7, ye eee ae BRD, Tavta th se a ia Wena es eb kee Wee delay ‘ ie Bek ae * F908. sae ae 4 88 We ye eee yh eet AON OC BRA eT As Soh BA in feed RP AN RA ARS ‘eek Wye 4 eee Were de eed 4 Ce Ue VAG Cae om eS PPE IN BUR Re aed Ae 4 EMOTES HEM Wy rete’ 4: AS Re eu f “ a7 ee on Soh ede R 2 ae AN rcs ae bd at «eawagery eed P Gao ee SO a Se a a alg BT wee aN 4: ae es i Dia BS iS ee A A awn e “4" i? ey aa wats eee ea ea ee, #4) pra pe ih ood aL ge a VM ae OH G28 BES cre ep Ve cee PAS eT if ALAS hh a eat OE Be Wat Ek RS . eis F, ie Ta es Vewiel peer tee 4s : AA ee Ai ee ok a wy! f a i eae ite By ee es ite : ¢ ene Stine a4 4" ewe pare ra ee cons TAN OA AE Malte wees as Mare’) ade V4 ANA tt Ah ee Ue a tal ‘ wa ee. ne Sue Ad Fat satay ocae te 12 ¥ wee Y 4 wT a Sagal da fp By een sf PA RAS Ph 4 aah CR dias OU, LARA ae TR GR ea hu ‘ i ee. a) et e By re ih, erie a es al ‘eve AW Oe a a vat eee ae ee z ea renee he ee Re ae he at ASE Ut ae MS rb Peden Stieber ak Hk Wo rs ve fi aa aus €e ‘4h ta Teas YAS Pl eis aah Pt ee eR ! i, WON teh eee “eh & 4, we 2 ae HOE Td 48 Ce Ae *\ * a x ee ae eo weg ae, ne aoe v ne Ht ‘ ( \ . i 2 ye = , v My f us t i t ; ' +> o = Nina , h 36: i fu ti \ \ i } 4 ts : i, Ry a D: th k | ¥ i n F ' if i { i i "he ; THE LONDON, EDINBURGH, anv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Kyr. LL.D. F.R.S. &e. AND WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S. ‘¢ Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib.i. cap. 1. Not. VOL. XIX.—FIFTH SERIES. JANUARY—JUNE 18835. —— a ee TES, Wisi d LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, SOLD BY LONGMANS, GREEN, AND CO.; KENT AND CO.; SIMPKIN, MARSHALL, AND CO.; AND WHITTAKER AND CO.;—AND BY ADAM AND CHARLES BLACK, AND T. AND T. CLARK, EDINBURGH}; SMITH AND SON, GLASGOW ;—— HODGES, FOSTER, AND CO., DUBLIN ;—-PUTNAM, NEW YORK ;— VEUVE J. BOYVEAU, PARIS ;—AND ASHER AND CO., BERLIN. “‘Meditationis est perscrutari occulta; contemplationis est admirari perspicua..... Admiratio generat queestionem, queestio investigationem, investigatio inventionem.”—Hugo de S. Victore. —‘Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas, Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” J. B. Pirelli ad Mazonium CONTENTS OF VOL. XIX. (FIFTH SERIES). NUMBER CXVI.—JANUARY 1885, Dr. C. R. Alder Wright and Mr. C. Thompson on the Deter- mination of Chemical Affinity in terms of Electromotive Un no) och sf oye vn gape he = Sie ype = ee Dr. James Croll on Arctic Interglacial Periods ............ Mr. A. M. Worthington on a Capillary Multiplier. (Plate I. PUM. oo Sees a Ss owing on 8,4 <8 oe gos ye ote Mr. A. M. Worthington on a Point in the Theory of Pendent Mere ettie Lo fiGS 9-0.) 6 ee eee ene ae Dr. A. Elsass on anew Form of Monochord .............. Prof. W. N. Hartley on the Influence of Atomic Arrangement on the Physical Properties of Compounds .............. Mr. R. H. M. Bosanquet on Permanent Magnets.—II. On Magnetic Decay ; with a Correction to the Value of H at ei aN So a oie oe ah. 2ys ss a) sp topo wie we ora sled behave Notices respecting New Books :— Geology of Wisconsin, Survey of 1873-79. Vol. I. Part I. General Geology. IL. Natural History. III. MetetersbietneCSOULCES: (2.2 ce cin cine sles ep cn ete ss Mr. A. J. Jukes-Browne’s Student’s Handbook of Phy- ROG Ns card tie Te a nats a oc ale wr shige city Winle ead sace Proceedings of the Geological Society :— Prof. A. H. Green on a Section near Lianberis........ J. Starkie Gardner on the Tertiary Basaltic Formation in 2 FELZILG. | ee oe co arr cp naar Fer On the Employment of Marsh-gas for producing exceedingly Low Temperature, by M. Cailletet .................... On the Value of Poisson’s Coefficient for Caoutchouc, by E. H. Tey. 200 VTE OOD AU DS ORNS OPEL Elementary Phyilotaxy, by Pliny Earle Chase, LL.D. ...... On a new Form of Polarizing Prism, by C. D. Ahrens...... On the Penetration of Daylight in the Water of the Lake of Geneva, by MM. Fol and Hd. Sarasin ..,............. NUMBER CXVII.—FEBRUARY. Mr. R. H. M. Bosanquet on Electromagnets.—II. On the Magnetic Permeability of Iron and Steel, with a new Theory SONPONICLISME 2. Sts wie ce eee tee ne ew slnnee Page 46 48 515) 57 iv CONTENTS OF VOL. XIX.—FIFTH SERIES. Page Profs. A. W. Reinold and A. W. Riicker on the Influence of an Electric Current in Modifying the Rate of Thinning of a Taquid Filta. @ 3¢... 2S ee ea: Oe ee 94 Prof. G. F. Fitzgerald on the Rotation of the Plane of Polari- zation of Light by Reflection from the Pole of a Magnet .. 100 Dr. C. R. Alder Wright and Mr. C. Thompson on the Determi- nation of Chemical Affinity in terms of Electromotive Force. Part UX. oie i. oma ieee 102 Prof. E. Edlund’s Observations on the Behaviour of Electricity im arefied Air) 421 Vee tak Oe. eo 125 Mr. 8. Tolver Preston on some Electromagnetic Experiments of Faraday and Plucker. .(Plate Il.) 2.7... : 22s en eee 131 Notices respecting New Books :— Mr. A. Gray’s Absolute Measurements in Electricity and Magnetisin a+. ss. Ge See «woe 9, to 141 Mr. R. EH. Day’s Exercises on Electrical and Magnetic MieaSUPEMeNG. iéo.4'iri. Sickie ee ee oy oe ee 142 Mr. 8. Lupton’s Numerical Tables and Constants...... 142 Proceedings of the Geological Society: — Prof. C. Lloyd Morgan on the South-western Extension of the Clitton Fault’ i.) 5.00.2. 2 143 Mr. G. Hughes on some West-Indian Phosphate Deposits. 144 Mr. J. J. Harris Teall on the Metamorphism of Dolerite into (Elornblende-sehist. 2 752. 2. - ja4.55e eee 145 Captain F. W. Hutton’s Sketch of the Geology of New Aaa” Gi. epi geese hein ee ae Sa ene eee Cee 146 Mr. T. Mellard Reade on the Drift-deposits of Colwyn Bay. 147 A new Method of Determining the Constant of Gravitation, by A. Wonie and. Richarze. 3.00. 3. oe 148 Results for Use in Calculations with Manometers with Com- pressed Air, by Hi. 7H. Amagatiy 22050 0. 2. a 150 On Gas-engine Indicator-diagrams ..................0005 152 NUMBER CXVIIT.—MARCH. Prof. O. J. Lodge on the Seat of the Electromotive Forces in the: Voltaie Cells. .4 ah eeinek ss cece Bo eee eee 153 Dr. Pliny Earle Chase on some Principles and Results of Elarmonic: Motions. nai .v.citele «wel. ve pete ee 190 Dr. C. R. Alder Wright and Mr. C. Thompson on the Determi- nation of Chemical Affinity in terms of Electromotive Force. 2 Part DXi) ofa Pek eRRieY G ening 8 a Se ee 197 Mr. S. Tolver Preston on some Electromagnetic Experiments. —No. II. Diverse views of Faraday, Ampére, and Weber. 215 Mr. A. M. Worthington on Prof. Edlund’s Theory that a Vacuum is a Conductor of Blectricity...... //2) 2.25 see 218 Dr. J. Wilsing on the Application of the Pendulum to the Determination of the Mean Density of the Earth CONTENTS OF VOL. XIX.—FIFTH SERIES. Vv Page Notices respecting New Books :— Mr. M. M. Pattison Muir’s Treatise on the Principles of DRS eso) 1S SI a Hig ad AAS ata dl ales 222 Proceedings of the Geological Society :— Mr. A. J. Jukes-Browne on the Boulder-clays of Lincoln- NEE RE trae aj Side Wisk bee ace he a dle « Ol 225 Mr, J. H. Collins on the Geology of the Rio-Tinto Mines, with some general Remarks on the Pyritic Region of Mae IAP NIOLOND ..p¥:cis' Ai. esis dRy onln as SUE ale whe 227 Mr. J. W. Judd on the Tertiary and Older Peridotites of Be MGR e sey =o fe nec dN ww alen Wren ee ay ds 228 Mr. T. Mellard Reade on the Boulders wedged in the Falls of the Cynfael, Ffestiniog ..:.....5...5..64. 229 On Combinations of Silver Chloride, Bromide, and Iodide with Colouring-Matters, by M. Cary Lea, Philadelphia ........ 229 On a Selenium-Actinometer, by M. H. Morize, of Rio Janeiro. 231 On the Synthesis of Trimethylamine and Pyrrol from Coal- gas; and on the Occlusion of Hydrogen by Zinc-dust, by Beemer taiinama. HORS s (aues Si oa s 2 AG eel Bate SRS 232, NUMBER CXIX.—APRIL. Werner Siemens’s Contributions to the Theory of Magnetism... 237 Prof. O. J. Lodge on the Seat of the Electromotive Forces in ILE TLS1S CCL A ee ree oa ee er a eae 254 Miss S. Marks on the Uses of a Line- ihendes SOP ere 280 Dr. A. Macfarlane on the Logical Spectrum .............. 286 Dr. J. Hopkinson on the Quadrant-Electrometer .......... 291 Profs. W. E. Ayrton and J. Perry on the most Economical Potential-difference to employ with Incandescent Lamps .. 304 On the Limit of the Density and on the Atomic Volume of Gases, and particularly Oxygen and Hydrogen, by E. H. OEM eae Hoth: Sich seo sala) 1a ye wets OE EI OA 313 On the Electromotive Action of Illuminated Selenium disco- vered by Mr. Fritts of New York, by Werner Siemens.... 315 NUMBER CXX.—MAY. Mr. J. C. M‘Connel’s Notes on the Use of Nicol’s Prism .... 317 Mr. kh. H. M. Bosanquet on Electromagnets.—III. Iron and Steel. New Theory of Magnetism.........7...... 0045 333 Prof. O. J. Lodge on the Seat of the Electromotive Forces in pit Onna, Cellsy. thay uw fei iS’. oid ete eae OGL PO 340 Mr. E. Cleminshaw’s Lecture-Experiments on Spectrum Ana- lysis vl CONTENTS OF VOL. XIX.—FIFTH SERIES. e Dr. J. A. Fleming on the Characteristic Curves and Surfaces ; of Imcandescence Lamps \.)sc% . 0.20) 0G ee 368 Prof. W. C. Rontgen’s Experiments on the. Electromagnetic Action of Dielectric Polarization... .. ....0./.0 5.25.0 385 Notices respecting. New Books :— Mr. Charles Pendlebury’s Lenses and Systems of Lenses, treated after the manner of Gauss ................ 388 Mr, Latimer Clark’s Transit Tables for 1885 .......... 389 Dr. R. Wormell’s Electrical Units, their Relation to one another, and other Physical Units ................ 389 Proceedings of the Geological Society :— . Mr. Frank Rutley on Fulgurite from Mont Blane...... 389 Mr. Frank Rutley on Brecciated Porfido-rosso-antico .. 390 Dr. C. Callaway on the Granitic and Schistose Rocks of _ Donegal and some other parts of Ireland .......... 390 Mr. G, A. J. Cole on Hollow Spherulites and their oc- currence in ancient British Lavas ........./...... 391 Rev. A. Irving ona General Section of the Bagshot Strata from Aldershot to. Wokingham .~..).'..22 02/00. ae 392 Experimental Researches upon the Determination of the Di- electric Constant of some Gases, by Dr. Ignaz Klemencic.. 393 Formation of a Stalactite by Vapour, by J. Brown ........ 395 Measurement of Strong Electrical Currents, by John Trowbridge 396 NUMBER CXXI.—JUNE. Mr. O. Heaviside on the Electromagnetic Wave-surface .... 397 Mr. EK. H. Hall on the Rotation of the Equipotential Lines of an Electric Current by Magnetic Action................ 419 Prof. G. F. Fitzgerald on the Structure of Mechanicai Models illustrating some Properties of the Aither .............. 438 Lord Rayleigh on the Theory of Illumination in a Fog...... 443 Lord Rayleigh on a Monochromatic Telescope, with Applica- tion, to Photometry. 5 lai). dah. Feo vat. El 2 eee 446 Prof. O. J. Lodge on a slight Error in the customaty Specifica- tion of Thermoelectric Current-direction, and a Query with regard to a point in Thermodynamics. (Plate III.)...... 448 Dr. W. W. J. Nicol on Supersaturation of Salt-Solutions.... 453 Colonel Malcolm on Binocular Glasses adjustable to Hyes havine, unequal Mocalslensths Us) GO e728 ee eee 461 Prof. A. W. Riicker on the Self-Regulation of the Compound 1) FOC hi Omar a penn Mr aE RA eh A ne Pee es ohh anc. § s 462 Prof. O. Lodge on the Identity of Energy, in connection with Mr. Poynting’s Paper on the Transfer of Energy in an Hlectromagnetic Field; and on the two Fundamental Forms OL Mnersyo Cee Cea ee ea aa ee 8 eee nal ee enone nernege A482 CONTENTS OF VOL. XIX.—FIFTH SERIES. Prof. O. Lodge on the Paths of Electric Energy in Voltaic Cir- cuits. Appendix to Paper on the Seat of the Electromotive Forces in the Voltaic Cell. (Plates IV. & V.) .......... F. Braun on the Thermoelectricity of Molten Metals ...... Mr. J. W. L. Glaisher on the Expression for the Complete Elliptic Integral of the Second Kind as a Series proceeding by Sines of Multiples of the Modular Angle ............ Notices respecting New Books :— Mr. B. Wilhamson and Dr. F. A. Tarleton’s Elementary Treatise on Dynamics, containing BE Canons to Ther- SMMNIPEEENEE DEST, 2 LOLS Se Ee ROS od oe Ea wa ae Mr. W. Paice’s Energy and Giioton! A Textbook of Seemcmnaby Mechanics ©... ie et ee we ee ene Proceedings of the Geological Society :— Dr. R. von Lendenfeld on the Glacial Period in Australia. Dr. H. J. Johnston-Lavis on the Physical Conditions involved in the Injection, Extrusion, and Cooling of mre arCh ss net eso ee ses Application of Photography to Electrical Measurements, by John Trowbridge and Hammond Vinton Hayes.......... On an Instrument resembling the Sextant, by which Angles with the Horizon can be Measured, by E. H. Amagat .... On the Production of Alternating Currents by means of a Di- rect-current Dynamo-electric Machine, by John Trowbridge emer IMMONO VISOR HAVES... . «ew ey ojo eee eee ee Thermo-electro-photo-baric Unit, by Dr. Pliny Earle Chase .. The Chase-Maxwell Ratio, by Dr. Pliny Earle Chase........ Vil Page 487 PLATES. I, Illustrative of Mr. A. M. Worthington’s Papers on a Capillary Multiplier, and on the Theory of Pendent Drops. II. Illustrative of Mr. 8. Tolver Preston’s Paper on some Electro- magnetic Experiments of Faraday and Plucker. III. Illustrative of Prof. O. Lodge’s Paper on a slight Error in the cus- tomary Specification of Thermoelectric Current-direction. IV. and V. Illustrative of Prof. O. Lodge’s Paper on the Paths of Electric Energy in Voltaic Circuits. THE LONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES. ] PAN UA hi Y 28885; I. On the Determination of Chemical Affinity in terms of _ Electromotive Force.—Part IX. By C. R. ALDER WricHT, D.Sc. (Lond.), F.RS., Lecturer on Chemistry and Physics, and ©. THompson, F.C.S., Demonstrator of Chemistry, in St. Mary's Hospital Medical School*. On Voltaic and Thermovoltaic Constants. 164. eae experiments described in Part VIII.+ show that the difference in E.M.F. between two two-fluid cells containing metallic salts in solution, and alike in all respects save that one of the fluids is of different degrees of concentration in the two cells respectively, can be readily obtained by opposing the two cells to one another, and mea- suring the current set up through a total resistance large enough to reduce the current to such an extent that its den- sity, in reference to the plate-surfaces in the cells, falls below a certain limiting value variable with the details of the con- struction of the cells; and, further, that the same value is obtained by means of “‘diffusion-cells,” consisting of two vessels containing respectively the two solutions of different degrees of concentration but containing the same salt, united by a siphon-tube, or constituting a “ gravity’? arrangement, If a be the increment in E.M.F. thus measured, due to a given Increase in the strength of the fluid surrounding the plate acquiring the higher potential, and 6 be the corresponding * Communicated by the Physical Society. Read November 8, 1884, t Phil. Mag. vol. xvii, pp. 282, 377. Phil. Mag. S. 5. Vol. 19. No. 116. Jan, 1885. B 2 Messrs. Wright and Thompson on the Determination of decrement* due to a given increase in strength of the other fluid, then E and e, the electromotive forces of the cell when containing the two stronger and the two weaker fluids respec- tively, are related so that, within experimental-error limits, H=e+a—b. Tt follows from this fact, and from the circumstance that in many cases the values of a and 6 are considerable fractions of e, that the great majority of the valuations hitherto made and published of the electromotive forces of various two-fluid cells cannot be properly compared with the heat-evolutions due to the net chemical actions taking place in the cells ; because no. accurate valuations having been made of the strengths of the solutions used, and the precise character of the plate-surfaces employed not having been noted, the values of the terms a and } cannot be calculated with precision so as to enable the values of H to be deduced for some given standard-strength of solution (e. g. for strength MSO, 100H,0, or MCI, 100H,O, &c.). Differences of several centivolts, and even decivolts, exist between the values assigned to certain voltaic combi- nations by different observers, mainly due to this cause. Accordingly it becomes necessary to repeat most of the work of previous experimenters with due regard to these points before comparisons can be satisfactorily instituted. A large number of cells have therefore been examined during the last four years, under strictly comparable conditions, in order to obtain sufficiently accurate values for the purpose of tracing out the correlations subsisting in different cases between the heat-evolution due to the net chemical change and the maxi- mum H.M.F’. actually developed, when so small a current flows as to cause no appreciable diminution by “ polarization.” All these observitions completely confirm the conclusions already arrived at, that Volta’s law of summation holds within the limits of experimental error, and that the effect of a given alteration in the molecular strength of a saline solution sur- rounding one of the plates of a two-fluid cell is sensibly indepen- dent of the nature of the other fluid and the other plate. It hence becomes possible to assign numerical values or constants to given metals immersed in’ solutions of their salts of given nature and strength, such that the E.M.F. of a voltaic com- bination formed by combining two such immersed metals (by allowing the two solutions to interdiffuse, e. g. ina Raoult cell * With cells set up with acid fluids (e. g. dilute sulphuric acid) sur- rounding the plate acquiring the lower potential, increasing the strength of the acid fluid not infrequently causes an increment, and not a decre- ment, in the E.M.F. of the combination; e.g. in Daniell cells (§§ 112-114, Part) Va): Chemical Affinity in terms of Electromotive Force. 3 or ina “gravity ”’ cell) is calculable by taking the difference between the constants ; 7. e. by employing the formula K=C,—C,, where E is the E.M.F. of the combination, and C,; and C, the two constants involved, such that if C,—C, is of + sign the metal to which C, applies acquires the higher potential, whilst if C;—C, is of — sign the metal to which C, applies acquires the higher potential. For instance, if C, apply to zine and C, to copper in sulphate solution, C;—C,= +1'114, and copper acquires the higher potential ; whilst if C, refer to magnesium, C,—C,= —°725, and zinc acquires the higher potential. 165. The value of the voltaic constant thus applicable to any given metal is variable, within certain limits, with its surface- conditions (according as bright fused metal, electro-deposited, amalgamated, &c.), and also with the nature and strength of the solution of its salt in which it is immersed, and probably also with the temperature, but is independent of the nature of the other half of the cell. In order to fix the numerical value some convention must be made as regards the zero to be adopted as starting-point. For this purpose, and in view of the comparisons desired to be instituted between the values of C,—C, and the heat-evolutions due to the net chemical actions taking place, the most convenient assumption appears to be this :—that the potential of an amalgamated zinc plate immersed in a solution of a given salt of zinc of given mole- cular strength is assumed to be zero, for the purpose of fixing the numerical value of the potential of a plate of the metal to be examined when immersed in an equally strong solution of the corresponding salt of that metal, the two solutions being allowed to interdiffuse (e. g. in a “ gravity”’ cell or in a “ Raoult” cell). For instance, when plates of electro-copper or cadmium are respectively immersed in solutions of the sulphates of these metals, and opposed to amalgamated zinc immersed in zinc- sulphate solution, the molecular strength throughout being 1:0 MSO, 100H,0, the potentials of the copper and cadmium plates are respectively +1:114 and +-360 volt higher than the potential of the zinc plate; which values are accordingly the “voltaic constants’’ for electro-copper in 1°0CuSOQO, 100H,O, and for electro-cadmium in 1:0CdSO, 100H,O respectively: whence it results that the H.M.F. of a cell set up with electro-copper and electro-cadmium plates and solu- tions of the sulphates of these metals of molecular strength 1:0MSO, 100 H,0 will be H=C,—C,=1:114—°360=°754, which in point of fact is the case. On the other hand, when magnesium is opposed in the same way to zinc in sulphate B 2 4 Messrs. Wright and Thompson on the Determination of solutions of strength 1:°0MSO, 100H,0, the former metal acquires a potential lower by *725 volt than that of the latter; whence it results that —°725 is the voltaic constant for mag- nesium in sulphate solution of this strength; wherefore the potential difference set up between magnesium and copper in sulphate solutions of this strength will be 1:114—(—°725)= 1°839 volt, which in practice is found to be the case. Hyi- dently Volta’s law of summation is involved in the proposition that the E.M.I. of a voltaic combination is the algebraic dif- ference between the values of the voltaic constants as thus defined. If the value of a given voltaic constant applying to a given metal immersed in a solution of one of its salts of given strength be known, that for any other given strength is readily calculable by means of the formula =e+a—b when tables of the values of a and 0 are extant, like those given in Part VIII. for certain kinds of plate-surtaces in chloride and sulphate solutions. Out of a large number of voltaic combinations examined, consisting of two metals immersed in solutions of their salts of a given kind (e. g. sulphates, chlorides, nitrates, or acetates), only a few have been found to possess an .M.F’. which, when at its maximum, ditfers by but little from the value calculated from the heat-evolution during the net chemical action taking place in the cell, 7. e. from the difference between the heats of formation of the two salt solutions forming the electrolytes ; the great majority either fall short of this value, or exceed it by quantities well outside of the limits of experimental error. In cells of the latter class, it is evident that the extra work which can be done by the passage of a current through a large external resistance over and above that due to the net chemical change, must be accomplished by a transformation of sensible heat into electric energy; i. e. it is done at the expense of sensible heat, such cells resembling in this respect various of the dif- fusion-cells described in Part VIII. A still more remarkable class of cells has been found, however, in which the current flows in the direction opposite to that deducible from the rela- tive heats of formation of the electrolytes, so that, instead of the plate immersed in the solution of the salt of greater heat of formation acquiring the lower potential (as the zine plate in a Daniell cell), it actually acquires the higher potential. The passage of a current in such cases, consequently, is accompanied by a twofold transformation of sensible heat into current energy, actual or potential; for the chemical changes that take place in the cell are accompanied on the whole by heat-absorption, whilst any work done externally must be Chemical Affinity in terms of Electromotive Force. 5 performed at the expense of sensible heat*. Twenty such combinations have been examined, vide § 209. 166. An attentive consideration of these and other allied phenomena leads to the conclusions that, since only in excep- tional cases does the formula hold, Ey =Hh= C, ram C, (where Hy is the E.M.F. corresponding to the net heat-evolu- tion due to chemical change in the cell), the H.M.F. actually generated must be due to other causes in addition to the heat of chemical change ; and that all the observed phenomena may be clearly accounted for if it be assumed that the difference of potential set up between the two plates of the voltaic com- binations examined 7s due to the superposition of two causes— one, the net heat-development or difference in heat of forma- tion of the two electrolytes surrounding the two plates respec- tively; the other, an action akin to that taking place in a thermoelectric combination, and, like that action, expressible numerically by the algebraic difference between two constants applicable to the two halves of the combination respectively ; so that if £, and k, be the two thermovoltaic constants appli- eable respectively to the metals (and corresponding with the voltaic constants C, and C,), and Hy be the E.M.F. corre- sponding with the difference between these heats of formation, then H=(Q,—C,=Ey +h, — hy. 5 If, then, k;—%, does not differ greatly from zero, E and Ey are nearly equal; if, on the other hand, £;—/, has a consider- able value, E exceeds or falls short of Ey according as that value is positive or negative in sign. If k,—, is negative in sign and also is numerically greater than Hy, E is of the opposite sign to Hy. This case corresponds with the class of cells above referred to in which the metal actually acquiring the higher potential is the one which would be expected to acquire the lower one, were the heat of chemical action the sole cause of potential difference in the cell. The value of the thermovoltaic constant applicable to any given metal necessarily varies in the same way as that of the voltaic constant ; 2. e. it is to some extent dependent on the nature of the metal surface, and varies with the nature and strength of the solution of the salt of the metal employed to * A somewhat analogous phenomenon is presented by gravity-diffusion cells set up with platinum plates and nitric acid of different degrees of concentration. With certain strengths an E.M.F. is set up superior to that calculable from the heat of intermixture of the two acid fluids; so that when a current flows through a large external resistance, part of the work done is performed at the expense of sensible heat; whilst the passage of the current reduces the concentrated acid to lower oxides of nitrogen (precisely as in a Grove’s cell), thereby absorbing additional heat. 6 Messrs. Wright and Thompson on the Determination of surround the plate, and probably also with the temperature”. In some few cases the constant is of positive sign for some solution-strengths or kinds of salts, and negative for others : in these cases the numerical value of the thermovoltaic con- stant is never great, not exceeding a few centivolts at most. If, on the other hand, a metal possess a thermovoltaic constant of considerable magnitude for one class of salts, the sign is the same for all classes of salts examined. So that practically metals may be divided into three classes, viz.:—those where the thermovoltaic constant has uniformly a more or less consider- able negative value, e. g. lead and silver; those where the value is sometimes positive and sometimes negative but never large, e. g. copper and cadmium ; and those where the value is considerable and always positive, e. g. iron, mercury, mag- nesium, and aluminium. In order to have a standard for reduction, it is convenient to make the same convention as that above referred to for voltaic constants, viz. that the thermovoltaic constant for amalgamated zinc is taken as zero when immersed in a solution of a zine-salt corresponding in nature and molecular strength with the solution of the salt surrounding the other plate. As regards the actual numerical values assigned below to the voltaic and thermovoltaic constants, it has been thought best to adhere to the same fundamental assumptions as have been hitherto made throughout this series of papers, viz.:—that the B.A. unit of resistance is actually one earth-quadrant per second; that the factor for converting gramme-degrees into volts is 4410; and that the E.M.F. of Clark’s cell at 15°5 is 1°457 volt, that of a Daniell cell set up with amalgamated- zine and electro-copper plates and solutions of zinc and copper sulphates of equal molecular strength being °765 x 1-457 +0005, or 1:114+°0005 volt. The present state of our knowledge would introduce corrections in all three of these values; but these corrections would so far balance one another that the most probable end result is that all the numerical values given are about 1°6 to 2°2 per cent. too high. Trirst, * §. Czapski has recently found (Annalen der Physik, xxi. p. 209) that zinc-silver-chloride and cadmium-silver-chloride cells diminish in E.M.F. as the temperature rises; whilst iron-mercurous-chloride, cad- mium-mercurous-chloride, and zinc-mereurous-bromide cellsrise in E.M.F. with increasing temperature. In the former class of cell the E.M.F. actually set up is less, and in the latter gveater, than that corresponding with the heat-evolution due to the net chemical change. But it would seem that if there be any general law connecting the variations in E.M.F. with temperature, it is less simple than might appear from these particular results; for Clark’s cells (zinc-mercurous-sulphate) obviously belong to the same class as zinc-mercurous-bromide and cadmium-mercurous- chloride cells; and yet the E.M.F. of a Clark’s cell falls instead of rising as the temperature rises (§§ 139 and 179). | Chemical Affinity in terms of Ldlectromotive Force. 7 the true value of the B.A. unit is about 1:3 per cent. lower than that thus assumed; next, Lord Rayleigh’s recent valua- tions of the H.M.F. of Clark’s cell indicate 1:434 instead of 1-457, or 1°6 per cent. lower (this correction including the previous one). Still smaller values, 1:427 to 1°483 volt, or from 1°7 to 2:1 per cent. lower than Clark’s value, have recently been obtained by Von Httingshausen (Zeitsch. fir Fllectrotechnik, 1884, Heft xvi.); whilst, lastly, the value of Jf, the factor for converting heat units into volts, as deduced from the most recent experiments of Mascart, Kohlrausch, and Lord Rayleigh, is nearly as much below 4410; these three observers finding for the C.G.S. electrochemical equivalent of silver respectively the values ‘01124, -011183, and between °01118 and °01119, from which a mean value of close to ‘0112 results ; so that F= = ='0001038 ; whence, taking J =41°55 x 10°, it follows that JF=4313, or 2:2 per cent. below 4410. So that, on the whole, both EK and Ey are uni- formly overvalued below by amounts probably amounting to between 1°6 and 2-2 per cent.; whence their differences will evidently be overvalued to sensibly the same extent. The errors thus introduced into the values assigned to the various thermovoltaic constants calculated are in no case of such magnitude as to interfere with the general character of the inferences drawn from the numbers thus deduced. 167. A number of cells have been examined, in which a sparingly soluble electrolyte was employed in the form of the solid salt suspended in a solution of some other salt (usually the one surrounding the other plate), e.g. zine-silver-chloride cells, where the silver plate was surrounded by a magma of silver chloride suspended in zinc-chloride solution; or cad- mium-lead-sulphate cells, where lead sulphate suspended in eadmium-sulphate solution surrounded the lead plate. Some noteworthy peculiarities have been observed with such cells as regards the fluctuations in the values of a and 6 in the formula H=e+a—b with variations in solution-strength. Thus, with zinc-lead-sulphate cells (set up with a magma of lead-sulphate and zinc-sulphate solution round the lead plate) the effect of variation in the strength of the zinc-sulphate solution surrounding the lead plate is not the same, either in magnitude or sign, as the effect of the sane variation in the strength of the zinc-sulphate solution surrounding the zinc plate. In the latter case (as already shown, Part VIII.) the effect is of this kind, that as the solution-strength increases the numerical value of ) continually increases, its sign being always the same, viz. positive; but in the former case this is not so, the numerical value of a increasing with the strength S Messrs. Wright and Thompson on the Determination of of the zinc-sulphate solution in which the lead sulphate is suspended up to a certain strength, after which the value again decreases, the sign being negative throughout. Thus the following Table represents the relative values of a and 6 for solution-strengths mZnS8O, 100 H,0, the values of 6 being those described in § 153 for amalgamated-zinc plates, and those of a similarly obtained by means of a series of diffusion- celis set up with electro-coated lead plates immersed in mag- mas of recently precipitated well-washed lead-sulphate and zinc-sulphate solutions of varying strengths; the values are given in millivolts. Value of mm. (it. b. iL 0 0 5 — 6-0 +11-1 1-0 — 95 +163 2:0 —14:0 +22°6 30 —18-0 +27°7 4:0 —16°5 +33°9 5-0 —11-0 +389°5 5:5 — 35 +43°5 Curve no. 1, fig. 1, indicates these values of a as ordinates, the values of m being abscisse. On substituting solutions of cadmium sulphate for those of zinc sulphate as the menstrua in which to suspend lead sul- phate in cells containing lead and its sulphate as one half of the element, analogous results were obtained as regards the general character of the curve, the mean numerical values of a obtained by means of diffusion-cells being given in milli- volts in the following Table, and represented by curve no. 2; Bigs 1: Millivolts. the third column in the table and curve no. 3 represent the corresponding values obtained with diffusion-cells containing Chemical Affinity in terms of Electromotive Force. 9 mercurous sulphate suspended in zinc-sulphate solutions of varying strengths, the plate-surfaces being in this case pure mercury (the “ plates ”’ being the upper surfaces of mercury oc- cupying the lowest portions of the vessels constituting the cells). Values of @ in cells Values of ain cells containing lead sul- containing mercurous Waines of 7. phate Beaded in sulphate Saree in mOdSO, 100 H,0. mZo08O, 100 H,0. me 0 0 “ak —2'3 — 50 1:0 —52 — 66 2°0 —9-2 — 95 3:0 —81 —116 4:0 —69 —12:2 5:0 —56 —12°7 55 —50 —13°0 6:0 —43 it is here evident that whilst the sign of a@ is in all cases negative, the numerical value attains a maximum in the case of lead sulphate suspended in either zinc- or cadmium-sul- phate solution and then diminishes, whereas it continually increases in the case of mercurous sulphate suspended in zinc sulphate. On the other hand, cells containing electro- silver plates immersed in magmas of recently precipitated well-washed silver chloride and solutions of zine chloride of varying strengths, gave values for a negative in sign for low solution-strengths, and increasing in numerical value to a negative maximum as the strength increased, after which the value diminished again to 0, finally becoming positive, and increasing continuously ; these values are given in millivolts in the following table, and indicated by curve no. 4. Value of a in cells containing Value of m. silver chloride suspended in mZnCl, 100 H,O. “25 0 5 — 50 1-0 —12°0 2:0 —20-1 30 —10°2 6-0 + 01 10:0 + 7:0 Analogous values were obtained with cells containing mercurous chloride suspended in zine-chloride solution, a being negative in sign with strengths where. m<6-0, but positive where m=10°0. 168. It is evident that cells of the type now under discus- sion, where the electrolyte surrounding the plate acquiring 10 Messrs. Wright and Thompson on the Determination of the higher potential is of a mixed character (2. e. containing two salts), are to a certain extent comparable with Daniell cells in which the copper plate is surrounded by a mixed solution of zinc and copper sulphates, the only essential dif- ference being in the greater solubility of copper sulphate as compared with lead sulphate, &c. It seemed of interest, therefore, to examine in detail the influence on the numerical value of the H.M.F’. of a Daniell cell exerted by addition of zinc sulphate to the copper-sulphate solution used. Accord- ingly a number of cells were set up containing mixed sulphate solutions of strengths mCuSO,, nZnSO, 100 H.0, the values of m and n varying in the different cases, but all else being the same. The following remarkable results were thus obtained, electro-copper plates being used throughout :— 1. With solutions such that m constantly =1-77, the value of a with continually increasing values of n is never nega- tive, being sensibly =O as long as does not exceed °5, and being +, and continually increasing in numerical value as n increases above ‘9. 