably beyond it, the obscure space h, Fig. 587, beyond the red extremity possesising a higher temperature than the red band itself ; so that it is evident, that when undulations are propagated through a prism, a certain number of them move with too little rapidity to communicate to the eye the sensation of light, and are only to be recognised by their calorific effects. These rays of non-luminous heat are less refrangible than the rays of red light, and are therefore found in thegreatest abundance beyond the band of that colour. Inese calorific rays, like those of liffht, are subject to Taried degrees of absorption, according to the refracting medium of which the prism is constructed ; being, according to Seebeck, in the greatest number in the yellow band, when a prism of water is employed ; in the orange, with one of sulphuric acid ; in the middle of the red, with crown-, and beyond the red, with flint- glass. These phenomena are explicable on the supposition that there exist in the solar beams, rays of heat of different refrangi- bilities. Consequently the absorptive power for heat of the medium of which the prism is composed will materially affisct the dispersion of radiant heat over the luminous spectrum. From the observations of Nobili and Mel loni, on a spectram produced by a rock-salt prism, the highest temperature was found beyond the red, and about as far distant from it on one side as the blue band was from it on the other. The following temperatures were observed by Sir H. Englefield in the different coloured portions of the solar spectmm : in the blue, 56" F.; green, 58'; yellow, 62'; red, 72'; beyond the red, 79°. 1106. The chemical action of solar light, in prodocing oombina- tion and decomposition, has been long known, and this, like the heating power, appears to reside in greater intensity at one end of the spectrum than the other. This may be shown by dippinff in a solution of nitrate of silver a slip of paper, previously waued over with a solution of common salt ; on drying this, and exposing it to the action of the solar spectrum, a veiy remarkable e^ct will be observed. In the course of a few minutes the chloride cS silver with which the paper has been imbued, will become of a deep slate colour in the violet, and in the sombre space beyond it ; CiiLOSIFIC AHD CHEUIOAL RATS. 628 whilst in the yellow, orange, and red, it will remain scarcely affected, its colonr being less altered in the blue than in the violet, and still less changed in the green. Thus the chemical action of the different rays of the spectrum appears to be most intense in the violet band, and in the dark space beyond it, at the directly opposite end to the seat of the principal calorific rays. There is reason to believe that those undulations which are propagated through a prism with too great rapidity to act on the oi*gan of vision, possess the power of exertmg certain chemical effects on many substances, in the same manner that calorific effects are exerted by those undulations which move with too little rapidity to produce the sensation of light. Granting this, we meet with another circumstance in which the propagation of light and of sound correspond : it has been already shown that to most persons aerial waves moving with a velocity sufficient to strike the ear less than 16, or more than about 24,000 times in a second, are Inaudible (568) ; whilst luminiferous undulations, if less frequently rei)eated than 458 millions of millions, or more frequently than 727 millions of millions of times in a second, are incapable of acting on the visual organs. 1107. If DB, Fig. 594, represent the solar spectrum produced by flint-glass, and ab^ ds, the non-luminous portions beyond it, at each extremity, the curves acd, grb, will give an idea of the relative position of the calorific and chemical rays. The longest ordinate of the curve e h b falls without the red ray b in the ob- scure space beyond it, where the calorific effects are most manifest ; and the longest ordinate of the chemical curve acd falls in the dark space beyond the violet ray y, where the action on chloride of silver appears to be most intense : both curves rise abruptly, and gradually decline to zero at the opposite ends of the spectrum. Spectrum Analysis. — ^The progress of this department of physics has of late years been matly facilitated b^ the introduction of the spectroscope (Ch. Xa.), an instrument in which a telescope for viewing, and a divided circle for measuring, the lines of the spectrum are conveniently combined with a pnsm, or combination of prisms for separating them. 1108. The spectrum formed by electric light was first observed by Frot Wheatstone to consist principally of a few bright lines, 624 CHE0MATIC8. the cbaracter of which depends on the nature of the sahstanoes hetween which the spark was transmitted ; but these obserrations remained for many years unheeded, and it is to the researches of Bunsen and Kircnon that the present great development of this department of ph^^sical science is mainly due. It was ascertained by those distinguished observers that all simple bodies, when raised to a state of incandescent Tapoor, emit light which, when submitted to prismatic analysis, does not present a continnous spectrum like sun-light, bat one consisting of isolated coloured bands, of various but definite degrees of le- frangibility. These luminous bands are found to be constant for the same substances ; and when two or more elements are com- bined, no new bands are produced, but merely a superposition of those peculiar to each. Tne existence therefore of a known band of lignt in any given spectrum may be taken as evidence of the existence of an elementary body to which it appertains ; and con- versely, bands previously unknown demonstrate the presence of some element, the existence of which has not hitaerto been recognised. It may be further remarked, that the quantity of anjr element capable of producing a definite spectrum is so infinitesimally small, as to be inappreciable by any chemical tests : hence, if the spectra of all known elementary bodies be carefully observed, and tabulated, spectrum-analysis becomes a fertile means of detecting the presence of a new and unknown element. To this mode of investigation the discovery of several new metals is due :— of caesium and nibidium by Bunsen and Kircho£^ and of thallium by Mr. W. Crookes,* who in 1861 was occnpied in examining a seleniferous deposit from a vitriol-chamber at Tilkevode, in the Harz mountains. Availing himself of the then new method of spectrum-analysis, he inferred the presence of some new element, from the appearance of an unknown paie-green line. He possessed a very small quantity of material for investigation, but oy the exercise of much skill, and by persevering^ reference to the spectroscope at each stage of his chemical manipulations, in order to track the whereabouts of the stranger, he succeeded in isolating a new metallic element, to which he ^ve the name of thaUiumt from the resemblance of the colour of its peculiar band to that of a sprouting twig (Gr. OoXXtfc)- This metal resemUes lead in its external characters ; it has been found most abundant in some varieties of iron pyrites, but not in greater proportion than 10 ounces to the ton. The position of the principal lines of csesium and thallium is shown in Fiff. 595. 1109. From the observations of Mr. Attfield, it appears that when an electric discharge takes place through rarefied atmo* spheres of the compounds of 0, H, N, and G, the spectra prodoced are the superposed spectra of the individual elements : wnile fnun • Phil. Tnmi. 1862. BPECTSUM-ANALYBIS. 625 thoee of HH. PUicker and Hittorf,* it is shovrn that the spectra of ignited gases and vapours vair considerably in their character with changes of temperature. For example, below a certain tem- perature nitrogen emits only eold-colourea light, giving a spectrum of gradually-shaded bands ; beyond this temperature, the light is bluiiih violet, and the spectrum consists of channelled spaces. At a still higher temperature, the light is whiter and more bril- liant, and bright bands appear in the spectram ; these increase in breadth, and at the highest temperatures approach the character of a continuous spectrum. 1110. Messrs. Huggins and Millerf have observed that the lines of the solar spectrum present different characters ; some are sharply defined, while some, even with a narrow slit, are always nebulous at their edges : some dark bands consist of a haze, not resolvable into lines by any power applied, but others evidently oonidst of double or multiple lines, placed too close together for separate measurement. The same observers have remarked that in the spectra of the metals, several lines of different metals are quite comcident ; and many others so nearly so, aa to be inseparable when superposed. In several instances, particular lines of three different spectra very nearly coincide ; m one case, four lines, and in another, five, are also veiy nearly coincident. A series of observations has been made by M. Janssenf on the spectrum of aqueous vapours as manifested by the additional lines vihible in the solar spectrum during the afternoon hours, and as>- Bumed to be due to evaporation from the earth's surface, under the influence of solar heat. This spectrum consists chiefly of two bands at a, Fig. 592, of one below b, of several faint bands above o, and of a broad and dark band below i>. This last accounts for the relative prevalence of rays belonging to the lower end of the. spectrum towards Bunset in clear weather. 1111. One of the most important results of spectrum-analysis IB the insight thereby attained into the physical constitutioiL of the Bolar and stellar photospheres. It has been satisfactorily proved by experiment that a luminous vapour, capable of emitting rays 01 a given rdfrangibility will arreift or absorb those same rays, when transmitted through it from an independent source of light. This is most readily shown by transmitting through a prism the light of a spirit-lamp with a salted wick; when the well-known yellow double sodium line will be thrown upon a screen. If a portion of incandescent vapour of sodium be now interposed in the path of the refracted rays, the bright sodium line is replaced by a dark band, which moreover exactly coincides with Fraun- hofer's double line d, in the solar spectrum. It is thence infern/d with a veiy high degree of probabinty that this dark line is due « FhiL Trans. 1895. f Ibid. 1863. X Beport Brit. A^iociatioD, 18(i«. B B to Ibe pretenoe of lodinm Tapoar in tlie immediabi riciiutj of tlta tan; and a Birailnr carrespoDdenM aiiiU villi ragani to faanj other metallic gpectra. For eiaiDple, mora than fiftj brufit bands in the iran-snctrain bave their correipnnding r«pre«Dt»- tivet in the dark liasi of the aoUr epectnim, one of which ii Fraunhiifer'a line i : moreover c and r are hvdn^ea-linca, netthrr of vhlch has been obaerred alone ; and b beloDfTa to mMgaatiuia. It thui appears that hydrogen, Kidium, potaaiiimi, magneaiiun, calcinm, aluialniuni, banum, chraminm, iron, copper, xjnc, loaii- gnnese, and nickel in all probahililyeiutintheaolarpfaoloapfaerc: and the eoilium lino haa alio been observed in the ipecln of Ibe sUn Aldnbaran, Algol, Belelgeux, and Pollux. It farther appean from tbe obsM-Tationa of Meisn. Hug^na and Miller* that ihe Bpeclrum of AJdebarar cnmpriBea the lines of hydropen, aotGom, nuigneaiuiD, calcium, iron, biBinulh, tellurium, antimony, and mercury; tbtt of a Orionia (Belelgeui), ■odium, ma^nedom, calcium, iron, and hiBmuth ; and that of Siriua, hydrogen, ■odium, ma^neHium, and iron. They haie alto observed that tbe spectra of eonis nebuln consiist only of bright linea ; while otbera preaecc 1112. A remarkable unknown itar described aa " Ten- briOiant, of about tbe second magnitude'' was observed bv Ur. J. Biminp. hum, of Tuam, on 1B66, May 12 (perbaps tbe saute aa tbai observed by Sir J. Hersobel on 1842, June 9), in the rainatelUlioii Corona Burealis : it was observed by Mr. Baiendell, of Man- chester, on Mar 15, and thtn appennMl of about the third sM(:ai' tude; and by Messrs. HuirgiiiiBanJ Miller,ton May 16, to whom 1 1 llien appeared (o be conaiclerablT below tbe third magnitude, but presented a spectrum unlike any previuunly obumM, Fig. 596, conaisting of absorption -bandi like the solar spectnmi and ■!« ol bright bands, like the gaseous spectra. Of the four bri|clit baoda the brifihlest coincided with r, another between r and o, and i fainter band nearly coincided with o ; the fourtb orcopied nearli the position of c in the aolar apectrum : hencs the preanKC »i iucandeioent hydrogen may be inrelred. Of th« dark baadisi • Fiiii. Tiiu. IMS. t BiU. uag. FLU0BE8CBNCE. 627 the lower end of the spectrum the principal were two above c, one below d, and one nearly coinciding with d ; in the upper part of the spectrum they were veiy cloee and numerous. The position of the principal groups shows that the light of the photosphere after passing through the absorbent atmosphere is yellow ; but the light of the green and blue bright lines compensated the loss by absorption in that portion of the continuous spectrum, and to the eye tne star appeared neariy white. It is remarkable that Mr. Bazendell, without knowing the results of prismatic analysis, described his yisual impression to be " as if the yellow of the star were seen through an overlying film of a blue tint.*' On May 24 this celestial apparition haa declined to below the eighth magni- tude; having afibrded a conspicuous example of the amount of otherwise unattainable information to be derived from spectrum- aoalysis. 1113. A very remarkable action is exerted by several bodies on light, to which attention was some ^ears since directed by Sir John Herschel, who observed this action in a variety of fluor spar, and in solutions of salts of two organic alkaloids, quinine ana cesculine : it is best observed in a solution of disulphate of quinine in water acidulated with sulphuric acid. The fluid, although really colourless as water, disperses a lively blue light, which, when examined by viewing it through a prism, appears ouite free from the pure red rays, part of the orange, and all the yellow: this was termed ^poUc dispersion (JiriiroX^, a surfaced from the peculiar action having been supposed to take place at tlie surface of the liquid. But as subsequent observations have shown that this effect is by no means conflned to the sur&ce of bodies, the term " epipolic" must necessarily be abandoned. The light trans- mitted throueh the solution of quinine has undergone a physical change, and is no longer capable of developing toe blue tint in another portion of the same Kolution, or in any other body pos- sessing a similar property. This may^ be shown by filline a glass trough with water, and placing behind it a tube filled with & solution of quinine, taking care, by screens, to cut. off all side- light; the blue dispersed light will be beautifully distinct. Then replace the water m the trough by a solution of quinine, and th« blue tint previously visible in the tube will no lon^r be perceived. It was likewise observed by the same profound pnilosopher, that some opaque substances appeared to possess analogous properties of reflecting ravs not reflected from other surfaces ; when, for example, Uie solar spectrum is received on a piece of ivory, or tur- meric paper, the lavender band (1087) becomes distinctlv visible. 1114. These, and some similar phenomena observed bv Sir D. Brewster, led to a careful investigation of the subject by Prof Stokes, from which has resulted the most important recent dis- covery in physical optics, namely, a change produced by certain substances in the velocity, and consequent refrangibility of the B 8 2 628 CHROMATICS. rajTB of light ; and not only of the ▼isible rays, but also of inviable rays, far more refrannble than the visible spectrani, which are thus rendered cognisable by the sense of vision, and the existence of which was previously unknown. The following substances have been found to possess the greatest power in changing the refrangibility of rays : — The mineral called uranite ; some salts of uranium, and glass coloured by peroxide of uranium, commonly known as "canary glass.' An alcoholic solution of chlorophyll (the colouring matter of A weak infusion of horse-chestnut bark. A weak acidulated solution of disulphate of quinine. A particular green variety of fluor spar. Various red sea-weeds, and their cold infusions. An alcoholic infusion of the seeds of Datura stramonium. Paper washed with a pretty strong solution of quinine ; or with a tincture of stramonium seeds, or turmeric. Glass is found to be perfectly opaque to many rays of veiy high refrangibility, which are trausmisMible through quartz; therefore prisms and lenses of quartz must be employed in order to obtain an extensive invisible spectrum. When the spectrum formed by a series of two or three qnartz prisms in a dark room is permitted to fall on a piece of canarp^ glass, or on a solution of qumine or sesculine (the active principle of the horse-chestnut bark), the sudden illumination of the fflass with bright yellowish- green light, and of either of the solutions with that of a pale bluish tint, presents a truly marvellous, it might almost be said, a supernatural appearance. 1115. The spectrum of invisible rays of high refrangibility trans- mitted through quartz prisms has been observed to extend beyond the violet rays to more than double the length of the whole visible spectrum ; Fig. 596 represents a map of the fixed lines in the first half of the invisible spectrum, given by Prof. Stokes, in which he has designated some more conspicuous bands by italic letters. Fig, 696. Group H. Group L Group w. Group «. Group p. It appears from some further observations of Pro£ Stokes* that the spectrum of electric light is peculiarly rich in invisible rays ; having been ascertained by fluorescence in uranium-glass to extend to six or eight times the length of the visible spectrum. • Phil. Tnot. 1863. FLUORE8CE2ECS. 629 Altboogli glasa is opatjne to the rajs of veiy high refrangtbility, it transmits a Urge portion of those belonging to the yiolet re^ou of the spectram, which are convertible by compounds of oranium, and by the solutions above mentioned; hence results a ready mode of exhibiting the more striking phenomena without the aid of prisms or direct sunlight. This consists in closing an aperture in the window-shutter of a darkened room with a piece of purple or deep blue glass (some specimens of which answer better than others) which transmits a very small portion of the lower and more luminous rays of the spectrum ; a piece of canary glass, or crystals of nitrate of uranium, or the solution of quinine or ssscn- line, when held in the transmitted light, become instantly self- luminous by emission of the converted rays. 1116. For a detail of the many very interesting experiments, as well as of the various means of observation employed, the reader must be referred to the original memoirs,* but the following are the more important results : — 1. True internal dispersion (which has been designated by Pro! Stokes dA fivorucence) is a totally different phenomenon from the mere reBection of ordinary rays from opaque suspended par- ticles, which might be termed /oJM internal dispersion. 2. In the phenomenon of internal dispersion (properly so called), the retraogibiHty of rays is changed, incident rays of de« finite refran^bility giving rise to dispersed rays of very various refrai^bilities. 8. The refrangibility of any given ray is never exceeded by that of any of the dispersed rays arising from it. 4. The colour of light is in general changed by internal dis- penion, the new colour always corresponding to the new refrangi- bility ; and this is equally true whether the incident rays belong to the visible or invisible part of the spectrum. 6. The nature and intensity of ligbt, dispersed by a solution, appear to be entirely independent of the state of polarization of the incident rajs. Moreover, the dispersed light presents no traces of polarisation, whether the incident rays be polarized, or otherwise. 6. The power of changing the refiiangibuity of rays appears to be possessed b^ a great maoy bodies, especially b^ organic sub- ' stances, in which it is almost always manifested in a greater or less degree. Of this the crvstalline lens is a conspicuous example. 7. ^e phenomena of fluorescence oppose fresh difficulties to the supposition that the luminous, chemical, and phosphorogenio rays are of a different nature ; but they are perfectly conformable to the supposition that the production of light, of chemical action, and of phosphorescence, are merely different effects of the same cause. The phosphorogenic rays of an electric spark which, ^ as it is alread;|r Imown, are intercepted by glass, appear to be nothing more than invisible rays of excessively high reuiingibility, whi^ • 7hiLTruH.1668,pwt8s and 18S3, pwt 1. 630 CHROUATICi*. there is no reason for supposing to be of a different nature from the rays of Hpfht. 1117. Both iluorescence and spectnim-analysis have been ap- pealed to to demonstrate the wonderful rapidity with which certain substances taken into the stomach are absorbed, and de- posited from the blood in eyery part of the system, even in tho non-vascular tissues. Thus quinine has been detected in the human crystalline lens, remoyed on account of cataract, 2) hours after it had been administered : and two grains of chloride of lithium having been given to a guinea-pig, after 6 hours the lithium lines were visible in the combustion of alt the tissues. In another experiment no trace of lithium could be detected after six days : it appears that the removal of any particular substance from the various tifsuos by absorption is by no means so rapid « process as its deposition. 1118. Photphoreaeence, — ^The property of emitting light, either spontaneously, or in consequence of exposure to intense li^ht, or to a moderate heat, is \ffTmeA phoaphorescenoA. The luminosity of phosphorus, of the glow-worm and fire-fly, of various marine moilusca, and of decaying animal and vegetable matter, is probably of a chemical ori^n, and might be called cAemico/ phosphorescence in contradistinction to phyncal phosphorescence, produced by the agency of light and gentle heat. The phenomena of phospho- rescence, produced by the action of light, appear to be intimately related to those of fluorescence: while the phosphorescence resulting from the application of gentle heat, as in the minerals apatite and fluor spar, appear to be eoually related to certain heat- pnenomena to be nereafter described, and which Prof. T^dall lias designated as " calorescence.*' Of the latter substance it may be remarked, that, after having once been rendeVed phosphorescent by heat, it will not again phos^oresce under similar circumstance^ until an electric spark has been repeatedly passed over its surface. In this fact ma^ be recognised the intimate relations existing between electricity, light, and heat. It is very questionable whether these phenomena of fluorescence by heat, and ordinary incandescence are not identical ; differing only in the temperatura at which in^ different substances heat-motion impressed on the molecules is imparted as light-motion to the surrounding medium. The character of the rays emitted bv a phosphorescent bodr appears to be quite independent of the character of those by which this peculiar property is called into actfon : thus, a portion of cal- cined oyster-sneli, if placed in the red, yellow, or violet rays of the solar spectrum, will present those respective colours to the eye — * that is, the rays reflected by the superficial particles will be un- altered ; but when removea from the spectrum, it will in either case emit, for a short time, the same pide light, thus showing that a portion of the various coloured rays has undergone the same change by the molecular action of the substance on which they CHROMATIC ABEBRATION. 631 impinged. The sulphorels of the alkaline earths, strontia, baryta, and lime, are amongst the most powerful phospbori ; from these M. £. Becquerel obtained, by change of temperature and other appropriate treatment, the yarious clours of the spectrum in their pnosphoresoent emanations. In some bodies, the property of phos- phorescence is extremely transient ; but the existence of this pro- perty in several of the most powerfully fluorescent bodies hcM been ingeniously demonstrated by M. Becquerel, by means of the phot- phorotcope. In this instrument, a small vertical cylinder about one inch in diameter, and six or seven in length, and capable of being put in rapid rotation, is so placed at the angle of a dark chamber, that atwut one-fourth of the circumference is presented inwards, the remainder appearing externally. When the chamber was illuminated with the electric light (808^, and the surface of the cylinder covered with any of tne eartny phosphcri above mentioned, a moderately rapid rotation suflSced to render the whole of the exposed surface of tne cylinder equally luminous. With a little increased velocity of rotation, the same result was obtained when the surface of the cylinder was covered (by evaporatinj^ h solution) with sulphate of quinine, or with SBSculine. When simi- larly covered with nitrate of uranium, a very rapid rotation (not less than 300 revolutions in a second) was required to develope the phoephorescent effect, and even then not more than half the exposed surface of the cylinder was illuminated, the light appearing like a beautiful band of lambent flame emanating from the aperture. It would thence appear that in this substance the duration of phos- phorescence could hardly exceed the thousandth part of a second. The very attenuated media in some of the tubes prepared by Geissler and others for exhibiting the remarkable stratifications in the electric discharge (811, 812), are highly phosphorescent, as shown at the moment of the cessation of the discharge : and the luminous trace of a flash of lightning has been ascribed by Faraday* to the phosphorescence of the oxygen in the atmosphere. 1119. When bght passes through a prism, it is resolved into a series of coloured rays, of which the more refrangible are bent towards the base of the prism (1082) ; but when it passes through lenses, an analogous resolution into coloured rays is not so readily observed, although it does exist, and to so great a degree as to interfere most seriously with the perfection of microscopes and telescopes, causing the image to be tinted at its edges with ^' ^^' various colours, the result of ehromatic aberrcUum, The section of a convex lens may be represented by two CUB A, B, Fig. 697, placed to base, and that of a • Phil. Magasine, June, 1867. 632 CHROMATICS. ooncAT6 lens by two others c, d, with their apices id contBci. On a ray of light being incident upon snch elementary prisms, it Qn- dergoes refraction and resolution into coloured rays ; and the moat refrangible, the yiolet rays v, y, are brought to a focus nearer the lens, and the least refrangible, or red, b, b, to one at a ereater dis- tance ; so that, on placing a piece of paper at e f, the image of the sun or other luminous body will be seen surrounded by a Tiolet or a purple border, which will be replaced by a red one on moving the paper to o h. 1120. The greatest improTement ever mnde in optical instni- ments consists in the discovery of achromatic lenses ; these are formed by combining a concave and a convex lens, constructed of substances of different dispersive powvrs Fig, 698. (1 101). Thus, if a convex lens made of crown* glass, of which the dispersive power is 0*089, be combined with a concave lens of flint-glass in which the power of dispersion is 0'048, a componnd.lens will be constructed capable of refracting white light to a colourless focus. This combination would be perfect, if the coloured bands prodnoed by prisms of these two glasses were respectively of equal breadth ; but, in consequence of the irrationality of the spectra (1098), this perfect neutralization of tint takes place only with toe extreme rays, the violet and red ; the intermediate ones imperfectly de- stroying each other, cause the object viewed through such com- pound lenses to be bordered by fringes, which, however, are so faint that for all ordinary purposes uie combination may be con- sidered as achromatic. By employing certain fluids, as hydro- chloric acid, confined between two lenses of crown-glass, Dr. Blair overcame this remaining difficulty, and obtained a compound lent, perfectly achromatic for the intermediate as well as for the extreme rays. In order to produce a more perfect degree of achromatiBm in the object-glasses of telescopes, a combination of three lenses is frequently employed : for this purpose a flint-glass lens is placed between two of plate-glass ; the adjacent surfaces being cemented with Canada balsam, in order to prevent the loss of light by reflection from so many surfaces. The course of the rays will be better understood by a reference to Fig. 591, supposing a second and thinner crown-glass prism to be placed in the same direction oo the contrary side of the prism of flint-glass. The rav in its passage through the two prisms there represented is dispersea without being refracted, and if the angle of the third prism be such that its disper- sion will be just equal to that of the other two, but in a contrarv di- rection, the ra^ will finally emer^ refracted, but almost colomieaSw In the object-glasses of microscopes, owing to the large difference between the angles of incidence of the central and peripheral rays on the first surface, it is impossible to correct the IKTEKFERBXCE OF BATS. 68S aberrations by a single combination ; it has therefore been found desirable in practice to employ two achromatic combinations in " objectiYes*' of 0*7 inch or of any greater focal length, and three, in tnoee of 0'5 inch, an^ all higher powers. The principal part of the magnifying power is always thrown on the external or anterior combination, and the correction of the aberrations on the posterior ; the spherical, chiefly by the middle one. 1121. When two or more undulations act simultaneously on a particle of matter, it oscillates with an intensity corresponding to the combined force of the undulations : the same thing occurs, provided the latter are of equal length, or differ by a given number of entire undulations, even when they emanate from different sources. But if the waves actine on a particle differ by any odd nnmber of half undulations, they interfere and oppose each other^s action, and thus actually produce partial or total darkness. This may be rendered more intelligible by drawing two sets of waves containing the same number of undulations, as ▲, b, Fig. 599 ; any particle at o must be made to assume a movement corresponding to the combined -ZV* fr- action of A and B, and a corresponding intensity of light will result. By alter- ^ ing the relative position of a, b, so that ^ A may begin one half an undulation later \^ than B. as at a', b', it will at once be ^ been tnat they will be always in oppo- site phases, and any particle at d will be acted on in opposite directions by a' and tl ; for whilst the impulse at w is from right to left, that at e is in an opposite direction, and tnese mutually opposing eaOh other, the particle^ at c will remain at rest — darkness thus results from the conflict of two luminous undulations. If the waves of light, instead of meeting at the end of an entire half-undulation, encounter at any fractional part of one, partial interference will ensue, and colours will be developed, bearing a relation to the length and velocity of the undolations remaining undestroyed. 1122. It lias already been seen that the interference of sonorous undulations produces silence (549—554) ; and in the extension of this fact to luminous waves, there appears a striking analogy between the oscillations of li^ht and those of sound, the difference being rather in decree than in kind. The alternately increased and diminished effect of combined luminous undulations, bears a remarkable analogy to the beats in music (549), which are pro- duced when sonorous vibrations, differing in their rapidihr by a fractional portion of the. period of either wave, interfere, ana by so doing alternately intensifjr and diminish each other's eflfocts. 1123. An ex^rimental demonstration of the interference of lu- minous undulations may be obtained by an apparatus first pro- 634 CHROMATICS. posed by M. Fresnel. He allowed a ray of liglit to fall in the direction of p c, Fig. 600, npon ±tg, eoo. g^ prism, c, with an cx- ' -^ ceedingljobtuse angle. ^^x^^TSif^^j^-^vv-^ Then the eye placed at ^-'^'^'^^^^^Ty$wOO&'&0^^».AJLS&^^ A will see the radiant "^^^ — >yVyW^X^^ point double, appa* ^*^**-v^^*^^^^^4^^^^ ^ rently in the directions ^^_^^^:J-it7r^^*^ A B, A D, and between D- — '"" those two points, a series of dark and bright lines perpendicular to a line joining the two images. If homogeneous light (1082) be employed, as that from a spirit-lamp with a salted wick, the lines will be alternately yellow and black ; but if common light be employed, they will be tinted with the prismatic colours. The explanation of these colours is not difficnit ; the two images B, 1), may be regarded as the centres of two series of undulations; but as has been shown in the case of two series of waves in water (466), when these undulations meet in the same phase, lisrht is developed, and when in opposite phases, interference is proanced, and darkness or coloured light occurs, according to the interfering waves. In the above figure, the dotted curves show the poaitions of the opposing, and the entire curves those of the coincidinff un- dulations. The series of dots show the points where lummoas interference occurs. A fine eacperimentum cmcis, proving the real origin of these dark bands, is made by covering up one half of the prism ; the interfering rays are then cut off, and the bands instantly disappear. 1124. An interesting set oF illustrations of the doctrine of lumi- nous interference is met with in the phenomena of difou;tion dis- covered by Grimaldi, a Jesuit of Bologna. To observe these pro- perly, a l)eam of diverging^ light is necessary ; this may be obtained by making a small hole in a window-shutter, and receiving the light on a screen at the distance of some feet. If a convex lens, of small focal length, be fitted in the hole in the shutter, the li^t is refracted almost to a point, from whence it diverges in a manner very well fitted for experiments on difi&action. For small experi- ments, a p>|ramidal box, a b d c, Fig. 601, about two feet long, and blackenea inside, may be advantageously employed ; at e, a convex lens, of an inch focus, is fixed, on which, by means of the plane mirror o, a sunbeam can be readily thrown. The light is refracted by the lens to a point, and then diverging, is received on a sheet of white paper placed at the bottom of toe box ; by means of a door shown at f in the section, the bottom becomes easily visible^ without admitting any considerable quantity of extraneous light. 1 125. If any small opaque bodies, as hairs, pins, &o., he held in the beam of diverging light, bl l, their shadows will be thrown DIFFRACTION OF LIQBT. 635 Fiff, 601. on the bottom of the box, wirrounded by coloured fringes. If h be A section of a pin thus exposed, the fringes nre seen surrounding its shadow, a^ though thej were produced by coloured rays passing by its margin, notm straight lines, but in hyperbolic curves, as shown by intercepting them at different dis- tances by a piece of card ; when their decrease in extent will be found to be much more gradual than if the light passed by h, in right lines ; this dis- turbance of the rectuinear course of the rays is termed diffraction, Besidesthese external fringes, there are internal ones within the shadow, which, if the body be narrow, as a pin, becomes completely filled with them. These colours are, as Lord Brougham* has long since shown, in harmonic proportion, like those of the solar spectrum. The tints of the coloiued fringes, reckoning from the shadow, succeed each other in the foUowmg manner : — 1st fringe — violet, indigo, blue, green, yellow, red. 2nd fringe — blue, yellow, red, 3rd fringe — ^pale blue, pale yellow, red. If homogeneouM light (^1082) be employed, the fringes will be of the same colour as this li^ht, and their intervals will appear black. The fringes are broadest in red, narrowest in violet, and of inter* mediate breadth in the other colours of the spectrum. 1126. These phenomena admit of ready explanation on the theory of interference (1121), forwhen the diverging rays which are infletied on one side of the pin, meet those which are inflected on the oppo- site side in the same phase of undulation (369), thev coincide, and produce a line of white light, which ought to occupy the middle of the shadow ; whilst rays which differ in their paths, as those which pass obliquely past the pin into its shadow, meeting with those which pass more directly on the opposite side, encounter each other under different phases, and interfere, either producing darkness, as when homogeneous light is used, or so interfering as to produce a coloured frinffe. 1127. In shadows of this kind, formed by narrow bodies, the middle is always occupied by a luminous Hue, as though the light had passed directly through the centre of the diffracting body. This very curious fact is best observed by holding a small disc of metal on a slip of glass, in the diverging pencil (1125) ; the rays passing bv its circumference are inflected, and meet after traversing equal paths in similar phases in the centre of the shadow, producing • Fhfl. Tnwa. 1796. A brilliant spot of light ; tlie shadow thus precigely lewinUM lliat of a circular diec perforated in the centre. This beaatiM «xperi- tneut is best perfonoBd b; meuiB of a drop of thick black Ink, or a mixture of Ump-black and siro, placed on a plate of glaio, ao aa to form a circalar spot about the tenth of an inch in diameter : this modificatioD ot the original experiment of F^«tnel waa Di- gested b; the late Prof. Powell. 1128. Ifa diBc, perforated with a verT imatl hole in th« centre, be held in the beam of diTerging light (IISS), the conTerae of tbe Ust experiment will be obserted: forthoee andnlationa which paM directl,v through the aperture, interfering with thon paaamg more ohIiqaeN, produce a dark spot on that part of tha shadow cor- responding to the hole in the disc. Thui we find light TirtaaUf changed to darkness, and darknen to light, b; the tfuoord or om- a/rd nf the luminous waves. 1129. If two knife-edges be held very near each otber in the diTorgent beam, beautimllT coloured fringes will be obserTed to bordur their shadow, and a lUrk line will, IT thej be tfj. Wi. sufScientlj near, be seen to occnp; the middle of tbe space, at which the; are reall; aepaiate. This result of luminous iolorference may be readily sbown by placing a slip of lin-foil On a plate of glass, dividing It longitndinall;, and very slightly separating the divided portions at one end, so that they mar fonn a very acute ansla with ea<;h other, as in Hg. 602. Let this be held in the diverging light of the apparatus before described (ll!d), about six inches rran tbe 10 that it may form a well-deGned shadow. Tha a ponding hns will be covered with a beantiful set of fringes diverging from each other as they approach Uie Bpeiofiheacnteangle, r, Fig.60iS,andbi ' ' on eacb side b; hyperbolic curves, with parts of the carved fringes oorrespond to the apex of the angle fbrmed by the slips of tin-foil. In the figure, raa represents the pngeotioo of tb« slit in the foil on the paper on wnioti tho ahadaw falls. ThiBexperiii>entiBaneM7,althiMwhRingji mode of repeating Hewton's obaenation* with the kniie-edKoa.* 1130. The explanation of the production of colours bydiDndMn (1125) is well illnstrated by placing a card on onende, and cm a pUne above or below the bed; h, Fig. 601, so as to intercept some of the incident or diSiiicted light: the fringe* then dis- appear, because one set of the undutaijona producing intsrfemiee ■Optlog. Ub.lil.pusf. obLia DIFFRACTION OF UOUT. 637 Fig.Wi. has been cut oiT. If a transparent body be substitated for the card, the fringe# lindergo a remarkable change, from the retardo' Hon of those uddalatious which are propagated through the traus^ parent screen. 1 131 . The beantifnl phenomena of diffraction may be easily ob- served by Yiewiog, in a darkened room, through a piece of the: finest copper-wire gauze, a series of objects, Fig. 604, fixed in a laree screen of black pasteboard, so placed as to prevent any light reach-' ing the eye, except such as passes through the object. The following give particularly interesting results. A. Fix six sewing-needles over a hole cut in a Siece of blackened wood, taking care their mutual istances correspond to the thickness of a needle. On viewing this object at a proper distance through the gaujse, each needle will apnear transparent, the centre of each being occupied oy a line of reddish light. B. Examine in a similar manner a piece of tin- foil, in which a fine slit, about one-twentieth of an inch wide, has been carefully cut. The slit will seem widened from light entering the shadow, its centre being occupied by two vertical lines of bluish black, whilst a series of coloured bands will extend to a distance of half an inch on each side of the slit C. Make a line of small holes in a piece of tin-foil by means of a fine needle. Each hole will appear bordered with a reddish margin, whilst a series of spectral coloured openings will appear in the foil for half an inch on each side of the real aperture. D. Perforate a piece of tin-foil with a very fine needle, as shown in the figure. Each opening will, when examined as above, present nine coloured squares like a window, and the spectra will be so numerous, that the foil will appoar full of holes, admitting li^ht of different colours. A convenient form of apparatus has been de\ised by Mr. Bridge, consisting of a lens placed in an aperture in a dark screen, on which direct sun-light is reflected by a mirror. When the image of the sun in the focus of the lens is viewed, by a telescope, through transparent apertures of various shapes in an opaque film of col- lodion, produced by photography, the effects produced are ex- tremely varied and beautiful. 1132. The brilliant tints of soap-bubbles, and of thin plates of various transparent bodies, afford further examples of interference of light : for the undulations reflected from their first surfaces interfere with those reflected from the second (1034); and upon the amount of retardation thus experienced by the luminous 638 CBB0MATIG8. wayeB, the yarietieB of colours observed in these thin platos depend. The colours of soap-bubbles are well seen bj boiling a small quantity of soap with distilled water in a bottle, and corking it whilst boiling hot. The whole being secured from air, is allowed to cool, and on adroitly shaking the bottle, a laige bubble, pre- senting the coloured bands with great beauty, maj be readilj fonned ; this bubble is permanent for several hours, and afibrdi every facility for examining its tints. Soap-bubbles may be blown from a mixture of soap and glycerine which will last for a oood- derable time without bursting. 1133. The colours of thin plates of air may be obsenred by {>reRsing a convex lens on a plate of glass, and nolding it in the ight, so that rays reflected from it will pass to the eye. At the point of apparent contact with the lens and ^lass, a black spot will, under these circumstances, be visible ; this is surrounded oy a great number of rines of different colours, each series of tints consisting of fewer colours as they recede from the centre. On holding the glasses between the eye and the light, a set of rings will be observed, differing in colour from those seen by reflection ; and complementary (1091) to them, each ring possessing that colour, which by mixing with the tint of the corres]^ndiDg re- flectea ring, would produce white light. The following are the colours of the rings, observed by reflection and transmission, com< mencing from the centre or point of apparent contact, as given by Newton.* By reflection; — ^Black, blue, white, yellow, red, yiolet, blue, green, yellow, red, purple, blue, green, yellow, red, green, red, greenish-blue, red. By transmission; — ^White, yellowish-red, black, violet, blue, white, yellow, red, violet, blue, green, yellow, red, violet, greenish- blue, red, bluish green, red. 1134. Tlie following table contains the thicknesses, expressed in millionth parts of an inch, of plates of air, water, and glass, re- quired to produce the different coloured rings : — By aid of this table, the thickness of thin Alms of air, water, or glass may be readily determined by observing the colours they reflect. The comparative thickness of plates of two substances, reflecting the same colour, is in the inverse ratio of their indices of refraction (1067). These rings may be exhibited by merely placing together two plates of window- glass, about four inches square, and pressing them in the centre by means of a pointed piece of metal. The different coloured rings, somewhat eccentrically arranged, will appear with great beauty around the point where the presaare is applied. 1135. When these rings are observed by homogeneom light, they present the same hue as that of the light itself, alternating * Optice. Lib. ii. pars S. C0L0UB8 OP THIX FLATE8. 639 Berieaor orders of ooloors. Oolonra leen bj relleotion. First . . < /Very black Black Blackish Pale sky-blae White (like polished silver) . . Straw-coloar Orange red (dried orange-peel) . ^Red (geranium sanguine um) ^Violet (vapour of iodine) . . . Indigo Blue Orange (fresh rind of oranges) . Bright red vDusky red Third Purple (flower of flax) . Indigo Prussian blue .... Grass-green . . . . Pale yellow . . . . Bose-red V Bluish- red Fourth . Fifll>. Sixth . Seventh 'Bluish-green . Emerald-green YKllowishgreen ,Pale rose-red . fSea-g^en . . . Pale rose-red . . (Greenish-bine . . Pale rose-red . . (Greenish-blue Pale reddish-white Thioknesa of pUtes producing them. Air. 0*50 1-00 2-00 2-40 5-26 711 8-00 900 1117 12-83 1400 1612 16-29 17-22 1833 19-67 2100 2210 23-40 26-20 27-14 2900 3200 3400 3629 3600 40-33 4600 52-60 58-75 6600 71-00 77-00 Vaster. 0-38 0-76 1-50 1-80 3-88 6-03 6-00 6-76 8-38 9-62 10-50 11-33 12-20 13-00 13-75 14-75 15'75 16-57 17-66 18-90 20-33 21-75 24-00 25-50 26-50 "27-00 30-25 3410 39-38 44-00 48-75 53-25 57-67 Glass. 0-33 0-66 1-30 1-55 3-40 4-60 517 6-80 7-20 8-18 900 9-70 10-40 11-11 11-84 12-66 13-06 14-25 1610 16-26 17-50 18-70 20-66 2200 22-80 23-22 26-00 29-66 3400 3800 4200 45-80 49-66 J with dark and almost non-luminous rings; and thej appear to have the greatest breadth in red, and the least in violet light. These 640 CBBCUATICS. rings appear to be larger, in proportion as they are seen io a more oblique direction ; this is best seen by examining the rings produced, when the slant side of a rectangular glass prism is pressed on the surface of a convex lens of yenr small curvature. The coloured rings thus exhibited by thin plates, are produced by the interference of the light reflected by the first surface with that reflected from the second, for when either of these reflected rays is intercepted, the colours cntirelpr vanish. 1136. The rings seen by transmission are produced by those undulations which are not reflected, and are consequently pro- pagated through the thickness of both glasses. Those luminoos ravs, which, when combined with the reflected rays, produced white li^ht, being propagated through the glass, produce the transmitted, or complementary (1133) rings. From Newton's table (1135), it appears that air, at or below a thickness of half a millionth of an iuch, and water and glass at a thickness of about ou,e-third of a millionth of an inch, cease to reflect light, and ajvpear, consequently, black. Films and fibres of quartz, so minute as to be incapable of propagatinglnminoas undu- lations, have been met with and described by Sir L>. Brewster. 1137. It is by no means necessary that very thin plates should be used to exhibit colours, for plates of any thickness, so arranged as to cause the interference ofluminous undulations, will produce the same effect. This may be shown bv fixing two slips of plate glass about 0*1 inch distant from each other, by means of two pieces of wax, and then by pressing one end of each plate together they may be so fixed as to describe a very acute angle with each other. On looking at a candle through that part^ of the plates nearest each other, numerous reflected images of it will become visible : the first of them appears crossed by a series of beautiful bands or fringes. These increase in breadth by diminishing the inclination oi the plates ; they are produced by the interference of the waves of light reflected from tne two surfaces of each plate, 1188. The coloured rings observed by regarding the sun, or other luminous body, through a piece of glass covered with minute particles, as of dust, lycopodium, &c., or of water, by breathing on it, are all owing to the interference of luminous undulations infli'cted round the particles (1125). A similar explanation will apply to the colours seen by scattering fine powders or dust on, or before, a mirror exposed to the solar rays. The beautiful tints presented by mother of pearl, and other natural or artificial sub- stances of which the surfaces are marked by minute strise, are all explicable on the hypothesis of interference ; all that is requisite to produce these colours being, that the depression shall be of anch a aepth as to cause an alteration in the paths of rays incident upon them, equal to some aliquot part of tne length of an undo- lation. 1139. If a series of reiy fine and close parallel lines be roled THB SAIKBOW. 641 apon a sar&cei the reflected light will be oolonred hv thoee tajB, of the length of the undaUtionB of which the inter valB of the lines are a multiple, the others being partially destroyed bv interference ; the colours thus produced have been ornamentally applied in the manufacture of what were well known as Barton* t btUtons; but philosophy in buttons not having been appreciated by the public, it has long been difficnlt to obtain a specimen. An elegant confirmation of the undulatory theory is due to the ingenuity of M. Robert, who has succeeded in ruling bands of lines on glass so exceedingly fine, and truly equidistant, as to reflect well-defined prismatic colours. The bands are about 12 in number, of which the widest reflects the coloora of the lower end of the spectrum, and four or five of the narrowest reflect no colour, being multiples of the wayes of invisible rays. If the piece of glass, which is suitably bevelled at the edge, be now so j^aced that the incident rays mav pass through the edge, and be received by the eye after internal reflection, the ravs are retarded by their passage tnroagh the denser medium, and the higher rays of the spectrum (using the terms higher and lower in relation to the refrangibility of rays^, are now reflected from the narrower bands, all the coloured rays aavancin^ in the series of bands, according to their degree of retardation. Nobert's lines form an extremely interesting micro- scopic object. 1140. Among the natural phenomena which serve to illustrate the laws and principles laid down in this and the preceding chapters, the well-luiowii rainbow, and less frequent mirage, especially deserve attention. The former consists of a coloured arch, apparently suspended in the sky, and opposite to the sun, and is frequently composed of two bows, termed primary and secondary, and sometimes even of other supplementary arches. The rainbow is never seen unless a shower of rain «^^ ^f^^^ is falling, or the spray of water, as from a cataract, rising between the spectator and that portion of the sky opposite to the sun. To explain the cause of these bows, let B, F, Fig. 605, be two drops of water, and sb, sf solar rays inci- dent npon each of them, then those which enter near their centre will be refracted to a focus, as in a sphere of glass (1069) : but those which enter near their upper part suffer refraction, daring which the light is resolyed, as in pris- matic refraction (1082^, and colours are consequently produced. And such of these refracted rays as are incident at the back of the drop, within the limiting angle (1060,) there undergo total reflection, and emerge at the lower part, as c, in the drop b. But T T 642 CHBOUATICB. most of these small pencils of coloured rays are diTereeDt after they emerge from the small aqueous spheres, and blending with one another, reproduce white light. There is, however, one particular angular position for each prismatic colour, in which a globule of water may be placed in relation to the sun and the eye, uiat a parallel pencil of that colour may emerge parallel, and reach the eye ; and as that position will vary for the different colours, in proportion to the aifference of their refractive indices (963), the colours will, as in the prismatic spectrum, be presented in succession to the eye. Moreover, all points in the circumfe- rence of any circle described round a line joining the sun and eye, as an axis, will be similarly situated in relation to the sun and the eve ; consequently, the several colours will appear in a circular arc, of which the centre is some point in a line drawn from the sun, through the position of the eye, and present to the spectator a bow of the prismatic colours, bounded alK>ve by the red, and below by the violet rays. The several coloured solar rays that enter the lower hemisphere of the drops of rain in certain positions, as at o, B, are retncted to the back of the drop, undergoing the same resolution into coloured rays, hence they are successively reflected to the top, and to the front of the drop, whence, in one particular angular posi- tion of the aqueous globules for each colour, thev emerge parallel, and reach the eye, presenting to the spectator the appearance of a second bow, exterior to the first, and with its tints much fainter ; and reversed in position, in consequence of the rays having suffered two reflections m o, h, whilst in k, f they underwent but one.* The phenomena of mirage arise from the reflection of terrestrial objects from the common surface of two or more horizontal strata of atmosphere of different densities. When the rays fall on llie surface of a rarer stratum at a very large angle of incidence, as when a spectator is looking towards the horizon, they will fre- quently exceed the limiting angle (1060), and total reflection will then take place. The objects from which the rajs proceed will then appear to be inverted ; sometimes both an erect and an in- verted image of a distant object will become simultaneously visible. * For a fall in^f stigaUon of the phenomena of the rainbow, and of the sparious bows frequently observed to acooropany it, the reader is rererred to a memoir by Prof. Miller, in the seventh Toliime of the Caaibrid|{e Philo- •ophiotl Transactions. 643 CHAPTER XX. OPTICAL 1N8TBUMENT8. 1141. Optical instniments maj be divided into the catoptric, including thoee depending upon reflection ; the dioptric^ or those acting by refraction; and tnose depending on the combination action of both effects, or cata-dioptrie instruments. Of optical instruments depending on reflection, the various forms of mirrors already described constitute the most important. The common looking glass, the theoretical action of \Knich has already been explained (1036), is too well known to need description ; and the convex mirror, formerly a common ornament in large rooms, is chiefly employed on account of the diminished images of objects which it produces (1045), and thus the whole extent of a landscape becomes, as it were, compressed into the space of a few square inches. The concave mirror is a very important instrument, and, besides its application to science, it has formed one of the most valuable resources of charlatans and jugglers, on account of the power it possesses of forming in the air an image of any object 5 laced beyond its principal focus (1044). Thus, if any object, as a agger, strongly illuminated, be held towards a concave mirror, an image of it will be formed in the conjugate focus, so vividly and periectly painted in the air, that the person who holds the dagger can scarcely believe that the weapon which advances to meet mm, is but a spectral image of the one with which be is armed. 1142. The most important application of concave reflectors is to the construction of telescopes, in which the image of a distant object, as one of the celestial bodies, is formed in the principal focus of a concaye mirror, and magnified by means of conyex lenses (1080). The sim- jp. ^^ plest reflecting telescope is that constructed by New- ton in 1666: this consists of a concave parabolic (1050) metallic reflector AB, fixed at the end of a tube CDB Fig. 606. A small plane mirror, in- clined at 45", or, still bet- ter, a rectangular prism p, is fixed in the tabe, between the specu- lum A B, and the image formed in its focus. The image is thus ro- T T 2 644 OPTICAL IHSTXUlfERTS. fleeted towards an opening in the side of the tnbe, where it is viewed through a convex lens for the purpose of magnifying it.* The advantage of a prism over a plane mirror, for the purpoM of reflecting the ima^ of the distant ohject towards f, is sufficiently ohvious, for, hy tntenuU reflection (1060) from the back of ^m prism, nearly all the rays are reflected to the eye; whereas, if a plane metailic speculum were substituted, about 45 per cent, of the rays would be lost (1034), from the undulations producing them being absorbed on reaching the surface of the metal. For the purpose of preventing spherical aberration (1081) from interfering vnth the distinctness of the image, Newton placed a plate of metal pierced with a small hole between the eye and the convex lens, through which he viewed the object 1143. The Gregorian reflecting telescope was invented in 1660, by Dr. Gregory, but not actuaUy constructed until some years subsequently to that of Newton. In this instrument, the iDcoooh venience of taking a lateral view is avoided ; it consists of a oon- cave speculum fixed in a tube, but pierced in the centre with a hole, through which, by means of a lens, or a comlnnation of lenses, the image of the object is viewed. The rays after fonning an image of the object in Dr. Gregory's telescope, are received on a small concave mirror, placed opposite the aperture in the larger one, and form a fresh image which is viewed through that aperture. The observer, in using this telescope, is placed in a line with the object, whilst in Newton's, he is at right angles to it. 1144. When a cohvex mirror is substituted for the small con- cave one in Dr. Gregory's instrument, we have Caasegrsin's telescope. In this, the magnifying power is less than in either of the preceding, but the image is more (tistinct than in any other construction, as but one image is formed ; and as one speonlnm is concave, and the other convex, they have a tendency to ooirect each other's spherical aberration. 1145. In astronomical reflecting telescopes the Newtonian cod> struction has generally been adopted. The oUiq^ue mirror has hitherto been supnorted by a single stem from the side of the tube, the vibration of wnich in some degree impairs the definition of the image : in telescopes of very large dimensions, as in those of Sir W. Herschel and the Earl of Rosse, this inconvenience is obviated by placing the speculum a little obliquely, and thus bringing Ibe image to the side of the tube ; but a sl^ht loss of definition from oblique reflection is thus introduced. Astronomical telescopes of lai^ size have generally what is called an eqiuitorial mounting; in this the telesoope is attached transversely to a rotating axis, which is acy^B^d parallel to the polar axis of the earth. If this, the polar axis, be made to rotate (frequently by clockwork) in a direction opposite to that of the * Newton, Optioe, lib. i. prop. 8, prob. S. 645 eutb's rotation, and nilh u equal velocitT, it ia clear that • fixed hsavenl^ body, as a »tar, once m tbo field of the ingtrumBnt will remain ia it ax ioog aa maj be required ; bnt if ■ montUe ^oif, tm the mooD or a planet, be under obeenation, theta Itt owti Mn^ tootion, aa weQ ae the earth's rolatioa, must be compenmltBd by k notion ^vea to the inatnuQent, in order that tki objeei t!a*^ AatroiKHDioal reflecting tele- Flf-ttt. derate coat hare been c ■tmcted hj Hr. Browning, one of which ia repreaented in f>g;. 607. The Btand here ahown ia called an "eqoatoHal moDnting :" a firmly fixed iron pillar, a, mp- porta the honr-cinJe, c, which 1 by meai -,- ._.„ , - The j_ clination-aiia, d, ia at right angrliM to the polar axii ; to one end of thia the teleacope ia attached, tai a bMTy maaa of metal, B, at & cnunteipoiae to tha other end I the position of the teleeoope ia de- termined by the KjadaalAil circle •nd vernier, h. The specnlom, a, ~ U pUced in the bottom of the teleacope, and the ej^pjece, ■, u Kiewad into a rotating cylindrical cap, in order that it may be tnmed in any direction moat conTenlent for obeerration. A amall t«leacope, r, i* attached paiallel to the aiia of the laiver one, haying croas-wirea in the centre of the field of view ; this la called ■ " finder." When correctly adjnrted, ar^ object brought to co- incide with the ptnnt of croaaing will be m the field of the large teleacope. 1146. The apecnlnm employed in thia teleacope ia one of silvered glasa (1062), the bottom of which ia made perfecCly plane ; thin ia clamped by a ring into a oell (be bottom of which is also tralj plane; the apecnTaiii may therefore be removed fur cleamDg or — I'lhiag, and replaced, wilhont doatroying its adjuatment „„ „ -,Fig,6 , diao it along bv three piecea of strong obronometer-balanoe-ipring ' wire, pUoed edgewise towarda tbs Bpeooliim ; and to this diso the oblique refleclor i« nttached bj Bcrewg Tor the pncpoae or&ii^uttiitg j^ jm tlio direction of the reflectine aurfaca. The niirTor is also capnble of being sdjoHUd laUrall;, bv means of the screWB, c, c, c ; aad it is much lc9B liable to vibration than with llie ordinaiy ninglo Bupport. 1147. If, instead of ^mtiUlng the immge to be painted on the lelina of the efo, it be re- ceiied on a screen, then Ihe iDBtniment bocomM either a cajneni obscurfl, or a Bolttr roicroBcopa, according to the wrangement emploj-ed. If a coniei lena be lized in a hole made lu one end of a box, made a iitlle longer than the focal IvDgth ot the lens, and painted intcrriallj with some black pigment, fur the parpoae of absorbing all eitranpoua light, the image of a landscape, to which the lens is presented, will be beamifullj end vividly painted, in an inverted position, on a aheet of paper Gied at the end "«■«*■ of the boi oppoflite to tbe I lens. SomelinieB, inalead of receiving tbe image on a »lieet of paper, it is in- flected by a plane mirror, A, Fig. 609, placed at aa angle of 45°, towanla the upper part of the box ; * sheet of white paper, or » pioee of ground glsas, n, being there jilaced to receive it. In thi* mode the image appears erect, and inverted only as regards the right or lefl portions, and is usually preferred for the purpose of RKetching distant views. As the lateral portiona of the picture are indistinct from spherical aberration, a meoiscna (1068) is preferable to any other form of single convex lens, for the porpose of reducing 1148. If any small object, strongly illominated, be placed oat- side a csmera obacura, having a lens of high power, and a little beyond tho principal focus of the lens (1065), an image of tbe object will be depicted on the paper screen at the end of the box. An instrument tlius arranged has been termed • Megaaoope : hat it is not olUn employed. 