2. With solutions such that m does not exceed °5, the value of ais always negative, increasing in numerical value as n increases. 3. With solutions such that m= from 1:0 to 1°42, the value of a is at first negative, increasing to a negative maximum as nm increases, then diminishing to zero, and finally becoming positive, and continuously increasing in numerical value. Fig. 2. Millivolts. The following tables represent these results, which are also indicated by curves 1 to 6 (fig. 2) ; the values are given in millivolts. Chemical Affinity in terms of Electromotive Force. Value of m=1:77. (Curve No. 1.) Value of 2. H.M.F. of cell. Value of a. 0 11140 “1 1114-0 0 5 1114-0 0 1-0 1114-1 + 1 15 Lie Sr + 7 2°0 1117°9 +3°9 m=1:42. (Curve No. 2.) Or 11140 29) 11126 —14 1:0 1112-0 —2:0 15 1111°9 —21 20 t112-1 —1'9 30 1115:0 +1:0 40 1119°5 +5°5 m= 1:28. (Curve No. 3.) 0 1114-0 1-0 1111°8 —2:2 15 1111-0 —30 30 1110-9 —31 40 1115-2 +1:2 5-0 1118-7 +47 m=1:00. (Curve No. 4.) 0 1114-0 25 11133 Ls aly 9) 11126 —14 1:0 1111-7 —2°3 15 11110 —30 2:0 11109 —31 30 1110°8 —32 40 1111:9 —31 5-0 1114-2 +9 m="5. (Curve No. 5.) 1114-0 1113°6 — 1113°3 = 11126 —1 11115 —2 1110-0 —4+ 1107-7 -6 1106°7 —7 m='25. (Curve No. 6.) 11140 1113-1 —0:9 1111-4 —2°6 1108-4 —5d'6 1106°1 —79 11 12 Messrs. Wright and Thompson on the Determination of Hence it appears that cells containing very sparingly so- luble compounds like lead sulphate, silver chloride, &c., sus- pended in solutions of more soluble salts, are comparable with Daniell cells in which the copper plates are surrounded with solutions containing only small quantities of copper sulphate, together with varying quantities of zinc sulphate, increasing the strength of the solution of the more soluble salt, in the first case producing the same general effect on the H.M.F. of the cell as addition of more zinc sulphate to the copper- sulphate solution in the second. 169. A probable explanation of these results is the fol- lowing :—The passage of a current, however feeble, decom- poses both electrolytes in the mixed fluid simultaneously ; so that, for example, in the Daniell cell containing mixed zinc- and copper-sulphate solution round the copper plate, both zinc and copper would be thrown down simultaneously in the metallic state, were it not that whilst still nascent the zine acts on the copper-sulphate solution by a secondary action, precipitating the equivalent amount of copper, and becoming itself zinc-sulphate solution. A portion of the energy gained by this secondary action is nonadjuvant, the amount of nonadjuvant energy depending, inter alia, on the number of molecules of zinc sulphate thus reproduced relatively to that of copper sulphate in solution, in such a fashion that the stronger the copper-sulphate solution, ceteris paribus, the less is the amount of nonadjuvant energy. Hence, from this cause the E.M.F. of a Daniell cell would be necessarily diminished by addition of zinc sulphate to the copper-sulphate solution. But this addition produces also an effect of another kind ; for addition of zine sulphate to the fluid surrounding the plate acquiring the higher potential, making that fluid stronger so far as zinc sulphate is concerned, must set up an interdiffusion effect which will be superposed upon the other sources of difference of potential, tending to raise the potential of the late immersed in the fluid thus strengthened relatively to that of the other plate. Hence there are two causes, acting in opposite directions, thus brought into play, tending to affect the potential-difference set up between the two plates of the cell: if the one predominate, the E.M.F. of the cell as a whole is lowered ; if the other predominate, the E.M.F. is raised. With weak solutions of copper sulphate the former tendency is always greater than the latter, and the H.M.F. falls continuously as zinc sulphate is added to the copper- sulphate solution, as indicated in curves nos. 5 and 6, fig. 2. With strong solutions of copper sulphate the latter tendency is Chemical Affinity in terms of Electromotive Force. 13 always greater than the former, so that in this case the H.M.F. continuously increases in value as zinc sulphate is added to the copper sulphate, as indicated in curve no. 1. With in- termediate strengths of copper-sulphate solution, the former tendency at first predominates over the latter one, the H.M.F. of the cell falling as more zinc sulphate is inter- mixed with the copper sulphate ; but by and by the second tendency becomes stronger relatively to the first, and finally overpowers it, thus causing the H.M.I’. of the cell first to cease diminishing, and then to rise continuously untilit reaches and even surpasses the first value. Mutatis mutandis, evidently the same kind of explanation applies in the case of cells where the mixed electrolyte is a magma of a sparingly soluble salt suspended in a solution of a more soluble one. kt should hence evidently result that the effect of “ polari- zation’ on cells set up with such magmas (2. e. the depre- ciation in H.M.F’. observed with increasing current-density) should be much more marked than with cells containing only readily soluble salts in moderately concentrated solution; since the film of fluid surrounding the plate on which metal is deposited must, with such a magma, become very rapidly de- preciated, as regards the amount in solution of the sparingly soluble salt, on account of the decomposition of that salt caused by the passage of the current. This is, in fact, the case, depreciation of some tenths of a millivolt being readily ob- servable even with currents of density too small to produce any measurable effect on such diffusion-cells as those described in Part VIII. In order to avoid errors from this cause ex- ceeding 0°5 millivolt in magnitude, it was found indispensable to work with currents of density not exceeding from ‘01 to ‘02 microampere per square centimetre when cells containing such magmas were employed ; so that with plates exposing some 3 or 4 square centimetres of surface, and cells of near to 1 volt in H.M.F., a total resistance of at least a megohm, and usually of several megohms, was employed ; and proportion- ately in other cases. . It should further result, if the above explanation be correct, that if two cells be compared, alike in all respects save that in one the copper plate is surrounded by a mixed solution m CuSQ,, n ZnSO, 100 H,0, and in the other by a solution of copper sulphate only, of equal strength, viz. (m +n)CuSO, 100 H,O, the difference between the H.M.F.’s of the two for a given value of the ratio = will not be constant, but will 14 Messrs. Wright and Thompson on the Determination of increase as the value of m diminishes, 7. e. as the mixed solution is weaker so far as the copper sulphate contained is concerned. This is in fact the case, as shown by the following Table, representing the H.M.F.’s of such pairs of cells uniformly containing amalgamated-zine and electro-copper plates, the former immersed in m ZnSO, 100 H,O; the E.M.F.’s of the cells containing m CuSO,, n ZnSO, 100 H,O are derived from the preceding tables, and those of the cells containing (m+n)CuSQ, 100 HO are calculated by means of the for- mula H=1114+a, in which 1114 is the constant H.M.F. in millivolts of an ordinary Daniell cell containing m MSO, 100 H,O, where m is constant for both zinc- and copper-sul- phate solutions (§ 170, footnote), whilst a is derived from the table given in Part VIII. § 154. E.M.F. of cells containing m. aor ee a ce ee (m+n)CuSO, | mCuSO,, » ZnSO, | ence.| m 100 H,0. 100 H,0. Merit ie nes) 1116-9 11140 29 | -28 1-42 | 5 1116-9 1112°6 4°3 339) 1-42 | 10 1120°2 1112-0 8-2 “70 1:00 | 25 1115-6 11133 2°3 "25 100 | °d 1117-2 11126 4-6 ‘50 1:00 | 1:0 1120°4 1111-7 87 | 1:0 1:00 | 15 1123°4. 1111-0 12:47 5 ‘1 1114-9 11136 1:3 2 5 "25 11163 1113°3 3:0 yo 9) 5 1118-6 11126 6:0 | 1:0 5 10 1121°8 1111-5 10°3 | 2:0 D 1°5 1125-0 1110°7 14:3 | 30 5 -| 2:0 1128-0 1110-0 18:0 | 4:0 "25 | °25 1119°6 1113-1 65 | 1:0 20:1 "1:0 1125°8 1111-4 144 | 40 25 | 2:0 1132-1 1109-9 22°2 | 8-0 Fig. 3 represents these numbers, the values of — being the abscissze and those of the “differences ’”’ the ordinates of the curves drawn, which are evidently such that the curve where m has the highest value overlies the others; and similarly throughout. Chemical Affinity in terms of Electromotive Force. 15 n Values o1 —, m Determination of the Numerical Values of the Voltaic Constants and Lhermovoltaic Constants applicable to various kinds of Two-fluid Cells. 170. In all the cells examined, wherever possible, the plates used were coated over by an electro-deposited coat of metal, thrown down by a moderately weak current from a strong solution of a pure salt of the metal. The plates employed usually exposed a total surface of 3 or 4 square centimetres, and the electro-coating was effected by passing the current from three to five Leclanché quart-cells in series through a decomposing cell, in which the plate to be coated formed the negative electrode, the positive one being a plate of the same metal in as great a state of purity as practicable ; the elec- trodes were usually some 3 or 4 centimetres apart. Under these circumstances the coating of metal formed was fairly tough and coherent, although in certain cases somewhat erystalline on the surface. Copper thus deposited from a strong solution of copper sulphate formed a coating of great regularity and toughness. In some cases, however, bright plates of fused metal were necessarily employed, e. g. with iron and aluminium. With zinc the -plates always consisted 16 Messrs. Wright and Thompson on the Determination of of pure metal superficially amalgamated with pure mercury. The cells employed were uniformly constructed of two small beakers or porcelain vessels containing respectively the metals and fluids employed, and united by a siphon-tube, consisting of an inverted Y-tube, the lower ends of which were covered over with thin animal membrane secured by a silk thread, and rendered watertight, when requisite, at the junction of the glass and membrane by the application of a little melted gutta- percha, so that no leakage into or from the siphon took place, saving by osmosis through the membrane. In all cases the temperature varied from 18° C. by only + a few degrees. Saving in the case of certain experiments quoted from pre- vious portions of these researches, and a few others made for special reasons with the quadrant-electrometer, all the obser- vations were made by means of the galvanometer, currents being used of such small density as to produce no sensible depreciation in the E.M.F.; in most cases an external resist- ance of a megohm (and in many of much more) being employed, the valuation being obtained by comparing the readings of the cell to be examined with those of an Alder- Wright’s normal Daniell cell* through the same resistance, using the formula B=1-114x ”, n where m is the average reading of the cell to be valued, and n that of the standard Daniell. Usually alternate readings of the two cells were taken for 20-30 minutes after first setting up, and averaged to obtain the values of m and n. A. Voliaic and Thermovoltaic Constants of Metals immersed in Solutions of their Sulphates. I. Copper. 171. Hlectro-copper presents the remarkable and almost * The term “normal Daniell cell” has been applied by different observers to very different forms of cell, varying several per cents. in E.M.F. amongst themselves, principally according as sulphuric acid of one strength or another, or zinc-sulphate solution saturated or otherwise, is used to surround the zinc plate. What is here referred to as an “ Alder-Wright’s normal Daniell” is a cell set up after Raoult’s form of construction, with amalgamated-pure-zinc and electro-copper plates im- _ mersed in pure solutions of their respective sulphates of the same molecular strength, preferably of strength mMSO, 100 H,O, where m is near to 2:0, 2. e. with copper-sulphate solution nearly but not absolutely saturated, so as not to deposit crystals by chilling or slight evaporation. The ratio of the E.M.F. of such a cell to that of a Clark’s cell at 15°°5 has been found to be sensibly ‘765 to unity. Chemical Affinity in terms of Electromotive Force. 17 unique peculiarity, that the value of its voltaic constant in sulphate solution, as above defined, is practically uniform for all solution-strengths ; for, as already shown, the H.M.F’. of a zinc-copper-sulphate cell is sensibly the same whatever the solution-strength when amalgamated-zine and electro-copper plates are used, viz. (on the assumptions above discussed, § 166) 1:114+-:0005 volt; so that the voltaic constant for electro-copper in sulphate solution is sensibly +1:114 for all solution-strengths (i. e. when referred to amalgamated zinc in zinc-sulphate solution of the same strength as zero). The thermovoltaic constant of electro-copper also shows the same independence ; for the experiments described in § 160 show that the heats of dilution of zinc- and copper-sulphate solutions are sensibly identical for equal dilution-ranges; hence the heats of formation of zinc- and copper-sulphate solutions both of strength m MSO, 100H,0 (where m is the same) must differ by a constant amount whatever the value of m: this amount for m=°25 (and therefore for all other values of m) is, from Thomsen’s results :— Zn, O, SO; aq.=106090 Cu, O, SO3aq.= 55960 ~50130=1:105 volt. Hence, finally, since H=1:114 and H,=1°105 for all solu- tion-strengths, the thermovoltaic constant for electro-copper in sulphate solution is constantly 1°114—1:105=+:009 for all solution-strengths. Il. Cadmium. 172. The experiments with the quadrant-electrometer described in Part VI. show that the electromotive forces of all zine-cadmium-sulphate cells set up with solutions of zine and cadmium sulphate of the same strength, m MSO, 100H,0, are comprised within the limits °360+°0015, when m is between "08 and 2:0, and that those of the analogous copper-cadmium- sulphate cells are similarly comprised within the limits 1525 +0015. The experiments described in Part VIII., however, enable still more exact figures to be deduced. Applying the formula -H=e+a—2, and taking the values of a and 6 from the tables quoted, the following figures result as the most probable ones, the probable error in no case being so great as +002 volt:— Phil. Mag. 8. 5. Vol. i9. No. 116. Jan. 1885. C 18 Messrs. Wright and Thompson on the Determination of WE Hogrome. E.M.F. of cad- /Voltaic constant Value of m. ne ee. cel], | mium-copper for electro- cell. cadmium. Pi 362 752 +°362 “25 "362 “752 +°362 23) 361 "753 +°361 1-0 "360 "754 +°360 2-0 309 JOO - +°359 3°0 308 +°358 4-0 8575 +°3575 5:0 307 +°357 Unlike that of copper therefore, the voltaic constant for electro-cadmium immersed in m CdSO, 100H,O, referred to amalgamated zinc in zinc-sulphate solution of the same strength as zero, varies with the value of m, decreasing as m increases. From these values the corresponding thermovoltaie con- stants are thus calculable. According to Julius Thomsen the heats of formation of zine and cadmium sulphates in solution of strength °25 MSO, 100H,0 differ by 16210 :— Zn, O, SO3 aq. = 106090 Cd, O, SO; aq.= 89880* —— —_ ___. — 16210 The heats of dilution to this strength of more-concentrated solutions are not equal in the two cases: calling them respec- tivelv h, and hg, the heat of displacement per gramme-molecule of cadmium from m CdSO,100H,0 by zine is calculable by the formula H=16210—(h,—A,), when m, h,, and hz have the following values :— mm. hy. hy | 16210—(2,—,). | Co™mesponding 25 0 0 16210 357 5 0 25 16235 358 10 0 75 16285 359 20 50 | 275 16435 362 3-0 100 | 450 16560 365 4-0 175 | 625 16660 367 5-0 375 | 825 16660 367 mel j Hence the values of the thermovoltaic constants for electro- * Thermochenusche Untersuchungen, vol. iii. p. 285. In the calcula- tions given in Part VI. the value 89500 is assigned, taken from Thomsen’s earlier publications (Jowrn. prakt. Chem. xi. p. 401). Chemical Affinity in terms of Electromotive Force. 19 cadmium immersed in mCdSO, 100H,0O (referred to amalga- mated zinc immersed in equally strong zinc-sulphate solutions) are postive for weak solution-strengths and negative for con- siderably strong solutions, being in no case numerically great, viz. as tollows :— | at | ne ba ae Thermovoltaic H. constant. 2 25, bode es 15 +:005 ‘5 “S01 | 2 °7358 +003 1:0 “360 359 +001 20 *359 *362 — .003 30 398 *365 — ‘C07 4-0 "3079 | *367 — “0095 | 5:0 OO. | *367 —°010 Til. Silver. 173. The experiments already described in Part VI. show that the H.M.F.’s of zinc-silver-sulphate cells and the corre- sponding cadmium- and copper-silver cells are respectively 1°536, 1°1805, and -4235, when amalgamated-zine and electro- silver, -copper, and -cadmium plates are used with solutions of (042 MSO, 100 H,O throughout. The probable error attaching to these values was in each case between +°001 and +0015. Hence, referred to amalgamated zine in zinc- sulphate solution of this strength as zero, the following values result for the voltaic constant of electro-silver in saturated silver-sulphate solution :— Semen iver cells... 2. we et ee eee 1:536 From Cadmium -Silver + Zince-Cadmium eells 1:1805+ °362=1°5425 From Copper-Silver + Zinc-Coppercells.. 1°114 4+°4285=1-:5375 These three valuations do not accord so well as those obtained in most of the experiments subsequently detailed and made by means of the galvanometer ; the chief causes of the dis- erepancies lie in the greater want of permanence and wider range of fluctuation noticed with these cells (vide $§ 125-128, Part VI.), probably due to the extremely weak solutions necessarily employed owing to the sparing degree of solu- bility of silver sulphate. Taking the mean value 1:539 volt as the voltaic constant for electro-silver in saturated silver-sulphate solution, it results that the corresponding thermovoltaic constant has a large negative value ; for J rae Thomsen finds that Ag,, O 2 p] 20 Messrs. Wright and Thompson on the Determination of SO 3 aq. =20390, whence the heat of displacement of silver from silver-sulphate solution by zine is 85700 gramme- degrees=1°890 volt, so that the thermovoltaic constant k=HK—H,=15389—1-390= — dol. IV. Lead. 174. A number of cells were examined set up with well- washed recently precipitated lead sulphate (prepared from clear lead-acetate solution and pure sulphuric acid in excess, boiled up many times with distilled water, and washed by decantation), suspended in zinc- or cadmium-sulphate solutions of varying strength. Hlectro-coated lead plates immersed in these magmas were opposed to amalgamated-zine plates immersed in zinc-sulphate solution with the following results, to which are also joined the figures obtained with similar cells, in which electro-copper and electro-cadmium plates immersed in solutions of their sulphates respectively were opposed to the lead piates. The probable error of each value is in almost every instance considerably below +:001 volt, and in no case exceeds +'002 volt. ‘The values refer to cells containing on both sides solutions of the same molecular strength mM” MSO, 100 1eLAG): | Lead sulphate suspended in ie fi nee aye an zinc-sulphate solution. Sb ae ere at - phate solution. . Cadmium-| Lead- : Lead- | Zinc- Lead. Teed Copper. Zinc-Lead. @apeen 0-1 ‘537 173 “DTT ‘550 564 0-5 520 ‘160 “594. 537 ‘OTT 150 ‘512 152 603 *529 D085 2:0 501 "142 ‘611 ‘b19 596 | 3-0 491 133 | +514 | 4-0 ‘487 | ‘509 a 50 ‘487 "505 5°75 487 ‘501 | From these various cell-values, together with those above described for zinc-copper and zinc-cadmium, the following valuations are deducible for the voltaic constants of electro- lead immersed in a magma of lead sulphate in m ZnSO, 100 H,O, or in a magma of lead sulphate in m CdSQO, 100 H,0. Chemical Affinity in terms of Electromotive Force. 21 Lead Sulphate suspended in Zinc-sulphate Solution. = Zine-Cadmium Zinc-Copper p | — +Cadmium-Lead. — Copper-Lead. He | os | i. | : 0-1 587 | 3g9 | = 53 a l= 37 | 536 | . “AE "160 = l= 1-114 mule = | 5 520 a Bett =) ee ae 504 | =520 | -520 Par SL =) ators Sa. peer epee | | 10 512 se} —512 | _ 603 | =5l | 512 | 142) Tae a ee ee, | 20 501 Hey root has i= 0s fh-802 ioc oO) 491 |, geg | = 491 491 40 | -487 487 | e| --487 487 | 5°75 487 487 | Lead Sulphate suspended in Cadmium-sulphate Solution. mM. Zinc-Lead. ieee recat Mean. 0-1 50 | Tit —-550 | -550 05 587 “577 (= 087 | 887 la} oe . 10 ot ea a 586 | =529 | -529 fs 1114) _, as 2:0 BI aoe 506} =518 | -5185 30 514 514 40 509 509 50 OS 505 | 575 501 501 From these mean values for the voltaic constants the following numbers are deduced as the thermovoltaic constants for electro-lead in contact with solid lead sulphate suspended In zinc- or cadmium-sulphate solution ; the heat of displace- ment of lead from (solid) lead sulphate by zine forming solution of zinc sulphate of strength m ZnSO, 100 H,O being 106090 —73800 —h=32290—A); where 106090= Zn, O, SO3 aq. (m='25), 73800 = Pb, O, SO aq. (solid), h=heat of dilution of m ZnSO, 100 H,O to 25 ZnSO, 100 H,O (§ 160). 22 Messrs. Wright and Thompson on the Determination of Lead sulphate suspen- a ee See ded in zine sulphate. Bhaegenic | m h. a sulphate. \. | KE. | B-E_. E. iE | H IL. | O-1 Q |) 712 "536 — 176 "550 — 162 0-5 0 | 712 520 —°192 537 — 175 10 Os ail2 512 —°200 "529 — 183 2-0 SO: gia 502 — 209 5185 — 1925 30 100 | -710 ‘491 —219 ‘514 — 196 4:0 175 | “708 “487 —*221 “509 — 199 50 375 | “704 487 — 217 "505 — 199 5°75 487 ‘501 Hence electro-lead in connexion with its sulphate is analogous to silver, the thermovoltaic constant possessing a considerable negative value ; so that zinc-lead-sulphate and cadmium-lead-sulphate celis have H.M.F.’s notably below the values corresponding with the net chemical actions taking place therein. On the other hand, since the thermoyoltaic constant for copper is a small positive value (+:°009 for all solution-strengths), and that for lead is in all cases a con- siderably larger negative value, whilst copper is the metal acquiring the higher potential in a lead-copper-sulphate cell, it follows that the value of £,—f, in such a cell is always a considerable + quantity, varying from +°009—(—:162) to +:009—(—°221); that is from +°171 to +°230, according as the lead sulphate is suspended in zinc- or cadmium-sulphate solution, and according as the molecular strength of the solutions is low or high. In other words, a lead-copper-sul- phate cell gives an effective maximum H.M.F. of from ‘171 to °230 volt above that corresponding with the net chemical action taking place there. ‘This chemical action represents a heat-evolution of 73800—55960=17840 gramme-degrees per gramme-molecule, corresponding with -398 volt only. The actually observed values consequently correspond to an incre- ment of about 50 per cent. in the H.M.F. of the cell above that due to chemical action. | On the other hand, since the thermovoltaic constant for silver in contact with saturated silver-sulphate solution is a negative quantity numerically greater than that for lead, whilst in lead-silver-sulphate cells silver is the metal acquiring the higher potential, the value of k;—, in such cells must be negative. Thus a cell set up with electro-silver immersed in saturated silver-sulphate solution opposed to electro-lead immersed in a magma of lead sulphate suspended in -042 ZnSO, 100 H,O, must yield a value for kj—k, close to —351—(—'176)=—'175 ; that is, the H.M.F. of such a Chemical Affinity in terms of Electromotive Force. 23 cell must be close to 1:1775—'175 =1-0025 volt, since the heat of displacement of silver from silver-sulphate solution by lead forming solid lead sulphate is 73800—20390=538410 gramme-degrees per gramme-molecule, equivalent to 11775 volt. On trying the experiment, the following values were observed with a number of similar cells :-— Maximum cell-value=1-:008 volt. Minimum a —— (1 bon ee Average as == 03) eae Probable error = 00S... the average observed value being thus sensibly identical with the calculated one. V. Tron. 175. A number of cells were examined set up with electro- copper plates immersed in copper-sulphate solution, opposed to plates of brightened sheet iron of as high a degree of purity as could be obtained, immersed in freshly prepared ferrous- sulphate solution ; and, similarly, numerous observations were made with analogous cells containing electro-cadmium plates immersed in cadmium-sulphate solution, amalgamated-zine plates immersed in zinc-sulphate solution, or electro-lead plates immersed in amagma of lead sulphate suspended in zinc-sulphate solution. ‘The following average values were obtained: with soiutions of molecular strength throughout ‘1 MSO,100 H,0, the cells exhibited far greater want of permanence and much wider fluctuations in H.M.F’. than were noticed with cells of strength 1:0 MSO, 100 H,0; so that, whilst the probable error in the former class of cells ranged from +°003 to +‘U05, that in the latter class was only from +001 to +°002. The negative sign attached to the values for the iron-cadmium cells indicates that iron was the metal acquiring the higher potential, contrary to what might @ priori be anticipated trom the heats of formation, viz. Fe, O, SO; aq. =93200 and Cd, O, SO; aq. = 89880 *. Becme. | Memeaee | Mie we ms —— e Le ees | 399 “445 Tron-Cidmium .. ......... —-035 —'073 PR R-LCAG...6o5 02 00sseoves ‘112 120 Tron-Copper ..........0+0s ‘715 "685 * This peculiarity of iron-cadmium-sulphate cells has been already noticed by Braun (Annalen der Physik, xvi. p. 561). 24 Messrs. Wright and Thompson on the Determination of These values, together with those above cited for zine- cadmium, zinc-lead, and zine-copper cells, give the following valuations for the voltaic constant for polished metallic iron in ferrous-sulphate solution :— : Zine-Cadmium—| Zinc-Lead— Zine-Copper— HUN MON Unilin. | beabiber Copper-Iron. Mem. °360 512 1-114 399 \ 395 } -400 | 399 | 398 +:°035 —1i2 (alee °362 De 1114 Ol} -445 } 435 eA ag \429 | -432 +:073 —'120 — ‘685 It results from these figures that the thermovoltaic constant for polished iron in ferrous-sulphate solutions must always have a notable positive value. Admitting, what is doubtless the case, that the heats of dilution of ferrous- and zinc-sulphate solutions from the molecular strengths 1:0 MSO, 100 H,O to 0-25 MSO, 100 H,O are not widely different, so that their difference is negligible, the heat of displacement of iron from 1:0 FeSO, 100 HO by zine is 106090—93200=12890 gramme-degrees per gramme-molecule, corresponding with 284 volt. Since iron acquires the higher potential in zinc- iron-sulphate cells, the value of 4,—, must be positive and ='398 —°284—+:114; whence the thermovoltaic constant for iron must be +114 for 1:0 FeSO, 100 H,O; and must con- sequently have higher values still for weaker solutions, approxi- mating to °432—'284= +:°148 volt for 0-1 FeSO, 100 H,O. Hence wron is an example of a class of metals opposite in thermovoltaic power to silver and lead, and differmg from copper and cadmium in that, whilst with the last two metals the thermovoltaic constant has never a value largely above or below zero, with silver and lead it has considerable negative values, and with iron it has a notable positive value. One result of this is that a zinc-iron-sulphate cell is analo- gous to a copper-lead-sulphate cell, in that it affords a consi- derably higher effective H.M.F. than corresponds with the net chemical action, viz. from °398 to -4382 instead of +284. Another result is that, since the thermovoltaic constants for cadmium and iron (in solutions 1:0 MSO, 100 H,O) are respectively +°001 and +:°114, if iron were to displace cad- mium from solution of this strength, there would be evolved 93200 —(89880—75)=3395 gramme-degrees per gramme- molecule (75 being the heat of dilution from 1:0 CdSO, 100 H,O to *25 CdSO, 100 H,O), corresponding with a value Chemical Affinity in terms of Electromotive Force. 25 for Ey of -075 volt, cadmium acquiring the higher potential ; but upon this chemical source of potential-difference there is superposed the thermovoltaic action ky —k, = +'001—"114= —'118 ; hence the net effective H.M.F’. is +°075—1138=—:038: | that is, instead of cadmium acquiring the higher potential, iron does so,and a current flows with an H.M.F. of —:038 volt (mean observed value = —‘035 volt). As regards iron-lead-sulphate cells, it is to be remarked that, since lead acquires the higher potential and since the thermo- voltaic constant of lead is a considerable negative quantity whilst that of iron is also a considerable positive quantity, the value of k; —k, is largely negative, viz. for solutions of strengths 1:0 MSO, 100 H,O (zinc-sulphate solution being used to suspend lead sulphate in), —-200—-114=—-314. That is to say, whilst the value of Ey corresponding to this displacement of lead from lead sulphate (solid) by iron is ‘428 volt (corre- sponding with 93200—73800=19400 gramme- -degrees per gramme-molecule), the effective H.M.F. of the cell is little more than one fourth of this, viz. -428—°314=:114 (mean observed value =‘112 volt). The same kind of remark applies to iron-copper-sulphate cells in a less degree, the value of k,—/, being here (for 1:0 MSO, 100 H,O) +:009—-114=—-105 ; that is, whilst the value of Hy is ‘821 (corresponding with 93200—55960= 37240 gramme-degrees per gramme-molecule), the effective H.M.F. of the cell is only °821—:105=-716 (mean observed value =°715 volt). It should consequently result that, if a cell be set up with an electro-silver plate immersed in saturated silver-sulphate solution opposed to bright iron in an equally strong ferrous- sulphate solution, viz. ‘042 FeSO, 100 HO, the value of k,—ky will be largely negative, approximating to —°351—"148= —499 ; so that as Hq is, in this case, 1-605 (corresponding with 93200—20390= 72810 gramme-degrees per gramme- molecule), the effective H.M.I’. will be near to 1:605—-499= 1:106 volt. In point of fact, a number of such cells gave on examination the average value 1:103 with a probable error of +°0038 volt. Lifect of varying the Plate- surface in Lron-copper-sulphate Cells ; and Late of Depreciation of L.M.L’. of such Cells with increasing Current-density. 176. Some experiments were carried out precisely as de- scribed in §§ 115, 124, and 181, with cells set up with polished 26 Messrs. Wright and Thompson on the Determination of iron plates immersed in a strong solution of ferrous sulphate opposed to electro-copper plates in copper-sulphate solution. The values obtained show that, whilst with zince-copper, zinc- cadmium, cadmium-copper, zinc-silver, and copper-silver cells halving the area of the piate on which metal is deposited usually causes a greater decrease in the H.M.F. for a given rate of current-flow than is caused by halving the area of the other plate, the reverse is the case with iron-copper cells. Thus, for example, in one experiment the following numbers were obtained, and similarly in other cases :— ~ | Effect of halving area of the Current in micro- alperes. Tron plate. Copper plate. 500 008 005 1000 ‘010 ‘006 2000 012 ‘008 5U00 ‘O17 ‘O12 10,000 "027 021 With iron-copper-sulphate cells the rate at which the H.M.F, of the cell diminishes as the current-density increases is dis- tinctly more rapid than with cadmium-copper-sulphate cells, or with Daniell cells (zinc-copper-sulphate): thus, for instance: — Rate of current-flow in microamperes per Average E.M.F. Fall in E.M.F, square centimetre. 0 711 20 “708 ‘003 40 698 013 100 685 026 200 “671 040 400 "656 055 1000 632 ‘079 2000 “604 107 It is noticeable that the substitution of dilute sulphuric acid for ferrous-sulphate solution in an iron-copper cell uniformly tends to lower the H.M.F., also rendering the cell-values less permanent and subject to wider ranges of fluctuation than before, probably on account of the “‘ local action ”’ of the acid on the iron; a similar result is also brought about by the substitution of dilute hydrochloric acid for ferrous-chloride solution in cells containing iron and other metals with chloride solutions. Chemical Affinity in terms of Electromotive Force. 27 VI. Magnesium. 177. Two sets of cells were examined containing bright magnesium (wire) immersed in magnesium-sulphate solution opposed to amalgamated zinc and electro-copper in their sul- phate solutions respectively, the solution-strength being 1:0 MSO, 100 H,0 throughout. The galvanometer-readings showed a slight increase in each case as time elapsed after first setting up; the following figures represent the mean readings of each cell during the first half hour after setting up, reduced to volts :— Magnesium-Zine. | Magnesium-Copper. = —— Maximum mean reading ... “740 1-854 Minimum ,, ‘5 oy fale 1-827 Average ,, a ai "724 1:840 IPEODAME CLLOL «2... ccasceoeee. +:0042 +:0041 Hence the following valuations of the voltaic constant result; these values are negative, since zinc acquires the higher, and magnesium the lower potential :— Manis Miaemesiam Cell 025. .c6c.s cei ecececsscscsetessese —°724 Magnesium-Copper + Zinc-Copper... ‘ a —-796 —— Mean = —°725 Julius Thomsen finds Mg, O, SO; aq. =180180 for -25 MgSO, 100 H,O, whence for this strength Hyg=—1°634. Moreover, he finds practically no difference between the heats of dilution of magnesium and zinc-sulphate solutions of strength 1:0 MSO, 100 H,0, so for this strength also Hy sensibly =—1'634. Hence the thermovoltaic constant for bright magnesium in 1:0 MgSO, 100 H,0 is —°725 —(—1°634)= +:909. VII. Aluminium. 178. Two sets of cells were examined, containing bright aluminium plates opposed to amalgamated zine and electro- copper respectively, immersed in sulphate solutions of strength ‘-5 MSO, 100 H,O (instead of using aluminium sulphate, pure -potash alum was employed, the potassium sulphate present 28 Messrs. Wright and Thompson on the Determination of therein being left out of consideration in valuing the molecular strength). From the heat of formation of aluminium-sulphate solution being greater than that of zinc-sulphate, it might naturally be expected that zinc would acquire the higher potential, as with magnesium-zince cells ; but this was not the case, aluminium-zinc-sulphate cells resembling cadmium-iron- sulphate cells (§ 175) in that the current actually generated flows in the direction opposite to that predicable from the heats of formation of the electrolytes : for this reason the cell-values are marked with the — sign. The following figures represent the mean readings during the first half hour after setting up: with aluminium-zine cells the readings slightly diminished in numerical value as time elapsed, and vice versa with the copper- aluminium cells :— Zinc-Aluminium. | Aluminium-Copper. Maximum mean reading ... — 548 +:588 Minimum ,, a — 526 +566 Average = 55 ties —°538 +:578 iPropableverror ce esescaesees +:0034 +:0030 From these figures the following valuations of the voltaic constant result; this constant is of + sign, since aluminium acquires the higher, and zinc the lower potential :— Varin = AALTNVINTUETA 3s « <'- ve sieiaicinieie baie euiseidaeelh sae eee +°538 Zince-Copper— Aluminium-Copper { ee = +536 Mean = +°537 Julius Thomsen finds that Alz, O, SO3 aq.=150630; whence Ey=—‘982 volt. This value is probably not strictly appli- cable in the case of the cells now under discussion (which contained potash alum and not aluminium sulphate); but the error introduced by taking this value is but small as compared with the thermovyoltaic constant deduced, viz. 537 —(—982) = +1519. VIII. Mercurous-Zine-sulphate Cells. 179. A number of cells were examined consisting of amal- gamated-zine plates immersed in zinc-sulphate solution on the Chemical Affinity in terms of Electromotive Force. 29 one side, and of pure mercury with a magma of mercurous- sulphate and zinc-sulphate solution on the other, the zinc sulphate being of the same strength on each side : with these cells the H.M.F. continually fell as the solution-strength rose*. It is evident that these cells differ but little from a cold- prepared Clark’s cell, the essential difference being that in the latter the zinc rod is not coated with fluid mercury to begin with, and is immersed, not in pure zinc-sulphate solution, but in the same magma of mercurous-sulphate and zinc-sulphate solution as surrounds the mercury. This difference in con- struction gives rise to a slight difference in H.M.F. with weaker solutions of zinc sulphate, the Clark’s cell uniformly reading lowest ; with saturated or very strong solutions the difference between the two kinds of cell is less than the expe- rimental errors. Thus the following average values were obtained as the voltaic constants of mercury in contactwith mer- curous sulphate and m ZnSO, 100 H,0, and as the E.M.F.’s of cells like Clark’s but set up with m ZnSO, 100 H,O instead of saturated zinc-sulphate solution :— M. Voltaic constant. E.M.F. of Clark’s cell. Volt. Volt. 5 pls. 1-457 1-457 4:89 1-462 1-462 4°33 1-466 1:465 3°58 1-471 1-469 | 27 1477 1-475 ‘1 1°514 1:510 | The heat of formation of mercurous sulphate being unknown, the corresponding thermovoltaic constants cannot be exactly calculated ; in all probability, however, the value of Eg is near to 1°202 volt, the value for mercurous-zinc-nitrate cells, when m="25 (§ 192), so that the thermovoltaic constant is a large positive quantity, near to +°25 volt at least. [To be continued. | * It may be noticed that mercurous sulphate is about three times as soluble in saturated zinc-sulphate solution as in distilled water. Three saturated solutions gave, on analysis, numbers represented by the following formulee :— Mestllcd water. 3.06 cites cee ene ‘0017 Hg,SO, 100 H,0. Zinc-sulphate solution, about one- BeREEREAAUTALCG, . 32s 5 oie scene ‘0042 Hg,SO,, 2:0 ZnSO,, 100 H.0. Saturated zinc-sulphate solution .. ‘0054 Hg,SO,, 5°75 ZaSO,, 100 H,O. Pana IL. On Arctic Interglacial Periods. By James Croui, LLD., FR.S.* ae Interglacial Periods more marked than the Glacial. —In a former paper f, and also in ‘ Climate and Time’ (chap. xvi.), it was pointed out that in temperate regions the cold periods of the glacial epoch would be far more marked than the warm interglacial periods. In temperate regions the condition of things which prevailed during the cold periods would differ far more widely from that which now prevails than would the condition of things during the warm periods. But as regards the polar regions the reverse would be the case; there the warm interglacial periods would be more marked than the cold periods. ‘The condition of things prevailing in these regions during the warm periods would be in strongest contrast to what now obtains ; but this would not hold true in reference to the cold periods, during which matters would be pretty much the same as at present, only somewhat more severe. In short, the glacial state is the normal condition of the polar regions, the interglacial the abnormal. At present Greenland and other parts of the Arctic regions are almost wholly covered with snow and ice, and, consequently, nearly destitute of vegetable life. In fact, as regards organic life in those regions, matters during the glacial epoch would not probably be much worse than they are at the present day. Greenland and the Antarctic con- tinent are to-day almost as destitute of plant-life as they could possibly be. Although, in opposition to what is found to be true in reference to the temperate regions, the polar inter- glacial periods were more marked than the glacial, it does not follow that on this account the relics of the interglacial periods which remain ought to be more abundant in polar than in temperate regions. On the contrary, the reverse ought to be the case. In the polar regions, undoubtedly, there is least likelihood of finding traces of interglacial periods ; for there, of all other places, the destruction of such traces would be most complete. ‘The more severe the glacia- tion following a warm period, the more complete would be the removal of the remains belonging to the period. If in such places as Scotland and Scandinavia so little is left of the wreck of interglacial periods, it need be a matter of no surprise that in Arctic regions scarcely a relic of those periods remains. ‘The comparative absence in polar regions of * Communicated by the Author. + Phil. Mag. May 1884, p. 375; American Journal of Science, Jue 1884. Dr. J. Croll on Arctic Interglacial Periods. dl organic remains belonging to a mild interglacial period cannot therefore be adduced as evidence against the probable existence of such a period. Who would expect to find such remains in ice-covered regions like Greenland and Spitzber- gen? Although not a trace is now to be found, it is never- theless quite possible that during interglacial periods those regions may have enjoyed a comparatively mild and equable climate. Evidence from the Mammoth in Siberia.—This comparative absence of the remains of a warmer condition of climate in Arctic regions during Pleistocene times holds true, however, only in regard to those parts, like Greenland, which have undergone severe glaciation. When we examine Siberia and other places which appear to have escaped the destructive power of the ice, we find, from a class of facts the physical importance of which appears to have been greatly overlooked, abundant proofs of a mild and equable condition of climate. I refer to facts connected with the climatic condition under which the Siberian Mammoth and his congeners lived. The simple fact that the Mammoth lived in Northern Siberia proves that at the time the climate of that region must have been far different from what it is at the present day. The opinion was long held, and is still held by some, that the Mammoth did not live in Northern Siberia, where his remains are found, but in more southern latitudes, and that these remains were carried down byrivers. It was considered incredible that an animal allied to the Elephant, which now lives only in tropical regions, should have existed under a climate so rigorous as that of Siberia. The opinion that the remains were floated down the Siberian rivers is now, however, abandoned by Russian naturalists and other observers who have carefully examined the country. I shall here give a brief statement of the facts and argu- ments which have been adduced in support of the theory that the Mammoth lived and died where its remains were found. For these facts Iam mainly indebted to the admirable papers by Mr. Howorth on the “ Mammoth in Siberia,” which appeared in the ‘ Geological Magazine’ for 1880. Had the remains of the Mammoth been carried down from the far south by the Siberian rivers, they would have been found mainly, if not exclusively, on the banks of the long rivers, such as the Obi, Yenissei, and the Lena, and in the deltas formed at their mouths. But such is not the case, ‘‘hese are,” says Mr. Howorth, “found even more abun- dantly on the banks of the very short rivers east of the Lena, They are found not only on the deltas of these rivers, but far 32 Dr. J. Croll on Arctic away to the north, in the islands of New Siberia, beyond the reach of the currents of the small rivers, whose mouths are opposite those islands.’’ But a more convincing proof is that “they are found not only in North Central Siberia, where the main arteries of the country flow, but in great numbers east of the river Lena, in the vast peninsula of the Chukchi, in the country of the Yukagirs, and in Kamtskatka, where there are no rivers down which they could have floated from more temperate regions.” Besides, it is not merely in the deltas and banks of rivers that the remains are found, but in nearly all parts of the open tundra; and Wrangell says* that the best as well as the greatest number of remains are found at a certain depth below the surface in clay-hills, and more in those of some elevation than along the low coast or in the flat tundra. Had the Mammoth lived in the south we should, as Mr. Howorth further remarks, have found its remains most abundant in the south, whereas the further north we go the remains become more abundant, and in the islands of the Liachof archipelago, in about latitude 74°, the greatest quantities have been discovered. Again, according to Heden- strom, the bones and tusks found in the north are not so large and heavy as those in the south; a fact which still further confirms the opinion that the Mammoth lived where his remains are found, inasmuch as the greater severity of the climate in northern parts would certainly hinder the growth and full development of the animal. Northern Siberia much Warmer during the Mammoth Epoch than now.—It is true that the Mammoth and the Rhinoceros tichorhinus were furnished with a woolly covering which would protect them from cold; but it is nevertheless highly improbable that they could have endured a climate so severe as that of Northern Siberia at the present day, where the ground is covered with snow for nine months in the year and the temperature is seldom much above zero Fahr. And even if they could have endured the cold, they would have starved for want of food. Some parts of Siberia are no doubt fertile, as, for example, the valley of the Yenisei, described by Nordenskjoldf ; but there is little doubt, as Mr. Howorth remarks, that the larger portion of Northern Siberia, where the Mammoth and the Rhinoceros lived, is now a naked tundra covered with moss, on which no tree will grow. On such ground it is physically impossible that the Mammoth and Rhinoceros could exist, for they cannot graze close to * ‘Polar Sea Expedition,’ English translation, p. 275. + ‘Nature,’ Dec. 2, 1875. Interglacial Periods. dd the ground like oxen. ‘They live on long grass and on the foliage and small branches of trees. Evidence from Wood.—The fact that the Mammoth was most abundant beyond the present northern limit of wood is pretty good evidence that the climatic condition of Northern Siberia must have been milder than now. Wood must have extended, in the days of the Mammoth, far beyond its present limit, probably as far north as New Siberia: facts of obser- vation support this conclusion. The wood found in Northern Siberia consists of two classes—the one is the result of drift, the other grew on the spot. The natives call the former “ Noashina,” and the latter *‘Adamshina;” and the division is supported by Goppert, “who separates the trunks of timber found in Northern Siberia into a northern series, with narrow rings of annual growth, and asouthern, with wider ones. The latter doubtless floated down the rivers, as great quantities do still; while the former probably grew here with the Mammoth.” In the middle of October 1810 Hedenstrom went across the tundra direct to Ustiansk. “On this occasion,” he says, “ T observed a remarkable natural phenomenon on the Chas- tach Lake. This lake is 14 versts long and 6 broad, and every autumn throws up a quantity of bituminous fragments of wood, with which its shores in many places are covered to the depth of more than 2 feet. Among these are pieces of a hard transparent resinous substance, burning like amber, though without its agreeable perfume. It is probably the hardened resin of the larch tree. The Chastach Lake is situated 115 versts from the sea and 80 versts from the nearest forest.” * On the same journey Hedenstrom noticed “ on the tundra, equally remote from the present line of forest, among the steep sandy banks of the lakes and rivers, large birch trees, com- plete, with bark, branches, and root. At the first glance they appeared to have been well preserved by the earth; but, on digging them up, they are found to be in a thorough state of decay. On being lighted they glow, but never emit a flame: nevertheless the inhabitants of the neighbourhood use them as fuel, and designate these subterranean trees as Adamoushtshina, or of Adam’s time. The first living birch tree is not found nearer than three degrees to the south, and then only in the form of a shrub.” F On the hills in the interior of the island of Koteloni “ Sannikow found the skulls and bones of horses, buffaloes, * Wrangell, p. 491. + Ibid. p. 492. fii. Mag. 8. 5. Vol. 19. No. 116. Jan. 1885. D 34 Dr. J. Croll on Aretic oxen, and sheep in such abundance that these animals must formerly have lived there in large herds. At present, how- ever, the icy wilderness produces nothing that could afford them nourishment, nor would they be able to endure the climate. Sannikow concludes that a milder climate must formerly have prevailed here, and that these animals may therefore have been contemporary with the Mammoth, whose remains are found in every part of the island.” * ‘‘ Herr von Ruprecht reported to Brandt that, at the mouth of the Indiga, in 67° 39’ N. lat., on a small peninsula called Chernoi Noss, where at present only very small birch bushes grow, he found rotten birch trunks still standing upright, of the thickness of a man’s leg and the height of aman. In going up the river he met with no traces of wood until he reached the port of Indiga. Here he noticed the first light- fir woods growing among still standing but dead trunks. And higher up the river still, the living woods fairly began.” f Schmidt says that, “‘ where the lakes on the tundra have grown small and shallow, we find on and near their banks a layer of turf, under which, in many places, are remains of trees in good condition, which support the other proofs that the northern limit of trees has retrogressed, and that the climate here has grown colder. I found, on the way from Dudino to the Ural Moun- tains, ina place where larches now only grow in sheltered river- ‘valleys, in turf on the top of the tundra, prostrate larch trees still bearing cones.’’t Schmidt also states that he was informed that at Dudino, just at the limit of the woods, there had been found in a miserable larch wood the lower part of a stem sticking in the ground, apparently rooted, which was three feet in diameter. He also states that, “eleven versts above Krestowkoje, in lat. 72°, he found, in a layer of soil covered with clay on the upper edge of the banks of the Yenissei, well-preserved stems like those of the birch, with their bark intact, and sometimes with their roots attached, and three to four inches in diameter. Professor Merklin recognizes them as those of the Alnaster fruticosus, which still grows as a bush on the islands of the Yenissei, in lat. 704° N.” | Evidence from Shells.—In the freshwater deposits in which the bones of the’ Mammoth are found, there are freshwater- and land-shells, which indicate a warmer condition of climate. I quote the following from Mr. Howorth’s memoir :— “ Schmidt found “Helix schrencki in freshwater deposits on * Wrangell, p. 496. + Bull. of Soc. of Nat. of Moscow; quoted by Howorth. t Schmidt, as quoted by Howorth. Interglacial Periods. 5) the tundra below Dudino and beyond the present range of trees. Lopatim found recent shells of it, with well-preserved colours, 9° further south, in lat. 68° and 69°, within the present range of trees, at the mouth of the Awamka. The most northern limit hitherto known for this shell was in lat. 60° N., where they were found by Maak in gold-washings on the Pit.” “In the freshwater clay of the tundra by Tolstoi Noss, Schmidt found Planorbis albus, Valvata cristata, and Limnea auricularia in a subfossil state ; Cyclas calyculata and Valvata ptscinalis he found thrown up on the banks of the Yenissei, and on a rotten drifted trunk, Limaw agrestis; Anodonta anatina he also found on the banks of the Yenissei as far as Tolstoi Noss, but no further. Pisidiwm fontinale still lives in the pools on the tundra ; as does Succinea putris on the branches of the Alnaster on the Brijochof Islands.” Mr. Belt mentions* that the Cyrena fluminalis is found in Siberia in the same deposits which contain the remains of the Mammoth and the Rhinoceros tichorhinus. “The evidence, then,” says Mr. Howorth, “ of the débris of vegetation, and of the freshwater- and land-shells found with the Mammoth-remains, amply confirms the a priori conclusion that the climate of Northern Siberia was at the epoch of the Mammoth much more temperate than now. It seems that the botanical facies of the district was not unlike that of Southern Siberia, that the larch, the willow, and the Alnaster were pro- bably the prevailing trees, that the limit of woods extended far to the north of its present range and doubtless as far as the Arctic Sea; that not only the mean temperature was much higher, but it is probable that the winters were of atemperate and not of an Arctic type.” (Geol. Mag. Dec. 1880.) The Mammoth Interglacial—lt need be a matter of no surprise that the climate of Northern Siberia during the time of the Mammoth was more mild and equable than now, if we only admit thai the Mammoth was interglacial. That it was of interglacial age is a conclusion which, | think, has been well established by Prof. J. Geikie and others. Into the facts and arguments which have been advanced in support of this con- clusion I need not here enter. The subject will, however, be found discussed at great length in Prof. Geikie’s ‘ Prehistoric Europe’ and in ‘ The Great Ice-Age’ (second edition). Mr, R. A. Wallace considers that one of the last intercalated inild periods of the glacial epoch seems to offer all the necessary conditions for the existence of the Mammoth in Siberia. That the Mammoth was interglacial will be further evident when we consider the climatic conditions of Europe at the * Quart. Journ. pate Soe. yol. xxx, p 464, 36 Dr. J. Croll on Aretie time that it lived there. Before doing so, it may be as well to glance at what evidently were the main characteristics of the interglacial periods. Main Characteristics of Interglacial Climate——They are as follows :— 1. Interglacial conditions neither did nor could exist simul- taneously on both hemispheres. ‘They existed only on one hemisphere at a time, viz. on the hemisphere which had its winter solstice in perihelion. 2. During interglacial periods the climate was more equable than it is at present; that is to say, the difference between the summer and winter temperatures was much less than it is now. The summers may not have been warmer or even so warm as they are at present, but the temperature of the winters was much above what it is at the present day. 3. During interglacial periods the quantity of equatorial heat conveyed by ocean-currents into temperate and polar regions was far in excess of what it is at present. On this account a greater uniformity of climate then prevailed : that is to say, the difference of climatic conditions between the subtropical and the temperate and polar regions was less marked than at present—the temperature not differing so much with latitude as it now does. 4. Mildness, or a comparative absence of high winds, cha- racterized interglacial climate. ‘This partial exemption from high winds resulted from the fact that the difference of tem- perature between the equator and the poles, the primary cause of the winds, was much less than at the present day. 5. Another character of interglacial climate was a higher mean temperature than now prevails. This, amongst other causes, resulted from the great amount of heat then transferred by ocean-currents from the glacial to the interglacial hemi- sphere. 6. During interglacial periods the climate was not only more equable, mild, and uniform than now, but it was also more moist. This was doubtless owing mainly to the fact of the presence then in temperate and polar regions of so large an amount of warm intertropical water. In short, it was the presence of so much warm water from intertropical regions which mainly gave to the climate of the interglacial periods its peculiar character. All these characteristics of interglacial climate have been fully established by the facts of geology, but they are also, as we have secn, deducible @ priori from physical principles. They follow as necessary consequences from those pliysical agencies which brought about the glacial epoch. Interglacial Periods, Si Evidence from the Mammoth in Europe.—Skeletons and detached remains of the Mammoth have been found in nearly every country in Europe. Mr. Howorth, in his memoir*, gives the details of the finding of these in various parts of Russia, Germany, Denmark, Sweden, Belgium, France, Eng- land, and other countries. It is shown that the conditions ~ under which the Mammoth-remains have been found in Hurope are almost identically the same as those under which they are found in Siberia, with the exception, of course, that in Hurope no careases with their flesh intact have been met with. Again, the deposit in which the Mammoth-remains are found in Hurope is the same as that in which they occur in Siberia. The deposit is a freshwater one, consisting of marly clay and gravel, and containing plant-remains and land- and freshwater-shells. When these plants and shells are examined : they are found to indicate the same interglacial condition of climate as that which prevailed in Siberia during the time the Mammoth lived in that region. In the case of land-plants it is, of course, only under excep- tional circumstances, as Prof. J. Geikie remarks, that they can be found in a conditicn suitable for the botanist. Now and again, however, beds with well-preserved plants are met with, buried under lacustrine deposits. In a still better state of preservation are the plant-remains and shells which have been discovered in the masses of calcareous tufa which have been formed upon the borders of incrustating springs. An exami- nation of the plant-remains found under those conditions shows that during Pleistocene times, when the deposits in which the Mammoth bones are found were being formed, the climate was more equable and uniform than it is at the present day. The fossiliferous remains yielded by the tufas have led to most important results as to the climatic condition of the Pleistocene period, into the details of which I need not here enter. These will be found at full length in Prof. J. Geikie’s ‘Prehistoric Hurope, chap. iv.f It will suffice at present simply to refer to the general conclusions to which these researches have led, in so far as they bear on the climatic conditions prevailing at the time the Mammoth lived so abundantly in EKurope. In the tufa deposits of Tuscany have been found numbers of plant-remains of indigenous species, commingled with others which now no longer grow in Tuscany. Amongst the latter is the Canary laurel, which now flourishes so luxuriantly in the Canary Islands, on the northern slopes of the mountains, * Geol. Mag. May 1881. + See also Mr. Howorth’s memoir, Geol. Mag. June 1881, 38 Dr. J. Croll on Arctie at an elevation of from 2000 to 5000 feet above the sea-level— a region, remarks Prof. J. Geikie, nearly always enveloped in steaming vapours, and exposed to heavy rains in winter. In that deposit is also found the common laurel, associated with the beech. This is not now the case, as the laurel requires more shade than it can find there at present, while the beech has retreated to the northern flanks of the Apennines to obtain a cooler climate. In the tufas of Provence are found groups the same as those which flourish there at present, but commingled with them are also the Canary laurel and other plants which are no longer natives of Provence. Saporta directs attention to the fact that species such as the Aleppo pine and the olive, demanding consi- derable summer-heat rather than a moist climate, are entirely wanting in the tufas. . Similar to those of Provence are the tufas of Montpellier. Saporta concludes that when all those species lived together the climate must necessarily have been move equable and humid than at present. In other words, the summers were not so dry and the winters were milder than they are now. The deposit near Moret, in the valley of the Seine, is still more remarkable in showing the equable condition of climate which then prevailed. The assemblage of plants found there tells a tale, says Prof. J. Geikie, which there is no possibility of misreading. “ Here,” he says, ‘we have the clearest evidence of a genial, humid, and equable climate having formerly characterized Northern France. The presence of the laurel, and that variety of it which is most susceptible to cold, shows us that the winters must have been mild, for this plant flowers during that season, and repeated frosts, says Saporta, would prevent it reproducing its kind. It is a mild winter rather than a hot summer which the laurei demands, and the same may be said of the fig-tree. The olive, on the other hand, requires prolonged summer heat to enable it to perform its vital functions. Saporta describes the fig-tree of the La-Celle tufa as closely approximating, in the size and shape of its leaves and fruit, to that of the tufas in the south of France, and to those of Asia Minor, Kur- distan, and Armenia. But if the winters in Northern France were formerly mild and genial, the summers were certainly more humid, and probably notso hot. ‘This is proved by the presence of several plants in the tufa of La Celle which cannot endure a hot arid climate, but abound in the shady woods of Northern France and Germany.” The plants found in the tufas of Canstadt are much similar to those of Moret. Mr. Howorth, in regard to the deposits of Interglacial Periods. og those places, says :—“The coexistence of the species found there, remarks M. Saporta, proves very clearly that, notwith- standing the variations due to latitude, Hurope, from the Medi- terranean to its central districts, offered fewer contrasts, and was more uniform than itis now. A more equable climate, damp and clement, allowed the Acer pseudo-platanus and the fig to live associated together near Paris, as it allowed the reindeer and hyzna. The Acer grows with difficulty now where the Ficus grows wild, while the latter has to be pro- tected in winter in the latitude of Paris.’’* Hqually conclusive is the testimony borne by the Mollusca of the tufas. In the tufas and marls of Moret, in the vailey of the Seine, thirty-five species were discovered. The majority of these must have lived in damp and shady places, in the recesses of moist woods, and on the leaves of marsh-plants. The shells, M. Tournouér concludes, bespeak a condition of climate more uniform, damp, and equable than now prevails in that region, with a somewhat higher mean annual tempe- rature. In the alluvial deposits of Canstadt, in Wiirtem- berg, a class of shells indicating a similar condition of climate has been discovered. ) The evidence furnished by the animals found most abun- dantly with the Mammoth in Hurope and Siberia, Mr. Howorth thinks, points to the same conclusion as that of the plants and mollusca. The same mild and equable condition which allowed of the Mammoth living in Northern Siberia during Pleistocene times thus equa!ly prevailed over the whole of Hurope. We have seen that, according to the Physical Theory, this con- dition of climate was in every respect precisely what it ought to have been on the supposition that it was interglacial. It was a condition mild, equable, uniform, humid, and of a higher mean annual temperature than we have at the present day. There is, however, direct and positive evidence that this condition of climate was interglacial; for the facts both of geology and of palzontology show that it was preceded and succeeded by a state of things of a wholly opposite character. Lhe Mammoth Glacial as well as Interglanal.— Although the Mammoth could have lived in Arctic Siberia only during an interglacial period, it does not foliow that it must have perished during the succeeding glacial period. When the cold came on, and the vegetation on which it subsisted began to disappear, it would move southwards, and would continue its march as the cold and severity of the winters increased. * Geol. Mag. June 1881. AO Dr. J. Cro! on Arctic During the continuance of the ten or twelve thousand years of Arctic conditions it would find in Southern Hurope and elsewhere places where it could exist. At the end of the cold period, and when the climate again began to grow mild and equable, it would retrace its steps northwards. There is, however, little doubt that during the severity of a glacial period, and when necessarily confined to a more limited area, its numbers would be greatly diminished. There is every reason for believing that the Mammoth outlived all that suc- cession of cold and warm periods known as the glacial epoch proper, and did not finally disappear till recent postglacial times. It was probably about the commencement of a cold period, and before the Mammoth had retreated from Northern Siberia, that those individuals perished whose carcases have been found frozen in the cliffs. The way in which they probably perished and became imbedded in the frozen mud and ice, has, I think, been ingeniously shown by Dr. Rae*. Arctic America during Interglacial times.—We have seen that the eastern continent in Pleistocene times enjoyed in the Arctic regions interglacial conditions of climate. It is true that on the western continent we have not in Arctic regions such clear and satisfactory evidence of an interglacial period. But it would be rash to infer from this that the western con- tinent was, in this respect, less favoured than the eastern. That we should find less evidence at the present day of former interglacial periods in Arctic America than in Arctic Asia, is what is to be expected, for the glaciation which succeeded interglacial periods has been far more severe in the former region than in the latter. The remains of the Mammoth have, however, been found in Arctic America, in ice-cliffs at Kotzebue Sound, under conditions exactly similar to those of Siberia. In Banks’s Land, Prince Patrick’s Island, and Melville Island, as in Northern Siberia, full-grown trees have been found in abundance at considerable distances in the interior, and at elevations of two or three hundred feet above sea-level. The bark on many of them was in a perfect state. Capt. McClure, Capt. Osborn, and Lieut. Mecham, by whom they were found, all agreed in thinking that they grew in the place where they were found. It is true that more recent Arctic voyagers have come to the conclusion that these trees must have been drifted down the rivers from the south. There can be little doubt that the greater part of the wood found there, as in Siberia, is drift- wood. But may there not be also, as in Siberia, two kinds * Phil. Mag. for July 1874, p. 60. Interglacial Periods. Al of wood ?—a “ Noashina”’ and an ‘“‘Adamshina,”’ a kind which was drifted and another kind which grew on the spot. This is a point which will require to be determined. That so little has as yet been done in the way of searching for such evidence of interglacial periods, is, doubtless, in a great measure due to the fact that most of those, if not all, who have visited those regions entertained the belief that there is an @ priort improbability that a condition of climate which would have allowed the growth of trees in such a place prevailed so recently as Post-tertiary times. Hven supposing those Arctic voyagers had considered the finding of inter- glacial deposits a likely thing, and had in addition made special search for them, the simple fact that they should have failed to find any trace of them could not, as we have already shown, be regarded as even presumptive evidence that none existed. Take Scotland as an example. Abundant relics of interglacial age have there been found from time to time ; butamongst the many geologists who visit that country year by year, how few of them have the good fortune of dis- covering a single relic. In fact a geologist might search for months, and yet fail to meet with an interglacial deposit. The reason is obvious. The last ice-sheet, under which Scotland was buried, was so enormous as to remove every remnant of the preceding interglacial land-surface, except here and there in deep and sheltered hollows, or in spots where it may happen to have been protected from the grinding power of the ice by projecting rocks. But all those places are now so com- pletely covered with boulder-clay and other deposits that it is only in the sinking of pits, quarries, in railway-cuttings, and other deep excavations that traces of them accidentally turn up. Now if it is so difficult to find in temperate regions, in a place like Scotland, interglacial remains, how much more difficult must it be to meet with them in Arctic regions, where the destructive power of the ice must have been so much greater. Something like indications of an interglacial period appear to have been found by Professor Nordenskjéld in Spitzbergen. “Tn the interior of Ice-fjord,” he says, “and at several other _ places on the coast of Spitzbergen, one meets with indications either that the polar tracts were less completely covered with ice during the glacial era than is usually supposed, or that, in conformity with what has been observed in Switzerland, interglacial periods have also occurred in the polar regions. In some sandbeds not very much raised above the level of the sea one may, in fact, find the large shells of a mussel (Mytilus edulis) still living in the waters encircling the Scan- dinavian coast. It is now no longer found in the sea around AQ On Arctic Interglacial Periods. Spitzbergen, having been probably routed out by the ice- masses constantly driven by the ocean-currents along the coasts.” * This testimony is the more valuable as it is given by an experienced geologist so much opposed to the theory ef inter- glacial periods. A more special and thorough search of those beds might probably reveal further indications of inter- glacial age. Was Greenland free from Ice during any of the Interglacial Periods ?—There is nothing whatever improbable in the sup- position that during some of the earlier interglacial periods, when the eccentricity was about a maximum, the ice might have completely disappeared from Greenland, and the country become covered with vegetation. Mr. Wallace thinks that the existence at present of an ice-sheet on Greenland is to be explained only by the fact that cold currents from the polar area flow down both sides of that continent. He farilien thinks that could these two Arctic currents be diverted from Greenland, “that country would become free from ice, and lige. even be completely forest-clad and habitable.”’ 7 I am inclined to agree with Mr. Wallace in thinking that the withdrawal of the two cold currents in question would effectually remove the ice. We know that Greenland is at present buried under ice, as has been shown on former occa- sions, simply because there happens to be about two inches more of ice annually formed than is actually melted. It certainly would not require any very great change in the present physical and climatic conditions of things to melt two additional inches per annum. If this were done the ice would ultimately disappear. A simple decrease in the volume of the two currents might possibly bring about such a result. A cause more effectual would, however, be an increase in the temperature and volume of the Arctic branch of the Gulf-stream. Norr.