1149. The best form of camera obscnra is that in which internal (1060) instead of specnlar reflection is employed to prevent the loss of light attenduit on the latter. The box is then made of a pyramidal form, a B c i>, Fig. GIO, and a rectangular prism, having one of its faces, a, convex, and another, b, concave, is placed over an aperture in the top of the box. The rays from a distant object will be made to converge afler impinging on the convex sniface, o, and being reflected in the interior of tbe priam, will pats into the 647 box, and paint the image on t. liieet oF paper placed at the botiom, c D, to rccoiTe il. The picture thae obtained is extremelj vivid, Irom tlie perfect reflectioD of raji _ from the bock of the priam, and tniiD tiie spherical aberration being to a grea extent CDunteracted by the cuncave fac of the pmm. Aa these meniscua prism •re not re>dilj obtained, tliej may b advBnt»geoitslj replaced bj a rBctanKDliir priBm baniig a planD-cDnvei and a plano- concave leng, of suitable focal lengths, cemented by Canada balsam on two of its faces OS shown at e, in the figure. 1150. Wlwn a virid pencil of light, before being made to convBiga bj re- fractioll through a lens, passes through a amall transparent body placed before it, at a distance a little greater tben ita focal length, aa enlarged image of the object will be painted on a screen placed at a proper distance behind uielenB; this is the principle of the solar microBcope. The simplest form ot this inBtrnment consists of a pyramidal box abdc. Fig. 611, fbmisbed with a door at E, like the camera obscura. The solar rays falling directly, or "*■ *^'' reSecled by a common lookiiig-glaaB plane ntiiTDr F, are tranamilted t plano-convex lena a, whste they nndeipj refractioD, and fall on an abject placed a E, nearly in the principal Iccas of a. Thi light then passes through two plane convex lenses, each of about half an inch focal length, at l, moveable by met radiWDrk at h, forming a widely diverging bundle of convergent pencils, and paints a highly magniOed image of the object at the bottom of the box, where it may be viewed through the door k. To prevent as macb as possible sphGrical aberration (lOHI), a diaphragm of metal, pierced with a small bole, sbonld be placed between the two lenses at h. if the mirror P be removed, and the direct light of on Ai^nd lamp be incident on a, this becomes the tucernaT, and if the light of lime ignited by mixed oxygen and hydrogen gases be employed, the oiy-hydrogen microscope. Where high magnilVing powera are required, more complex object-glasses must be employed. 1151. The magic-lantern differs scarcely at all in principle from the three last-described instruments. The light of a lamp, placed in a tin box, is reflected by means of a concave mimir, tuiQ oon- dented by a lens, on figures pointed in vivid transparent colonn 648 OPnOAL nrSTBUMBKTB. Bf.611. ^; I A \ / > * _ff on a Blide of glass ; the light then is refracted through two convex lenses placed near the object, and capable, hy a sGding tube, of bein^ a<^'usted to such a distance as to cause the image, when received on a white opaque screen, to be as vivid and distinct as pOMible; the aiagio-latitem being nothing more than a lucernal miorotcope of low magnifjing power. If the screen on which the object IS painted be transparent, and the spectator be placed behind it tlie ittAg« will, in a dark room, appear to be painted spectie- like in the air, constituting the well-known phantasmagoria. 116t. A very valuable mstrument, termed the eatnera luada, for taking drawings of landscapes, &c^ depending upon internal reflection, was contrived bj Dr. Wollaston : this ooii> sista of a quadrangular prism, a b d c, Fig. 612, the angle b, being 90*, D 67•5^ and c 185°. Bajrs ns, evolved from any distant object, will, after in- cidence on oi>, be reflected in the in- terior of the glass to c a, and thence to the eye placed above the edge a. And as all objects appear to be placed in the direction of the rays which eventually reach the eye, the image will appear to be painted on a screen or sheet of paper at o n ; and if « perforated piece of metal be placed on a n, so that one-half only of the aperture be over the angle a, the image and paper will both be visible to the eye placed over the aperture; and a sketch of the object may thus be taken with extreme accuracy, by simply oopylng the oullineB of the figure, as it appeara depicted oii«a. The most convenient mode of using this instrument with the miotoscope is to nlaoe the body of the latter horizontally, and to view the image airectly, and the paper by reflection. 115S. A very exoellent instrument, advantageously leplacing the oamera lucida, especially in making microscopic drawings, is the mirror of Soemmering : this consista of a small round plane speculum of steel, about one-fourth of an inch in diameter. Tbia b^ing fixed before the e^e-glass of a mioroecope, at an angle of 45** with the axis of the instrument, a person looking into it (the body of the microecope being arranged horiaontaHy) will see a reflected image of the table, but from the small size of the mirror, a portion of the rays proceeding from an image of the object enter the eye simultaneously, and thus the image appears superpoeed upon a sheet of paper placed on the table, and with a little ma- nagement, the outhnes of the image may be readily traced with, a pencil on the paper. 1154. Instruments designed for presenting to the eye a mag- nified image of an object aie called miero$cc>pe$» When single TBI UHTU MIOIOBODra. M9 laiMU are tutd for nmpla nucTOKopeij it ia imporfamt to diioinuili ■pberical ftberraticn tw mncb na pooaible, br pennittiDg onlj tboas raTB vbicb pua Dear tbe ceatre of the leni to reach the tje. I Thi«ni»j,to»gre»leil«nt, be effected by Dr. WoIImIod'i metbod ' of [Jscing between two plano^oiiTex lenaea, a piece of metal per- I fonited in the centre, commonlj called a dK^ragm. A better mode of obtainiag tbe ume effect it b; grinding away the eqaatorial poitiona of a apberioal lena, aa ia the well-known Cod- dui^on iena, which ia tfie moet ptn^t ample lena hitherto conatincted. The Stanhope leni ia another toit nsefol modiEoation for the purpoae of a simple microacope ; thia ia a thick lena with two Bphericsl anrfaoea, so amnxed that the foci of all pamllel peDcila Kfracted at one mrTaoe ahall approximately ooincida with the other anrface ; conaeqnenlly aoy minate oinecta depoaited on the latter, will be diitinctly bmq mnch magnified, on viewing them thmogli the former. If the ocnlar aurfaM or the Stanhop* lens be tnnwd towarda ft •oorce of light, and the atgect be liewed by a Coddington lena ot ■hart rocm, a high magnifying power will be obtained, accompanied bj extnmely good definition, owing to the yerj aconiale manner in which the object ia illuminated Xl 165). : 1156. One of the beit forms of aunple microBcopc for a certain olaaa of olgnctt, on account of the great dis- '■ tinctneaa of tbe image, is the doublet of Dr. '"'* *"- WoUaaton. Thia conaiats of two small filano-eonTei lenses, of which the focal engths are as 1 : 3, fixed in the braaa cop a, « Hg. 613, the leaat oonrex lena being nearest tbe eye. The hrssa labe b ia about six inches long, famished below with a plane minor St p ; a circular apertnre is made in a diaphragm placed aboTe it, throogh which the light reflected from r passes throngh the conrei leas B, so as to (ona a distinct circalar image of tbe apertnre at the distance of about O'B inch from i. Tbe object to be examined ia placed on a slip of glaia on p P, and the lensei in a are adjnstedbymeans ofa screw at s. By this instrument many delicnie morkinga, and fine strinon rei^minale cbjects, may be clearly seen. In all simple microscopes, the centre and edges of the magriifled image are never equally dialinct, ^m the spherical aberration of theleBses (1061). To remedy this, diaphragms are placed in the body of the microeoope, to exclude thoae raya which are refracted from the edgea of tbe lenses. Y ' ""^ — "^ ■* lensea oontrtTed by Sir John I 650 OPTICAL IS8TEUMENT8. prevent this aberration from interfering with the distinctness of the image. 1156. A microscope, composed of two or more lenses, is nerer- theless termed fimpUf provided they are combined to form an image, as in the Woliaston doublet ; but when an image formed by one lens or combination is magnified by another, as the object itself would have been magnified, then the instrument is called a compound microscope, and is commonly preferred to the simple instrument, from its having a larger field of view, and, when pro- perly constructed, not fatiguing the eye so much as those consist- ing of a single lens, or combination, of very short focal distance. In the compoand microscope, in its simplest form, a magnified image of an object is formed, by allowing the rays passingthrungh, or reflected firom it, to be refracted through a lens, or combination, of short focal distance, called an object^uiss ; the image thus pro- duced is further magnified by a second lens of much lower magni- fying power, called the eye-glast; hence this instrument requires much more care in its construction, to ensure an accurate and perfect ima^, because the eye-glass magnifies the errors of aber- ration existing in the image formed by the object-glaaa, in addition to the similar errors that itself introduces. Let a b o. Fig. 614, Fi 614. ^ ^ ^^^ ^^ brass, blackened inside to abeorb 8up«r- ^' fluous light, and provided with a small lens at c ; ^ an object placed in its focus at p, strongly illnmi- ^^ , nated by light reflected from a mirror placed below ' ^'^ it, will have an image formed in the focus of the eye-glass A at /*, and a ^rtion of this may be viewed through a, by which the rays divei^ng from f are made to enter the eye in parallel pencils. For tne purpose of increasing the field of view, a third lens b, called the JiMylass, of less ma^ify- ing power than the eye-glass, is generally mtro- duced ; this causes the converging rays going to form the image to converge still more, and a smaller imase, as shown by the dark arrow, is formed at ^ The distance of the object-giase c from the eye-glass a must considerably exceed the sum of their focal lengths. 1157. A compound achromatic lens, the construction of which has already been described (1120), forms an excellent object-glass for a compound microscope, giving a nearly colourless image of the object, which will bear a higher magnifying power in the eye- glass than an image formed by an ordinaiy lens of equal focal length. Among other advantages presented by an achromatic olgect- glass, is the fine illumination of tne image, arising from the larger pencil of rajs which can be admitted into the bodv of the inatrti- ment. This may be readily understood by a reference to what ▲CHEOMATIC OBJECT-GLASSES. 651 has been already stated with regard to the use of diaphragms or stops, in the constmction of optical instruments. These are per- forated pieces of metal so placed as to cut off the more external rajs of a pencil passing through a lens, and thus permitting only the central rajs to reach the eye ; and in this manner many of the aberrations of a lens are practically reduced to a minimum, although at the expense of a great loss of light. The achromatic construction, by allowing the transmission of a larger pencil of rays, enables us to use high magnifying powers with a perfection of illumination previously unknown. The advantages of a large angle of aperture in an object-glass are not by any means confined to the increase of the quantity of light transmitted: in many colourless and transparent objectSi such as the siliceous shells of the various diatomacese, the structure is indicated by differences of thickness so minute, that no visible di.sturbance of the transmitted rays takes place, unless they pass venr obliquely, or in other words, none but very oblique rays will render the structure visible. The truth of this observa- tion may be readily shown by experiment : — ^many difficult test- objects may be discerned by a small margin of the peripheral rays of an object-glass of large aperture, the central rays being stopped out ;^ although when the object is much more iUuminated by the admission of the latter, and the exclusion of the peripheral rays, the structure previously recognised will remain wholly invisible. 1158. As it is a matter of great practical difficulty to balance the chromatic and spherical aberrations perfectly in a single com- bination of lenses, a great advantage is gained by the union of two or three combinations, in which & aMrrations of each are mu- tually balanced. Object-glasses constructed on this principle have, in the experienced hands of Messrs. Boss, Powell and Lealand, and Smith and Beck, been brought to an amount of perfection which could scarcely have been anticipated. In the nigher powers three double, and sometimes even triple, com- binations are employed : and the larger amount of magnifying povver being obtained by the anterior or external combination, its positive aberration (1048) is corrected by an exoess of negative aberration in the two posterior or internal combinations. When three combinations are employed, the middle one is generally a meniscus (1068) for the purpose of correcting the spherical aberra- tion, or curvature of the image, in order to produce a flat field. 1 1 59. So delicatel V are the aberrations of a well-made achromatic object-^laas balanced, that merely covering an object under ex- amination with a piece of thin glass, or mica, is sufficient to inter- fere with the perfection of the image. This effect is practically perceptible only when object-glasses of high power are employed ; and we are indebted to the ingenuity of the late Mr. Andrew aoss for a knowledge of the mode of correcting it. Kf.eit. tood by a n . . . F1^. 616, ia vhich, let f be the focas of u I object glisa, corrected for ancoTered ob- ■ peripb«rKl rar, ftod Bra nj ixii of the pencil, cr. If a pUu I of thin glau di be now inteipoeed, ihe I rajB A F, B r will be refruted on CDteiiaK I the plate, in the directiona Ao, ■&, and J *ill emerge in the directions af^ bf,, and a certain amonat of ncKatiTB aberratlMi, repreaeDted b; rf,, will be introdnced : in order to con«ct tl^ or to make f, anii ^ again coincide with r, it ia neceaaaij to incnase the refractian of the raja a and b, but of a tnoch more than B. This is effected br approiimating the anterior to the two posterior combinations, bj which the raj a is compelled to paaa Ihrongh the anlenor lens nearer to its margin tbaii before, and therefore throoKh a portion forming a more obtnie wedge, where it consequeDtlj taonn mone letiaction. The otgect^lasses posseasing this erBat improvement are cod- ■tmcted with a mecbaniBm ahowa ia !ng. 616. The two poaterior Bchromatio lenses are fixed in tbs end of the tnbe, b ; Dp«i this slides a cvlinder, a a, carrjing at the lower snd the thiid or anteKor leu, which, hj taming the screwed ring, o c, maj be approximated to, or separated from, the olber two lenna. The proper diitance fiir the a<)j<»^ ment of theae lease* fbr nncorered objects is known b^ a Ene marked on the tabe, a, coinciding with one on the tnbe, b ; and, when ohjecta ate examined which «■« corend with S'»m, or immetaed in a flaid, the stance of the third lens froqi the other two ii altered bj turning the ring, cc, no^l the bant definitioo i^ the object is obtained. 1160. The image of an object thns formed bran achnmatie combination of lenses i> eiamloed throngh e;e-piece9 of different Diagni^ing powera ; these are rariooslr constructed, bnt Ihe moat approved ore the Ho^enian, or mgataie, and Bamsden's, or the potitiee eje-piece. Of these the ncgatiTe eje-piece ii b; far the most frequently omplojed ; it consiata of two lenses, ■ a, and r r. Fig. 617, each being plano-conTei, with their ooDTexitiea lowanls the object.glass. i B ia termed the eje-glass, and r f the field- gloai, for reasons alread; poinled out (I lOS). A perfbrmted H^ or diaphragm is placed at b b, to cat off ths extreme raji that ooxbubd AonoH of thb btv-pisoe axd OBJBcr-oLAfla. 658 Jiy. 617. might interfere with the perfection of the ima^. It most fortn- nately happens that the arrangement of lenses m the Hnygenian eje-piece possesses the property of correcting not only tneir own aberrations, bat ako those of the object-glass, as first pointed out by Mr. Ross.* The positive eye-piece also consists of two plano-convex lenses, but the convexity of the field-glass is upwards, and the principal focus of the combination is external to tne field- glass. The ^ principal use of Bamsden's eye-piece is in the construction of a micro- meter ; for thispuipose, a scale marked with a diamond on a plate of ^lass is placed in the principal focus, and its image, being consequently superposed on that of the object, serves the purpose of measuring the magnitude of an object, when the value oi the divisions of the scale is known. 1161. All that is essential to the construction of a perfect mi- croscope is then, a good achromatic combination of lenses to form an image of an object, and a well-made eye-piece to magnify this image. It is obvious that the mi^nifving power of a microeoope can be increased in two modes ; by increasing the magnifying power of the object-glass, and thus forming a larger image ox the object, or by examining this image with a deeper eye-piece (t.e., one of higher magnifying power). The first mode is undoubtedW the most accurate, as by tne second we magnify any errors which may enat in the ima^ formed by the object-glass, as well as the image itself: still, with good and trustworthy obiect-glasses, we may not inconveniently examine the image with different eye- pieces, and thus avoid the necessity of altering the position of the object, or removing the object-glass. Acconiingly, some of the continental microscopes, as those made by Oberhauser, are pro- vided with a series of six eye-pieces of different magnifying powers ; English microscopes have, however, seldom more than three or four. When very high magnifying powers are required, as 2500 diameters and upwards, there is a third mode of augmenting the power, which is sometimes very available, namely, bv increasing the length of the body, or the distance between the objective and the eye-piece. It is evident from what has preceded (1079), that if an im^e be formed at any nven distance firom a lens, the diameter of the imaee will m doubled, if it be formed at double the distance ; hence ue power of a microscope will be doubled by doubling the length of the body. With any given objective, and at any rate the third eye-piece, it is ouite obvious that both defi- nition and illumination are improved by lengthening the body in * P«imy p7olop«dia. Art. Miorosoope. 65* oPTi prefersBce to using a deeper eje-pi«ce, ad3 the wnter it incKn«d *« beliere, from repeated oWrvntian, that bejond » certain limit, better reeolt is obtained by lengtlieDiiig the bodr, tlun hj ei bjectiTc, that limit being probablj aa objectii an inch focus, few Tran, Bchromatic ohjectiTea ofi'^hofaa ioch focuB were the higbest powers eiistlog; objectives of -^th Rnd Ath of an inch focus were Enit conBtraclBd by Mr. Wenbam, and have aince been made by Messrs. Powell and LeaUnd ; objrc- tivOB of 1°™ (^Atli inch) focus have also been made by IL Hartnack of Paris, and in America; but the writer has not aeen any equal in defining power to the English glasseB. 1162. The greatest recent improrement in the tninvscope hu been the appliEBtion of binocolar viaii — —' •■" "■" -' ' ■- n relief (see Stereoscope). This ._. 1.., means of prisms, hut Wenham pitsduces unqueatioDBbly the best r requires description. A priam, of which A b C D, Fig. 618, is a side view, is ao placed just above diflerent ways by means of priams, hut as the method da« to the ineenuity of Mr. Wenham pi-oducea unqueation " - '' ' ■ suits, that alone requires description. A priam, Fig. 618, is aside riew, is so . Flu. ms, ,1,^ object-gU™, that the edge meeting the angte In, binects the bundle of pencils proceeding from the object, so that one-half of the penciu pass directiy up the body in the direction E p, white .. , . , nied by 0 , . horizontal surface of the prism d c, and being twice internally reflected, emerges perpendicu- larly, and thercrore without rerraction, from the surface a b. and proceeding towards H, enters a second body inclined at a suitable angle to the original body, and is there magnified by a second eye-piece. In order to suit tho TBriouB distancoa between the centres of the pupils of the eye in different individuals, the distance between the centres of the eye- pieces is B^JUBts^ hy elongating or shortening the divergent bodies, shown in Fig. 619, by means of two racks and a pinion- By this arrangement the images received hy the two eyes an very mnch the same as they would be if a similarly enlarged ob< ject were viewed by unaided viaion ; and it is well known that the mental combination of two dissimilar pictures produces the Krception of rilUfin a solid object. It is evident that the per- il ^fiuition of the object must in all probability be slightly im- paired hy tho tranamission of half the pencils through the nriim, but as the other half reaches the eye undiatnrbeil by reflection w refraction, a perfect image is perceived ; justaa a goal atereoacop'o effect may be produced by the combinatioD of a feeble with a well developed photograph. In all other binocular arrangementa, both halvea of the visual rays aro equally submitted to some kind of prismatic diatturbance, and the low of definition thereby i« *«ry perceptible. 1 163. TKetnccluiiical anangementB of a microscope are ecarcelj of lesa importiuice tlian tbe perfection of lenaes. As a nneral rule, tbat form of support wliicb combines sMbititj with tlie ETeatest facility for the necessarj adjustmeDte is to be proferred. Ths eta^ ahnuld alvaja be a fiitnre, and the ndjustnieiitB to focus eSecled hy moving the bodj of tbe instrnment. Many forms of support for the optical part of the microscope have been con- ilructed by Messni. Pritchard, Powell, Koss, and Smith and Beck, ID thiH country, and each has probably, in the opinion of variona observers, its peculiar ncommendationa. Aa a really verking inetnunent, capable of I>eing applied to any purpose for which a microscope can he employed, and compriainE all the most recent improve men Is, [he one cnnttructed by Mr. Boss, lepreaented in Fig, 619, ia prubably the best. Tlie whole instrument is supported on tvo standards, resting on » firm triangular foot. The double body, a. isconnecledby an arm, b, to a rectangular piece that tlidea within a box, c, attached by an axis to the two lege, in order that the instrument may 656 OPTIOA.L IH8TBITMBirT8. be placed in a oonvenient inclined position, as in the ^gnre. A Sair of e je-pieces, b, b, are inserted in the upper end of each cylin- er, and an object-glass, o,li8 screwed on to the lower end, wiiich is brought into adjustment hj raising or lowering the sliding piece by means of a rack and a pinion attached to the milled heao, d; this is called the eoarBe aajustment. The >Sne adjuMtment^ which is necessary for the high powers, consists of a lever enclosed in the arm, b, acted on by a very fine screw, f, which moves by a vexy unall quantity an inner sliding tube to which the object-glaas is screwed. The binocular prism, a o. Fig. 618, is inserted in a sliding frame, p, so that it may be interposed in the path of the rays proceeding from the objective, or withdrawn at pleasure. When the priam la withdrawn, the whole of the rays enter the vertical tube, as usual; but when it is in its place, the pencil, b f, enters the vertical, and o H, the oblique tube. In the use of tiiis instrument it is desirable first to bring the object into focus with one eye, then to adjust Uie eye-pieces to the distance between the eyes, so that both images may be seen $imvltanext<:rior aurface of a cnne of rays iasaiDg from the itiuminatur. nnd neetiog in afocua atn, vhere the ot ject is plac«l. If a conBiderable piirtiim aJ the centre of this cone, as ci>, be ebul oat hj an opaqne stop, then a coaicat tJitU of raTB only will full upon the object, tbroDgli the sBTerol portions of nhicb the; will be Torionsl; reflected sad re fnicted. Now if fq, the object-glasi employed in viewing the object, be such that IF, Eo, the extreme ra7a that cnn eater it, lie within o b and DE produced, which are the innermost of the illuminaliDg r*;Bi >t is eTidunt that no portion of these rays can enter tbe object-glus, and ccnseqnendy where the Reld of view is vscHnt, it is perleotlr dark, the onlv isja entering the object-glass being those the path of which is altered in pasaing through the object This mode of illumination may be effected either by plaoiDg an opaqne stop in the centre of the pencil incident on an aplonatio comtnnatioD, a b ; or the pencils abc, deb, may be reflected from the inlerior of a truncated cuncare parabolic mirror with an opaque stop in ^centre, as proposed by Mr, Wenham; or inlemally re- flected from the sur&ce of a truncated paraboloid of glass, the truncated end terminating in a hollow spherical surface of which the focDB of the parabola is the centre, in order that the rays reflected towards the focna may emerge from the glass without Tefraotion, as contrived by Hr. SbodboTt. By cementing a small truncated paraboloid of glass to the under ■"'^^ce of a slide, Mr. Wenbam has sacceeded in brilliantly iliu- kting the shells of diatomacete mounted in Canada balsam by ■uriace of 'iCondenter. — TheulilityofanymachtneiggTBatl; augmented by rendering the interchange of moTeable parts as easT of accomplishment as possible; and microtcopic obiiervers will Bed this to be especiollT the cs«e with regard to the TarieCies of iljominatiag apparatus Uiat have been propoead ; of all these, however, the condenser, Ti^. 631, designed by Mr. Oillett, appears to be the most comprehensive in its application. The base, A b; fits into the rotating ring of the secondary stage, i., Fig. 619; D d2 the optical arreDfcemeDt, a, is that of a | inch abject-gUu (ai ■«- preaented at tha aide of the figure) aod Iraaimita a pencil of aboat B0° aperture: bat the great improrement consiati in the adap- tatioD of a wuoer-»h»ped disc, the rim of ■'*■■*'■ wbicb is « truncated oone, aud so placed @ that the aarface of the rim may paaa per- peodjcntarlj ibrouf^h the commoa aiie of the leuBea c, aud immediately below (be Burface of the lowest lans. Varioiu aper- turea. for modifying the illutninatii^ E pencil, are placed ronad tha circumferenoe of the rim, each of which may be placed central!; under the lensea, by meana of • . atop, r, at the end of a aprine, e r: tbeae oonsiit of a serias of circular oalea, which iHry in diameter from o, which tranmiita thaeuttM pennl, toi, which tranamita one of only about 10'';alao apertures, la C, d, with oeotral discs, aupported esch by a slender Mr, of which the lar^n^st, d, will produce a daii ground (1166) with the i or ^ inch object-glass, and the other, e, with the powers below these. A tourmaline, t, ia fitted into another aper- tnra, by which a polariied pencil may be obtained, with no nioiv trouble than that of turning round the cone with the Guger and thumb. Another aperture, o, is stopped ap, all except a amall lateral portion, which transmits an oblique pencil inclined about 8&° to tDs ails, and which may be made to tiavel round the axia by the rotatory movement : thia modification of the ill aminating pencil, to which we shall presently recur, is sometiniea canTGDJent. If a pencil of perfectly colourlesa polsrlzed light be required, it u focnd oonvenient to psss up a amsil Nicol's priam (lOSS) in tha iuterior of the tube beaeath the lenses. The coaveniencea which thia inttniment affords for the examination of objects either on ■ bright or dark ground, or by ohiiqae, or polarized light, witboat any disturbance of a^ioatmeDtB, can acarcely be overesdmatod bj mietDBcopic obserTcrs. The writer has found that a more effectiTe illumination fbr rerj high poirera ia prodoced by employing the optical combination of the AinchobjecliTO of Mr. Eoea, inplacHof I as aboTO described : alao if a plane horizenta la combinations of the apertures and stops, every requidta modification of the illuminating pencil may be oblained. 1168. OUiqtie lUumination.— It haa already been stated (1 167} ID eiplanation of the practical nlility of object-glasses haring » lai^ angle of aperture, that the more minute structure of aome ob.|acts is cognizable otUj/ by ita infiuence on rays traTeniag tite olyect with conaiderable obliquity. In default of paaaeMUig aodi (lt1jec^glA■set (wliicli are difficult of constmction, and conae- queotlj eipeniiTi), o umilar reBiilt niaj be much leu perfectlj Btlained bj illaniinatin^ the object b; a pencil of oblique nja only : but oblique light is at best a treocfaerous (UI7 of (he micro- scDpiBt, and never to be depeudMi upon, as tbe appearances pro- dncod are eitramel; fallHCious, but vhich neTertheless serve occBsianaill/ to indluats what might be revealed bj more perfect optical appliances. Eieveral modea of producing an oblique itlumi- nation have been devised, of ivliich tie pnEm of Amia la the be«t : this, as coiDmonly emnlored, is an obtuse j^. gu. iaoscetea prism, of ivbich the two equal sides have apherieal surfaces ; this is placed late- rall; beueBlh the Btaze,the back of ihe prism being nearly parallel to the plane of the stage. A pencil derived from a light placed aidevajB is refracted through one spherical surface, and after Internal refiection at tbe back of the prism, Is Bgaiu refracted at the second apberical surface, mi at the second surlace of a convex lens, and comes to a focus at the under side cf a transparent object. The writer has found the niOBt convenient mode of mounting an Amici priam to bo that reprosonted in tig. 623 : in this case tbo section of the prism tfg must be a right-angled, or an acute, in place of an obtuse isosceles triangle. It is attached to the top of a tube, he, (which fits iato the rotating ring of the secondary stage, l, Fig, 619,) by two anpports, c, so placed aa not tointeirupt the pencil of light, and between whifji it maybe moved, so an to vary the inclination ofthebackof thepHsm. Another prism, atcfl, equivalent to two right-angled prismi, a be, oca onited, is placed beneath, bj which a central pencil, t, is transferred to the side of the tube d ■ after two internal re- fleclione ; it is then in succession refracted at the spherical surface fg, reflected from the back of the priam tg, and refracted at ef, whence the raya come to a focua at b, which point may be brought to coincide with the axis of rotation, as tbe support, c, turns on a oenlre, and is attached to a dove-tail piece, sliding in a groove in the upper surface of d. This arrangement aSbrds a much larger pencil than that mentioned in the preceding description of Gillett't condenser, and, by the rotatory raBvement, the aiis of the obliquo pencil may be made to rotate nmnd the axis of the microscope : it moat howevor be boriie io mind Ihat obliqae illnraination is, alter all, to be considered ^t as a Uet Msonroe. It is Dttneceeaary to describe l)i« In^iooe prism of Kachet de- signed for tbe aame fmt^mM, M tt is not eq«ai In llhiniiniitinK power to that alreadv described, and moreover the inclination of the oblique pencil i> mvariable. Beflecting microscopes, on the same principle as Newton'a fi62 OPTICAL INBTRUMK^tTS. telescope (1092), have been constructed by Professor Amici of Modena, and olners. In these instruments, the object is placed in one focus of a small and finelj-polished elliptical speculum (e. Fig. 572), and its image formed in the other focus is examined by means of a magnifying eje-piece, consisting of one or more lenses. 1169. The reiracting telescope was invented in the thirteenth century, although the discovery appears to bave been nearly lost until the sixteenth. The simplest telescope is that employed for astronomical purposes, and consists of a c«>nvex lens of long focal distance fixed at one end of a tube, and exposed to the object, the image of which, when formed in the focus of the lens, is examined by a second convex lens, or eye-glass, of shorter focus. These lenses should, for distant objects, be placed at a distance from each other corresponding to the sum of their focal lengths. In Fig. 623, A B is the object-glass, and o d, which must always be of a shorter focus, ^'^^' the eye-glass, and placed, it the fiicua of the former were eight, and that of the latter two inches, at a mutual distance of ten inches. To accommodate this instnjment to olgecta at different distances, the eye-glass is usually fixed in a tube which slides within that containing the object-glass, and thus permits a ready a^ustment of the instrument. In this telescope, the object appears inverted from the crossing of the rays after refraction through the object-glass, and hence its use is limited almost entirely to astronomical purposes. An erect image may be obtained by adding two other convex lenses, of the Fame focal length, behind o d ; these are called erecHnff-glaue$, but a loss of li^ht is necessarily produced by their use. Aberration maj be diminished as much as possible, by the same means as those em- ployed in the construction of compound microscopes. The mag- nifpng power of these telescopes is found by dividing the focal length of the object1aced that each receives the pencil at the angle of minimum deviation (1082), and the colourea rays being thus separated, tlie spectrum is viewed by a telescope, b c, naving an achromatic olgectp glass at B and a negative eye-piece (1160) at o adjustible to focus by a rack and pinion. The telescope has a radial motion, and may be adjusted to any required part of the spectrum by a tan- gent-screw at F : by means of which also the angular measure- ments are taken. Sometimes, instead of one or more prisms of dense flint glass, a hollow prism containing bisulphide of carbon, which possesses a very high dispersive power (1097) is employed. This is efiected by grinding away portions of the sides of a glass bottle in the direction of two planes containing an angle of 60**, and cementing on two pieces of polished plate glass. Spectroscopes have been construct-ed with as many as ten prisms arranged in a concentric circle on the plate ; by means of which a much wider separation of the lines of the spectrum takes place. For the purpose of comparing the lines of any two given spectra, a portion of the narrow slit is covered by a right-angled prism, bv means of which a pencil of light falling laterally on one face of the prism is intemaUy reflected from the oase, and pasacp onwards through the tube e d, parallel to that which paases di- rectly through the remaining portion of the slit. 1174. A ngid spectroscope, in which all the parts are immo- vably fixed, has been constructed by Mr. Browning for Mr.Gassiot, for the purpose of determining the variation of refraction, if any, due to change of the force of gravitation. In this instrument a pencil of light passing through a slit is rendered parallel by an achromatic lens, and heing transmitted through two and a half prisms is reflected back perpendicularly from the silvered outer surface of the half prism, and naving been again further separated by the other two, tne spectram is brought to a focus bpr the same lens, and being then reflected at right angles by a n^htrangled prism, the image is examined by a micrometer eye-piece. The separation of the spectrum is thus equivalent to that produced by a train of five prisms each of 45**. Tlie prisms are adjusted to the position of minimum deviation for the hue d of the solar spec- trum. Sufficient time has not yet elapsed for any decisive results to be obtained by means of this instrument. 1175. Straight Spectroscopes, — ^Two diflferent modes have been devised by which the mean rays of the spectrum emeige in the 665 ction ss the incident pencil, knd in wbicfa conMqDtnlly oacope becomes a atnight Inatrument, vkich is more t for ma.ay purpOHOB of obKrvatioD, aa it maj be mora Tected to the lonrce of liglit. these is a red Qpli cation iy Hr. Browning of a priini by Sir J. Henchel. u A DC, Fie. 628, is "* "" ;1ed at A ; toe pencil | ut D, is iDternall; I at E and p, and I at o in a direction I tu that of its inci- | it tUoa paninei the ■ L-durse through a aecond similar priiDi placed in a re- >0!>i tion, aa in (he figure, bj which the separation du« to prism is doubled. c other mode of construction two rigbt-ai^«d flint-ghus ,. Fig 627, «.!.»,. „ Kitween three of crown- r anglea of I 6. Tbia latter form has been adopted by Mr. Biowning in nstrDclion of his ipeelro-mia-04cope, in wbich tbe ipectro- ie adapted to the ejepiece of a _ _ land microecope ; into tba body b is adiuttible for rayi of diffs- refrangibil . The combini . , placed above the e^e- 1. Forthe poipose of comparing difierent ipectia, a portion of the is covered bj a rigbt-angled pHsm, If taj traiuparent bodj the spcc- n of which it required, for eiaiuple lU conUining a coloared liquid, plated in the fruno " '' i^bl re M passea throngh the apertur i being intBrnally reflected upwards by p, passes tbroogb the iljBiag piiitni telween b and c, b^ the eicio of the pencil pro- iJinglniDilheohjflct nnder the mioroMopo. By theae means e peculiar ipeclnini may be obtained from verr mioate qaan- iei of any nibataiice (M of blood, for example) either diy, by Beded liAt, or nhen sospended in a fluid, by transmitted light. 1117. 1m £(l)wlat.— In sooie inTestigatkna on points of pby- 666 OPTICAL 1X8TRU1IEKT8. Bical optics it is desirable to maintain a solar beam continuooalj direoteil to one point, for a certain length of time. This object is attained by means of a heUostat^ in which, hj means of some mechanism, the rotation of a mirror is made to compensate the rotation of the earth. In the simplest form of this instrument, the heliostat of Fabrenheit, a ^laiie mirror is jointed to the end of an axis rotating by clockworJE onoe in twenty-fonr boors, and placed parallel to the earth's axis, and is so inclined as to reflect a sunbeam in the direction of the axis produced ; this direction of the reflected pencil will consequently be maintained by the rotation of the mirror. This pencil falls upon a second stationary mirror, by which it may be again reflected in any required direc- tion. The inconTenience of this instrument is the great loss of light occasioned by two consecutive reflections ; and in conseqnenoe more complicated forms of mechanism have been devised, in which the required direction of the reflected rays is obtained by one re- flection. These are all constructed on the obvious principle that if a normal to the mirror be made constantlv to bisect the angle contained between the line of incidence and that of the required reflection, the direction of the reflected ray will remain constant. In the heliostat of Sgravesande of Leyden, the earliest of this kind, and in those of Gambey and Foucault, the required result is obtained on the principle that in an isosceles triangle a line bisecting the vertical angle is perpendicular to the base ; if then one of two equal sides of the triangle be fixed in the reaoired direction, and the other be maintained in the direction of tne in- cident beam, and by making the plane of the mirror coincide with its base, the bisecting line remains always a normal to the mirror, it is clear that the desired result will be obtained. 1178. These instruments are more complicated and consequently more costly (although sometimes a little smoother in tlieir action) than that of M. Silbermann, which is constructed on a similar principle ; namely, that in a trapezium of which the sides are equal m pairs, the line joining the angles contained by the equal sides bisects them both. In this instrument a circular base, a b. Fig. 629, rests on a tripod adjustible horizontally by levelling screws ; this supports, by a horizontal axis passing through d n, a clock movement, c c, the central axis of which makes one rotation in 24 hours. A line drawn on the base, a b, at right angles to the direction of d e, must be made to coincide with the meridian Hne of the place of observation, and clamped in that position by the screw, F ; and if an arc of latitude, I ^ attached to the clock be now set to the latitude of the place, the axis of the clock wiU necessarily be parallel to that of the earth. A fixed tubular stem rising per- pendicularly from the surface of the clock, carries the hour cijirJe, A h ; through this the axis passes, carrying an index on the hoar- circle, and terminated by a square block, p, with a damping-sciew, through which passes a declination-arc, d i. Outside the tubolar stem IS a seoond tube, q, having at its upper end a block and w, throngfa whicli pauea aDothar Are, b h, oonoentna dd. , H M, is 10 placed that the centre of iU nHectinjc lea with the centre of the *iiM,di t^vA hh'; it u 7^. m». it 0 and a' to tvo framei taming freel v on radial atema the two area at H and d, to that in &tl poaitiona of the itre of the mirror, k, loaintaina a fiied position. A le mirror at i ia conetrained to bisect continnonslj the ned betwann the directioDS of its supports, hk, iIi, ezial airangement before alluded lo. For this pur- ed bar, or, ii attached perpendicnlarl; to the pbine or at Uie point a; two equal linka (162), pr, or, are {oal distances Irom o to tne tvo fr&mes, and the two innected with a pin sliding fraelj in the slot of the B clear, tberefore, that the angle p o 17 ( ^ 8 xd^iBKT) be bisected by 0 r, and conaequentlj a k t bj e n, a le mirror; hence if bk be the direction of the incident, hat of the reflected beam. to adjnst the instrument the declination-arc must bo n's declioalion ; but if that he not knuwn, it maj be liing to the arc, dd, a small plate, m, with a cross anothur, «, with a Btoall hole, so placed that a line lole and the oentre of the crosa may be parallel iat.d; an be nored antil a eonbeam paasing through n fall I at m, it is clear that the direction of the incident illcoinadeTithEdl The an HB'mustnoir beahifled 668 OPTICAL INSTRUMENTS. and tamed abont the axis, until the reflected pencil, k t, is in the required direction, 'n-hen the arc must be clamped to its snpport, o, and that to the surface of the clock, br a screw, r. It is evident from what has preceded that the reflected beam must aJwaji remain in the direction h k, which is now a fixed ]ine. In order that the reflected beam may be free from jerking and unsteadiness, it is necessary that the joints at o, p, q^ and r should all work freely, but at the same time without any lateral motion ; and to this end, the iinns op, 09, and the links, should be aa long as they can conveniently be made. n79. The construction of some of the mors impoTtaiit optical instruments having been explained, the student will be enabled, from the preceding obeervations, to understand the mode in which the eve acts upon lights so as to prepare it for oommo- nicating to the eensonnm the perception of surrounding objects, and thus to develops the sense of sight. The following ol^erva- tions, it must be borne in mind, apply only to the eye, consi- dered as an optical instrument of the most perfect kind, and unconnected with the phynologiosl relations of tne suljeot, except SQch as are essential to a knowledge of the phytd<^ te^oo of the organ of vision. Hg. 630 reprssents a honsontal sectiMi of the left eye (human), mMe bv a plane passing through the line of iunction of the eyelids. The form of the eye is nearly spherical, four-fifths of its ciroumference, a b jl, being nearly circular, the re- maining fifth, A A^ constituting the transparent portion, being more convex^ and forming a curve of a lesser sphere. After removing the muscles attached to the eyeball, the most external coat he- comes visible : this is a tough, pearly, opaoue membrane, termed ^^ 030^ the aderotie coat, extending from the entrance of the optic nerve, o, Fig. 630, on the nasal side of the optic axis, CD, to A A, whers it f. terminates in a circular open- ing, furnished at its margin with a grooved edge into which fits the transparent cornea, in the same manner as a watch-glass fits into the grooved circular frame of metal made to receive it. The oomea 18 as transparent as glass, and is about one-third of a line in thick- ness. A delicate mucous membrane, termed the conjunctiva, is expanded over the cornea and sclerotic, and thence reflected to the inner surface of the eyelids. Lining the sclerotic coat is the choroid membrane, extending from o to the anterior part of the eye contiguous to the mar^n of the cornea, where it terminates in the cuiary body, constituting a bond of union between the choroid sclerotic, and iris. The choroid coat is here thrown into 8TBUCTUBE OP THE BTB. 669 a number of puckered folds, the interior surfaces of which, as veil as of the whole extent of the membrane, are cohered with a black pigment. The optic nerve, o, enters the eye on the nasal side of the optic axis, and expands into a third coat termed the refiaa, which passes towards tne anterior part of the eye, and terminates in a well-defined edge. The retina is the membrane upon which the images formed by the refracting structares of the eye are de- picted : a delicate transparent double membrane, termed Jttcob^B membrane, intervenes between the choroid coat, and the retina. A delicate fibrous contractile structure, named from its various colours the iris, is suspended vertically from the ciliary ligament, havine in the centre an aperture, termed the pupil, which is capable of being enlarged or diminished involuntarily, under the stimulus of light. The iris is shown in the section at i, i ; the space between it and the cornea is termed the anterior chamber of the eye, and is filled with a fluid known as the aqueous humour. Behind the iris is suspended in a capsule a transparent double convex lens, l, of which the posterior is greater than its anterior convexity : this is termed the crvstalline lens. The remaining portion of the ball of the eye is filled up by a refracting structure, termed the vitreous humour, in the anterior portion of which the lens, L, is embedded : this is made up of a fluid contained in the convoluted folds of the transparent hyaloid membrane. The total length of the eye, along the optic axis, o d, is about 0*91 of an inch. 1180. From the investigations of Sir David Brewster, the fol- lowing are the refractive indices of the different transparent struc- tures of the eye, when light is incident upon them from air, or from each other: — From air into the aqueous humour ^=1*3366 From air into the vitreous humour „ 1*3394 From air into the crystalline lens „ 1*3839 From the aqueous humour to the crystalline lens . „ 1*0353 From the vitreous humour to the crystalline lens . „ 1*0332 Bays of light, on impinging upon the eye, are refracted through the transparent oomea, those incident on the sclerotic being re- flected or absorbed. The cornea may be regarded as constituting the anterior surface of a meniscus lens, of which the posterior surface is formed by the anterior capsule of the crystalline lens ; the aqueous humour forming the refracting medium of this fluid refractor. The rays of light which thus tend to be refracted to a focus, pass through the pupillary opening of the iris, those passing too near the margin of the lens formed by the anterior cnamber being reflected or absorbed : the iris, answering the purpose of the perforated diaphragms in microscopes (1 1 55), and telescopes (1 170), and being capable of varying its aperture, possesses advantages altogether unattainable in rigid diaphragms. The pencil of rays 670 OPTICAL IK8TBD1IEKT8. having pasaed through the flaid meniscus, impinges on the ayt- talline lens, and is there considerahly refracted ; tois refraction is modified by the action of the vitreons humour, the last medimn into which the pencil passes ; and finally an inverted image of the object, from the several points of which the rays of light are pro- pagated, is painted upon the retina. All rays which are reflected in the intenor of the eye, or pass too obliouely for distinct visioii, are absorbed by the black pi^nent, with wnich the interstices and folds of the choroid coat are imbued. It appears from the observations of Mr. Templeton* on the distances at which objects could be distinctly seen through aper- tures of different sizes in a thin sheet of brass, that the angle subtended by the diameter of the aperture at any point of Sie object, should be about 19^ or a little more : hence whenever by an act of volition the eye is directed to a near object, the iris is observed to contract, in order to limit as far as possible the visual pencil to the aperture most suitable for distinct vision. The same observer has also inferred that the diameter of the space on the surface of the retina occupied by the image of any point of an object is about 0'041"«« 1 181. The refracting structures of the eye thus act upon light, and produce an imaee of any object upon the retina in the same manner as a convex lens, with the advantsge of increased clear- ness of the picture from the absence of both spherical (1081) and chromatic (1119) aberration, produced by the curved form of the retina, and by the structure of the crystalline lens ; the refractive power of its centre beinggreater than that of its surface, in the ratio of 1*399 : 1'377. The diminution of aberration is also a^ sisted bv the pupil, which acts in the same manner in preventing spherical aberration, by being placed between the fluid meniacus and the crystalline convex lens, as does the perforated diaphragm in the Woilaston doublet, or the excavated sioes in the Coddington lens (1 154). Chromatic aberration is doubtless to a certain extent compensated in the eye bv the different dispersive powers (1101) of its several structures ; but this oivan is by no meana perfectly- achromatic, as mav be shown bv the spec^td colours observed fringing minute boaies held near the eye : some of which, however, are probably due to diffraction fll25). 1182. The eye in all warm-blooded animals is formed upon the type of that of man, with the occasional addition of supplementary structures, better fitting the organ for the perfoimanoe of vision in the particular animal. In fishes, residing m a medium of nearly the same refractive index as the aqueous humour, thecnrvatnreof the cornea becomes useless, and the aqueous humour is replaced by a viscid secretion of greater refractive power. The ciystalfine lens is, in these animals, nearly spherical, and placed very near to the cornea, and the iris, which is close to the latter, is imdilft- • PhiL Mag. sad Anaals, I>eo. 18M. DiVERTED lUAOE OK THE RETINA. 67l table. In insects tlie eye is yerj simplei consisting of a lenticular cornea, placed in front of a nervous expansion. The curvatures of the several refracting surfaces of the eye, and their relative distances from the retina, have been observed to vary considerably in the different orders and classes of the animal kingdom. 1183. Although it is demonstrable that images of external objects are formed upon the retina, it has been doubted by some whether the latter membrane is the seat of vision, as in certain species of cattle-fish an opaque membrane is found between the vitreous Humour and retina. The choroid coat, and vitreous hu- mour, have each been supposed to be -the true seat of vision. It is a curious &ct, that the point where the optic nerve enters the eye is absolutely incapable of visual perception, and the image of any object falling upon it ceases to be visible. This mavbe shown by placing three watisrs on the table about two inches distant from eacn other, and having closed one eye, look at the outside wafer on the same side as the closed eye : at the distance of about eight or ten inches from it, the two outer wafers will be distinctly seen, whilst the middle one will be qjuite invisible. 1184. When an object is viewed with both eyes in a healthy condition, it appears single, whilst it is obvious that a distinct image is paintea upon each retina. This is readily explained by tiie fact, tnat the two images, formed on corresponding portions of each retina, are mentally combined, and virtually produce but one impression. If the optic axes be not brought to coincide at the place of the object, the two images do not correspond, and then, as in the case of SQuinting persons, the object appears doubled, or confused. 1185. Many mgenious arguments have been used to explain why objects appear erect, whilst their images painted upon the retina are inverted, although a little reflection on this circum- Btanoe renders it probable that such must necessarily occur, from the law, that all objects appear to be placed in the direction pur- sued by the rays which eventually reach the eye. If a b, Fig. 631 , bean object from which i.. ... the rays following the ^*^' ^^* direction of the lines shown in the figure pass into the eye, they be- come refracted towards the retina, and paint upon it the image c d. Tnen if the retina be aasomed to be the seat of vision, the impression communicated by it to the sensorium is that of an erect object : for the part d of the image will appear to be placed in the direction of the rays d a, and the up]^er part, c, will appear to correspond with the lower part, B, of the ooject, which will appear to be situate in the direction of the rays o b. Consequently, although the image painted upon the 672 OPTICAL IVSTRUMENTB. retina is really inverted, it canyeys to (he mind the impression of an erect object; obtained, probably, in the first instance, by the comparison of Yisual impressions with those commnnicated by the sense of touch. 1 186. The Eye. — ^The wonderful perfection of mechanism in the eye, as an optical instrument, is most conspicuous in its power of adapting itself to various focal distances. It is well known, that in viewing objects through a telescope, the distance of the lenses from each other requires to be altered by drawing out, or thrusting in, the slides of the telescope, whereas the eye appears intuitively to accommodate itself to the various distances at which objects happen to be placed. The quiescent, or ordinary state of the eye when in its perfect or natural condition, is that of culaptation to Sarallel rays, that is, to the perfect vision of objects at considerable istances ; the alteration of focal distance takes place in adapt- ing the eye to the distinct vision of near objects, and consequently consists in an increase of that distance. There can be little donbt that this change is effected chiefly by a displacement of the crys- talline lens forwards, eflfected probably by the distension of the vessels of the ciliary processes, which constitute an erectile tissue ; and partly bv the contraction of the muscular fibres of the ciHary ring, the probable effect of which would seem to be a slight elonga- tion of the axis of the e^e, and an increase of the convexity of th« cornea : all of these actions would evidently tend to bring mrwards the focus of the refracted rays. The contraction of the iris that invcariably accompanies the adaptation of the eye to near objects, is probably only accessory in cutting off the peripheral rays in which the aberration is necessarily greatest, and not the essential means of adaptation as was supposed by Sir C. Bell. The variation of focal length of the eve has been attributed by some physiologists to an alteration in the form of the ciystallina lens bv the contraction of its own fibres ; but the structare of muscular fibre is so completely identical, from whatever part of the animal kingdom it may have been obtained, and so essentially different from the fibrous structure of the lens, that it appears difficult to conceive the existence of muscularity in that organ ; moreover, in all the higher orders of animals, the muscular struc- tures are copiously supplied with blood-vessels and nerves, neither of which have been detected in the crystalline lens. It has been very confidently assumed by Prof. Donders* to be proved that the acconmiodation of the eye to the distinct vision of near objects is chiefly effected by a passive increase of the convexity of the ■ crystalline lens, due to external pressure on its peripherv ; but he fails to explain how this is, or can bo, effected. This point is con- sidered to be placed beyond controversy by an experiment of * On the Anomftliea of Aocommodation and Befraotion of the Eye. 18M. (TraQBlation pnbliahed by the Kew Sydenham Society.) Cramer,* in which Ihe relative poaitions of the images of a candle placed at a diatance of 30° from the optic axis, and reflected from faces of the lens, are compared, as seen, flnt, when the eje is a state of qiiieBcence ; and aecondly, when accommodated to a ne nhject. These images are thua represented bj the observer : a, Fig. 633, is the image formed at the surface of the cornea, and b, e, those at the anterior and posterior surfacea of the lena respectively, when a healthy eye is in a quiescent state ; and d, e,/, are the correaponding im^iea, when the eye has been adapted to a near ol^ect. It is imdonbtedly obvions from tbe ap- proiimatioD of (he image e to i^ that the anterior aurface of the less moat have approached the cornea ; bat it is b; no means eqaalij obvioua frma the change of the form of the image from bto «, that the curvature of the lens has been incisaaed, or from the comparatively slight change from e tof. that tbe poater^or surface of the lena has not been brought forward, and that the axis of the lena muathave been elongated. These pointa, however, require a much more elaborate consideration than apace here permits: all that can be taken sa really proved by this ex- periment with resard to the mechanism of adaptation is, that Ihe anterior sorioce of the lena is appraiimaCed to the cornea. IIBT. In order that vision ma^ be distinct, it is necessary that corresponding points of the oliject and of the retina ahoald be conjugate ibci of tbe eye ; or in other words, that the pencils of rays diverging from each point of the object, and entering the pnpil, should converge to a focns on the retina. If, aa in Tnyopic or abort-sighted persons, Ihe rays convei^e to a focus before tjiey roach tbe retina, from the too great convexity either of the lens or coniea, they impinge on that sensitive organ in a atate of diver- gence, then the pencils proceeding from conliguons points of any oliject are superposed upon, and conaequentlj confuse each other: and the fnrtlier the focoa of incident rsya is fram the refracting aurfaces of the eye, the farther the focus of refracted rays will be from the retina, and conseqneotly tbe greater the confaaion : hence, with persons thus affected, the difhcult; of diaoeming ob- jecta increases with their distance from the eve. The very term " myopic" is derived from the effort naturally made to diminish the ajwrtnre of the transmitted pencils, and consequently the confusion, by partially closing the eyelids: on the same principle that an oliject placed very nearto the eye may he seen distinctly through a pin-hole in a card. A concave lens of suitable power. ij increasing the divergeoce of the incident pendl (1073), will ' Hm aeeoBnudatle-ietswgin, ph^olnciieh toegeliotit. Haarlna, 1853. 674 OPTICAL ISSTRUMRMTB. diminish the convergence of the refracted ra.VB, and conseqnentlj carry back each focal point towards the retina ; and this is tM kina of leiis in spectacles worn by short-sighted persons. In presbyopic^ or Umg-aighted persons, on the contniiy, the lens or the cornea is not sufficiently convex, and as the foci of refracted pencils are consequently situate behind the retina, a similar super- position and confusion of contiguous pencils ensues. In this case It is necessary to diminish the divergence of the incident Tays, which is effected by a convex lens (1071), and the convergence of the refracted pencils being thus increased, their foci will be Drought forward to the surface of the retina. As the t^irm "presbyopic" implies, this is the state of vision incidental to old age, and arises {>rincipally from the diminution in the convexity of the crystalline ens tnat naturally takes place in advancing ^ears ; but partly also from the. diminished power of accommodating the eye to the distinct vision of near objects. 1 188. A remarkable defect of vision has occasionally been ob- served, which consists of a want of agreement between the refrac- tion of the eye in some two perpendicuUr planes passing through the axis of the organ; this has been termed tutigv/uUitm, and cannot be remedied by a lens of any kind having spherical surfaces only: the excess of refraction in one direction must be reduced by a suitable concave cylindrical surface, or its defect in the perpen- dicular direction augmented by a conoex cylindrical surface. This defect of vision was first recognised in bis own person by the present Astronomer Royal, and to his habitual sagacity we are indebted for the appropriate remedy : he found that one eye, from the imperfect vision of which he apprehended serious incon- venience in the discharge of his important functions, was more short-sighted in a nearly vertical than in the perpendicular direc- tion ; and vision sufficiently perfect for ordinary purposes was re- stored by a lens with a concave spherical surface of Z\ inches radius, and a concave cylindrical surface of 44 inches radius, which was turned from the eye, and its axis placed a little obliquely. The following method of correcting astigmatism has been pro- posed b^ Prof. Stokes : — Let a plano-convex, and a planoKM)ncaTe cylindncal lens, of moderate but equal curvature, be each set in a circular frame with their plane surfaces in contact, so that one may be made to rotate on the other : when the axes of the two surfaces are parallel, no refraction will take place, as the united thickness of the two lenses will be everywhere the same, bat when the axes of the surfaces are perpendicular to each other, the com- pound lens will be convex in the direction of one axis, concave in that of the other, and neutral at 45"* between these directions. As the angle contained between the direction of the axes is dimi- nished from 90° to 0", the difference of the refractive powers of the compound lens in two perpendicular directions will be reduced from its maximum value, to nothing ; and some intermediate poei- IHCIDEHTAL OB SPECTBAL COLOURS. 675 tion may be found, in which the coniponnd lens will correct the astigmatism of any given eye, and when combined, if necessary, with a spherical concave nr convex lens of suitable power, will produce correct vision : and from the curvature and relative posi- tion of the cylindrical surfaces, and the curvature, if any, of the spherical surfaces, the requisite surfaces for a single lens, that will completely correct the given visual errors, may readily be determined. 1189. The impression of an image npon the retina lasts for an appreciable time after it has ceased to be formed, and hence the eve may be rapidly closed and opened, without losing sight of an object. If a burning stick or red-hot ball be made to revolve so rapidly, that the whole revolution may be completed in about 0'14P, an entire luminous circle is produced. Phe impression thus vividly excited upon the retina appears to continue about one-seventh part of a second of time. The duration of this impres- sion on the retina varies considerably with the intensity oi the light producing it ; with direct solar rays, or those of a powerful electnc light, an image of the source of light will remain for several seconds imprinted on the retina. The persistence of visual impressions has been made the basis of many optical toys ; thus, if the figure of a horse be placed on one side of a circular card, and another of a rider be suitably placed on the other side, on whirling the card by two bits of string attached to the two ends of a diameter in the proper direction, the rider will appear mounted on the horse, from the two impressions being constantly superposed on' the retina. Also if a number of pictures representing successive phases of the same action be placed equidistantly round the circumference of a rotating disc, and they be viewea by reflection through an equal number of aper- tures in the same disc, so placed that each in succession may be- come visible only at the moment that it occupies the place of the preceding picture, the successive visual impressions are mentally blended mto a continuous action ; thus a steam-engine in motion, boys playing at leap-frog, couples waltzing, &c. &c., may, with sufficient attention to the successive positions depicted, be very vividly represented. This apparatus was termed tae p?tant(ucope. 1190. It has been shown (1091) that the rays of ordinary light may be resolved into two sets, producing upon the retina different colours complementaiT to each other ; or which, when^ entering the eye together, will produce the impression of white light. When any person gazes upon a red wafer, strongly illuminated, for some seconds, and then suddenly turns the eye to a white surface near it, a spectral imase of the wafer, but of a green colour, will become visible. If the wafer be yellow, and placed on a black surface, the spectral image will be deep violet when viewed on a white ground ; in the same manner a white wafer is attended by its black spectral figure. Thus wafers, or other coloured ob- zz2 676 OPTICAL IHSTEUUENTB. jects, produce spectra of colonre complementary to their own. The complementarj tints thus produced are termed incidental colours, and may be found by reference to Newton's list of colours in thin plates of air (11 33), the reflected and trauBmitted tinta being complementary to each other. 1191. The most complete mode of demonstrating these coloors is the following, for which the late author was indebted to the late Prof. Cowper. Cut in a folded piece of cardboard a series of holes, ^.633. ^^^ whole resembling open lattice-work, and provide some sheets ot thin tissue-paper of Tarious bright colours, selecting those present- ing strongly defined tints ; place one of theae between the folds of the cardboard and hold it up to a vivid light, keeping the eye fixed on the lattice- work, whilst the -light penetrates the coloured paper : in a few seconds the whiteness of the pasteboard will disappear, and be re- placed by a strongly-marked tint complementary to that of the paper placed in it ; thus with yellow paper the framework will appear violet, with blue it will be orange, and with red it will be green. The illusion is so complete, that it always excites sur prise in those who see it for the first time. 1192. These incidental tints have been explained by Sir David Brewster in the following manner : — The eye being strongly ex- cited by gazing on a coloared body, as a red wafer, becomes partially paralvsed to the action of undulations producing that tint, and this influence on the retina spreads itself bevond the spaces actnallv impressed ; on then allowing white light to im- pinge upon tne eye, those undulations which produce npon an nnexcited eye the sensation of a colour corresponding to that of the wafer or coloured paper, are without action on the partially and temporarily paralyf^d organ : and the remaining sets of undulations are alone active, producing on the retina the impres- sion of a tint complementary to that of the coloured surface. 1193. A remarkable case of the resolution of light into its com- f>lementary tints, by unequally exciting the eyes with colouriess i^ht, has been described by Mr. Smith.* On holding a slender slip of white paper vertically about a foot from the eyes, and fixing them upon an object at some distance bevond it, so as to see tne paper double, if the light of a candle be allowed to act vividly on the ri^ht eye, without affecting the left, the left-hand image of the stnp of paper will appear to be bright green, whilst the other will exhibit the complementary colour, or red : if the contrary eye be now illuminated, the position of the compk»- mentary tints will be reversed. 1 1 94. Individuals are not unirequently met with, whose eyes are as insensible to certain tints, as the ears of others are to particular * £dm. Joom. Sdence, iii. p. 1. BIKOCOLAR YIBIOir. 677 soandfl. Sereral cases of this kind have been described, in which the following colours haye been confounded by the persons affected with this curious defect of the visual organs :* Bright green, with grajish-brown and flesh red : Rose red, with green and gray : Scarlet, with dark green and hair brown : Sky-blue, with grayish-blue and lilac-gray : Brownish-yellow, with yellowish-brown and grass-green : Brick- red and rust-brown, with deep olive green: Dark-violet, with deep blue. This remarkable ^ate occasionally occnrs in disease, and disap- pears on the patient*8 recovery, llie late author once treated a case of cerebral disease, in which vision was previously perfect, but during the attack the patient confounded several tints with each other. The colours mistaken for each other in this instance were in general the complementary ones ; red being mistaken for green, ana orange being confounded with blue : of the physical cause of this remarkable state, however, nothing is known. 1195. If an image of a picture be formed in a common camera obscura (1147), it matters not in what position the instrument is held vrith regard to the picture, the relative position of all its points will be the same iu the image ; but when a solid object, as a house or a tree, is depicted in the camera, this is notoriously not the case, but the relative position of the several points of the image will vaiy with the position of the instrument, just as we see the object under a different aspect, whenever we change our point of view : that is, a different picture is painted on the retina with every different position of the eye. Consequently two slightly different pictures of any object in relief will be simulta- neously impressed on the two eyes ; the amount of difference of the two pictures depending upon the amount of relief, or relative distance of different parts of the object from the eye. That this difference of the two pictures actually exists may be proved by a very simple experiment : place a lighted candle about three feet in front of the face, and hold up the fore-finger between the candle and the nose ; the finger and candle appear on the contrary sides of each other when viewed by the two eyes separately. A correct knowledge of the principles of binocular vision^ that is, of the mental impression derived from the combination of two simulta- neous visual images, is due to the ingenuity of Prof. Wheatstone, who first directed the attention of phvsiologists to the fact, that the mind derives the perception of relief or solidity from the com- bination or superposition of two dissimilar visual images, simulta- neously depicted on the two retinae ; and this he has proved to be the case by showing, that if two pictures of an object be taken in the direction in which it would be viewed by the two eyes sepa- * Beebeek ; Pogyendorf, AniuJen, zliii. 177. Tstclj (for whlcli pnn>os« none can be bo perfect u photngnpha). ftnd these picturea be lo prenntei] to the two eveii, tbat llieir — c_ii __ .„__ 1; — — «i™. „f fj^g ratJDK, the 1196- The inatrumcnt by which these tralj magic eflecta uv produceii is called Ibc tttTeo4eopt, and is of tiro kind*: Prod WheaCstoae's oiiginal inBtrument, the reflecting BtcreoKop«, rD. Brewater: a modification Grst, it is believed, proposed by Sir D. Brewati portable little inatrunient, and Dow generally applied to si Bcopic pholograpbs of the ordinary email aite. The reflecting stereoscope, Fig. 634, coDsista, in ita simpleat form, of a horizontal board, about 15 inches long by 4 Or 5 inchea wide, in tile middle of which are two Bmall plane mirrors, placed Tertically and at right angles to each other, and at the enda are two Tertical frameB with grooves, iu which the two pictures, dravn or mounted on stiff paper or card-board, ma; be placed. The eyes iV.ai. [*?. ^ of the spectator are placed in front of the mirrors, so at to aet one of the pictures reflected from each, and the pictures are adjusted by monng them backwards or forwards in the grooves, until their images exactly overlap each other, when the tlereoscopie effect will immediately be discovered ; spectacles will be necessary for those who are accuntonied to use them. The apparent realtt; of the impreasion derived from the superposition of the two imazc* tia ess. ^" ''^P^'"^ "" '''* correctness with which the pictures are taken at the visnal atigle; '* that of about 7" or 8° is commonly feund to answer the purpose leiy well. The refracting stereoscope consists either of a pyramidal box, as more frequently ceo- Btrucled, or of two parallel boards, separated 6 or 7 inches by a third placed perpendicn- ilarly between them, as represented in fig. 6SS, and when these ai« connectod by hingea, they ma; be folded up, for the sake of porta- bilitj. Id either c«m the pictures are placed in the botttm of the THE 8TERBOSCOPE. 679 instrament, and viewed through two priflmatic lenses, ▲, n, contained in short tubes placed at the distance of the eyes from each other at the top of tne instrament The rays proceeding from the pic- tures p, o, in the directions o a, d b, are refracted through the prisms a b, and entering the ejes in the directions e a, e b, apoear to coincide at e. Two pieces of a common double conyex lens cut in quarters were originally proposed for this instrument, and answer sufficiently well for common purposes, but a far better effect is produced by an achromatic combmation of two prisms, haying different dispersive powers (1096). Two simple figures have been selected for illustration, as they are both susceptible of an easy explanation. In the reflecting stereoscope, Fig. 634, the pictures are circles with a vertical dia- meter, and an arrow placed obliquely across it; but it will be remarked, that the arrow cresses the vertical diameter in appotUe directions in the two pictures, and as such images can only be formed in reality when the arrow is inclined to the plane of the circle, that inclination is mentally inferred from the superposition of the two images. The reader may readily satisfy nimself of this fact by drawing a circle and a diameter on paper laid hoii- zontally, and placing a pencil or any other thin straight object through the centre, when, if the line and rod are both in a vertical plane passing between the eyes, the images of the rod presented to the two eyes will be on opposite sides of the line. In the refracting stereoscope, Fig. 635, the pictures are squares containing smaller ones placed eccentrically, with lines joining their corresponding angles. These present the impression of a square pyramid, the truncated apex of which is placed towards or from the eye, according as we combine the pictures f, o, or o, p. This will be rendered more intelligible, by considering the relativo position of the, rays proceeding from the several points of the pyra- mid to the eye. Let tlie pyramid, a, Fig. 636, placed on the table, b, be viewed by the eyes of a person looking perpendicularly down upon it, and suppose that lines drawn from the «^ several comers of the pyramid to each ^' eye be intercepted b v a screen, c, placed ^ ■■ ^ mr _ {)arallel to b ; of these the four back **Tri \^ ines onl^ are drawn in the diagram. i\ \ \ ,fj\ "By joinmg the several points where i V\\ '/f;\ these lines pass through tne screen, we j ^^^^-j^H c:\ obtain the figures drawn on it, which * — : — \ ,w : — r — are the projectiont of the pyramid, and .J(' .At, 1 which correspond with the images pro- i /Jf — v\ \ duced on the two retinae. It will be . U^-yy-\S4 1 seen from the relative position of the / [/""jl \^ B \ lines drawn from the two eyes to the / \ pyramid, that the projections on c will be necessarily dissimilar, the interior squares being nearer to the contiguOnK aiileB of tlie outer oats; and it iafrom tberape , of these disaiiuilftr images that the mind infer* the elsTation (rf'tke rnnaller iquaro aboTC, or in front of, the larger one, and «■«- qnently, the trao relatiTe poaition of the linea drawn from one to the other, farmtng tbe Intenil edge* of the prnimid. If t)w pv sitiun af the pyramid were reversed, the relative poaition of Uk iDiier and outer xgunres in the projectiorM uraold be icTeraed like- wiBo. M at (i, V. Fig. 635. The line (liagtnmB for the refracting stereoacope are conmMBl; CD a black ground, of which Fig, 637 ia a apecimeii ; the projec- tions A,^wbe .... cone resting od itg base, and the projectioiu a, a, that of the h cone in an inrerled poaition. Hint of onr r«adeni maj aneeead in Huperpoeing the two adjacent image* withont the aid of a ttereo- HCiipe, hy pbcing thisdisRraru about 12 inches from the ojea, aiid loofcintc Bteadil; at the point of the finger held about fmr incbea from the paper, aad betvncn it and a point midwa; between the eyes ; if the attenlioc be then directed to the diagram, bat with- out moriag the eyei, the slercoiicapic eBect will probably be produced ; and \>y a little practice, the same may be e&ct«d Hilh any ordinary slereoscnpic slide, without the aid of a itcreo- acope, iu which case the slide will appear to cooaist of thi«e pictures, tlie centre one being in relief 1197. The Fseudoicopt. — Another important fact in tbe phy- siology of Tiaion baa been demonstraled by ProC WlwatxtODC. namely, that the perception of the relative distaoces of otjects depends upon the de^o of convergence of the optic axea, wheo the eyes nre Buccossivcly directed to them. If the eyes be di- rected to nn object placed at a, Fig. 638, the linai of tiana] di- rection of the two eyva will evidently meet at a laiver angle ibaa when they converge to a more remote point, b : and tbe acDaorial power probably appreciates the variHtioa of angle by the amoimt of nmscalar action necessnry to produce the reqaired chaon of position of the eyes. This is proved to be the caae by an inn- nioUB inalrument, the pttudoteopt, bj wbich the relative direcaao □r rays reaching the eyea is inverted, and a correipiHidiDg in- pressian of inverted relative poaitiou of the difleisnt parta of ao object ii produced ; and the illuaion ia moat eitraoidinary, a can. ce, M » bowl, g If I i«ctaiigular Pis- ex. priomi, c, □, be iiit«rpt. — This instrument has formed an important addition to the visaal means of investigating morbid conditions of the various atructares tbat enter into tbe tormation of tbe eyeball. In its simplest form it consisU of a small concave mirror with 'V- •a»- an aperture in ihe centre, ihrougb which the intericr of the eye is examined (with the aid of a lens, if required), when that cavity is illuminated by the rays from a lamp retifcted ^m, and con- densed by, the mirror. A more conve- nient form oF apparatus designed by Liel)reich, and somewhat improved by Messrs. Becli, is represented in Fig. 639. In this a stand, A, supports a rest for the chin of the peison nnder observadon, the height of which is adjusted by a sliding tube, b, and a ctunping screw, c. Tbe opbtholrao- ecope is moontedonaboard, d, runoing on three small castors, that it may he moved readily in any direction, for ad- t' istment. The tulw, B, is supported oiiiontally on a stem having a rack and pinion a4f'"^ont nt F, and hat at one end a perforated concave mirror, a, 682 OPTICAL IKBTBUHEHTB. and at tbo other a lenr, h, both being moveable or Tertical ajEes. The lamp, i, is supported by a horizontal aim, k, from the upper part of the stem, so that the horiaontal position of the plane of incidence and reflection is unaffected by the Tertical adjustments ; and the arm, k, also supports a shade, l, by which the eye is sheltered from the direct rays of the lamp. In order to steady the eye for the examination of its different parts, it is directed to be fixed on an ivor^ ball, m , which is capable of being moved in any required direction by means of a sliding tube, x, and a ball-and-socket joint, o. The eye is illuminated by rays reflected from the mirror, o, and condensed by the lens, h, which serves also to give a magnified imase of any part observed through the aperture in the centre of the mirror. 1199. Some other instmment8 have also been devised for the visual examination of interior living structures. The larfpngo- scope, for examining the actions and condition of the interior of the larynx, consists of a concave reflector, with a central aperture, for illuminating the larynx, and a small square plane mirror with rounded comers, placed comerwise at an angle of 45** with the direction of a straight stem ; this is held, by means of the stem, at the back of the open mouth, when the opening of the glottis, and the action of the various parts during the production of vocal sounds, is readily brought into view, through the aperture in the mirror. This instrument has served to show the fallacy of the ideas that have long passed current, as to the mechanism by which the glottis is closed, as in the act of swallowing : the chorda voceUes, instead of being, as was supposed, everted, are folded in> wards, and protected by the closure of the mucous membrane over them. 'J'he interior of the urethra has been sucoeaafnlly submitted to ocular inspection by means of the endoaeope; this iustrament consists of a straight silver tube capable of introduction, which is widened oat at its outer end, so as to receive a small perforated plane mirror, placed at an angle of 45** with the axis of the tube. The light of a lamp j>laced laterally is reflected by this mirror to the further extremity of the tube, and a small portion of the mucous lining of the canal may be distinctly seen on looking down the tube, through the aperture in the centre of the mirror. 683 CHAPTER XXI. POLARISED LIGHT. 1200. Iir order that the ytirious properties of light might he ■acceBsfuUy inyestigated, the rays were in the first instance con- sidered homogeneous, to obtain the general results of reflection and refraction (Ch. XYIll.) The heterogeneous character of luminous rajs has subsequently been considered (Ch. XIX A but without any reference to the physical structure of the meaium on which they impinge, or through which they pass, or to the influence of that structure on tne course of the reflected or refracted rays, or on the direction in which the undulations of any given ray take place : it now remains^ to consider some very remarkable properties of refracting media, and of reflecting sur- faces, by which the nature of the rays is variously modified. The intimate and constant relation between the nature of the wave-motion transmitted to the eye, and the molecular arrange- ment of the substance on which the waves impinge would seem to indicate that the motion must necessarily be transmitted by the molecules of the body itself, and not by any hypothetical fluid existing in its interstices: it is very difiBcult to conceive tho physical pro^rties of this fluid to be so extraordinarily modified Dj mere contiguity ; and the hypothesis is needless, if the mole- cules of the body suffice for the transmission of the waves of light. One of the most familiar phenomena is that of double refrac- Hon; a power possessed by certain crystallized substances of separating an incident pencil of light into two portions, differing from each other in their physical properties. Let A H, Fi^. 640, be a rhombohedron (24, Y.) of calcite, or Iceland spar, resting on one of its faces, a line joinmg a, ii being the axis of the crystal ; and let a ray of light, BT, be incident perpendicularly upon one of its surfaces, a h ; i.nstead of passing through without refraction, as it would through glass, it will be divided into two rays, one of which, to, pursues the direction of the original ray, bt, and is consequently unrefracted, and another, TB, which is bent or refracted in the 1^.610. plane a h h b, in which the aziB a x lies : the former is called tha 684 POLABIZED LIOUT. oriHnary^ and the latter the extraordinary ^ rar. If the direction of the ray b t, instead of being a normal to one of the faces, were oblique, it would, on entering the crystal, be separated into two rays, one of them the ordinary ray, obeying the general law of refraction (1054), snd the other the extraordinaiy ray, following a different law, being refracted from the axis an; or, in other words, being so refracted, as to form a greater angle with the direction of the axis than the ordinary ray. 1201. The double refraction of the incident ray may be readily obseryed by viewing a small circular hole in a card through a crystal of calcite : on looking throneh the thickness of the crystal at the card, two holes will be visible, from the li^ht that enters the aperture in the card dividing, whilst traversing the CTystai, into two rays, which reach the eye separately. On taming the crystal round, whilst the object remains fixed, one of the spots of light will appear to revolve round the other ; the fixed spot corre- sponding to the ordinary ray. Any object, as a line drawn on paper, will appear double, in consequence of this property of double refraction ; and if the rhombohedron be gentl v turned round whilst on the line, one of the two lines at first visible will gradually ap- proach the other ; and when the line on the paper lies in the same plane with the axis of the crystal, they will overlap each other, and appear to form a single line. The plane, ahnb, passing through the axis of the crystal, and dividing it into two triang^ar prisms, is termed the prindpai section of the rhombohedron. It two sections be made perpendi- cular to the axis of the rhombohedron, a ray incident perpendi- cularly on the plate thus formed, will suffer no refraction ; that is, no double retraction takes place in a direction parallel to the axis. 1202. The property of resolving transmitted undulations into two series differing in velocity, and conseouently producing double refraction, is not confined to the crystals of calcite, but belongs in general to all crystals not comprised in the cubio system (24, 1.). In all doubly refracting crystals, there are either one or two lines of direction in whicn no double refraction is observed to take place ; these are termed the optic axes. In the case of calcite, there is but a single optic axis, which coincides with the axis of the rhombohedron (Fig. 641). In uniaxial crystals, the optic corresponds with the geometrical axis, a line around which the constituent molecules are symmetrically arranged. It occasionally happens that no double refraction exists in some particular direc- tion, in consequence of the presence of two doubly refractive forces neutralizing each other, as in mica ; this is then termed the re- euUant axis, in contradistinction to a real optic axis. 1203. Crystals with one optic axis, corresponding with the geometrical axis of the crystal, termed untoxtoi cirstals, include all those which belong to the Pyramidal and KhombohedFal systems (24 ; II., V.). The relation of the extraordinary raj to the optic sxiB is constant for eitch uoiaiifil crystal, b fnicted either loiearilii it, aa in qaarti, or from it, as in Tboee crjatala in wliich tbie rayis bent tovanis the axis to have a poiiiive, and when bent from it, a negaiinf opi The quality of the rollowiag crystala baa been oOBerred :- Axit Piiniine. Diaplase. Apopbjltite. Salphateorin |jotasb. Boracite. I FeiTocyanate ofpotaah. Phosphate of magneda Axil Negativi Calcite. I Emerald. TourmaliDe. Mica (some Tsrieties^ Sapphire. I Cyanide of mercury. 1204. With regard to the ralalive velocity of the two seta of nndulatiooa into which light incident on a doublr refracting ciyatal is raaolTed, Hujgeaa hai demimatrated that the iliiTtronce between the squarea of the velocitieB ie equal to unity divided by the square of (he aina of the angle fonned by the ray with the axis. Id calcite, the ordinary ray therefore moves with a greater velocity than the eitraordinarj one. 1205. The law of double refraction will bo more readily under- itood by BnpposiLig a rhombohedron j^, ^41. of calcite, tig. Ml, of nhieh axis is AX, to & formed into a ap of wbich o ie the centre, and c diameter perpendicular to A x. found that wben a pencil is tr milled along the axia a i, the index of refraction ia l'€54, and ia the same for both ibn ordinary and ex- traordinary raya ; for a ray in the direction d o, the index of refraction is (he name for the ordinary ray, bu t it i a l'4Hit Ibrtheoitraotdiaary, the diSerence of which is 0171 : tho difference of the indicea is a maximum at the equator, and ia found to diminish graduitlly to either pule. It ia aJao obaerved that the index of extraordinary refraction is the same for all radii of the eqiiaturial plane { and that it ia the same in the direction of all linKa joining o, and a point in the circumference of a circle parallel to the ei: -. Tha 8 for finding the index of exlraordinnry refraction at any reijuired point of the sphere. Produce e o, Fig. 530, to e, d, take ocoroeams polarized at right angles to each other ; by sticking a wafer or a piece of black paper over the point of emergence of one polarized ray, the other may be ob- tained in a state of isolation. A more convenient mode of procuring a single pencil of pola- rized light from this crystal, is to divide the rnombohedron into two wedge-shaped portions, by a plane intersecting the axis at o, Fig. 641, and perpendicular to one of the principal planes, and in- clined at such an angle to the faces of the crystal which it intersects, as may be between the limiting angles of incidence (1060) for the two rays ; and then to cement them together with Canada balsam. The layer of balsam thus included allows one of the doubly-reiraoted rays to be readily transmitted, whilst it causes the other to be totally reflected from its sdrface, and to be thrown altogether out of the field of vision. This arrangement is known by tiie name ti the $ingle-imagef or Nicol's prism. 1213. If it be required to retain both the ordinary and extra- ordinary rays, but at the same time to separate them more widely from each other than the simple rhombohedron of calcite is capable of separating them, this may be effected bv cutting firom that crystal, F^. 580, a wedge-shaped piece by a plane passing through the solid angle h, and two P, becomes dispersed in a nebulous manner, whilst the other, v s, u transmitted ; Uie transmitted rs^ being lUwrnys polariaed in a plane parallel to the direction of the nliceous layers of the nuneraL A thin plate of agate may also transmit a ray polarised in a directioB perpendicular to its laprers, and disperse one polariaed in an oppo> site direction. The direction of these layers may be readily made out, even in thin sections of agate, by the lines visible in their substance. A plate of agate may thus be employed to furnish polarized light ; it does not, however, oompletoly separate a be^n of light into two polarised rays, and is the least satislactofy of the oidinary means of effecting polarization. 1215. The tourmaline, a siliceous mineral, and especially the varieties of a yellow or hai^brown colour, when cut into thin plates parallel to the axis of the« crystal, separate a ray, incident perpen- diculwly on their surface, into two nys polarized at right angles to each other ; one of which, the ordinary ny, is transmitted, and the extraordinary rav is absorbed by the mineraL This actioa of the tourmaUne on lignt is very remarkable, as no stratified structure can be detected in this mineral, which, as in the case of agate, would even help to explain its powerful polarising influence. The action of a plate of tourmaline, or asate, on oommaD U^ht, may be familiarly illnstrated by fixing two slips of pasteboard u a direction at right angles to each other, as n s, o d, fV. 644^ repre- senting respectively the two planes in which the undulations aie resolved at their incidence on the polarizing substance ; let a l k t be a*Bmall frame of wood, having a number of wires fixed across it, as shown by the lines in the figure. Let a k be supposed to represent a plate of tourmaline, the bars being parallel to the axis, and the ^per figure, m o sd, a ray of lieht ; when the latter is brought into contact with the former, the slip of pi^r v s will Pjg 044^ readily pass between the wires, but 0 D will be checked ; k s wiB here represent a transmitted ray of li^ht polarized in the direction of a pnn- cipal plane (1201). Let t ▲ be now tamed round, until the cd will then psas throagh, and irs will be stopped. By this little apparatus, the action of polarizing plates of tourmaline or other minerals, actinic in the same manner, is readily impressed upon the memory : but it must not be forgotten that the comparison of a set of parallel bars POLAKIZATIOH BT ▲BSOBPTIOV. 691 to a tourmaline plate is strictly hypothetical, and although avail- able as pointing out the effects of this substance in different posi- tions on a beam of light, yet it must not be considered as present- ing a correct view of the real modus agendi of such polarizing plates on common li^ht. 1216. Dr. Bird Herapath discovered a new salt,* which ap- pears to be much superior to the toarmaline as a polarizing agent, on account of its giving scarcely any tint to the transmitted ray, as well as from its caosing so little loss of light, on account of the extreme thinness of the lamion employed : a specimen of this salt, the sulphate of iodo-quina, suflScient for microscopic examination, may be very readily prepared. For this purpose a drop of a solu- tion of disulphate of quinine, in acetic acid, is placed on a slip of glass, and a very minute portion of tincture of iodine is added : the whole becomes immediately tnrbid, but soon afterwards minute crystals, of almost metallic lustre, are formed in the fluid. After the fluid has eva^rated, a drop of Canada balsam should be added, and a piece of thin glass placed over it as a cover. The specimen thus prepared, when examined by the microscope with an object- glass of |-inch focus, is seen to be made up of minute laminie with acuminated ends, nearly colourless, except when they cross each other : at these points light is more or less intercepted ; and if the crystalline plates lie on each side at rieht angles, the point of intersection is very deep violet, or perfecUy black. All the light transmitted through one of these crystals is polarized in one plane, and is of course incapable of being completely transmitted by a superposed crystal, unless they happen to lie on the glass com- pletely parallel to each other. If sucn a specimen be placed on a plate of selenite, iUaminated with polarized light, and then examined with the microscope, a veiy beautiful result occurs ; the little crystals analyse the light passing through the parts of the selenite on which they are placed, and present a beautiful display of the complementary colours. To prepare this salt for the formation ot polarizing laminae, the following plan may be adopted : dissolve 50 ^ains of disulphate of quinine in two fluid ounces of acetic acid, and two of proof spirit, warmed to ISO** in a very wide-mouthed flask, or glass beaker ; then slowly add 50 drops of a solution of 40 grains of iodine in an ounce of rectified spirit ; agitate the mixture, and then set it carefully aside for six hours, in an apartment main- tained at a temperature of about 50** F. The utmost care must be taken to avoid any motion of the vessel ; indeed all accidental vibrations should be guarded against by suspending the vessel by a string, or by allowing it to rest on a mass of cotton wool. If in six hours the large laminae of the salt have not formed, warm the * It has bera proposed to name tbii moet valuable addition to our pola- rizing media, Herapathiie, after iu ini^uioaa diacoTerer. Y y 2 6d2 FOLARIZBD LIGHT. Fig. 646. fluid with a spirit-lamp, and when it has become clear, add a few drops of the solution of iodine in spirit. The large laminae form on the top of the fluid, and should bo remoTed carefully by glidine under one of them a circular piece of thin glass. The specimen snould be drained by resting the edge of the glass on a piece of bibulous paper, but it must not be touched, on account of its extreme fragihty : if any small crystals adhere to its surface, they must be washed off by pouring oyer it a few drops of watery solution of iodine. When dry, the specimen should be placed for a few minutes under a bell-glasa, by the side of a watch-glass, containing a few drops of tincture of ioaine ; and lastly, a little very fluid Canada balsam should be dropped on it, and a thin glass cover applied without heat. Specimens may thus be obtained of extreme thinness, and half an inch in diameter, or even larger, possessing scarcely the slightest colour, and yet oom* pletely polarizing transmitted light 1217. The mode of obtaining polarized liffht by reflection waa first discovered in 1810, by the celebrated philosopher Mains, an officer in the French engineers. M. Malus, whilst examining the light reflected from the windows of the Luxembourg throusb a rhombobedron of calcite, observed that light, when reflected mnn the suriace of ^lass at an angle of about 56°, acquired the very same properties as one of the beams obtained by submitting light to double refraction in calcite : haT- ing, in fact, become polarised in the plane of reflection. This discovery was so quickly followed up by others, and so snccessfolly studied by the iUustrious philosophers of the age, Uiat it has led to the development of some of the most beautiful and impor- tant physical facts that have ever been discovered. The most convenient mode of repeating the experiments of Malus, is by means of the^ apparatus represented in Flf. 643. This consists of two uprights of wood, supporting a mirror and frame, c d, ood- structed like a common looking-glaas. A circular plate of wood, e f, rests on the pillars, and has a circular aperture in the middle about three inches in diameter ; a ring of wood, M N, moveable round a circular projection on b p, suppoita two pillars, m o, h h, between which rests, by means of screws, a frame, k l, like c d, but somewhat smaller. A slip of paper gra- duated into 360^ is fixed on that portion of b f which projects be- vond M H, a black line being marked on the latter, to serve as an index, and to point to zero on the graduated paper, when the ptllari M a, s H, are exactly over the supports of the lower frvne, c o. A FR0PEBTIS8 OF F0LA2UZBD LIGHT. 693 plate of glass rests over the aperture in the centre of e p, to serve MS a stage on which objects to be submitted to the action of pola- rized light may be placed. A plate of glass, covered at the back with a black varnish, is fixed m the lower frame, c d, and a similar one in k l. The for* mer is termed the polarizing^ and the latter the analysina^ plate. As, however, it is of ^ importance to obtain as bright a beam of polarized light as possible, it is better to make the lower frame, o D, deeper, and to place in it a dozen or more thin plates of sheet glass pressed together bj means of a piece of wood at the back ; le hindmost plate being blackened, ny this contrivance a very bright beam of reflected polarized light may be obtained, since many of the rays transmitted by the first plate will be polarized by reflection from the second, . and so on. This instrument, which was first suggested by M. Biot,* is the most convenient that can be used for experiments on polarized light \ it may be conveniently termed a Polariscope. 1218. Place a lighted candle at a short distance from the j^ola- rizing plate, p, and adjust the latter so that the light may be inci- dent upon it at an angle of 66* 45' ; then bv means of the side- screws fix the upper^or analysing nlate, so that the ray reflected from p may be incident upon it at the same angle of 56* 45' : the section of the plates showing their relative position is shown in Fig. 646, 1. light, on being incident on p, in the direction a p, is resolved into two portions, j- one being polarized in a plane per- pendicular to the plane of refleo- tion, and mixed with much com- mon light, passes through the flass, p, and is abaorbedj the un- ulations beiue checked by the black paint with which its liack is covered. The other portion, po- larized in the plane of incidence and reflection, is reflected to the upper plate, a, and thence to the eye of the spectator at b, who sees an image of the candle in a. Then turn round the plate, b, still keeping it at the same angle, by moving the collar mh * Pr^fl de Physique, torn. H. p. 476. Paris, 1824. t It is, perhaps, hardly necesssry to remind the reader, that the angle at whieh Hght ahouid be inoident on reflecting sarfiMes for complete polarisation, is mettsored from • normal to the reflecting sur&oe. On the continent, light is QSoaUy directed to be incident upon the reflector at an an|{le measored from its sorfsoe; which will be oomplemenUiy to the true polarising angle. Thus the angle at which light is polarised by reflection from glass is 68° 46' measured from a line pernendioolar to its sonace, and SS° 16' measored from the reflecting snr£soe itself. ^.648. -f \ 694 POULBIZED UOHT. on the wooden collar ef, Fig. 646, and when r ib at right angles to p, as in Fig. 646, 2, the image of the candle will atmoat eiitirelj disappear. This might be indeed anticipated, for the rav reflected from p is polarized in the plane of reflection ; bat this plane is now perpendicular to the plane of incidence on the npper plate, B, and as there is therefore no motion remaining to be re- solved in that plane of incidence, no rajs are reflected, but the polarized ray passes through the glass, and is absorbed hj the black paint at its back; so that, in looking at b in this fKwitioii, scarcelj a vestige of light is to be seen reflected from it. On moving r round through another anffle of 90"*, as at Fig. 646» 3, the light and figure of the candle wiU reappear in r, as the planes of polarization (1210) and reflection coincide, being both identical with a plane passing through a p r b. At the intermediate ares of rotation, the light in r will increase or decrease in intensitj, according as it approaches to, or recedes from, the positions diown in 1 and 3. In tnese three figures, aba shows the position of the plane of primitive polarisation, and ban the position of that of reflection, in passing from the position, 1, of the apparatus, to 2, the light reflected from r decreases in the ratio of the square of the cosine of the angle formed hy the pjanes of polariEation and reflection. 1219. The intensitj of the polarized light reflected in variona positions of the upper mirror (1027), corresponding t« the di^rent angles contained oj the planes of reflection and primitive polari- zation, maj be illustrated bj Fig. 647. The lines in the inner circle point out the different positions of the plane of reflection ; and the radial distance between the circumference of the circle, and the two curved outlines a, b, represents the amount of reflected fig. e«7. greatest amount of light is reflected, as the lines e b, a d^ are the longest which can be drawn from the circum- ference of the inner circle to the limits of the curved figures. At 45**, the in- tensitj of reflected light will be leas than at 0^ as the line e p is shorter than e b, whilst at 90* and 270* it will attain a minimum, as the diameter connecting these numbers, if produced, will not be in- cluded in an J portion of the outer curves. The eflfect of extinguishine light, bj altering the relative po- sition of the reflectors, is analogous to that produced bj crossing two tourmaline plates. If two similar plates of that nuneral be placed together in the same direction, so that light polariied bj one maj be transmitted bj the other, oljects maj be distinctly seen through them; but on turning one at right angles to the other, nearij absolute darbiess ensues, as the second plate absorbs most of the light transmitted bj the first. This efiect may be ^ JUa AKALT8I8 OF FOLJLBIZBD LIGHT. 695 readilj nnderatood bj placing two gratings, i.b,cd, Fig. 648, opposite each other, bo that the bars of one may be ver- ^^' ^^' tical« and those of the other horizontal, and attempting to tbrost the paper iiRnre, K 8 c D (966), through tnem. __ Although, when the bars of -• ^ v|ff ■ the two gratings were in the > same position, one or other of the paper slips m s, c d, passes through, yet, when crossed, they effectually prevent the pMsage of either ; for one, as c d, although it may ^ass the first grating, is stopped by the second, whilst £e slip N 8 IS checked by the nrst. Two plates of tourmaline thus placed may be conveniently em- ployed m examining the action on a pencil of polarized light of any substance placed between them ; the plate nearer to the eye transmitting those rays that have been depolarized by the inter- vening object. Whenever any two polarizmg arrangements are thus employed, that nearer to the eye is termed the analyter, A very compact and portable polariscope was oonstmcted on this principle oy the late Mr. H. J. Brooke ; this will be found a conve- nient instrument for the examination of the polarizing properties of crystals. 1220. If one of the beams of polarized light obtained by double reiraction (1200) be used instead of the light reflected from p (1217), it will present the very same phenomena on turning round the plate b, as the b'ght polarized by reflection from p ; and if light be polarized by the absorption of one of its component beams by a tourmaline (1215), or bj Herapathite (1216), the same effects will be observed; so that m whatever manner light is polarized, it possesses the same properties, jprovided only that its planes of polarization be in the same position. Thus, plates of tourmaline or Herapathite may be used for the purpose ofanalysing polarized fight, in place of the analysing ^ate of the polariscope ; the analysis being performed by transmission instead of by reflection. 1221. It has been already stated (1029) that a portion of the light refracted through glass, when incident at toe polarizing angle, is polarized, and in a plane at right angles to the reflected beam. This refracted polarized light may be obtained very ft«e from common light b^ placing a dozen or more plates of thin sheet l^ass toother, and nzmg them obliquely in a tube, so that they may be inclined at an angle of about 25" to its axis. On allowing a beam of liffht to traverse this tube, it will emerge polarized in a plane at right angles to that at which the reflected light is under similar circumstances polarized ; a system of plates thus arranged in a tube constitutes an excellent mooe of analysing light polarized by reflection, and developing the colours of donb^ refracting 696 POLARIZED UOBT, crystalB (1202^. Sir Da^d Brewster has found, that bj increasbe the number of glass plates, the refracted light becomes pcilarixea at a much sm^ler angle of incidence : thus, light is coroj^letely polarized by refraction through one plate of glass at an incidence of 81"* 38'; through two at 77'' 16'; through six at 71*" 50'; and through forty-one at 45^. The best glass for polarising light b^ refraction is that which is used to cover microscopic objects ; it may be obtained of extreme thinness, and is peculiarly valuable for this purpose. 1222. If the reflecting plate p (1217) be placed at any other angle except that for complete polarization, a certain portion only of reflectea light will be polanzed. Very different opinions hare been offered on the nature of this partially polarized light ; it has been generally considered as made up of common lights mixed with a small quantity of completely polarized light. The follow- ine table, given by Sir David Brewster,* shows the number of reflections required to completely polarize light at certain anglesi above or below the polarizing angle, 56" 45'. No. ABglM. No. Angles. 1 2 3 4 56* 45' 50 26 46 30 43 51 62» 30' 65 33 67 33 5 6 7 8 41* 43' 40 0 38 33 37 20 69* 1' 70 9 71 6 71 51 1223. In the preceding observations, light polarized by refleo- tion from glass alone has been considered ; the same physical characters may, however, be communicated to light by reflection from the surface of almost any non-metallic substance ; that re- flected from metallic surfaces (1275) differs in its propertiea from plane polarized light, now under consideration. All bodies have their peculiar polarizing angle, in the same manner as they have their index of refraction ; thus, the angle for glass is 56^ 45', and for water 58" 11'. The effects of the difference of the polarudng angles of two transparent media upon polarized light may be shown by an experiment described by Sir D. Brewster. Having fixed the plates p, a, Fig. 646, 2, at the angles of 56" 45', and with the planes of reflection and polarization perpendicular to each other, the image of the candle will be invisiole in a : breathe upon the latter, so as to cover it with a film of water, and immediately the candle will become visible, from a portion of the polariaea beam undergoing reflection from the vapour condensed on r. 1224. The angle of complete nolariaatum for any substance may be readily determined by the law discovered by Sir D» • Optios, p. 173^ sad Phfl. Trans. 1830. AHOIiB or OOXPLBTS FOLABIZATIOV. 697 Brewster, namelji that the rayi polartzed by refection, and by refraction, are perpendicular to each other; or, in other words, that the index of refraction i$ the tangent of the an^ of polari- zation. Thus, if the polariziDg angle of water, of which the index of refraction is 1*336, he, Teqnire<^ on looking for that number in a table of natural tangents, the corresponding angle of 53° 1 1' will be found. The polarizing angle of crown-glass is 56° 45^ ; for, as its index of refraction is 1*525, that numoer in the table of tangents corresponds very nearly with the angle mentioned. 1225. Light may be polarissed by reflection from the second surface of bodies, or by internal reflection ; and the angle for com- plete polarization has its cotangent equal to the index of refrac- tion of Uie substance, and may he found by looking for the latter number in a table of cotaoffents. This, in the case of water will be 36° W, and of crown-^ass, 83° 15' : so that the polarizing angle at the second surface is equal to the complement of that for the first surface of a medium ; whence it follows, that a conside* rabie portion of the tight transmitted by the first surface of a plate, will be polarized by reflection at the second or internal surface. 1226. If, instead of using white light, any one of the coloured rays of the spectrum be incident on a reflecting medium, it will undeigo polarization in the same manner as common light, but at a different angle for each ray. The yalue of the polarizing angle for each, may be found from its index of refraction, by means of the law of taugents (1224) : thus, the polarizing an^Ie, when water is used, is ^° 4' for the red, and 53 Id' for tne violet ray ; and when plate-glass is employed, 56° 34' for the red, and 56° 55' for the violet ray. From the data contained in Fraunhofer's table (1101), the polarizing angle for the rays corresponding with each of his seven lines may be readily computed. The polarizing an^Ie of the mean rays of the spectrum is taken to be the polarizing angle for colourless light; but b^ careful observation, the ex- tinction of the coloured rays at their appropriate angles may be observed. 1227. When the sky is tolerably free from clouds, a certain portion of the light becomes more or less polarized in its passage to the earth, 'rhe maximum of polarization takes place in a plane passing through the earth's axis at 90° from the sun, con- sequently the amount of polarization varies in difierent parts of the sky according to the position of the sun. According to Araeo, the rays reflected from the moon also contain a considerable qnantityof polarized light. 1228. On the above relation between the hour-angle and the plane of polarization of light from the sky, Prof. Wheatstone has founded an ingenious device called the polar clo^, Fig. 649. In this instrument, a tube, a, the axis of which must be placed parallel to that of the earth, passes moveably through the aial| b, nulled with the honra, &nd canieB Ml index. Tha tube oaa- n. UD tdna A peculiar smDgement of poluicing media, which iadiote the podtion of the plane of polarizadon bj the diBappearaoce of crdonred raja (1230) : and as the plus ofpdaTiiatioii U alwaya 90° from the bdd, thft index once set right, will alwaja ptant to the hoDi when the colonre diaappcar. Tha polaiiiing airangement coniigta of a doMU'magepritm (1213),a«Bjieje-piece, and a small hole covered hj a plate g/ setenite at the fdither end of the tube, A- The upright to which the dial ii at- tached, is conneoled with the baae Iai«« of polartsatiim. E. I» the phenomena ef intetferenee prodtieed bw ray* that hoM undergone dovhU refraction, a d^ffertmee of hidf an MaAt loCim fltutt in tome eatti be aSoaad, a* one of the rayt of light it retarded to that amount. The truth of the first of these laws. A, maj be readilj verified by employing a plane polarized raj in any of " ""* " ia already detailed (112fr— 1131). DTTERFEKSRCB OF POLABUED LIGHT. 699 The second, B, may be tested by transmittiiig two small pencils, deriyed from the sun s image in the ibcus of a small lens, either throueh two parallel narrow slits in a piece of thin sheet copper, placed perpendicularly to the path of the pencils, or through cor- respondinff portions of the prism represented in Fig. 600 ; if two portions m a plate cut very truly irom a homogeneous crystal of tourmaline, be placed over the apertures so as to intercept the two pencilB, it will be found that the usual phenomena of interference will be produced when the optic axes of the two pieces are pa> rallel, but will wholly disappear when they are at right angles to each other ; that is, when tne planes of polarization of the two rays are perpendicular to each other. Tnis ascertained fact might have been inferred, 2k priori^ from the dynamical theory ; for since no portion of the motion in either set of undulations can be resolved in the direction of the other set, it is clear that no concurrence or opposition of similar motions, or in other words, no interference, can take place. A very simple addition to the arrangements just described suf- fices to demonstrate the truth of the third law, C ; the optic axes of the tourmalines being placed perpendicularly to each other, let a rhombohedron of calcite be placed in front of them, so as to tran»> mit both pencils, its principal plane being inclined 45° to each of the planes of polarization. The two polarized rays will now each be resolved into two others, of which the pairs that describe eoual fatha, being similarly polarized, might be expected to interwre, ut no interference is observed to take place. The experimental proof of the fourth and fifth laws is more complicated ; it will be found in the treatise already quoted.* The retarded half undulation mentioned in (£) will be again referred to (1257V 1230. To exhioit the tints produced by polarized light, place on the glass stage of the polariscope (1217),^ a thin lamina of aelenite, of uniform thickness, and allow a pencil of light, polarized by reflection from the lower plate, p, to pass through it to x. The source of light ma^ be the 8un*s rays, or diffused daylight, or still better, the ught of a lamp or candle provided with a ground-glass shade. Let the index on mn be placed at 0 on the graduated circle ef, when the plates b,p, will be placed as in Fig. 646, 1. Let B and p be fixed at the polarizing angle (1218), then, on looking into the analysing plate, b, the image of the selenite will be seen, not colourless, but possessing a tint varying with the thickness of the plate. Let us suppose the film of selenite to be of such a thickness as to appear red when its imag^ is viewed in the ana- lysing Phite ; slowly turn round the selenite, and the colour will gradually disappear and ultimately vanish; at this point the plane of primitive polarization will pass through one of the optic • BucydopMlia HetropoUtana, art. Lights § 800-871. 700 POLABUEO UORT. ftzefl of the selenite, and no prodnction of colour can enmie. On oontinuinff to turn roond the selenite, the red 'v- lane of reflection, and therefore reaches the eve, giving a green ima^e of the seleuite; the other image bemg polarized in an opposite plane, passes through the analysing plate, and by looking through the latter whilst inclined at a consi- derable angle to the ray, a red image of the selenite will be visible. The same tint is produced by reflection if the analysing plate be rotated through 90°, as the plane of reflection will then coincide with the plane of polarisation of the red, which is contrary to that of the g^en rays. 1234. A very instructive mode of analysing the polarized pencil after it has passed the film of selenite, is to transmit it through a rhombohedron of calcite ; the transmitted ray will be divided into two coloured images which will be both visible at the same time. The red and green images are complementary to each other, and, if superposed, would constitute white light; this may be proved by holding the calcite at a proper distance, when the two images will partly overlap each other, pro- ducing white light, as in Fig. 651. On this account no colours were seen when the selenite was viewed with- out the analyser, as both pencils then reached the eye together, and produced a colourless image. 1235. In the above experiments with selenite or mica, the rays of incident polarized light were considered as nearly parallel ; if^ however, a convergent pencil enter a crystal so as to traverse its optic axis (1202), a new and splendid series of phenomena becomes visible. Let a pencil of light be incident, at tlie pola- rizing angle, on a bundle of plates of glass, ab, Fig. 652, placed on a black surface, so that a bright beam of polarized light may be renected to the ere at s, which thus is placed at the apex of a cone of rays. If a plate of a doubly refracting crystal, as calcite, cut at right JV«063. 702 FOULRIZED LIGHT. angles to its axis, be placed at d, it is obTioiu that the rajrs of polarized light will traverse it with yarions degrees of obliqoitj, and thus Yirtnallj permeate different thicknesses of the sectioii. The central rays which pass through the optic axis do not suffer double refraction, and therefore will appear to the eje at b, the same as if no crystal had been present, but the other rays which pass a little obliquely through the crystal wiU undergo donhle refraction, each bein^ resoWea into an ordinary and extraordinary ray, as is the case with ordinary li^ht (1200). These rays, how- ever, reaching the eye together, will not produce any ooloor, and cannot be distinguished firom common light. To render the pheno- mena of coloured polarization obvious, an analysing eye-pieoe must be placed between the plate of doubly refracting crystal and the eye. Let this be a NicoVs prism, or a plate of tuunnaline, so placed as not to transmit the polarized light reflected from a b, iif the crystal, d, were absent. It will then be found that the liefat reflected from ab has undergone some physical change whilst traversing d, as some of it has acquired the power of passing through the analysing plate of tourmaline, and a beautiful sym- metrical image, paintedT with the most gorgeous colours, becomes visible ; this image is composed of a senes of concentric coloured carves, and traversed by a black cross. Let the analyser be then turned round 90^, and an image complementary to the first will be visible, its black cross being replaced by a white one. 1286. The origin of these beautiful coloured rings may be thus explained : the rays which do not pass through the optic axis are divided into two pencils, an ordinary and extraordinary, polarized in contrary planes, and hence one series is absorbed and the other transmitted by an analyser, according as it is placed so as to transmit or a1>sorb the originally polarized ray ; but this, although 8u£Bcient to explain the production of two images, is not suflScient to explain the phenomena of coloured rings. It must be ieool> lected that the rays pass through the plate of the crystal, d, with various degrees of ouiquity, and hence some suffer more retarda- tion of their motion than others : the rays are thus placed in the yery condition required for the phenomena of interference, and the consequent production of coloured fringes, as in the case of common light. The ordinary rays being polarized in the same plane, mutually interfere to produce one of the coloured images, and the extraordinary interfere to produce the other: the two images being complementary to each other, and, if superposed, produce white light. The figure of the rings results from the rays which pene- trate the crystal at equal distances from the optic axis, pasdng through similar thicknesses of the plate, and consequently under- going the same amount of retardation, and producing siimlar tints at equal distances from the centre. The smgular appeaniDce of the black cross is owing to tlie ra^s which traverse uie ciystel in the direction of the planes of primitive polarization emerging un- maoa n calcitb. 703 cbwgBd, tnd in these two directiong the dark blue or black »pp«Br- ance presented by th« reflector, ab, Fig. 652, when vieved throagh the anul jKT nlone, will be lidble as the arms of a black crtwa ; tSe ■nns of the cross end in bnuhea, and attpBar to eitenc' siderable distance: Fig. 603, a, ahowa tma bcautilitl a; Let the analysar ba then tDtatod through 90°, so as to irannnii th« light reflected from A B. the Bgme B will then be Tiaible, all the coumri in the rings of which are complementaij to then in a, ■nd a white croaa takes ths plaoe of the black oae. 1237. If the plate of calcite b« rotated on its axis, no change whatsTer occnra in the rings, and if a portion be covered np with a piece of black paper, the uncovered portion of the plate will exhibit the rings as pericctl; as the whole plale. This mar be reaJilr nnJentood bj lecollecling that the optic axis in these crystals is not a Bied line, but merelj a fixed direction, and exists as completal; in the smalleiit fragment as in a large plate of a iSiystal. If the plate of calcilo be thinner, the rings will appear wider, and less closely packed together : the diameters of the nogs beinR invfrsel; as the squara-roet of the thickness of the plate. 1338. Ifa similar plate be cnt from anTOtberaDiaxiafcr]-'-' will exhibit tbe same beantifol rings, when placed ir of the pencil of polarized light. If a crystal with a positire optic axis (1012), as dnwn or ice, ba examined, the nn^ will be identical with those of calcite, which has a negative axis: but if n plate of zircon be placed on one of calcite, and the combination be examined, they will be fonnd to interfere with each other's tints, so that, if of proper relative tbit^ness, no colound image will be visible. 1239. If| instead of allowing ordinary colourless light to be inci- On the polarizinc plate, ab (1235), Lomog«neo(u light lie ' ' ' ' . mU be observed as when white 70* depend on tlie colonr of the ligbt, the riaga being Ui^eat id &t meet refrangible or violet, and BmalleaC in red light. 1240. In cryBlaU posgeBBiag two optio &iei, inclndinff bj ttt the gre&ter praporlion of natural and artificial crjrBtalliied bodies somewhat different pbenomena are obeerred of which the tendenej to ellipticitf in the rinei, and the presence of a black bar acroM UwiD, ooDBtitnte the chief. In hiaiial ciyatali, in which the axel are at a Terj amall aagalar diiUoce from each other, both ajMemi of rii^ niaj be observed at once, one around each axis, a« in Ultra, arragoaite, and some ipecimeng of fertocjanate of potaab. In the ^at majorit;, however, the aiea are so ur wpai»tBd, that bat a single i;atem can be seen at a lime. inclined about 65° to each other. Let a ray of polarixod light, p z, incident ob- j \ )"' 1 liquel; on this ciyatal, be viewed by I 'Y I means of an analysing eye-piece in the j'--'''''^^-, direction OD. An elliptio system of rinei traversed by a black bar, will b« visible, provided the aye-piece be so placed as lo absorb the onginal ray, when not traversing the clTBtat! If the plate be then altered in position so that the poUriied ray may pass in the direction o ■ F, a second system of rings precisely similar to thoee seen in the Erection c D will beoome visible : thiu,rKaaiid cor represent the directions of the two optic axes of the plate of topai. If Ibe eyepiece be rotated through 90*, a &gan complementary to the last will be ob- served, all the red rings being replaced « readily discoverei] by a piece of the ordic taie oTthe shop*, about J i holding a piece of the ordinaiy taie of the shop*, about J inch thick, in an indined porition ai near to the eye-fnece as pcanUe, and allowing a ray of polariied light to pais throngh it : but one system is visible at a dme, as the axn an so mocfa in- clined to each other. IT dn rings be not at fint viaible, thej reuilv become to by moving the nuca. The figure is gene- BlXaS a BIAXIAL GBTVTAia. 706 rally nearly circular, as in Fig. 654, and traversed by a black bar, wbicb is replaced by a white one, when the complementanr figure is obtained by rotating the eye-piece through. 90*. rlatee of borax, or sugar-cand^, cut perpendicularly to one of their optic axes, may be conreniently used to exhibit these rings. 1243. In most biaxial crvstals in which the angular distance of the axes is considerable, the system of rings is always elongated into an elliptical figure (1241^, and the tints are not arranged with the symmetry we meet with m crystals with one axis: this is beaa- tifully shown in sections of the Ifochelle salt, the potassio-tartrate of soda. If a plate cut transversely to one of the axes of this salt, in the manner described in the case of nitre (1244), be examinea by polarized light, a splendid elliptic system of rinss, traversed as usual by a black or ratner a deep-blue bar, will be observed. These rings are most gorgeously tinted, but the colours are not equally arranged, the red predominating at one end of the long axis of the ellipse, and green or blue at the other, adding indeed much to the beauty of the figure. In some crystals presenting these pheno- mena, the red ends of the rings are within the resultant axes, whilst in others the blue ends are thus placed. To the former belong phosphate of soda, sugar, carbonate of lead, &c., whilst the Rochelle salt, sulphate of magivesia, and topaz, affi>rd examples of the latter. 