—This will probably be my last paper on questions relating to geological climate. There are many points I should have wished to consider more fully, but advancing years and declining health have rendered it necessary for me to abandon the subject altogether in order to be able to finish some work, in a wholly different field of inquiry, which has been laid aside for upwards of a quarter of a century. * ‘Qn former Climate of Polar senna? Geol. Mag. Nov. 1875, p. 531. See also “Geology of bt Geol. Mag. 1876, p. 267. + ‘Island Life,’ p. 149. Peo «| Ill. A Capillary Multiplier. By A. M. Worrturineton, M.A.* [Plate I. figs. 1 & 2.] : veer little instrument (Plate I. fig. 1) consists simply of a rectangular strip of platinum foil of known length rolled into a cylindrical coil, whose successive convolutions are kept separate at a distance of about 2 mm. by means of a strip of glass beads in the upper portion of the coil. The lower edges of all the convolutions are in the same plane ; and the instrument when in use hangs from one end of a balance- beam with this plane horizontal. The liquid whose surface-tension is to be determined is placed below the coil in a vessel which can be raised till the free surface touches the base of the coil. The pull now exerted on the coil is measured by weights placed in the other pan ; and these weights afford, when certain precautions shortly to be mentioned are taken, an accurate measure of the surface-tension of the liquid. The method is really that used twenty years ago by Wil- helmyt, and more recently by M. Duprét, who, however, employed only a single cylindrical sheet of platinum instead ofa coil, and an hydrometer instead ofa balance for measuring the pull. The only novelty lies in the substitution of the coil for the single sheet, by which the sensitiveness of the method is increased many-fold. The principles involved may be briefly explained as follows : When any liquid is placed in a vessel whose sides it wets, 2. e. against which the edge-angle of the liquid is 0°, the liquid is raised round the edge above the level of the free surface, and the weight of liquid so raised is equal to the surface- tension of the liquid multiplied by the periphery across which the surface-tension acts. When the periphery (p) is known and the weight (wv) of liquid raised is known, then the tension per unit of length is known to be =, When a capillary tube is used for measuring the surface- tension, the periphery across which the force acts is the internal perimeter of the tube, and this is too small to be * Communicated by the Physical Society: read November 22, 1884 (communicated by J. H. Poynting). Tt Poggendortf’s Annalen, 1863, No. 6, p. 177. t See Théorie mécanique de la Chaleur, par M. A. Dupré (Paris, 1869), p. 245 et seq. 44 Mr. A. M. Worthington on capable of very exact measurement ; while the weight of liquid raised is that of a column whose height can indeed be accu- rately measured, but whose sectional area is again too small to be very correctly determined. | If a very wide tube be used, the perimeter can be measured with much greater accuracy ; but the weight of liquid raised cannot now be determined in the same way as before, since the volume included between the surface of the meniscus and a horizontal plane touching its lowest point is now an import- ant part of the whole volume raised. But the weight of the liquid raised along both the inside and outside perimeters of the tube is equal to the reactionary pull downwards of the liquid on the tube and may be determined by measuring this latter. M. Dupre’s wide cylinder of platinum foil was simply a tube whose inner and outer perimeters were sensibly equal and accurately known, and the pull across this perimeter could be determined in the way described. The great advantage of the coil over the single sheet is that the periphery across which the tension acts may be made very great, while the diameter of the coil, and consequently the quantity of liquid required and the area of its exposed surface, remains small. Thus one of my coils is made of a strip 50 centim. long and presents a perimeter of 1 metre, while its diameter is only 3 centim., and the pull of water on this is about 8 grams. The beads of which the strip is composed for separating the convolutions are made of hard glass, and strung on fine platinum wire, so that the instrument may be very readily cleaned by heating to a bright heat in the Bunsen flame. The beads should not reach within 2 or 3 centim. of the lower edge of the coil, in order that the liquid which rises between the convolutions may not reach so high as to wet the glass. If the consecutive coils are 2 millim. apart, then water (which is raised higher than any other known liquid) will attain a height of about °8 centim. But since the coil is liable to be dragged down into the liquid, it is well to leave an ample margin. If the coil dips below the plane surface of the liquid, there is a correction necessary on account of the buoyancy of the liquid. If, on the other hand, the base of the coil is raised above the free surface, there is a traction to correct for, due to the adhesion of the liquid to the horizontal section of the spiral edge. By adjusting the level of the liquid-surface after it has wetted the coil to the level of the base of the coil, when the balance-beam is horizontal, the necessity for these a Capillary Multiplier. 45 corrections is avoided. The thickest foil that I use is ‘0025 centim. thick, and the correction due to an error of adjust- ment of the surface, amounting to 1 millim., would, in a measure of the surface-tension of alcohol, amount to 34, of the whole ; and it is easy to make the adjustment within much narrower limits than 1 millim. Method of Use. In order to prevent the coil from being dragged below the surface, or, on the other hand, separated from it, I find it convenient to fix two stops A and B (see fig. 2), just above and below the beam of the small unmounted balance that I employ : two stout pins stuck in a cork that is held in its place by a rod (as in the figure) serve the purpose very well. After cleaning the coil in the Bunsen flame, adjusting its base so as to be horizontal by means of the three suspending cords, which are made of silk and are provided with beads through which the silk forms nooses like a tent-rope, and accurately counterpoising, a block C is placed below the right-hand pan at such a height that the pan rests on it when the beam is horizontal. Then the liquid to be tested is placed in a thin beaker, which stands on a small table, whose height can be easily adjusted by a ratchet-screw (the end of an optical lantern with a card on the top does very well). This is raised till the platinum is wetted, when it is at once drawn as far below the surface (4 or 5 millim.) as the position of the stop A will permit. The pan D is now pressed down by hand on the block C and held there, while the level of the liquid surface is adjusted to the base of the coil. Then D is released, C removed, and weights added to restore equilibrium. It will be observed that the coil is, by the process of putting on the weights, gradually drawn out of the liquid, so that the topmost element of the elevated liquid will everywhere be in contact with a portion of the coil that has been thoroughly wetted, which will with most liquids reduce the contact-angle to zero. A few points may be usefully mentioned about the con- struction of the coil. To make the strip of glass beads I use combustion-tubing drawn out to a diameter of about 2 millim. and cut first into lengths of about 20 centim. Out of a number of such pieces, a careful selection is made of those of most uniform thickness ; these are then accurately cut to a length of about 2 centim., and of the beads thus made the strip is put together by passing through each in turn in opposite directions the two ends of a fine platinum wire (size no. 36). The smoothness of the glass strip allows the platinum coil to 46 Mr. A. M. Worthington on a Point slide within it, so that by gentle pressure against a hard plane surface the edges of the convolutions can at any time be very accurately adjusted to the same plane. Other forms might doubtless be given to the multiplier, but the cylin- drical coil is the most compact and requires for its use the smallest amount of liquid. The labour of double-threading the long strip of beads is considerable, and I have tried to avoid it by substituting a strip of asbestos cardboard, which would allow the coil to be cleansed by the action of the flame as before. But though in other respects satisfactory, the asbestos very rapidly gains in weight through the absorption of the vapour of many liquids, and cannot therefore be used unless wrapped in very thin platinum foil; but when so wrapped it is troublesome to coil, and does not allow the same ready adjustment of the edges of the coil to one plane. Clifton College, Bristol, October 16, 1884. IV. Note on a Point in the Theory of Pendent Drops. By A. M. Worruineton, M.A. * [Plate I. figs. 3-6. | N a paper on Pendent Drops (Proc. Roy. Soc. no. 214, 1881) I explained how, from a tracing of the outline of a drop pendent from a circular base, the value of the surface- tension of the liquid could be deduced with an accuracy that compared favourably with that of any other method. The most difficult part of the process is the measurement at various levels of the inclination of the tangent of the curve to the axis; and I find that this difficulty does not disappear, as I hoped it might, when a photograph of the magnified image of the drop is substituted for a tracing made by hand. It is essential to the success of the method to measure this inclination at levels where the horizontal sectional area of the drop is widely different. Thus in a drop shaped as in fig. 3 Plate I. it would be desirable to measure the inclination, say, at the level AB and again at the level CD. Now at AB, where the inclination changes very slowly, its value may be very accurately determined ; but at CD the change of incli- nation is rapid and its determination difficult. Tt has lately occurred to me that the necessity of finding the value of the inclination at more than one level may be * Communicated by the Physical Society: read November 22, 1884 (communicated by J. H. Poynting). in the Theory of Pendent Drops. AT avoided, while that level may be so chosen that the tangent is there vertical or changes its inclination very slowly. Let ADCE (fig. 4) represent a horizontal circular section of the pendent drop taken at any level ; ABC the generating curve in the plane of the paper; DBE the same curve ina plane at right angles to the paper. Consider first the equi- librium as regards vertical forces of the mass of liquid below the plane section. We may equate the vertical component of the surface-tension (T) round the circumference ADCH, to the weight (W) of the liquid below the section + the pressure on the area ADCH; so that, signifying by 2 the unknown distance of this section from the level of the free surface of the liquid, and by A the weight of unit volume of the liquid, we have TcosO0x7AC=W+7AO*'#A. . . . (i) Again, if we consider the equilibrium, as regards horizontal forces parallel to the plane of the paper, of the mass ABDOH, we see that the surface-tension acting horizontally round the periphery DBE is equal to the hydrostatic pressure on the area DBE + the sum of the tensions across each element of the semicircumference DAKE, each resolved first horizontally and then normally to DH. Now the hydrostatic pressure is equal to the area DBE x density of liquid x depth of the centre of gravity G of the area below the level of the free surface, and this depth =OG-+z2; and I have found that OG can be determined with great accuracy by cutting the figure out of carefully selected writing-paper, and balan- cing ; again the sum of the horizontal tensions across the semicircumference resolved normally to DE=T sin ODE; so that T x length DBH=T sin @DE +area DBE (OG+z2) A, or T(length ABC — AC sin 0)=area ABC (OG+2)A; (ii.) and from these two equations 2 can be eliminated and T found. Now the section can be chosen at a place of contrary flexure, where the value of cos @ can be obtained with very great accuracy ; or, again, if the circular base from which the drop depends be small enough the drop will assume the form shown in fig. 5, in which at a certain level MN the curve is vertical, and sin@=0. When this is the case equation (i.) becomes Poem == We aA ga es 25, (lly) 48 Dr. A. Elsass on a new while (ii.) becomes T'x ABC=area ABC(OG +2) A. iG The method here shown of considering separately the equilibrium first of vertical and then of horizontal forces is equally applicable to sessile drops and to portions of liquid raised by adhesion to a base, and brings out very clearly many results which have hitherto usually been obtained as special cases by rather complicated processes of integration. Clifton College, Oct. 27, 1884. V. On a new Form of Monochord. By Dr. A. Etsass of Marburg”. FHXHE monochord has been employed from time immemorial to demonstrate the laws of transverse vibrations. It is used to show that, in producing its fundamental note, a string vibrates in its whole length, but that, in producing the higher partial tones, nodes are formed; and by its means the law of Mersenne can be demonstrated, according to which the fun- damental note of a string depends upon its length, its tension, and its mass. In recent times Melde’s apparatus has also been employed to show the mode of vibration of the string, which by its means may be made evident to a large audience. The essential parts of this apparatus are a tuning-fork and a stretched yielding thread, one end of which is attached to the tuning-fork. If the tuning-fork is made to sound, its vibra- tory motion induces a transversal vibration of the thread, both when the motion of the tuning-fork takes place at right angles to the thread and when it takes place in the direction of its length and the magnitude of the vibrations of the thread is so great that they can be observed from some dis- tance off. The present communication describes a new form of vibration-apparatus which combines the advantages of the monochord and of Melde’s apparatus. In Melde’s apparatus the thread is made to assume different forms of vibration by altering its tension, and with it the ratio of its oscillation-period to that of the body which produces the motion; but the oscillation-period itself, which depends upon the period of the exciting body, is not subject to variation. In the arrangement to be described, however, all variations can be obtained with the same thread by altering the period of the exciting body, so that the law connecting the normal * Translated from the Zettschrift fii Instrumentenkunde for October 1824, frcm a separate impression communicated by the Author. Form of Monochord. 49 vibration-form of the thread and the period of corresponding number of vibrations can be at once exhibited. The problem, how to excite a thread to vibration by an external periodic action the period of which can be varied at pleasure, can only be solved by employing a motion of rotation to excite the vibration. If one end of the thread is to be used as the exciting-point, then, in order that the external motion shall take place at right angles to the thread, this point must be fastened in sucha way that it cannot be displaced in the direc- tion of the thread, but is capable of motion at right angles to it. This is nearly the case if the thread is attached to a rigid lever capable of motion, without much friction, on fixed points round an axis at right angles to the thread. If, then, by means of a revolving toothed wheel or some similar arrange- ment, periodical impulses can be given, this arrangement will render possible the solution of the problem proposed. As far as the nature of the vibrations of the thread thus produced is concerned, it is clear that stationary vibrations of the thread can only take place when the period of the external motion stands in some simple ratio to the period ofa component of the natural vibrations of the thread—if, at least, we make the assumption that the lever comes into contact with the rotating body only during an indefinitely small time in each impulse. We see at once that the vibrations of a thread of which one end is not fixed but takes part in the vibration cannot take place in the same manner as the free vibrations of a thread of which both ends are fixed. The mathematical theory, how- ever, which [ intend to give in another place, shows that the difference between the form of the constrained vibrations with which we are concerned and that of the free vibrations of the thread is only of small amount. In the constrained vibrations the thread swings without true nodes, i. e. points which are absolutely at rest; but instead it has apparent nodes which are points of minimum amplitude of vibration, and the moving end of the thread itself is such a node of minimum amplitude. This remark, of course, holds good only upon the assumption that the end of the thread attached to the lever makes only very small excursions. li is easy to take account of the relation which must exist between the period of the external excitation and the period of the vibrations of the thread. Let us Fig. 1. imagine that the oscillations of a pendulum are maintained by periodical blows, taking m—> @ wees. e place always in the same direction. Let a b a and 6 (fig. 1) denote the limiting positions Phil. Mag. 8.5. Vol. 19. No. 116. Jan. 1885. iD) 50 Dr. A. Elsass on a new of the bob of a pendulum; then it is only necessary each time that it comes into the position a to give it a blow in the direc- tion ab. The motion will be sustained if the period T of the excitation is equal to the period of the oscillation. We see, however, that the motion of the pendulum may also be sus- tained by impulses of the periods 2T, 3T, &c.; for if the pendulum-bob is at a at the times 0, T, 2T, 37, &c., it is suffi- cient that it should receive an impulse in the direction ab at the instants T, 3T, 5T in order to replace the energy lost by friction. It is seen, however, that the amplitude of the pendulum-oscillations will be greatest for equality of periods, if the impulses are in all cases of equal intensity. From these considerations we should expect that, in the constrained vibrations of the thread, the mth partial vibration whose period T,, = =i is equal to the mth part of the period of the fundamental vibration, would appear if the period (T) of the excitation is equal to T,,, 2Tn, 3T,,, &c. The phenomena of oscillation, however, are not so complicated with the appa- ratus here described as might appear from this. A small wheel is fixed somewhat excentrically upon the axis of the, siren (fig. 2) (the excentricity amounts to about 0°5 millim.), and to the uprights carrying the wheelwork is fixed, by means of two screws, a support for a little bent lever, the conically- pointed axis of which rests in two steel screws passing through the support, and moves in it with a small amount of friction. The wheel itself and the supports for the lever are of cast brass. The lever (as shown in fig. 2) is ca- pable of motionin a vertical plane, presses with its vertical armagainst the excentric wheel, and has its horizontal arm attached to the stretched thread, which is hori- zontal and at right angles to the axis of the lever. The tension of the thread retains the lever in its position when the siren is at rest, and brings it back into its position of rest when the siren is sounding, and the revolving excentric wheel imparts to it periodically a small motion. It is not necessary, nor possible with a considerable ten- sion of the thread, that the lever should touch the wheel Form of Monochord. 51 in all positions; it is sufficient if the wheel comes into contact with the lever for a short interval of time. The degree of contact may also be easily regulated. At the proper dis- tance from the siren, and opposite to it, a wooden stand is placed, carrying a pulley-wheel turning very easily, such as the wheel of an Atwood’s machine. The wheel is adjusted at such a height that the thread which passes over it may be horizontal when stretched by means of weights placed in a little scale-pan attached to it. If the friction between the wheel and the lever is too great in the horizontal position of the thread, the support carrying the pulley-wheel may be raised a little, so that the horizontal arm of the lever may be pulled up a little and the vertical arm thus removed somewhat from the wheel. If the lever does not touch the wheel at all, the support must be lowered somewhat. When the friction has been properly regulated, the siren may be put into action and its note gradually raised. At first the motion of the thread may be followed through its separate phases with the eye, but when the velocity of rotation of the siren becomes greater there is to be observed only an uncertain trem- bling of the thread, and the friction of the lever on the wheel produces a noise ; then this suddenly ceases, and the thread is seen to be in stationary oscillation of the fundamental form. The amplitude is considerable, and with threads of 1 metre long is often of three fingers’ breadth, if the dimensions of the thread have been well chosen. As soon as the thread has settled down to perform its fundamental oscillation with constant amplitude, it is found to be very easy to maintain the velocity of the siren constant. Hvery one who has used a siren to determine the pitch of a note must have remarked how diffi- cult it is to maintain the note of a definite pitch if there is no arrangement for regulating the pressure of air. I must acknowledge that I had not expected to see this difficulty so easily removed ; and it is certainly a peculiar action of the friction between the lever and the wheel, though one easily to be explained*, which causes that a change in the pressure of the air delivered by the bellows produces only a change in the intensity of the note given by the siren, and not at once any change in the velocity of rotation—if this coincides with the ~ velocity of vibration of the thread. ‘The tone of the siren and the vibration of the thread can equally easily be maintained constant, when the velocity of rotation of the siren is increased * The thread performing its own proper vibration is, as it were, in a condition of rigidity, out of which itis not easily brought (unless its mass is altogether too small), and thus acts, by means of the friction between the lever and the wheel, as a regulator to the siren. Ki 2 ED) Dr. A. Elsass on a new so much that the thread shows its second, third, or fourth mode of vibration ; and the period of excitation becomes equal to 3T,, 4T,, 11, where T, denotes the period of the fundamental vibration of the thread. According to theory, a definite form of vibration of the thread must make its appearance when the time of rotation of the siren T=2T,,, 3T,, &e. ; so that, for example, if T=2?T,=37,, the thread vibrates in four half- waves, and for T=Z7,=2T; the thread shows its third form of vibration. The velocity of rotation of the siren can be maintained constant without trouble only when the period of excitation is equal to that of the vibration of the thread ; and if a vibration of the thread belonging to some other ratio of periods shows itself for a moment, it does not produce any perceptible disturbance. It is precisely this peculiarity—that the vibrations of the thread can be maintained without change only when the periods are equal—that renders this form of apparatus so suitable for the demonstration of the laws of the vibrations of threads. We may now give some examples of the use of the apparatus. In order to show that the numbers of vibrations of the over- tones of a thread are in the ratio of the natural numbers, it is only necessary to count the revolutions of the siren when it puts a thread ora thin metallic wire into vibration with 1, 2, 3, &c. half-waves. In Table I. I have brought together four series of observations, made with four different threads each 1 metre in length. JI. denotes a cotton thread with a tension of 50 gr.; Il. bookbinders’ thread with a tension of 50 gr. ; III. a thread of button-hole silk with a tension of 9 gr. ; and IV. a brass wire of about 0°15 millim. diameter and 200 gr. tension. The number denotes the order of the vibration and N the number of vibrations. TABLE I. n. Na 45 Nie Nui. Nv. sate ABB iy ese ts 16g 565 oe S6B Mi o6T 1) 336 112°7 Beck 1291 | 100-2 50'4 168-2 A cna) \ meee eek Or dl” |) 60 neta The number of vibrations N was determined from three independent observations—by reading the dials of the siren every 2 minutes, adding together the numbers of revolutions, Form of Monochord. 53 and dividing by 360. The numbers of vibrations of the fol- lowing Tables were determined in the same way. Itis not possible to raise the tone of the siren to any extent, and thus to render visible the higher partial vibrations of the same thread. But for lecture-experiments it will always be sufiucient to show the law of overtones for the slower vibrations; and if it is desired to go further than in the experiments I have described, it is only necessary to replace the excentric wheel by an elliptical wheel, or by a toothed wheel exactly centred, with, say, four teeth, so that for the same velocity of rotation the number of shocks is doubled or increased fourfold. Ihave obtained the best results with toothed wheels of various forms, but think it more convenient so to choose the thread, its length and tension, that the excentric wheel suffices for the experiment. In order to demonstrate the Law of lengths, it is advisable to take a longer piece of a not too thin white silk thread, which will be nearly the same length for great differences of tension, and to stretch it over a measure and mark off equal distances with India ink. Thus, in the experiments to which Table II. relates, a thread of button-hole silk 2 metres long, and marked off into lengths of 10 centim., was attached: to the lever of the apparatus, so that the first mark fell at the point of attachment, passed over the pulley, and stretched with a force of 60 gr. by weighting the scale-pan with shot. Between the siren and the upright carrying the pulley-wheel I placed a table, carrying a small iron support with a clamp to grip the thread. In the Table, / denotes the length of the vibrating thread and N the number of oscillations for the fundamental note. TaBuE LI. N, N, é: N. Nn Z. N. Nn eee metre 1:00 54:0 1 1:00 54:0 ] 1:00 49:0 1:10 0:90 59°8 0:90 1:20 45°1 1:18 0°80 67°8 0°79 1°30 41:8 1529 0-70 17:3 0:70 1:40. 38'4 128 0:60 90°7 0:59 We have therefore N,: N,=/,:1,; the deviations from the law which the table shows are within the limits of experimental errors. Thirdly, in order to show that, with threads of the same 54 On a new Form of Monochord. material and of the same length, the number of oscillations is proportional to the square root of the tension, a thread of the same silk used in the last experiment and 1 metre long was subjected to various tensiuns. The tension to begin with was 9 er., obtained by weighting a small pill-box with shot, and the higher tensions were obtained by adding weights. In Table III., P denotes the load, N the number of oscillations for the fundamental note ; the second and third columns show SPL ONe that Se —/ Pi N, TABLE III. Pp Rey VP, Nn Speen = 3 ms oa or er. 3 17-2 3 49 7 40°8 7-04 16 4+ 93-4 4-08 64 8 46:2 8:02 25 5 29:4 5-12 Sl 9 51-1 8:97 36 6 34:1 5:98 In order to show that the vibration-numbers of threads of equal length and tension vary inversely as their masses, it is best to employ thin metallic wires, since they are heavier than threads, and consequently a small error in the weights is not so perceptible. The weights, py, of wires employed for the fol- lowing experiments were determined by weighing four metres of each wire ; after being weighed a length of 1:20 metre was cut off and stretched between the siren and the pulley-wheel, so that the length of the vibrating portion was 1 metre; the tension (200 gr.) was chosen so great that the portion of the wire depending from the pulley-wheel did not need to be taken into account. TABLE LV. : D N Material. : Py de oh N. ae e p uf. ie Nv er. German-silver ... 0-660 i 90:5 1 MSTAGSics oo. aoe ee 1604 0641 BY (a 0-63 Prone ace to ke 9912 0:545 50°6 0:56 After this description of the demonstration of Mersenne’s laws by means of this apparatus, it will not be necessary to On Atomic Arrangement in Compounds. 5d say more of the advantages which it offers to the demonstrator of physics. Itis, however, perhaps not superfluous to remark, that the apparatus is so little costly that any institution at which instruction in physics is given may be able to obtain it. A bellows and wind-chest for organ-pipes and a siren belong to the necessary apparatus of instruction in acoustics; we require in addition only a small piece of apparatus which may easily be fitted to any siren. The lever arrangement must, however, be well made, so as to avoid disturbing noises, which might easily be produced by the friction of the lever against the revolving wheel. The apparatus for my own experiments was made by the University apparatus-maker, Herr Engel, of Marburg. VI. The Influence of Atonic Arrangement on the Physical Properties of Compounds. By W. N. Hartizy, £.B.S., Professor of Chemistry, Royal College of Science, Dublin*. N the Philosophical Magazine for March 1882, Dr. Carnelley states that Professor Julius Thomsen, of Co- penhagen, has concluded from the heat of combustion of benzene that the six carbon-atoms in the compound “are not bound by three double and three single linkings, thus, Bruhl, however, as we shall see presently, concludes from the * Communicated by the Author. 56 On Atomic Arrangement in Compounds. specific refraction of benzene that the old view is the correct one.’ I presume that Dr. Carnelley was here referring to the paper in the Berlin Berichte, vol. xiii. p. 1808 (1880); and if this is so, there is little doubt that he has misinterpreted Thomsen’s conclusions, as the formula given represents only six single linkings. The ‘heat of combustion of benzene, if the carbons are linked as in Kekulé’s formula, would amount to 846,000 units, whereas if there are nine single linkings in the molecule it would be 802,330 units. The experimental number obtained by Thomsen was found to be 805,800; hence he concludes that the six carbon-atoms in benzene are nine times singly linked with each other.”” J quote here from my own paper, entitled “ Researches on the Relation between the Molecular Structure of Carbon Compounds and their Absorp- tion-Spectra,” published in the Journal of the Chemical Society for April 1881; and my conclusion was that, “ subject to the correciness of this deduction, I consider the following conclusion to be established :—No molecular arrangement of carbon-atoms causes selective absorption unless each carben is itself united to other three-carbon atoms, as in the case of benzene.” In accordance with this view, benzene could be represented by a formula such as the following :— which is practically the same as Ladenburg’s prism ; and we have yet to learn that this is not in harmony with Bruhl’s determination of the refraction equivalent. It may be ob- served that I have carefully guarded myself against uncon- ditionally accepting this last expression, since there are other considerations which tend towards favouring that of Kekulé. Single, double, or treble linkings are simply an incomplete method of representing the relation of the carbon-atoms to each other at some particular phase of their vibrations. Such representations are fictitious, since they give us no idea of the vibrations which are the cause of all the properties of these Mr. Bosanquet on Permanent Magnets. DY compounds. I therefore regard that expression as the best which commits one in the least degree to any very decided view of the inner construction of benzene, and such a repre- sentation is the simple hexagon. VII. Permanent Magnets —Il. On Magnetic Decay; with a Correction to the Value of H at Oxford. By R. H. M. Bosanquet, St. John’s College, Oxford. To the Hditors of the Philosophical Magazine and Journal. GENTLEMEN, Hj decay of the magnetism of permanent magnets is a subject of the greatest practical importance. Some of the best makers of electrical measuring instruments continue to relie to a considerable extent on permanent magnets, and the change of these is not easily eliminated with accuracy. Among the methods employed for the discovery of the changes in permanent magnets, the direct determination of their moments, which accompanies the ordinary process for the determination of the horizontal component of the earth’s magnetism, seems to be free from objection. This is the method some further results of which I propose now to communicate. _ The existence of the decay or diminution of magnetic mo- ments has been pointed out by Joule*, and is alluded to in my former paper (Phil. Mag. xvii. p. 438). The values now dealt with form a sequel to those given in that paper. _ It is important to consider the justification offered for the continued use of magnets as standards, and this depends on the process used for the redetermination of the constants involved. One of the processes consists ultimately in the reference to a Clark’s cell, which is supposed to remain perfectly constant. The assumption is justified by the fact that two such cells similarly prepared at the same time do not vary relatively to- each other, though their values are not generally identical. It appears, however, that two such similar cells, being exposed always to the same influences, might be expected to make any changes they do make in common. At all events, without some further check, there is nothing in the shape of absoltite proof attainable by this method as to the constancy of the ultimate standard. * Reprint, i. p. 591. 58 Mr. R. H. M, Bosanquet on The temporary effects of changes of temperature on per- manent magnets are also well known to be such as would certainly vitiate any accurate measurements founded on such magnets, in the absence of special precautions. ‘he following Table contains the mean results of sets of observations made at different times during the present year. The first two entries contain the observations made use of in the paper above referred to, but divided into two groups and corrected for an improved value of the moments of inertia of the magnets. Mean date. SERIES M. Ee Place. sets. February 18 ... 9 12039 "18044 | Nonmagnetic room. Waren asses ac 6 11822 "18075 53 x i; Sal dane ee 12 11767 17261 | Laboratory. SANOPIL GS eeaaun ccs 11 11620 "17224 = September 18... 16 11119 "18020 | Nonmagnetic room. - a 14 11121 "17370 | Laboratory. 2,000 Ne ES 11,000 5 0 0 0 0 0 0 0 0 0 February. March, April. May. June, July. August. Sept. Oct. Permanent Magnets. 