1244. When the inclination of the axes is small, both systems of rings can be seen at once. To show these, take a crystal of nitre, and by means of a fine saw cut off a thick plate, at riffht angles to the axis of the prism. The best mode of rendering this sufficiently thin, is to rub it on a fine file moistened with water ; and it ma^ be polished on a plate of glass or wood, moistened with water. A plate one-sixth of an inch in thickness catf thus readily be procured, and should be preserved between plates of glass vrith Canada balsam. In general these sections of nitre are perfectly transparent- only at their margins, being im- perfectly crystallized in the centre. This is, however, of no con- seouenc^, as the transparent edge shows the rin^ very beauti- fully. For this purpose, the plate should be held in the course of the polarized ray, as near as possible to the eye, armed with a tourmaline, or a plate of Herapathite. which answer best for this purpose, as they allow the crvstal to be brought nearer to the eye than a Nicol's prism, or other analyser. Ihe beautiful figure shown in Fig. 656 will be visible, or will readily become so, bv slightly altering the position of the plate. The two systems 01 rinffl are distinct and splendidly coloured, and the outer rings of bo£ systems coalesce, and surround the whole figure with a sort of elliptic border. H whilst the eye-piece is fixed, the plate of nitre is slowly rotated, the black arms of the cross will open, and when the line connecting the two axes of the crystal is in- clined 45° to the plane of pnmitive polarization, the appearance z z n«Mnt«< Been ; the black crossed liDei beiav repUced hj w Kd rii^ t>v green, the 7ellow by mdigu, &a. IS46, Ttie double eyetem of ringe may often b« Guelv awo in ferrocyanats of potaah ; this salt is laminalsd, and nuMlj *pfitt in the direction of its la^ra. A plate aliaiild be ^it off about a quarter of an inch thrck, and if not qnite imwith, slxmld be polished hy friction o^net a piece of wood Dxneteiied with water. Bj bolding Boch a piece in Uie direction of a poUiued ray, uid analysing it with a tounaalioe, a fine doable sfBtem of rings wiU be often soon, No ult, however, has bean observed lo Tai; in the direction of its aies so mnch aa tUs: in aome Epeciment tbey are nearly merged into one, en as to be Tirtnaltr uniaxial, whilst in others they are conaidenblf aeparated : this is probsUr owing to tome Dndiuoveted complenlf m the pbjncal itractare of the crystals mbinitted to ' oryslallino plates, may be e&cted by e Tionsly described ; it may also be GonTenicu«i_^ lutkuQ u, iquduuuu from a elass pUte, which should be ae small ae ptoseible; a picca of blaci glass, one-fonrth of an inch in diameter, fixed to a little arm of bnss, so as to allow of its being inclined at any angle, and rotated on its axis, constitntes a conrenient form of an^yver, which, indeed, wae the one used by Sir David Brewster in hii elaborate researches on the riogs in crystslB. But a much motv convenient inetrument for theae parposes is the iiolari-«icrotoo« of Prof Descloiseaui, varioDsly modified by M. Hoffinann, of Faiv^ Mid other opticians. This instmment is analogous to the polaii. seope, F!g. 64S, of H. ffiot ; but the pa1ariE«d rkjB are brought to a focmi at the atage by a combiniituin of Isnsei ; and the raja, tranamittfld by the e^eot their' ^i--**^ -« aT.vrtir^arj Kir an anaiigement of leniei uialD^m ■e produced bj thU apparatus, ■ enabled to receive cooTergiog peacils which «re inclined at conaideTable angles to oach other. 1S4T. Bj means of the propertj poaaeBsed by polarized light of deyeloping these coloured rin^s, which alwajs, in titit and sirangeaieDt, bear a constant relation to the physical structure of the crystal producing them, we are enabled frequently to make out theexiatence of certain peculiaritiea of ntolecufar aggr^atioa ; and thus acquire a new ana powerful mode of iureatigsling the intomal arrangement of some of those simple but wonderful btruc- tores, presented to us so copionel;^ in both the crsanic and in- oi^auic world. This may be beautifully illuBtrated b^ aubjecting nnannealed glaas to the action of polarised light : it has been afaowu that glass, by anequally heating or cooling, acquire! the property of doable refraction (ISOS). If the glass be properly prepared, by healing it red hot, and rapidly cooling it, the strain npon its iatenial molecules is permanent. 8uch a piece of glass appears, when viewed by ordinary light, liiie any other ; nor can •ny peculiar feature be detectecl In it, in wbicn it difTera from r specimens of that anbetance. But if a piece of this ' ' ' ' ' ... - •■ nolariacope (12 ^. lie in the analyaii plate; whilst, under eimilar circumstances, the glass would ni nealed glass be placed On the stage of the polariacope (121T), a beautiful coloured image »'" ' ' before heating, exhibit the sligbteet colour. 1246. A solid cylinder of glass carefully heated and cooled qoickly is generally found to be uniaxial, and whea examined by polsriied Bght, by placing a trans- Terse section of it on the stage ^' of the polariscope, the planes of reflection and poUrizatioa being at right angles, llie system of rings shown in Fig. 658, much resem- bling those seen in caldte, will be j Tiaible. The apparent optic axis ia, j however, generally somewhat eccen- I trie, so that, on rolating the cylinder, \ • slight tendency to distortion in the armsof the croasis observed. There is this essential distiuctioa between therings visible in nuatinealed Elass, and tboae in natural ur artificial cr^itali, that in the latter they may be detected in the minutest particle, so that if any port of the crystal be covered np, the ODCOfered 708 POLARIZED LIGHT. portion (1237) will show these rings as perfect! j as the whole crystal : on the other hand, if any part of a piece of onannealed glass be covered with black paper, the^ corresponding portioiL of the rings and cross developea by polarized light will cease to he visible. 1249. Let the planes of the polarizing and analysing plates be at right angles (Fig. 646, 2), the index being at 90°, then if the glass be shaped into a square plate, the beautifol figare, i.. Fig. 659, will appear. The circular curves in the angles possess the most vivid liues, in which red and green predominate \ the centre being occupied by a black cross. On turning the analysing plate round 90^ so that the planes of reflection and polarization may coincide, the colours, whicn almost entirely vanish at 45**, will undergo a remarkable change, and the figure B will appear, all the colours of which are complementary to those of ▲, and the black cross will be replaced hy white spaces. If the plate of unannealed glass be square, and about one-third as thick as it is long, the elegant figure shown at ▲, Fig. 660, wiU be visible when the analysing plate is set at 90°, so that the plane of reflection may be perpenmcular to the plane of polarizatiofn: the complementery figure, b, replacing it, when the analysinft plate is placed at 0* or 180°, so that the planes of reflecUon and polarization coincide with each other. LECOD>t's POIilBUCOFE. 709 1250. The dork lioeB formia^; the bl&ck crou teen when thcM pktea are submitted to poUnied light, mast be cnaddered u pointing oat the poaition of the directians in which the polariied nj paageg through onchaneed, an^ are henee convenienu; called Una of no polarisation. If the Kg.Kl. •nalysing pUte be Gied, and the Duaunealed glass b« slowly turned round, the black cross wiU begin to open, and ila arms to separate in elegant currea, until lis re- •pltant axes (1202) are incHoed 45° to the planes of polarization and reflection, when a beautiful BjninietriGal figure vill he Ttsi- ble, aa io Tig. 661. On con- tinuing to turn the plate of glass the dark crons gnidu&Uy reap- pears, and attains its greatest intansitji when two of ita arms correspond with the plane of pola- rization, aud the others with that of refleolion. 1351. The beaulifhl Ggores thoe visible in uuannealed glass are rendered more bnlliant bj allowing the polarized nf to pass twice through the piece submitted to experiment. For this purpose, the very simple apparatus Tor polarizing light proposed Bj LecouDt, can he conveniently employed ; it coOBistBof a small looking glass, i, ^g. 662, placed on the table, aud a frame, D, fastened to the toirror by a hinge at c, containing about j^.oaa. ten plates of common nlale window-glass, ,^^ which is fixed in an inclined position to the mirror bj means of a support, d. The piece of unannealed glass is placed ou the mirror, audit is riflwed in the direction s r, when the figures become beantifully distinct, ihe rings being much more numereus than when examined in the ordinary manner. Com- mon light is incident on a in the direction ar, and is divided into two oppoaitely pol which is transmitted and the other is reUecCed towards the mirror, pasno^ in its course through the unannealed glasa plate; trom the mirror it is reflected back again, passing througb the plate, and being partly depolarixed, paasos iu part through the inclined glass plates, rendering the Genre visible from e. 1252. When a mass of animal jelly is placed oo the stageaftli» polariscope, no colours are visible in the analysing plate, so long as the jelly is not submitted to pressure ; but as soon as it is com- pressed with sufficient forcp, it assumes a doubly refracting stmc- tore, and a series of tints traiersed by a black cross become vi- rible, provided the analysing plat« be so placed that the planes of reflection and polarizalion are at right anglts to each other. 710 POLAB1ZBD UGBT. Jelly, solutions of gnm, and albuminous fluids, allowed to ^^AP^* rate spontaneously, so as to leave an indurated mass, also exhibit the four coloured sectors, traversed by a black cross. A slip of glass, pTevionslv without action on polarized light, develops a series of tints, by bending it, or submitting it to preaaare by means of an iron frame and a screw. Fragments of ordinary quills, and other indurated animal struc- tures, also exhibit these tints, when submitted to the action of polarized light, in an extremely beautiful manner. 1253. No series of objects exhibits the tints of polarized liefat more beautifully than the crystalline lenses of animals, enpeciaily of fishes : to examine these, they should, to prevent their bringing the incident rays to a focus, l>e immersed in a glass vessel con- taining oil, or some fluid possessing nearlv the same refnctivo power as the lens. The crystalline lens of the cod-fish exhibits twelve beautiful coloured sectors, separated by two darkconoentric circles of no polarization, and traversed by a black cross. 1254. Many interesting results maj be obtained by examining sections of organized structures, or minute crystals, in a polarizing microscope : all that is required for this punpose is to place under the stage of an achromatic microscope a KicoPs prism, or aome other of those means bv which the lignt transmitted through any object on the stage will be rectilinearly polarized. The analyser should be a short Nicol's prism, fixed over the diaphragm in the body of the microscope, or as this must slightly interfere with the achromatism of the instrument, the same, or a thin nlateof brown or grey tourmaline, may be placed over the eyeglass. In this manner the molecular arrangement of quills, horns, hoofs, teeth, and other animal structures, is most beautifully developed. 1255. A magnificent class of objects for the polarizing micro- scope ^ is found in crystals of different doubly refracting bodies deposited on glass plates by allowing their solutions to evaponte spontaneously. To preserve them thev should be coverea with a second plate of glass, some Canada oalsam being allowed to run between them. Chlorate of potaas, nitre, salicine, acetate of lead, sulphate of copper, camphor, and ferrocyanate of potaas, are objects of really gorgeous beauty when thus examined. Scnne bodies exhibit toe coloured rings traversed by a black cross, like calcite, and are peculiarlv beautiful. The spherical crystals of carbonate of lime, which the late author found to be spontaneonaly deposited in abundance from the urine of the horse, nnely exhibit these figures. A rare salt, the oxalurate of ammonia, exhibits the same phenomena. All the varieties of starch, as that of the potato, tous-les-mois, plantain, cassava, &c., show the black oroBS well defined. In some of these varieties the granules are more or less regularly oval in their form, as in those of arrow-root and tous-les-mois, but the centre of the black cross is always veiy near to one end of the granule, indicating an eooentric atmctura ; 1256. Orcvlar iUartmfton.— When t< It thna generated will not be raetiliBear, ■■ in tlie TArietfofpoUriicd Win-ta. lit;ht juat examined, but ciicular. Tbe nature of the wn*e nauliiDg from the coinpOBitioQ of two plftDo wBTei in perpendi- cular directioni will be more full? andentood b; a reference to the appa- raloB represented in Kg. 663. An open reotan- gnlar frame, a. b, bai ila oppodte vertical lidea, AC, BD, filled Bp with a ■erieB of parallel alipa, which leave narrow equal and equiiiislant spaces between them. A series of nxU of equal length, each having a bead of enamel >t one end, paae through the correaponding oppwite vertical spaces; and when tbeia rods rest on the bottom of the frame, and the beads against the face ofsD, thej form a atraight line. The individual ceptible of an^ reqnired vertieal diapUcement, hr raising ttie nvla to which thej are attached parallel to their original position ; and of an; required horizontal displacement by tbmating the rods out from the face of the frame, and these two dienUcementj may take place quile independently of each other, while the poution of the wads will indicate the joint, or resultant eSect of both. Let two aeries of equal wavea be accurately cut traniTemely on two rectangular bars of maho^njr (as being least likely to warp), and let one of theae, e, banog its wave ana-face horiiontal, be placed under the rods in the frame A D, and the other, r, with ita wave surface veKicsl, agunat the ends of the lodi projeoling through the back of Ihe frame A c. It is evident that the row of beads, repreaenting a row of vibrating molecules, will be dieptaced in a vertical wave correaponding with the mi^ (see of K, and also in a horizontal wave equivalent to f, and the form of the resultant wave will depend on the relative poaitioni 13ST. Tha tthct predaeed on the rwiiIUiit wvn, hy tPwWnJw differant phases (369) of its components, hu next to b« tEaMdaoi. For thii purpose, four diSennt combiaktioni of the irBma ftre lepnsented bf a, h, c, d, Fig. 661, and the ing resultant waves hy a,b,e,d: in eaufa of thesa oombiiimliau the horitontal vbts, which liea to the right, maj be lepnasBted by a, and the vortiol w»vb by L. If R and I. be combined as in jt, either of them being balf aa ondulation in adrance of the other, that ii. the cmt of one wan cnrreapanding with the trough of the other, the tcsoltani, n, i« a plane wave, hoI inttrmedialt in direction between the plana oC the two componenta. And cooveracly, if the ware, a, be reaoind into two, in the direction of Ihe perpendicular planet a and i, one of them will, ai in a, he half an nndulation in adrance of the other : this will probably account for tha diflerence of half an aa- dntation in the paths of two rays simnltaneaualj polaiiied in perpendicnlar planes, mentioned in 1 1!9, E. If E iajof an nndulation in aJraiuw q/'L.ai in B, the ivraltaM Ifa and L coincide, as in c, the resnlt will be a plane w ., _, in a position intermiduitt between > and h. And converaelr, a plane wave, e, in an intermediate position, may be reaolred nrlo two perpendicular coincident waves, c a, c u If a is I of an undulation bekind L, at in n, the reanltant van, d, will be circniar. and the locos of the distothed paiticlaa ^riglo- ktmded cylindrical spiral. 1SS8. It may be readily shown by the tame apparato^ that when the coincident phases of the component wares ■ and l are inlennediate between a and b, or a and a, the resnllaat wan wiU be a lefl-handed elliptical spiral, the mi^or aiis of tbe elliptic base leaning towanta the direction of o in the former caae:, and towards that of e in the Utter. When the coneapondinK phasra of the compouenU are intermediate between o and d, or between o and A (for it is precisely the same thing, whether a i* half aa andolation hefi>rt or UkiTtd l), the retollanta will aiinilariy be right-handed elliptio spirals. It wiU readily be seen fivm fig. 668, that in drcDlarij and ellipticalli palBriz«<] Ugbt, tbe path of each displaced particle in the HTBTe-ntint is a circle, or &□ ellipea respectiTelj, jnat u the path mait be a Btnight liue in plane, or rectilinearly polarized ligDt. 1259. Circulartf polarised light amy ibe produced in several waja; perhape tlie readiest ia that propoaed b/ Mr. Air;. Ha •Uowa a ray of plane polarized light Iii be transmitted ihroDgh a lamina of mica nr Mlenite of lulEcient thickneag to retard the orfinaij ray (1200), an odd nnmber of qnarter undulalioni more than tbe eitraurdinaiy raj ; ander these circumatancea, tbe emer- gent light will he circuhirlj polarized. Another proceea is that of M. Fremel, hf allowing a ra? of plane polarized light, Jlb, Fig. 665, to anfler two reflecliona from the internal Burfaces of a parallelopiped of crown-glasa, tbe snrAlcei of which meet at k, l, at an angle of Gt° SC ; the emergent ray, or>, will be drculaii]' polarized. The plane of reSection, ahcd, ■bonld form an angle of 45° with the plane of polarization of tbe raj, xn. Bj each of these internal reSectiona, a retardation of coe^ighlh of an nndulalinn is produced in c ' ' into which tbe incident light ia resAlved on raflec^oo at the internal anrface, k h. If the nuus of glass be of snfficient length, the ra; will emerge polarized circularly aftfr two, BIX, ten, &c., '2(2n— 1] reSectione, and rectilinearly, after fonr, eight, (welTe, ail- t«eD, &c., i n reflectiona. CircnlaKv polarized Hght may be readily diiCingnisbed from tbe rectilinear form by eiamining it with an * analyaing eye-pieoa (1246): for it will merely gradnallj- decrease in iatenaity aa the latter ia rotated to tba right or to tbe left. ocTer diaappearing and reappearing twice in each TCTolation (1216). 1260. Let a plate of re^arly cryslallized qnartz be cnt in a direction perpendicular to its axis, and placed on a alagBof the polariacope ; on looking into the analysing plate, no black cross will be visible, as in calcite, unless tbe plate be aufficientlj thick, and then if held near tbe ej;e in the manner already described for examining cryalala, a binish ill-defined cross will be seen. Coloured rings are not generaLy risible ualess the plate be beld near the eye, that it may receive as wide a I^. MS. cone of nys aa poMible. Wheneinmined — on tbe stage of the polariscope, or at some distance from tbe eye, the whole plate presents an uniform tint, as in Fig. 666 ; , and DO rings will he seen at tbe circum- I ference of tbe crystnl, the whole being I filled np by an uniform tint, providpd the ' plate he of the same thiclcnesa throagboat ; otherwise it will vary, as tbe iotensit; of 714 FOLARISBD LIORT. colour depends on the thickness of the plate. If the cdoar be red, slowljr rotate the analysing plate, and the tint will be changed to orange, yellow, greon, and ultimately to Tio^ : at though the analysing plate had, during its rotaUoUi acquired the power of reflecting these different coloun. In some specimens of quartz, and other crystals possessing this power of circular polarization, the colours are chan^ped from red to violet when the analysing plate is turned from right to left, and in others, when it is moved from left to right Hence these crystals are termed right-handed, or left-handed, according as they possess the propertv of causing the planes of polarization to revolve spirally in a direction from right to left, or from left to right (1257). The succession of cMours is represented in Fig. 667. ^.667. RICKT-HAHDEO RED IHDICO^ NYELLOW BLUE# \cREEN CREENi JBUJE RED LEFT-iMRDED RED YEUOVV^ XiNDJCO OREEN \aLUE BLUE. JCREEN INOIOo\ JrVASm VI OLZrSv^^^^^^^/^RAHCt 1261. A plate of left-handed quartz, 0*3 inch thick, when placed on the stage of the polariscope, so that a polarized ray may pass through it, appears of a 6ne olue when viewed through an ana- Ivser held m such manner as to receive the ray transmitted through the crystal. On turning the quartz round on its axis, no change of colour ensues : bnt on rotating the analyser, the follow- ing changes of colour are observed at dSferent azimuths: — AfimtttlM. Ooloor. Asimaths. 1 Ooloor. 0' or 180* 28 „ 208 73 „ 253 Fine blue. Pea green. Greenish yellow 98* or 278* 115 „ 295 145 „ 325 Tawny orange. Vivid red. Violet, The phenomena thus observed are the same as would necessarily occur if the polarized light had been, by passing through theqi resolved into a series of homogeneous rays, and become dii in different planes radiating from the centre of a circle, as i in Fig. 668, representing Newton*s chromatio circle, in one half of which the colours of tne spectrum are arranged. The thicker the plate of quarts employed, the greater is tne aro required to BOTATXON OF THB FLAXB OF FOLARIZATIOH. 715 Iig.9n. effect the convenioii of the image into one of s different tint ; to that, although in the ahoTO experiment a rotation of the analyiing e^e-piece through an arc of 180** was soffi- ^,en, cient to develop the series of coloured images, jet, on increasing the thickness of the plate, a mnch larger arc is required to proauce the same effect. 1262. In plane polarized light it was shown I that the maximum of light is reflected bj 1 the analysing plate (12 ItJ, when the plane of ' reflection coincides with tnat of polarization ; and the minimum, when the plane of reflec- tion is perpendicular to that of polarization ; this, howcTer, is not the case with circnlarlj polarized light. To make this intelligible, place on the stage of a polariscope a plate of right-handed quartz 0*04 inch thick, and illuminate it with homo- geneous light, as b^r that transmitted through a piece of red glass. The greatest intensity of the light will not be any longer at 0° and 180 , but at lO"* and 199, and the least at 109"* and 289^ instead of 90' and 270^ asifthe plane of polarization had been tnmed ' round 19 towards the right. This may be illustrated by Fig. 669, simi- lar t^ that employed in 1219. It is evident that the line produced from 0* and 180** is not now the longest that can be drawn within the external curves, bnt that the longest line must now be drawn 19' from its former position, or in the direo- tion of the dotted line, A b. 1263. If homogeneous liffht of other tints had been employed, a still frreater alteration in the position of the plane of polarization would have been observed : thus, for the mean coloured rays with a similar plate of quartz, the deviations of the plane amounted, from Biots experiments, to the following: — ^Bed, 19**; Orange, 21" ; Yellow, 23' ; Green, 28* ; Blue, 32* ; Indigo, 36-; Violet, 41\ This alteration in the position of the planes increases with the thickness of the plate of quartz. Thus, if a deviation of 19" is produced by a plate of quartz 0*04 inch thick in red light, one of 88' is produced by a plate 006 inch thick, and of 95° by one 0*2 inch thick. 1264. The colours visible by polarized light in quartz are never simple when white light is usea ; for as the different coloured rays arethusshownto be unequally dispersed, it follows that although an excess of one tint may he visible at a time, so as to give a well-marked colour to the transmitted rays ; yet it most in every case be a mixture of several. To comprehend this, let the series of curves in ▲ o b b, Fig. 670, represent the intensities of b s l^e 716 POLABIZBD LIQRT. red, TT the yellow, BBtbebloe, and yt the violet nije renpec- tively. Let a plate of right-haDded quartz 0'2 inch thick be tnen ^ ..Q examined by polarized light, ^' * the analyser being bo placed as not to reflect the polarised ray, if the quartz were absent. If homogeneons light be em- ployed, the red ray will ob- tain its greatest intensity at 95" and 275^ and iU least at 5** and 185^ the depth of the cnrres on the line b b being the greatest at the former an* gle, and least at the latter. In the same manner the curves on the lines r t, bb, and vt, re- present the intensity of the yellow, blue, and violet rays at difib- lent angles. Let homogeneous be replaced by white polarized light, and the tints produced by its passage through the qaartz may be obeerved at 0** ; on referring to the figure, the blue and violet rays will predo- minate, the yellow and red oeing sparingly reflected ; at 5° the red attains its minimum, and the image will be the darkest from the presence of excess of violet light. At 95^ red will predominate in the image, but mixed with much yellow light ; at 1 1 5*, the yellow will attain its greatest intensity, at 160" the blue, and at 205* the violet will be at their maximum. Thos, in no case can a pure homogeneous tint be obtained when white polarized light traverses quartz, all the colours being mixtures of several, of which, however^ one predominates over the rest. 1265. One of the most interesting contributions to science, for which we are indebted to Prof. Faraday, is the discovery of the ex> citcment of a molecular change in various snbstances, as glassy water, alcohol, oil, when under the influence of the magnetic force, sufficient to cause the rotation of a polarized ray. To show this «^^ Q^^ with the magnet, a piece of flint glass, ▲, Fig. 671, or ^^ much better, a slip of heavr ^^,,^jC^^ glass, the fused borate of leaa, n 2 inoties square and 0*5 inch thick, is placed between the poles, H, B, of a powerful eiec- tro-magnet (877), so that tiie lines of force (592) may pass through the len^h of the glass. A beam of Ti^ht, b d, ia Jolarized in a vertical plane glass, D, and passing thnnuHi t£e glass, A, is examined at d through a Nicol's pnam (1212). So BOTATIOM UVDBB UAONBTIO IHFLUBKCZ. 717 long as the bars n and s are not magnetic, the rays are transmitted or extinguisheil as usual during the revolution of the prism. Let this be then turned ho that light is eztiDruished, then on con> necting the wires c, z, with the battery, the bar instantly becomes magnetic, and some rays are transmitted. It will be necessary to rotate the prism to the right to extinguish the rays which have, •under the influence of the developed magnetism, been made to rotate. If the north pole be next the observer, as in the figure, the plane of polarization will be rotated to the right, but il the poles be reversed, the rotation will be to the left. 1266. When a glass tube is filled with water, and placed in the axis of a long helix of wire traversed by a current from a Grove's battery of ten pairs of plates, the water assumes a similar rotatory power over a rectiliuearly polarized ray, turning it to the riflpht or the left according to the direction of the current, the ray always rotating in the direction in which the positive current traverses the wire of the helix. When a wide tube of glass is filled with water, and the helix traversed by the current immersed in it, the water in the centre of the helix will alone exert any action on a transmitted polarized ray, that lying between the exterior of the coil and the side of the tube having no rotatory power. A piece of borate of lead glass placed in the helix acquires a similar power. Thus by the inductioo of magnetic force Prof. Faraday communi- cated temporarily to glass the rotatory power naturally possessed by quartz (1260j, and to water and other fluids the power proper to syrup, and oil of turpentine.* The intensity of this acquired power IS shown in the following table \ that in water being taken as unity : — Oil of turpentine 11*8 examined naturally. Heavy glass 6'0\ Flint glass 2-8 . , j x. Rock ilt 2-2 I ?"»>ned under the y/g^XQj j^.^ Vintluence of electno Alcohol! ; ; iesi than'witer currents. Ether . . . less than alcohol / 1267. Solutions of su^r, camphor, and a large number of organic fluids, naturally develop the phenomena of circular pola- rization. If a tube, closed at the lower end with a plate of glass, and about six or eight inches in length, be filled with oil of turpentine, and placed on the stage of the polariscope, the richly, coloured images (1261), and a rotation of the plane of polarization finom right to left, will be observed. A test-tube, the bottom of which rests in a drop of water (to diminish the refraction}, will answer the same purpose. It is far better to examine the circularly polarizing power of fluids by means of a polariscope constructed for that piu|K>8e. The * Phil. Truu.l846,p.l4. 718 FOLARIZED LIGHT. Fig, 972* following IB ft T617 BiiDDle one, which the late aaUior need for eome yeani, consisting of a oondle of plates of sheet-p^laes, a, Fig. 679, as a polarizing mirror, fixed to an arm, so as to admit of ready motion, and supported bj a screw from a common retort-stand, and a tube of brass, b, an inch in diameter, and ei^ht inches lonff, closed at its lower end with a plate ofglass holding the floM to be examined, l^e transmitted raj is analysed by an analyser, o, oonsistinr of a single-image prism (1212), or bnmue of thin glass plates (i221)^capable of being placed at any azim nth. The action of oil 73. a polished steel plate at on au^e of 75°, then tlie reflected ray will be found to diOer materially fhon the taj before reflection, as it does trat vanish when viewed tbiougb a tourma- line or other analysing eye-piece under • the same circnmstances as it did before reflection from the steel plate : it has; in fact, been converted into elliplieally polarized Ueht. _ The best test of thig kind of light is the modification it produces in the rings of calcite (123GX Dio^iha Tniu, ISW, ud Fret Powd, IB Pkil- ZLIiIPTIC OPTICAL COMBTA.RT8. 723 the transmitted light being analysed as nsaal. Under these cir« cumstances the appearance shown in Fig. 673 will be seen, which differs from that seen by ordinary polarized light, in the distortion of the black cross and diulocation of the rings, as if a film of selenite capable of producing a blue tint had been placed across the plate of calcite. The conversion of a plane into an elHptically-polarized ray may be effected b^ replacing the reflecting steel plate by^ a thin film of mica, previousK beated red-hot, so as to split it into in- numerable buninse, and communicate to it a silvery lustre. This discovery is due to Prof. Forbes of Edinburgh. 1277. The angle at which a ray of plane polarized light becomes elliptic, by a single reflection from a metallic surface, differs with different metallic substances. The following are some among a series given by Sir D. Brewster : — Mercuiy 78" 27' j Bismuth 74" OS' J Zinc . . 72" SQf Steel . 75 00 ^ Silver . 73 40 ! Gfold alloy 70 45 The late Prof. Powell observed that in ^neral the elliptically polarizing power of metals is greatly dimmished by oxidation. 1278. Elliptically polarized light is produced by any odd number of reflections from surfaces of steel, and is restored to a state of plane polarization by an even number : thus, a plane polarized ray becomes elliptic with 1, 3, 5, 7, &c., reflections from steel at 75°, and is restored to its primitive state by 2, 4, 6, 8, &c., similar reflections. 1279. Several extensive series of observations have been made by M. Jamin* and the Rev. S. Hanffhton,t ^^ ^^^ subject of elliptic polarization ; and from these the following optical con- stants 01 various substances have been determined. The prineipcd incidence (I) is defined to be that angle of inci- dence at which rays polarized in any plane inclined to the plane of incidence have the major axis of the elliptic path resulting from reflection situated in the plane of incidence and reflection : and the coefficient of refraction (p) is the tangent of the principal incidence. The coefficient of reflection (R), is the cotangent of the angle contained between the plane of incidence and the plane of polarization of those rays that, after reflection at the principal incidence, become circularlv polarized. In a large number of allocs of the last two metals, the values of I and p were all intermediate, but in no certain ratio. 1280. Many varieties of crystals present different colours, ac- cording to the direction in which hght is transmitted through them ; this property is called dichroism. An excellent example of this is met with in the chloride of palladium, which is deep red, ♦ Ann, Ch. Pbys., [3] xix. to xxix. f Plul. Tr»M. 1888. 3 a2 724 POLIBISBD LIGHT. when viewed in tbe direction of its axis, and yivid green, wlien examined transverselj. Similar phenomena are observed in the Subetance. I P B Munich glass .... 66» or 1-4287 00780 Fluor-spar 54 46 1-4158 00053 Glass of antimony . . 58 49 1-6519 00199 Quartz 56 47 1-5274 0-0144 Speculum metal . . . 76 33 4-1901 0-6865 Silver, rolled .... 72 07 3-1016 0-8901 78 07 4-7522 0-9255 Gold 75 37 3-8994 0-9073 Mercury 81 04 6-3616 07315 Platinum 76 37 4-2030 0-7265 Palladium 77 37 4-5546 0-7058 Lead 69 37 2-6918 03265 Bismuth 73 37 3-4013 0-6993 Tin 75 07 3-7627 0-7341 Iron 76 07 4*0458 0-5163 Steel 77 87 45621 0-5197 Aluminium .... 77 07 4-3721 0-6457 Copper 71 53 30662 0-8656 Zinc 77 22 4-4723 07281 iolite or dichroitc, and some other natural and artificial nub- stances. When such crystals are placed on the stage of the pdari- Uniaxial. Sapphire . Emerald . Blue beryl Quartz. . Amethyst Tourmaline Tdocrase . Mellite . Lilac apatite Biaxial, Topaz, blue . green pink . Cyanite . . Dichroite . . Epidote, olive-gr whitish-gr. Yellowish green Yellowish green Bluish white. . Wbite. . . . Blue .... Greenish white . Yellow . . . Yellow . . . Bluish .... White . White . Pink . White . Blue . Brown. Pinkish white Blue. Bluish green. Blue. Faint brown. Pink. Bluish green. Green. Bluisb men. Reddish white. Blue. Green. White. Blue. Y'ellowish white. Sap-green. Yellowish white. BEFEBBNCB8. 725 scope, their colours will be found to vary with the inclination of the principal section (1201) to the plane of polarization. The preceding list contains some of the results of Sir David Brewster'tf researches on this sahject, showing the colours of the two images, when crystals possessing the property of dichroism are submitted to polarized light. The colours in the first column are those seen when an optic axis is situate in the plane of polarization ; those in the second column are seen when the same axis lies in a plane perpendicular to that of polarization. Beferencbs. In the able and comprehensive Treatise on Light in the Encyclo- paedia Metropolitana, by Sir J. Herschel, the student will find a most valuable source of reference on all points connected with physical optics. The Essav on Optics by Sir D. Brewster, in Laraner^B Cyclopsedia, will be found an excellent guide for the less advanced student. For further information on the subjects treated of in the last four chapters, in addition to the general treatises on physics before referred to, the reader should consult Dr. Young's Lectures on Natural Philosophy. The subject is geometrically treated bv Newton, and more or less analytically in the treatises bv Wood, Codington, and Griffin; and, more recently, in that by Prof. Potter. In addition to the Treatise on Light in the Enc^clopiedia Me- tropolitana, and to Sir D. Brewster's work on Optics, and to his papers diffused through the Philosophical Transactions, the student may with advantage be directed for further information on pola- rized light to the General View of the Undulatory Theory, by the late Bev. Baden Powell, 1841 ; to the Lectures on Polarized Light, by the late Dr. Pereira, in the second and third volumes of the I^armaceutical Journal, and subsequently published in a senarate form ; and to apaper by Dr. Leeson in the Journal of the (Jhemi- cal Society. Tne more advanced student will consult with great advantage the Undulatory Theory of Optics, in a volume of mathematical tracts by the present Astronomer Royal, and some papers on Physical Optics by the same author, in the Cambridge Phil. Trans., vol. iv. ; also a concise mathematical investigation of the laws of double refraction, by Mr. Griffin. The works of Biot will also yield much information ; and several able papers by Jamin, on the subject of elliptic ])olarization, and of many other observers on circular polarization, will be found in PoggendorfTs Annalen, and in the Annales de Chimie et de la Physique. LLl-i.~J! .'.U^^- ■ J"-* UJ-^T f , 726 CHAPTER XXn. CHEMICAL ACTIOH OF UGHT; PHOTOOBAPHT. 1281. The chemical iniiaence exerted by the solar rays upon Baits of silver has been already referred to (1106). The earliest investigation of the action of light on silver compounds appears to have been made by Scheele, in the year 1777 : he discovered that the different coloured rays were not equally active in pro- ducing the observed chemical changes. These phenomena haTe much more recently been made the subject of carefiil stndy, and with so much success, tbat a property, long sunposed to be peculiar to a few argentine combinations, bas been snown to be of a much more general character. The labours of Sir John Herschel have been among the most interesting and important in this inquiry, and this ^at philosopher has shown tnat there scarcely exists a combination, whether of organic or minenl origin, the molecular constitution of which is not more or less i^ected by the solar rays. The study of these extraoidinazy effects constitutes the science of Photography. 1282. If a piece of naper be moistened with a solution of com- mon salt, and then with one of nitrate of silver, a thin covering of chloride of silver will be formed on its surface, and it is then sensi- tive to the action of light. If a piece of such paper, commonly ddled senaiiive^ be exposed to the sun*s rays, or to the diffined light of day, it becomes darkened in colour, and assumes a brown, bluish, or black hue, according to the length of exposnre, or to the proportion of silver present. The chemical change thus ex- perienced by the chloride of silver is not yet satisfactorily luder- stood ; it, however, appears probable that a partial conversion into oxide, or even reduction to the metallic state with evolution of chlorine, occurs. It is certain that some important molecular change does take place ; for if a piece of paper thus blackened by exposure to light, be digested in a solution of hyposulphite of soda (in which chloride of silver is readily soluble), it giyes np but a small proportion of the silver, all the chloride which has been changed b;^ the action of the sun's rays being insoloble in that saline solution. 1283. Metuurement of Solar Chemiad Action. — ^A careful series of investigations on this subject has been made by Profs. Bnnsen and Roscoe.* The method pursued was that of exposing paper • PhiL Trtts. 1863, put I. TSTESeaY OF OHBMICAL ACTIOH. 727 coated with a definite layer of cUoride of silver to the inflnenoe of either direct solar rays, or difihsed daylight, for known hnt gradually varying periods of time ; and then comparing the action on the paper with a definite grey tint. The paper was first salted hy immersion in a solution con- taining 3 per cent, of pure chloride of sodium, and dried : this strength was chosen because it was found that the paper ab- stracted equivalent quantities of the salt and water, and therefore left the strength of the solution unchanged. The paper was then floated for two minutes on a 12 per cent, solution of crystallized nitrate of silver, and dried in the dark. This strength was adopted because it was found that two-thirds of the silver-bath mignt be used up before the strength of the solution fell below 8 per cent., which was found still adequate to saturate the chlorine. The paper was subjected to the action of light by placing it beneath a parallel slit in a horizontal plate of metal, which was covered by a thin lamina of mica blackened : this was withdrawn and replaced by the swing of a pendulum, from the time of oscil- lation of which the time of exposure of each portion of the paper was readily calculated ; and a table is given of the times of eX' poBure of each successive millimetre of tne paper. The standard tint was obtained by triturating together 1000 parts of oxide of zinc with one part of pure carbon, obtained from the smoke of a turpentine lamp. It was found that by drving ihe mixture and re-grinding on a glass plate, the tint was deep- ened; but after several repetitions of this process, the tint was not susceptible of further change : it is therefore at all times definitely reproducible. It was also tbe result of observation that equal products ofths ifUenaities and the times of exposure produce equal shades of blackness: hence, adopting as the unit of measurement the in- tensity of light which produces in one second tbe standard tint upon the standard sensitive paper, it became easy to institute a comparison of the chemical action of daylight, at different times or places, and under different circumstances. Many interesting observations have been made by Prof. Roscoe : in regard to the chemical brightness of different parts of the sun^s disc he has ascertained that, takinfl; the luminosity of the centre of the disc to be 100, at 15*^ from its edge the luminosities were at the— N. Pole, 38-8 ; Equator, 484 ; S. Pole, 68-1 : and at the edge of the disc, the corresponding intensities were 18-7; 80-2; 282. The total solar action was found to be generally proportional to the sun's zenith distance : at the summer solstice, the equi- noxes, and the winter solstice, the intensities observed at Owen's College, Manchester, were in the ratio of the numbers 1 1 3 : 33 : 5.* * Proceedings of the Bojal InstitutioD, toL It. p. 652. 728 .. CHKUICAL ACnOK OF LIGHT. 1284. The relative powers of the atmosphere to tnuisniit and reflect solar rays have also been observed by Prof. Boecoe, bj in- tercepting the direct rays of the sun by means of an opaque disc, and observing the difference of action on the standard sensi- tive paper of totu daylight, and of the same minus the direct solar rays. From these experiments it appeared that the chemical action of direct sunlight was much less than would have been anticipated from its visual intensity. Thas it was found at Man- chester that, at an altitude of the sun of 12° 3', not more than 5 per cent, of the chemical rays falling on a horizontal surface were due to direct sunlight ; while at the same time the direct beam contained 60 per cent, of the visual rays. And on some occa- sions it was observed by Dr. Wolkoff, at Heidelberg, that, at ele- Tations not exceeding 13^ the bright sunbeam seemed totaDj devoid of chemical rays, as no difference of action resulted from its obscuration. At an altitude of about 25** the chemical in- tensity of the direct rays was half that of diffused d^ight, and at about 40° the two intensities were equal. But at Para it was observed that the action of direct rays was only one-half that of diffused light at the sun*s altitude of from 60° to 77°. This remarkable power of the atmosphere to transmit the lower rays of the spectrum, and to disperse or reflect the rays of higher lefrangibility, is identical with the property known as opalesceneef and is due to the suspension in the atmosphere of particles of aqueous vapour or other matter. The absorption or dispersion of the chemical rays may be thus illustrated. If a minute quantity of finely-dividea sulphur be suspended in water (0*1 gram to a gallon) it will be rendered very slightly turbid, but nevertheless sufficiently so to intercept nearly all the chemical rays: this may^ be shown by the following experiment. If equivalent pro- portions of chlorine and hydrogen be introduced into a glass bulb^ on exposure to a bright hght, those elements will combine with explosive force, provided the chemical rays be not intercepted. If the rays of an electric lamp (810) transmitted through yellow ^lasB fall on the bulb, it will remain intact ; but if blue glass be interposed, the bulb will explode in a few seconds. The same re- sult will ensue if the rays pass through clear water ; but the slight opalescence in the sulphur-water above mentioned wiU en- tirely prevent the explosion. The rich blue tint of the summer sky, as well as the varied and mellow tints of evening, are probably alike doe to the same pro- perty of opalescence in the atmosphere. It appears also from the observations of M. Janssen* that many of the chemical rays of higher refrangibilify are inter- cepted by- aqueous vapour, which is always prevalent in the at- mosphere in clear weather during the aflemoon hours. The effect of this will evidently be to lower the position in the • Beport Brit. Aaioo. 1860. OPPOBTTB BPrBCIS OP 80LAS BATS. 729 spectraiii of the mean chemical rajs, and hence to lengthen the chemical focus by a small quantity : this is a fact well known to photogrnphers. 1285. When a slip of senBitive paper is exposed to the^ solar spectrum (1082), it is most darkened in the violet raj, and in the space bejond it, occupied by the lavender band (1087). In the locality of the less refrangible rays, the paper is scarcely affected, except that occasionally it is observed to assume a very faint tint, bearing some resemblance in hue to the coloured bands of the spectrum, which thus, within certain limits, imprint their own tints upon the paper. Tbe following table shows the results of an experiment in which the paper was rendered sensitive with chloride of silver : — Ooloimd bftad of speotnon. Tint impretMd on the p«p«r. Bed None. Orange . . Orange-yellow Yellow , . Tellowish-green Green . . . Bluish-green . Blae . . . Violet . . . Lavender . . To the agency in the Faint brick-red. Brick-red. Bed passing into green. Dull bottle-green. Ditto passing into bluish. Sombre blue. Black passing into metallic yellow. Ditto. Violet or purplish black. ^ sunbeam which is capable of exciting chemical influence, as distinguished from heat and light, the term Actiniam, or ray-force, has been applied ; but the term is not dis- tinctive, as light and heat are e perties by the action of light, that it became insoluble in certain essential oils. A metallic plate, covered with this substance, was placed to receive the image of any proposed object in the camera, and the portions of bitumen unchanged by light were subsequently removed by solution, the image remaining depicted in bitumen. This, however, was found to be a very slow and unsatiafiMitofy process, and was soon abandoned. 1293. The Fkotographie Oamerti, — This invaluable appamtus should be provided witn a good achromatic (1120) lens, or com- binstion of lenKB, and be capablo of wljmtmeiil by meuu of a jlidinK tube at a, Fig. 676, furnished with a r»ck and pinion ; ths farther end of the boi ehonld be made to slide within (he anterinr ertioQ, in order to obUia a rongh mljustment to focna, acd shonld prondfld withgrooTes, ioaa to admit either a wooden frame o or a pane of ground glass, at will : in either caaa these mnst m fit the grooves, as to prevent tbe admission of eitraneous light. To use this instrnment, the end n should be closed bymeaiiBof the plate of ground class, for the purpose of Teceiving the 'V- WS. image produced bj the lene. On phtcing the camera on a convenient support opposite the landscape or object to be oojiied, its image will be visible on the ground glass, which sbould he adjusted until the image becomes as I perfect and nell-defiued as possible. In cameras desigaed for taking landscaMs a ringle achromnlio meniscns (1068) ij some- times employed, the concave side being tomed towards the ob- ject. Ii. front of the lens a diaphra-m is placed, the aperture of which may be large, if the parts of the object are nearly in the ■ame plane, as the elevation of a building ; bat in a landscape the apertore must be diminished in proportion to the space between the foreKTound and the distance. As both fore and background Mnnot be in Socaa at the game time, the eonfnsiou of the image fiom the oToriappmg of contignous pencils is diminished by re- ducing their angular aperture, aa in myopic vision (1 187). in the best constructed landscape cameras, the frame is capable of a little inclination in any required direction: this is often roond convenient for the duo preserratioa of perspective in wchifectural photographs, ^ 1294. In cameras for taking portraits (for which shortness of time IB an object), a larger amount of inddent light, aod conse- quently a larger angle of aperture of the ill mnina ting penoil,beeomeg necessary ; and then in order to correct the increased amoiuit of aberration, a double achromatic com- bination is employed: of these the Fv,.«7ti. front 18 plano-convex (Fig. 598), the coQToi surface being turned towards the object, as at a, Fig. 676. Tte pos- terior combination, b, which is Mpa- rated from the anterior by a space about equal to the diameter of the latter, coDBists of a conoavo^Muvei 736 PHOTOGKAPHT. bein^ exposed to the yaponr of iodine^ which is best efifected br placing at the bottom of a wooden box a piece of thin deal, saturated with a solution of iodine in alcohol, and resting the plate, with the silver face downwards, on two little projecting ledges in the interior of the box, so that it may be a couple of inches above the iodized wood. In this manner a delicate yellow coating of iodide of silver is formed over the plate : this is extremelj sen- sitive to light, and therefore must not be exposed to its influence nntil placed in the camera. The surface may be rendered still more sensitive by suspending it for a short time over a solution of chloride of bromine, by which the yellow colour of the iodized plate is converted into a pale rose-red. These operations should be, like all preparatory photographic processes, performed in a room illuminated only by the rays transmitted through yeUbw or red glass. The prepared plate oeing placed in its frame, and the lid closed to shield it from light, it should then be placed in the camera, previously carefully adjusted to focus, and the sliding cover being withdrawn, the sensitive surface of the plate is ex- posed to the action of the rays forming the image. In the course of a few seconds the full effect is generally ob- tained, and the closed frame, with the plate, should be transferred to the photographic room. The plate being then removed, will not appear to have undergone any visible change, the picture being present, but latent. To render it visible, the plate is suspended in a dark box over a capsule of mercury, gently neated by a spirit- lamp to a temperature of about 140° F. The ledges whicn support the plate should be so placed that the latter may rest at an angle of 45 degrees to the side of the box. The mercury will slowly rise in vapour, and will adhere in the form of extremely minute grey globules to those parts of the plate where the light has nJlen, leaving the parts corresponding to the shadows of the picture untouched. In this way the picture may be seen gndnally unfolding itself, and this beautiful part of the process may be watched by the light of a taper through a little yellow window in the box. As soon as the picture has obtained its maximum of distinctness, the plate must oe removed, and being placed in a yessel, should be covered with a weak solution of hyposulphite buted over the sensitive surface ; and as exceedingly minute quantities of organic or other foreign matter, will frequently be found to mar the beauty of the effect, it is desirable to avoid as much as possible the contact of brushes, sponges, or other bibu- lous bodies, with the sensitive surface. The best mode of applying the requisite solutions is generally either by immersion, or by floating the paper on the surface of the solution placed in a shallow glass or earthenware dish, and then holding it edgewise to drain on a piece of blotting-paper. In those cases in which the preparation would be rapidly deteriorated by oiganic matter derived from the paper, it is desirable to lay the paper on a piece of plate-glass a little BmulUr than the paper, so as to leave a narrow projecting margin, and having poured a small quantity of the solution on the paper, to distribute it over the surface by a straight glass rod, which, for the convenience of holding, may be bent twice at right angles, thus : — \ The object of the projecting margin of paper is to prevent any portion of the fluid, tiiat reaches the edge, from passing behind the paper by capillary attraction. This is most important in negative (1291) photographs, as any stains on the back will be re- produced in the positive copies. 1304. As nitrate of silver is an important ingredient in atmcst all practical photography, a solution of 50 erains of crystallized, or colourless fused nitrate of silver in one nuid ounce of diadlled water may be understood to be the solution subsequently mentioned. 1305. Argentotype. — The employment of chloride of silver has already been mentioned (1282); a paper msy be prepared with this salt of sufficient sensibility to receive the impression of an image in the camera (1293), after an exposure of from ten minutes to half an hour : but the picture will be far inferior in beauty and distinctness to those obtained by other processes. For this pur- pose the paper should be first covered witn a solution of 20 grains of chloriao of sodium (common salt), drained and dried ; and then with the solution of nitrate of silver, after which it may be again dried, but it is more eficctive if used at once, ¥rithout diying. A leas sensitive paper, for copying botanical specimens, or other ob- POSITIVE PH0T0OBAPH8. 739 jects, hy superpositioii, may be prepared with a solution contain- ing one half the quantity of nitrate of silver. More sensitive papers may be prepared by applying first a 20-grain solution of iodide or bromide of potassium, and subse- quently the solution of nitrate of silver. It appears that these three preparations, although closely re- Bemblmg each other, are acted upon differently by the chemical rays of me spectrum: thus, if slips of these different papers be exposed to the spectrum, the paper prepared with the chloride of silver will be most darkened in the blue ray ; that with the iodide, beyond the violet : and that with the bromide will be blackened for nearly the whole length of the spectrum, but most intensely in the indigo ray. The pictures impressed on these papers may be fixed by wash- ing them first in warm distilled water, to remove any portion of unchanged nitrate of silver remaining in the paper, and then in a solution of hyposulphite of soda containing two drachms in the fluid ounce : which will require to be warmed in cold weather, in order to facilitate the solution of the iodide or bromide of silver not acted on by light. The hyposulphite of silver may then be removed by washing in plain water, until it no longer presents a sweet flavour. It may be remarked that the neutral iodide and bromide of silver are scarcely sensitive to light ; but they acquire this pro- perty by the presence of an excess of nitrate of silver. 1306. The photographs obtained by the processes hitherto de- scribed are all negative | it is, however, possible to prepare a poBitive paper t or one which will at once give a picture with its lights and shades in their proper position ; the following is the process contrived by Mr. Hunt for this purpose. The photogra- phic paper is soaked for a few minutes m a solution of ten grains of chloride of sodium in an ounce of water: it is then drained, dried, and washed over with the solution of nitrate of silver, to one ounce of which are added two fluid drachms of alcohol : the paper is then exposed to the sun, which darkens it immediately ; the solution of silver is again to be applied, and the paper once more exposed to the sun, until it assumes an uniform chocolate colour ; it is then to be dried in the dark. To use this paper, it should be covered with a solution of thirty grains of iodide of potassium in an ounce of water: and if placed whilst moist in the camera it will be impressed with a beautiful sepia-coloured posi- tive picture in half an hour. These pictures are best fixed by washing them with water, to remove the excess of iodide ; but unfortunately they are liable to fade. 1307. If any of the sensitive papers (1305) be exposed in the camera for too short a time, either no picture at all, or at least a barely visible one, will be noticed ; still the absence of a visible impression is no proof that a sufficient efiect is not produced. This 3 B 2 740 PHOTOOSAFHT. maj indeed be demonstrated hj the application of some reducing agent, as gallic, pyrogallic, or succinic acid, proto^ulphate of iron, &o., which would act either more slowly, or not at all upon the paper before exposure : we have, founded on these principiea, some processes for preparing paper of extreme sensibility ; and of these the first whicn merits attention is the eaJtotype, 1308. The first communication made to the Koyal Society by Mr. Fox Talbot, in January, 1839, comprised only the applicatioD of chloride of silver to the copying of objects superposed on the prepared paper, and subsequently obtaining a potitive (1291) cop^ of the negative photograph thus produced : tne repetition of positive copies, from the same negative, forms an important fea- ture of this contribution to science. The ealotype process was patented by Mr. Fox Talbot at the beginning of the year 1841 ; and as at present practised, diflfers little from that originally proposed. The paper is firvt coated evenly with a 20-grain solution* of iodide of potassium, and dried ; it is then covered with a 30-grain solution of nitrate of silver, washed in pure water, and again dried. The paper thns prepared may be kept for a considerable time. When prepared for use, in order to g^ve the iodized paper its maximum of send* bilit^, it must be rapidly covered with equal parts of the solution of nitrate of silver, to which one-sixth part of strong acetic acid has been added, and of a cold saturated solution of gallic add ; then immerse it for a moment in distilled water, and drain it on blotting-paper. Tn this state it is remarkably sensitive, and when nearly dry, may be exposed in the camera ; but a short time, often a few seconds, is sufficient to obtain a beautiful picture. The paper should then be removed, and the picture impressed upon it, although as yet invisible, must be developed bv again washing it with the mixed solution of silver and gaUic acid, keep- ing the paper warm, especially in cold weather, by placing it in a dish over boiling water. The picture thusproducea may be fixed by washing first with warm water, and then with a warm solution of hyposulphite of soda ^1298) for a few minutes; after which, it should be again soaked m warm water, and dried between folds of blotting paper. These pictures, which are among the most beau- tiful in the photographic art, are negatives. 1309. Some photographers prefer preparing the iodized paper bjr a process called the " single waui : for this the silver con- tained in the solntion is precipitated in the form of iodide, by the addition of iodide of potassium: the precipitate is then washed, and dissolved in a strong solution of iodide of potassinm. The paper is floated on this solution, drained, and immersed in a bath of^pure water ; when the iodide of silver is thrown down on ita surface in a finely divided state, being almost insoluble in a dUute solution of iodide of potassium. * Twentj gr»ina to one fluid ounce of dlstiUrd wat«r. PR0CBB8 BUITABLB FOB ABTIFICIAL UOHT. 741 1310. It has been found that the sensitiveneBS of the calotjpe paper is considerably increased by adding some chloride of sodium, or ammonium, to the solution ot* iodide of potassium. The fluid recommended by Mr. Cundell contains twenty grains of iodide of potassium, and^ five grains of chloride of sodium, in an ounce of water. A similar quantity of chloride of ammonium is preferred by some photographers. 1311. The original project of Mr. Fox Talbot has received some modifications and iinprovements ; but its general details have re- mained unaltered. It will not be necessary to allude to more than the process sug^sted by Mr. Channing of Boston, which has the great merit of simplicity. He directs the paper to be first carefully washed over with the solution of nitrate of silver, and when dry, with a solution of ten grains of iodide of potassium, and five of chloride of sodium, in an ounce of water : aher which it is to be washed with water, and dried between folds of blotting paper. The paper is then fit for use, and may be placed in the camera without any further preparation. After exposure, the latent picture is brought out by washing with tbe mixture of gallic acid and nitrate of silver, as in Mr. Talbot's process. A mere aqueous solution of gallic acid is, however, quite capable of developmg the picture, if the dish, containing the paper, be placed over a vessel of boiling water, after adding the gaUic acid. The picture may then be fixed as usual, by means of the solution of nyposulphite of soda. 1312. Availing himself of the greater susceptibility of the bromide of silver to the less refrangible rays of the spectrum, the present editor of this treatise devised a preparation of considerable sensibility, especially to the feeble chemical rays of a lamp- or gaa- light, wblch has been for some years past suocessfally employed at the Royal Observatory, Greenwich, and elsewhere, in the automatic registration of magnetic (624), barometric (495), and thermometric (1234) variations. His process is the foUowme : — one surface of well glazed paper is covered with a solution of twelve grains of bromide of potassium, eight of iodide of potassium, and four of isinglass, in an ounce of distilled water ; care must be taken to apply the solution equally over the paper, which is then to be dried. When required for use, it is washed over with the solution of nitrate of silver ; the only light used in this process must be that transmitted through yellow glass. ^ This j)aper should be used whilst damp ; a few minutes are sufficient for its ex- posnre, when employed in the camera, and on removal, it should be covered with the aceto-gallo-nitrate solution (1308), when in a few seconds the picture will hecome visible. As soon as it is sufficiently developed, tne process should be stopped by immersing the paper in water, and fixing the picture in tne usual manner. With ttds paper a sharp impression has been obtained in a few seconds from the image of a narrow slit illuminated by gas-light formed at a 742 PBOTOORAPRT. distaooe of seyeral feet in the conjngate focus of the concaTe mirror of the registering apparatus. 1313. Waxed Paper JProeeta. — Very beantiinl results maj he ob- tained by this process. The paper is first waxed, by placing it on a plate of hot iron, and rubbing a piece of white wax smoothW and eyenlv over its surface ; it is thus rendered transparent It is desirable to procure pure white wax for this purpose, as the commercial white wax, sold in cakes, is usually aaulterated with some fatty substance. Pieces of paper of the proper size should be allowed to soak for some hours m the solution of chloride of sodium, or, still better, in that suggested by Mr. Cundell (1310) ; they are then removed and carefully dried. Some photographers prefer iodizing the waxed paper with a mixed solution of iodide and oromide of potassium, to which a little free iodine has been added. Immediately before exposure in the camera, the paper is passed over the surface of the solution of nitrate of silver, to which one- sixth part of acetic acid has been added. After draining for a minute or two in a darkened room, the paper may be placed in the camera in the usual manner. After a safficient exposure, the latent picture is brought out b^ means of a saturated solution of galKc acid, or by the gallic acid mixture before mentioned, and fixed in the ordinary manner by means of the hyposulphite of soda. 1314. Atbuminixed ^per has been frequently employed ; it is thus prepared : 40 grams of chloride of sodium or ammonium ars dissolved in one fluid ounce of water, and placed with three fluid ounces of albumen (white of egg) in a bottle capable of containing nearly double the quantity ; the mixture is shaken, until it to be ropy, and the sediment allowed to subside. The clear portion of the mixture is poured into a shallow vessel, and the paper floated on its surface, until it is thoroughly wetted, and then orainedj and dried ; when required for use, it is rendered sensitive by the acetonitrate bath, as in the waxed paper process, and ex- posed whilst moist in the camera. A very brief exposure is saf- ficient to form a latent picture, which is developed by means of the gallic acid solution, ana fixed by the hyposulphite. It has been stated by Mr. Cousins that the paper is rendered more sensitive by albuminizing it by means of a mixture of twenty-two grains of iodide of potassium, six grains of bromide of potassium, and two grains of chloride of sodium, with one fluid ounce of white of egg. 1315. Many varieties oi ferrotype haye been described ; these are all indebted for their sensibility to light to the per-«alta of iron, which become wholly or partially reduced by the solar rays. The most convenient salt for this purpose is the ammonio-citrate ; if paper be washed over with a solution of this salt in ten or eleven parts of water, and carefully dried in the dark, it is remarkaUy sensitive to light ; if any object be superposed on a piece of this Saner, and exposed for half an hour to the sun, a sharp and well- enned picture will be obtained. If, however, the buu'b rays be CTANOTTPES. 743 not verj bright, or the expoBure to their influence be mucb eborter, a Bcarcelj visible impression will be formed ; but as all the points exposed to the light have undergone a change, from the partial conyersion of the sesqui-citrate into a proto-salt, on washing the paper with a solution of the red pnissiate of potass (ferro-sesqui* cyanide of potassium], a pretty picture will appear in yellow on a blue ground, the prussiate acting only on the reduced portion of iron salt. In the same way a solution of nitrate of silver will pro- duce a fawn-coloured picture on a blackish-brown ^und, and a neutral solution of chloride of gold will produce a picture with a splendid purple g^und, which is the chrysotype of Sir J. Herschel. 1316. Many other salts of silver may be employed with more or less success as photographic agents, their range of sensibility differing very considerably; among these compounds, one pro- duced by the action of ferrocvanate of potass or iodide of silver, discovered by Mr. Hunt, is the most emcacious ; this, the eyano- type^ is thus prepared, and is wurtlw of notice from its presenting a close approach to the beauty of the calotype pictures. The paper is washed over on one side with the solution of nitrate of silver (1304), qm'ckly dried, and a second time washed with the same solution ; it is then immersed for a minute in a solution of 20 grains of iodide of potassium, in one ounce of distilled water, removed, and gently washed with pure water, and, lastly dried in the dark. The paper, so far prepared, may be kept for any length of time, and to render it highly sensitive, it is only necessary to moisten it with a solution of one part of ferrocyanate of potass in eight of water. These papers are only sensitive whilst moist, for if allowed to dry in the dark, they become nearly insensible to tiie influence of light; immediately, however, acquiring their susceptibiUty to light by merely moistening them with pure water. The pictures taken in the camera oy this process are readily fixed, by bein^ washed first with water, and then with the solution of hyposulphite of soda, and then washed sgain, as before. It was on this kind of paper that the curious result of an impressed coloured spectrum was first obtained. 1317. llie eyainotyp€9 are very beautiful, and some of them have peculiar claims to our attention. One of the best is made by washing paper with a solution of the red prussiate of potash, and when dry, .exposing it to the sun, with tne object to be copied pressed in close contact with it by a plate of glass. The effect of the light is to evolve prussian blue, which remains deposited on the paper. On soaking the picture thus produced in water, the unchanged prussiate is removed, and a white picture on a beauti- ful blue ground results. This easily prepared paper affi>rds a ready and excellent means for copying ferns||pr other objects by super- position, but it is not sufficiently sensitive for the camera. 1318. The most sensitive cyanotypes hitherto obtained are those prepared by the following processes, devised by Sir J. 744 PHOTOGRAPBT. Herschel. Mix together equal parts of a cold saturated Bolatkn of bichloride of mercury, with one of the ammonib-citrate of iron (1 part of the citrate to 11 of water) ; and before any precipitatMO occurs, wash over the paper with this fluid, and diy it ; pa]>er thus prepared may be kept for some time without being deterio- rated. A piece of this should be placed in the camera, until a decided, although faint impression is just visible ; it should^ then be removed, and rapidly washed over with a saturated solution of ferrocyanide of potassium, diluted with three times its bulk of strong gnm -water; the picture then gradually unfolds itself in an extremely beautiful manner, and should be allowed to dry in the dark, where it should remain for some days ; after whicn it will bear a strong light with impunity. If a picture thus obtained be heated, it is converted from a blue positive, into a brown negative one : by keeping, however, it recovers its positive character and its original colour. The term amphUype has, on that accoont, been applied to this process. 1319. The diromoiifpe affords a sensitive paper of sufficient delicacy fur copying superposed objects, and may be made by simply washing thin paper with a solution of bichromate of potass, and drying it quickly before a fire. Let an object be placed in the pressure-frame (1290) on this paper (which possesses a fine yellow colour), and exposed to the direct rays of the sun until the yellow colour of tne paper is changed to a rich brown, on re- moving the object, its outline will be found beautifully defined on the paper, the drawing being yellow on 'a brown ground. To secure this from further change, all that is necessarv is to soak the paper in water, to remove the unchanged bichromate, by whicn process the picture is left nearly white on a brownish yellow ground, and may be preserved without further chan^ The rationale of this process is found in the reduction of a portion of the chromic acid to the state of oxide. 1320. From the elaborate researches of Sir J. Herschel, it has been proved that scarcely any coloured fluid from the vegetable kii\gdom, or any compound with which chemistry has made va acquainted, exists, which is not more or less sensitive to the chemical influence of light. He succeeded in obtaining well- defined photographs, by merely using paper impregnated with the coloured juices of flowers and other parts of vegetables ; and to these the generic term of arUhotype has been applied. For an account of these interesting researohes, the reader must be referred to the original papers in the Philosophical Transactions. 1321. It is worthy of remark, that all the photogranhio pro- cesses are considerably expedited by the apphcationof a gentle heat. Sir J. Herschel found that in many instances of photo- graphic action produced by exposing a strip of prepared paper to tne solar spectrum, the cnanges which would have reqnired a considerable time to be effected, were rapidly produced by hold- POSIflVE PRIKTIKO. 745 ing behind the paper, whilst thas exposed, an iron heated below redness. In the account of the calotjpe process (1308) of Mr. Fox Talbot, it has been mentioned that the paper must be heated to bring out the picture properly. In the cyanotype pictures (1318) we have seen that an actual alteration of colour, and the conversion of a positive into a negative picture, takes place by the mere application of heat. The agent in producing this curious change is considered by Sir J. Herschel to consist of rays existing in, and below, the red and orange region of the solar spectrum, and emitted by bodies heated just below redness. These rays, for which the term of parathermie has been proposed, appear to bear the same relation to the true calorific rays, as those active in producing chemical and photographic phenomena do to the luminous rays. 1322. Positive Frinting. — The paper selected for printing positive photographs shoufd have as fine a texture, and as smooth a surface as poesibie ; and the right side of the sheet, which can generally be detected by reflected light, should be chosen. The albuminized paper already described (1314), is very effective. Another solution frequently employea contains 8 gp'ains of chloride of ammonium, 1 of gelatine, and 3 of Iceland moss in each fluid ounce. Either of these pre^red papers roa^ be rendered sensitive by floating on the solution of nitrate of silver, then draining, and drying in the dark. The impressions may be fixed in the usual manner bv the hyposulphite solution, but a picture on the latter paper will be much strengthened if it be fixed in a toning bath, containing half a grain of chloride of gold, 4 grains of nitrate of silver, and half an ounce of hyposulphite of soda, in each fluid ounce. In preparing this bath, the three salts most be separately dissolved, and first, the solution of gold, and subsequently that of silver, stirred gradually into the solution of the hyposulphite, in order to effect a complete solution. The ammonio-nitrate of silver is preferred by some photo- graphers as a sensitizing solution : this is prepared by precipi- tating the oxide of silver, by adding gradually caustic ammonia to the nitrate solution, and then dissolving the precipitate in an excess of ammonia. This process is more difficult than the former, but when successful, the results are very satisfactory; it is not applicable to the albuminized paper. In ordec to avoid subsequent fading, it is desirable that every trace of hyposulphite be removed by washing in pure water. 1323. Collodion Frocessea. — ^The most important improvement in the photographic art has been the employment of collodion, for which science is almost entirely indebtea to the researches of the late Mr. Archer; no process has yet been contrived which famishes such satisfactory results, even in the hands of an inex- perienced operator. The basis of collodion \% pyroxyline^ a sub- stance formed by the action of a mixture of nitric and sulphuric 746 PHOTOGSAPHT. acids on cotton- wool, or some other form of vegetable fibre : the change produced in the fibre probably consisting of the subetitn- tion of one equivalent of the peroxide of nitrogen (N O^) for an equivalent of hydrogen. Pjroxvline maj be convenientlj pre- pared in a small quantity by immersing one drachm of cotton- wool for 10 minutes in a mixture of 6 fluid ounces of sulphurio acid, and one of water, to which 3 ounces (troy) of dry powdered nitre have been gradually added. When removed from the acid mixture, the pyroxyline should be rapidly washed in a large quantity of cold water. The temperature of the mixture should be 140'' F. Collodion is pre{)ared by dissolving 80 grains of pyroxyline in a mixture of 5 fluid ounces of sulphuric ether, ana 3 of highly rectified alcohol, so as to furnish a solntion suffi- ciently viscid to leave a transparent coherent pellicle when a lew drops are allowed to evaporate on a plate of glass : if too little alcohol be emplo^red, the film dries too rapidly, if too much be used, or not sufficiently rectified, the film loses its cohesion, and the surface is broken up in washing. The collodion is then iodized in the following manner: prepare a saturated solution of iodide of potassium in rectified spirits of wine, and add to it aa much frasnly precipitated iodide of silver as it will dissolve : after repose, decant the clear fluid, and add about five drops of it to an ounce of collodion. After agitation aud careful subaidenoe for a few days, this iodized collodion will be ready for use. This preparation is not veir durable, as the iodide of potassium be- comes decomposed, and free iodine is liberated, wnich may be recognised by the gradual darkening of the fluid. Collodion iodized by the addition of four or five grains of the iodide of cadmium to each fluid ounce is a more stHblei and not less efieotive compound. 1324. A piece of colourless thin plate-glass, fitting into the sliding frame of the camera, should be carefnlly washed, and polished with a silk handkerchief; holding this plate bv one end, pour over it enough of the iodized collodion to flow freely over it : when thus covered, allow the excess to drain ofl^ by inclining one comer of the plate over the bottle of collodion : some care is re- quired, and a certain oscillating movement of the plate in the hand, to produce a film of perfect uniformity. After a minute's repose, let the plate be earned into a dark room, and by the aid of a feeble yellow light carefully plunged into the nitrate bath. This consists of a solution of 30 grains of nitrate of silver to the fluid oimce of distilled water, which must be saturated with iodide of silver, to prevent its taking up any iodine from the ooUodion film. This is effected by dissolving the whole of the nitrate of silver to be employed in a small quantity of water, and adding a few grains of iodide of silver, which will be dissolved after a little agitation. More water is then added, to make up the re- quired quantity, when a portion of the dissolved iodide of silver DBYELOPMBRT OF HEGATXYE8. 747 will be a^ain precipitated, but the flaid will remain saturated, fifteen minims of alcohol should be added to each fluid ouncei to prepare it for use. A narrow flat vessel, placed obliquely, in which the plate may be completely immerBed, is the most conve- nient form of bath. The plate should remain in the bath about one minute, and having been carefully lifted out and drained by resting the lower ed^ on blotting-paper, should be placed in the sliding frame; it is then ready for tne camera. Having carefully ac^'usted the camera to the object in the usual manner, the plate of ground-glass is removed, and replaced by the frame containing the prepared plate ; the screen is tnen drawn up, and the picture allowea to fail on the plate. It is not easy to state with any accuracy the time required to produce an impression on the sen- sitive sur&ce, as it varies from a few seconds to a minute or two, according to the intensity of light, and other circumstances. 1325. After a sufficient exposure, the frame is taken into the dark room, and the plate removed from it Nothing will be visi- ble on its surface, until after the application of the developinjg agent. For this purpose a solution of three grains of pyrogallio acid, and one fluid drachm of strong acetic acid, in one fluid ounce of water, is employed. The plate being placed on a leveUing stand, or on a porcelain dish, with the &ce upwards, enough of this solution is poured on its surface to cover it completelv. The picture will rapidly appear, and when its details are distinctly visible, further action must be stopped by gently pouring some pure water over it : then a small quantity of a strong solution of hyposulphite of soda should be poured over its surface, and allowed to remain for a minute or two. The plate should then be repeatedly but gently drawn through a basin of water, or placed under a eentle stream of running water, then drained, and slowly dried. By this plan, which is exceedingly simple in practice, pictures are produced possessing a sharpness of outline, and an artistic beauty, which can scarcely be equalled bv any other known process. Photo^phers are likewise indebted to Mr. Archer for the first application of that most powerful reducing agent, pyro- gallic acid. 1326. The pictures obtained by this process are negative, and will yield an unlimited number of positive pictures by placing the plate with the picture downwards on a piece of positive paper (1322) in the pressure frame (1291). A few minutes' exposure to the light of tne sun, or if that be too powerful, to bright diflused daylight, will print off 9k beautiful picture on paper, which may be fixed in the usual manner. Before the collodion negative is made use of for printing positives, it is desirable that the film be protected from abrasion oy a varnish. For this purpose, a solu- tion of one ounce of white stick lac, and one drachm of picked gum-sandrac, in 12 fluid ounces of alcohol (sp.gr. 0*815) is recom- mended by Mr. Hardwich. A good varnish tor this purpose is 748 PHOTOORAPHT. made by digesting piecee of amber (or animd ?) in chloroform : perfectly clear white mastic spirit varnish will, however, answer the purpose exceedingly well. 1327. CoUodion Positive*. — Any collodion negative may be converted into a poeitive, by coating the film with an opaque black varnish, and viewing the picture through the glass, by n- flected light. This process, which in fact constitutes the staple of cheap photography, requires some variations from the pre- viously described negative processes. Opacity and depth of tint, BO essential for negatives, are not here so much needed as bril- liancy under reflected lignt, from the deposition of metallic silver in a state of minute subdivision. For iodizing, Mr. Hardwich re- commends a solution of 6 grains of iodide of ammonium, 4 of bromide of ammonium, and 8 of iodide of cadmium in one fluid ounce of alcohol (sp. gr. 0*815), to be added to 3 fluid onnces of the plain collodion ; and the nitrate bath to be very dighUy acidu- lated with nitric acid. The required tone of development is more readily effected by a proto-salt of iron, than by pyrogallic acid ; good results may be obtained by a solution of 15 grains of proto- sulphate of iron in one fluid ounce of water, to which is added half a fluid drachm of alcohol, and of strong acetic acid, to which some photographers add 10 grains of nitre. The best fixing solution for positives is one containing from 5 to 10 grains of cyanide of potassium in each fluid ounce, to which some add one grain of nitrate of silver. This solution must be cautiously applied, especially the stronger, as otherwise it wiQ efface the half-tints of the picture. 1328. When washed and dried, the positive picture may be first protected with one of the transparent varnishes already mentioned (1326), and then coated with a solution of 3 grains of caoutchouc, and 25 grains of asphaltum, in one fluid ounce of mineral naphtha. It has been recommended by Mr. Fav to place a piece of thin gutta-percha in the bottle of prepared collodion ; although scarcely any visibly dissolves, yet the viscidity of the fluid and the tenacity of the resulting film are said to be increased. 1329. Dry CoUodion Processea. — ^Various processes have been devised for the preservation of the prepared film of collodion in .a moist state, in which it is very much more sensitive, than when dry. A solution of a highly deliquescent salt, the nitrate of magnesia, was employed by Messrs. Spiller and Crookes; but it was found to impair the sensibility of the film. Honey was emploved by Mr. Shadbolt, and a mixture of honey and acetic acid by Mr. Llewelyn, with the same view ; but in both cases the film was found to become gradually less and less sensitive ; the attention of photographers was consequently directed to some process by which the collodion surface might remain sen- sitive when perfectly dry. One of the most successful of manj plans that have been proposed is that of Mr. Fotheigill. This RBPBODUOTXOH OF HATUBAL C0L0UB8. .749 consists in slightlj washing the plate when removed from the silver-bath, so as not entirely to remove the solution of silver from its ^ surface, then pouring over it a dilute solution of albumen, which, being gently rinsed off, the plate is left to drv. Another effective dry process is that of Major Bussell. In this the glass plate is first covered with a solution of 20 grains of gelatine in 8 ounces of distilled water and 5 drops of strong acetic acid. The gelatine should be allowed to swell thoroughly in the water, be- fore it is heated for solution. When cold, add to this three grains each of iodide and bromide of cadmium and a small piece of iodine, all first dissolved in a small quantity of water. The plate is then dried slowly, and coated as usual with collodion : it is then im- mersed for five minutes in a thirty-grain silver-bath, and the free nitrate of silver being carefully removed by washine, the plate is covered with a filtered solution of 6 or 7 g^us of tannin to an ounce of water : this solution is then washed ofij and the plate is drained and dried in the dark. The developing solution is 14 grains of pvrogallic acid to the ounce of water, to which at the moment of use is added a few drops of a solution of 20 grains of nitrate of silver, and 40 grains of citrio acid in an ounce of water. In all dry collodion processes the addition of a small quantity of a solution of nitrate of silver to the developing solu- tion is indispensable. 1330. Betore the discovery of the value of collodion as a photo- graphic agent, starch, casein, and albumen were employed; of these the latter has, in the processes of Mr. Mayall and Mr. Martin, produced very pleasing results. To use cUbuminized gkuSj add ten drops of a saturated solution of iodide of potassium to the white of a fresh eg^. Beat this into a froth and allow it to repose for a few hours, ana strain through muslin. Then having polished the surface of a glass plate, pour over it a quantity of the pre- pared albumen, aUow the excess to run off and the plate to dry on a levelling stand. Then, in a dark room, immerse its prepared face into a bath of 50 grains of nitrate of silver to 1 ounce of distilled water with 1 fluid drachm of acetic acid for about ten seconds, and dip it into a vessel of distilled water : the plate is then allowed to dry, and will remain fit for the camera for some dajrs. About five minutes' exposure is required for a eood picture, which is developed by means of a saturated solution of gaUic acid, and fixed in the usual manner. 1331. Beprodudion of Natural Colours^ — It has been already stated (1285) that when a solar spectrum falls on paper coated with chloride of silver, various tints, more or less resembling those of the rajB producing them, are produced on the paper: and it has ever been a problem to photographers to reproduce more perfectly the natural colours. This object has to a certain extent been attained by M. Poitevin, by a comj^licated process. A sheet of paper is first covered with a layer of violet subchlorido ^■^■cz^ 750 PHOTOORAPHT. of Bilver, obtained by reduction in the light of the white chloride, in the presence of a reducing salt. Equal Tolnmea of saturated solutions of bichromate of potash, and of sulphate of copper, and of a sohition containing fiye per cent, of chloride of potauium, are then applied to the paper. The image of the solar spectrum im- pressed on this paper is developed by applying, firat, a dilute solution of chromic acid, secondly, a solution of bichloride of mer- curj, and thirdly, a solution of nitrate of lead. This is not, how> ever, a process of any practical utility, since the coloured picture thus obtained will not bear exposure to light, and the paper is not sufficiently sensitire for use m the camera. 1332. A very interesting extension of photography to micro- Bcopic drawings has been made ; Mr. Delves, Mr. ShadboH, Mr. 8. Highley, and others, have successfully pursued this subject : they have all adopted some collodion process. For this purpose the body of the microscope is placed horizontally, its eye-piece removed, and a tube of pasteboard lined with blacc velvet, to cut off all lateral reflections, is placed in the body : the upper end is then inserted into the brass tube of a camera from which the lens has been removed, a collar of black velvet being placed over the juncture to exclude light. The object is then placed as usual on the sta^, and a strong light being thrown on it by the con- denser, a snarp well-defined image of the object, when carefiiDy adjusted to focus, will be formecT on the ground-glass plate of the camera ; the prepared collodion plate is then introduced into the camera, and a picture is obtained in the manner already described. Bright daylight, or direct sunlight, always affords the best pic- tures, although by artificial light, especially by that of a camphine or belmontine lamp, or still better, an electric lamp, very satisfac- tory fesults have been obtained. With a half-inch object-glass good pictures have been obtained in a few seconds. There is some difficulty in obtaining an accurate focus in con- sequence of the intentional over-eorr^xtion of the achromatic ob- ject-glass, by which the violet rays are projected beyond the lower rays of the spectrum. Hence the collodion plate should be placed a Mule further from the lens than is required for the sharp defini- tion of the picture. This difficulty has been overcome in the large achromatic combinations for the camera, Mr. Ross and others having constructed lenses, in which the actinic and visual foci are made to coincide accurately with each other. 1333. Micrthphotographs. — This interesting class of micro- scopic objects na9 lieen for some years in vogue : these photo- graphs are of such small dimensions as to be almost inappreciable to tne naked eye, but when seen under a low power in a compound microscope, they come out with marvellous distinctness. Many admirable portraits are thus produced in oval spaces not exceed- ing -rV*^ of an inch in width. The mode of obtaining these is precisely the converse of the preceding, the sensitive soriace CEIA6TIAL PHOTOOBAPHT. 751 now occnpjing the place of the object, and vice verad. Unusual care is neceesary in the preparation of the collodion for this kind of work, as any stroctural imperfections in the film become so magnified as to mar the effect of the photograph. The late Mr. T. Jackson, Mr. Shadbolt, Mr. Dancer, and others have been very Bucoessful in producing ihese curious objects. 1334. Of all the stereoscopic effects, none are so grateful to the eye as those resulting from two well-a(^usted photographs ; from tae unerring truthfulness of each delineation, the most perfect impression of relief is produced. For inanimate objects the two pictures may be successively taken by the same camera, its position being suitably altered ; the great depth of relief thus produced is truly surprismg. For portraits, it is desirable to take the two pictures simultaneously, by a double camera. 1 335. Oelestud Photography. — The first attempts were made by the late Prof. Bond in America, who placed some daguerreotypes of the moon in the Great Exhibition of 1851. Since that period the subject has been successfully pursued by Mr. Warren de la Rue,* who has succeeded in obtaining most beautiful and instractiye lunar photographs on collodion, by a reflecting telescope f 1092). The variations in the angular position of the moon's visiole disc, termed by astronomers her libration, afford opportunities of ob- taining lunar photographs at various angular distances from her mean position. By an appropriate combination of these, very striking stereoscopic effects oave been produced : the variations of surface on our satellite have thus been brought out in as strong re- lief, as they would be, if an exact model of the moon were placed at a moderate distance from the eye. The moon's greatest libra- tion measured diagonally amounts to nearly 21°, and as the maxi- mum stereoscopic angle does not exceed 15^°, it is evident that any amount of *' relief" may be thus obtained: the view, in fact, as Sir John Herschel has remarked, is such as would be seen by a giant with eyes thousands of miles apart I so greatly may our visual perceptions be aided by the " giant eyes of science." It appears that the visual and chemical rays are not proper- tionabfy reflected from the lunar suriace, for the brighter portions of the moon's apparent disc do not always produce the brighter photographic images. The lines converging to a prominent object on the moon's surface are shown to be furrows, one of which ex- tends through a space of 45'', and another over 100" of latitude. The physical structure of the lunar surface is wonderfully re- vealed by examining these photographs by the aid of a compound microscope of low magnifying power. Various attempts have been made to obtain solar photographs, by employing surfaces of small sensibility, and by reducing the intensity of the solar rays by transmission through coloured glass, but without any satisfactory results. This object has been suo- • Report Brit. Aasoo. 1859. 752 PROTOOBAPUT. cessfuUy attained by allowing a very narrow slit in an opaque screen to pass rapidfy across the primary focns in the telescope ; each portion of tne sensitive surface is thus successive] j acted on during only a verj small fraction of a second, and correct delinea- tions of the sun*s disc have thus been obtained. A highly interesting series of solar photographs were thus taken by Mr. De la Roe in Spain, during the total eclipse of the sun in May, 1858. The distribution of chemical and visual rays at the moment of total obscuration appears from these to have been by no means identicaL 1336. Carbon-printing. — This and the succeeding processes depend on the property of chromic acid, discovered by Mungo Ponton, of coagulating under the influence of light, and thai rendering insoluble, a thin layer of gum or gelatine. In this pro- cess of M. Poitevin, finely-divided carbon is suspended in a solu- tion of bichromate of potash, with g^m or gelatine, and the mixture is evenly distributed on paper and dried. This prepara> tion is not suitable for the camera, but a positive copy may be obtained by the superposition of a negative, in the ordinaiy manner. After sufficient exposure, the paper is washed by meaos of a sponge, or still better, by a copious stream of water, when the still soluble organic matter, protected from light by the darkened portions of the negative, is washed away, and thoa the lights of the picture are brought out. The oxide of chromium, or chromic acid, which is reduced by organic matter under the influence of light, is a substance deno- minated "mordant," having an affinity for colouring matters. Hence various pigments, as well as carbon, so employed, will remain fixed upon the image, thus producing coloured pictures. Suitable pigments may thus be deposited on a surface of glaaa or porcelain, and subsequently burnt in ; by which means many beautiful and permanent effects have been produced in enameL 1337. Photo-lithography^ and -zincograpny. — ^For the purposes of transferring an impressed image to a surface of stone or zinc, for subsequent printing, the defects of M. Poitevin^s process are, that a negative picture is obtained in the camera ; and a poidtive picture ootained by the superposition of an ordinary negative photograph is identical in position with the object, and will there- tore print revened copies, just as printers* type is set up baek- tDaraSf in order to be retLdfonoarda, Mr. Osborne communicated, in 1859, a paper to the Melbonme Institute (a very flourishing colonial scientific body) on a process analogous to tnat of M. Poitevin, but differing from it in im- portant points. In this process the solution pf the bichromate and gelatine is applied to paper, and the light-impressed film is sahse- quently transterred to the stone or sine plate. The whole surface 18 then inked by a roller, and the unaltered gelatine washed away, 'as in carbon-printing. The solution employed is one of 100 grains of gelatine, and 56 of bichromate of potash, in an ounce PH0TO4CULFTUKE. 753 of wann water; to this, when cooled to ahont 110* F. is added i of an ounce of fresh albumen. The paper coated with this is dried in the dark, and glazed by pressure. It receives the impression through a negatiye in about a minute ; and (accord- ing to a subsequent process of Mr. Osborne) it is then inked all over with lithographic ink, and floated on boiling water for about an hour, when portions of the film not acted on, together with the ink covering them maj be removed by a sponge. The paper is then dried, and the impression transferred to the stone or zinc plate in the usual manner. Woodcuts and engravings may thus oe copied with wonderful precision and sharpness. A process independently discovered by M. Asser, of Amsterdam, and adopted by tne Ordnance Survey Department at Southamp- ton, is very similar to that of Mr. Osborne. It has been there observed by Col. Sir H. James, that the development of the half- tinte is greatly improved by keeping the prepared paper for a con- aiderable period of time before it is used in the camera. 1338. Motoglyphy. — ^This brief outline of the chemical and physical actions of hght (or, more correctly speaking, of the lumi- niiorous undulations) would be incomplete without some notice of the above ingenious processes. Photoglyphy is a method, due to Mr. Fox Talbot, of impressing a photograph on a steel plate by corrosion of ite surface. If a steel plate coated with a solution (n bichromate of potash and gelatine be submitted to the action of light in the camera, those portions of theeelatinous film that have been exposed to light are rendered partiafly insoluble. The plate is then covered with a solution of perchloride of iron, which, pene- trating the soluble portions of the film, corrodes the plate, and thus etelu» the picture. 1339. PhoUHfcUvanography, — This is an analogous process due to Herr Pl^tsch of Vienna, in which a plate of glass is covered with the same solution, and submitted to the action of light The plate is then moistened, and those portions of the surface whicn have not been impressed by light, oecome raised by the imbibition of moisture. A mould of the surface is token in gutta- percha ; an electrotype taken from this mould will be evidently capable of printing, by the ordinary means, a stereotyped copy of the original photographic impression. 1340. Fhoto-sculpiure. — ^Photography has been in a remark- able manner made available to the sculptor, in afifordin^ a series of exact outlines, from which, if sufficiently numerous, the whole contour may be very readily filled up. For this purpose a dozen or more cameras of equal dimensions are placed equidistantly round a circular room lighted by a skylight, the optical axis of each being directed to the centre. The intended subject of s por- trait is placed in the centre of the room, and photographs in as many different azimuths are simultaneously taken by all the cameras. The outlines thus produced are cooied at corresponding 3 o 754 PROTOORAPHT. azimuths iind in any required dimensions, on the block of mar- ble, by means of an arrangement analogous to the pentagrapii, the action of which depends on the constrained similarity of two triangles haying moveable sides. The intervening portions oi the bust may be so readily filled in by the hand of the sculptor, that he has succeeded in producing an admirable likenese of a perwn whom he has never seen. 1341. As the successful practice of photography depends en- tirely on the accurate adjustment of nicely balanced, but unntaUe, chemical affinities, an accurate knowledge of the nature and manipulation of the chemical elements is essential to the soooesa- ful pursuit of photography as a branch of science ; without that knowledge, it is but the practice of an empirical art. From the extremely delicate nature of some of the processes, it is essential that many minute, and apparently trivial directions, shoold be carefully observed, since small errors of time, temperature, quan- tity, or succession of steps, will frequently be founa to mar the re- sult. For the same reasons, the most scrupulous deofdintn mast be observed in all the materials and implements employed ; not only as regards actual dirtj but also any undue admixture of the minutest portions of the chemical elements themselves : thus, fcv example, most porcelain dishes that have been used for the fixing bath of hyposulphite of soda, are permanently disqualified for use us a nitrate of silver bath, in consequence of a minute quantity of the former salt having penetrated the substance of the earthen- ware, which cannot bo removed by washing. Beferenges. For further information on the early history and progress of the interesting subjects of this chapter the student is referred to the papers of Sir J. Herschel in the Philosophical Transactions, and to a Treatise on Photogrnphy by Mr. Hunt. Most ample details of the mutual relations and manipolaiMn of the photographic elements will be found in Hard^dch's Manual of Photographic Chemistry (Churchill, 1864). On Micro-photography, the papers of Mr. Delves, and Mr. Shadbolt in the Microscopical Journal may be consulted. 756 CHAPTER XXm. THBBMIG8, 1342. Thb same difference of opinion has existed amons^ philo- sophers with regard to the nature of heat, as that which nas ex isted respecting light : some have contended that the evolution of heat, as that from the son and other sources, depends upon the emission of indefinitely minute particles of matter, to which the general term caloric has heen applied. Others have subsequently applied the undulatory hypothesis to the explanation of the phe- nomena of heat, as to that of light (1019), and have entertained the opinion that both are alike the results of wave motion. The dynamic theoiy of heat is readily adapted to explain the phe- nomena of roiHation (Chap. XXIV.), but less obviously to those oimscific (1218), and latent (1223), heat. The dynamic theory of heat is, however, a doctrine of very long standing : it was thus pithily enunciated by Locke : " Heat U a very hmk agitation of the tnaensible parte of the ohjectj tohu^ produces in us that eenstxtion Jrom whence we denominate the object hot; so what in our sensation is heat, in the object is nothing but motion.'' 1343. The chief proximate cause of heat is the sun, whose rayp convey to us this important agent in common with light. There are, however, other exciting causes having a dynamic, electric, or chemical origin, to which it is necessaiy to allude. A. JMction. — ^Heat is produced whenever two bodies are rubbed leather. Thus, when two pieces of ice are rubbed tog[ether, sufficient heat is generated to melt their surfaces. Among uncivilized nations, fire is commonly produced bj the friction of pieces of wood against each other : and the old-fashioned flint-and-steel, now superseaed by lucifer matches, and percussion caps, is an examnle of the ignition of minute particles of steel bv the heat developea in scraping them off. Count Bumford found that in the operation of boring a brass cannon, 7^ inches in diameter, and the borer making thirhr-two revolutions in a minute with a pressure of 10,000 pounds, sufficient heat was generated to boil eighteen pounds of water, in which it was immersed, in 24 hours. The friction of two iron plates against each other has been applied in N. America as a practical source of heat. The development of heat by friction has been neatly illustrated by Fhif. Tynaall, by attaching a vertical brass tube containing do2 756 THBIBIIOB. water to the mandrel of a wborling teble (321) and pressing its sides during rotation by two grooved pieces of wood hineed togetber like a lemon-squeezer. Tbe water may be thna raised to tbe boiling-point in a few minutes. B. Percussion. — ^Tbis is anotber dynamic source of beat, and appears to depend upon molecular displacement, or upon tbe in- ternal friction arising from tbe condensation of Ae body atmck, for, as a general rule, wbenever bodies are diminished in bulk, beat is evolved. This is well illustrated in tbe coining press. BertboUet submitted a piece of copper to tbe strokes of a press, and found tbat tbe greatest evolution of beat occurred at the first blow, and diminished with each succeeding one : tbe quantities of beat evolved at tbe three first strokes having been 9*6', 4-2% and 1-05 C. respectively. Tbe country blacksmith used to light bis forge by an iron rod heated by repeated blows on tbe anvil. A leaden bullet will be fused and scattered in splashes, and a steel or cbiUed iron shot rendered exceedingly hot by its impact on an iron target. 0. Chemical Action,— A constant source of heat, in all cases in which a combination of heterogeneous particles takes place, as in combustion, or in tbe union of hydrogen and some other bodies with chlorine. D. Electrical -4cf ion.— Examples of this mode of evolving beat have been already given (816) ; it appears to be connected with the resistance afforded by conductors to tbe transference of elec- tric motion through them. Tbe beat developed by resisted magnetic induction has been well exemplified by Prof. Tyndall. If a btdlow cylinder of copper filled with fusible metal (1409), be placed across tbe lines of mag- netic force (592), between the poles of a powerful electro-magnet, and be there made to rotate rapidly on its axis, it will in a few minutes become sufficiently heated to melt the alloy contained in its interior.* . ,., , , E. Vital Action.— 'hX\ beings possessing life have the property of evolving heat, and generally maintaining a temperature above that of the medium in which they live. In tbe case of animaU, at least, it is beyond doubt tbat tbe evolution of beat depends upon a slow combustion going on in tbe organism : carbon and • This fket is mftiiifMtly eoBfirmatoiy of the dvnamio theory of dcctridtT ; for if eleotrieitr and maimetism be nothing bat ipina WKve-motaoo, like that of circularly polarised light (1867), thia reaolt woiUd be a dynunioal^ neceeearr oonBeqnence ; for the motion of each diktorbed particle will be cms of revolution round the line of direction of magnetic force, and the t«eia> tanoe of the maM to rotation will be the aum of the reaiatanoea of each molecule to a change of the direction of ita axis of rotation, or aa it is aometimes expressed, the sum of the inertia of rotation of each molecaK as exempUaed by the grrasoope (865). The intenial fHetion arisiog from the oonaiant change ordirection of the plane of the orbit of each particie will fully account for the heat dcTeloped, which moat eridently be in pro> Dortion jointly to the molecular energy of rotation, •••., to the intenai^ of Se magnetic Ibros^ and to the amount of orbital diapkoement^ Cs^io dw DTHAMIO EQITITALBHT OF HEAT. 757 hydrogen being slowly conyerted into carbonic acid and water, not only in the Inngs, but in eyeiy portion of the capillary system (1007) : a theory long since advanced, and to which notice has been subsequently drawn by the ingenious arguments of the late Prof. Liebig. 1344. The correlation of heat with dynamic force is a principle that has arisen in many other intelligent minds than that of Locke; heat was denominated by Crawford,^ "a force or power belonging to bodies," but to Count Romford' the first direct ex- perimental proof is due. Having noticed the great. amount of heat deyeloped by the boring of cannon, he remarked, " It appears tome extremely cufficnlt, if not quite impossible, to form any distinct idea of anything capable of bein^ thus excited and commanicated, except it be motion." And it is remarkable that the estimated yalue of the dynamic equivalent of heat, which he roughly deduced from this process, does not differ unreasonably from this result of more precise subsequent investigations. The dynamic origin of heat was confirmed by an experiment of BUt H. Davy,' in which liquefaction resultedi from rubbing two pieces of ice together in the yacuum of an air-pump. The constant relation existing between heat and force is further confirmed by the experiments of Dulong,^ which show that equal yolumes of all gaseous fluids, at the same temperature and pres- sure, on being suddenly compressed or dilated to any equal volumes, disengage or absorb the same amount of heat. Mr. Joule confirmed in 1840 the correlation existing between heat, and other modes of motion resulting from impressed force :— 1st, That the heat evolyed by any yoltaic pair is proportional eeeteri$ paribtUf to its electromotive force.' 2nd, That the heat eyolved by the combustion of a body is proportional to the inten- sity of its affinity for oxygen.* He also showed in 1844 that the beat absorbed by the rarefaction, or evolved by the con- densation of air is proportional to the force evolved or absorbed by those operations respectively,^ and these observations are confirmed by those of M. ceguin on the dilatation of steam." uiumnt of work raaployed in rotating the maw. But from this another qneation arise* : does e&otrio wave^motion take plaoe in palpable matter, or in impalpable and imponderable ether f clearly not in the latter, beoaoae a moleooie destitute of attraction towards anj other molecule in the nnlTerae can baTC neither inertia nor energy, and therefore cannot do " work :" and if then palpable matter be susceptible of the ascertained velocity of electric notion, why should it not be equally sut ceptible of the less rapid motion of light and heat? and if so, to what good purpose does the interstitial— im- ponderable—impalpable— ether hypotheeis tend P 1 On Animal Heat, p. 15. * Phil Trans. toL zriii. p. 28e. ' Elements of Chemical Philosof'hy, p. 94. * H^m. de I'Aead. des Sciences, torn. z. p. 188. 9 Fhil. Mag. vol. zix. p. 276. • Ibid. toI. zz. p. 11. 7 Ibid. vol. zzvi. pp. 876, 879. • Comptes Bendns, torn. zzt. p. 421. 768 THBHMICa. G. Bebenstein* proposed some Utopian schemes for the practi- cal production of heat by the employment of dynamical force ; but his mind does not appear to have reab'zed the true relations of beat and force. 1345. The Dynamic Equivalent of Heat. — An extensiTe series of experiments was made oy Mr. J. P. Joole, for the pmpoae of determining the number of units of work (842) or foot-pountU t^ quired to be done, in order to produce an elevation of tenDperatore amounting to 1° F. in one pound of water at about 50° F. Thefrree expefnded was measured by the descent of weights employed in rotating the apparatus, and the heat etfohed by the iHction of water, mercury, and cast iron was carefully estimated. The mean results of these experiments show the dynamic equivalent of heat to be veiy nearly 722 units of work.f As 1* C. {i.e, in the centi- grade scale) is now much more frequently employed as the scale- unit of thermal measurement than l^F. (in Fahrenheit's scale), it will be convenient to state that the corresponding centigraae unit is 1890 foot-pounds veiy nearly. It should here oe remarked that the element of time has been erroneously introduced into the dynamic equivalent of heat in some elementary treatises ; this is likely to lead to much misconeeptioo, since, provided a ^ven amount of work be done, it is abeomtelj immaterial (mmaking dynamically) what amount of time may be occupied in doing it 1^6. Several other reciprocal relations between heat and *' work*' have been observed. Thus air gives out heat on com- pression, and its temperature is lowered on dilatation. A stretched piece of vulcanized caoutchouc contracts on the application of heat (a property common to this substance, and to water between the tem^ratures of 0° C. and 4°) ; and if suddenl;^ compressed it manifests loss of heat. Similarly water diminishes m volmne from 0° to 4*", and it has been observed by Mr. Joule that if water between these temperatures be suljected to a pressure of 24 atmo- spheres, it manifests a depression of 0*008** C. If the hoe of a thermopile be placed in contact with the surface of a flat rod. aad the rod be suddenly stretched by a weight of half a ton, and there- fore increased in volume, it shows a loss of beat 1347. It has been demonstrated by Mr. Joule, that If no wmk be done by the expansion of a gas, there is no loss of heat For this purpose two strong copper vessels of the same aiie were made to communicate by a tuoe furnished with a stop-cock. One was exhausted and the other filled with 20 volumes of air, and the whole immersed in a water-bath. When the whole had arrived at a unifonn temperature, the stopcock was opened, and the air allowed to rush from one vessel into the other. The con- densed vessel and its contents became cooled ; but by a Ices of * WMrme-ErregnnfT ohse BrsimiDtttcriaL BTHnberv. 18SS. t Phil. Traat. 1860, p. 83. DILATATION OF B0DIB8 BT HXAT. 759 exactly the amount of heat produced by friction and impact in the tube and exhausted vessel : for on carefully stirring the water, no change of temperature was obseryed to take place. 1348. The Point of Absolute Negation of Heat.—li has been obseryed that for each increment of 1** C.| there is a corresponding increase of elastic force in a gaseous body equal to yfj of the force at 0* C. If the same law hold good below that point, it is evident that at —273** there would be no elastic force, and consequently no heat ; it is, however, probable that the law does not progress downwards uniformly, and we have no means of determining the temperature at which all substances would assume a solid form* 1349. When a body has acquired the power of communicating the sensation of heat it is said to be hot^ and when, on the con- trary, it takes heat from the hand when brought near it, the body is said to be oold. But within considerable limits our perceptions of heat and cold ara rather relative than absolute : uius, if two basins be filled, one with hot and the other with cold water, and a third, placed between them, with equal parts of both ; and if the hands be held for a short time in the outer basins, and then plunged into the middle one, the same water will feel warm to one hand, and cool tO the other, by contrast. It may here be further remarked that the sensihle effects of heat and cold are very similar ; and both extremes- are equally destructive of organization — the sensation of touching a globule of frozen mercury is the same as that of touching a hot iron ; and the frost-bitten extremities of the inhabitants of the cold regions evince the destructive power of intense cold. Kot the slightest difference of weight takes place in bodies by the abstraction or addition of heat; a mass of matter so cold as to freeze a little water when placed upon it, weighing the same as when at the temperature of ooiling water: the volume of the body alone undergoes a change. 1350. As the heat of Dodies is increased, they, with few excep- tions, increase in bulk : when this force is impressed on bodies their molecules become forcibly separated, causing, first, an in* crease in bulk, next, a change of tne physical condition of the solid ; it becomes changed into a liquid, and, lastly, it assumes the gaseous state, if the repulsive action of heat be sufficient (9). Solids expand less, and gases more, than liquids, for equal incre- ments of temperature. Several methods have been pursued for determining the ex- pansion of solids : the ordinair apparatus consists of a horizontal water-bath, capable of being heated by a row of gas-jets, through the ends of which a cylindrical rod of the substance to be ex- amined passes water-tight, one end of the rod resting against a fixed point, and the other against a lever near its fulcrum : the long arm of this rests against another lever, also near its fulcrum, and in the movement of the extremity of the long arm of this, the expan- 760 THEBHIC8. Bion of the rod is confiiderablj amplified, and may be approzi- matelj determined. A much better result maj, howeyer, be obtained by attaching a small mirror to the axis of the first lever ; a small pencil of light from a lamp, or other source, may be reflected from this on to a scale at any required distance, and thus the indications may be amplified to any required extent. The readiest, and probably not the least accurate mode of deter- mining expansion, is by means of taking the specific grayity (412) of the body, at several difierent obsenred temperatures, from these, and the known expansion of the fluid in which the specific graTity is taken, the expansion in volume of the body may readily be determined. One-third of this value will represent the lintar expansion. This method has the advantage ofbeing independent of the quanti^ or form of the body examined. The following table shows the increase in length, or Imear expannofij of bars of diflercnt substances, from 0** G. to 100": — Crown-glass 1000792 J Aluminium 1001087$ Copper 1001717 Flint- „ 1*000812 Cast-iron . 1*001127^ Brass . I'OOISM French „ 1000872 Steel .... 1*001145S Silver . 1001910 Hard „ 1*000897 Iron, drawn 10012355 Tin . . 1*001970 Platinum . . 1000884 S Bismuth . . 1*001392^ Lead. . 1*002818 Palladium . 1001005^ Gold .... 1*001466^ Zinc . . 1002976 Many practical applications have been made of the expansion and contraction of metals by heat : thus, the tire of a wheel is put on hot, and by its contraction firmly binds the other parts of the wheel together ; and if the engineer requires a collar to be veiy tightly fixed on a rod or bar, he drives it on while hot : and for similar reasons, boiler plates are riveted together with red-hot rivets. The successful manufacture of the Armstrong gun, in which the welded coils are successively shrunk on, is a further illustration of the same principle. By Molard, the walls of a building that had bulged, were arawn together by the contraction of an iron bar passing through them, and secured by nuts tightened on the outside whilst the bar was hot ; and a similar proceeding was adopted in the cathedral at Armagh. The middle of the centre arch of the c^uthwark iron bridge rises one inch in the heat of summer : and the eflect of a sudden gleam of hot sunshine on the Britannia bridge, which crosses the Menai Strait, is immediately perceptible in producing both vertical and lateral curvature of tne rectangular tubes. The linear expansion of this wonderful structure is provided for bv the whole being {)Iaced on friction rollers : and when great lengths of iron pipe are aid down for the conveyance of steam or hot- water, sliding-joints are necessar]^ to prevent injury either to the apparatus, or to the building in which it is placed. By multiplying the linear expansion of bodies by 8, the total ZZPANSIOll OF GLABS AND WATER. 761 increment in balk, or the cubical ea^pofinon, is generally obtained with sufficient accuracy : the algebr€ncal reason of this is obvious. 1351. By the same elevation of tem^rature from 0* C. to 100°, the increase in bulk of the following ilmds has been ascertained : — Mercury . . 00019! Ether .... 00070 \ Fixed oil . . 00080 Water . . . 00046! Oil of tup. . 00070 1 Alcohol . . . 00110 JExparmon of Glass, Water^ and Mercury. — An elaborate series of investigations has oeen made by Dr. A. Matthiessen,* for the purpose of accurately determining the expansion by heat of water ana mercury. Having found the expansion of a gla^ rod between 0** G. and 100° to be 0000729 of its length, he employed this value in calculating the expansion of water and mercury. Water beug at its greatest density at 4"* C. very nearly. Dr. Matthiessen found that he could not represent the volumes at different temperatures (in which calculation and experiment agreed very nearly) by any single formula involving the powers, up to the fourth, of t— 4 ; but he found that the volumes from 4** to 32° were very nearly represented by the formula, — F/b1-0'0000026S (f-4)+0-0000006389 (<-4)*- 0*00000007178 (<-4}*» and those between 32° and 100^ by the formula, — F<>iO-980605+OH)0000647M^-0-000000011fe <*. It thus appears that the variation of volume is far from constant. The following table shows the expansion of water for 1 ° at the temperatures specified : — «°a ^1+1-^. Diff. «°C7. Vt^i'Vt Diff. 5° 10 15 20 25 30 35 40 45 50 0*000022 0000098 0000162 0000215 0000259 0000290 0-000345 0 000388 0 000428 0-000466 76 64 53 44 31 55 43 40 38 37 55° 60 65 70 75 80 85 90 95 99 0000503 0-000538 0000572 0-000604 0-000634 0-000662 0-000689 0000714 0000737 0000755 85 34 32 30 28 27 25 23 18 From this teble it appears that expansion oontinuallpr increases with increase of temperature, but that the rate of increase, as shown by the columns of differences, is a ^aduall^ decreasing rate. There is an evident want of smoothness m the diminution of this rate near the point at which the formula is changed, which was • FhU. Tmnf. 1830. 762 THEBMICS. empirically determined by equating the two formnln, and finding the value of t in that equation. The coefficient of ex|MinBion of mercury obtained by Dr. Mat- thiessen from careful weighings in water is I7«=£?b (1+0-0001812 0; which agrees very nearly with that obtained from direct measure- ment by Begnaulti viz. — In accurate th^rmometric experiments, when the bulb and a porlion only of the tube is immersed, a small correction is needed for the expansion of the mercury in the remaining portion of the lube. If N be the number of centigrade degrees in the column extant, T the temperature to be obwrved, and t that of the surrounding atmosphere, then according to Kopp, correction= ^(T- 0 x 0*0001545. 1352. Gaseous bodies have been supposed to expand equally for equal increments of temperature, 1 volome of air at 0** C. oeing increased to 1*375 at 100^ and the same amount of dilatation in volume was long considered to take place in all other aeriform bodies. The expansion of gases has been observed by Rndbeig, and according to his researches, one volume of gas at 0" C, b^mes 1*865 at lOO"" ; if so, a gas expands 000365 of its volnme for each centigrade degree, instead of 0*00375, as generally stated. If the volume of a gas at 0** C. be 1, its volume at any higher tempera- ture may be readily found by the formula : — Volume at t* C. = 1 + 000365 1. According to the more accurate researches of Regnault and Magnus, the expansions of various gaseous bodies are not precisely equal ; the following are the volumes of various gases at 100^ C, the volume at 0* bemg 1 : — GMes. • BegMult. UAffsn. Hydrogjen Carbonic oxide Carbonic acid Nitrons oxide Cyanogen Solpburous acid 1-36613 1-36688 1-37099 1-37195 1-38767 1*39028 1-36566 1-36909 1-38563 1353. There are very few known exceptions to the general law of bodies continuously dilating by heat, and contracting in pro- portion as they are cooled, and the most important of these excep- ▲IB THBBMOICBTKB. 763 tions occnra in the case of water : the others are cast-iron, hismnth, antimony, and Tulcanized caontchonc. If water at an ordinary tem- perature be heated to its boiling point, it will expand like other uqmds, and if then it be allowed to cool, it will be found to contract in hoik continuously, until it attains a temperature of 4° C. ; at which point it will be at its maximum of density. . On a further diminution of temperature, the water will dilate in bulk until it attains the freezing point, or 0" C. ; and if it be cooled below this point without freezing, by ayoiding all agitation, it will still con- tinue to expand. The yolume of equal weights of water at 8^ and at 0^ is the same. In the act of freezing, a more marked an ount of dilatation occurs ; the bursting of water-pipes in winter from this cause is a phenomenon familiar to every one. An iron plug weigh- ing three pounds was used to close a bomb-shell filled with water, and on freezing the flaid the plug was projected with violence to the distance of 415 feet. The great importance of water being the exception to the gene- ral law of the condensation of bodies b^ cold, may be illustrated by a reference to what would occur if this were not the case. When in winter the surface of our rivers and lakes is covered with a omst of ice, this would sink to the bottom, and the fresh surface of water thus exposed would in its turn freeze, and another layer of ice would sink : and thus congelation might go on, during a severe winter, until dur lakes and rivers were converted uto solid masses of ice, and all their inhabitants would perish. But it has been ordained by Infinite Wisdom that water should expand, instead of contracting, below the temperature of 4", and thus the sheet of ice once formed beine lighter than the sub- jacent water, floats on its surface instead of sinking, -2V* ®79. and helps to protect the fluid below, with its various inhabitants, from the further influence of cold. 1354. Before proceeding in his researches on the properties of heat it is necessary for the inquirer to be ramished with some means of obtaining a measure of its intensity. This important object is fulfilled by in- struments termed ihermometerij or measures of heat ; all depending for their action upon the expansion of bodies by heat. The first of these instruments was oontrived by Sanctorius, an Italian physician in the 16th century, and is now known as the air-thermometer, because the indications it a£fords depend upon the ex- pansion of included air. It consists of a glass tube. Fig. 679| having a bulb blown at one end ; the tube is then filled as far as the bulb with a coloured fluid, and inverted in a vessel containing a similar liquid. The bulb is thus full of air, and on approaching a heated body towiurds it, the included air expands and depresses the fluid o 764 THSBMIGB. in the tabe, a gradaated scale attached to which marin tiie amonnt of snbBiaenoe of the flnid, and oonseqaently of the ex- pansion of air in the tube. These instruments are Teiy delicate in their indications, bat are rarely used, except as therfno§eope»t in conseqaence of their inability to measure any considerable range oi temperature, 1355. It may here be remarked that from 0" 0. to 100* the ex- pansion of air IS proportional to its temperature, as indicated by a mercurial thermometer, but aboye 100*^ it diminishes slightly. According to the observations of Magnus, the Yolumes of a given mass of air under a constant pressure, at different teroperaturafli as indicated by a mercurial thermometer, are as follows : — Temperature . 0*C. 100* 200* 300' Volume of air. 10 1-366508 1-72385 2*0794; hence the corresponding temperatures, as indicated by a thermo- meter filled with mercury and one filled with air, are, Mercury . . 0* C. 100* 200' 300* Air .... 