59 The curve in the figure exhibits the course of the values of M. In seven months it has diminished very nearly in the proportion of 12 to 11. These magnets are of what is called best cast steel, and are as hard as they possibly can be made. They were prepared about February 8th. It is incumbent on those who maintain that permanent magnets can be made subject only to insignificant changes, to submit their magnets to some long-continued series of tests of equal conclusiveness with the above. I hope to continue the series. The new value of the moment of inertia of the magnets was obtained by a series of forty experiments, in which the mag- nets were vibrated alternately alone*and with the standard brass bar which was made for the purpose. The wire used for suspension was better than that employed on the former occasion. ‘The torsion due to it was considerably less than that of the former wire, and was very nearly the same for all weights. The values of the moment of inertia arrived at were, Mia isi72. Wl £43369,. the old values were R= 13370. TL 213384; which were observed upon at the time as unsatisfactory. The correction due to this change is obtained by adding to the log.’s of both M and H the number ‘00111. Applying this correction to the ultimate value of H formerly obtained, we have :— Olitvalnerot Heo. ESOEL Corrected value» 9.1: ..-:,:7 8056 for the beginning of March 1884. The mean of the values for March and September is "18038. The mean Greenwich value for the year, according to the formula in Everett’s ‘ Book of Units,’ is "13186. peo" VIII. Notices respecting New Books. Geology of Wisconsin. Survey of 1873-9. Vol. I. Part 1. General Geology. IL. Natural Mistory. ILI. Industrial Resources, Pub- lished under the durection of the chief Geologist, by the Commissioners of Publie Printing, wa accordance with Legislatwe Enactment. 8vo, pages 1-xxiv, and 1-725. With 11 plates, and 157 other figures. [Madison ?] 1883. - agreement with the plan laid down at first, the general intro- ductory volume is here published last*, although termed “vol. i.” The “ General Geology ” is treated under several heads, so that any one, taking up and desiring to understand the results of the Geological Survey, may make himself acquainted with the principles of the science by which the Survey is carried out. Thus the Chief Geologist, Prof. T. C. Chamberlin, has been called on to supply, and does supply very satisfactorily, a good series of obser- vations and teachings on—I. Chemical Geology, in relation to the Earth’s Crust; II. Lithological Geology, as to rocks in groups and individually,—offering a system of nomenclature, and defining technical terms; LI. Historical Geology, under the subordinate headings of Laurentian, Huronian, Keweenawan, Cambrian and Potsdam, Lower-Silurian or Cambro-Silurian, Upper-Silurian, De- vonian, Carboniferous, Reptilian, Tertiary, and Quaternary periods, aud their stratal representatives; with many interesting remarks on the processes, results, and concomitants, occurring from time to time in the geographical and biological conditions of the EHarth’s surface. Part II. contains chemical analyses of minerals, rocks, ores, and waters of Wisconsin, some compiled by R. D. Salisbury (pp. 303— 308); some made, in a classified system, by R. D. Irving (pp. 309- 339); and the lithology of Wisconsin by the same (pp. 340-361). R. P. Whitfield gives a valuable classified list of the Fossils of Wisconsin (pp. 362-375); G. D. Swezey catalogues the Pheeno- gamous and Vascular-Cryptogamous plants of Wisconsin (pp. 376— 395). A partial list of the Fungi of Wisconsin, with descriptions of new species, is contributed by W. F. Bundy (pp. 396-401), who gives also an account of the Crustacean Fauna of Wisconsin, with descriptions of little-known species of Cambarus (pp. 402-405). Other interesting natural-history communications are—the Cata- logue of the Wisconsin Lepidoptera (pp. 406-421), and of the Cold-blooded Vertebrates of Wisconsin (pp. 422-485), both by P. R. Hoy. The late Moses Strong’s list of the Mammals of Wis- consin follows (pp. 437-440). ) | Of the “‘ Economic relations of Wisconsin Birds” an elaborate, careful, and useful (at all events .suggestively useful) memoir, by F. H. King, is given (pp. 472-610). The results of the examina- tion of stomachs and food are shown by notes and tables very fully, as to the cases in which Birds are beneficial,—destroying “ noxious * See Phil, Mag. for April 1880, p. 302. Notices respecting New Books. 61 plants,” “injurious mammals,” “detrimental birds,” “injurious reptiles,” ‘noxious insects,” “injurious molluscs,” and other noxious forms of life, and when feeding on carrion. So also of harmful Birds, which destroy useful creatures, their young or their egos, or when eating the parasites hurtful to obnoxious animals. The relations of Birds to different industries, also their habits, seasons, value as food, esthetic value, and economic classification, are all considered. Numerous figures of Birds and their various prey are freely inserted in the descriptions. Part IIT. treats of Economic Geology. The Iron-ores are de- seribed by R. D. Irving (pp. 613-636). The late Moses Strong wrote the Chapter (for the most part) on Lead and Zinc-ores (pp. 637-655). Prof. T. ©. Chamberlin has contributed the remaining Chapters—‘‘ Economic Suggestions as to Copper, Silver, and other ores” (pp. 656-662); on “ Building Material” (pp.663- 677); on the “Soils and Subsoils of Wisconsin ” (pp. 678-688) ; and on “ Artesian Wells” (pp. 689-701). A short Note on the Geodetic Survey of the State, and its progress, is given at p. 7U2, and plate xi. is a map in illustration. The good Index (pp. 703-725) is well worthy of this excellently useful volume. Containing much that is of interest to Botanist, Ornithologist, and other Naturalists, this volume is also very useful to the Geo- logist and Mineralogist. By the Geologist the many figures of fossils, and the highly suggestive hypothetical maps of the North- American land in the several periods of the Huronian, Potsdam, Trenton, Niagara, and Hamilton formations—and again during the First and Second Glacial Epochs—will be fully appreciated. We cordially thank the Scientific Staff and the State Authorities of Wisconsin for this and the other volumes of their carefully-worked Survey of the State. The Student’s Handbook of Physical Geology. By A. J. JUKES- Browne, B.A., F.G.S. 8vo. Pp. xu, 514. London: George Bell and Sons. 1884. ELEVEN years have now elapsed since the second edition of Jukes’s ‘School Manual of Geology’ was prepared by his nephew, the author of the present work. Now the School (or Student’s) Manual has, we are informed, been allowed to fall out of circu- lation, and the ‘Student’s Handbook of Physical Geology’ in a measure takes its place, dealing with a portion of geological science under the headings of Dynamical, Structural, and Physiographical Geology. The Paleontological and Historical sections are left to form another volume. The work before us, although differing from it in arrangement, is a capital introduction to the more elaborate treatise by Prof. A. H. Green, a new edition of which was issued in 1882. We trust that Mr. Jukes-Browne may complete the second portion of his work more speedily than has been the case with Prof. Green; and 62 Notices respecting New Books. if it prove, which we do not doubt it will prove, as clear and syste- matic as the ‘ Physical Geology,’ it will furnish a welcome guide to those who may be dismayed at the size and cost of such a work as that produced by Dr. A. Geikie. If, however, one work leads up to the other, the success will be satisfactory, both to student and author. We might naturally expect to find Mr. Jukes-Browne more “at home” when he comes to deal with the succession of stratified roeks and their fossils, a subject reserved for his second volume; for he is perhaps best known to geologists through his successful labours among the Cretaceous and Post-Tertiary deposits. But a perusal of the present work enables us to speak in the highest terms of the wide research and full treatment of the subjects he has now brought before us. Illustrations are drawn from all parts of the world, and the author evidently gathers inspiration, as well as many duly acknowledged explanations, from the works of Lyell, Jukes, A. Geikie, O. Fisher, and other past and present leaders in Geology. Here and there we are disposed to differ in the use of terms or on theoretical questions. For instance, on p. 67 the author speaks of “the detrition of a district,” and ‘the denudation of fresh rock-surfaces,” when we should transpose the terms. Mr. Jukes- Browne strongly advocates the hypothesis that our Boulder-clay was chiefly formed by Coast-ice, or, in other words, that it was a marine deposit formed near ice-clad shores, but always under water. It has, however, not been shown that Coast-ice is capable of forming a comparatively uniform deposit of Boulder-clay spread over a wide area, usually devoid of any appearance of stratification, and con- taining no marine shells that lived on the spots where their remains are imbedded. It is true that the advocates of the formation of Boulder-clay by land-ice have to be equally guided by inference; but the frequent contortions and disturbances in beds underlying Boulder-clay, evidently produced by the agent which formed this glacial drift, seem to indicate a force more potent and extensive than coast-ice. Mr. Jukes-Browne has, however, taken pains to state the opinions opposed to those he may express or adopt; and we doubt not it will be some time before there is unanimity amongst geolo- gists on the subject of the formation of Boulder-clay. We should not omit to mention that Prof. T. G. Bonney con- tributes to this work a short chapter on “Original or Igneous Rocks.” The subject of rocks or of minerals cannot be made interesting, in the ordinary sense, to the student; nor for that matter can we say that the present volume is one to be read through lightly and easily by a general reader. But it is full of facts and information, and as such is just the work to be appreciated by the young and earnest student, who desires to learn about volcanoes and earthquakes, springs, the formation of various deposits, the structure of rocks, and the origin of hill and valley, mountain, lake, and river. [ 63 | IX. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. (Continued from vol. xviii. p. 386. | November 5, 1884.—Prof. T. G. Bonney, D.Se., LL.D., F.B.S., President, in the Chair. HE following communications were read :—- 1. On a new Deposit of Phocene Age at St. Erth, 15 miles east of the Land’s End, Cornwall.” By 8. V. Wood, Esq., F.G.S. 2. ‘The Cretaceous Beds at Black Ven, near Lyme Regis, with some supplementary remarks on the Blackdown Beds.” By the Rey. W. Downes, B.A., F.G.S. 3. “On some Recent Discoveries in the Submerged Forest of Torbay.” By D. Pidgeon, Esq., F.G.S. November 19.—Prof. T.G. Bonney, D.Sc., LL.D., F.R.S., President, in the Chair. The following communications were read :— 1. “ Note on ihe Resemblance of the Upper Molar Teeth of an Eocene Mammai (Nzoplagiaulax, Lemoine) to those of Tritylodon.” By Sir Richard Owen, K.C.B., F.R.S., F.G.S. 2. “On the Discovery in one of the Bone-caves of Creswell Crag of a portion of the Upper Jaw of Hlephas primigenius, con- taining, 2m situ, the first and second Milk-molars (right side).” By A. T. Metcalfe, Esq., F.G.S. 3. “ Notes on the Remains of Hlephas primigenius from the Creswell Bone-cave.” By Sir R. Owen, K.C.B., F.R.S., F.G.8., &e. 4, “On the Stratigraphical Position of the Lower and Middle Jurassic Trigonie of North Oxfordshire and adjacent districts.” By Edwin A. Walford, Esq., F.G.S. December 3.—Prof. T. G. Bonney, D.Sc., LL.D., F.R.S., President, in the Chair. The following communications were read :— 1. «Note on a Section near Llanberis.” By Professor A. H. Green, F.G.S. In this paper the author described a section showing actual un- conformity at the base of the Cambrian. In one of the cuttings on the railway that runs from the Dinorwig quarries along the north-western shore of Llyn Padarn, the basement conglomerate of the Harlech and Llanberis group, dipping N.W. at a moderate angle, rests upon vertical flaky beds, one of which is a breccia. 64 Geological Society. The author believes that the section described is one of which a different reading was given by Sir A. Ramsay in the Geological- Survey Memoir on North Wales. In that work the conglomerate was regarded as a continuation of the breccia of the underlying beds sharply turned over. The microscopic characters of the lower series show that these beds are probably coarse volcanic tuffs, and that they resemble the rocks at St. David’s, called Pebidian by Dr. Hicks. The uncon- formity observed does not necessarily indicate great difference of age between the conglomerate and the underlying beds. In volcanic rocks such breaks may be merely local. Further north-west, in the same railway section, a junction is seen between the Cambrian conglomerate and quartz-felsite. It is uncertain whether the junction is a fault or not. The matrix of the conglomerate is chiefly composed of felsite fragments so per- fectly cemented together as to bear a close superficial resemblance to the original rock even under the microscope, unless a high power be used. 2. “The Tertiary Basaltic Formation in Iceland.” By J. Starkie Gardner, Esq., F.L.S., F.G.8. The country explored stretches from the N.E. corner to the S.W. Every locality in which lignite had been met with was visited. The most northerly of these, at Husavik, presents a coast-section showing 200 feet of tuffs with bands of lignite, 200 feet of the same with marine shells, and an immense series of overlying tuffs, which are unfossiliferous, aud were followed, ten miles further north, to Tjornes, almost within the Arctic Circle. The shells, a series of which were exhibited, indicate a warmer sea, and, in the author’s opinion, are of an age a little anterior to the Crag. It is hoped that Dr. Gwyn Jeffreys, who has several times examined them, may pronounce a definite opinion in regard to this. A number of sections towards the interior were visited, one of the finest being in a canon near Hof, where the sides are upwards of 1000 feet high, and nearly vertical, exhibiting an alternation of semicolumnar basalts, ash- beds, and laterites, capped by rhyolites. These rhyolites are very beautiful, and cap the basalts over a wide area, being themselves overlain by other and more irregular streams of basalt and tufts. The country has been subjected to immense denudation, and is ent up into rolling flat-topped hills such as characterize basaltic regions elsewhere. The horizon from which most, if not all, the fossil plants from Iceland have been obtained, is that of the rhyolites— a more recent series than any represented in the British Isles or even in the Fardes. Their age may have been correctly assigned to the Miocene. 3. “On the Lower Eocene Plant-beds of the Basaltic Formation of Ulster.” By J. Starkie Gardner, Esq., F.G.S. [ 6 ] X. Intelligence and Miscellaneous Articles. ON THE EMPLOYMENT OF MARSH-GAS FOR PRODUCING EXCEED- INGLY LOW TEMPERATURE. BY M. CAILLETET. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, I HAVE just received the September Number of the Philoso- phical Magazine, in which I read with surprise a communication by Professor J. Dewar claiming the priority for employing marsh- gas in order to obtain very low temperature. Mr. J. Dewar, to rove his claim, alludes to a note published by him in ‘ Nature’ of the 4th of October, 1883, which, he says, “will prove that my experiments with liquid marsh-gas were made a year in advance of those made recently by M. Cailletet.” It is to be regretted that Mr. J. Dewar, who must be well acquainted with the contents of the communications presented by me to the French Academy of Sciences on the use of Marsh-gas, as well as the date of its presentation, has not spoken of the Notice I was obliged to publish a few weeks afterwards to refute the unjust claim of priority alleged by M. Wroblewski. This Note was deposited by me, closed and sealed, in the hands of the President of the French Academy on the 12th of December, 1881, that is to say, two years previous to the publication made by Mr. J. Dewar in ‘ Nature. The Note was opened at my request and read in the Academical Meeting of the 4th of last August. It contains these words :—‘“ I am busy working up researches, at this moment, which will take me a long time, and will not be published before a lengthened period. I have been obliged to speak of the details of these researches to several persons; it is therefore quite necessary for me to establish early my rights to priority in case any author were to take precedence, and for that object 1 write this note, which contains the summary ot my work. I am trying to obtain greater cold than that obtained until now by scientific men..... ‘“« By means of a pump, the piston-rod of which is covered with mercury, preventing thereby air and other injurious impediments, I can obtain the liquefaction of great quantities of carbonic acid and protoxide of nitrogen, as also of marsh-gas and ethylene, whose critical points are greatly inferior to those of carbonic acid. I am nearly certain to obtain very low temperature by plunging my instruments in these liquefied gases. I hope, lastly, to be able to liquefy oxygen, nitrogen, and other gases completely by refrigera- ting them by means of ethylene or marsh-gas boiling, after having compressed them in a curved tube by employing the instrument invented by me and which is well known to the Academy.” This Note cannot leave, I trust, any doubt of the priority of my researches over those of Mr. J. Dewar; and it is certainly owing to his not haying known it that he has published in the Philosophical Magazine the article which I feel entitled to answer. L. CatnLEeret, Paris, 10 décembre, 1884, Membre de ? Académie des Sciences, Phil. Mag. 8. 5. Vol. 19. No. 116. Jan. 1885. EF 66 Intelligence and Miscellaneous Articles. ON THE VALUE OF POISSON ’S COEFFICIENT FOR CAOUTCHOUC. BY H. H. AMAGAT. It is known that scientific men are far from being in agreement as to the numerical value to be given to whatis known as Potsson’s Coefficient. According to the theories of Poisson, Navier, M. de Saint Venant, and the experiments of Cagniard de Latour, and of M. Cornu, this coefficient should be equal to 4; according to Wertheim it is equal to 1; from the researches of Cauchy, of Lamé, and of Kirchhoff, all that can be affirmed is that it is between zero and 3; finally, according to MM. Schneebeli and Okatow it varies not only from one body to another, but also with the same body according to its physical condition. The latter physicist had the idea of utilizing the great extensibility of caoutchouc to determine the coefficient in question by the well-known method; and MM. Naccari and Bellati have made analogous experiments by Regnault’s method. Tt has been observed with justice that experiments made with caoutchouc are but little conclusive; they present great irregula- rities, due more especially to permanent deformations ; and, on the other hand, the body has but little homogeneity. It may be added that the very magnitude of the deformations has put it outside the theoretical conditions, which suppose the deformations to be very small. I propose to show that by following a totally different path we ~ may arrive, in the case of caoutchouc, at conclusions which can only be invalidated by supposing errors of experiment quite out of pro- portion to those which can be really committed. In order to make these experiments, and others which are not concluded, I have had a piezometer made, in which, as in that of Regnault, the pressure may be transmitted in the interior or on the exterior at the same time or separately. The apparatus is, however, double; two spheres or two cylinders may be placed in it side by side, which are under precisely the same pressure and at the same temperature—conditions which are very favourable for rather delicate comparative experiments. This is not the case of the present experiments, which, as we shall see, do not claim great accuracy. I call « Poisson’s coefficient, K the coefiicient of cubical compressi- bility, a the coefficient of elongation or the inverse of the coefficient of elasticity, and A and p the two constants. We have the ratios :— IN es arate a (2) K= 38a(1—2c), 1 3A—2 (3) Velho For two different bodies, “ K_sG~2e) Intelligence and Miscellaneous Articles. 67 I place in the different apparatus two spheres, one of caoutchouc and the other of bronze, which I assume are exactly identical, so as to simplify the reasoning; a few millimetres of pressure are sufficient to raise the water 300 divisions in the rod of the caout- chouc sphere ; in the other the motion of the meniscus is barely perceptible, and it cannot be measured with accuracy. It follows from this that (referring to the formula, which gives in this case the variation of the internal volume), whatever may be in the case of bronze the value’of « between zero and 3 (the accented letters refer to bronze), a is very great in reference to a’. It might be feared that in this case a considerable amount of the diminution of volume arises from a change of form; but this first operation might be replaced by a direct determination of a by means of traction; we obtain the same result. In one of my . a ° experiments -, was equal to 60,000 in round numbers. a That being so, let us compress internally and externally at the same time: according to the formula relative to this case, the changes of internal volume will be proportional to K and K’; K should therefore be very great in comparison with K’, the compressibility would even be relatively negligible, and the liquid should ascend in the stem of the caoutchouc sphere; but nothing of this kind takes place: the water sinks whatever be the pressure, and gives the inevitable irregularities with caoutchouc. It would be difficult to say whether the variation of volume has been greater with this body or for bronze, so small is the mean difference ; hence ais comparable to a’, and is perhaps even smaller. It evidently follows from this that the ratio (4) can only be satisfied provided that a = ° is very small, and therefore o very little different —A0 from 4. Assuming for o’ the number 3, we have from the preceding K 1 GB Re eR i 2( K’ * T80000 Whatever errors may be attributed to want of homogeneity, to small deformations, and to permanent deformations, even if the results found were double, or even tenfold, it may be said that o would still be very little different from 34, and far higher for example than 0-499. We may, moreover, by means of general formule and without comparing caoutchouc to another body, arrive at the same conclusion in different ways, which essentially amount to this: the coefficient of cubical compressibility is very small, as actual experiment shows; as moreover it is equal to 3a(1—2c), and since a is very great, 1—2o must be very small, and therefore o very near 4. There is nothing contradictory in this result. It follows from that and from the ratio (1) that » is very small; and therefore from ratio (3) that a is very great: this is in fact the case. But here a great difficulty presents itself. The various caout- 68 Intelligence and Miscellaneous Articles. choucs which I have examined have all led to the same result; it would certainly be the same with that which Wertheim used, and this physicist found, by measuring directly the diminution of cross section,o=3. Since then MM. Naccari and Bellati have shown, by Regnault’s method, that for the same substance the value of o may amount to 0°41; but this number satisfies the ratio (4) no better than that of Wertheim; assuming o’=3 it would give ae = 0:36, —240 a value quite out of proportion to that which should be found. As it is difficult to assume that Wertheim, and then MM. Naccari and Bellati, have made experimental errors as great as appears from the preceding,—as, on the other hand, there is no reason why caoutchouc supposed to be homogeneous, and submitted to small deformations, should not conform to general laws, it may be asked how far the formule assumed are really the expression of these laws. It is not, then, superfluous to submit these formule to the test of experiment, following in this the advice given by Regnault ; it is with this object that I have had made the differ- ential apparatus mentioned above ; these researches are in course of execution.—Comptes Rendus, July 21, 1884. ELEMENTARY PHYLLOTAXY. BY PLINY EARLE CHASE, 11,7 I have shown? that the “numerics” of the chemical elements can be better represented by various phyllotactic divisors than by Prout’s law. Phyllotactic submultiples of the organic elements C, H, O, N give a mean residual ratio of -05654, while Prout’s law gives ‘12007, the probable ratio of merely accidental residual being -18394. This indicates comparative aggregate probabilities which are represented by the reciprocals of :05654, -12007°, and 18394", or by 1999 x 10°°, 1098 x 10°, and 1. In the Philosophical Magazine for November 1884, Dr. Edmund J. Mills gives additional evidences of phyllotactic influence. He represents all the elementary numerics, except that of hydrogen, by the equation y= p15—15(-9375). This introduces the first five numbers of the phyllotactic series 1, 2, 3, 5, 8, being of the form 5x 3, p—(8x38+2~x 8)*]. The sum of the infinite series which is represented by 15x (5x 3+2 x 8)* is the product of the first five phyllotactic numbers, 1x2x3x5x8. The series itself is of the form (n+n-+1 1)*, thus representing cumulative harmonic rupturing tendencies, of the same kind as are shown in the inter-stellar influence upon plane- tary positions (Phil. Mag. September 1884, p. 197). * Communicated by the Author. + Proc. Amer, Phil. Soc. xix. pp. 591-601; xx. p. 431, &e. Intelligence and Miscellaneous Articles. 69 ON A NEW FORM OF POLARIZING PRISM, BY C. D. AHRENS. The prism which I desire to bring to the notice of the Society is intended for use either as a polarizer or an analyzer. It will, I hope, be found especially useful as an analyzer for the microscope. The employment of a Nicol prism above the eye-lens is subject to the great inconvenience that, owing to the necessary length of the prism, the eye of an observer is so far removed from the lens that a portion of the field is cut off. Double-image prisms of the usual construction are shorter, but they have another defect, viz. that the angular separation of the rays is so slight that the eye sees both images at once, and some confusion is thus caused. My object in constructing this improved prism has been to obtain a much wider separation of the two beams of light; so that one of them, although not actually removed entirely by total reflection (as in the Nicol prism), is so far refracted to one side that it may be neglected altogether. I made several attempts to construct such a prism some years ago, but failed (as probably others have done) owing to the difficulty or impossibility of avoid- ing distortion and colour, and of obtaining a wide separation of the ordinary and extraordinary rays in a prism made up of only two pieces of Iceland spar. I have now effected the desired object by making the prism of three wedges of spar cemented together by Canada balsam, as shown in the accompanying drawing (fig. 1). Fig. 1. The optic axis in the two outer wedges is parallel to the refracting edge, while in the middle wedge it is : perpendicular to the refracting edge, and lies in a plane bisecting the refracting angle. This disposition of the optic axis is the one originally suggested by Dr. Wollaston, and has the effect of causing a greater angular separation of the rays than Rochon’s construc- tion. By the employment of three prisms instead of two I am able to give the middle prism a very large angle, and yet to correct the deviation of the rays so far that on emergence they make approximately equal angles with the central line of the combination. Nearly in contact with one of the terminal faces of the prism I place a prism of dense glass of such an angle that it just corrects the deviation of one of the rays and also achromatizes it, while it increases the deviation of the other ray to such an extent that it may be practically disregarded altogether; an eye, even when placed almost close to the prism, receiving only the direct beam. This beam is, of course, perfectly polarized in one plane, and can, by a proper arrangement of the glass compensator, be rendered practically free from distortion and colour. Other methods of effecting the compensation have suggested themselves in the course of my work; and I have obtained the best results by adopting the arrangement represented in fig. 2. 70 Intelligence and Miscellaneous Articles. In this, the glass compensating prism, instead of Fie. 2 being mounted separately, is cemented upon one of sant the terminal faces of the compound spar-prism ; the gees angle of this latter, and also of the other terminal face, being suitably modified. This seems distinctly preferable to the original arrangement, for several reasons. 1. The total length of the compound prism is rather less, being scarcely more than twice its breadth. 2. The field is rather larger, so that the prism can be used over microscope eye-pieces (A andB) without any of the field of view being cut off. 3. The whole arrangement is more compact, all the components being firmly cemented together, and therefore not liable to acci- dental displacement. 4, There is less loss of light by reflection, the reflecting surfaces being reduced to two. A ray of light entering the prism in a direction parallel to its axis is divided into two rays; one of which, on emergence, follows a course parallel to that of the original incident ray, and is practi- cally free from distortion and colour; the other ray is deviated to the extent of about 59° 30’ (for yellow sodium-light), being, of course, strongly coloured and distorted. The angular separation is so great that this latter ray does not interfere with ordinary observations. L hope that the prism, which has cost me much time and labour, will meet with the approval of the Society, and take a place as a useful accessory to the microscope and other optical instruments.— Journal of the Royal Microscopical Society, August 1884. ON THE PENETRATION OF DAYLIGHT IN THE WATER OF THE LAKE OF GENEVA. BY MM. FOL AND ED. SARASIN. Questions relating to the absorption of light by more or less thick layers of the very pure water of the Lake of Geneva have been the object of a series of experiments, undertaken by a Com- mission of the Socicté de Physique et d’Histoire naturelle of Geneva, on the incentive, and under the direction, of M. Louis Soret*. We have been charged more particularly to examine, by means of photography, the extreme depth which daylight reaches. Our experiments consisted in exposing a photographic plate at various depths in that part of the lake where the water is deepest. We used Monckhoven’s rapid gelatino-bromide plates. They were placed in a special apparatus designed by one of us for these experiments. It consists of a brass photographie back, the two * Comptes Rendus, March 10, 1884, : 624, and Archives des Sciences physiques et naturelles, vol. xi. p. 827, vol. xii. p. 158, 1884. + This apparatus was constructed according to the designs and instruc- tions of M. Fol by the Société génevoise d’instruments de Physique. oS ee eee Intelligence and Miscellaneous Articles, 71 slides of which are closed by the action of a pair of levers joined like scissors and drawn by a weight ; they separate by the action of an antagonistic spring, as soon as the weight of the lead in touching the bottom ceases to act on the levers. Knowing the depth, we can regulate the length of the line by which the weight is suspended to the apparatus, soas to have the photographic plate exposed in a horizontal position, at a given distance below the surface of the water. After a given exposure the apparatus is withdrawn, and rapidly closes under the action of the weight. The time of expo- sure was ten minutes inall cases. ‘The development was made with the normal oxalate-of-iron developer, which was caused to act uni- formly for ten minutes on each plate. They were all of the same lot, and therefore coated with the same emulsion*. The experiments were made in front of Evian, where the lake has over a large surface a depth of 315 metres. Dr. Marcet was kind enough to place at our disposal on two occasions his steam- yacht, the ‘ Heron.’ Professor Forel, of Morges, had the goodness not only to lend us his sounding-line, but also to accompany us, and help us with his advice and his experience. On the 16th of August, in calm weather and with a brilliant sun, we exposed :— 1, At 237 metres deep two plates, one at half-past twelve and the other at seven minutes past one. 2. At 113 metres a plate at twenty minutes after two. 3. At 300 metres deep (15 metres from the bottom) a plate at forty- four minutes past two. On the 23rd of September, 1884, in cloudy, but fine weather, the clouds slight and rather luminous, light wind varying from east to north, we exposed :— 4, At 147 metres a plate at 1 o’clock. By sy) 170 bs ys 26 minutes past 2. 6, ,, 118 ” ” 3 ” 3. 7% » 95 4 ” 34 ” . As a comparison, we exposed on the 15th of August at 10 p.m., ona clear night, but without moon :— 8. A plate in the open air for ten minutes. 2. Nata © ” five ,, On developing, it was found that the plate 5 (800 metres deep) had re- ceived no luminous impression whatever. The same was the case with plate 1. Plate 5 at 170 metres was slightly clouded, almost like plate 9, which was exposed at night for 5 minutes. Plate 4 at 147 metres had been slightly acted on, more so than the plate which had been exposed at night for ten minutes. Of the two plates at 113 metres, the plate 6 of the * Preliminary experiments in rather shallow water showed that the apparatus worked as well as could be desired, and that when closed it could be left in full sunlight without any light getting to the plate. During exposure the glass was uppermost and towards the light. On this side characters and numbers were traced in black varnish. The sharpness with which these signs were produced in white on the developed plate, the purity of the edges of the image, which, restricted by the separation of the covering plates, only extended to the middle of the sensitive layer, prove that light could not penetrate accidentally. 12 Intelligence and Miscellaneous Articles. second day was strongly blackened, while plate 2 of the first day was no more affected than plate 4 of the second day. Finally, plate 7, exposed at 90 metres, was so acted upon that the lines which had been traced on the back were only imperfectly seen on the dark ground of the developed layer. Comparing the results obtained on the two days of the experi- ments, we are struck by the fact that the photographic action was greater on the 23rd September than on the 16th August. Weare thus led to conclude from these first attempts ; 1. That daylight penetrates into the water of the Lake of Geneva to a depth of 170 metres, and probably further; that at this depth the illumination in full daylight is just comparable to that which we observe on a fine night when there is no moon. 2. That at 120 metres the light is still very strong. 3. That in September, in cloudy weather the light penetrates in larger quantity and to a greater depth than in August, in perfectly bright weather. Further experiments will have to decide whether this difference is to be attributed to the greater transparency of water in autumn and in winter, which the experiments of M. Forel* have put beyond doubt, or whether the light diffused from the clouds penetrates further than the more or less oblique rays of the sun. Previous to our experiments, M. Aspert had exposed gelatino- bromide plates in the Lake of Zurich at depths varying from 40 to 90 metres. He immersed them at night, and withdrew them the following night. But the darkest night is still bright for a rapid gelatino-bromide plate. Our experiments seem then to be made under more trying circumstances. We intend to pursue: these experiments in the summer of 1885. We are desirous also, if possible, of making analogous experi- ments in the sea, where the greater transparency of the water leads to the supposition that the extreme limit of the luminous rays is at a still lower level. In this respect satisfactory data are wanting, for the experiments of the cruise of the ‘Porcupine’ have remained in the state of project, as the apparatus devised by Sir W. Siemens refused to act. The depth to which daylight penetrates in the sea is therefore still to be found.