0 100 197-5 294-5. 1356. Leslie's D'fferential Thermometer. — ^An air thermometer of a very different kind was devised by Sir J. Leslie, whose in- strument has been of essential service in r-^ Fig, 680. ^ elucidating many of the more obscure propep> J^fiL ^ ties of heat : it consists of a tube bent twice at right angles, each end tenninatine in a bulb, Fig. &0. Before hermeticallT closiiuf both the bulbs, the tube is partly mled with sulphuric acid, tinted with carmine or indigo, so that both bulbs are left full of air, and tbe bent tube partly full of coloured fluid. This instrument does not indicate any changes of temperature in the surrounding air, becaose so lone as the air in both bulbs is equally heated, the fluid will stand at the same point in the tube. If, however, a heated booy, as the hand, approach one bulb, the incloded air will expand and depress the fluid in the tube beneath, driving it into the other bulb. The amount of deprea- sion of the fluid in the tube is measured by means of a grados^ed scale attached to one arm of the instrument. This convenient apparatus is termed the differential ikermameter. because it indi- cates a difference of temperature in the air inclnded in the two bulbs. 1357. The expansion of liquids has been long used to indicate diflerences of temperature, and instruments thus constructed have the advantage or being uniform in their indications, and of being capable of measuring considerable ranges of temperature. The 8CALB8 OF TEMPBRATUBX. 765 two flnidB now generally used for thermometere are alcohol and mercury ; of these alcohol is of most service in the «.^ aoi measarement of very law temperatures, as it has ^' ^^' never yet been froEen, bat the comparatively low temperature at whioh it is converted into vapour renders it unfit for the examination of temperatures above, or even near to, its boiling point. Whatever fluid is used in their construction, these instruments are always similarly formed, consisting merely of a tube of fine bore, terminating at one extremity in a bulb, and filled with the fluid raised to a sumcient temperature to ensure the expulsion of air. The tube is fixed to a piece of hard wood, ivory, metal, or glass, on which a scale is engraved. The lower end of this sometimes moves on a hinge, as in Fig. 681, BO as to allow the ready immersion of the bulb in any liquid. 1358. To enable the indications of different ther- mometers to be comparable with each other, some fixed points, from which the graduation of the scale may be made, are absolutely necessary. The fixed points are the temperatures of melting ice, and of the steam issuing from boiling distilled water under a mean barome- tric pressure of 30 inches ^493). The space between these points has been divided in an aroitrary manner according to the views of different philosophers. Reaumur divided it into 80 equal parts, or degrees, of which 0° corresponded to the temp<>rature of melt- ing ice (or freezing water) ana 80** to that of boiling water : this gniduation has been extensively employed on the Continent. Celsius of Sweden divided the same space into 100 degrees, jnving rise to the centigrade thermometer, now in general use in franco and Grermany : and it is very much to be regretted that this scale is not universally adopted, for the sake of uniformity in the nume- rical estimation, of results. The division of the thermometrio ecale usually employed in England is that of Fahrenheit, a Ger- man artist, who assumed for his zero the temperature produced by a mixture of equal weights of dry snow and salt, ana he divided the space between this and the temperature of boiling water into 212 degrees, of which the point 32** corresponds to the tempera- ture of freezing water, and to the 0° or zero of Reaumur's, and of the centigrade scales ; the space between the temperature of boil- ing and freezing water has thus been divided by Reaumur into 80, by Celsius into 100, and by Fahrenheit into 180 equal parts. The scale of Fahrenheit is purely arbitrary, and is not recom- mended by any one consideration, either theoretical or practical; and as much confusion has resulted from the use of these different scales, it is customary to indicate which graduation has been em- ployed, by placing after the figure the letters R, C, F, respectively. 766 THESMICS. It 18, however, very easy to convert the indications afforded hj oae scale into those of another hy remembering the ratio borne by the degree of one scale to that of the other. Thns, a degree of Fahrenheit's scale is eqaal to ^ of one of Reaumur's, and to {^ of a centigrade degree. In practice, the following roles will be found nsefal for the conversion of the different thennometric degrees into each other. To convert the degrees of Fahrenheit into those of Reaumur : — MvUij^y the numher leas 82 &^ 4, and divide the product bjf 9. Ex.l86*F.-32 = 153, x4=612,-=-9=68<»R. To convert the degrees of Reaumur into those of Fahrenheit :-^ Multiply the numher by 2, add iofitj and alio 32 : — Ex. 16'R. x2i=32+4=36, +32=68'F. To convert the degrees of Fahrenheit into centigrade degrees: — Multiply the number less 32 by 5, and divide the product by 9. Ex.212'F.-32 = 180, x 6=900, -7-9= 100* C. To convert centigrade degrees into those of Fahrenheit: — Multiply the numher by 2, nlbtract ^ ofit, and add 32 : — Ex.20°C.x({=)2-J=40-4=36, +32=68'F. To convert Reaumur's scale into the centigrade : — add ^. 1359. The curvature arising from the unequal elongation of two strips of different metals, soldered or riveted together, has been employed as an indication of the change of temperature by which the curvature has been effected :^ the metal of greatest expansion lying, of course, on the convex side of the curve. An instrument has bcon constructed on this principle by Fig. 68S. M^ Breguet of Paris : this consists of a delicate ribbon of platinum soldered to one of silver, by a very thin layer of gold. This compound bar is twisted into a spiral coil, Fig. 682, one end of which is ued to a support, the other carries a delicate gold needle as an index. As the two metals, of which the coil is composed, expand veiy differently for equal increments of tem- perature, it follows that the heh'x of ribbon will uncoil, or become closer twisted, ac* cording to the temj^rature to which it is subjected, which ¥nll be indicated by the motion of the needle over a graduated circle. 1360. Johnson^ » Deep-tea TJiermometer. — ^The same principle has been employed by Mr. H. Johnson in the constructioiL of an inatninieDt for observing the temperatnre at the bottom of the sea. Two componnd born, b, Fig, 6e3, are riveted at e to a stout plate of metal, a, thew are oounooted by links at d, d, a. na with a croBS bar on an aiig eanying an inden, e, ■^' along a scale, k. Two other unconnected indices _^ jf, are puahed bv the former to the extremes of its range, and indicate the mnxunum andmimniutn temperatarea to vbich the itiBtriunent has been ei posed. The whole is enclosed in a cylindrical oasi, 1 1, tiimished with rings for Ibe attachment of the sonDdiog-liDe and the "lead." 1361. Maximum and Minimum Thermottuteri. — Instruments so coDstmcted, as to indicate the ex- treme points of temperatnre which the; hairit in expanding flows past the index, the eilremily of wbich lerefore marks the point of lowest temperature. This, as veil as the former steel index, must be replocM by a small magnet, after each observation. The objection lo an alcohol thermometer, espe- cially in the horizontal position, is that an uncertain quantity may be retained by adhesion to the sides of the tube, and therefore the apparent position of the snriiice of the eolnmn may not be correct. tor very low temperalures, however, alcohol is indispcnsahta, as it has never yet been reduced to a solid state. 1362. Mereurial MajHmum Thermomeler. — A great improve- ment lias been made in the maxim nm thermometer by MM. 768 TBKKlflCS. Negretd and Zambra ; tliis consiits in introducing into the tnbe near the bulb a minute particle ofiduai which is retained in ita position b J a bend in the tube. Tne mercory readily pasMa ths obstacle in expanding, but on subsequentlj oontraclin^, the thread of metal breaks at this pointy and the mercury retiree into the bulb, leaving the column itself to indicate its maximum eleYatioo. The mercury may be readily shaken past the obetmction, in order to prepare ror another obserration. 'The same ingenious axtitts have also constructed a mercurial minimum thermometer : in this instmment a bit of a steel needle, obtusely pointed at the broken end, rests on the surface of the mercury, and follows ii in deaeent ; but on the subsequent ascent of the column, the mercoir flows past the needle, without displacing it, and the lower end of the needle consequently indicates the minimum temperatore. 1363. (kueSkCs Minimum Thermometer. — ^Thia inatmment appears to be the most certain in its indications of any that haTe been oonstracted. A lateral tube, a, Fig. 684, haTing a huge J^. 684. ^^ comes off from the stem of the thermometer, near the bolb, and is bent as shown in the figure. The wide bore ends abruptly at n, where a pear-shaped cavity, c, opens into it by a narrow neck, wider, however, than the bore of the thermometer. When adjusted for use, this instn- ment is placed horizontally, with the mercniy filling tbe tobe ▲ up to B, out leaving the chamber, o, empty. ^ As the temperature falls, the mercury will be retained by adhesion to the transverse surface at b, and sink in the stem ; but when the temperature again rises, the expanding mercury meeting less reaistanee at the orifice of the chamber, c, than m the stem, will enter it, and remain stationary in the stem : and thus the point of lowest tesi- perature will be indicated. The instrument is set for further observation by gently raising the bulb, until the mercury leaves the chamber c empty. 1364. The Aetinometer. — ^This instmment for meaauing the heating effect of direct solar ravs consists of a thermometer with a large bulb, and an open scale, for indicating small chaogesi Observations are made with this instrummit by niacing it alter- nately in shade and in sunshine for equal intervati of a minute or a minute and-a-half ; then the difference between a reading in sunshine, and the mean of two adjacent readings in shade, vriU be a measure of the solar influence. With any given instmment this measure is arbitrary, and will give only comparative resalts : in order to render different series of observations comparable, it is very desirable that some authoritative standard of compaiiaoB should be established. A very convenient and portable form of aetinometer has been INDEX EXROBS. 769 deTised by the BeT. G. C. Hodgkinson.* In order that ob8er?»- tions may be made throagh a wide range of temperature without a acale of inconveDient length, a second bulb is made at the top of the scale to which a portion of the coloured fluid may be trans- ferred, so as to bring tne observationSi made at any ooe period within the range of a scale about 10 inches long. A polished piece of german silver drawn tube 18 inches lon^, and 2^ inches in diameter, serves as a case to pack a couple of instruments, and also as a shade, when in use ; for the latter purpose the tube has at its middle point a lateral socket in which the actinometer may be fixed by means of a perforated cork, so aa to place the bulb in the middle of the tube : there is also a means of attachment to a vertical rod planted in the ^und, and furnished with a ball-and* socket ioint, so that the axis of the tube may be directed to the mm ; when a cap corering the end of the tube will shade the bulb. By means of this instrument Mr. Hodgkinson observed the ton's heating power at the summit of Mont Blanc to exceed that at Chamonix by from 20 to 25 per cent. 1365. If, in the graduation of a thermometer, the interval between the marked points of freezing and boiling water be equally divided into 100 or 180 parts, then, in order that these degrees should accurately represent equal increments of temperature, it is necessary that the bore of the tube, forming the stem of the instru- ment, should be perfectly uniform. As this is rarely if ever the case in practice, it becomes requisite in all trustworthy instruments to determine carefully several intermediate points by comparison with a standard thermometer of ascertained accuracy. The uni- formity of the bore of a tube, and its consequent fitness for the construction of an accurate instrument, may be ascertained by measuring the length occupied bv a given (quantity of mercury in diflferent parts of the tube. Where precision is required it is in- dispensable that the scale should be engraved on the stem of the instrument ; and this is efifected by a dividing engine, in the hands of the best makers: the stem being coated with a varnish, a portion of this is removed by the dividing point, and the figures being similarly marked by removal of the varnish, both scale and figures are etched in by nuorhydric acid. 1366. Index Errors. — Fluid thermometers are liable to several sources of error, both temporary and permanent, in consequence of a change in the capacity of the bulb ; and in all accurate thermometric results, these must be allowed for, or corrected. After a thermometer-bulb has been blown (and especially if it has not been carefully annealed), it undereoes a gradual contraction, during a period of several months. In the large and long cvlin- drical bulbs employed by the writer in the construction of his thermographs (1367), this error has been observed to amount to + 1*6'*F. m tubes tilled shortly after they were blown, but after • Prooeedingi pf the Boyal Society, Jsa. 1S07. 3 D 770 THEBIIICB. BIX or eiffht months, no farther permanent change was obserted to take place : it is therefore desirable that a thermometer designed to be an instmmeut of exact obseryation should not be graduated for at least six months after its manufactare. If, after the freezing-point has been marked on the stem, the boiling-point is marked, on again immersing the bulb in the melt- ing ice, the colmnn will be found to fall below the former freenng- pomt by 0'2* or 0*3°, the dilatation of the bulb not having yet had time to subside : and several days must elapse before the colomn again reaches the mark. Hence it follows that, in pointing a ther- mometer, at least a fortnight ehonid elapse after its expoeore to any high temperature ; that the freezing-point should be first marked, then the intermediate points, from "Mow vpward»; and lastly, the boiling-point. Also, if a thermometer be pointed in a vertical position, its readings in a horizontal position will have a small positive error, and especially if the bore oe large, because the hydrostatic pressmn of the column will tend to streteh the bulb : a tnermometer shoold therefore be pointed in the direction, whether horizontal or ver- tical, in which it is intended to be used. 1367. Thermography orSel/regitterinq Thermometer. — Varioiis mechanical contrivances for effecting the antomatic registration of atmospheric temperature have been proposed by Kreil, DoDond, and others. The photographic method of^ registration applied by the writer to the magnetometers (624), and to the barometer (495), has been extended to the thermometer, and peychrometer (1426), and thus a continuous record of all their respective variations is maintained. The bulbs of these instruments are freely exposed underneath a table, which supports a revolving cylinder ooveied with the sensitive paper, analogous to that represented in FSg. 329 ; their stems pass vertically upwards through the taUe, and are placed between the opposite sides of the cylinder, and two lights. A narrow vertical Ime of light, brought to a focus b^ a cylindrical lens, falls on the stem of the thermometer, and nasBing through the empty portion of the bore, affects the preparea paper. The boundary between the darkened and undancvned portioos indicates the position of the mercury in the stem of Uie thermo- meter. Fine lines, corresponding to the degrees, are etched across the stems of the instruments, and broader lines at every lOtk degree, as well as at certain other fixed points of the scale, namely, 32°, 64°, 76°, and 98* F. The shadows of these lines protect from the action of light the portions of the photographic paper on which they fall, the darkened surface of the paper is conseqoentlv traversed by a series of parallel pale lines, and the relative posi- tions of the broad and narrow lines readily explain the temperatore indicated by the register. As this apparatus is necessarily placed in the open air, when in actual operation, it is provided vnth ss inner cylindrical zinc case, with sliding doors to protect the sensi- XfKtLDf ACTOMinO 1368. AppoU'f Aatomatie Temperature-rtguiaUir, — Thi» U one or the man; ingenious ftpplicationi of phjncsl prindple* to doniMtic cnmfort made bv Eha Ute Mr. J.Q. Appold, to whom mbo the world u --'-■^-^ '--^ -'— ■ '"-" • '^— o. Ths tube, tad aboDt half of each bulb are filled with mercury ; and ball •□ inch of ether floata on the menmr; loaiDtaiDBlhe column of higher level in the bulb, B. Beneath the wood a wfiffbt, d, ia ■o attached that it may be shifUd by a aorew, E, in order to •Iter the poulion of the centre orgrsiitv of the whole apparatna, vUch !■ nupended Hko a acaie-beem on a knife-edge at r. The size of the bdbs is Sncli that at the ordiuaiy temperatnre of a room a rise of TP. will laisa an ounce of mercurj 3 inches. A cord, a, is attached to the cod of a projecting arm, h, which control! the Bupply.ralre of a stove, or tbe damper of a furnace. It is erident from theconetrDC- tion that ao elevation of temperature will make B preponderate, and bj depiouing h, will cloie the valve and damp the Ere ; and that a fall of temperature will have the contrary eSect. The position of the weight, d, may be bo adjaated by trial, that the apparstns ahall maiotain iM mean poaition at any required tem- perature, and a corresponding ecale may be marked on O. A thermometer, i, ia sealed into the top of i, and another, l, is attached to the apparatus, for the purpose of observation and com- Earieon. The action of the arm, h, is limited in both directiona V a bent rod passing over it, which ia inserted in holes in a fixed plate behind it. Hr. Appold also contrived ■ hjgrometric regulator, by the movement of which the droppii^ of water "" ■" — ™ — ' — •■-- enpora&in was controlled. This mainly 0 773 lontal tab«, harinK eth«r on the larftM »f th* merciiry i'b bolk bnlbe, one of which ii covered with wet mBalin, the Tenable er*- paralion from whicb conl> and coadenMi the etfaar-Tapuiir, aod thai altera the centre of ^;ravitj of the tuba. 1369. Wedguiood't Pyromtter. — For thajpnipiwe of meaanring degrees of temperature, mgher than that af^ boiling mcrcnrj, in- ■tnimeats termed pjroinetora bave been emplojed. Of ibeae tliat contrived bj Mr. Wedgwood va< long held in repute : it coiuiitad of a «eriea of perfectly similar cjlindera of baked daj, and a na- dnated scale lo allow of their accurate meaaDremeiit. On«of theae Gjlindera vae then eipoeed lo the lemperature to be meaanred; to praportion aa it becione bested it contracted in bnlk, and tkU cootraotion, meuuted when the cylinder had cooled, became an indication of the temperature to irhioh it had been anbjecled. In addition to other eoarcoB of error, the fact that pieces of claj will nndergo the same amoant of contraclion by a moderate heat leeg continued, aa bj an exposure for a shorter time to an iatenae beat, becomes an insuperable objection to a reliance on the iudicstiaDi of thia inslrutnent. 1370. i>imielri ^/ronieter, — A much more tnalworthy pyro- meter ia that of Prof. Uaniell: itconaiata es^ntially of a alender bar of plaliuum or hammered iron, of which the linear expaniioii, when heated ia a tube of plumbagn, is maaanred by means ot a little piece of porcelain reating upon the top of the bar, which i* pushed forwanl during iu expamioD, When the appai«tiu hai cooled, the displacement of the porcelain iodei becomes a mearare of the expansion of the bar, and consequently of the temperatwe to which it has been exposed. The amount of displacement i* measured by means of a delicately graduated scale, fumiahed with 1371. Bffilrdm'i Hgdro-pynmuitar, — Whenever moderatetr ■mall cbimgea of temperatnre are required to be indicated, more reliable observaHons may ba ob- ^■^^- tained by means of this inilmiDent, the principle of which ii that » baU of metal of known weight eipoaed to the heat of the funiace oommtmi- cates its heat to a known weight of water, the temperature of whidi, bo- tbre and after tQe accession of best, ii observed by a mercurial thennonieter. The contrivance by which the bkll ia heated and then rapidly transiemd to the water-chamber, is shown in I^. 686. A perforated ball, *, of steel or plalinnm, aocordiog to the lemperatnra to be observed, is carried through the pipe, d r, by a bant wire, e^ lo tbe extremity of a muffle or closed chamber, ■■, which pixgmata THBBMIO UNIT. ' 773 from the inner suriace of the wall into the fnmace, and the pipe is then closed by a plug of claj at d. After a snfficient time has elapsed for the ball to acquire the temperature of the fiimace, the rod, c, is withdrawn, and the ball beinjr detached from it by a pro- jection. A, on which the rod rests, rolls down the pipe, a k, and drops through a Talve, l, into the water-chamber, which consists of a closed metallic Tossel encased with wood. With 300 grammes of water, and a steel ball weighing 7 gprammes, a range of 5" C. of change of temperature in the water*bath cor- responds with a range of about 1000" in the furnace ; and with a platinum ball weighing 8 grammes, a change of 4** corresponds with a range of about 25^" of furnace-heat: it is, therefore, desirable to use a steel ball up to 1000°, and a platinum ball above that temperature. From the known data of volumes and soecifio heats, a table of equiyalent values may readily be calculatea. 1372. Thermic Dnii. — ^AU the requisite means of obtaining eomparaHve thermometric measurements by differential expansion having been described, it becomes necessary, in order to obtain ahtohUe results, to establish some unit quantity of heat, or thermic unity as a measure of other amounts of heat which it may be desired to determine. As the dynamic equivalent of heat (1345), or as it may be termed, the dynamo4hermic unit,* has been de- fined to be the amount of work used up in raising lib. of water 1** C, so the thermic unit may be conveniently assumed to be the amount of heat necessary to raise lib. of water 1** C. It will sub- sequently apjpear that in order to define the unit with complete accuracy, it is necessanr to specify at what part of the scale the 1" is situated : it will prooably oe found most convenient to adopt the interval between 0** and 1°, as shown by a mercurial thermometer. 1373. Conduction of Heat, — It is a familiar fact that beat is conducted by different bodies with very different degrees of faci- lity. Thus, a small piece of charcoal may be held by^ one end in the hand wnilst the other end is red-hot; while a similar piece of iron would soon cease to be tenable, if one end were plunged in boiling water only. Among bodies of the same class, as metals, a great difference of conductibility exists ; thus, a piece of plati- num can easily be held in the hand whilst one end is red-hot ; but a piece of copper of the same length similarly circumstanced will speedily bum the fingers. Twist together the adjacent ends of a piece of copper and one of platinum wire, each about six inches long, and place on the further end of each a minute piece of phospnorus. If the point of junction be heated by the flame of a spirit-lamp^ Fig. 687, * It may h«re be oonrenitfiit to adopt tbe Mune mode of phrsMology that hat been previously (076) adopted in ezpreMiog the relation ot heat and eUotfieity : a dfpMmo^hervne nnit may be taken to mean the value in work of an onit of Itiai, and a tkmwihdpia'mio unit, the value in heat of an onii of work. •■■«— ^ 774 THBEMICB. in a few seconds the phosphorus attached to the copper wire - will burst into flam«, whilst F^g. 887. ^^^ ^^ the platinum will remain unafiected for a much longer period. If a series of cylindrical rods of equal diameter, and three or four inches in length, composed of dif- ferent material!, soch as wood, ivory, glass, slate, marble, and various metals, tie inserted at a little distance from each other in the side of a vessel contain- ing water kept boiling, and a small bullet be cemented with wax to the end of each, the relative number of seconds that elapse between the filling of the vessel and their falling off, will approxi- mately show the conductivities of the several substances. The couducting power of several metaUic bodies is shown in the following table by Wiedemann and Franz, in which that of silTer is taken at 1000 as the standard: — Metal. Heat Eleo. MetoL Heat. Elee. 1 226 130 • • 107 Metal. Heat. 64 63 60 18 Dee. 103 • • • 19 1 Silver . CJopper Gold . Brass . 1000 736 632 236 1000 733 585 216 1 Tin . Iron . Steel Lead 146 119 116 86 Platinum . Palladium Ger. silver Bismuth . The nearly parallel electrical conductivity of various metals (805), as determined by Lenz, is shown in the second columns of numbers. It must hero be remarked that the transmission of htat and of stngible temperature are not necessarily identical ; this is shown by an experiment of Prof. Tyndall. If two prisms be made of the same* shape and equal volume, one of bismuth, and the other of iron, and one end of each being thinly coated with wax, they be placed with the coated ends upwards on some heated body, th3 wax will be melted first on the bismuth, although it appears from the table to be a much worse conductor than iron. This is due to the greater specific heat of iron, that is, the greater amount ot heat necessary to produce a given elevation of temperature. 1374. The following general law of the propagation of heat by conduction has been oetermined : if one end of a bar of metal be placed in connexion with a source of heat^ it will be found that for distances measured from this point in arithmetical progressioo, the excess of temperature above the surrounding memum will be in ^metrical progression. Tliis may be proved experimentally by inserting thermometers in holes made at equal distances in the VARIJLTIOKB OP COHDDCTIVITT. 775 ride of a bar of metal, one end of which is maintained at a constant high temperature. 1375. tnfiueneeof Organic Structvreon Conductivity, — A series of experiments has been made by Prof. Tjrndall,* on the power of yarious kinds of wood to transmit heat in three perpendicnhir directions, viz., longitudinal, radial, and tangential. For this pur- pose, cubes 0.3 inch each way were cut so that their edges were m these three directions ; these were successively placed in each direction between two cushions of mercury, each bounded by a plane surface of thin membrane. One of these was warmed by an inunersed coil of platinum wire heated by a constant voltaic cur- rent, and the heat transmitted by the wood in one minute was com- municated by the other portion of mercury to the united ends of a thermo-electrio element of bismuth and antimony (962), and the heat was measured by the deflection of a galvanometer needle (856). A tan^nt galvanometer (861), and a rheostat (804), were inter- posed m the voltaic circuit, and the deflection of this needle kept uniform by the rheostat. The relative conductivity of different kinds tif wood in the several directions was found to be closely in accordance with the relative elasticities as manifested by the transmission of sound (546). The heat transmitted in the several directions tmeasored by the deflections of the needle), by some varieties of wood is shown in the following table : — Kind of wood. Scotch fir . . Elm . « . . Oak ... . Walnut . . . Satin wood . Box wood . . Quebec pine . American birch Lour. Had. Tang. I 22 10-0 120 24 100 110 27 80 9:4 28 110 130 30 11-9 12-3 31 9-9 12-0 33 10-0 110 35 90 11-0 There appears to be no assignable relation between the hard- ness of the wood and its conducting power. 1376. Infiuence of Ttmperatwre on ConducUviJty, — Principal Forbes has carefully observed the conductivity of a square bar of iron 1*25 inches thick at temperatures varying from 0^ C. to 275**. His assumed unit of heat is the amount necessary to raise the temperature of a cubic foot of water at 0° G. one degree ; and if a body of unit conductivity were formed into a plate one foot thick, and its opposite rides maintained at temperatures differing by l^'C, one square foot of this plate would in one minute transmit an unit of heat. The observed conductivities at different tempe- ratures were as follows : — • Phil Trans. 18o3. ■^^•^ 776 THEBMICB. O'C. . 0-01337 MOO'C. . 001012 ) «00'C. . 0*00876 25 „ . 0 01235 ; 125 „ . 000966 225 „ . 0-00651 60 „ . 0*01144 M50 „ . 0-00934 250 „ . 0*00826 75 „ . 001070 i 175 „ . 000904 ! 275 „ . 0-00601 In another bar one inch square smaller differences were ohaerved. The numerical values here given must be multiplied by 62*321 (425), if required in terras of the deffre£ thermic unit (1372). 1377. Influence of Molecular AggregcUum on Condwetwiiy. — It has been satisfactorily proved by Dr. Senannont that there is an accordance between the optical and thermal elasticities of crystals, su far an his observations extended. He cut thin plates in different directions from various crystals, and having coated a surface with a thin film of wax, and passed a wire through a hole in the middle of the plate, he heated the wire by a constant voltaic current. The melted surface of wax extended itself gra- dually from the hole, and ita outline must clearW be an iMotkenitial lintf or boundary of equal hetU-toave-motion. If the condnctivitr of the plate be equal in all directions, it is clear that this line wiU be a circle, but if unequal in two perpendicular directions, it must be an ellipse. It was thus ascertained that in some rhombohedral cr^tak the crystallographic or optic axis (24, V. ; 1203) was the direction of greatest conductivity, and that in a plate cut perpendicularly to the axis, the conductivity was equal in all directions ; in this case, therefore, the thermal, like the optical (1209), wave-front must be a spheroid. In crystals belonging to the cubic system (24, I.), whSch are optically anaxial, the isothermal line ought to be in aU directiona a circle, and the thermal wave-front a sphere; while in biaxial crystals, the thermal wave-front would probably in all cases be found to be an ellipsoid. A similar temporary variation of conductivity has been obeerv^d by Dr. Maggi to be produced by magnetic energy in an iron plate resting on the poles of an excited electro-magnet : the plate being amilarly coated with wax, and heated bv steam traversing a pipe passing through its centre. It was founa that the melted sorfaoe presented an ovial form, the long diameter of which was across -. _g the lines of direction of magnetic energy ; ^^' ' thus showing that thermic waves meet with increased resistance in the direction in which magnetic waves are already travelling. 1378. Li()uids are very bad conductors of heat ; on this account, if water be froaen at the bottom of a test tube, more water poured npon the ice may be made to boil by holding a spirit-lamp near the upper part of the tube, as in Fig. 688, and yet the ice will remain unmelted. U, however, C03IDUCJTIVITT OF BODIES. 777 the heat he applied to the lower part of the tuhe, the ice will speedily melt, and the whole he made to hoil ; not, indeed, from heat heing oondacted upwards, hat from the ascent of heated particles of water from the bottom of the tube, on account of their being specificallj lighter than the colder portion to which thejr give place (1382), and thns the whole of the fluid becomes heated Djr the constant interchange of position of the particles. 1379. Gaseous bodies conduct heat even worse than liquids; this property is frequently employed to confine or exclude heat, as in the double door of furnaces, in the double casing of iron sates, and in the double windows now so frequently used m houses ; the layers of air confined between the cases being the best possible barrier to the transmission of heat by conduction. It is on this account that the contact of very hot air can be endured by the human body, whilst exposure to a liquid of the same temperature would produce intense pain.* But if the heated air impinge upon the surface a» a current^ then its contact will be intolerable, in consequence of the repeated application of fresh portions to the surface. The same remark applies to intensely cold air ; thus in the Arctic regions, men have been exposed to a degree of cold below that of freezing mercuiy without injury, so long as the air is calm, but upon the slightest wind occurring, the repeated con- tact of fresh portions of cold air will carry on so much heat as to freease the extremities, if they be not most carefully protected. ^ 1380. A practical application of the badly conducting power of air is found in the various articles of dross, which are generally wanner in proportion to the quantity of air entangled in the in* terstices of the material of which they are composed. Count Bumford suspended a thermometer in a glass tube, and interposed between it and the bulb of the thermometer the substance, the conducting power of which he wished to determine. The whole was first plunged into boiling water, and then removed into meltine ice. The time required for the thermometer to cool from lOO"* F. to 54*5" was then noted in seconds, which thus became a com- parative measure of the conducting power of the body, by which it was surrounded. In this way he found that when air was alone interposed it required 676 seconds to cool down to 54*5**: but when the bulb was surrounded with equal quantities (16 grains of yarious substances, the times of coolmg were as follows : — Sewing silk . . . 817* Finelmt .... 1032 Cotton 1046 Wool 1118 * The wrirer oooe remained for serenl minates in a drying-store heft^ed to WP F. The sensible effeot of this hi|(h te-Dperiftture wns a momenUrT priekiDfl; sensation over the exposed sorfiioe of the faoe and hands, followed Dj proflue perspiration. Baw silk . . . . 1284' Beaver's fur . . 1296 Eider down . . 1305 Hare's fur . . 1315 778 TBBRiiicai. A beaotiful iUuBtration of this jyropertj ocean in tlie chanffO of clothing of many animals ; hair being in winter, and in tLe Arctic repons, n^plaoed by wool ; and feathers, by down. 1381. THa familiar fact that a piece of iron or marble always feeU colder than wood, flannel, or fnr, although at the same tem- perature, is explained by their different conducting powers. Thus, iron being a good conductor, rapidly absorbs heat from the hand, and hence feels cold : whilst a piece of fnr, or woollen cloth, being a bad conductor, does not remote heat so rapidly, and thus feels comparatively warm. That the temperature of these bodies is really the same, may beproved by means of a thermometer. 1 3iB2. OonveeUon of Meat. — ^As all bodies, the particles of which are widely separated from each other as in fluids or gases, are had conductors of heat, it is obvious that when heat is applic»d to one part of their surface, its rapid communication to other portions of fluid must depend upon a process distinct from that of conduction. This has been illustrated oy the case of a fluid heated in a tube (1378), where the difiiision of heat depends upon the ascent of heated particles; a process conveniently termed conofcCvm. When air is heated it ascends, because it becomes specifically lie'hter than the surrounding colder portion ; this is the rationale of tne balloon contrived by Montgolfier, which consisted of a lai^ air-tight hag, having its open mouth downwards ; beneath this a fire was main- tained in the car, which rarefying the air in the bag rendered the whole machine specifically lighter than the surrounding medium, and it oonsequentl v ascended. The heated air at the eouator thns asceiids, and travels towards the poles, whence an unaer current of cold air passes towards the tropical regions of the earth (1886). 1388. As heat is diffused through fluids by the process of con- vection, it follows that whatever diminishes, or interferes with, the mobility of the particles of fluid, will prevent the rapid trans- ference of heat from one part of the liquid mass to another. On this account viscid fluids, as water to which starch has been added, require a longer time to boil than pure water ; and conse- quently a longer time to cool. 1884. Hot-waJter Apparatus. — ^The convection of heat by water is the principle on which various apparatus are constructed for the purpose of conveying or distributing heat bv the circnla- tion of not water, in pipe* or other closed channels. For this purpose one extremity of a system of pipes opens into the upper part of a closed boiler, and the other extremity into the lower part; and in order that the cooled water may, by its mater specific gravity, displace the warmer portion of the fluia, it is necessary that no part of the circulating system should be below the level of the boiler. This method of communicating heat may be familiarly illustrated by the apparatus, Fig. 689, in which a, a, are two pieces of fflass tube bent at a right angle ; o, d, two re- tort receivers, of which c has a lateral aperture, and x is a spirit cientlj indicated. Tbe whole apparatai being; aupported on t, retort Bt*ad, snd the Ump K applied to D somewhat late- rkllj, u in the EKQre, a circnlatinn of the Snid in tbe direction indicated by the arrow! will apeedily commence, and maj be rendered manifeBt hj filling the tube* and lower BagV wiih water, and haiins inserted tbem in tbe npper one, by filling that with water coloured with a little aolphata of indigo or other con lenient colouring matter. The coDYection of heat in caeeona Bnida may be readily ufaown by the «une appuatna filled wilh air only, if the upper globe h» held in the path of a beam of electric light transmitted ibroagh a lens, and thrown on a screen : the flow of heated air will be rendered 1386. Law of'Convectioa by Oatti. It appean from some ablo researuhes by HM. Dulong and Petit that the rate of convection by a gna is entirely independent of the nalnre of the aarrace of the heated bod;, and is proportional to a conitant power of the diflerence of s also found that the if temperature temperature of tbe body and gas. it was cooling power of a given gas lor a giren e depends on its pressure only. The following formohe for the qnantitiei of heat conreyed, by certain gases at a presaare of p™*, in one minnte from oDe square foot of any surface heated t'G. abore tbe gas in contact with it, expressed in thermic units (1372), have been emprically detenoiued : — Hydrogen . 0-0183(^J°"l'«»; Olefiant gas . 0-0071 (^) t'™: Air. . . .0.0M3(,^„)2-"i CarboDicaeid 00368/a^]"" t'-™; 1386. The trade-mindt, and the Gvlf-tlrtam, by which tbe climate ofdiSenint portlous of the earlh'i surface is so matenaUj iuflueooed, are large results due to the couTectiou of heat. Tu 780 THEBMIGS. mass of ftir, beated by contignitj to tbe surface of tbe eartb in the Tropics, rises continually to tbe upper regions, and its place is supplied by under currents flowing towards tbe torrid from the temperate zones. These masses of air proceed from localities of less to one of greater linear velocity of rotation, and themfore lag behind the earth's suiface, t.tf., tbe^ have a relative toegterlv motion, and by the composition of motion (284), the currents north of the equator will be from N.E., and those south of that line, from 8.E. ; these two currents constitute the trade-winds. SimilaHy the heated air moving in the higher regions from the equator towards the poles has both its absolute and relative motions in opposite directions to the former, and giires rise to S.W. currents in tbe northeni, and to N.W. currents in the southern hemisphere ; these constitute the retum-tradei. Tbe direction of those has occasionally been demonstrated by the course of a cloud of volcanic ashes thrown up into the upper regions of the atmosphere. Tbe well known land- ana sea-breezea of summer may be simi- larly explained: the air being more warmed by radiation from the earth's surface, than from tbe water, continually ascends, and is replaced bv cooler air from the surface of the water, forming the sea-breeze : but in the evening cooling is greatest over the land, and bonce the land-breeze. Similarly the equatorial surface-water, being of less density, flows across the Atlantic from Africa to the West Indies and the Gulf of Mexico, and is carried direct north-east to tbe shores of Ireland and Great Britain, and on to Norway.* To this is owing tbe immense difference between the climate of the north of Canada, and that of the south of Ireland, which are in nearly the same parallel of latitude, and therefore similarly circumstanced as to solar beat. 1387. The relative distribution of heat on the earth^s sarfaoe has recently been the subject of elaborate investigation ; and by connecting the points ascertained to possess the same mean tem- perature, a copious series of isothermal lines has been laid down by F^of Dove. These have been published under the auspices of the British Association, and form an important contribution to physical geography. 1388. Specific Heat, — ^All bodies do not appear to have the same capacity for heat : thus, water requires nearly twice as much heat to raise it to a given temperature, as an e^ual weight of ether; hence water is said to have a greater capacity for heat than ether. All bodies thus possess a property denominated their spe^c Aeat, indicating the comparative amount of heat required to raise them to a given temperature. If equal Quantities of the same licjuid at different temperatures be mixed, ttie temperature of the mixture will be the mean of the * Humboldt, Cosmofl^ vol. 1. CALORlMETEKa. 781 two ; thos, if a pomid of water at 60" be mixed with the same quan- tity at 212°) the mixtare will possess a temperature of 136°. But if equal weights oi different fluids be mixed, the resulting tempe- rature of the mixture will not be the mean of the two. A pound of mercury at 40^ mixed with the same quantity of water at 156*, will produce a temperature of 152*3*. Thus, while the tempera* tare of the water is only depressed 8'7*, enough heat must have been evolved to raise the temperature of the fluid metal 112*3*. Then if the capacity of water for heat be assumed as the standard unit, that of the mercuiy will be but 0'033, for \ 112-3 : 3-7 : : 1 : 0*033. I A bar of copper weighing a pound, heated to the temperature of 300**, and immersed in a pound of water at 50*, will give up its excess of heat to the water, and both will acquire a temperature of 71*7*. The copper has consequently lost 228*3* and the water gained 21*7*, and hence the specific heat of copper b 0*095, for ^ 228*3 : 21*7 : : 1 : 0095. Ihe mode of proceeding for the determination of specific heat pursued in these examples has been termed the tnethoa of mixture, 1389. Calorimeters. — ^This term has been applied to apparatus employed in determining the specific heat of bodies. In the calo- rimeter of Lavoisier and Laplace the result is obtained by observ- ing the quantity of ice liquefied by a body of known weight at a known temperature. For this purpose a triple cylindrical metallic vessel is employed, the spaces between the inner and middle, and the middle and outer vessels are filled with fraCTients of ice, and have separate outletsfor the escape of the liquefied fluid. Hie body having been raised to a given temperature ^generally 100* C.) is rapidly transferred to the empty inner cylinaer, its cover applied, and the remaining space in the middle cylinder filled in with ice ; this is then covered, and the outer cylinder similarly filled up with ice and covered. The only object of the outer jacket of ice is to pre- vent that surrounding the inner cylinder from liquefaction by external heat. The amount of ice liquefied by the heated body is measured by the quantity of water escaping from the middle space ; and this is an approximate measure of the specific heat of the body enclosed in the inner cylinder. This apparatus is liable to several sources of error, the chief of which is that the whole of the water does not escape, a portion of nncertain amount remaining adherent to the fragments of ice and the surface of .the vessel, llie method here employed has been designated the method of cooling. 1390. More reliable results have been obtained by the calori- metere of M. Begnault and Prof. Kopp. The former of these consists of a closed hollow cylindrical vessel, the internal diameter of which is about one-third the external, supplied with steam from a small boiler, having also an outlet pipe for the condensation of 782 THBRMIC8. the steam in a wonn-tub. This cylinder is enveloped by ftn air- tiffbt jacket to diminish the loss of beat by external radiatioo. The body to be examined, being reduced to fragments, is placed aronnd the long cylindrical bnlb of a thermometer in a arenlar basket of wire gauze, which is suspended by silk threads in the central cavity : the stem of the thermometer passes throngh a cork plug by which the top of the inner cylinaer is cloeed, and which supports it independently of the basket When the thermometer has attained a constant temperatnre (which requires from 2 to 3 hours) a very thin brass vessel, con- taining a Known weight of water, and suspended by silken cords to three uprights on a stand mnidng on castors, is placed beneath the former vessel, and a valve being withdrawn from the bottom of it, the wire basket and its contents are rapidly lowered into the water-vessel ; this is then removed, and the water stirred to equalize the heat acquired from the heated body, and its tern- Sirature accurately noted, and from the heat gained by the water e specific heat of the body may be readily calculated. 1391. Prof. Kopp*s process differs somewhat from the pi^ ceding : the body to be examined is placed in a test-tube ; and if solid, together with some fluid in which it is^ not soluble, to aid the conduction of heat to every part of the solid fragments. This supported by a wire inserted in the cork, is immersed in a cylinder containing mercury, which is surrounded by a jacket of oil, which is heated by a spirit-lamp, until a thermometer placed beaido the test-tube* shows a constant temperature. When the constant temperature (which should be about 50* C.) is attained, 10 minutes were found to suffice for the tube waA its contents to assume the same temperature : it is then rapidly transferred to a water-vessel similar to that of Regnanlt, and tho water is stirred by a pair of horizontal plates moved np and down by a wire to which they are attached. It was found desirable to have the temperature of the water-bath a little below that of the sir, so that its maximum of derived heat should about bring it np to that of the surrounding atmosphere. If, in regard to gain or loss of heat, the glass in contact with the water be equivalent to x parts of water, and /, the weight of the liquid m the tube, pf the specific heat of that liquid, ffi, the weight of the solid, M, the weight of the water, together with the equivalent in water of the immersed thermometer, and the vessel, and stirrer; * In Prof. Kopp*s drawing (Phil. Trsai. 1866, pt i.) the thennomefcr bss a tpherieal bulb : in all cmm in which the tempentiire of a fluid b^Ui it required to be aooarately determined, the writer prefim a long €fU»dr»eml bnlD, by which the Tarying temperaturea of diflbrant parts are iniegrated, or redaeed to an aTarage. ■PBGIFIC HEAT. 783 - T, the teroperatare of the mercar j bath ; and t/ that to which the contents of the tnbe are estimated to sink in the water; tf that of the water-bath before, and I', the maximnm after the immention of the tnbe ; then sp. heat=.-^(^-^)-l^t/^)iJ^O The flnid employed in the tabes was coal-tar naphtha carefnllj rec- tified for this parpose. This methoa has an advantage over that of Regnault in enabling the experiments to be made much more rapidly : but as very much smaller quantities were operated on, the errors of observation have a greater relative value ; and the results obtained by Regnault must b« looked upon as the most trustworthy. 1392. It was established by Dulong and retit, that the specific capacity of bodies for heat increases as their temperature rises, so that it requires less heat to raise a body from 100* to 105", than from 200"* to 205", although in either ease equal increments of temperature are indicated by the thermometer. Thus, the specific heat of water at 0" C. being taken as 1, that of water at 100" will be 1*01. The variation of specific heat is generally small at a considerable distance from the point of fusion ; but it increases rapidly where sensible softening commences. The following table gives the specific heat of several bodies, chiefly from the accurate experiments of Begnault, that of water being taken as unity : — Alcohol . . 0-6603 Graphite . 0-2018 j ' Copper 00951 Ether . . 0-6207 Glass . . 0*1977 ArHenic . 0-0814 Nitric acid 0-4425 Phosphorus 0-1895 Silver . . 00570 Oil of turp. 0-4259 Diamond . 01468 ; [Tin . . 0-0562 Sulphuric ac 8oheTes is ffiven in p. 288. This is the principle of the well-known Spin's digester, a strong iron vessel capable of being closed air-tight, in which various nutritious animal subeCances may, by preventing the escape of steam, be submitted to as high a tem- perature as mav be necessary for the solution of animal matter not soluble at the ordinary temperature of boiling water. In order that the " boiling-point" of water may be accurately defined, the British Commisidoi) on standard weights and measures have assumed 212** F. to be the temperature of steam under a Sressure of 29*905 inches of mercury at 32^ in the latitude of Lon- on ; the pressura corresponding to each tenth, from V below to 1° above that point is given in the following table : — T«mp. PreMore. Tamp. PrcMore. t Temp. Presrare. 2110 29-816 211-7 29-727 212-4 30-143 2111 29-374 211-8 29*786 212-6 30-203 211-2 29-432 211-9 29846 212*6 30*263 211-3 29-491 212-0 29-906 •: 212-7 30-323 211-4 29-660 212-1 29-964 212*8 30-384 211-6. 29-609 212-2 30024 212-9 30-444 211-6 29*668 212-3 30083 < 213-0 30-506 The following table contains the boiling-points, in Fahrenheit's scale, of a few liquids at a mean barometric pressure of 29*9 inches. Chlorid. ethyl. 61*9 j Wood-spirit Aldehyde . . 69-4 | Acetic ether Ether . . . 948 1 Alcohol . Bisulp. carbon 118*6 | Benzole . Bromine . . 146'4 f Formic acid 149-9 \ Acetic acid . 243*1 164-9 i Oil of turn. . 560*0 173-1 I Linseed oil . 6020 176*8 ! Sulphuric ac. 6400 221-5 } Mercury . . 662*0 The material of which the evaporating vessel is composed, makes a marked difference in the boiling-point of many fluids, especially if they be capable of forcibly adhering to its surface ; thus, water will boil at 212° in a metallic, but at 214° in a porce- lain vessel : and in a glass vessel the temperature may be nearly 2° higher still. 1413. Prof. H. Kopp has clearly established some remarkable relations between the ooiling-points of certain organic fluids, and their chemical composition. He has found, on comparison of the boiling-points assigned by a large number of observera with his own calculations, that in many membere of the alcoholic series represented by the formula C||H«+,0„ and of acids represented by C«H«04, as well as the isomeric compound ethera, an elemen- tary difference of p x C,H, is attended oy a corresponding diffe- rence of 2» X 19** C. in the boiling points : also, that a compound 792 THESlilCf. ether Cnl^n^* ^^ vary delirable Temore all the air from the interior the boiler, the firat portion of miied Taponr that rises is allowed to escape bj a small tabe beneath o into a small vessel codImo- ing wiier, which absorbs (he Ammonia, and allows the air ta escape throagh it in bubbles ; and Che escape is permitted to continne, nntn the air-bubbles cease to appear. 1421. Wotiatkm'i CryophoruM. — The prodnclion of ioe bj the OTBporationof water (1419) is well shown in an elegant contri- Tance of Dr. WoUastoD, which he termed the eryophortu or &ost- bearer; it conBisti of a tube bent twice at nght angles, and ftimishsd with a bnlb at each •nd. Fie. 691. Enough water to nf.m.. ueariv half fill one of the bulbs is , ■■ -. introduced, and after bein(! made JC ~jL to boil violently for a few minutes, ^^ _J b^d the apparatus is hermetically ^"^ sealed : thus it containe a quantity of water conSned in vacun, or nither in an atmosphere of aqueous vapour. If the empty bulb be placed ia a Ireeiing mixture, the vapour will be condensed, and a vacnom being tbns restored, further portions of the water in the other bulb will be evaporoited, and carrying off beat, will past over into the cooled bulb, leaving at length the reit of the water (Hmverted into ice. In the constmction oF this inatniment, it is necanary Chat the bulb containing the wal«r sbould be a little less than half filled, as the freenng water is likely to burst the bnlb by its expansion, if more than a hemispherical space be occupied by the ice. 1422. Although at ordinary pressnres water binis at 312* yet ■low evaporatioD will go on from its aor&ce at any temperature, even below the fiMdiw point. The vapour thas evolved mixes vith, and is dissolved by, the ur, which is never absolutely dry, bnt always contains a certain portion of aqueona vapour. The wanner the air, the greater the proportion of watery vapoDr it ii 796 THBXMICB. capable of holding in solution. The pressure of aqneooa Yaponr at various temperatures has already been considered C519). 1423. The Dew-point. — ^If a solidi surrounded by a mixture of air and vapour, be cooled down below the temperature corre- spottding to the density of the vapour in the mixture, the stratnm iu immediate contact with the solid will be cooled, and the ex- cess of vapour contained in it will be deposited on the mrface of the solid, in the form of dew ; which may be made to disappear by raising the temperature of the solid above that which cone- Bponds to the density of the vapour. The lotcett temperature at which the whole of the vapcnr con* tained in any mixture of air and vapour is capable of remaining in the elastic state, is called the dew-point. It may be determined practically by cooling a bulb of glass, or polished metal, and ob- serving its temperature when dew begins to be deposited on it : then suffer the temperature of the bulb to be gradually raised, and observe the temperature at which the dew disappears. These two observed temperatures are one less, and the other greater, than the dew-point, but will be found to differ very little from each other, if the experiment be carefully conducted ; their mean may there- fore be considered as the dew-point. 1424. DaniePs Hygrometer, — Observations on the dew-pmnt may be conveniently made by this instrument, which consists of a pflass tube with a bulb at each end of it, which is bent near the middle twice at right angles, so that both extremities may be vertical, and at a re w inches' distance from each other. The bulb of a small and delicate thermometer is enclosed in one of the bulbs, which also contains a little distilled water, its stem occupy- ing the tube ; the other bulb is covered with muslin. When an observation is to be made, the covered bulb is wetted with ether, the evaporation of which cools its contents, and thus causes ooo- densation of the vapour, whioh How begins to rise from the water in the uncovered bulb, the temperature of which is thus lowered, as is shown by the enclosed thermometer, which is observed at the instant that the deposition of dew commences. Afler the evaporation of the ether, the bulb containing the thermometer gradually regains the temperature of the surrounding atmosphere ; and the point of disappearance of the dew may be observed. Raemtz* considered this to be the best instrument, but it is not convenient for repeated observations. 1425. RegnauWe Hydrometer. — ^This, which is probably the most convenient form ot instrument, consists of a very sensitive thermometer, a, divided in half degrees, the stem of which passior through an air-tight plug, the bulb is enclosed in a highly polishea silver bottle, b, which at the time of observation is sufficiently filled with ether, that the bulb may be entirely immersed. A * Httdbaeh der Meteorologie. MA801I 8 HrOKOlffETEB. 797 jPV- 6es. flexible tube, d, is attached to a mudl silver pipe, that enters the neck of the bottle, and passes down nearly to tne bottom of it ; and the cavity of the hollow stem, c, opens into the bottle at the point of support. To make an observation, the bottle bein^ carefnlly wiped quite dry^ and su£BcientIy filled with ether, a current of air is blown through that fluid by means of the tube, d ; the temperature of the bottle and its contents is thus lowered, until a deposition of dew is observed to commence, when the temperature in- dicated by the thermometer, a, is recorded, as well as tbat of the air, by the thermometer attached to the stem, c. Allowing the instrument to remain at rest, the temperature marked by ▲ will gradually rise to that ofthe surrounding atmosphere, and the point at which the dew dUappears^ is also noted. 7!lie mean between this, ana the point previously noted, will be the exact dew-point; and the two observations, if carefully made, will be found to differ very little from each other. 1426. MoMorCs Hygrometer. — ^The dew-point is frequently obtained by this instrument, which consists of two nearly e(]|ual thermometers placed side by side at a small distance from each other, on a stand, the bulb of one being covered with muslin, and kept wet with distilled water. The evaporation of the water from the muslin lowers the temperature of the covered bulb, and the amount of depression depends on the rapidity of evaporation, which itself depends on the dryness of the atmosphere. If the the temperature of the dry- and H that of the wet-bulb thermo- meter, p the pressure of the vapour in the atmosphere, j/ the pres- sure corresponding to the tempejatore f, and II the pressure of the atmosphere, then, according to the researches of Aug^, |/=|)-002239(t-f) —5—. Pr. Apjohn^s formula, which has been frequently made use of in this country, differs slightljr from that of August.* It has been stated by rouillet, on the'authority of August, that a current of air does not affect the result, although it increases the rapidity of evaporation. The Pnfekrometer, — ^The thermometer, the bulb of which is covered with muslin, and kept constantly wet, is sometimes called a peyekrometer, on account of its being employed to measure the quantity of moisture suspended in the atmosphere. 1427. The abstraction of heat by evaporation is of great im- * Uneh UMfbl informatioo on this labject mav be obtained fVom Mr. Glslshec^i elaborate little work on the Dry- and Wet-bulb ThemometerB. 798 TBBKM1C8. portance in the animal economy, aa being the principal means by which vital heat is regulated. In the healthy condition of the frame, superfluoaB heat is carried off, and the temperature of the surface lowered, by a copious evaporation of fluid, under the well- known form of perspiration, secreted by the wonderful mechanism of the skin, which it would be out of place here to describe. The oppressive feeling of a damp warm day, and the burning heat of fever, are alike due to the suppression of this natural process ; in the former case, by the already saturated condition ol the atmo- sphere, and in the latter, by the absence of secretion from the lUn. The absence of injury from the almost fabulously high tempera- tures, which some individuals are eaid to have sustained, is en- tirely due to the same cause, dryness of the air being in these cases an essential condition of immunity; the excessive secretion of fluid to which the skin is stimulated, carries off by evaporation the intense heat, as rapidl v as it is imbibed by the surface of the frame. 1428. Transiti4m from the SoUd to the Gaeeous State.— TYaa transition appears to take place in some substances without the visible intervention of the liquid state ; this is probably owing to the extreme volatility of the flnid, which is no sooner formed than it is dissipated in vapour. Arsenic, benzoic, and carbonic acids, iodine and camphor, present examples of this change of form. It is also well known that a gradual evaporation takes place from the surface of ice and snow : the writer has repeatedly observed the crystalline structure of a sheet of ice developed on its suriaoe by evaporation, just as that of a plate of zinc or tin may be, by the solution of the immediate suiiace by an acid. ] 429. Condensation of Gcuea. — Some gaseous bodies assume the liquid form from their strong affinity for some liquid : thus the eager absorption of ammonia by water has alreadv (1420) been spoken of as a source of cold. Hydrochloric and hydronaorio acids, and in a much more limited degree, carbonic aad, are ex- amples of condensation from this cause. It is also highly probable Uiat the phenomena of transoiration of gases, which have recently been elaborately investigatea by Mr. Graham, are further exam- ples of temporary liquefaction by affinity. All gases are probably capable of liquefaction at sofne tempera- ture, and by a sufficient amount of pressure, but the necessarj temperature and pressure vary very considerably. Faraday was one of the first woo pursued these investigations ; the result of his experiments has already been given (10). Caroonic acid, which, it appears, is uquefied at the freenng point by a pressure of 36**', is frequently employed as the best known means of producing intense cold, by its own spontaneous evaporation. The apparatus for this purpose, which was first con- trived by Thilorier, consists of a strong-closed iron vessel, in which are placed some substances capable of disengaging carbonic acid, as, for example, hydrochloric acid and broken wnite marble ; this communicates with an equally strong cylindrical iron receiver. COLD PRODUCED BT ETAPOXXTIOIT. 799 in which the gas is collected, and reduced to the flnid state under its own pressure. When the receiyer is sufficiently filled with the liquid acid it is allowed to escape by a stop-cock through a tube entering tangentially the side of a cylinorical box, which has two tubular apertures in the direction of its axis. A portion of the issuing liquid is instantly converted into vapour, and carries off so much heat, that the remainder is reduced to the state of snow, which is whirled round the circumference of the box by the force of the jet, while little more than the vapour escapes by the central tubes. This frozen carbonic acid, at a probable temperature of — 1 06** F., evaporates very slowly in a moderately cool atmosphere ; but evaporation constantly goes on from its surface, in consequence of which a portion may be placed in the hand, or even on the tongue with impunity, being prevented from actual contact with the living tissue by a film of badlv-conducting vapour, I'ust as in the case of liquids in the spheroidal state (1415). For the same reason, buys at an iron-foundry will sometimes step over the molten metal with naked feet, provided only it be hot enough ! — that is, — to raise from the surface of the skin a protecting layer of vapour. In order to bring the frozen acid into contact with other matter, it must be wetted with ether or alcohol ; the former is generally employed on account of the additional cold resulting from its evapo- ration : mercuiT placed on this mixture is rapidly frozen. B^ placing this mixture of ether and frozen acid under the receiver of ah air-pump, Faraday attained the probable temperature of — 166° F. But a much lower temperature nas been reached by Matterer, who by means of a mixture of liquid nitrous oxide and bisulphide of carbon, placed under an exhausted receiver, attained a supposed temperature of ~220''F. 1430. The chemical agency of heat is of the highest importance, as without its aid, a very large proportion of the results of modem chemical analysis must have been for ever concealed from us : the student will find this matter treated of in all works on chemistry. l*he heat evolved during chemical combination has been carefully studied by MM. Favre and Silbermann, and by Mr. Andrews ; the numbers of thermic units due to several combinations of lib. by weight of various substances, are given in the following table : — With Oxygen. \ Zinc . . . 