—Comptes Rendus, Noy. 10, 1884. * M. Forel investigated from 1873 the transparency of the waters of the Lake of Geneva by a photographic method ; he employed, however, albu- minized silver paper, which is less sensitive than gelatino-bromide. He immersed the sheets at night at various depths, and took them out after one or several twenty-four hours. This method gave for the limit of absolute darkness approximately 45 metres in summer and 100 metres in winter. The greater abundance of aquatic powders during summer, which is the cause of the greater opacity, is due to the thermal stratification of water during the hot season, from which results the power of holding in suspension powders of different densities (Archives des Sciences physiques et naturelles, vol. lix. p. 187, 1877). + Archives des Sciences physiques et naturelles, vol. vi. p. 318, 1881. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] FEBRUARY 1885. XI. Electromagnets—II. On the Magnetic Permeability of Lron and Steel, with a new Theory of Magnetism. By R.H. M. BosanquEt, St. John’s College, Oxford. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, ORs attempting to draw rigorous experimental con- clusions as to the effect of the magnetic properties of Tron and Steel on electromagnets made of these metals, it is necessary to obtain some further information as to the mag- netic properties in question. Hitherto I have accepted the results of Rowland’s experi- ments with rings*; but I have now repeated and varied these experiments, with special regard to the following points:— To find the average properties assigned by this method to the Iron and Steel I commonly use; To assign to the results formule of a more general and more manageable type than that employed by Rowland ; And to justify experimentally the assumption that the per- meability, as calculated from the experiments, is independent of the size and proportions of the rings examined. A new theory of these magnetic properties will be enun- ciated and applied. The iron upon which most of the following experiments have been made is what is called ordinary bar-iron. It is what I commonly use for electromagnets. It is moderately soft and admits of being easily forged. It is stamped with a * Phil. Mag. [4] xlvi. p. 140 (1878). Phil. Mag. 8. 5. Vol. 19. No. 117. Feb. 1885. G 74 Mr. R. H. M. Bosanquet on the Magnetic crown, and I shall speak of it as crown iron. One ring of best Lowmoor has also been examined. The steel ring J was forged from the remainder of the bar of cast steel from which the divided magnet was made, which is called A in my paper I. on Permanent Magnets (Phil. Mag. August 1884, p. 142). It was first examined soft, and then after hardening. The method employed was substantially that of Rowland. The rings were uniformly wound with coils through which the magnetizing current was transmitted. The current em- ployed was a small derived current from the circuit of the dynamo machine; so that it could be opened, closed, or reversed without upsetting the main circuit. The current was measured by means of two galvanometers of Helmholtz’s pattern, the one having two coils, the other eighteen. The galvanometers were always erected on the brick stand which forms the standard position for which values of H are deter- mined in the laboratory. The observations were all made by reversal. A number of induction-coils, varying from 250 to 1, were wound round the ring to be examined. In circuit with these coils were the ballistic galvanometer and the earth induction- coil, for the reduction of the readings to absolute measure. Two earth induction-coils were employed. ‘The first had 21 turns, with a mean diameter of 51°30 centim.; the other 250 turns, with a mean circumference of 166°53 centim. With both of these coils the impulse of the galvanometer due to half a turn about a vertical axis in the standard position* was about 7°. But in the case of the larger coil, a deflection cor- responds to about twelve times as great an induction as with the smaller coil, so that a very large range is secured. The galvanometer has a circular scale which reads, by reflection, directly to 5’ and by estimation to single minutes. The mode of calculation adopted is precisely equivalent to that of Rowland. Rowland’s Mis current-turns per unit length, = a in our notation. Then his expression connecting p, the permeability, with the total number of lines of force is, lines of force =r" a(n?) : and for the magnetic induction, or lines of force per unit area, * The positions of rest between which the half turn is made are such that the plane of the coil is at right angles to the magnetic meridian. Hence the coil cuts the lines of force of H twice in the half turn. Permeability of Lron and Steel. 15 we have GB =47 = fb. Now 47Cn is the total magnetic potential exerted on the ring by the magnetizing coil ; whence potential 1 a which is what I call the magnetic resistance*. is then cal- culated really both by Rowland and myself from the formula 1% l om potential , magnetic resistance ; though of course the form and the letters Rowland uses are different. The whole process of calculation of an experiment is embodied in the following formule. Let « be the deflection of the ballistic galvanometer due to reversal, with m induction-coils ; then 2mSB = ka (S = sectional area of bar). Let 8 = deflection due to half turn of earth induction-coil (N = number of coils, A = mean area) ; then 2NAH=«8. Combining these, we have . a NAH B= 3 nS Let G be that part of the tangent-galvanometer coefticient which is independent of H, so that we have for the current C=GH tan 6. Then potential =4arnC=4rnGH tan 6, magnetic resistance potential — = ee. G which is independent of H ; and r l —— p where / is the mean circumference of the ring. The following Tables exhibit the results of the various * See Phil. Mag. xvii. p. 531. G 2 76 Mr. R. H. M. Bosanquet on the Magnetic experiments thus made. They also show the degree of accuracy attained by the Fourier’s series, by which I have endeavoured to represent as a function of G. EH. Forged Ring Crown Iron. Mean diameter. . d@ =10:0385 centim. Bar-thickness: pa. 2 12935 Number of coils . n = ARG p cale.=144 + 221 cos 0 + 2000{sin 6+ sin 20+ 5) sin 30 +45 sin 46}, where g— 8 degrees 100 °° =a b be 35 | Dyers, 3. |————_ Ditts Obs. | Cale. Obs. | Cale. 129°7 | 437 | 4387 0 11516 | 1615 | 1625 | + 10 2391 | 493); 498 | + 5 | 13276 | 13881 | 1207 | —174 21743 | 1474 | 1470 | — 4 14017 | 1047 | 1017 | — 30 31869 | 1817 | 1836 | +19 | 15000 635 | 732 | + 97 5181°7 | 2163 | 2199 | +36 | 16380 218 | 349 |) +131 6403°4 | 2234 | 2229 | — 5 || 17245 11%.) 19 eae FE. Forged Ring Crown Iron. Mean diameter . . d =22:1 centim. Bar-thickness 6° 2R= 1:292 |. Number of coils. . » +=1118. pcale, = 200+ 1630{sin 6+4 sin 20+4 sin 80+ 4,sin 46}, where _ 8 é= 700 degrees. pe 3. —_—____—_—__| Ditfs. 45. Diffs. 15108 | 208 | 208 0 6438°4 | 1825 | 1847 | + 22 142°55 360 | 284 | —76 7655°3 | 1704 | 1749 | + 45 512/97 587 | 502 | —85 10767 1581 | 1481 | —100 2783'8 1592 | 1572 | —20 12537 1252 | 1258; + 6 3616°5 1784 | 1784 i) 13900 1000 |} 989; — 11 4282°6 1869 | 1858 | —11 15025 692 | 749 | + 57 57466 1895 | 1890 | — 5 18834 150 60 | — 90 Permeability of Iron and Steel. G. Forged Ring Crown Iron. Mean diameter. . d@ =21°5 centim. Bar-thickness . . 2R= 2°535 Number of coils . n =989. 7) pcale.= 290 (14-3 cos 0) + 2000{sin 8+4sin 26}, where e_ 8 decrees 100° pH. pt. BG. ie Ee a Da rice So 5: (ee ete te Dilrs Obs. | Cale. Obs. | Cale. a | Jae aa 11970 | 1555 | 1525 | — 30. 448-17 | 765 | 669| — 96 || 13710 | 1192 | 1047 | — 45 19725 | 1615 | 1419 | —196 || 14426 | 832| 867] + 35 6363-7 | 2501 | 2544| + 43 || 15505 | 664| 620| — 44 90033 | 2241 | 2280] + 48 || 16042 | 395 | 512| +117 11090 | 1763 | 1773/ + 10 || 17586 | 145 | 930] + 85 H. Forged Ring Crown Iron. Mean diameter. . d =10°735 centim. iBar-thickness.. . 2KR= ‘7137 -,, Number of coils . » =560. p cale.=217 +164 cos 0+ 1400{sin 6+ 3 sin 263, where £8 = 100 degrees. p. 5. BLU Sk ay JES ED Dire: 3. es Be Se DS Obs. | Cale. Obs. | Cale. 34:37 395 | 394 | — 286°85 418 | 486 | + 1079°4 817 | 769 | — 6025°5 1797 | 1816 | + + + 1 || 11261 | 1134 | 1198 | + 64 68 || 13355 885 | 769 | —116 48 || 14501 630 | 557 | — 73 19 || 14718 502 | 519 | + 17 54 || 15409 954 | 407 | +153 29 || 17642 Oe Og: | eI 7704-6 LIVE RAT 8435°7 1710 | 1681 9739°6 1354 | 1498 78 Mr. R. H. M. Bosanquet on the Magnetic K. Forged Ring Crown Iron. Mean diameter. . d@ =22:°725 centim. Bar-thickness . . 2R= °7544 ,, Number of coils . n =1217. pz calc. =380 cos 0—30+4 1770{sin 6+4 sin 20}, where G 6= —— decrees. 1002 p.- p- a. eS ie aio! (20) Dh af, 36. ies Reemenmn ieee |) [8h Obs. | Cale. Obs. | Cale. 67-293| 492 | 381| — 41 || 95982 | 1557 | 1660 | +103 29343 428 | 486 | + 58 10413 1531 | 1884 | —147 2174-7 1288 | 1278 | — 10 11511 1104 | 1357 | +2538 2337°5 1176 | 13438 | +167 12148 799 |} 953 | +154 39490 1766 | 18238 | + 57 13246 666 | 569 | — 97 4710°5 1982 | 1967 | — 15 13104 505 | 618 | +1138 57199 2070 | 2067 | — 3 13671 508 | 466 | +108 8677°4 1914 ; 1808 | —106 15053 1385 | 181} — 4 8889'8 1775 | 1764 | — 11 I. Forged Ring Best Lowmoor Iron. Mean diameter. . d =10°025 centim. Bar-thickness . . 2R= 1:293 _,, : es PASTA) Number of coils’. e = Age pe cale. = 250 +1800{sin 6+ sin 20+4 sin 30+ 4 sin 46}, where G é= desrees. 100 = pi. 38. Diffs 38. Hote ak Las Obs. | Cale. Obs. | Cale. 32/944) 271 272 |} + 1 7090:9 | 2173 | 2012 | —161 429°15 617 547 | — 70 8193°9 | 1935 | 1915 | — 20 1321°8 1024 | 1078 | + 54 9690°8 | 1842 | 1795 | — 47 1623°6 1427 | 1247 | —180 10400 1483 | 1730 | +247 2395°1 1558 | 1616 | + 58 13159 1188 | 1390 | +202 4541-5 2072 | 2116 | + 44 | 15050 818 851 | + 33 6324-2 2080 | 2077 | — 3 || 163809 592) oF - 18 6712°3 1993 | 2045 | + 52 || 16939 444 448; 4+ 4 6700°1 2033 | 2046 | + 18 | 193803 155 182 | + 37 | Permeability of Iron and Steel. J. Forged Ring Cast Steel (Soft). Mean diameter . . d@ =14'25 centim. Bar-thickness 2R= 1:421 _,, Number of coils. . » =1074. p calc. =120 + 340 sin 0, where é= Be degrees. i00. © It. Ie 33. ere deesie 25—|he DUTT, 35. Obs. | Cale. Obs. | Cale. 21°873| 126 121 — 5 5815-9 420 409 83°360!} 120 125 + 5 9467°8 461 459 2773 156 136 —20 11497 443 428 1825:9 248 226 —22 12443 326 400 2367-0 YAO 256 + 7 15352 154. 272 35166 314 312 — 2 18597 90 85 J. Forged Ring Cast Steel (Hard). Mean diameter . . d@ =14:25 centim. Bar-thickness 2R—= 1421 5. Number of coils. . 2» =1069. ucale.=45 + 90{sin 0+ sin 20}, where a3 8= -— decrees 100 °°8 pl. p. fee | ite ae Obs. | Cale. | Obs. | Cale. Fem 491. 451) 4 645 | 67 | 62 59°48 47 47 0 2189 | 115 110 120°8 48 48 0 4492 150 153 170°4 ed! 52 +] 6496 157 161 267°9 i Oe 58 —4. 8959 134 135 405 62 59 =3 13870 70 60 551 64 62 —2 First, as to the saturation-value. 19 In nearly all the rings of erown iron the saturation-value of the induction is under 18,000, although in ring F it appears to exceed 19,000. This agrees generally with Rowland’s result as to rings. In my paper on Electromagnets (Phil. Mag. xvii. p. 532) I have shown that in the case of the two bars there examined the saturation-values were higher, and did not appear to give evidence of having any fixed limit. This seems intelligible 80 Mr. R. H. M. Bosanquet on the Magnetic when we remember that in the bar the lines of force are crowded closely only at the equatorial section. The formula by which Rowland represented his results was of the type , phen Steere, in which A, C, D, and a are constants depending upon the kind and quality of the metal used. This type of formula is unmanageable; and it seemed to me necessary to attempt a more direct expression of the facts. Rowland’s formula offers the suggestion that we may regard values of « which occur in these experiments as corresponding to the first half of a periodic change, the whole of which would be completed for a value of 9% corresponding to about twice the saturation-value. This being so, it is theoretically pos- sible, according to Fourier’s theorem, to express any set of the experimental values of uw by a series of sines and cosines of an angle proportional to the induction and of the multiples of that angle; and the only difficulty is to find the coefficients of the different terms of the series. Unfortunately the distribution of the values obtained does not admit of the application of the simplest form of harmonic analysis; so that the accurate determination of the coefficients is attended with a good deal of difficulty; and after trial of various methods of solution of equations, including an extended application of the method of least squares, it was found that a process of trial and error was capable of giving better results than could be obtained in any other way. The representations thus obtained are not in all cases very close, but they are quite sufficient to show, by comparison of the different rings of the same iron, the uselessness of attempt- ing to define minutely the properties of a given kind of iron. For the analysis of the different sets these are as valuable, on account of the clearness of the expressions, as the representa- tions founded on my subsequent theory, which are as close or closer. As to the size of the rings. There are five rings of crown iron, H, F, G, H,K. Of these, E, H have approximately the same mean diameter; IF, G, IK have mean diameters rather more than twice as great. HH, K have about the same bar- thickness, H, F bar-thickness nearly twice as great, and G a bar-thickness between three and four times as great. But when we examine the expressions for u, we fail to find any syste- matic differences which appear to correspond with these dif- ferences in the dimensions. So that, so far as this small number of experiments goes, the fundamental suppositions are Permeability of Iron and Steel. 81 justified in leading to values of w independent of the dimen- sions of the rings. It is a question of particular interest whether the iron in the interior of thick bars is in any degree shielded by that which encloses it from the effects of magnetic potential. In rings we have this question detached from the complications caused by the ends of straight bars or tubes, and are face to face with the simple question:—Is magnetic potential so ab- sorbed in its passage through external layers of iron that its effect in the interior is sensibly diminished ? To answer this question it is convenient to make use of the e e e e si ° ordinary expression for magnetizing force (= — in the above tables), and to tabulate the values of the induction in the dif- ferent rings corresponding to a series of definite values of the magnetizing-force. If, then, there is absorption of the force in the external layers, the inside of the thickest rings should be the most shielded, and the induction should throughout be lower in those rings for the same magnetizing force. An inspection of the following Table will show that, if any- thing, the reverse of this is the case. Table of Values of % in the different Crown Iron Rings, cor- responding to certain Values of the Magnetizing Force. G EH a) H. K Mean diam....| 21:5 em. | 10°035 ecm. | 22:1 em. | 10°735 em. | 22°725 em. Bar-thickness.| 2°535 1-298 1:292 alten igs "7544 Maenetizing Force. , 126 73 65:3 82:4. 85 D Beit 270 224 208 214 u 1449 1293 840 675 885 2 4564 3952 Dao 2777 2417 5 9900 9147 8293 8479 8884 10 13023 13357 12540 11376 11388 20 14911 14653 14710 14066 13273 50 16217 15704 16062 15174 13890 100 17148 16677 17900 16134 14837 The thickest ring, G, has the highest inductions throughout. The thinnest rings fall a little behind on the whole, except in the initial values. It seems probable that this may be due to slight flaws of small surface-extent, which may not percep- tibly impair the magnetic conductivity of the thick ring, but may interfere with that of the thin ring. At all events the hypothesis of shielding is conclusively negatived. Returning to the general tables, the variations which strike 82 Mr. R. H. M. Bosanquet on the Magnetic us most are those in the initial values of s and those in the coefficient of sin 6. We can only conclude, either that the iron is of very variable quality, or that the forging of the rings is liable to introduce these large discrepancies. I may mention here that, in accordance with Rowland’s direction, a coating of at least } of an inch was removed in the lathe from the rings after forging. The ring K was turned out of the very heart of a forged ring originally nearly four times its ultimate thickness. The Lowmoor iron ring shows low initial permeability and a high saturation-point. In both respects it much resembles ring F, but the maximum permeability of the Lowmoor is greater than that of I’, though considerably less than that of Hi or G; in fact the differences due to the type of iron appear inconsiderable compared with the differences between different rings of the same iron. The soft steel ring presents very remarkable results. First we notice that the saturation-point is decidedly high ; that is to say, by the employment of sufficient force, as shown by the low values of the permeability, the induction in the soft steel was actually raised to over 18,000. The initial permeability is about one third of the average value for soft iron; the maximum permeability about one fifth of the average value for soft iron. But the strangest thing of all is that the variable part of the permeability appears to be completely represented by a single term involving the sine of the angle proportional to the induction, so that the maximum permeability corresponds to an induction of about 9000 instead of to an induction of between 5000 and 6000 as is usual in soft iron. In the case of the hard steel ring the power employed was insufficient to force the steel up to its saturation-point, and before the ring could be re-examined with a larger number of windings the tubes of the boiler broke down and put a stop to work for the present. But the observations already obtained are very fairly represented by a formula which would give a high saturation-point. The initial permeability is less than one half that of the soft steel. The maximum permeability is about one third that of the soft steel, and it corresponds to a somewhat lower value of the induction than in soft iron, instead of to a higher value as in soft steel ; that is to say, what we may call the octave term (sin 20), which vanishes for the soft steel, has for the hard steel the largest proportional value that occurs in any of the ringsexamined. The physical meaning of this will be given us by my new theory. In Rowland’s paper above referred to he observes that it is Permeability of Iron and Steel. 83 probable that Weber’s theory may be so modified as to give an equation of the type he employs. I am not aware that . this has been attempted, and it seems improbable on account of the nature of the equation. Further it is clear that the functions involved are continuous through the whole range of the magnetization. And the essence of Weber’s theory and of all modifications of it is to divide the course of events into separate portions, in which different causes are supposed to operate, and different expressions are obtained for the results. The statement that the results are continuous applies to the residual subpermanent magnetism as well as to that ob- tained by reversal; for although I have not made any deter- minations of residual magnetism, the data in Rowland’s table I. are sufficient to give a series of values of residual magnetism which determine the point. Using the same angle proportional to the total induction for 6, we can find a new quantity pw’, which we may call susceptibility to residual magnetism. The following table gives the results of this process as applied to Rowland’s table I.:— % or Q, total induction by reversal. %/ or P, subpermanent or residual induction (Q—T). #, Rowland’s value of the permeability. if 1 3 ; LB | eae — Then, if w/= potential’ potential in the same way that w= p= ps = from which the following values are calculated :— Initial values ‘ nea from first and third lines, by differences. ae pe’ or Susceptibility to Subpermanent Magnetism, from Rowland’s table I. ! 3. 35’. | | B. 33’. Q Pepe: pe. | 71:5 18-7; 390°7 102-7 || 8943 6369 2208 1572 600°5 2111; 868°7 305°4 | 10080 6838 1899 1288 966°7 438°7| 1129 512:4 |! 12270 7502 1448 885 | 2460 1572 | 1986 1237 12970 7666 1269 750 | 2923 1942 2078 1380 13630 | 7520 1137 aR | 8082 2064 2124 1422 14540 | 7989 824-1} 452°8 | 4959 | 3628 | 2433 | 1780 | 15770 | 8116 | 4618! 937-6 5482 | 3811 | 2470 | 1717 || 16270 | 7852 | 353-8] 170-7 | 2472 | 1715 || 16600 .| 7888 | 258 | 1996 6651 | 4746 | 2448 | 1747 || 17500 7473 | 5434 | 29367 | 1721 | | 84 Mr. R. H. M. Bosanquet on the Magnetic There is a slight discontinuity here near the maximum value of 4’; but nothing to obscure the general applicability of a continuous formula. We note that the initial value of yu’, though small, is by no means evanescent; that the curve formed by yw’ as ordinate and % as abscissa rises very steeply at starting; that p’ has a maximum value equal to nearly two thirds of the maxi- mum value of mw; and that, although the position of this maximum of pg’ is somewhat obscured by the small dis- continuity above referred to, yet it is substantially in the same position as the maximum of w. On the whole, then, the facts are incompatible with those with which Weber’s theory and Maxwell’s modification of it are framed to correspond; and it will be of interest to consider whether there be any hypothesis by which these facts can be represented. Prof. Hughes has recently put forward a theory, the funda- mental supposition of which appears to be identical with that of the theory of Weber; but I cannot find that it has been applied so as to give any quantitative account of magnetizing functions or permeabilities. I will now give an illustration of the suppositions as to molecular magnets, which would have to be made, in order that the principal term of the permeability may be propor- tional to the sine of an angle whose zero corresponds ap- proximately to the zero of magnetic induction, and 180° to saturation, the angle being proportional to magnetic induc- tion in between. The resulting theory is of an impossible character. Let a typical molecule be represented by a small magnet hung by a torsion-wire at the centre of a coil, and let the magnet be placed so that when no current is passing it stands nearly at right angles to the plane of the coil, but with the poles in the opposite direction to that which the action of the coil tends to make them assume. Suppose, then, that a current is sent through the coil; the needle will be deflected, and will rest at the point where the deflecting couple on the needle is balanced by the torsion of the wire. Now the couple due to the coil may be expressed as GC sin @; where C is the current, G a constant, and @ the deflection from a position at right angles to the coil. The torsion may be represented by 7(@—e), where « is small; or approximately by 7@, whence we have for the position of rest TO=GC sin 0. Permeability of Iron and Steel. 85 Let 0, or the rotation, represent the magnetic induction. It is clear that, however great C may be, it can never tend to increase @ beyond 180°, since this is the position in which the coil tends to place the needle independently of the torsion: this represents saturation. Further, C is proportional to the magnetic potential or magnetizing force, so that G iS proportional to w and Quen 6; so that p is represented approximately by a quantity proportional to the sine of an angle proportional to the induction. If the fundamental ideas of this illustration could be in any way applied to the behaviour of systems of molecules, it would be easy, by small modifications of the principal sup- positions, to take count of the smaller terms; but it seems quite impossible to carry out this application; and the illus- tration is only useful as showing the sort of circumstances which would have toe be imagined in order to obtain a formula of this sort from the hypothesis of molecular mag- nets. I will proceed to sketch another theory which appears to me more reasonable, and leads to forms of function by which we can represent the experiments very well. Suppose that every molecule of iron has one axis, and only one axis, through which magnetism can be transmitted. The molecules in an inert mass of iron are supposed to have their axes of transmission distributed in all directions. There will then be a very small proportion of molecules whose axes are so situated as to form continuous lines of transmissibility for magnetic lines of force proceeding in a given direction. Thus, for small magnetizing forces there will be a small trans- missibility or permeability. In the case in which molecules are so situated that the extremities of their axes do not join, the magnetic lines of force have to pass between the molecules as they would through ordinary space. We suppose that the transmissibility through the axes of the molecules is very great compared with that in ordinary space or in the interstices of the molecules. As the magnetic induction increases, couples are established by the action of the lines of force, which tend to move the axes of the molecules towards the direction of the lines of force. Consider a single molecule. Let the plane of the paper cut it in the plane containing its magnetic transmission axis and the axis of magnetization. ‘Then the lines of force will traverse the molecule somewhat in the way shown in the 86 Mr. R. H. M. Bosanquet on the Magnetic Lines of force. Axis of magnetizatior Lines of force. above figure, though they will only be parallel on the average to the mean axis of magnetization, where they issue from the molecule. Now it is known that many magnetic phenomena may be expressed by the hypothesis of a tension along the lines of force. If we suppose such a tension to exist here, we have a couple whose force is equal to the tension, and arm equal to the diameter of the molecule x sin @, tending to turn the axis of the molecule towards the axis of magnetization. If we suppose the molecules to give way to this force, the ends of the axes of the successive molecules approach each other, and the intermediate space, as well as the number of molecules, required to be traversed is diminished. This accounts for the increase of the permeability in the first part of the range of the induction. Without attempting to frame exact hypotheses we can see generally that the whole magnetic resistance may be ex- pressed by supposing the lines of force to form a zigzag, the obliquity of which diminishes as the tension of the lines of force increases. From this representation, assuming a law similar to Ohm’s law for electric circuits, we get the expression ae as representing the reduced resistance of a length / of COs the magnetic substance, 6 being an auxiliary angle represent- ing the mean obliquity of the zigzag. We have further to take into account the fact that all forms of iron and steel are capable of transmitting only a limited amount of magnetic induction through a given area. In the absence of any accurate knowledge as to the law which governs this part of the resistance of the molecules to the lines of force, I shall Permeability of Iron and Steel. 87 assume a factor in the permeability which vanishes for the saturation-value, namely (%3,, —%), where %_ isthe saturation- value of the induction. The resistance will then be propor- tional to the reduced length divided by this factor, so that resistance es jo A l ON (GB. — B)cos 6, or p=A(B, — B) cos 8. We may give some further account of the factor (%, —B) based on an analogy between the lines of magnetic force and solid wires. Ifa number of thin wires had to be packed into a cylindrical tube, by the time there were a certain number of them the hollow of the tube would be full, and no more could be got in. Also, if there were a less number, the space avail- able in the tube would be measured by the number of wires that could still be added. Now if our axis of transmission in the molecule represent the hollow tube, and the lines of force the wires, it is reason- able to assume that the permeability is proportional to the portion of the channel left open and unoccupied. And this is precisely given by (@,— %). It is only an analogy, but it seems to me not destitute of force. We may call (B, — B) “defect of saturation.” Let us return to the consideration of the equilibrium of the molecule. On the one hand we have the couple exerted by the lines of force ; on the other that arising from molecular attachments, which tends in the opposite direction. The simplest law of molecular attachments is the law of torsion ; and in considering a single molecule I assume that the couple tending to restore it to its place is proportional to the angular rotation from the position of rest. (The dis- placements of subpermanent and permanent magnetism are at first left out of the question.) If therefore p be the diameter of the molecule, k the torsion per degree, @ displacement from rest, @ inclination to direction of magnetization in disturbed position, %* psin 0=kad * J assume that the tension along the lines of force is proportional to 35 instead of to %, according to Maxwell. I shall return to the point ; but ‘may say here that the assumption of force proportional to 3§, led to formulz which failed to represent the experiments. 88 Mr. R. H. M. Bosanquet on the Magnetic expresses the condition of equilibrium ; is the unit angle, so that wd is d expressed in degrees. If we pass from the consideration of a single molecule to that of a molecular arrangement we are confronted with problems which, for the most part, must be regarded as insoluble. One point, however, is clear. If the axes of the molecules are arranged uniformly in all directions, the average inclination to any one line is 60°. For we may suppose the axes of transmissibility uniformly distributed over the surface of each hemisphere, and the hemi- sphere is divided into two equal portions by a cone whose semi-vertical angle is 60°. If therefore we represent the condition of the average molecule with respect to inclination by a single molecule, we must assume the initial inclination to the axis of magneti- zation to be 60°. And, in the above expression, when 0=0, op=60° ; so that op=60°—w0. And the equation becomes, p sind It only remains to connect @ with the auxiliary angle 6. In the absence of exact knowledge of the molecular arrange- ments, the only thing we can do is to assume the simplest connection possible. We shall assume b=, where fis a factor. We thus obtain the system of equations, w=A(B,, —33) cos 6, ay), k 60°— 0 dm p sin 9 This system of equations involves only the arbitrary constants A, &.,, f, and 4 for 60° cannot be called arbitrary. The equations are capable of representing very well the connection between » and %. The Fourier’s series are in some respects more flexible. But these equations are important as regards their physical bearing. As the computations present some difficulty, I here give a systematic scheme for adapting these equations to the representation of experimental series of values of % and yp. Given a series of experimental values of % and yw, it is required to represent them by the formule Permeability of Iron and Steel. 89 po Gear as) Cos0,) Teg Ge al. (CT) Cee Ge aig oh ey ae we a Le) k 60°—@a G3 — p ~sin@-* ° e ° e e ry a (3) Let 3%), », be the lowest pair of values given ; %., “ those corresponding to pz, the maximum value of p; 33. the saturation-value of % as estimated from the experiments or assumed. : The first process aims at determining A by trial and error, under the condition that the maximum value of w represented by the formulze shall belong to the value 93, given by expe- riment. The theory of this is as follows. Since w is a maximum, we have from (1), du=0= —d& cos 8—(B,, —B) sin 6 db, or aa dd en Ss) whence from (2), d& pee na de ene ay (B.—B)' ° a « (4) Again, differentiating (3), ok d% sin 0+ % cos 0 d0= — i dO, or ds % + sec 0 Wi te ta OE ua aca, vs (5) Combining (4) and (5), ak % + — sec 0 a , (6) f tané(S_—-By OS Rtg which is the condition for the maximum value of pm. tan 6= The work proceeds as follows:— Assume a value of A, (A’). Find wé, from cos 6, = WW. 38, : is M2 WO, from cos 6)= ANB. —B,) Phil. Mag. 8. 5. Vol. 19. No. 117. Feb. 1885. H 90 Mr. R. H. M. Bosanquet on the Magnetic (w x angle is used throughout to represent degrees, w being == i290). Let first approximation be denoted by one accent, second by two, and so on. Assume @6,/=60° Then fk 04 ih 60° 4 whence Sy oO! = aa ki - WY sin 6,/ p 60°—a6,! Second approximation. / w6,! J 60° — nae zt 31, , p y7__ ®071 vs w0,// whence pa b3 In general this will be enough, but there is no difficulty in repeating the process as often as necessary. Dropping the accents, we have for calculating the right- hand side of (6), k B., Ho, 08s, f, D From the result find tan 6, whence 4, or rather 6. If the condition as to the maximum is satisfied by the assumed value of A, this w6 will coincide with wd. If they differ, as they generally will, the assumed value of A is wrong. If w(d—6,)! is positive, A has to be increased, and vice versa. Another hypothesis as to the value of A has then to be made, and the work repeated, (A”). The final value #(@—0,)” thus obtained, compared with w(@—6@,)’, offers a means of estimating the true value of A, for which the maximum of w given by the equations corre- sponds to the proper value of %. But the convergence of the process is not quick enough to enable differences to be used for the estimation, unless close approximation | as been already Permeability of Iron and Steel. 91 attained. In this case A may be estimated from the formula w (5—8,)/ o(5—8,) —a(S—d)” where one accent refers to the first of two assumptions, two to the second. Before this way of estimating A was devised, the only way of approximating to it was to carry out the whole calculation of w from % for each assumed value of A, and then judge from the results. It was soon seen that the representations obtained differed in the position of the maximum of w. The following correspondences were thus obtained for ring H:— A ce (A/—A”) Assumed. Value of 1% for which p is A. a maximum. 1 Between 7000 and 11,000. = About 7000, still too late. 4 Before 6400, a little too early. An accurate judgment could be formed by the correspondences of uw before and behind the maximum. The application of the above method saved the great labour of these complete computations by way of trial. It is necessary to repeat the above processes until the resulting value of w(6—6,) is sensibly zero. The quantities f and — obtained in the computation which satisfies this con- dition are taken on for the final process. The next thing is to form the table connecting % and @, from equation (3). This is most conveniently done by form- O —wf ing a table of log ae once for all, for each degree from about 20° to 60°*. The addition of tliese logarithms to that of : gives the values of % corresponding to the degrees of w0. This table (%,0) is written out, with differences. The values of w§ corresponding to the experimental values of G are then found by interpolation. Multiplying @ by 7, we find 6 corresponding to each experimental value of %. With A, 6d, and G, pu is calculated from equation (1) for each experimental number %. ; The following are comparisons of this theory with experiment. '* For steel the table is formed for every 10” from 60° to 59° 59’, and then for every minute down to 59°. H2 92 Mr. R. H. M. Bosanquet on the Magnetic Hiquations. k 60°—o@8 p=A(B. —$) COs 6, 6=/0, 3 = p Tras. Ring E. ='3856 (17,500 —B) cos 6, log’ = 2°32208, log f='16153. 