1301 s Arsenic. . 994 Hydrogen . 34135 Tin ... 1233 Marsh-gas. 13085 < Copper . . 602 Olefiant gas 11900 j^ruj, Cfhlorine. Carbon . . 7990 Copper . . 961 Antimony . 707 With Bromine. Iron. . . 1277 Phosphorus 5747 > Potassium . 26o5 [ t«. , , Iron . . . 1745 Wuh lodwe. Zinc . . . 1529) Zinc. . . 819 Carb. oxide 2417 Sulphur . 2263 Iron . . . 1576 \ Tin. . . . 1079 Iron ... 463 800 THBBMICS. 1431. There is a peculiar action of beat, wbich has Doi yet been sufficiently investigatedi evinced in its power of actoating a chance of chemical composition; one result of this action has already been considered (1321). Mr. Grove has shown, in a communication to the Royal Society, that at a considerable ele- yation of temperature, the compound gases or vapctars are resolved into their constituents, as if the ^' <^99. disruptive power of heat had been sufficient, not only to sepa- JU,^^ ^ rate molecule from molecule, /^•■•^^^^"v^ %J ^* ^^^^ ^ ^^^ their consti- cr^jC ^^^l^^w^^ tuents from each other. He \>y§ ^*^"\0 found that an intensely ignited \ J y^ V}^ of platinum, indium, or ^ silica, plunged into water, de* V. composed the evolved steam intooxygen and hydrogen. The best mode of showing this im> portant fact is by bending a tu]be into the shape abb. Fig. 693, having platinum wire, z c, passing across its bulb. The whole is filled with water, and allowed to rest in a vessel of water. On connecting z c with a battery consisting of two of Grovels ele- ments (776), the water in the bulb will soon boil, and the bulb will be filled with steam ; the wire traversing it, becoming red- hot, will decompose the steam into oxygen and hydrogen, minute bubbles of which will rise through the water. 1432. Terrestrial Heat. — The solid mass of our earth owes its warmth to what is termed terrestrial heeU, for which it is not in- debted to the sun's rays, but to some internal cause. So far ss researches have extended, it appears probable that the tempera- ture of the earth increases one degree (Fahrenheit) for every 60 or 70 feet we descend beneath its surface, so that at a depth of a few milea the mass of the earth must be actually red-hot. A large proportion of the terrestrial heat is radiated into space, and is subsequently absorbed by the aqueous vapour suspen^d in the atmosphere ; the vapour itself then becomes in its turn a good radiator, and hence the temperature of the air decreases on ascending to any considerable elevation : this diminution of heat has been assumed to be one degree for every 290 feet above the level of the sea. From repeated observations it appears, that the mean, or averase, temperature of any place corresponds to the heat of the earth at a oistanoe of about 30 feet below its sur£ue. 801 CHAPTER XXIV. SAOULHT HEAT. Iv the preceding chapter the influence of heat on the state and physical propertiei or matter, and the laws of its transmission from molecnie to molecule of matter in its several solid, liquid, and gaseous states have been discussed : it now remains to con- sider the influences of matter on its transmission by radiation, preciselv in the same manner as light is transmitted through trans- parent bodies. 1433. Every one, when standine near a fire, must be aware that he feels a sensation of warmu, and consequently, if actual particles of matter do not pass from the fire to him, that some Lind of energy must emanate from it, which, on reaching his sur- face, excites tne sensation of heat, in the following account of the properties of radiant hecU, it must be recollected that this expression is applied to the effects of those undulating movements which are assumed to excite the sensation of heat, and not as referring to any form of matter. In this view also, a ray of heat must have a definition analogous to that already given of a ray of light (1019, 1020). When a body is heated in the air or in a vacuum, it continues to evolve rays of heat ; and manifestly so, until it attains the temperature of tne surrounding medium, lliese rays pass off in straight lines, and obey the laws of reflection and refraction, precisely like those of light. 1434. If a heated body, as a red-hot iron ball, a, Fig. 694, be placed in the principal focus (1040^ of a concave metallic mirror, b, radiant heat will pass from it to tne mirror, from which the rays will be reflected in pandlel lines. These, if ooUected bv a second mirror, o, placed ten or twelve feet from the first, will be equally brought to a focus, and the bulb of a differential thermometer, d, S laced near that pointy will be immediately acted upon by the re- ected heat, the fluid falling in the tube. In this manner phos- phorus or gunpowder may be easily inflamed at a considerable distance from the source of neat, by concentrating the thermic rays by means of a concave metallic mirror. 1435. If a mass of ice be substituted for the hot ball, the ther- mometer in the focus of the second mirror will indicate a de< pression of temperature. This was once erroneously assumed as ui illustration of the reflection of cold ray$, which in fact have no dF 802 RADIAHT HEAT. existence ; cold being merely the negation, or abBence, of beat. Id this arrangement of the experiment, the ball of the thermometer being warmer than the ice, plays the same part as the red-hot ixtm Fig. 694. ball (1434) ; it radiates bent, which is reflected by the mirror in the focus of which it is placed, and reaching the ice, becomes latent (1 156) in converting a portion of the ice into water. 1436. Theory of Exchange*. — ^The facts herestated are embodied in this theoiT of Prevoat, which assumes that every molecale emits continually heat rays, the energy of which is proportional to its temperature ; consequently, a particle that emits less enei^ than it imbibes, gains heat ; on the contrary, one that emits more energy than it appropriates, loses heat. It follows as an immediate consequence of this theoiy that the radiant and absorbent powers of any substance are necf«Mri2y equal : for suppose two bodies to be placed in a space surrounded by a complete envelope maintained at a constant temperature, they will soon arrive at, and subsequentlv maintain, tne same temperature. Suppose now that one of tnese bodies is able to radiaJte n times as much heat as the other, it follows of necessity that it must at the same time absorb n times as much heat, in order to maintain the constant temperature. It will subsequently appear that this law has been abundantly verified in the invaluaUe researches of Prof Tyndall. Suppose now one of the two enclosed bodies capable of reflect- ing 90 per cent, of the rays absorbed by the other, it can therefore absorb only 10 per cent, of those rays, and as its radiation must necessarily equal its absorption, it must radiate onlv 10 per cent, of the heat it receives ; therefore, aood r^Uctort of h^U are had radiators^ and vice verad; this law nas been proved ezperimentsdly by Leslie and others* Suppose the hypothetical envelope to be spherical, for the mke THXOBT OF EZCHAXGB8. 803 of simplicity ; it is self-evident tbat the temperature of the body wiQ not be affected by its position in the cavity : this mav m proved theoretically by the same geometrical oonsiderations woich were employed by Newton, to prove that the attraction of a spherical shell for a particle within it is independent of the position of the particle. This law has been proved experimentally by Lambert and Leslie, and may be thus enunciated : — If a poiiU receive from a given eurfaee of indefinite extent rays bounded by a conioal ewrface of any form, the same amount of heat vnU arrive at the potntf whatever may be the distanee, form, or poeUion of the «tir-, faeef provided only that the eeetionm area of the cone, at a given distancefrom the point, remain eonetant. This is merely a gene- ralization of the experimental proof in 1440. Suppose again one of the two included bodies to be a plate of some substance capable (as probably all substances are more or less) of absorbing some heat-rays and transmitting others — acting, in fact, as colouness glass does towards the supra-spectral rays (1114\ or coloured glass to some portion of the visible spectrum (1093), — rock>salt, ror example: it is clear that this plate; will ei^er transmit or intercept the radiations towards the other body from a portion of the sunace of the envelope ; but as the same amount of heat must reach the second body, as when the rock-salt plate is not interposed, that body must be capable of radiating the same quality, as well as quantity, of rays that it absorbs ; or in other words, a body abeoros moet freely those rays which it is capable of emitting: this has been proved experimentally by Mr. Balfour Stewart, with regard to rocK-salt. 1437. It is a noteworthy fact, and strongly corroborative of the identi^ of the nature of lignt and heat, that precisely the same laws that have here been enunciated with regard to heat-rays, hold good with respect to light : thus the converse relation of radiation to re- flection 18 shown by the fact that if the dross be skimmed off a pot of molten metal (as may be seen any day in a foundry), it glows much more brightly than the clean, and, therefore, good-reflecting surface of the metal, which may be observed to brighten up as the surface again becomes oxidated. Aeain, the coincidence of absorption and radiation may be shown thus : — I. It has been shown bpr Mr. B. Stewart, that if an encaustic tOe with a black and white pattern on it be made red-hot, and viewed in the dark, the black part of the pattern will come out bright, and the white part dull. II. A piece of coloured ^lass will radiate much more light than a colourless piece, if both be raised to the same temperature. m. When the piece of coloured glass has become heated in a olear fire, the colour of the glowing coals behind it will be very little affected, because it has acquired the power of replacing the absorbed rays by its own radiations. There is an obvious analogy between this result, and the reciprocation of sound (540). 8f2 804 RAVILKT HEAT. IV. If a tonrmaliDe be rendered incMidescent bj being pboed in the centre of a red-hot iron sheil, having a hole Uirongn whidi the crystal may radiate transrereely to its axis, the radiated Hgfat was found by Mr. B. Stewart to be polarised in a plane petpendicn- lar to that of the polarized rsrs wnich it wonid have tran»mitf$d. 1438. Bate of Cooling bv Madiation.-—\t is foond by experiment that a body radiates a fizea proportion of its heat, or in otber words^ that the amount of radiation at any moment is pn^rtionaltotbe temperature only : for if as** be radiated to a given point from a body at a temperature of y**, then if the body be raised to 2 y*, 2 x* wiH be radiated to the same point. Hence the rate of cooling hj radiation most be some function of the temperature only ; and if a body at a temperature T+ <, be surrounded by an envelope at a lower temperature, t^ then its rate of cooling will be a rmming balance of its debtor and creditor account with heat. If the rate « cooling at the temperature x be represented by i^x), tben the rata of coofing of the supposed surrounaed body wilibe /[T+o-/:*). If this expression represent the loss of heat by the body in question, in order that it may also represent the loss of tempera- dire, it will be necessary to assume that the specific heat (1888) of the body remains constant during the interval of temperatore under observation. Accurate observations on the numerical values of this function were first made by Dulonp: and Petit, by means of a thin sphere of copper, blackened inside, and immersed in a water-bath of known temperature, into the middle of which the bulb of a ther- mometer at a higher temperature than the bath was inserted, and the decrement of temperature during one minute was ob- served. In order to divest tne radiation of the interference of the air, as much as possible, the hollow sphere was exhausted by an air-pump. The observed rates of cooling for several different values of T and t are given in the following table : — VslBMOf 2*0. Valnetofl • 0°C. 20* 40=» aop 80" 240 10-69 12-40 14-35 • •• • •• 220 8-81 10-41 1198 ■ *• • •• 200 7-40 8-68 1001 11-64 13-45 180 610 704 8-20 955 1105 160 4-89 6-67 6-61 7-68 895 140 8-88 4-57 5-32 6-14 719 120 302 3-56 415 4-84 564 100 2-30 2-74 3-16 3-68 4-29 80 1-74 1-99 230 273 8*18 60 • • • 1-40 162 1-88 2-17 KATE or OOOLIRG. 805 It will here be found that while tM socoeeeiye Talnee of i have a eongtant common difference of 20% the corresponding rates of cooUng, for each and every valae of T have a eonetant common raHoot ri65 very nearly: hence result the general laws that. The rates of cooling of a heated body are in a geometrical cro- greesion, when the exceeeet of temperature aiwve that of the eurrounding medium are in an arithmetical progression: and The common ratio is the same for the same common difference^ whatever be the excess of temperature of the heated body. From these laws MM. Dnlong and Petit have inferred the form of the fonction/. The common ratio 1'165 found for 20*" must evidently be the 20th power of the common ratio x for 1% or «»=1165, in which the value of x is 1*0077 ; and for <° the common ratio will be 1*0077^: and the first term of each geometric series, con- tained in the second column, depends on T alone, and may be pnt under the form f{T): hence is derived the equation /(r+o-/(o=^(r;ioo77<=a<^(r). expanding /(?*+<) in ascending powers of Thy Taylor*s theorem, and expanding ^{T) also, there results f{t)-\-def{t). T+ &o.-/(0-a<(i4 T+B T« + &c.) then by equating the coefficients of like powers of T, dif{t)^A.a^=blogt a.a\ suppose, then by integrating this equation f[t) =b.a^ + const. similarly / (^ + Q = 6 . aT+ * + const. subtracting, /( r+ 0 —/(O =&(«''+*- «0. =6.o«(ar-.l). In the value thus found for the rate of cooling, the determina- tion of the value of the constant a has been purely empirical ; but its value has been confirmed by the investigations of MM. Pre- ▼ostaye and Desains: the value of the constant b will depend on the nature of the radiating body. For determining the absolute radiation from any particular substance and surface, the value of b in thermic units (1372) must be ascertained ; this has been done by the late Mr. W. Hopkins in a few instances, viz. : — Glass 6=1-367 Pry chalk 1*230 New red sandstone . . 1*197 Buildiuff sandstone . . 1*269 Polished limestone . . 1*301 The same unpolished . 1*829 The object of this quantitative determination bv Mr. Hopkins, was the determination of the probable thickness of the solid crust of the earth ; by ascertaining from the amount of radiation the 806 RADIAHT HEAT. dej^h at which the temperatifre wonld be above the point of fiitton of its ordinary materials : this problem is, however, still veiled in much uncertainty, and very dinerent estimates hare been fonned, according to the basis on which they have been made. 1439. BeUe of Cooling by Convection in Octaes. — This has been determined by a laborious process, bv MM. Dulong and Petit^ in relation to certain gases : tney have deduced the following laws : — 1. The rtUe of cooling hy gaseoua convection it independad of the nature of the turface. This is not the case with the rate of cooling by radiation. 2. Thie rate oc {excess of temperature) ^**". 8. This rcUSt for a g^ven excess of temperature, is a function of the pressure only. Combining the two last laws, it appears that — Rate of cooling =:m .p» . <***■•. It has been determined irom the researches of Mr. Hopkins, combined with the above, that the amount of heat lost by con- vection by one square foot of surface heated f* above the adjacent gas, the pressure of which is p centimetres of mercury, will be expressea in thermic units (1372) by the following formulse: — Pydrogen, 00184 (^) •'" t '« ; (•I \ 0.S17 JL) ti-w. 720/ 1440. Reflection of heat takes place from the surfaces of bodiea, and generally, the more highly polished these are, the more com- pletely do they reflect heat. If 100 rays of heat be incident at an angle of 60° on reflecting surfaces of the following substances, the proportion per cent, of heat reflected will be as f^lows : — Polished gold . 76 ; Unpolished brass 52 5 Glass blackened at the back . 12 Metal blackened 6 „ silver . 62 5 Lacquered brass 41 „ brass . 62 \ Looking-glass . 20 When heat is reflected in parallel rays from the surface of a good reflector, it scarcely seems to be afiected by the snace it may happen to traverse, except in being slightly diminianed in quantity oy the absorbing power of the medium through which it passes. If, however, heat be radiated from a small sorface, its intensity, if examined at different distances from the radiant FORM or THBRMOPILI XMPLOTSD. 807 bodyi will be found to decrease as the square of the distance increases, as is the case with light (1026) : this is, however, abso- lately true for radiation from a point only. The truth of this proposition may be readily demonstrated by directing the conical guard of a thermopile (968), b. Fig. 695, towards any extended and uniformly heated surface, and noting the deflection of the needle. If the thermopile be now removed to any neater or less distance, the deflection will remain unaltered, provided only that the area representing at the heated surfaoe the base of the cone produced, he wholly within that surface. Now it is clear that this area, and consequently the number of points radiating heat to the nile varies as (distance)' of the pile from the surface ; but the total amount of radiation is found to be constant, there- fore the heat received by the pile from each point of the heated sar- fiace must be inver$ely as its (distance)' from that surface : q.e,d. 1441. Heat, like light, admits of single and double refraction, and polarisation, — properties for the discovery of which science is almost exclusively indebted to the labours of M. Meiloni, and of Principal Forbes of Edinbureh : the latter physicist, indeed, is the diMoverer of the plane and circular polarization of heat. The application of a delicate thermopile (Fig. 548), in which an electric current, capable of affecting the needles of a sensitive galvanometer (856), is excited by very minute changes of temperature, has been the main source of these important discoveries, by enabling the physicist to detect changes of temperature otherwise utterly un- appreciable. The most complete apparatus of ^ this kind is that devised by Forbes, Fig. 695. The thermopile is enclosed in the case, a, and JFV. 095. supported by a stand, so as to be moveable in any direction. The bent wires, c, are connected with the terminal elements of the 808 BADIAXT BBAT. Httle batterji and oonnexion is thas readilj made with a delicate galvanometer, d, the indications of which are examined through a telescope, b, so that very small doTiations of the needle are easilj observed. The battery is so minute, that the section of a pre- sents an area of o^y 0*4 inch. The rays of heat are frequently concentrated on the* thermopile by means of a conical metalHc re- flector, B, and so delicate is this apparatus, that the mere approach of the hand towards the mouth of b will excite a current capable of deflecting the needle through seyeral d^rees. When observa- tions are made with this instrument, it is usual to inteipoee a screen consisting of two parallel plates of wood or pasteboard separated by an interval ot about an inch, between the sonroe of heat and the mouth of b, or the extremity of the pile, when the reflector is not used, and to remove it at the instant that all ia arranged for observation. ^ 1442. B^raeUcm of JJeot.— Heat-rays are capable of refrac- tion through prisms and lenses, in the same manner as lominoos rays. In experiments on heat, however, the refracting medium must be a substance capable of readily transmitting heat of aU kinds ; and for this purpose rock-salt is almost the only sohstaoce that can be employed, the extraordinary &cility with which it transmits more wmh 90 per cent, of incident heat, rendering it to heat-rays what glass is to those of light, or quarts (1114) to the invisible rays of hiffh refrangibility. If a convex lens no made of transparent rock-salt, it will with facility bring radiant heat and eopecially the rays of dark heat, or as they may be termed, hypo$peetral ray*^ to a focua. The rays from a vessel of boiling water can thus be brought to a ibcuB by a salt lens, with as much facility as luminous rays are by a lens of glass. The higher refrangibility of the heat-rays in the solar beam enables them to pass through ordinary convex lenses of glass, and the common burning-glass affords an instance of solar heat being thus brought to a focus toMther with the light. 1443. if heat be incident on a rocx-salt prism, it is, like light, resolved into a series of rays of unequal refrangibility (1088), and a heat-spectrum is the result. Tne refraction of heat may be readily shown with the following arrangement, in which the rays emanating from a vessel of boiling water, a. Fig. 696, after passing through an opening in a screen, d, are incident on a rock-salt prism, B, where they are refracted in the direction B c, and may he de- tected by the thermopile, o. 1444. When heat-rays emanating from different aouroes are in- cident on the prism in this apparatus, it u found that the angle of their incidence must be changed by moring the source of heat, in order to obtain the maximum action on the galvanometer ; or, what comes to the same thing, the position of the thermopile most be slightly altered. ^ The explanation of this is readil v found in the unequal refrangibility of the rays of heat : thus M Jlooi fonnd BSFRACnOV OF BBAT. 809 that the heat from incandescent platinum was refracted more than that from a hot plate of blackened copper. 1445. The existence of rajs of heat of yarions refrangibilitj piesents a key to the phjrsicd alteration produced in heat after trayersinff plates of different bodies. Thus, rock-salt allows rays of all refraogibilities to pass in nearly eqaal propNortions, a plate of alum intercepts all saye the least refrangible rays. Melloni coyered a plate of rock-salt with soot, and found that only rays of the highest refrangibility could pass, the plate becoming to heat what yiolet-colonred glass is to light; ana by combining with this a plate of alum, which refuses to transmit any but the less refrangible rays, dU heat was absolutely stopped, the combi- nation becoming absolutely atUathermanouSf or opaque to heat. When a plate of alum is combined with one of ereen glass, the brilliant light of a lamp, or eyen of the sun, is reaaily transmitted, hat their heat is absolutely stopped : these experiments show yery satisfactorily the analogous relations of light and heat It has preyiously been remarked (1107) that the most intense rays of the heat-spectrum are situate beyond the red end of the light-spectrum, and the curye she, Fig. 594, is intended to re- present the relative intensities as observed by Sir J. Herschel. With better means of observation, MiUler determined the point of maximum intensity of solar heat to be at a distance equal to about half its length beyond the extremity of the visible spectrum. The relative intensities of the heat-rays are represented b;^ the ordinates of the dotted curve ▲ b o, Fig. 697, of which the ordinate i> B represents the termination of the visible spectrum. 1446. But as it has been demonstrated by Prof. T^ndall that aqueous vapourisapowerfulabsorberof the heat-rays, it is more than probable that the sunbeam is robbed of most of those rays before It reaches us. And this supposition is fully borne out by the obser- tations of Prof. Tyndall on the heat-spectrum ofthe electric lamp, obtained by transmission through a lens and prism of rock-salt. In tbi« cue he found the btinntj of the ■pcctram to he tvfn- ■ented br the cnrre c E r D, the ordinate Di of MulWi corre being tftken u the onit of compariBoa. The point of BUxiiniUB mteniilf, r, coneipond* with e, that «f Unller'i cnire, bat th« amount of heat ii then mora than doubled. Semihle rsn of heal vere obaerred to extend u much ai half the leDgth cf the fiaiUe epectmni further into the itA ipace bejond A. 1447. Oalortteeiiee. — ABtheinlentilroflheobaciinra^efbeit appears to adfance^Niri HOW with the total heat emitted. It became an iotereding subject irf inquiry to diacover BomemeaDaofwpa- rating the Inminooi from the obscure heat-ran, and a higfaly im- portant aerioa of inreatigationB was made b; F>«f. Tj>BdaD.* He diacorered that iodine and bisolphide of caj'bon are both fnclj permeable hj obscure beat-rajs, and as iodine is tbtj aoloUe in that fluid, a stroog solutioD, eDclosed in a glass cell terminated bj pUles of rock-salt, was foutid to intercept entirely the lomiiMKts rays, but to tnnimit about 90 per ttaa. at I the obacnie raj ■ of heat. Tbess beiag bno^t I to a focus, Knnpowdsr, pnper, and otha* com- I boBtible bodies ma; readily be ignited. ' But a still more temarkable [JieDOBeiwa wasobserred when sooie incombustible bodies, I capaUe of freelj taking up the raTt, were pre- I sented to the focns. & [ueoe <^ platinum-fbal I platinised, i^., coated with flnel^-dirided pla- tinun b; electrolytic precipitation, being so placed BB to receive a focal image of the carboii electrode*, that image in a few seconds h-^sTnt plates ot rocK-saJt, B SURPACB-BADIATIOV. 811 words, their refrangibilitj is increased. This phenomenon, the converse of fluorescence (1116), haa been designated "calorescence'' by Prof. Tjndall. The same arrangement that heated the platinnm-foil to white- ness with the electric, or ozy-hjdrogen light, produced only dull redness with direct solar rays, thus demonstrating the absorption of the obscure rays by the atmosphere. 1448. The state of the surface of the radiating body materially a£fects its radiant power. It is not improbable that the impedi- ment that a polished surface offers to the radiation of heat, may bear some analog to the internal reflection of light (1060). Ab a general rule, lor the same substance, the radiating power is diminished by even slightly compressing its surface, as in bur- nishing ; and in the case of metals, it is increased by tarnishing or oxidation. The radiant power of bodies may be roughly illustrated by re- placing the hot ball in the focus of one of tne concave mirrors (1434) by a cubic canister of tin filled with hot water, the angles oeing provided with grooves, so that plates of substances may be slippea in. Or two sides may be coated with different substances, as lamp-black and white-leaa, if the radiant powers of such bodies are to be determined, and one of the remaining sides polished, while the other is made roueh by scratching it. In every case, that side of the canister which is to be examined, must be turned towards the surface of the mirror, in the focus of which it is placed. The indications of the thermometer, placed in the focus of the second mirror, become a measure of the heat radiated by the substance under examination. The radiating power of lamp- black is the most considerable of all bodies, and is assumed as tne standard of comparison with others in the following table : — Lamp-black . . 100 ^ Ice 85 ^ Clean lead 19 Writing-paper . 98 e Plumbago . . . 75 > Polished iron ... 15 Crown-glass . . 90 < Tarnished lead 46 \ Other bright metals 12 1449.' The rapidity of the cooling of different bodies depends jointly upon the radiating power of the substances of which they are composed, and upon the nature of their surfaces. Leslie filled a polished tin globular vessel with hot water ; it cooled down to a certain temperature, as indicated by a thermometer, in 156 minutes. On repeating the experiment, after covering the vessel with a thin layer of lamp-black, it cooled down to the same Soint in 81 minutes : thus the rapidity of cooling was nearly onbled by increasing the radiating power of the surface of the vessel. Count Rumford allowed hot water to cool in two polished brass cylinders, leaving one naked, and covering the other with a fold of linen: in the former the water cooled 10 degrees in 55 minutes, whilst in the latter, it lost the same amount of heat in 361 minutes. The good radiating surface of the linen thus acoe- 812 EADIAHT HBAT. lerated tbe loss of heat. For a similar reason, regetable ioliuioiiUL as tea, are best prepared in brislit metallio Tessels; nnglaaea earthenware, and especialljr a black tea-pot, radiates a laigo amount of heat. In heating rooms with tubes of hot air or steam, their surfaces should be roughened or blackened, to focili- tate the radiation of heat into the apartment ; whilst that portion of the pipe employed to convey^ the source of heat into the room should be kept bright or polished; or, still better, "jacketed," that is, enclosed in a second tube with a space of air interroning, in order to prevent unnecessary loss of heat by convection. 1450. During the nieht the temperature of the air ia alwaya many degrees colder £an in the day. The earth, therefore, radiates into space a portion of the heat it had absorbed in the day-time. Thus becoming cooled, a depoeition of the aqneoos vapour of the air takes place upon its surface, which is familiarly known b^ the name of dew. This, in oold weather, freezes in tlie act of being deposited, and constitutes hoar-frott, which is the ice of dew. Ihe greatest quantity of dew is always found deposited on that portion of any surface which radiates best; hence a meadow will often be found covered, whilst the smooth road by its side is nearly free, in consequence of grass radiating freely. If a polished plate of metal be exposed at night by the side of a piece of wooUen cloth, the latter will, in the morning, be found covered with dew, whilst the badly radiating metal wiU be free. Deposit tions of dew may be readily prevented by opposing any obstade to free radiation ; eveiy gardener is aware that he can prevent the deposition of dew over a portion of ground by merely supporting over it, by means of slips of wood, a thin cloth or handkerehi^ which prevents the free radiation of heat from the suifaoe thus protected. The demonstration of the real source of dew and noar*frost is due to the researches of Dr. Wells. 1451. In order that observationson terrestrial radiation may he in any degree comparable with each other, it is absolutely neceasaiy that not only the construction of the instruments used, but alM the mode of using them, should be strictlv defined, since otiierwise widely differing results may be obtained under preciselv similar circumstances. It appears from the observations of Mr. F. W. 8tow,* that an extreme difference of 2*5*' F. was observed be- tween thermometers of different constructions, placed in juxta- position on the same spot. It is probable that the most sensitive instruments will be found to be those having a bulb made of black flass, the surface of which has been eroded by fluorhydric add : ut it is very desirable that both the form and the sixe of the in- strument most suitable for such observations, and the precise nature of the surface on which it is to be placed, should be authoritatirely determined. * Proceedings of the Ifeteorolof ieal Society, roL iii. p. 188. MOSm's FIOUBES. 818 1452. The relation of the state of Buriace with the depoeition of Tapoar is well shown in the carious phenomena discovered bj Prof. Moeer, and known as MUnr't fgure$. To oheeire these, place a coin upon the surface of a piece of looking-glass, or of common glass, having the back covered with tin-foil, and allow a few sparks to fall upon the ooin from the prime conductor of an electnc machine. Bemoye the coin,^ and gentlj breathe over the surface of the glass^ when the outline of the impression on the coin will become partially defined upon the glaiis in minute glo- bules of water. It a series of plates be superposed, and the coin placed upon the upper one, and the sparks allowed to fall upon it, the upper surface of each plate will present similar phenomena when breathed upon. These figures may be renderea visible by exposure to the vapour of iodine or mercury, quite as well as by breathing upon them. Similar efifects have been shown, by Mr. Hunt, to result when a coin, gently heated, is allowed to rest on a plate of polished silver : on removing it and breathing on the plate, or exposing it to the vapour of meroury, the figure of the coin will be rendered distinctly visible. If a clean coin be allowed to rest on a looking-glass for some time in the sun, and be then removed, a tolerably distinct outline of the coin will appear, on gently breathing on the glass. 1453. The altered condition of the surface of the body, on which the vapour is deposited, must be owing to radiation from the coin or otner body placed on it. Founded on these curious iSscts is the art of Thermography, to which attention has been especially directed by Mr. Hunt. He found that to obtain a good image, the superposed body must be of a different material from the plate on which it is placed. Thus, when a sovereign, a shil- ling, and a penny are placed on a polished copper-plate, the latter gently warmed by passing the name of a spirit-lamp under it, then allowed to cool and the coins removed, pictures or the sove- reign and shilling will appear on exposing the plate to the vapour of meroury, whilst a scarcely visible image of the penny win be obtained. Pieces of blue, red, and orange-coloured glass, of white crown, and flint glass, mica, and paper, were placed on a plate of polished copper, and allowed to remain in close contact for half an hour. On removing them and exposing the plate to the Tapour of meroury, distinct images of the red, orange, flint, crown- slass, and paper were obtainea, whilst the blue glass and mica had scarcely produced any impression. A plate of copper being amalgamated, so as to present a bril- liant reflecting surface, by rubbing it with nitrate of mercuiy, a sheet of printed paper was placed on it with the letters downwards and pressed in close contact by several folds of paper on which a weignt was placed. The whole should be allowed to rest on a warm surface. In half an hour some emanation, probably of the yapour of oil, from the black letters will have produced a marked 814 KADU.HT HEAT. althoQgli as jet invisible, effect on the snrfaoe. To render this obvioQs the plate should he exposed to the raponr of mercnrj, which will adhere to those parts which corresponded to the white portion of the printed paper. It should next be exposed to the yapour of iodine, whicn will blacken the parts to which the mei^ curia! vapour has not adhered, and an accurate copj of the printed page will result. 1454. It has already (1486) been remarked that bodies which possess a high radiating power, are also universally endowed with the property of readily ah$orbing heat; and whilst the beftt radiatons are the best absorbers, they are the wont reflectore. In the experiment of the two mirrors (1350), it is found that the metallic plates of which they are composed do not become sensibly heated by the rays from the red-hot ball impinging upon them. But if their concave surfaces were covered with lamp-black, the mirror nearest to the ball would become hot from the abscxrptioa of heat, and scarcely any would reach the second mirror. The blackened surface would, however, continue to radiate the heat acquired from the ball until its temperature is reduced to that of the surroundine atmosphere. The observed reciprocity of radiation and absorption was as- sumed by Prof. Stokes to be a probable means of accounting for the existence of dark lines in the solar spectrum : the correctness of this hypothesis was fuUy demonstrated by the researchei of Bunsen and Kirchhoflr(1108, 1111). 1455. A highly important and exhaustive series of observations has been made bv Prof. Tyndall on the relations of the colours of bodies, and of pulverization to radiant heat.* From the time of Franklin*s experiments on the absorption of heat to the present time it has been accepted as an axiom that dark-coloured bodies are the best absorbers, and colourless or light-coloured bodies the worst, but Prof. Tyndall's researches have entirely nullified this conclusion. For example, if any two similar surfaces, as the bnlbs of a differential thermometer (1356) be coated, one with powdered alum, and the other with powdered iodine, which is to the eye quite black, and equally exposed to a source of heat, the move- ment of the column will show a great excess of absorbent power in the white powder. This result depends simply on the fact that the molecules of iodine are not in unison with — are incapable of appropriating to themselves — the wave-motion of the greater part ofihe heat rays ; while those of the alum do not labour under this disability. It would hence be naturally inferred that iodine would be found to be diathermanous to those rays which it it incapable of arresting, and it is proved by experiment that snch is the fact : while the notoriously adiathermanous quality of alum led to the trial of its relative absorbing power. 1456. One of the most important results of these invostigatioiit is • Fhtl. Trans. 1808, part I. RAOIATIOH FKOM POWDERB. 815 the establiBhmentof the paramovnt influence of chemical constitu- tion on the reciprocal phenomena of radiation and absorption. In the ezperimentB of Melloni, and also in those of Masson and Coort^p^,* the powdered substancCf on which they experimented was spread on a surface mixed with a solution of gimi or gelatins ; and it is somewhat surprising that it appears never to have occurred to these physicists to separate in a mat measure the influence of the substance examined from that of the adhesive material with which it was coated, by first lading the solution on the required surface, and then sifting over it as much of the powder as coold be re- tained by adhesion. ^ As gum and gelatine are both good radiators and absorbers, Prof. Tyndall p»referred to employ sulphur, which is yerv transcalent, as the adhesive material, and a solution of this in bisulphide of carbon was employed to attach the powders to the surfaces of observa- tion. When thus compared, tne radiatinfl^ powers of red oxide of lead, and biniodide of mercury Tboth bright red powders) were found to be as 74*1 : 39*7, or nearly as 2 : 1 ; but when mixed with gum, they were both alike 80, thus the influence of the particles was entirely masked by that of the varnish which coated them. In regard to chemical constit0tion, the results invariably showed that amongst powdered substances consisting of the same elements variously comoined^ increased complexity of atomic constitution is accon^anied bv increased powers of radiation and absorption. On comparing black and wnite powders with each other, their radiating powers were found to vary as extensively as in the case of red powders ; thus — Black : — ^Electrolytic platinum 59*0 ; protoxide of iron 81.3. White: — Chloride of silver . . 32*5; carbonate of sdno 77*7. As in the comparison of alum and iodine, so in other cases, it appears that the radiating or absorbing power of a white powder far exceeds that of a black one ; thus m white hydrated oxide of zinc it ia 80*4, while in platinum-black it is only 59*0. 1457. The radiating power appears to be very'slightly influenced by mere mechanical suodivision; for when surfaces of glass and rock salt were coated by simple adhesion with their own powders, the radiation was very little afiSscted by the removal of the powder with a camelVhair pencil : but this does not hold equally for the extreme state of comminution obtained by precipitation ; thus with bright platinum foil the radiation was only 6*0, while with the same platinized it was 45*2 : moreover this experiment shows the influence of surface-condensation (1448). Prof. Tyndall subsequently found that the powders might be made to adhere sufficientlv by electrical attraction only ; but the observed results did not oiffer materially from those obtained by means of the sulphur-cement. * Comptei R«ndos» vol. zzr. p. 038. 816 B^DIAST HSAT. In all these experiments the heat employed waatbat of boiling Uer, in a Leslie's cobe ; the following table shows the reUtiTe water amoimts of radiation : — Babttuoe. Bad. BvbiUiiM. Bad.- Kock salt . . . Biniod. mercury . Iodide of ,, Chloride of lead . Flnor Carbonate of lime . 35-8 39-7 46-6 55*4 68-4 70-2 Red oxide of lead . Sulphate of lime . Rea oxide of iron . Hjd. oxide of sine Black oxide of iron Lamp-black . . . 74-2 77-7 78-4 80-4 81-3 840 The relative amounts of absorption were found by experiment to be very nearly the same. 1458. The quantity of heat radiated having been detennined, the question next arose as to its quality ; and this was tested by die permeability of rock-salt to the radiations of various substances at the same temperature of 100** C. It was found that the amount of transmission was generally proportionate to the amount of radia- tion, but to this there were some exceptions. It was concluded by Melloni and Knoblauch that rock-salt is equally permeable to all kinds of beat-rays ; but the experiments of Mr. B. Stuart and Prof. Tyndall show that this is not ^e case ; the following are the ratios of absorption by a plate of rock-salt of heat radiated from the several sources. Sooree. Abt. Source. AIM. Blnck platinum Black oxide of iron Red ,, 3-7 130 160 Suffar ..... Chloride of silver . Rock-salt. . . . 17-3 22-6 29^9 Thus it appears that while rock-salt absorbs only 4 per cent, of the rays emitted by black platinum, it absorbs 30 per cent, of its own rays. It is quite natural to suppose that the molecnlea of a body would be found most in accordance with, and theieibre most absorptive of, its own emitted wave motion. It was also demonstrated by direct experiment that the relative absorption of various bodies closely corresponded with their relative radiation. 1459. A simple and convenient mode of comparing the abeorptive powers of two surfaces has been employed by Prof, l^dall: two tin plates are placed vertically on two stands and connected by a copper wire; to the middle of the back of each is soldered a amall bar of bismuth, and these bars are connected by wires with the ter- minals of the galvanometer coil. A source of heat being placed somewhere in a line joining the centres of the plates coated TSAMSCALBHOT OF 80LIDB. 817 witli two substances to be compared, if uneoaal atnonnts of heat are absorbedf the needle will be deflected 07 the difference of the two contrary currents, but if these be equal, it will remain unaffected. The squares of the relative distances of the source of heat from the two plates, will give the ratio of the absorptions bj their surfaces. 1460. Radiant heat is partially absorbed in trayersing the most transparent media ; it is supposed that the heat of the sun loses one fifth of its intensity in traversing a column of air 6000 feet in ]en^h. It must not, however, be supposed, that those media which are the most transparent with regard to light, possess the same property with regard to heat. Indeed, it has oeen satis- factorily proved that a piece of smoky quartz, so thick as to in- tercept the piissage of a considerable portion of light through it. yet allows the paHsage of rays of heat which are entirely absorbed by even thin plates of absolutely transparent alam, or citric acid. Media which allow of the free passage of heat, are termed diather- manouaf or transcalent^ those terms bearing the same relation to heat, that " diaphanous " and " transparent " do to light. 1461. Transcalent bodies differ greatly not only in the quantity of heat which they are able to transmit, but also in its quality, distin&;ui8hed only by its refrangibility. In general, beat accom> panied by light, or in other words that produced by undulations SabatancM. Looatelli Red-hot Copper at Copoer at lamp. 400»O. lOOPC. Bock-salt . . . 92-3 92-3 92-3 92-3 Sulphur . . . 74 77 60 54 Fluor .... 78 69 42 33 Calcite . . . 39 28 6 0 Plate-glass . . 39 24 6 0 Rock crystal 38 28 6 3 Smoky quartz . 37 28 6 3 Chrom. potash . 34 28 16 3 White topaz 83 24 4 0 Felspar . . . 23 19 6 0 Amethyst . . 21 9 2 0 Artificial amber 21 5 0 0 fiorax .... 18 12 8 0 Common gum . 18 3 0 0 Selenite . . . 14 5 0 0 Citric acid . . 11 2 0 0 Natural amber . 11 6 0 0 Alum .... 9 2 0 0 Sugarcandy . . 8 0 0 0 Ice 6 0 0 0 3 a 818 Badiaut rsat. of sufficient rapidity to affect the yisa&l organs, is ca|>able of penetrating most diatbermanous media, whilst the rays of dark neatj or those of less velocity, as those emanating from a metal heated below redness, or from boiling water, are absorbed by manv ▼ery transparent bodies. Solar heat, again, readily passes through glass, whilst the luminonn heat of a bright fire is almost com- pletely intercepted by a plate-glass screen. The preceding table presents the results of MeUoni's experiments on the percentage of rays of heat from several different sources transmitted by plates of various bodies, each 0*1 inch in thickness. 1462. Of the 20 substances in the above table, 12 only arepenne- able both by dark and luminous heat, but in very different propor- tions; the other eight are diatbermanous to luminous heat alone. The difference in quality of transmitting power is striking^v shown, in the relative transcalency of Fluor and Calcite. Of all bodies hitherto discovered, rock-salt transmits most of the incident rays of heat, and of all kinds of heat in very nearly equal propor- tions ; hence it must be regarded as the true glass of radiant heat. The oil-lamp used in these experiments is a very steadily-burning one, that of Locatelli. The incandescent platinum consisted of a coil of wire, ignited in the flame of a spint-lamp, and the copper used as the other sources of heat was blackened. 1463. After the thermic rays have traversed a transcalent body, thev appear to have undergone some physical change, for if allowed to &1I upon a second plate of the same substance, a much larger proportion of those transmitted by the first plate will traverse the second. It thus appears, that in the act of passing through a medium, the rays are separated into two portions, one of which is changed (1114) or absorbed, and the other transmitted; and thus, sifted from the non-transmissible rays, those transmitted are better able to traverse a second portion of the same medinm. From the last table it appears that but 9 per cent, of the rays emanating from an oil-lamp are transmitted by a plate of alum, but if these transmitted rays be allowed to fall upon a second plate of this substance, 90 per cent, will permeate it, and connequentlv but 1 0, instead of 91 per cent, will be absorbed. On the other hano, Melloni found that a slice of green tourmaline transmitted 18 per cent, of the calorific rays incident upon it, whilst it allowed but 1 per cent, of heat which has passed through alum, to traverse it, thus intercepting 99 per cent. The same slice of tourmaline, al- though thus nearly impervious to heat transmitted through alum, vet freely permitted the passage of 30 per cent, of the mys which had previously passed through black glass. There is also a striking contrast between the transcalency of chromate of potash, and of white topaz ; in the former, the ratio of red heat to dark heat transmitted is rather less than 2:1; in the latter, the same xatio is6:l. 1464. The probable reason why the thermic rays, that exist at TEAHSCALCHOT OP FLUIDS. 819 And bejond the lower end of the visible spectrum (1107), are not luminous, may be found in the fact that they are aosorbed hy the humours of the eye, and do not reach the retina. If a spectrum be formed, in a pencil of rays from an electric light, by a prism of rock-salt, and the thermopile be interposed in the path of the rays Dear the lower end of the visible spectrum, the galvanometer needle will be considerably deflected. If a elass ceU, containing the transparent vitreous humour (1 179) of the eye of an ox, be now so placed as to intercept the rays falling on the thermopile, the needle will shortly fall back to zero, although the light of the portion of the spectrnm passing through the cell will not be sen- sibly diminished ; thus showing that the hypospectral rays have been wholly absorbed. This inference has been impugned by Ftof. Tyndall, and undoubtedly under ordinary circumstances the heat that reaches the eye is cleared of its hypospectral rays bj soueous vapour: but the point requires some further consideration. Tnese phenomena bear a striking analogy to the absorption of certain portions of the spectrum by coloured media (1093), and possibly to the conversion of the more refrangible rays to others of lower refrangibility (1114). 1465. Rock-salt is represented in the above table as equally transcalent to heat from all the sources employed ; but it appears Irom the accarate experiments of MM. Prevostaye and Desains, that this is by no means the case with heat from all sources : and it has been shown by Mr. B. Stewart that rock-salt is peeu> liarly opaque to the radiations from a heated piece of the same substance. This fiict strikingl v confirms the universally observed reciprocity of both radiation ana absorption with transmission. The radiations from rock-salt, glass, and alum heated to the same temperature increase progressively just as their respective powers pf transmission are diminished. 1466. TranacaUncy of Fluida. — A series of experiments was made by Melloni on the proportion of heat radiated by an Argand lamp with a ^lass chimnev, which was transmitted through various fluids, m a glass cell containing a thickness of 0*36 inch of the fluid. The pronortion per cent, of the total radiation trans- mitted by several nuios is here given : — Bisulphide of carbon 63 ( Hydrate of ammonia 15 Oil of turpentine Olive oil . . Naphtha . . Oil of lavender Ether . . . Sulphuric acid 31 < Niiric acid .... 15 30 28 26 21 17 Alcohol 15 Hydrate of potash . 13 Acetic add ... 12 Solution of rock-salt . 12 Distilled water . . 11 Here it appears that the variation in the transcalency of fluids is not nearly so lu|;e, as in the case of solids ; it, however, amounts 8a2 d20 &i.DIAJrr RSAT. to nearlj the proportion of 6 : 1. It ap]>ears alao that water maiotains itN opacity alike in the solid ana in the flaid form. Bat in these results the truth is considerably masked by the known opacity of glass to a lai^e proportion of the rays of neat« Much more reliable results have been obtained by Prof. TyndaU, by confining the liquids under examination between two plates of rock-salt, and by separating these to different distances fmm each other, the relatiye aosorptions of the rays from a red-hot platiniim spiral by different thicknesses of the fluids were obtained. The aosorptions per cent, of yarious fluid plates from 0*02 to 0*27 inch in thickness are giyen in the following table : — Nune of liquid. Bisulphide of carbon Chloroform . . . Iodide of methyl . . „ ethyl . . Benzol Amylene . . . . Sulphuric ether . . Acetic Forroic Alcohol Water II II O'OS. 0-04. 007. 0-14. 6-5 8-4 12-6 15-2 16-6 250 350 460 36-1 4C-5 53-2 65-2 382 50-7 690 69-0 43-4 66-7 62-5 71-5 58-3 65-2 73-6 77*7 63-3 73-6 761 78-6 • ■ « 740 780 820 65-2 76-3 790 840 67-3 786 83-6 85-3 80-7 86-1 88-8 910 0^. 17-S 44*8 68-6 71-5 73-6 82-3 85-2 86-1 87*0 89-1 91-0 1467. InUrrud Absorption of Heat. — It is clearly shown by the experiments of Prof. Tyndall that the absorption of heat is an in- ternal molecular, and not a superficial, action ; and the amount de> pends on the thickness of the medium. This is equally true in respect of light ; for the light of an electric Ump transmitted through 15 feet of pure water, which in a tumbler is absolutely colonrless, assumes a decidedly bluish-green tint. Melloni has shown the same to be equally true with regard to radiant heat : the following are the results of Bome of liis experiments with platea of glass and of seleuite of different thicknesses, the same four Boui ces of heat having been employed : — ThiolnieM in mm.' Loontelli lamp. Red-hoi platinum. Copper ni 40U«C. Copper at 100»C. « ( 007 1 0-5 o (2-6 77 54 39 67 37 24 34 12 6 12 1 0 • I 001 1 ] 0-4 64 38 14 51 18 5 32 7 0 21 0 0 TRAV8CALEHCT OW OASBS. 821 In this table there is a manifest difference, in these two snb* stances, in the piwresidve rate of absorption, both of red-heat, and of the higher dark heat, indicating different values of mole* cular absorptive power. 1468. QitalUy of Badiant Heat. — Many of the preceding re* snlts clearlj indicate the fact that the difference in quality of the thermic rays of different refrangibilities must be precisely analo- gous to that of the luminous rays. Thus of the visual rays trans- mitted by any coloured glass a larger proportion will be transmitted throngh another piece of the same, than through a piece of any other colour : — so in heat ; if plates each 2'6™"' in thickness, of rock-salt, selenite, alum, and oichromate of potash, successively receive the heat-rays from a lamp, and the transmitted rays be again passed through a second plate of the same substance and thickness, the following percentage of the rajs surviving the first transmitted will also survive the second :— Rock-salt . . . 92*3 Selenite .... 91 Alum 90 Bichromate of potash 71 A comparison of this with a preceding table (1461) manifests the great difference that exists in each substance between its ab- sorptive power of the total rays, and of its own transmission : thus alum, which absorbs 91 per cent, of the total heat of the lamp, absorbs only 10 per cent, of its own transmitted rays. Siiuilarlv the beam of an electric lamp concentrated by glass lenses, and falling on the bulb of an air thermometer at 15 feet distance, produces no sensible effect on the instrument : because in its transit through the glass lenses, and the intervening air, the beam has been filtered of all the rays that either glass or air is capable of absorbing. 1 469. Transcaleney of Oases. — An extensive series of researches has, within the last few years, been made by Prof. Tyndall on the transmission, absorption, and radiation of heat by gaseous bodies, not less able and exhaustive, than those of his great predecessor at the Ro^al Institution on the properties of electricity.^ The means of investigation employed was the differential action of two sources of heat on the thermopile, the gas or vapour under examination being interposed on one side of the pile in a tube closed at both ends by plates of rock-salt, and connected with an air-pump : and in some cases, in order to divest the results of any conceivable error arising from the action of vapours on the surface of the transcalent plates, the effects were examined as the vapours flowed throngh the open tube, and also without even the inter- vention of any tube at all. By bringing the radiations from the two sources to an equality, the needle of the galvanometer stood at zero, and was, therefore, in the position most sensitive of small changes of energy. For all the precautionary details of Prof. TyncUtll's ingenious apparatus the reader must be referred to hii RADULRT BEAT. origin&I memoirs, or to his lucid treatise on heat : it need onlj be mentioned tbat, in all observations on the transcalent pro- perties of air, it was found to be absolutely necessary to free it entirely from aqueous vapour and carbonic acid : the first was best removed by passing the air through a tube filled with fragments of glass moistened with strong sulpburic acid, and the second br a tube containing fragments of pure white marble, moistened with caustic potash. 1470. When a Leslie's cube containing boiling water was em> ployed as the source of heat, the pure gases, oxygen, hydrogen, and nitrogen, and consequently air divested of all but oxygen and ni- trogen, were found to be almost completely transcalent to non-lmni- nous or hypospectral heat Olefiant gas, on the contraiy, was found to be very opaque ; and it was ascertained by experiment that for very small densities of the gas, the absorption of neat was pro- portional to the pressure : thus the unit of absorption being taat due to filtered air at mean pressure, and the unit volume oif the gas being 0*02 of a cubic inch, the observed absorptions, and those calculated by multiplying the absorption of one volome by the number of volumes, are given in the following table : — Units. OU. Calc. UniCt. Obs. Calo. 13-2 Unite. Obs. Cafe. 1 2-2 22 6 120 11 24 0 24-2 2 4-5 4-4 7 14-8 15-4 12 26-4 26*4 3 6-6 6-6 8 16-8 17-6 13 290 28-6 4 8-8 8-8 9 19 8 19 8 14 30-2 29-8 6 11-0 110 10 220 220 16 33-6 330 It may here be remarked that the capacity of the experimental tube was 220 cnbic inches: consequently, the density of the atmo- sphere being 1, the density of one measure of gas in the cube was only 0*00009, and the pressure, 00027 inch of mercury. 1471. The vapour of ether was found to be much more absorbent than olefiant gas ; up to a pressure of four inches of mercury the mean absorption was found to be 2*26 timc9 greater than that of the gas, but the ratio decreased gradually wiih increasing pressure, llie law of the constant ratio of absorption to tension was much earlier deviated from in the vapour than in the gas. The absorption of carbonic oxide was found to be about ten times less than of olefiant gas ; but the above law of the ratio of absorption to tension was observed to hold much fifirther than in the latter gas. 1472. The fact of the parallelism of radiation and absoiption wae demonstrated by allowing a stream of heated gases to pass across the mouth of the conical reflector of the thermopile, xhe radi*- ABBOEPTIOV BT OASES. 828 tioni from oxygen, nitrogen, air, and hydrogen were found to be insensible ; while those from four compound ^ases are compared with the absorptions of the same at a tension of 5 inches of mercury : — BmL Aba. Carbonic oxide . . . . 12 . . .18 Carbonic acid 18 ... 25 Nitrous oxide 29 ... 44 defiant gas 53 ... 61 The nearly corresponding pro^ssion of the powers of radiation and absorption is perfectly obvious. It hence appears that those puieous molecules which possess the greater power of arresting, nave also the greater power of imparting, heat-motion. 1473. The absorbent powers of various gases and vapours were •compared at pressures of 30 inches and 1 inch of mercury, the source of heat in these experiments being a plate of copper heated by an uniform jet of gas : the absorptions ot 0, N, and II being in each case taken as unity, the relative absorptions were found to be as foUows : — Ou. 30 in. lln. Om. 30. in. lin. Chlorine . . Bromine . . Carbonic oxide Nitrous „ 39 a • > 90 355 60 160 750 1860 Sulp. hydrogen Sulphurous ac. Olenant gas . Ammonia . . 390 710 970 1195 2100 8800 7950 7260 It appears from this table that the excess of absorbent power in compound above that in simple gases advances greatly with dimi- nished tension : it is also noteworthy that the only coloured gaseous bodies, chlorine and bromine, are the least absorbent. Likewise a striking difference may be observed in the relative absorbent powers of sulphurous acid, and of ammonia, at the two different pressures mentioned. 1474. The entire independence of the relative transparency and transcalency of different substances has just been exemplified in chlorine gas and bromine vapour : but precisely analogous facts may be observed in regard to both liquids and solids. Thus a layer of bromine contained between two parallel plates of glass, sufiBciently thick to extinguish entirely the flame of a lamp, will freely transmit the heat from a copper ball heated to dull redness ; also the absorption of heat by bisulphide of carbon was found not to be sensibly increased by a quantity of iodine in solution, sufficient to render it completely opaque. Similarly lamp-black, though per- fectly opaque to light, is by no means equally so to heat ; on the contrary, it is found to be considerably transcalent to the dark rays. A plate of rock-salt, so smoked as to be perfectly opaque, 824 KADIAST BBAT. will neyerthelem transmit 38 per cent, of the radiatiooB from llie black cube at the temperatm^ of boiling valer. 1475. Absorption by Vapours. — The amount of obserred absorp- tion bj Be viral different vaponrs, at pressures of 0*1, 0*5, and 1 inch, of the heat from Leslie's cube, is as follows: — Yaponr of Bisnlphide of carbon Iodide of methyl . Benzol Chloroform . . . Amylene .... Ether Formic ether . . . .Acetic „ . . . Boracic „ ... 0-lin. 0*6 in. Itn. No.ofaL 16 47 62 3 35 147 242 5 66 182 267 12 85 182 236 5 182 535 823 15 300 710 870 15 480 870 1075 11 590 980 1195 14 620 ■•• ••• 25 From the fourth column of this table, containing the number of atoms in each compound molectile, it appears that the absorbent power proCTesses irregularly with the complexity of atomic con- stitution ; just as friction is greater against rough, nneren surfaces, than it is against smooth ones. 1476. With vapours at a tension of 0*5 in. the absorption per cent of the total heat radiated by the red-hot platinum spiral (which was enclosed in a glass globe with a lateral aperture for free radiation) was as follows : — Bisulphide of carbon . 4*7 Chloroform . . . . 6'5 Iodide of methyl . . 96 Iodide of ethyl . . .17-7 Benzol 20*6 Amylene 27*5 Alcohol 28-1 Formic ether . • .31*4 Sulphuric „ ... 31 '9 Acetic .. ... 34*6 II With the first six of these the order of succe.«sion is the same as that of the fluids from which they were derived, but in the four last the order is varied thus : — • Liquids. Sulphuric elher. Acetic ether. Formic ether. Alcohol. Vspoors. Alcohol. Formic ether. Sulphnric ether. Acetic ether. This apparent deviation from the general law that the pR>> perties of radiation and ab8or|)tion are molecular, aud not de- pendent on the liquid or gaseous form, may be readily explained. The vapours at a constant pressure do not contnin equivalent quantities of matter: if, however, the specific gravities of tha fluids be divided by their vapour-dettsities, equivalent vaponr- 47 Roeemary • . 74 60 Chamomile . . 87 65 Cas8ia . . . 109 68 Aniseed . . . 372 ▲B80BFT10I BT AKOMATIC YAFOUBS. 826 Tolames will be obtained ; and if equal portions of tbeae be taken, the order of succession is foona to be the same for both fluids and their vapours. 1477. Ahaorptionhy Aromatic Vapours, — ^The vapours of variourt aromatic essential oils were introduced into the testing cylinder, and the absorption in anits of filtered air was in— Sandalwood . 