38 4) O. i Diffs Cale. Obs. @) 1 (e) 1 129°7 59 28 86 16 436 A37 — 1 939-1 59 2 86 4 AD7 493 — 36 2174:3 51 51 75 13 1508 1474 + 34 3187 48 36 70 30 1842 1817 + 25 5182 A 7 62 33 2190 2163 =k 6403 40 17 58 26 2235 2234 + 1 7208 38 37 56 10 2210 2206 + 4 11516 Bil 25) 45 34 1615 1615 6) 13276 29 Mal: 42, 20 1204 1382 —178 14017 28 20 41 6 1012 1047 — 39d 15000 97 16 40 8 io 635 +102 163880 25 55d at 25 342 218 +124 17245 1 24°53 36 «6 719 117 — 38 J. Soft Steel. fe=11 (20,000—B) cos 4, k eu x Og eae log f="17595. [le 33. 0. é. eR eel | DET, Cale. Obs. il ) 1 dl 57-6 | 59 59 567 | 8958 5 | 1223 | 123 ae, DHT Of 59 59 45°7 89 57 50 337 156 — 19 1826 59 58 28 89 5d 52 240 248 — § 2367 59 58 00 89 55 16 267 949 + 18 8517 59 57 2 89 53 46 329 314 + 15 5816 59 55 6 89 50 53 414 420 so 6 9468 59 52 2 89 46 19 A461 461 0 11497 59 50 19 89 43 41 444 443 + 1 12443 59 49 31 89 42 29 474 326 +102 15352 59 47 5 89 38 53 314 154 +160 18597 59 44 20 89 34 Al 114 90 + 24 Here %,, is a little overestimated. Probably 19,500 would be nearer the mark. A is the permeability of the molecules themselves per unit defect of saturation. For, putting 6=d=0, or supposing the Permeability of Iron and Steel. 93 axes all arranged in continuous chains parallel to the axis of magnetization, then ee G6. —B The molecular permeability for given %, under these circum- stances, is therefore . p=A(GB, —B), which -increases continually as % diminishes, and has the maximum values (G=0), hane BP .~ .. | p= 6748, J (soft steel) . w=220,000. Nothing is more surprising in these results than the enor- mous values of the molecular permeability of the soft steel, and the way in which the effect of this is suppressed by the comparative immobility of the molecules. Thus:— Extreme variation Extreme rota- of average tion of average inclination: molecule. Seturon ring .. 60°.... 24° 53! oa0 4 Saeco de 4... 60° « ae. 09° 44790" 15740" The molecular permeability of the soft steel is 28°5 times as great as that of the soft iron. The extreme rotation of the average molecule is 127 times as great in the soft iron as in the soft steel. P is 287 times as great in the soft steel as in the soft iron; so that, assuming that the mean diameter of the molecules is the same, the force of torsion arising from molecular attach- ment has this ratio in the two cases. Putting together the conditions associated with early and late maxima in the Fourier’s-series expressions and those of the present theory, we have Early Maxima. Late Maxima. Octave and higher Octave and higher termswelldeveloped. termssmallorabsent, New magnetic \ . Asmall. A large. equations. Fourier’s series. Recalling the meaning of A, we see that the development of the octave and higher terms in the Fourier’s series corresponds to low molecular permeability, other things being equal*. It * A depends on the absolute magnitudes of the p’s to be represented as well as on their course, 94 Professors Reinold and Riicker on the Influence of an will be of interest to see, when the hard-steel experiments are complete, how far the resulting inference of low molecular permeability in that case is borne out. As to the question whether the tension of the lines of force is proportional to % or to %b», it is a question for ex- periment, and I shall take an early opportunity of endeavouring to decideit. But in the mean time it appears quite clear that if lines of force mean anything, it is that their number is proportional to the force. Consider a magnet-pole. We may represent the distribution of force about it either by the law of the inverse square of the distance, or by a system of lines of force radiating from the pole. Ifthe two are equivalent, it involves the consequence that the force at any point is proportional to the number of lines of force. XII. The Influence of an Electric Current in Modifying the Rate of Thinning of a Liquid Film. By Prof. A. W. REINOLD, F.R.S., and Prof. A. W. Ricxrr, #.R.S.* 1% 1877 the results of some experiments made by us on liquid films were published in the Proceedings of the Royal Society (Proc. Roy. Soc., No. 182,1877). One object of the investigation was the determination of the electrical resistance of the films. The method of Wheatstone’s Bridge was employed for this purpose, and the current was passed through a film only at the moment when an observation was required. Under these circumstances the films generally thinned until they became black; and we succeeded in obtaining several measures of their resistance when this colour was dis- played. Subsequently this method was abandoned for another, in which continuous currents were passed through the film, and the difference of potential between two fine wires thrust into it was measured by an electrometer, and compared with that between two other points in the same circuit separated by a known resistancet. Although in many respects a great improvement, this method was in one point inferior to that previously employed. The behaviour of the films was very irregular when compared with that of those previously examined by the galvanometer, although they were formed of a liquid having the same com- position. Sometimes they thinned rapidly, sometimes slowly; * Communicated by the Physical Society. Read December 13, 1884. t “On the Electrical Resistance of Thin Liquid Films, with a Revision of Newton’s Table of Colours,” Phil. Trans, 1881. Electric Current on the Thinning of a Liquid Film. 95 at one time the black would appear after a comparatively short interval; at another, the film would persist for many hours without showing a trace of black. As at this time our atten- tion had not been directed to the possible influence of the current itself in modifying the rate of thinning of the film, no special precautions were taken with regard to the current, either as to its direction or intermittence ; but we now know that the apparently capricious behaviour of the films observed on many occasions was largely, if not entirely, due to want of method in managing the current. We have recently made some experiments with the definite object of determining the effect upon a liquid film of passing through it a current of electricity. Some of the results obtained were communicated to Section A of the British Association at the Montreal meeting. We propose to give in this paper a somewhat more detailed account of our obser- vations. The liquid employed consisted either of a solution of potash soap in water, or of Plateau’s liquide glycérique, containing a certain proportion of nitre to increase its conductivity. The films had the form of vertical cylinders, the upper and lower ring supports being of platinum, and about 33 millim. in diameter. ‘The cylinders were generally either 30 or 40 millim. long. Occasionally other lengths were employed. Three films were under examination at the same time; two being in one glass box, the third in a separate glass box. The two that were together were supported by platinum rings identically alike and sharply bevelled at the edge; the edges of the supports of the third were much thicker and were rounded. We had thus the means of ascertaining whether any difference in the behaviour of the films was due to the form or thickness of their supports. No such difference was observed. Hach of the film-boxes was placed in the centre of a water- tank with giass sides, in order to prevent rapid changes of temperature. In all cases the films were surrounded with air saturated with the vapour of the liquid of which they were made. The constancy of the hygrometric state of the air, and that of its temperature were indicated respectively by a hair-hy grometer and a thermometer inside the glass case. The films were blown with air which was first dried and then passed over some of the soap-solution in a wide tube. The state of the air inside the film was thus approximately the same as that on the outside. ; In the earlier experiments a battery of nine Leclanché cells was used, the electromotive force of which was about 12 volts. 96 Professors Reinold and Riicker on the Injluence of an More recently we have employed the current from a Siemens’ dynamo. ‘The current passed through a sensitive reflecting galvanometer, the deflection on the scale measuring approxi- mately the strength of the current. This varied from about 100 microamperes to half a microampere. We began our experiments by observing the behaviour of a number of films, each 40 millim. long, formed of potash- soap solution without any glycerine, which were allowed to thin in the ordinary way, no current passing through them. In less than a minute after the adjustment of the film to the cylindrical form narrow rings of colour appeared, and white of the first order of Newton’s rings was soon seen at the top, generally bordered by a narrow band of deep blue, the blue of the second order. The coloured bands did not extend beyond 10 miliim. from the top, the rest of the film being colourless. ‘This was the state of the case at the end of five or six minutes. In from eight to fifteen minutes from the moment of formation of the film a black ring appeared and slowly extended downwards. Nine films were examined, and all behaved substantially in the same way. We now tried the effect of passing a current through the films. It is unnecessary to describe all the observations that were made, as the object of many of them was merely to obtain confirmation of previous results. A few typical cases may be described. i. Downward Current. Plain Potash-soap Solution. (1) Film 40 millim. long. A current was passed through from the moment of its formation. Broad bands of colour formed and spread with great rapidity, soon occupying the whole area of the film. After six minutes the current was 2°6 microampéres (m.a.). In eleven minutes there was a ring of black, which in two minutes more increased to 8 millim. The curr ant was then stopped. It appears from this and a number of other experiments made in the same way that the effect of the downward current is to promote the thinning of the film. The bands are broader and spread out more rapidly than when no current is applied. (2) A film 40 millim. long had thinned until 2°5 millim. of black were formed. Next to the black came a band of deep blue. A downward current of 5°18 m.a. was applied. The blue changed to white, the black not being altered. After nine minutes the bine was still of about thes same breadth and the white had increased to 16 millim., the current being now 4-06 m.a. In two minutes after breakin g the circuit the white Electric Current on the Thinning of a Liquid Film. 97 had changed to black, the extent of which had become 19 millim., 2. e. nearly half the length of the film. The change from white to black in an experiment such as this is very striking: the black does not begin at the top and spread downwards as might have been expected, but the whole area of the white passes by insensible gradations into black, and it is difficult to say at times whether itis black or white. This intermediate condition between black and white can generally be obtained by accelerating the thinning of a film by a dewnward current until white has been formed, and then breaking the circuit and leaving the film to itself. This and similar observations show that a downward current has the remarkable effect of rapidly thinning that part of the film which is thicker than the black; but does not necessarily affect the latter. The film is, however, put into such a con- dition that, on the cessation of the current, the development of the black proceeds at a rapid rate. ; (3) A film 40 millim. long had a ring of black 2°5 millim. in breadth at the top. A downward current of 6°2 m.a. was applied. In one minute the black entirely disappeared, being replaced by white. The current rose to 6°5 m.a. The conditions in this case appear to be nearly the same as in the last. In each there are 2°5 millim. black, and the strength of current applied is about the same. Never- theless in the latter the effect is to destroy the black and increase the conductivity of the film. This is to be explained as follows :—When a film is formed between metal supports, the thin portion of the film is not immediately in contact with the metal. There is between them a thick ring of liquid of variable length, and from’ this the film proper hangs. As the film thins this massive ring of liquid is maintained more or less unaltered. Experiments were made with supports of various materials, shapes, and thicknesses, with the object of determining whether these had any marked effect on the mode or rate of thinning of the films. Glass, iron, and platinum have been used, and the edges of the supports made thick and rounded or finely bevelled. Although a thick and rounded edge would support a larger quantity of liquid than a sharp edge, the thinning of the films seemed little influenced by these modifications. When therefore a downward current is passed through a film having a certain area of black immediately depending from a ring of thick liquid, the current, carrying matter with it, soon floods the black with liquid and causes it to appear first grey and then white, its thickness and therefore its conductivity increasing. In the same way may be explained the fact that when a down- 98 Professors Reinold and Riicker on the Influence of an ward current flows through a film from the moment of its formation, although the film thins more or less rapidly to the white of the first order, it generally does not show the black so soon as it would have done if no current had been flowing. So long as a thick liquid fringe remains on the upper support, liquid is being carried downwards and the film prevented from thinning beyond a certain limit. As soon as the circuit is broken this downward passage of liquid ceases, and the white of the first order rapidly thins to black. The fact that the current sometimes does and sometimes does not destroy the black may be understood by reflecting that the increase or decrease in the thickness of any part of the film depends upon whether the quantity of matter carried into it exceeds or falls short of that transported away from it in the same time. Since both these effects are produced in part by gravity and in part by the action of the current, and are also probably modified by the thickness of the different parts of the film, it is possible that very slight differences in the conditions of the experiment may determine which of the two shall obtain the predominance. (4) Film 30 millim. long. A downward current of 24 m.a. applied from the beginning. In ten minutes the white ex- tended more than halfway down, and the current fell to 2°5 m.a. The circuit was then broken. The white turned to black so rapidly that in less than one minute the entire transformation was effected. In this case, the film being shorter, the same battery gave a stronger current, and the changes due to the current were accelerated. We will now describe a few typical cases of the action of an upward current. il. Upward Current. Plain Potash-soap Solution. (1) Film 40 millim. long. Current (9:2 m.a.) applied from the beginning. In twenty-four minutes there was a narrow band of white at the top succeeded by a narrow band of indigo-blue. Faint uniform tint below. The film was left for three quarters of an hour, but no black appeared. The current fell to 1°95 m.a. We have evidence here of the retarding action of the current, as the film would have ex- hibited black in ten or twelve minutes had there been no current. The current was too feeble to produce more marked changes. (2) Film 40 millim. long. There were 3 millim. of black and three millim. of white immediately below. An upward current of 4°9 m.a. was used. The lower edge of the black Electric Current on the Thinning of a Liquid Film. 99 became blurred and indistinct, and in two minutes the black had disappeared, white taking its place. The current rose to 5:32m.a. The circuit was then broken. Three millim. of black having been formed in seven minutes, the current was again put on (C=4°2 m.a.). The fuzziness at the edge reappeared at once, and in two minutes the black was all gone. The current rose to 4°62 m.a. (3) Film 19 millim. long, entirely black from top to bottom. Upward current of 3°12 m.a. put on. In thirty-eight minutes the current rose to 4°23m.a.,and the film was white throughout. (4) Film 30 millim. long. Black appeared in ten minutes. When it had increased to 5 millim. the circuit was completed. C = 5:05 m.a. In one minute all the black had disap- peared, and in two minutes more the film had a uniform tint throughout, while the current rose to 14°5 m.a. (5) Film 30 millim. long. Upward current passed through . from the beginning. It was not measured at first, but after five minutes its strength was 20 m.a. This increased to 28:5 m.a., which was maintained for several minutes, after which it slowly fell. The film was colourless. The ring of liquid on the upper platinum support was seen to increase in thickness and to become wavy along its lower edge. Pendent drops were formed, pointed at the bottom, and hanging from the liquid fringe. From the points of the drops tiny streamlets were seen flowing down the film. This is a very remarkable experi- ment. The up-current not only retards the thinning, but actually increases the thickness of the film. The strength of the current was not observed at first; but from the moment when it was observed until it reached its maxi- mum it increased by over 40 per cent., and the thickness of the film must have increased in nearly the same proportion. In opposition to gravity the current carries liquid to the top of the film, where it accumulates and from which it descends in liquid veins. The phenomena mentioned above recurred in several other films similarly treated. In some cases the film lasted long enough after the circuit was broken for black to be formed and to-extend to a considerable depth; and the curious spectacle was exhibited of pendent drops of thick colourless liquid penetrating through the black to a distance varying from 4 millim. to 93 millim. 100 Mr. G. F. Fitzgerald on the Rotation (6) Film 80 millim. long. When the black, which appeared in ten minutes, had increased to 14 millim. a current was passed. C=1°9 m.a. In five minutes the black was reduced to 8 millim., and then the film broke. This shows that even a feeble current is, at certain stages of a film’s existence, sufficient to destroy the black. (7) The last case we may mention was one in which two films, each 30 millim. long, were formed side by side. The current from the battery was divided and passed up one and down the other film. The effect was most striking. In twelve minutes, when one of the films broke, there were 15 millim. of black in the one, while the other was thick and colourless and liquid was streaming from the top of it. The experiments cited above were made with a solution of potash-soap (Brit. Pharm.) without any glycerine. The ad- vantage of using such a solution is that the films formed with it grow thin with tolerable rapidity, and in the course of two . or three hours several films may be observed with each appa- ratus. Similar experiments were carried out with liquide glycérique (made both with oleate of soda and potash-soap). The results were identical in kind with those enumerated above, but very different in degree. Films made with this solution are very persistent, but thin slowly. Generally three or four hours elapsed before any black appeared; and when a current was passed through, its effect was not so promptly manifested as in the case of the plain soap solution. The addition of nitrate of potassium may be partly accountable for this sluggishness, for it certainly increases the viscosity of the liquid. Nevertheless a great number of films made of the glycerine solution were observed, with currents flowing up or down. ‘The effect of the downward current was invariably to promote, of the upward current to retard, the thinning of the film. XIII. On the Rotation of the Plane of Polarization of Light by Feflection from the Pole of a Magnet. To the Editors of the Philosophical Magazine and Journal. 2 Trinity College, Dublin, GENTLEMEN, December 27, 1884. | a a A. KUNDT, in his paper translated from the Berlin Sitzungsberichte into the October number of the Phi- losophical Magazine does me the honour of noticing the theoretical explanation I have given (R. 8. Proc. xxv. p. 447) of the rotation of the plane of polarization of light by reflection of the Plane of Polurization of Light. 101 from the pole of a magnet. From the way in which he writes of my theory being refuted by his experiments, it is plain that he is unacquainted with my paper “ On the Hlectromagnetic Theory of the Reflection and Refraction of Light” (R. 8. Trans. 1880, part ii. p. 691), in which the following sentences occur (p. 709) :-— “In comparing these expressions with the results of Mr. Kerr’s admirable experiments, it is necessary to observe, as I mentioned before, that the introduction of a difference of phase between the reflected components is a question of a different order from that here discussed, and probably to some extent at least depends on the want of abruptness in the change from one medium to the other. For instance, my expressions give no change of plane of polarization when light is reflected normally from the end of a magnet, but they would lead one to expect that the only effect was a slight elliptic polarization, the major axis of the ellipse being in the same plane as the original plane of polarization. Now Mr. Kerr’s experiments show that there is some rotation of this plane by reflection, and a supposition similar to one long ago proposed to explain the known elliptic polarization of metallic reflection—namely, that the efficient reflecting surface has some depth—may easily be shown to lead to Mr. Kerr’s result. On this hypothesis the reflected ray is the resultant of the rays reflected from a small thickness at the surface of separation of the media; and in the case of normal reflection from the end of the pole of a magnet, each of these components would be slightly turned from its original plane of polarization owing to having passed through a very small thickness of a very powerful rotatory polarizing sub- stance—namely, this superficial layer of the magnet ; hence it is evident that their resultant would no longer be polarized in the same plane as the incident ray. I only give this as an instance of how this question of a difference of phase affects the results, and how the hypotheses that have been framed to explain it might be used to bring my results into complete accord with Mr. Kerr’s experiments.” | Prof. Kundt will see from this that I have anticipated the objection he raises, and have also anticipated him in pointing out in what direction to look for the explanation of the out- standing phenomena, to one of which he has called attention. Even in my first paper, the one with which Prof. Kundt is acquainted, I pointed out that it would be necessary to include the complications of metallic reflection in order to arrive at a complete theory. J cannot agree with Prof. Kundt in thinking that the incompleteness he has now pointed out and 102 Messrs. Wright and Thompson on the Determination of which I pointed out in 1880 is in any fair sense a refutation of my theory. [resnel’s theory of reflection cannot be fairly said to be refuted because it leaves unexplained the gradual change of phase of the components near the polarizing angle. All that is required in order to make my theory more complete is a little fearlessness as to complicated mathematics, which I regret to say either my laziness or my busyness prevents me from displaying, as it has till now prevented my noticing Prof. Kundt’s paper. I have roughly compared my formula with Prof. Kundt’s results, and find that the calculated rotations are of the same order of magnitude as he has observed. As he does not give experiments on the rotations produced by refiection and transmission under exactly similar conditions, any comparison must of necessity be rough. Yours obediently, GEORGE Francis FITZGERALD. XIV. On the Determination of Chemical Affinity in terms of Electromotive Force.-—Part 1X. By C. R. ALDER Waricat, D.Sc. (Lond.), P.BS., Lecturer on Chemistry and Physics, and C. Toomeson, F.C.S., Demonstrator of Chemistry, in St. Mary’s Hospital Medical School. [Continued from p..29.] B. Voltaic and Thermovoltaic Constants of Metals immersed in Solutions of their Chlorides. I. Cadmium. 180. A number of cells were set up with amalgamated-zine and electro-cadmium plates, and solutions of equal molecular strength, m MCI, 100 H,0, on each side, and examined pre- cisely as before. The following average values were obtained, the probable error in each case being from + ‘001 to + -002 volt. The values of Eq annexed are calculated from the heat-valuations of Julius Thomsen, viz. Zn, Cl, aq. =112840, and Cd, Cl, aq. = 96250, for molecular strength ‘25 MCI, 100 H,O ; so that the heat of displacement of cadmium by zine from chloride solution m CdCl, 100 H,O is 112840 —hy —(96250 —h,) = 16590 —(h, —A,), where /, and /, are the heats of dilution of zinc- and cadmium- chloride solutions respectively from the strength m MCl, 100 H,O to :25 MCI, 100 H,O: the values of h, and hy are derived from the table given in § 160, Part VIII. Chemical Affinity in terms of Electromotive Force. 103 Value of m. E. 16590—(h, —h,). i: E-—Eg. Oi ‘330 16590 "366 — 036 5 329 16190 357 — 028 10 ‘324 15340 338 —‘014 2:0 "315 13890 "306 + 009 4:0 ‘307 12290 ‘271 +036 6:0 "296 11390 "251 +045 8-0 "262 10890 ‘240 + 022 It is here evident that whilst the voltaic constant for cad- mium-zine-chloride cells continually diminishes as the solu- tion-strength increases, the value of Hy diminishes still more rapidly; so that the thermovoltaic constant is negative for weaker solutions and positive for stronger ones, the actual values of this constant being somewhat larger than those observed with zinc-cadmium-sulphate cells (§ 172), but still always under 5 centivolts. With the sulphate ceils the values of the constant were opposite in sign, viz. positive for weaker, and negative for stronger solutions. II. Copper. 181. On immersing a plate of clean metallic copper in a strong solution of cupric chloride, the plate speedily becomes visibly coated witha film of sparingly soluble cuprous chloride formed in virtue of the reaction Cu + CuCl,=Cu,Cly. With weaker solution the actual deposition of cuprous chlo- rides in the solid state is not always noticeable, although its formation and presence are readily detected analytically. It is hence evident that any cell containing as one half a solution of cupric chloride and a copper plate must really contain as the electrolyte on this side a mixture of cuprous chloride with more or less cupric chloride, the film of fluid in immediate contact with the copper plate containing but little if any of the latter salt in solution. In point of fact, on examining a number of similar cells set up with electro-copper plates immersed in +25 CuCl, 100 H;O on the one side and amalga- mated-zine plates immersed in *25 ZnCl, 100-H,O on the other, values were obtained fluctuating between 1:083 and 1:106 volt; whilst another series of analogous values fluc- tuating between almost exactly the same limits, and averaging practically the same value, was obtained with a corresponding set of cells in which the copper plate was immersed, not in cupric-chloride solution alone to begin with, but in a magma 104 Messrs. Wright and Thompson on the Determination of of cuprous-chloride crystals suspended in *25 CuCl, 100 H,O*. The values of the two series of observations combined were as follows :— Maximum Hi, Mialeeee ar. |) es ee Minimums). SMe itre se; «Dane ve par mOoes Average | a : on a pO Probable error of average allie - « OOS It is noticeable in this connection that precisely analogous results were obtained with other sets of cells, containing, on the one hand, cupric chloride alone, and on the other a magma of cuprous-chloride crystals and cupric chloride, when op- posed to cadmium; whilst similarly various mercury cells gave substantially the same values whether pure metallic mercury and corrosive-sublimate solution were used, or mer- cury anda magma of calomel and ‘corrosive- enorepats solution § 183 \ It ay from the above average value that the voltaic constant for electro-copper immersed in *25 CuCl, 100 H,O (or, what is the same thing, a magma of this solution and crystals of cuprous chloride) is +1:0985, when referred to amalgamated zinc immersed in 25 ZnCl, 100 H,O as zero. Sensibly the same value results as the sum of the H.M.F.’s of zinc-cadmium and cadmium-copper cells in solutions of strength -25 MC], 100 H,O throughout. With the latter cells the following numbers were obtained :— Masini ae eee ae ee ee Nii pee ee oer: ae WAVCT ADS Tee RAs ke ATO Probable error . . . .+:°0018 ' Voltaic constant from Zinc-copper cells. . . . =1:0985 Do. from Zine-cadmium -+ ees 330 +:769=1°099 copper cells . Mean) (0." 205099 The heat of displacement of copper from cuprous chloride by zine with formation of :25 ZnCl, 100 H,O results from Thomsen’s values, thus :— Zin, Clz, age) i. 20. 12840 Gi, Cl, Beir sa mood 0 47090=1:038 volt. * The cuprous chloride was prepared by boiling together copper- sulphate solution with common salt and spongy copper, filtering hot, and allowing cuprous chloride to crystallize out on cooling. Chemical Affinity in terms of Electromotive Force. 105 Whence the thermovoltaic constant for electro-copper in con- tact with cuprous chloride suspended in cupric-chloride solu- tion of strength :25 CuCl, 100 H,O is 1:099—1:038= +:061. The experiments detailed in § 174 indicated that when lead- sulphate was suspended in cadmium-sulphate solution a higher H.M.F. was observed, cvteris paribus, with zinc-lead-sulphate cells than when zinc-sulphate solution was employed ; from which it would seem probable that, if cuprous chloride be sus- pended in zine-, cadmium-, and copper-chloride solutions in three zinc-copper-chloride cells otherwise alike, the E.M.F. will be smallest in the first case and greatest in the last. This is in fact the case. The following values were obtained in a number of experiments on the point, indicating that the use of cadmium-chloride solution gives values intermediate be- tween those obtained with zinc- and copper-chloride solutions respectively. The solutions were in all cases of strength ‘25 MCI, 100 HO. ! Cu,Cl, suspended in | Cu,Cl, suspended in zine chloride. | cadmium chloride. | ee | | Maximum E.M-F. ... 993 | 1-011 | Minimum ,,... 980 993 | Average “- ae ‘988 1:001 | Probable error ...... +°0028 + -0035 | | Hence the thermovoltaic constants for electro-copper in contact with cuprous chloride suspended in zinc- or cadmium- chloride solutions of strength °25 MCI, 100 H,O are negative in sign, Viz. :— Suspended in zinc-chloride solution . *988—1:038=—-050 Fe cadmium ,, i . 1:001 —1°088= —:037 Tt should hence result that cells set up with electro-cadmium immersed in ‘25 CdCl, 100 H,O on the one side, and on the other side electro-copper immersed in a magma of cuprous chloride suspended in zine-chloride solution of the same strength, will have an H.M.F. of 672 —-050 —(— 036) =°658 ; and, similarly, that analogous cells set up with cuprous chlo- ride suspended in cadmium-chloride solution will have an E.M.F. of :672—:037—(—:‘036)=°671 (672 being the H.M.F. corresponding with the heat of displacement of copper Phil. Mag. 8. 5. Vol. 19. No. 117. Feb. 1885. I 106 Messrs. Wright and Thompson on the Determination of from cuprous chloride by cadmium =96250 — 65750 = 30500). On setting up a number of such cells the following values were obtained, the averages being sensibly identical with those thus calculated :— | | CuCl, suspended in | Cu,Cl, suspended in zine chloride. cadmium chloride. Maximum H.M.F....... 667 "674 Mamata. % fa fees | 654 666 Average eB cha aber 659 | 671 Probable error ......... +:0027 +:0016 It is noticeable in connection with these values, that whereas zinc-cadmium, cadmium-copper, and zinc-copper cells set up with sulphate solutions of various strengths possess H.M.F’s. in no case differing by more than +°010 volt from the values calculated from the difference between the heats of formation of the two electrolytes, the divergence between the two values is usually much greater when corresponding cells are set up with chloride solutions. Thus, for example :— Calculated. Observed. | Difference. Zinc-Cadmium (25MCl, 100H,O) .... “866 880 — -036 Do. (6-0MCI, 100H,0)...... ‘251 | 296 +045 Zinc-Copper (Cu, Cl, in ZnCl,) ......0.. 10388 988 —-050 Do. (Cu,Cl, in CdCl) ......... 1038 | 1-001 —-037 Do. (Qu, Cl, in CuCl,) ......... 1038 | 1099 +061 | Cadmium-Copper (Cu, Ol, in ZnCl,)...| 672-659 —013 | Do. (Ou,Ol, in CdOL,)..4) — “672 = ey —001 Do. (Cu,Cl, in CuCl,)...| 672 | -769 | +097 | ITI. Silver. 182. A number of cells were set up with anialgamated-zine and zinc-chloride solution on one side, and on the other side electro-silver immersed in a magma of freshly precipitated, well-washed silver chloride,suspended in zinc-chloride solution. The following values were finally obtained for cells where the zinc-chloride solution is of the same strength, mZnC], 100 H,0, Chemical Affinity in terms of Electromotive Force. 107 on each side. The probable error is in all cases below +°003. The thermovoltaic constants for electro-silver thus immersed are calculated from the heat of displacement of silver from silver chloride by zine forming mZnCl, 100 H,O, viz. :— 112840 —58760—h=54080—A; where 112840= Zn, Cl,, aq. (m='25), 58760=Ag,, Cl,, h =heat of dilution of mZnCl, 100 H,O to °25 ZnCl, 100 H,O (§ 160). | m. h, | 54080—%.