32 | Neroli . . Clove . . . 33'5 1 Lavender . Bose . . . 36*5 | Lemon . . Beigamot . . 44 | Thyme . . As the density of these vapours must be exceedingly small, it is evident that they roust possess, in common with other hydrocarbons, a very high absorbent power: but how much of the above diffe- rences depends on specific absorption, and how much on vapour- density, has not been determinea. It was fui-ther observed by Prof. Tyndall that although oxygen in its ordinary condition is very slightly absorbent, it is consider- ably so in its allotnipic form of ozone, rrobably the dense volume of ozone obtained from the ozone-generator already described (824) would have presented an almost opaque medium. 1478. The heat generated by friction when air was admitted into the nearly-exhausted testing cylinder, and the cold resulting from its expaniiion, when withdrawn by an air-pump, were alixe de- monstrated, wherever a feeble atmosphere of some good radiator was present to tell the tale ; and the relative radiations from the simple and compound gases themselves, when similarly admitted into an approximate vacnum, and subseouently withdrawn, were closely in accoi-dance with their observeu absorptions (1473). It has likewise been shown that if a heated body, whether solid or even gaseous, be coated or varnished with a layer of a good ga* aeons radiati)r, the radiation will be augmented ; just as the rama* tion of a metallic surface is increased hy ordinary varnishing. 1479. Internal Radiation. — ^The fact that radiation of heat is not a superficial, but an individual molecular, action has been fully established by the observations of Mr. B. Stewart on rock-salt ; from which it appears that the amount of heat radiated from plates of rock-salt of difierent thicknesses, and heated to the same temperature, increases with the thicknesa of the plates. The same observer has also shown in a round-about way that if fi be the index of the mean refraction of heat by a given transpa- rent medium, the amount internally radiated to a fixed unit of surface external to the medium will oc — |. The truth of this is evident from an inspection of Fig. 573, from which it appears that, K E and B p being the corresponding directions of incidence on the sur&ce of the medium, and refraction out of it, the heat radiated from a circukr area of which the radius Vi dk towards th« 826 SADIAHT BBAT. point, B,^ will be diBtributed bj refraction over the area of wbich l^e radius is cf\ and as the ratio of these areas is as e/* : dJ^^w AS fi* : 1, it follows that the amount of those rays of beat that reach an unit of the surface ef will oc — | : q.e.d. The same dependence of radiation on thickness has been shown hj Prof. Tjndall to be true for gases. From columns 3 and SS inches in length of four different gaseous bodies similarly heated bj frictioni the following radiations were obtained : — defiant gas Sin. 39. . . 33 in. 63 Sulphuric ether vapour . . . „ 1 1 . . . „ 64 Formic „ „ . . . „ 12 . . . „ 09 Acetic „ „ . . . „ 15 . . . „ 70 Here it appears that from the denaitj of the defiant gas, a considerable portion of the heat-rajs from molecules in the hinder part of the long tube is absorbed by the molecules in front of them, therefore the total radiation is not at all diminished in pro- portion to the diminished length of the radiating mass : but the much more attenuated vapours offer far less obstraction to the waves from behind, although their influence is still considerably felt : thus while in defiant gas, the volumes of the radiating matter being as 11:1, the radiations are less than 2 : 1, in sulphuric ether the radiations are nearly 6:1. 1480. Ahnorption by Aqueous Vapour. — ^It most be remarked respecting this, the most important to organic existence of the re- lations of heat and matter, that the term " vapour" has been as much popularly misunderstood, as that of " steam.'' That which we see hovering over the meadows in a summer evening, called in common parlance " vapour " is not vapour at all ; — it ceased to be vapour when it became visible : just as steam (the vapour ot boiling water) ceases to be steam when it becomes visible. Both alike are merely minute particles of water (eroundlessly assumed to be vesicles) floating (sometimes electrically suspended) in an atmosphere, of which the temperature is so reduced as to render it incapable of holding them any longer in solution. Takine as before the absorption of filtered air as the unit, it appearedthat with the atmosphere in its average state of moisture, the absorption was about 70 ; it was also found that when filtered air was saturated by passing through a U tube containing frag- ments of glass moistened with distilled water, the absorption amounted to 98. It was also found that in saturated air the ab- sorption progressed uniformly with the density : the observed are here compared with the calculated results : — PreMora. AhBorptioa. 20 in Obs. 64, Calc. 64 25 II • • • II 82, „ 80 Frenvre. Absorption. 5in. . . . Obs. 16, Calc. 16 10 ,1 ... „ 82, „ 32 1 ,1 • • • y, 49, ff 48 Ov ti • • • tt 9o> II 96 QUALITATITB ABSORPTION. 827 For Tarioas climatic applications of these physical facts the reader is referred to Prof. I'yndall's excellent treatise. 1481. lnfiv£fnce of Temperature on Absorption. — Hitherto the quantity of heat absorhedl)/ vapours has been alone considered; bat different resalts will be obtained when the qiMlity of heat is ▼aried by change of temperature. Il is evident that in order to enable the moiecnles of a substance to *' absorb'* or take np any particular kind of wave-motion, there must be a congruence be- tween the period of vibration of the wave and the molecule, and the oft exemplified analogies of light and heat irresistibly lead to the inference that the same kind of selective absorption, which is seen to take place in the various phenomena or colour, takes place equally with regard tc the rays of heat. As the temperature of an incandescent hody, the platinum spiral for example, is raised, it visibly emits in succession rays belonging to the higher portion o( the spectrum, and if the light- and heat-rays belonging to the same point of the spectrum, i.e., of the same degree of refran^- bility, be not identical, they must at all events be isoperiodic. Hence it is easy to conceive that this kind of selective absorption may take place in gases, and therefore that the relative absorp* tions may not be the same for heat of different wave-periods ; and such is proved to be the fact. Although the introduction into the heat-beam of rays of higher refrangibility necessitates the increase of the intensity of toe total beam, it must be borne in mind that the variations of absorption depend not on the increased intensity of the heam^ but on the varied quality of the rays. The absoi-ption by various vapours of the heat emitted by the platinum spiral, at fiur different degrees of incandescence, was observed, and the following values per cent, of the total radiations were obtained :-^ Name of Yapoor. Barely ▼isible. Briehfc red. White heat. Near fuBion. Bisulphide of carbon . Chloroform .... Iodide of methyl . . Todide of ethyl . . Benzol Amylene .... Sulphuric ether . . Formic „ . . Acetic „ . . 6-6 9-1 12-5 21-3 26-4 35-8 43*4 46-2 49-6 4-7 63 9-6 17-7 20-6 27-5 31-4 31-9 34-6 2-9 6-6 7-8 12-8 16-6 22-7 26-9 251 27-2 2-6 39 ■ • • • • • • • . • •• 23-7 21-3 The diminution of absorption by increase of temperature may here be remarked throughout, but the relative amount of absorp- tion by different bodies at different temperatures varies con- siderably : thos in the bisulphide of carbon tne ratio of absorption 828 ' R1.DI1.HT HB1.T. of barely ^inible to that of white heat is as 2*24 : 1, wfafle in chloroform the same ratio is only 1'62 : 1 ; from which it apoean that chloroform absorbs both absolutely and relatively more neat- rays belonging to the visible spectrum, than bisulphide of carbon. On referring to the absorption by vapours of heat emitted by Leslie's cube (1475), it will be seen that the ab^rption of chloro- form considerably exceeds that of iodide of methyl, thus again de- monstrating the selective power of absorption. Again, while sul* phuric ether absorbs less rays from the lower end of and beneath the visible spectrum than formic ether, it absorbs absolutely more ravs i'rom the higher sources, and especially from the highest of all ; hence its relative absorption of the highest rays mast be con- siderable, and it may be said that formic ether is much morv ther- mally " blue " or " violet '* than sulphuric ether. 1^1. Radiation from Flamet, — ^The absorption percent of the rays emitted from the brightest portion of a jet of g^ was com- pared with that of the heat accompanying the feebly luminous rays of a Bunsen's burner, in which the gas is mixed with air hefare ignition^ and the results were : — Jet Ban. Jat Bub. Bisiilph. carbon 9-8 Ill \ Amylene . . 30*2 24-2 Chloroform . . 12 0 6 2 \ ; Formic ether . 34-6 33-3 Iodide of ethyl 196 140 1 ; Sulph. ether . 35-7 31-9 Benzol . . . 22-0 179 ■ Acetic ether . 38-7 36 3 It^ here appears that the relative absorptions of amylene and formic ether vary considerably, while in bisulphide of carbon and chloroform the amount of abaorption is reversed. The capacity of (gaseous bodies to absorb their own radiations was conspicuously demonstrated in the absorption by aqueous vai>our of the heatrajs emitted by a flame of hyarogen gas, which mainly consists of incandescent aqueous vapour: tne atmosphere in its ordinary state of humiditv was founa to absorb more than 20 per cent. ; and even a thin layer of water proved equally ob> structive to the rays from the hydrogen flame. The power of aqneoos vapour to transmit the heat-rays of high refrangibility, but to absorb the lower rays is the chief and potent means of iire venting the undue dissipation of terrestrial heat by radiation from the earth^s surface. These, being hypospoctral rays, are frequently almost entirely anvsted by the aqueous vapour combined with the atmosphere. The S'imeprinciple was not less manifest in the absorption by carbonic acid of the rays fiom a flame of carbonic oxide: so much so that the physical test of ab> sorption was found to be nearly as accurate as the chemical test of combination, for the quantity of carbonic acid emitted from the lungs in respiration. The relative absorptions, by dried carbonic acid and olefiant gases at various pressures, of the heat emitted by a carbonic oxide flame are as follows : — In. O.G. O.A. ] ; !»• O.G. C.A. 1 . . . . 23-2 . . . . 480 ; ; 4 . , . . 50 6 . . . . 65 1 2 . . . . 34-7 . . > . 55.5 ; 5 . . , . 55*1 . . . . 68-6 3 . . . . 440 . . . . 60-3 \ ! 10 . . • . 65.5 . . . 74.3 829 1483. PdarizatUm of Heat, — Bays of heat are capable of being )K>1arized bj processes analogous to those by which light is pola- rized (Chap. XXI.) : these phenomena were first investigated by Principal Forbes. If a ray of heat be refracted through a very thin plate of brown tourmaline, it emerges partly polarized in one plane, the polarization being never so complete as when light is similarly treated. If the emergent ray be incident upon a second similar plate, it will be partly abflorbed, and the rest transmitted or dispersed, according to the positions of the axis in the sections of tourmaline. When the axes of the two plates are parallel, a considerable portion of the heat transmitted by the first plate iMisses the second also, and may be measured by the thermopile ; out if the axis of the second plate be at right angles to that of tho first, the greater portion of this heat will be absorbed. By com- paring the quantity of heat which reaches the thermopile, when the axes of the plates are parallel, with that which n*ache8 it when they are crossed, the proportion of heat polarized by the first tourmaline may be ascertained. 1484. The most satisfactory evidence of polarization U obtained when plates of mica are used instead of tourmaline. These should be split extremely thin, and a film should be ignited for some time in a clear fire. By the action of heat, the film becomes split into innumerable laminfe. and then is capable of exerting an exceed- ingly powerful polanzing power on heat and light. These i(;nited films need never be more than 0*001 inch in thickness, and should be placed in wooden or pasteboard tubes, to allow of readily mani- pulating with them. The films of mica thus prepared should be so placed either in the wooden tubes, or on the frames of thin wood, that the rays of heat may be incident upon them at an angle of about 56**. When beat is incident in the direction c, upon one film placed as shown at A, Fig. 699, a large proportion of it emerges polarized, and this will be either trans- j« ^^^ mitted or absorbed by ' a second inclined plate, ^S. /N^ according to its posi- ^s^ > ^^7 \b] tion. It will be trans- ^-^^ ^—^ U--^ mitted if the plates be 1* 2. parallel, as at 1, and absorbed if they are crossed as at 2, just as would happen to light, under similar circumstances. In this manner the following proportions per cent, of radiant heat from difierent sources may be polarized : — Argand lamp 82 Incandescent platinum 79 I I I t 880 RADIAVT HSAT. Brass heated to 440" C. 68 The heat from ditto transniitted through glass . 73 Boiling-water • 49 1485. Principal Forbes sncceeded in polarizing heat by refrac- tion through thin inclined plates of rock-salt, just as light is pola- rized by a bundle of glass plates (1217) ; when heat was incident at 35", ne found that with three plates, one seventh, and with six, one half, of the incident ra.ys were polarized. When plates of split mica were arranged so as to reflect inci- dent heat at an angle of 56", heac from three different sources was polarized in the following proportions per cent. : — Red-hot platinum, 65; brass at 440" C, 61 ; Argand lamp, 65. These last results are explained by the angle of incidence pro- bably approaching nearer to the polarizing angle for beat ra- diating from red-hot platinum, than to that of heat from the two other sources ; as the same observer has proved that heat of diffe- rent refrangibilities is unequally polarizable. 1486. It has been observed by M. H. Knoblauch* that when rays of solar heat polarized by transmission through a Nicol's prism are incident on a bundle of parallel plates of glass, the amount of transmitted rays is augmented, as the angle of incidence increases from 0" up to about 55", the polarizing angle, when the plane of refraction is perpendicular to the plane of polarization ; and it is a maximum at tne polarizing angle. With three plates, the amount transmitted is increased by about one-fourth, and with twelve plates, it is more than doubled by inclination. When the plane of polarization coincides with the plane of refraction, the amount of transmitted heat is always diminished, and mors rapidly as the number of plates is increased. 1487. It has been shown that polarized light is prevented reaching the eye by crossing the tourmalines fl215): and when reflecting plates are employed, by placing the planes of reflection and polarization at right angles to each other (1218). If a thin plate of mica, or selenite, bo placed between the polarizing and analysing plates, it causes the polarized ray to undergo a physical change termed depolarization (1330), by which it is enabled to undergo reflection and transmission, producing a brilliant display of complementary colours. Precisely analogous phenomena oocnr in the case of polarized heat, and are readily detected by the ther- mopile ; but, of course, no vinble effects occur, as is the case with light. 1488. The depolarizing effects of a thin film of mica are best observed, on account of the great diathermancy of this substance. For this purpose, let the heat radiating from any source, as a coil of platinum wire ignited b^ the flame of a spirit-lamp, a. Fig. 700, be polarized by refraction through the inclined film ef * Poggendorff, Amisleo, May, 1886. OIBOULAB POLABI«ATIOar OF BXiff BT BEFBACIIOH. 831 mica, A, in the manner before explained (1484). These rajs will be partly intercepted by the second mica plate, b, bo that bnt 21 per cent. wUl reach the thermopile, d. Having observed the e£fect Fiff. 700, on the galvanometer, produced by these transmitted rays, place between a and b, a film of mica, c, and if the optic axis (1202) of the film be inclined to the plane of polarization of the rays of heat, an increased deflection of the needle will be observed. This arises from the plane of polarization of the heat refracted through a, being altered by the doubly refracting film of mica, c, and thus a portion of the heat previously absorbed by b, now becomes enabled to traverse it. In four experiments, Principal Forbes found that the proportion of heat thus depolarized, when the optic axis of the film was inclined 45^ to the plane of polarization, compared with that which reached the thermopile wnen it corresponded to that plane, was as 126 : 100, 120 : 100, 120 : 100, 113 : 100; the mean of which is the ratio of 120 : 100, or of 6 : 6, very nearly. When the principal section of the mica plate, c, corresponded with the plane of polarization, no depolarizing eSeci was observed, pre- cisely as in the case of light. 14^9. Circular Polarization of Heat. — This has been efiected in two modes, by refraction through an exceedingly thin film of mica, and by FresnePs method of internal reflection. A test of the circular polarization of heat is found in the fact that if whilst the polarizing plates a and b. Fig. 700, are crossed, so that a mi- nimum of heat reaches the thermopile, a bod^r be interposed between them, capable of con verting the rectilinearlyintocircularly polarized heat, it will produce such a physical change in the thermic rays passmg through b, that no great difierence of efiect shall be shown by the thermopile, in whateverposition the analysingj^late is placed. 1490. A film of mica, which in ordinary polarized light ap- peared of the pale reddish-white colour of the first order of X^ewton's rings (1135), and which so far interfered with the plane polarized light as to partiallv convert it into circularly polarized tight, was first employed. When introduced between the two sets of mica plates, a and b, this film produced such a physical change in the heat, as to cause it to reach the thermopile in nearly equal proportions, whether the polarizing and analysing plates were parallel or crossed. When mcandescent platinum was employed aa the source of heat^ the quantity of circularly polarisea heat 832 KADIAHT BBAT. irUch thns passed the analysing plate under the iDfloence of tho mica fihn, amounted to 40 per cent, of the whole quantity whidi would have passed if ▲ and b were parallel, and the film absent. 1491. A very ingenious mode or causing plane polarized heat to ac<^nire the same properties was contrived oy Principal Forbes in imitation of Fresnel s mode of obtaining circularly polarised light by internal reflection (1259). For this purpose he procured a rhomb of i*ock-8alt haying two angles of 45**, and of sufficient length to allnw of the emergence of a ray after two internal re- flections. The most convenient arrangement for the experiment is shown in Fig. 701, where s is the source of heat, i, the pola- rizing, and K, the analysing mica plates placed in tabes of wood, JV* 701. and B is the rhomb of rock-salt. It was found that when the plane of reflection in b corresponded with, or was perpendicular to, the plane of polarization, the rays underwent no change, and either emerged from, or were absorbed by k, according to its posi- tion : but when the plane of internal reflection in b was inclined at an angle of 45" to that of polarization, the rays emei^ged from B, circularly polarized ; and neariy an equal proportion of them passed through k, whatever angle its plates formed with the pri- mitive plane of polarization. Repebbkces. The treatise on heat in the " Encjclopndia MetropoUtana" is an able digent of all that was known of heat at the date of its appear^ ance; and the "Elementary Treatise on Heat,'* by Mr. Baifour Stewart, comprises most of the important investigations of more recent continental observers. But by no one has so great an ad- vance been made in the amount of existing knowledge of the nature and properties of heat as by Prof, Tyndall ; and to his ad- mirable treatise on " Heat Considered as a Mode of Motion,'* the reader must be referred for many important details, the insertioD of which would have inconveniently extended the dimensions of this work. The original memoirs of Melloni, Fourier, Pre vest, Duloog and Petit, Clement and Desorraes, Forbes, Despretz, Regnanlt, Wiedemann and Franz, Favre, Siibermann, Andrews, and others , may with great advantage be consulted. LIST OF TABLES. J^J3.—Tk« numb$ri refer to paragraph §, not to pag§9. Abforption of heat bj fluids It ft |j"BCB ••• ••• a.. ,,, n f» perfiimes n M .• at different tempentares If II BOllQB ••• ••> >•• ••> „ ,1 Taponra ... Adhesion of varioas floida to glasa ,1 metals to mercory Amounts of reflected heat Boiling jpolnts of fluids CapiUiuncy of fluids Compasa-dsTiatlons in iron ships Compresiiibility of liquids ConuuctiTity (electric) of metals Crystals exhibiting dichroism Density of water at different temperatures Diamagnetic bodies DifiVisiye powers of ffases DisperslTe powers of various bodies Elasticity of various bodies Electrieal relations of various bodies H rosistance of metals and alloys Electro-positive and negative elements Elementary combinations of pore mechanism Elliptic optical constants Expansion, by heat| of solids •A y I U UlUo •■• ■•• ••• ■•• * A M laH^S** ••* *•■ ••• ••• „ „ water at various temperatures ... Heat-conducting powers of metals n n materials of dothing PI pf W^OOuS ■•• ••« ••■ ••« Heat reflected flrom various bodies Heating of metallic conductors by electricitv Height of the barometer in different latitudes n „ n at different altitudes Indices ofrefraction of various bodies „ „ Fraimhdfer's lines Intensity of light in differentparts of the spectrum . . . Light lost by reflection at dlflerent angles Magnetic and diamagnetic bodies HagnUyiug powers of the compound microscope Memng pmnts of various bodies 3 H • •• • •• 1406 ■ •• 1470. 1473 • •• ■ •• 1477 • •« • • • 1481 • •• • •• 1461 «■■ • •• 1476 ■ •• • •• 35 • •■ • ■• 35 • ■• • •» 1440 ••s • ■• 1413 • •• • •• 87 • •• • •• fl07 • •• • •• 382 ••• • • ■ 805 ■ •• • ■« 12S0 ■ •• • •• 422 • •• ••• 648 ■ •■ • • • 47 • ■• ■ •• 1097 • •• • • • 280 ■ •• • ■• 667,668 « •• ■ « ■ 9^,943 • •■ • •• 764 • •• • •• 160 • •a • •• 1279 • •■ • •• 1350 • •• • •• 1361 ««• • ■ ■ 1362 ■ • • • ■• 1361 • •• • •• 1373 • •• • ■• 1380 • *• ■ •■ 1375 ■ •• ■ • * 1440 • •■ • • • 733 m sm »•• 493 • •• • •• 419 • •• • •■ 1067 • •■ • •• 1101 • •■ ■ ■ • 1104 • •• • ■ ■ 1031 ■ •t • ■« 648 • • • • •• 1164 • •• • •a 1407 834 LIST OF TABLES. Miudcal intoiTolB ... ... ... ... ... ... ... ... 670 Komben of reflections required to polurize light 12S3 „ teeth and Btaves in wheels 189 „ Tibrations in coloured mjs 1087 Optic axes in uniaxial crystals U08 „ „ biaxial ciystals ISO PrassureofaqueousTapour atTBrioostemperatares 519 „ steam „ m ... ... ... 680 ProjMftioDB of heat transmitted through rock-salt 1468 RJMiating powers of various bodies 1467 Bates of cooling by radiation 1438 Beflection of heat from TarioussurfiMses 1410 Befraction of coloured rays lOM Belative temperature and pressure from 211° F. to 213° 1412 Besistances of TariouB bodies to oomprossion 18 Botation of the planes of polarization 1288 Specific gravities of solids, fluids, and gases 425 „ heat of solids and fluids 1902 M yi ICfUSvB ••• •■• ••• «•« ••■ ••• ••• ■•• A^HFS Temperature variation of dectric condQctivity 9^949 Tenacity of various metals 15 Thermoelectric series of metals 982 Tranacalen<7 of solids 1461 M UulQB ... ... ... ... ... ... ... A^K^v ff gases ... ... ... ... ... ... 147vy 1473 „ aromatic vapours ... ... ... 1477 •y T ttpOUlD ••■ ••• ••• •«• ••• ■•• ■■• A»V W Variahons of concert-pitch in music 671 „ magnetic declinatioa 609 „ „ inclination €14 Velocity of sound in some bodies 646 M wXDClo sst ••■ ••• ••■ ••■ ••• ••• «•• 09v Width of coloured bands in the solar speotnim 1083 ALPHABETICAL INDEX. Jf.B. — Tht number9 refer to paragraphe, not to pagee. ABB AIBI AIB Abemtion, ohromatio— , 1119;— of Hght, 1023 ; leaat mrole of—, 1047 ; —of a reflected ny, lOM; spheri- reotion of— lor temperfttnre, 487; diurnal variation ot— , 400 : mean diurnal height of — , 491 ; mean height of—, 403 ; mercurial — , 484 ; sel^registering— , 405 ; stuidard— , 486; syphon— ,485. Bart9n'9 buttons, 1139. Battery, electrio— , 724^ 726: tbet^ mo-dectric— a 968, 909; voltaie— , 766—796; Bun9en*»—, 777; Ontik- tkan^t^, 793; DamieiTa—^ 794, 795; frog—, 990; Oro9^»—t 796; SS-, 819, 820; L4e$im*»—, 781; arie Davy't—, 792 ; IfMOoO— , 779; Pulverwuuker'M — , 790; JKe- hertiTi—, 780; SeAoii6«wi'e— , 773; Sme^i—, 771, 772 ; fitrinafdlot^9^, 791; froUa«to»'»— , 703. Beam and scales, 114. Beats in music, 649. Beequtrelf on electrolysis, 632; his battery, 835 ; thermopile, 971. Bell-erank work, 221-223. Bells, electric—, 711, c. Bent lever, 112, 118. BemotUUPa formula for gMeoos em^ rents, 621;— theory of the tides, 473. Bevilled wheels, 177. Biaxial crystals, 1206, 1207. BiiHar magnet, 622 Binocular vision, 1195; — mioroaoope^ Wenham'*, 1163. Biot, on circular polarisadon, U87 ; — ^polariscope, 1217, 1218; static laws, 673. Electro-thermic effects, 976. Blectrotype, 776. Elliptic constants, 1279; — mirror, 1050 ;— pohurization of light^ 1276— 1279 ;— wheels, 236, 286. 840 IKDKX. BND FIE Sndlemband, 209: mode of shiftiog — . 218. EndleM screw, 202 ; diBgnised— , 206. EndoBCope, 1199. Sudounose, and ezo9inoee» 44—46; — influenced bj ft Toltaio oorrent, 46. Epif^oloidel teeth of wheeb, 183^ Equator, magnetio— , 612. Equatoiial moanting of telesoopefl, 1145. Equilibrated arch, 103—106. Equilibrium of a solid on its base, 93; stable—, 94, 06; unstable—, 96; indifferent — , 97; — ^related to path of centre of gravitV, 96—100 ;— of an arch, 104 ; — of the same in practice, 106— 108;— of fluids. 884, 886 ;— of the ocean, 473 ;— of floating bodies, 404, 406 ; stable or unstable—, 407, 406. EquiTalent, dynamio^, of heat, 1845. Errors, index-, 1366. Escapement, 266; verge — , 267; an- chor or lerer^, 268. Establishment of a port, 476. Evaporation of liqmds, 618;— in ani- mals, 1427. Exceptions to law of expansion b; heat, 1353. Exobangee, theorr of—, 1486. Excitation, electiie, 654. Exhausting syringe, 503. Expanding puller, 246. Expansion, cubical—, 1350; linear — of solids, 1850;— of liquids, 1361; relative— of glass, water, and mercury, 1861 ;— of intses, 1852. Extension, a property of matter, 8. Extrados of an arch, 102. Extraordinary ray, 1200, — ^refraction, 1061. Eye, the, optical structure of—, 1179 —1188 ; adaptation of —to focal distances, 1186 ; inversion of images in—, 1183. Eye-piece, Suygtn^ at the negative — , 1169 ; Ram$d«n'$ or the positive — , 1160. Fakrtnkeifi helioeUt, 1177; — ther- mometer-scale, 1868. Fabe balance, 116. Faradojf, researohes in diamagnetism, 641 — 648;— on induction, (wl ;— on magneto-electric indttotioQ, 904; — on organic electricity, 979; — on the action of magnets on polarized light, 1266 ; toUe of electnos, 668. Ferrotype, 1316. Field, magnetic, 698. FIG Figure of the earth, 324. Fire-engine, 410. Fire-damp indicator, 48. Fishes, electric, 976—081. FUgrw, ^(/m., forecasts of 626. FlexibiUty, 13. Flight of a rocket, 817. Floatation, plane of—, 406. Flosting battery, De la Biv0'» — , cnr j Floating bodiee, fluid diaplaoed bj — , 404 ; equilibrium of—, 406—407. FldVentine experiment, 881. Fluids, oompreseibiHty of — , S81; elastic ana inelastic— , 880 : expan- sion of— by heat, 1361 ; mobili^ of their particles, 379; downward prea- snre of—, 892; lateral presanre of — , 808—400; upward pressure of—, 397 ; pressure of—, in conical tabee, 486; resultant of pressure of—, 402, 403; properties of—, 379; spouting—, velocity of—, 4S6k 487 ; surface of— hbriaontal, 387; velocitT of— in tubes, 481 ; unduladoaa of—, 463—471. Ilnoreseence, 1113, 1114. Fooal length of lenses, 1072 ;— of mir> mirrors, 1039— 1041;— of a sphere, 1069. 1070. Fooal lines, 1048. Foci, coigngate— defined, 1090. Focus, neffim?e— defined, 1046 ; prin- dpsl— defined, lOia Fin'o«$, researches on the refraetioiB, and polarisation of beat, 14B3— 1491 ;-thermopae, 1441. Force, accelerating—, 273; centrifbgal — , 380— 885 ;— related to time, space, and velocity, 305$ electro- motive—, 802. Forced vibrations, theory of—, 680. Foroing-pump, 437. Foreeasts of weather, 626. Form an attribute of matter, 4. Forms of cams, 264 ; — of pulleys, 210 —216. Foucaulft glass speculum, 1068; mode of silvering—, 1068. Fountain, artifictu— , 482,611,0.; FranUinic electricity, 664—700. JF^utMin'i electric kite, 761 s-thrni- der house, 768. Frammk^€7'9 lines, 1099. Freesing in vacuo, by evaporatioo, 1420, 1421;- in red-hot vsbmIs, 1417. lVwn«r« experiments on interferenoe of light, 1123;— laws of poJsrised light, 1229;— rhomb. 1269. Friction, 62; a uniform retardiBg IKDEX. 841 TBO OSO aRO force, 64; ooefBdent of—, 66;—' of cordage, 66 j — of flaida, 434 ;— rollers, 67. Frog-bstteiy, 900 ;— rbeoaoope, 991. IfQlgaritea, 769. Pusee, the, 246. Fnaion, temperatare of—, 1407; in- flaenoeofmiztore of elements on—, 1409 ;— of pressure on — , 1408. Fose, Armtiron^t ooxtcusaion— , 280. OaUUtft telescope, 1171. Qalvam'i discoveries, 989. GaWanic knife, 816; — cautery, 816. Galranometer, 856; astatic—, 866; <7a«^«»'« tangenc— , 861 ; Tkomp^ ton* 9 marine—, 860; reflecting'—, 869. OalTanoscope, MaiteuceCt, 991. Oamnt in music, 668. Oases, condensation of—, 14S9 ; dif- fusion of—, 47 ; law of pressure of — , 488— 600;— liquefied by pres- sure, 10; relatiTe expansion of—, 1362; specific gravity of—, 423; specific beat of—, 1394; traiMpira- tion of—, 48. Oas-batiexy, Ofwo***— , 819, 820. Gas-engine, Lenoir^B — , 629. Gaugain's tangent galvanometer, 881. Gauge, air-pump—, 607; syphon—, Oauti^ agonic lines, 609. Gttuing, 178. Generating plate, 768. Geneva stop, 248. Genou, the, 130. Geometrical focus of reflected rays, 1039 ;— refracted— , 1066. Oersers explained, 4SB. Oiilett'i condenser, 1167. Glass, unannealed, optical properties of—, 1262 — 1266; photographic processes on—, 1323— 1330 ;— spe- culum, JVii«aai//'a — ^,1052; mode of silvering—, 1063. Gold, ductiHty of—, 12. Gold-leaf electroscope, 662. Oorkam*» colour-top, 1092. Grave harmonics, MB, Gravitation, 68; law of— , 69; con- sequences of—, 60—62; lateral—, 60. Gravity, centre ot-^, 75, 76 ; aeode> rating force of—, 296—300, Gravity, specific— v defined, 11;— of gases, 423;— of fluids, 416—400;— ofsolids, 412—416. Oregoty'i telescope, 1148. Gridiron pendulum, 854—366. Grooves in pulleys, forms of—, 210. HJO Qrovt^t air-pump, 606;— battery, 796; —gas-battery, 819, 820. Gulfstream, 1386. Gynmotus electrieus, 978; Faradag on the — , 979. Gyration, radius of—, 346. Gyraaoone, the, 866—367; theory of """, 366. Gyrometric governor, Sinuiuf — , 461. Haldatt on fluid pressure, 392. Hardness, 9. Harift hydrometer, 410. Harmomc sounds, 676. Hartuft unit jar, 737. HawlctbM*$ air-i)nmp, 604. Heat and light, identioal in their n^ ture,1437. Heat, absorption of— by gsses, 1470 —1473;— liquids, 1466 ;- solids. 1461 ; — ^vapours, 1475 ;— perfumea vapours, 1477; — in liquefaction of souds, 1400; — formation of vapours, 1406 ; chemical action of—, 1490; cir- cular polarixation of—, 1483; — by internal reflection, 1491^ — by re- fraction, 1486; conduction of—, 1373 ; convection of—, 1382, 1383 1 decomposition of water by — , 1481 1 dynamic theory of—, 1344 ; — equi- valent of—, 1346 ; evolution of—, by solidiflcation, 1401: expansion of 'fluids by— 1361 ;— of gases— , 1362 ; —of solids— ,1360; latent— , 1397 ; polarixation ^— by mica, 1484 ;— by reflection, 1491 ; — by tourmalines, 1483 ; proximate causes of—, 1343 1 radiant—, 1433; refraction of — through lenses, 1443 ; — through prisms, 1444; relations of — and cold, 1348; specific—, 1388— 1394 1 terrestrial—, 1432 : theoiies of—, 1342. Heat-spectrum of electric lamp, 1446. Heeling error of oompass, 607. Heliacfu conductors, 876. Heliostat, FakrenluUt—, 1177; SO- hermamie»—t 1178. RelmhoUt^ resonator, 639. Hemihedral forms of crystals, 27. Hemispheres, Kacdeburg — , 611, a. Hemitrope orystus, 28. SeiUsf'9 electrometer, 710. Herapathite, 1216. Heneh4L Sir J., researches in pho- to^aphy, 1816—1321 ;— table of lu- mmiferous undulations, 1086;— on animal electricity, 1016. Heterogeneous organic snbstanosa produce a current 1013. Hiero'a fountain, 448. EjortVB electro-magnetio engine, 886. 842 INDEX. HOA IKD Hoai^froat, 14S0. HaU^ indaotion machine, 701, 702. Hook^9 joint, 247 ; Tolocitj-ratio in ~, MB : ooropoand— , 248 ; itla8tra> tion oi— , in the aoimal economr, 260. Horuontal sorfaoe of a fluid at rest, 884,386. Horseshoe magnets, 635. Hot-water apparatus, 384. Homonrt of the ^e, refraction of the — , 1180. HwUer'a aoreWf 144 SMggetu^ eje-pieoe, 1 169. Hydraulio engines, 459 ; — lifting-jaok, 396; — ^panohingmaobine, 395; Bra- mak'§ — press, §94 ; — ^ram, the, 441. Hjdro-electrio machine, 698—700. Hydrometer, the, 418 ; Hart't—, 420; mekoUm't--, 419 ; Sgke$'$—, 418 ; Hydrodynamics, 426—476. HydrosUtics, 379->42o. HydrosUtio bellows, 393 ;~leTe1 388 ; -—principle of Arekimede$, 400. Hygrometer, DaitUU'§, 1424; Afo- «>»'»-, 1426; SeffnoHlft—, 1426; P§Uiwr'§ thermo-eleoirio — , 970. Hyperbolic mirrors, 1030. Hypospeotral rays not luminous, 1464. Ice-makinff machines, 1420. Identity of nature of light and heat, 1487. Idio-eleetrics, 657. Idle wheels, 226. Illumination, law of—, 1082;— of microscopic objects, 1165; dark- ground—, 1166 ; oblique — , 1167. Imsgea, formation of—, by lenses, 1077; — by mirrors, 1044, 1046; duration of— on the retina, 1189. Impact, direct — , of elastic bodies, 203—295 ;— of inelastic bodies, 291, 282 ; nature and effects of—, 297. Impenetrability of matter, 2. Incidence and reflection of elastic bo- dies, 296; angles of-of light, 1333. Incidental colours, 1190—1193. Inclination, magnetic — , 611. Inclined plane, 140 ; equilibrium on the—, l4l, 142; Telocity acquired on the— J 326. Indestructibility of matter, 8. Index of refraction ; 1057 ;— errors of thermometers, 1866. Indici^or (electric telegraph), 915. Induced rotation, 912, 913. Induction, electric, 676—678 ; electro- dynamic — , 871—914; — machine, SoW^—» 701, 702; magnetic—, 696, 696; speciflo— , 680. Indnctorium, XAiiTe, 90S I M0urd9^» — , 902 ; ^MJkMiborf 'e— , 901 ; Sle- «eiM and Kalmh?*—, 906. Inertia, 278; effects of—, 279; mCK ment of—, 846. Inferred nature of solar photocpheret 1111. Inflection of undulations, 407s^-of sound, 665 ;— of lieht, 1128. Insects, electric — ^ 982. Insulated wire, 856. Insulation, electric, 659. Intensity armature, 906 ;— of deetric charge, 674 ;— of sound, 634— 6M. Interference of light, 1121—1139 ;— of sound, 640, 5w ;— of nndnUtioiw, aeo. Intervals in music. 674b Inteados of an aron, 102. Inversor, electric, 854. luTisible spectrum, lines in the, 1116. Involute teeth of wheels, 186w lodo-quina, sulphate of, 1216. Iron, passive, 778. Irrationality of the spectrum, 1098. Isochroniam of vibrations, 378; — of the pendulum, 831, 332. Isoclinal lines, 612. Isodynamio lines, 627. Isothermal Unes, 1387. •ToeoM's electetvmagDetio engine^ 88(; — method of magnetiiing, 634. Jacketed pipes, 1403. Jaequard loom, 950;— telegraph, 984. Jar. Leyden — , 720 ; diamond—, 728. JeiUt's saccharometer, U72a. Johnson' $ pressnre>-gange, 883;— d«ep- sea thermometer, 1360. Jointed discharger. 728. JouU, on the mechanical equivalent of heat, 1846. Jupiter's satdUtea, ooenltetkm ol^ 1028. Kaleidoscope, 1088. Kaisr'i pendulum, 850. Kopp*9 oalorimeter, 1389. KfuffPt law of the magaetie dip, 618. Laeovhtre on fluid-motion, 489. Lagnxvifa organic battery, 1013. Lantf* discharger, 706. Lantern or trundle^ 174. Laryngoscope, IISO. Latent heat, 1897—1406 ;— of steam, 1405;— of Tapours, 1406;— of va- rious bodies, 1899;— of water, 1887. Lateral accumulation of waves, 4(B; — explosion, 748 1 — gravitatioo, 68 ; •^pressure of fluids, 896. IVDEX. 843 LAV LIN Lavender band of specinnii, 1087. Law of graritation, 69 ;— beneath the earth's sarfaoe, 64 ;— of sines, 1054 ; —of srnunetry, in crystals, 26. Lawsonnotion, JITtfwton'f^, 282—287; eleotroeutic— » 673;— of interfe- rence of polarised light, 1229. Leaning towers, stability of, 93. Least circle of aberration, 1047. Zeeouni'i polsriscope, 1261. 'Lt—onf* battery, 781. Left-handed quarts, 27, 1260;— screws, 202. Leichienberfft electric figures of— ,736. X«ttotr'f gas-engine, 629. Lenses, varieties of, 1068 ; spherical — , 1069; focus of—, 1072; coavex — , focns of— , 1071 ; conoaTe— , virtual focus of—, 1073 ; combined — , focus of—, 1076. Xie*Ue'§ differential thermometer, 1366; — freezing proeess, 1419; — on the radiation of heat, 1438. Level, hydrostatic — , 388; spirit — , 886 ;— surface of a fluid at rest, 385. Lever, the straight—, 110, 111 ; the bent — , 112, 113; different classes of—, 121 — 126 ; compound — , 126 ; —escapement, 268 ; the pneumatic —,627. Leverage of muscles, 148 — 150. L^den jar, 720 ;— battery, 724;— vacuum, 707. Liebig, researches in organic electri- city, 1010. Lifting-jack, hydraulic-, 396. Liftf the hydraulic — , 440. Lifting pump, 436. Light, aberration of—, 1023; — and heat identical in their nature, 1437 ; absorption of—, 1093, 1004 ; corpus- cular theory of—, 1018 ; prismatic decomposition of—, 1062; diflVac- tion of—, 1125—1138 ; epipoKo dis- fersion of—, 1113: fluorescence of 113 ; inflection of—, 1126 ; inter- ference of—, 1121 — , polarised—, 1200; reflectionof— , 1033; refrac- tion of—', 1064; undttlatory theory of—, 1019—1022; velocity of—, 1023 ; relations of heat and—, 1437. Limiting angle of refraction, 1060; —of resistance, 56. Line of action, 165, 168;— centres, 155. Lines, aclinic—, 612: agonic — , 609, focal—, 1048 ; isoclinal—, 612 ; iso- dynamic— , 627 ; isothermal — , 1387 ; —of magnetic force, 692 ; — i>a«M- A^/^r's— , 1099;— of invisible spec- trum, 1116;— of no polarixatioo, 1260. LIN MAB Link-work defined, 167: velocity- ratio in — , 162 : parallel motion by — , 217, 218^ mode of obtaining a given velocity-ratio in — , 219, 2^ ; — of pedal harps, 262 ; oscillations multiplied by — , 284 ; variable velo- city oDtained by—, 263. Liquefaction of gases by pressure, 10, 6U0. Liquids, compressibilitT of, 382; — COD vey pressure in all directions, 384 ; diffusion of—, 60 ; f|[enend pro- perties of—-, 379 ; mobility of the particles of—, 379 ; spheroidal state of—, 1416. 1416. Loadstone, 691. Lobed wheels, 237, 238. Longitudinal vibrations, 376; pro- gressive and stationary — , illns- trated, 377. Luiiar-diomal change of declination, 617. Haded crystals, 28. Magdeburg hemispheres, 611. Magic lantern, 1161. Msgne>ci7Stauio axis, 653. Magnet, electro-. 806 ; permanent — , 692, Ac. ; revolution of a— round a conductor, 866. Magnetic force, annual change of—, 618 ; horisontal and vertical com- ponents of—, 619. Majgnetism, 553; — excited by eleotri- city, 871, 872; action of— on pola- rised light, 1265. Magnetic declination, 609 ;— dip, 611 ; — e<)uator, 612 ;— field, 698 ;— incli- nation, 611 ; — induction, 596; — Klines of force, 592 : — ^metals, &SiO ;^polea of the earth, 608 ;— registration, 624 ; — variations, annual — , 618 ; lunar-dinmal — , 617 ; solar^iinmal, 615 ; secular—, 609. Magneto-electric machine, 906 — 907 ; -telegraph, 921 ;— Sinstfiu'- , 922 ; TFAMtofoiM'f— , 920. Magnetometers, 622. Magnets, natural—, 691 ; artificial — , 691. Magnifying |>ower of lenses, 1060; — of a refracting telescope, 1160;— of object-glasses, 1164. Magnwt* formula and table, 619. Mahu^ discovery of polarised light, 1217. Mangle-racks, 263; -wheels, 261, 36S. Marcet*9 apparatus for artifioial re- spiration, 613. Mareut' thermopile, 971. Maris Davg'i pile, 792. 844 INDEX. MAB MOB Hftriner'i oompMS, 601 ;— card 602. Mown* 9 hygrometer, 1^. Mass of a bodj defined, 274. Matter, finite divisibilirf of—, 1 ; ixn* peaetrabili^ of— ,2; extension of — , 3 ; indestructibility of—. 8 ; den- sity of— , 11 ; diyisibility of—, 12. Mait4ueeCi researches la organic electricity, 990, 901. Maynooik battery, 779. Mean height of the barometer, 491. Mechanical powers, 110—144. Mechanism, animsL 148 — 162; prin- ciples of— defined, 163—160. Meffsseope, the, 1148. If «»/«'« acoustic apparatus, 677. Melloni't researches on heat, 1461 — 1463. Melting-point, 1407 ; influence of mix- ture of elements on — , 1409; — of presaure on—, 1406. Meniscus lens, 1068. Mercurial barometer, 484 ; syphon — , 486; standard—, 486;— thermo- meter, 1357 ;— and air — compared, 1863 ; scales of division of—, 1358 ; maximum—, 1362; — nBinimnm — ^ 1363. Mercury and air, ratio of densities of — , 616 ; capillary repulsion of—, 41. Metacentre, the, 406. Metals, conductivity of, 806 ; elliptic polarization by reflection from — , 1276 i magnetic and diamagaetic — , 648; thermo-electric series of—, 963 ; yoltaic series of—, 764. Meteors, 760. Mica, action of—, on polarised light» 1232; oolonred rings in— , 1942; action of— on heat, 1484, 1486, 1488 ; mode of preparing — , 1481. Microscope, achromatic — , 1167; com- pound— , 1166; lucemal — , 1160; simple—, 1164; solar—, 1160; illu- minating apparatus for the—, 1166 —1168. Mini^ ball, principle of the— , 316. Mirage, 1061. Mirrors, refleotion firom — , 1039 — 1061. Modulus of elasticity, 289. Moment of a couple, 81 ;— of a pres- sure, 77 ; — of inertia, 346. Moments, equilibrium of—, 78 — 80. Momentum defined, 276 j — ^firequently confounded with vis viva, 277. MotUgolJler^i air-balloon, 1382. JfoHn'ff apparatus, 301. Mont alphabet, 928; — electric tele- graph, 927;— key, 926 ;— printing telegraph. MOB OEB Mortice wheels, 175. 2f&0r-« figures, 1452. Motion, absolute, rdatiye, anifbrm, accelerated, retarded, 270; modes of communicating — , 156 ;— commu- nicated by rolling contact, 170 ; — wheels of^a clock, 228 ; — of prcgW* tiles, 307—314. Movable diagram of reiraction, 1060. Multiple inductor, 741. Multiplier, yoltaic—, 866; nstetaea 856 ; thermo— , 968. 909. Mnsdes, leverage of, 148— 160l Musouls^ currents, 930. Musical intervals, 674 ;— reprcaented graphically, 674. Myopso vision, 1186. Natural cxystals, 20;— magnets, 691. Neap-tides, 474. Needle, magnetic — , 60S ;— eleotrie tele^ph, 916. Negative electricity, 660 ;— opCio axis, 1203. Nerye-cnrrents,906. Nefcton't first law of motion, 282 ; second law, 283; third law, 286 ; ita consequences, 287 ; — ^rlngs, 1133; — table of colours, 1136; — teleaoopSL 1142. Nichol$om*i hydrometer, 419. Nickel, magnetism ol^ 630. NieoPt prism, 1212. Niipc^i disooTcries in photogrspliy. Nitre, oolonred rings in—, 1244. 2fob«re§ line^ 1139. NobilC$ astatic galvanometer, 866. Nodal lines, 683 ; — points of a chord, 675 ; — points of a vibrating body,S73. Non-conductors, eLectrio— . 659. Nose-piece, Brooke't double—, finr microscopes, 1163. Notations for dock-trains, 229, 230. Notes in music, 668 ; relative lengths of waves in — ^ 670; relatiye num- bers of waves in — , 670. Objeot-glass, achromatic, 1156, 1160 ; angle of aperture of—, 1158 ; ad- justment of— -for aberration, 1160; magnifjring powers of—, 116^ Oblique reflection, 1048; — iUmnina- tion, 1167 ; — system of crjstab^ 24, IT. ; — ^hemihedral crystals, 27. Ocean, equilibrium of the^ 472. Octave in music, 570. Odontograph, WiUiiTi, 109. CB^taajr magnetic process, 633. OtrtUtu piesometer, 381 ;— elcetro- djnamic researches^ 860, 851. INDEX. 846 OHM PHO PHO Okm*$ theory, 797, 799. Opaque bodies defined, 1024. Ophibalmoacope, 1196. Optic ftzee of crystals, 1808. Optical acoustic figures, 6fi3. Optical instruments, 1141—1199. Ordinary ray, 1200. Organic electricity, 976 — 1017 ; struc- tures, polarising power of—, 1868 —1866. Oscillation of a body, 389 ;— in a cy- oloidal arc, 830 ; time of an — in a cycloid, 331:— in a small circular arc, 332 ;— of a pendulum, thne of — , 333 ; centre of—, 347, 349. Ozida^n, a source of aidmal eleo- tricity, 1007. Oxygen, magnetism of—, 616. Osone, 640, 823;— generator, 824. Pallets, 288, 867. Paper, photographic processes on—, 1301—1328. P^^s digester, 1418. Parabolic path of a prcgeetile, 806 ; —reflector, 1060. Parallel absorption and radiation in gase^l478. Parallel hemihedral aystals, 27. Parallel pressures, resultant of two — , 76, 76:— of any number of—, 79; ease of constant equillibrium of—, 80 :— motion bv Unk-work, 817, 818. Parallelogram of statical pressures, 70 ;— of Tclocities, 284. Parameters of a crystal, 23. Paratonnerres, 767, 768. Path of the centre of graTity, 96—100; —of a projectile, in practice, 314. Pedal-hup, link-work m tbe— , 262. Pendulum, applied to physical geo- graphy, 366—367 ; conical—, §S3 ; oorrection of unequal arcs, 332; gridiron—, 354; Xaier'*—, 360; len^h of—, 383 ; mercurial compen- sation of—, 366; rotation of— ,367; oscillations of—, 838. FeltUr'i electrometer, 666 ;— thermo- electric hygrometer, 970. Penetration of electric churge, 726. Percussion, centre of—, 851—363; ener^ of—-, 297. Periodicity of distnrbaaoe-Tariations, 681. Persian wheel, 449. FetgvaVt orthoscopic lens, 1896. Phases of a wave, 369. Phonograph, 8eoU and £bm^»— , 651 ; Linajottt and i^MOtiw— , 668. Phosphorescence, 1118; — ^from elec- tric disdiarge, 734, P08 Photo-galTanography, 1339; -glyphy, 1338; •lithography, 1337; -sotUpture, 1340; •■incograpby, 1337. Photographic camera, 1293 ; — paper, 1302 ; — ^processes on paper^ ISUl— 1322 ;— registration of the baro- meter, 496 ;— of magnetometers, 624 ;— of the thermometer, 1367. Photographs, positiTC, and negatiTO, 1291. Photography, 1289— 1341; celestial—, 1836. Photometiry, 1027. Physiologic effecta of an eleotrio current, 997. Picture-firame (photography), 1297. Piesometer, OtnMTt—, 881; B^g- nmilf§ — , 382. Pile, Mari€ Dav^9—, 798; Pafotfr- maekei'*^, 790 ; FoZ^o't— , 788, 789; Zamboni'9^, 761. Pin-and-aHt motion, 241. Pin-wheels, 188, 1«). Pinion in clockwork, 176. Pistol, the electric, 711, o. PitehAdrcle of wheel*, 173. Pitch, concert-, in music, 671. Pith-ball electroscope, 661. Plane of floaUtion,40tf. Plane, the inclined, 140; equilibrium on — , 141; experimentally illus- trated, 142 ; time of descent on— , 326. Plane mirror, reflection flrom ft— , 1U36. Planes of polarisation, 1210. Plate eleotrio machine, 692. Plates, colours of thin, 1138. Flweket'M magnetic researches, 662. Plumb-line, deriation of th»— , 69. Pneumatics, 477-629. Pneumatic leTer, the, 627. points and knobs, discharge by—', 689. Polar dock, WheaMo»t^$, 1228. Polarisoope, JSto^r— , 1217 ; BrookTt —,1219: Leeounf 9— ,1251. PoUriied light, plane—, 1210; eircu* larly— , 1256 ; eUiptically- , 1276 j —heat, 1483-1491;— b^ pUtea of mica, 1484 ;-^^ retraction through rock-salt, 14B6; — of solar heat 1486; circular-, 1469, 1490;— by Frtmtrs rhomb, 1491. Polarised reUy, Sitmmu^-^, 931. Poles, magnetic, 693 ;— of the eafth» 606. Polygon of pressures, 73. Port, esiabushment of a, 476. Positire electricity, 666 ;— optic axis, 1803;— photographs, 1891, 1327. 846 IKDEZ. POT PUM PUN Fotesaiam, ndnetion of—, 839. Potential, elaotric, diflfuaioa of—, 736; —of the etmosphere, 747 — 763} — of doada, 764—766. Power ^xohMieed for time, 109. Powers, meoDanioil— , 109 ; — of lenaea, 1079. Precticu eqailibrimn of en aroh, 106 —106. f Presbyopic vision, 1187. Pressore of fluids, 386 ;— on the base of a Teasel, 392 ; l&teral— , 398—400 ; upward— , 397 ; centre of— , 401 ; — proportionid to sorfaoe, 394 ;— on a plane immersed, 401 ; — of gases^^aw of— ,*498— 600 ;— of Tapoors, 618 ;— of aqneons vapour, 619 ;— of gaseous mixtures. 616 ; — measured bj *' atmospheres," 620. Pressure-irame (photography), 1290. Pressure-gauffe, Joknton »— , 383 ; AUan'$—, 602. PreestireSj composition of—, 09: eqni ibnum of—, 66 ; — ^represented by lines and numbers, 67 : resolu- tion of—, 69 ; statical — denned, 66. PrtUeh't process of photo-gal ?ano- naphy,lS39. Pnmary coil, 886 ;r-oo1ours, 1089 ;— focus, 1048 ;— forms of crystals, 26. Prime conductor, 691. Primitive polarisation, plane of—, 1244. Principal focus of a lens, 1072 ;— of a {;lass sphere, 1069 j— of a mirror, 039. Principal section of crystals, 1201. Principle of virtual velocities, 126;— of the rifle, 316. Principles of mechanism deflned, 163. Prismatic system of crystals, 24, ui. ; —dispersion of Ught^ 1062. Projectiles, motion or—, 307; path of— , a parabola, 306;— in a resist- ing meaium, 314 ; horiiontal range of^, 312 ; time of flight of—, 311. Projection, velocity of, 309. Propagation of heat, law of—, 1374. Propeller, the screw, 453. PropelmeDts,269; Wh0aUlon^a~,2S9. Pseodoscope, the, 1197. Psychrometer, 1426. Pulley, the, 132 ; single moveable—, 133; expanding— , 246. Pulleys, systems of—, 134—136. Puhtermacher'g battery, 790. Pump, the California—, 439; the ceo- trifugal— . 442; AppoUTM—, 443; chain and bucket — ,444; forcing-, 437; lifting—, 436; rope— , 416; stomach-, 438. BEG Punching machine, hydraulic — , Pyramidal sjstem of crystals, 24, xx. Pjro-electric minerals, 670. Pyrometer, DaxM/^f- , 1370;hydxo- —,1^71; IFm^«woo«I'«—, 1389. Quadrant electrometer, 710. Quality, variable—, of heat, 1468 ; meana of comparing — , 14fi9;— H>f transealency, 1461. Quantity armature, 907. Quarts, crystalline form of^ 27; cir- cular polarising power of, 1260. QueteUion mas>netio variations, <14« Quina, iodo-, sulphate of—, 1216. Quinine, optical properties of^— , 1114. Ratchet-wheel and dick, 266. Rack and pinion, 178 ; mangie— , 263. Radiant heat, 1433—1401. Radiation and absorption of heat, parallel properties, 1464 ;— of hcttt, 1456 — 1472 ;— influenced by diemi- cal constitution, 1456 ;^>y oom* minution, 1456 ; — from gase^ I4n t perceptiOD of—, 1433 ; ibtenial — oc solids, 1479 ;— from flames, 1482. Radius of gyration, 349. Rainbow, 1140. Kam, the hydraulic—, 441. Rate of cooling l^ convectioQ, 1438; —by radiation, 1438. Ray of light, modiflcationa of a—, 1090; ordinary and extraordinair —,1200. Rays, chemical—, action of^ 1281 — 1288; convergent, divergent, and parallel—, defined, 1036 ;— lost by reflection, 1034. Reciprocation of sound, 610. Reeas ; free reeds, 682. Reflecting teleecope, 1143. Reflection of elastic bodiea, 296 1'^ti heat, 1434, 1436;— of lig-ht, 1083; — from concave aurfacea, 1099; from convex—, 1042; fVom plane — , 1036 ; internal—, 1060 ; obliqne^ — , 1048; total—, 1060 ;— of sound, 660— 662;— of undulations, 464, 466. Refracting telescope, 1109 ; erecting glasses of a-, 1170; magnifying power of a—, 1160. Refraction of light, 1064; douUe— ^ 1200; index oT— , 1067; moveable diagram of—, 1066; — of cokmred rays, 1084; prismatic—, 1082; un- usual-, 1061;— of heat, 1413—1444 — of sound, 663. R^elation, 1410. Registration of magnetie Tariati, 9; cspillary — , 41 ; electric—, W5 ;— oi electric onrrenta, 884. Betidoal charge of electricity, 728. BesinooB electricity, 858. Benatance to oompreuion, 18. Be8istinfl[ mediam, motion of a pro- jectile m a — , 314. Bmolntion of statical preuorea, 89. Besonator ot StUnkolU^ 639. Beeultant axis, 1202;— of two pree- Borea, 70 ;— of any number of prea- aurea, 71 ;— of two equal parallel preaaurea, 75 ; — ^unequal — , 78 ;— of any preasurea in a plane, 76; — of any parallel—, 79 ;— of fluid prea- aure. 402. Betarded motion, 870. Bheometer, 865. Rheostat, 804. Bhombohedral ayatem of cryatals, 24, V. Bifle, principle of the, 316. Bight-banded quarta, 27, 1280; — acrew, 202. Bigidity of oordage, 139; — of atruo- torea, 14. Binga, NnstonX 1136 ;— by polarized light, 12S8. Itiiehie'* rotating electro-magnet,879. Soberts't battery, 780. Boberval'i balance, 128. Book-salt, action of—, on heat, 1481 ; — l4rmulas for cob- Terting- , 1358. Scape» or awing-wheel, 228. Sekeibler'i tonometer, 573. Sehihtbein'i battery, ^8;^on osone^ 684 ;— on passive iron, 778. Scktoeigger'M galvanometer, 866. Screw, ihe, 143 ;— and nut, 202 ; eod- lesa- , 203—206 ; Hutder't—^ 144 ,*— of Arehimedet, 449 ; right- and lelt- handed—, 202;— propeller, the, 453. Secondary coil, 887 ;— eurrenta, 886; — focua, 1048 ;— planea of cryatala. 25. Section, principal — , of cryatala, 1201. Secular magnetic raiiationa, 814. Selenite, action of—, on polariaed liffht, 1230, 1231. Sel^luminous bodiea, 10S4. Self-regiatering baromet«r, 496 j~- magnetom^tera, — 824; — thexmo- meters, 1367. Sensibility of a balance, 116. Strrin'B electric lamp, 810. 8hadbolf$ parabolic reflector, 1186. Shadow, acoustic — , 565. Sheph^d'§ eleetrio clock, 963 ; — aetro- nomical— , 959. Shifting endless band, mode of—, SIS* Shock, electric— , 717. SUberwutnn' 9 heU telegraph, 922 ;— polariaed relay, Ml, — submarine cabla^ 808. Silent click, the, 268. Silicon, redaction of—, 833. Silurus eleotricua, (M31. Simple machinea, 109 ;— microaoopa. 1164 Since, Uw of, 1054—1058. Single-iniige priam, 1218;— tonoh, magnetisation by — , 632. Siriua, the light of—, 1027. Sliding contact, 156 ; motion oomma- nicated bijr— , 180. Smeatou'i air-pump, 606. 848 INDEX. 8MB BTA Boap-bnbblep ooloun of i^— , 1132. Somain, redaction of—, 839. 80fkD6S8, 9. Bolar-dinnuJ Tarutionof deoliiiation, 615, 616. Solar photoepbere, its nature in- ferred, 1111. SoIm speotram, 1063; fixed lines in — ,1099,1107: innriUerajein — , 1107; irraUonelitT of—, 1098. Solids, expansion of—hj bsat, 1350. Sotfsi«imii/« mirror, 1163. Sondhaut^ aoonstic lens, 664. Sonoroos ribrations, 681; interfe- renoe of<— , 649. Sound, the production of—, 590; — requires a conducting medium, 638 ; causes affecting its transmission, 636 ; direction of the propagation of-- 1 668; inflection or— ,666; in- tensitT of—, 634-^636 : interference of— ,549, 650; reflection of— . 560 ; reoiproeation of—, 540; Tcilocitj of—, in air, 648 ;— in Tsrious media, 646—648. Bounds, barmonio—, 575 ; toosJ— ,688. Space, time, yelocitj, and force re- lated, 305. Sparks, electric—, 686. Speoiflc capacity of gases, 1396. Specific gravitj, 412 ;— of fluids, 418— 480;— of gases, 483;— of solids, 412— il5 ; table of—. 485. Specific heat, 1388— 1394 ;— of Tari- ous bodies, 1392;— of gsses, 1394; —of water at vanons temperatures, 1393; influence of temperature on—, 1393. Spectral colours, 1190—1198. Spectroscope, 1173; rigid—, 1174; straight—, 1175. Speotro-microsoope, 1176. Spectrum, solar—, 1082;— snaljsis, 1106— 1112;— of a temporary star, 1112. Speculum defined, 1051; Foueaulfi — , 1062 ; mode of silvenns — , 1063. Spherical aberration of mirrors, 1046 ; —of lenses, 1081. Spheroida] sUte of fluids, 1416, 1416; —figure of the earth, 324. Spiral; SofMfi eleotrioal— , 666. Spirit-level, 386. Spouting finids, Telodtyof-^, 426, 427. Spring-tides, 474. Spur-wheels, 176. Stability of a supported body, 98, 99, 100:— of a suspended body, 98; —of a floating boojr, 407. Stable equilibrium deflnsd, 94. 8TA TEE StoHhope lens, 1164. Star, electrio— , 703. Starch, action of — , on li^t, 1255. Statical couples, 81 — 63 ;— Suilibrium of—, 66 ; comparison — , 67 ; composition of—, 09 : resolution of— ,69 ;— problemSt im- portance of, 84. Stationary ribrations, 372. Steam-engine, atmospheric , 465; high-pressure—, 457; Wait 9^, 466 ; — Shammer, 460. Steel, magnetasm of—, 501 ; tenacity of—, 16. Steelyard, the, 120. Stereometer, Uie, 421. Stereoscope, the, 1196; theory of— ^ 1195. Sioke», Prof., on flnoreserace, 1113, 1114 ;— on astigmatism, 1188. Stop, the Oenera— , 218. Straight lerer, the, 110, 111. Stratified discharge, 811. 8irMk^» experiments, 664. SMi^aitm't battery, 791. Structure influencing condnctirity, 1375. Submarine telegraphy, 837—047. Suction pump, 486. Sugar, action of— , on polsrixed light, 1269. Superficial distribution of electricity, Superpoaition of small motiectral rays, chemical action Surface of a fluid at rest, horisontal, 884. Surface radiation, 1448. Sutton' 9 panoramic lens, 1296, Swash plate, 255. •Vyitef' hydrometer, 418. Syphon, the, 446;— barometer, 466; —gauge, 607; the Wirtembung— , 417. Syringe, condensing, 609; exhnist* ing— , 608. System, rotation of a— Tabasheer, refraction of, 1070. Talboe9,Ur. 7.,calotype, 1806;— pbo- toglyphy, 1838, TalbotjFpe, 1306. i TofUMut* cup, 447. Tappets, 254 Teeth and staTss of wheds, forms of — , 188; necessary number of—, 180. I Teeth of wheels, uniform action of, 180— 188| episydoidal and hypo- INDEX. 849 TBL Till qjoknaal— , 18S; radial—, 184;— aod pina, 188; mvolate — , 186; forms of— in praotioe, 197 — dOl. Telejpi^h, sAeotric,Bain*tciundoal — , 992; 3akew«lff$ oopTing^, 035; magiteto-elcotrio— y MO; Mont^§ printing— , 920 ; needle—, 016; in- dioator of—, 017 ; Bonald/'-^. 016; Sitm€uf magneto—, 922; Wh^od' ttone't diao— y 010 ;— magneto- eleotrio— , 921 ;— rainttng— , 838» OM ;— priTate— , 02S. Telegnpny* electro-, 015—061; mb- marlne — ^,937. Teleioope, aatronomieal— , 1160; GMM^ram**— , UM; OnUUift^, 1171; Qfgarftr^, 1143; HmoUm'a —,1142. Temponuj star, speotmm of a—, Tenaoitj, 16. Teireetnal heat, 1432; relation of tnnioalenaj to—, 1482 r— radiation, 1460 ; means of oomparinfl^- 1461. Testa, eleotrioal— , 041—040 ;— of in- solatioD, 044; — of indnotion, 046: —for £Milto. 046, 047;— in land Hnes, 048 ;- for the resistaooe of a Utterj, 040. Thallinm disoovered by qpeotnun- analysifl, 1108. Theory of oonples, 81—83 ;— of ex- changes, 1436;— of foroed Tibn- tions, 600 .—of tides, 47^ 478. Thermies, 1342—1432. Thermic rajrs of the spedamm, 1107. Thermic unit, 1872. Thermopile, 068, 060 ; JOSsMMrcTr—, 071; IfaraM'- , 071; Jbrfrw*— , 1441. Thermo-electrio hygrometer, 070; — rotation, 066,067. Thermo-eleetrioity, 062—076. Thermography, 1468. Thermometer, air — , 1364; BngtttCt — , 1360 ; differential—, 1866 ; Jdkw 9on*9 deep-sea—, 1360; mazimnm and mini mnm — , ButkemnreT*, 1361 ; meronrial — . 1367 ; graduation of—, 1368: self-registering—. 1367; al- oohol— , 1861; NeorUtpB meronrial maximnm— , and rhiiUpt*—, 1362; Cauelc^t mercurial minimum — , 1868. Thermophone, 687. Three-throw crank, principle of the —,80. Thunder-house, the, 768. Tides, theoiyof— ,472; BerfumiUCt—, 473 ; Xop/otf/t— ,478 1 interference of—, 476 ; spring and ne^H-, 474. Timbre of soondSk 667. 3 TIM UNI Time and power exchanged, 100. Time, space, reloeity, and force re- nted, 806. Tints in a soap-bnbble, 1138. Tonometer. JfeUibUr^w^, 673. Toothed wheels, action of—, 178 j— with obBqne teeth, 170. Topaa, coloured rings' in, 1241. Torpedo, eleotrio organs of TorrieMFt theorem, 426;— Taoaom, 484. Torsion eIeotrometer,Gn(fesi6's— ,664. Total reileotion, 1060. Tourmaline, crystalline form of—, 27 ; optical ^perties of—, 1216 ; pyro-eleoMoity of—, 670. Tous-lea-mois, optical properties of— , 1266. Trade-winds^ 1886. Trains of wheels, 224—231; forelocks, 228—280; notation for—, 280. Transcalency and transparency con- trasted, 1446. Transcalenoy of gases, 1460 ;— at dif- ferent densities, 1470;— of liquids. 1406 ,— of solids, 1461. Translucent bodies defined, 1024. Transparent bodies defined, 1024. TransTcrseTibrations, 876. 2WMlvaa'f experiments, 687. Triangle of preasureL 72. Trundle or umtem, 174. Tubes, capillary—. 88—40; friction of fluids in—, 434 ; Tslooi^ of fluids in — ,-431; vibrations or air in — , 670—681. Tuning*fbr^ experiments with a^^, 664,666. Turbine, the, 461. Twin crystals, 28. Tfmpannm, effect of ribrations on the— ,641. J)fndaie§ magnetic researches, 658 ; —on transcalency of gases, 1468. Unannealed glass, optical properties of—, 1208, 1247—1260. Undulatory theory of light, 1019— 1023 r-hypotheees, 1 138. Undulations, phases of—, 360 ; pro- gresaiT»— , 871 ; stationary— ,872; —of air, 480-471;— of iluids, 462-471 ; reflection of— , 464, 486 ; interference of—, 466; liberal- accumulation of—, 468. Uniaxial crystals, 1208—1206. Uniform accelerating forces, 296— 305 ;— motion defined, 270. Unipolar bodies, 746. UniflOQ in music, 674. ' 850 iin>Bx« UBTI VOL Unit-Jir, BarrVt, 797. Unit of work, 349 )— of beat, or tho^ mio unit, 187S. UniTeraal diachanar, 729. Unstable aqniUbrnim. 98— lOL . Upward preasnre of noida, 397. Ursninm-glaaa. optioal propertiea of-iluSr^ Tacnmn, luminoaa diaobarga In •-*-, 7067L«jdaii— , 707 ; Torrio^Wi j 484. VaUiTi deotrio reaMrahea, 960. yaporia»tionofflaida,lil8; abaoip- tionofheatin— , 1419. Taponr at oommon tempflratoraa, 1422. Tariation of themagnetio needle^ 608; — of pitoh, in mono, 671. Farle]i*$ mmtiple indnotor, 741. Taimah for ooUodion pictnrea, 1826. Vtdj/'i aaaroid barometer, 496L Yegetablea, eleotrioit j of— ^ 1017. Yfllooitiea, paraUelogram of—, 284} Tirtoal— ,126. Yelooi^ defined, 271 ; relative—, 272 : relation of— to SfMoe, time^ ana force. 806;— of li^i, 1023 r-of Bonna in air, 642—644 s^in Tariona media. 645—648; —of apontinff floida, 426 ;— of wmda, 628. Velodty-ratio defined, IM;— in oon- taot motiona^ 163;— in linkworl^ 162. Vena oontraota of floida, 488. Terge eaoaiMment, 266. Tibrationa,iaoohrooooa— , 878 : longi- tudinal—, 876 ;— of a row ok parti- dea, 877 ; profpieaaiTe— , 371 ; aono- roua— , Hal; stationary — , 872; tnuarene— , 876 ; — of air in tobea, 679 — 681; modes of exdting^, 682 ;— of ehord^ 371—873 ;— or elaattc platea, 683; Jbivulinr** ez- perimenta on—, SM; — of a neated [Mur, 687;— of membranes. 666;— of roda, 870; theory of Ibroed— , 600 ;— of oonduotora, 800. Tlrtnal yelodtiea, prindpie of— k 126 ; — iUustrated, 127: Vis Tira oonfonnded with momentom, 277; conservation of—, 840; when a in^TOWiWHT or wiwliwmw^ 841 i-^KD' pHed to meehanism, 846. Yuion,binooular— , 1196; oonditiooa of diatinot— , 1186 ; myopio— « 1186; preabyopio— . 1187. Yitreona deotndty, 666. Yooal aonnd^ 688, 688. Yo]tai«leolK)m«ter»828. ' YOL wnr 768;— diacharge^ 806r-deetricity, 761. Fojla'adeetrophorus, 686 ;— pila, 788, 789f— rpaearehea in argaoio electri* oily, 964. Yolume of a body defined, 275l Youawin of an axoh, 102: vaifimn —,106. Yowd Boonda, 669. Water, eompreaaibiHty of — ^, 381 ; greatest density of — , 1361 ; deeoss- posttton of — by heat, 14S1 ; dee- trolysis of—, 821;— ^wheels, 460. Ware-i^paratos, 877, 1266. Wave, phases of a—, 869;— fJraat, 1209. Waves of light vaiiooaly modified, 1030; mDllant— ^1267, 1268; taUe of lengths of—, 1066. Waxed paper photooapUo prooesa, 1818. B^cAer^creseanhes on vibnting oord^ 676L Wedge, the^ 146 ; power gained by the — »148. WedgwootFi experiments in l^do* graphy, 1289 ;— pyrometer, 1909. Weigniag marhineu thsw 129 ; meAod oTdooble-, 117. Weight, 63, 64. Wdght lost by a body immeraed iaa flmd, 410. WdU, on dew, 1460. W^iUuun*i panbolio refieetor, 1166 ; — binoenlar miorosoope^ 1162. WheatMion^t bridge, 800^ 801; — obronoeoope^ 967;— disotdegraph, 919 ;— magneto- eleetiio teleiraph, 920, 021;— photometer, 1087;— polar dodc, 1228;— printiaf dec- trio tdegrai^, OU ;— prapdmeBt, 269;— pseudoeoope, 1197;— dieo- stat. 804;— stereoeoopeb 1196. Wheel and axle^ the^ 181. Wheels, mortice—, 176; mr— , pin—, erown— , annular—, 179; bevlDed -, 177 : breast-, 478 ; eeoentno-, 289; elliptio— , 286, 236 ; lobed-^ 237, 238; forms of teeth of—-, 189—201; idle—, 226; mangle , 261,262; overshot— , 4m, c ; paddle —,462; tzainsof— k228— 281| nn- dernhot— , 460. WiU^M msgneto-deotno machine 911. WitkbuoH^a dectciod msearches, 990. WUliiTi odontogn^ 199. Winoh, the, 181. L IXDEZ. 851 wnr woL Wmd]M8,the,181. WindmiU mOs, 464. Windi, Telooitj of—, 6SS. Wire, insulated— ,866; Tibnlang^-^ oOV. WoUaaton't battory, 793;— oamtra looida, 1162 ;— oryoplimu, 1481 ;— dcmblet, 1166. WOB ZIN Work, unit of—, Stf ; aooumulited— t 348 i— related to vis viva, 344. Wn^ping oonneoton, 167 ; motion by — , i06— 816 ) yariaUe— , a44>-a4B. Zantboni^M pilee, 818. Zero of thermometer toalea, 1368. I Zinoy amalgamated—, 766. THE END. LOVIMV: •▲TILL, IDWASOI JOnt CO., PBIVTSBS, OKAVDOI 8TBVXT, OOTXlfT ai.u>sv. ^