| Eq. | og E—Eg. "25 0 54080 17192 1-080 — 112 5 400 53680 1184 1:068 —'116 1-0 1250 52830 1-165 1-049 —'116 30 3800 50280 1-109 | 1:026 —°083 | 6-0 | 5300 | 48780 | 1076 | 1-014 —-062 Hence it results that both the voltaic and thermovoltaic constants diminish in value as the solutions become stronger; and that whilst the thermovoltaic value of silver in contact with silver chloride (suspended in zinc-chloride solution) is negative in sign as with the sulphate, its numerical value is considerably less than in that instance. Some cells were next examined, containing on the one side electro-silver plates immersed in a magma of silver chloride suspended in zinc-chloride solution, and on the other side electro-copper or electro-cadmium in their respective chloride solutions, the solution-strength being *25MC1,100H,0 through- out. The following values were obtained, sensibly agreeing with the value —*112 for the thermovoltaic constant above obtained with zinc-silver-chloride cells for this molecular strength. It is to be noticed that the values of Hy with these two kinds of cells respectively are °827 and °154, correspond- ing with the heat-evolutions 96250—58760=37490, and 65750 —58760=6990. In the former case Hy+(k,—4,) is positive in sign, in the latter case negative ; so that the copper- silver cells are analogous to the zinc-cadmium-sulphate and 12 108 Messrs. Wright and Thompson on the Determination of cadmium-iron-sulphate cells above described, in that the metal actually acquiring the higher potential is not the one predic- able from the formation-heats of the electrolytes, but the other one—a result indicated by the’— sign prefixed to the values of H. Cadmium-Silver. Copper-Silver. Maximum E.M.F. observed...... ‘758 — 017 Minimum 4 BA St sa "743 —'025 Average oy RIC “751 --'020 Probableverror vscsee cases eeseace: +:0017 +:0015 : (|+ .751 — -020 Value of thermovoltaic con- | |+ “8380 +1:099 stant deduced from average{ | ~~ Sea d EMF, 0.00... | [FLO8l +1-079 oben | |—1-192 — 1192 UP Se Sot eS 2 The general average of the three values —*112, —:111, and — ‘113 thus obtained with zinc-silver, cadmium-silver, and copper-silver ceils respectively is —:112, representing the thermovoltaic constant for electro-silver in contact with preci- pitated silver chloride suspended in zinc-chloride solution of strength ‘25 ZnCl, 100 H,0. In precisely similar fashion six other kinds of cells were examined, containing respectively zine in zinc-chloride, cad- mium in cadmium-chloride, and copper in cupric-chloride solutions, opposed in one series to silver immersed in silver chloride suspended in cadmium-chloride solution, and in the other to silver immersed in silver chloride suspended in cupric- chloride solution, the solution-strength being ‘25 MCI, 100 H,O throughout. In the copper-silver cells, where the silver chloride was suspended in cadmium-chloride solution, the same peculiarity is observable as when suspended in zinc- chloride solution, viz. that the copper, and not the silver, acquires the higher potential ; but where the silver chloride is suspended in cupric-chloride solution this is not the case, the silver here acquiring the higher potential, and the current flowing in the direction predicable from the heats of formation of the electrolytes, and not in the opposite direction. The following values were obtained :— Chemical Affinity in terms of Electromotive Force. 109) Silver Chloride suspended in Cadmium-Chloride Solution. Zinc-Silver Cadmium- Copper-Silver ; Silver. BP ; WVSGRIBITOM oo. 505 +05 05--s- 1-091 ‘766 —:009 WerninnT J23¢6.5..-6.-2- 1082 weve —°014 PEVOEABE! foc... 5seetwun 159 3. Summary of the work done by the more modern experimenters— Hankel, Ayrton and Perry, Clifton, Pellat ..............5. 160 4, Experimental inquiry into, and general discussion of, the etfect of atmosphere on Volta effects.— Pfaff, De la Rive, Brown, Thomson, Pellat,;Schulze=Berge; Vion Zam 27. oii ois a 0» lotus e 'yokl vale 167 5. Views of Exner. Papers of Knott'and Hart .......\.. eee 179 6. Account of other papers bearing on the subject; and views of Banaday: 050.450 60k idle Wye ac PRE ectincane fo o/a elke ra ah one eae 184 1. The subject chosen for the present discussion illustrates in a remarkable way the need for such conversations. It is scarcely credible, at the present rate of progress, that eighty- four years after the discovery of the voltaic pile, opinion should still be utterly divided as to the seat of the main H.M.F. in it. I venture to hope that it may now be decided, and a substantial agreement arrived at with respect to it. My busi- ness is to open the discussion; but it so happens that for some seven or eight years I have believed myself to see more or less clearly to the root of this particular matter, and a labori- ous review of the literature of the subject has only strengthened my conviction. Having, therefore, strong and definite views I can hardly help letting them appear; and without assuming prematurely that these views are agreed with, they may yet serve as a link with which to connect the facts and the mul- tifarious observations thereon. In the course of my reading on the subject I have found only two great and epoch-making papers, that of Volta in 1801, and that of Sir William Thomson in 1851. The other contributions are some of them keen, like those of Faraday and Clerk Maxwell; some of them laborious, like those of Hankel and Ayrton and Perry ; but none contain anything essentially and powerfully new except those two: unless, indeed, we include in the subject the immensely important phenomena of Seebeck and of Peltier, and Faraday’s funda- mental law of electro-chemical decomposition. Volta* showed that when two metals were put into contact and separated, the insulated one was charged with electricity sufficient to make gold leaves diverge. fie also stated that the contact force between any two metals was independent of intermediate metals, so that the metals could be arranged in a definite numerical series ; and he gave the first series of the kind:— Zn——~ Pbs—~Sn\— Fe— Cu Ag. 5 1 i 2 3 * Volta, Gehler’s Worterbuch, iv. p, 616. See also a carefully edited version, Annales de Chim, 1 ser. xl. p. 225 (1801). Electromotive Forces in the Voltaic Cell. 155 Moreover, he started a hypothesis to account for the action, a sort of impulsion or attraction of electricity by matter—an idea subsequently elaborated by Helmholtz. Fabroni* ob- jected to Volta’s explanation of his experiment. He denied contact force, and considered that the electricity was developed by chemical action. Then the fight began, and lasted on and off some half-century. On the one side were Volta, Davy, Pfaff, Péclet, Marianini, Buff, Fechner, Zamboni, Matteucci, and Kohlrausch. On the other were Fabroni, Wollaston, Parrot, Girsted, Ritchie, Pouillet, Schénbein, Becquerel, De la Rive, and Faraday. It was not all fighting: part of it resulted in a more thorough investigation of voltaic phenomena ; and very often the original point of dispute was lost sight of, and Volta’s fact itself was doubted in the eagerness to disprove Volta’s explanation. The experiments of Pfaff and Péclety, however, fairly well established the correctness of his observation; and Kohlrausch showed how, by means of a Daniell’s cell combined with a condenser, to measure Volta forces absolutely, thus in- venting a method which has been employed with modifications by Hankel, by Gerland, by Clifton, by Ayrton and Perry, by Von Zahn, and by most other experimenters on the subjectf. * Fabroni, Journal de Physique de l Abbé Romer, xlix. p. 348. + Péclet on the Contact of Good Conductors: Comptes Rendus, 1838, p. 980; Poge. Ann. xlvi. 1839, p. 346; Ann. de Chim. 1842 and 1541, 3 ser. li. p. 233. Pfaff, Letter to Gay Lussac: Ann. de Chim. 2 ser. xli. p. 256 (1829).— Pfaff: For and against the production of Electricity by Chemical Pro- cesses, aS a consequence of some experiments on the H.M.F. of liquids and metals: Poge. Ann. xli. 1840, pp. 110 and 197.—Pfaff: Experimen- tam crucis in favour of the Contact Theory: Pogg. Ann. lili. 1841, p. 803. This crux is on p. 306, and consists in substituting ZnSO, for H,SO, in a Grove cell, and showing that the current through a thin wire galvano- meter is stronger than before. This, he says, leaves no further shift or evasion (Ausflucht) for the chemical theory. It is a fact we have grown accustomed to, but it 2s rather surprising, that the E.M.F. given by ZnSO, should be even higher than that given by H,SO,. A convenient “‘ Aus- flucht” could nevertheless be provided for the chemical theory by pointing out that the combustion heat Zn, 2NO, is greater than Zn, SO,—H,SO, +2(H,NO,), if indeed the fact be so. Another shift is to talk about basic sulphate and the sourness of ZnSO,; another is to use the word “ dissociation.” {¢ Kohlrausch’s method consisted in bringing the plates of the two metals close together, connecting them by a wire for an instant, sepa- rating them, and putting one into connection with a Dellman electrometer, the other with the earth. The observation is repeated with a Daniell in the connecting wire, first one way, then the other. Thus three equations are obtained, yf’ ha, D+M/M’=k8, D—M/M'=hy; whence me Me Siew” # M/M Sets ot ge (Pogg. Ann. vols. lxxy. p. 88, lxxxii. pp. 1 and 40, and Ixxxviii. p. 465, 1851 and 1853.) He gets his results much Jower than later experi- menters ; only } a volt for Zn/Cu, and °58 for Zn/Pt, M 2 156 Prof. Oliver Lodge on the Seat of the Fig. 1.—Kohlrausch’s Early Form of Condenser. Both the plates are insulated by silk threads. The fixed wire, d, with which the raised plate comes into contact, leads to a Dellman electro- meter. The connections are arranged for determining the “ electro- scopic tension” on the poles of an open battery, to see if it is the same as the H.M.F. (See Poge. Ann. 1848, vol. xxv. pp. 88 and 220,) This apparatus he also used to measure the Volta effect between two metals, his classical memoir on the subject being in Poggendorff’s Annalen, 1851, vol. Ixxxii. p. 1. Later he improved the condenser, bringing it into the form shown in the following figure. Vig. 2.—Kohlrausch’s Later Form of Condenser. (See Poge, Ann, 1853, vol. Ixxxviii. p. 464.) a as Electromotive Forces in the Voltaic Cell. 157 Wherever electrostatic methods were employed, and where the electroscope was the instrument of research, contact theo- rists had it all their own way ; and it was only by apparent effort and twisting of experiments that chemical theorists could maintain their ground. But when electric currents were dealt with, and the galvanometer used, then the chemists had their turn, and they showed most conclusively that no mere contact could maintain a current unless heat disappeared or chemical action occurred : a fact obvious enough to us to- day on the principles so laboriously and finally established by Joule. By means of the galvanometer, the contact theory was so belaboured by Faraday that it ultimately seemed to give up the ghost, and the chemical doctrines triumphed. So much so, that Volta’s original fact, in spite of the evidence which had been accumulated, was again doubted; and one finds in text-books culled from this period statements that Volta must have had wet fingers, or that he rubbed the plates together, or that there was moisture in the air. Also hints are given that films existed on the plate, that squeezed coats of varnish or lacquer might produce some electricity, and so on. It was pointed out, moreover, by De la Rive*, how minute a trace of chemical action could produce how much electricity, and how little electrictity could affect an electro- scope. But it is to be noted that any chemical action caused by damp on the plates, or moisture in the air, would be of the nature of local action, and local action is not a satisfactory pro- ducer of manageable electricity. Sir Humphry Davy is very clear on this head. He shows that chemical action need pro- duce no electricity, instancing the burning of iron nitre on charcoal, potash and acid in a crucible or an electroscope, &.; a plate of zinc placed on mercury and separated is found posi- tive, but if left long enough to amalgamate, the compound shows no signs of electricity. Davy’s views are singularly advanced, and are worth quoting. * De la Rive: Traté @électricité, ii.p. 776 ; Annales de Chimie, xxxix. p. 311 (1828). t+ Davy, Bakerian Lecture, 1806 (see Phil. Trans. 1807, p. 39) :—“ As the chemical attraction between two bodies seems to be destroyed by giving one of them an electrical state different from that which it naturally possesses ..... so it may be increased by exalting its natural energy. Thus, while zinc is incapable of combining with oxygen when negatively electrified in the circuit even by a feeble power, silver easily unites to it when positively electrified... .. . Among the substances that combine chemically, all those, the electrical energies of which are well known, exhibit opposite electrical states... .In the present state of our knowledge it would be useless to attempt to speculate on the remote cause of the electrical energy, or the reason why diiferent bodies after being brought into contact should be found differently electrified ; its relation to chemi- cal affinity is, however, sufficiently evident. May it not be identical with 158 Prof. Oliver Lodge on the Seat of the Quite detached from any connection with the controversy, because at that time quite unintelligible to all but one or two here and there, two papers appeared in 1851 by the President of this Section, which were the triumph and apotheosis of the chemical theory of the source of the current in the voltaic cell*. In one of these papers (that on “ Hlectrolysis ”) it is irrefutably established, on the basis of the conservation of it, and an essential property of matter ?”—Page 44: “The great tendency of the attraction of the different chemical agents by the positive and nega- tive surfaces in the Voltaic apparatus seems to be to restore the electrical equilibrium... .The electrical energies of the metals with regard to each other or the substance dissolved in the water, seems to be the cause that disturbs the equilibrium, and the chemical changes the cause that tends to restore the equilibrium; and the phenomena most probably depend on their joint agency.” He then gives a very Voltaic account of the action of the pile—much in agreement with Sir Wm. Thomscn ; and endeavours to reconcile chemical and contact theorists by pointing out how essential a part chemical action plays in the production of a current, a most clear- sighted thing to do at that date. One more sentence may be quoted from this remarkable paper, though it is not quite so striking as the preceding. —Page 49: “These ideas are evidently directly in contradiction to the opinions advanced by Fabroni, and which in the early stage of the investi- gation appeared extremely probable, viz. that chemical changes are the primary cause of the phenomena of Galvanism. Before the experiments of M. Volta on the electricity. excited by mere contact of metals were published, I had to a certain extent adopted this opinion; but the new fact immediately proved that another power must necessarily be con- cerned, for it was not possible to refer the electricity exhibited by the opposition of metallic surfaces to any chemical alterations, particularly as the effect is more distinct in a dry atmosphere, in which even the most oxidizable metals do not change, than in a moist one, in which many metals undergo oxidation.” * Sir W. Thomson :—1. “ On the Mechanical Theory of Electrolysis and the Applications of the Principle of Mechanical Effect to the Measurement of Electromotive Forces in Absolute Units,” Phil. Mag. December 1858. Reprint of Mathematical and Physical Papers, vol. i. pp. 472 and 490. 2. On the Dynamical Theory of Heat, part vi. Thermoelectric Cur- rents: ’ Proc. R. 8. Edin. Dec. 1851 ; Trans. R. S. Edin. 1854; Math. and Phys. Papers, vol. 1. pp. 232 and 316. Helmholtz also clearly applied the conservation of energy to Voltaic circuits in his memoir Dre Erhaltung der Kraft, read before the Physical Society of Berlin, 23 July, 1847. In this powerful memoir Prof. Helm- holtz sails placidly through a great part of physics, applying to various phenomena the then new principle of the conservation of energy. He regards all action as occurring at a distance, and shows, as is well known, that, on this hypothesis, central forces are the necessary and sufficient condition of conserved energy. This part may now be regarded as super- seded; but in the more special portions, among other things, he develops the mechanical theory of the H.M.F. of voltaic cells, of thermoelectric piles, and of magneto-machines ; anticipating in many respects the some- what later though independent work of Sir W. Thomson on these subjects. Prof. Helmholtz’s memoir is easily accessible through a translation, by J[ohn] Tyndall |, which appeared, in May 1853, in the “new series” of ‘Scientific Memoirs,’ issued by Taylor and Francis. Electromotive Forces in the Voltaic Cell. 159 energy, that, making exception of such irreversible effects as are not readily brought into calculation, and allowing for certain possible reversible effects to be investigated thermo- electrically, the H.M.F. of a cell is not only dependent on the chemical action going on, but is calculable numerically in absolute measure on purely chemical data supplied provision- ally by Dr. Andrews. It is proper to say, however, that this brilliant theory is avowedly based on the laborious and acute experimental work of Joule on the conservation of energy in the voltaic circuit™. In the other of the two papers (that on “ Thermo-eleciricity ’’) it was shown that, from the fact that a current absorbed or generated heat at a metallic junction, an H.M.F. was neces- sarily situated there—in other words, that the Peltier effect necessitated the previously discovered Seebeck one. The establishment of the conservation of energy, by Joule, for ever placed beyond doubt the fact that the energy of the electric current produced by a battery was due to, and was the equivalent of, the chemical actions going on there ; but it was supposed, and is still supposed (though, as I venture to think, quite erroneously), to leave untouched the question us to the precise seat of the H.M.F. in a battery. However that may be, the success of the chemical theory of the electric current naturally caused it to be still more certainly assumed that the apparent contact-force of Volta could also be accounted for by accidental chemical action, and that without some chemical action somewhere no Volta effect could be produced. ‘This, also, I believe to be quite false ; provided always that the phrase “ chemical action ”’ be used in its ordinary sense as meaning combination, and that the word “action ’’ be not explained away as meaning anything what- ever. : 2. The triumph of the chemical theorists with regard to the Volta effect was, however, shortlived, for, from 1860, the in- vention of the quadrant electrometer put into the hands of electrostatic experimenters a far more refined and delicate in- strument than could have been thought possible a few years before ; and the illustrious inventor of that instrument him- self for ever put the truth of Volta’s phenomenon beyond doubt, by the most simple and beautiful device of suspending a charged torsion-arm over a zinc-copper junction. By com- paring the deflection so produced with that caused by a * Joule :—‘ On Heat evolved in Metals and during Electrolysis,” Phil. Mag. [3] xix. p. 260 (1841); “On the Electric Origin of the Heat of Combustion,” 2b7d. xx. p. 98, and xxii. p. 204; ‘‘ On the Heat disengaged in Chemical Combination,” Phil. Mag. [4] ii. p. 481. See also Reprint of Joule’s papers by the Physical Society of London (Taylor & Francis). 160 Prof. Oliver Lodge on the Seat of the Daniell cell, an absolute measure of the so-called contact-force was made ; and it was shown that, uniting the copper and zine by a drop of water, instead of by a metal, no deflection was produced. It was also shown that the deflection was greatest when the zine was clean and the copper oxidized”. But Sir William Thomson went further than this: he sounded a theoretic note, and in a sentence revived the whole controversy about the seat of power in the pile. The sentence is this:—‘* For nearly two years I have felt quite sure that the proper explanation of voltaic action in the common voltaic arrangement is something very near Volta’s, which fell into discredit. because Volta or his followers neglected the prin- ciple of the conservation of force. I now think it quite certain that two metals dipped into one electrolytic liquid will (when polarization is done away with) be at the same potential.” And then he goes on to one of those brilliant and extraordinary speculations characteristic of no one else, and applies this apparent contact-force to determine a lower limit to the size of atoms—an application obviously of tran- scendent interest, and of more importance than all the previous outcome of contact discussions put together f. The whole subject now acquired a fresh interest, and the new series of experimental determinations of contact-force began. 3. Hankel’s and Gerland’s measurements belong to this period in point of date (1861-69), though in method and motive they probably are the outcome of the earlier period{. Hankel uses a modified Kohlrausch method and a Bohnenberger or * Proc. Lit. and Phil. Soc. Manchester. Letter from Prof. W. Thomson to the president, Dr. Joule, Jan. 21, 1862: “New Proof of Contact- Electricity.” See reprint of papers on Electrostatics and Magnetism, p. 317. + “There cannot be a doubt that the whole theory is simply chemical action at a distance. Zinc and copper connected by a metal wire attract each other from any distance, so do platinum plates coated with oxygen and hydrogen respectively. I can now tell the amount of the force, and calculate how great a proportion of chemical affinity is used up electro- lytically before two such disks come within any specified small distance down to a limit within which molecular heterogeneousness becomes sen- sible. This of course gives a definite limit for the size of atoms.”— Letter to Dr. Joule, 1862, cited above. See also Thomson and Tait, Nat. Phil., Part II. Appendix F. t Hankel, Electr. Untersuchungen, Abh. der kinigl. Stchs. Gesellschaft, math.-phys. Klasse, i861 and 1865. See also Pogg. Ann. cxv. p. 57, and cxxvi. pp. 286 and 440; exxxi. p. 607. Gerland, “On the E.M.F. between Water and some Metals,” Poge. Ann. cxxxiil. 1868, p. 513; exxxvii. 1869, p. 552. In his second paper, to get over the air effect, Gerland joins two metals through a galva- nometer, and then dipping them into a liquid, observes the first swing of the needle. He also compensates the E.M.F. by Poggendortt’s method. He thus determines the value of M/M'+ M'/Liquid+ Liquid, M. Electromotive Forces in the Voltaic Cell. 161 Hankel electroscope ; his special merit is the determination of metal-liquid contact-foreces without introducing blotting paper, glass, or fingers, as the earlier experimenters had done. Fig. 3.—Hankel’s Arrangement for observing the Volta Effect between a Metal and a Liquid. The liquid, L, is in a funnel-tube, A, B; C is a copper plate, and M the metal under observation. First, » touches C for an instant, then C is raised and made to touch p’, which leads to a Hankel electrometer. This gives Cu/M+M/L=kaea. Then the liquid is ren out of the funnel, a plate of the metal M is placed on its mouth, and the experiment repeated. This gives Cu/M=A48. To eliminate & substitute a plate of zinc for M, and get Cu/Zn=ky. Then, finally, M/L=%—* ou/m. Y In all these expressions air contact-forces are, as usual, neglected. But it is very tempting to try if, by increasing the number of such equations, one cannot calculate some metal/air contact-forces. Thus the special case when M is copper gives one more equation. We can then take zine instead of M, and can also make the condenser-plate of zine instead of copper, and so on; but we get no forwarder, fresh unknowns appear as fast as additional equations, and some of the equatious are liable to degenerate into identities. So far back as 1824 Becquerel* attempted the investiga- tion of metal-liquid contacts ; and Buffft made some measure- ments in 1842, but his results are scarcely likely to be reliable considering the poor experimental resources of that date. Professor Clifton employed Kohlrausch’s method in 1877, using a Thomson electrometer and a Clark cell as standard of H.M.F. He has only published a preliminary papert, in which he overlooks minutiz such as change of contact- * Becquerel, Ann. de Chime, 1824. He put the liquid in a copper capsule on the plate of an electroscope, and connected it with the con- denser plate by his fingers. + Buff, Liebig’s Ann. Chem. u. Pharm. 1842. He made the lower plate of his condenser the metal to be examined; on it he placed glass, and then filter paper soaked in the liquid, which he connected with the metal plate by a wire of the same metal. } Chfton, Proc. Royal Soc. xxvi. p. 299 (1877). 162 Prof. Oliver Lodge on the Seat of the force by time and adventitious circumstances. When he touches on theory he agrees with Thomson. Professor Clifton has examined the Volta effects for the substances ordinarily used in batteries with great care, and has probably elicited the maximum of accuracy possible to his method. He gives the E.M.F. of numerous virgin cells in which no current has circulated. Ayrton and Perry in 1876 devised in Japan a very ingenious but somewhat unwieldy modification of Kohl- rausch’s method, and with the help of students carried out a most extensive and laborious series of determinations of metal/metal, metal/liquid, and liquid/liquid contacts*. Fig. 4.—Ayrton and Perry’s Apparatus for measuring the Volta effect with all sorts of substances. 7, q AVANYULALALALADAALY LLL 244) . 34 UA: Ve CZ) wh The substances are arranged on the lower platform, as, for instance, the metal and liquid shown in the figure at P and L. The platform, A B, is capable of rotation through 180° on its railway, R. 3 and 4 are carefully insulated gilt plates fixed to a bar which can be raised and lowered. The experiment consists in lowering these plates close to the surfaces to be tested, and connecting them with each other for a short time; then raise them, rotate the platform through 180°, lower again, and connect them with a quadrant-electrometer. * Ayrton and Perry, Brit. Assoc. Glasgow, 1876. No abstract printed. Part L., Proc. Royal Soc. 1877 or 1878, is a preliminary account. Part II. describes a metallic voltaic cell of magnesium and platinum and mercury, also some experiments on electrolytes of high resistance. Part I1T., Phil. Trans. 1880, is the complete account of their published electroscopic experiments. Ss Electromotive Forces in the Voltaic Cell. 163 Fig. 5.—End view of Ayrton and Perry’s Apparatus. On the appearance of Clifton’s paper the year after, they issued a strongly worded claim* in respect both of priority and completeness—a claim which seems to me well established, for their results are the most comprehensive yet obtained, and the energy needed to devise, construct, and use such an apparatus as the one they depict must have been immense. A convenient summary of their numbers is to be found in Hverett’s ‘ Units,’ second edition. The main result achieved by them is the experimental establishment of the summation law for all substances (this is not to be confused with Volta’s summation or series law, which is only applicable to metals), viz. that the total E.M.F. of a closed circuit of any number of substances may he reckoned by adding up the Volta forces observed electrostatically for every pair of substances in con- tact. This law is, it seems to me, for reasons given later (§. 7), very probable theoretically ; but still it was quite essential to have it experimentally established, especially as Ayrton and Perry point out that it is often called in question without good ground. The establishment of this law is, | say, perhaps their main work in this matter, besides the : is — and Perry: Letter published in 1877 by Meiklejohn (Yoko- ama). 164 Prof. Oliver Lodge on the Seat of the observation of the Volta effect for various difficult substances, especially liquids and liquids. Clifton arrives at the same conclusion with regard to sum- mation, and gives handy diagrams, reproduced in Jenkins’s ‘ Hlectricity,’ of the contact-force at the different junctions. My own opinion is that the intended and obvious significance of these diagrams is theoretically wrong, but they embody certain experimental results conveniently, and they can be interpreted properly. Both Clifton and Ayrton and Perry appear to believe in the great constancy of the value Zn/Cu. Clifton gives it as 8516 volt (“ Quelle précision ! ’’ somewhat sarcastically eja- culates Pellat, who himself finds it to vary between °63 and °92). Ayrton and Perry assert that it is more constant than a Daniell. I believe that both Professor Clifton and Pro- fessors Ayrton and Perry have made several experiments besides those recorded in their communications to the Royal Society ; but as they have not been published, I can give no account of them. Among the Théses presented to the Faculty of Science in Paris in 1881 we find an important memoir by Pellat*, which reviews the whole position very clearly, and records a series of determinations of Volta force among metals, determinations which are evidently the most accurate and satisfactory yet made. He adopts the capital experimental method of neutralizing the charge of a condenser bya Pog- gendortf or compensation method, and thus convefts Kohl- rausch’s into a null method, for which a very sensitive elec- troscope is all that is needed. The plates of the two metals set face to face are connected, not directly, but by a greater or less length of a graduated wire conveying a current ; and the position of the slider on the wire is adjusted by con- tinually separating the plates and testing until no charge at all is found. The step of potential on the wire is then pre- cisely equal to the “contact-force ”’ between the plates ; for this would have caused a charge in a similar but uncom- pensated condenser, and the step of potential on the wire has neutralized it. Compensation methods of a sort had been used before by * Theses présentées a la Faculté des Sciences de Paris, pour obtenir le Grade de Docteur-és-Sciences physiques, par M. H. Pellat, Professeur de Physique au Lycée Louis le Grand, No. 461; Juin 22, 1881. See also Journal de Physique, 1881, xvi. p. 68, and May 1 1880: ‘ Ditférence de potential des couches électriques qui recouvrent deux métaux en contact.” Ellectromotive Forces in the Voltate Cell. 165 Fig. 6.—Diagram of Pellat’s Method. Légende. KL, compensateur. m, interrupteur. C, curseur. F, feuille dor. R, rhéostat. A et A’, plateaux attractifs de P, piles Daniell fournissant le l’électroscope. courant du compensateur. 6b, batteries de 100 volts chacune p'p, plateaux du condensateur pour charger les plateaux (p fixe, p’ mobile). AA’. The diagram, fig. 6, pretty well explains itself. The contact at m is broken the instant before p’ is raised. Fig. 7.—Pellat’s Condenser. Fig. 7 shows how this was done in practice. Pulling the string, A, raises a sliding-pin with a shoulder, g, fixed to it a millimetre below the bar, B. The pin thus first breaks contact near H, and then raises the hinged bar BB, to which the upper plate, M, is attached. The upper plate, being always in connection with a battery, requires no special insula- tion, The lower plate is carefully supported by a Thomson insulator, I. The lower plate was considerably smaller than the upper one, and it was further protected from stray inductions by aguard-screen. Screws, ec, served to regulate the distance between the plates. 166 Prof. Oliver Lodge on the Seat of the Gerland and by Thomson. Grerland applied compensation to determine the .M.F. of two metals dipped into a liquid, and Thomson applied it to the divided-ring experiment, thus making it very analogous to that of Pellat *. Pellat also adopts Sir William Thomson’s view that the Volta effect is due to a true contact-force between the metals, and that it represents a real difference of potential between them when in contact ; at the same time he is careful to point out that no rigorous proof can be given of this, and that all that is really and certainly measured electrostatically is the difference of potential between what he calls the electric coats (les couches électriques), or what may be more simply called the air-films, on the two touching metals. The following is a summary of some of Pellat’s measure- ments, gold being the metal with which all are compared, and the numbers being given in volts. ‘¢ Difference of Potential of the Hlectric Coats which cover a Metal and Standard Gold metallically connected, and both Woy Jeanie," H.M.F. in volts. E.M.F. in volts. With surface | strongly With very | With surface | With very scratched Metals used.| clean but strongly || Metals used.{ clean but | by rubbing scarcely scratched scarcely with emery, seratched | by rubbing scratched jor in some of surface. with emery. surface. the last cases with cloth or filter-paper. ZAR CPR Sees "85 1:08 Ne MarOTaeeice cae "29 “38 ead ses ‘70 crue Br aSSycosce ‘29 ey 4 DLA eesti ere ‘60 ‘73 || Copper ...... 14 "22 Antimony ... “44 “45 Platinum ... —'03 +:°06 Nickel v5.0: "38 "AD Golda. aie: — “04 +07 Bismuth...... “36 "48 Silvera. ease: —°06 +04 Steel... 2... "29 “44 * I find indeed that Sir W. Thomson completely anticipated Pellat in the application of galvanic compensation to the measurement of Volta effects; for in ‘Nature,’ April 14, 1881 (vol. xxiii. p. 567), is printed an account, given in brief at the Swansea meeting of the British Association (see Trans. of Sects. 1880, p. 494), which relates how the divided-ring experiment naturally developed into more complete compensation with slide resistances, and that an extensive series of measurements were made on this plan in the years 1859-61 with results quite in agreement with those published by Hankel in 1862. Other experiments were made since 1861 with results confirmatory of those of Pfaff, 1821, showing the Volta effect to be independent of the surrounding gas. The description of all these experiments was therefore withheld till something new should be obtained by the method, and was not published until Pellat’s paper had Electromotive Forces in the Voltaic Cell. 167 4. Meanwhile some experimenters, starting with a belief in the chemical origin of the Volta effect, had made experi- ments supposed to support this view. Mr. J. Brown, of Bel- fast, in 1878, repeated Thomson’s divided-ring experiment *, as well as Kohlrausch’s condenser-experiment, in other gases than air; and found a very decided difference, and even a reversal of sign, when sulphuretted hydrogen was substituted for air. The metals Brown used were copper and iron, and he obtained a 1l-centimetre deflection in the direction indicating iron + in air; while in SH, he obtained a 3-centimetre de- flection, indicating that iron was —. On readmitting air, the deflection again reversed, and so on until the copper coated itself with a blue film of sulphide, when the deflection became undecided, owing, as Brown supposes, to “the cessation of chemical action.” Fig. 8.—Mr. J. Brown’s Arrangement for observing the Volta Effect in different Gases by Sir William Thomson’s Method of a bimetallic ring with an electrified needle hanging over it. i (il appeared in the Journal de Physique, May 1880. Fig. 10 sufficiently exhibits Sir William’s arrangement. In a postscript are described a few additional experiments of the same kind as those published in 1881 by Schulze-Berge, in which a platinum plate is soaked for a certain time in dry hydrogen or oxygen, and then used in the Volta condenser. The observation is made that merely soaking a plate im gas is more effective than electroplating it with the same gas with an E.M.F. of a volt. * J. Brown, Phil. Mag. August 1878, Feb. 1879, and March 1881; see” also Brit. Assoc. Trans. of Sect. 1881, and ‘ Electrician,’ vol. vii. p. 165. 168 Prof. Oliver Lodge on the Seat of the In 1881 he observed a time-change (decrease) of the Volta effect at a copper-zine junction, and reckoned that at the first instant after cleaning the potential. difference would be as high as ‘9 Daniell, “‘ which,” he says, “agrees with J. Thom- sen’s determination of the difference of the heats of combus- tion of zinc and copper and oxygen.” He here gives a hint of holding a heterodox notion which I do not find in any other of his w ritings, and which I believe he abandoned, even if he ever really held it. In 1879 Brown tried a copper-nickel divided ring, substi- tuting HCl for air, and here also succeeded in obtaining a reversal of sign. He also arranged a divided ring of wet blotting-paper, and showed that there was a difference of potential when the two halves were touched with a zinc- copper couple (which is not remarkable); but he then goes on to draw a moral, and to say that the slit of the divided ring corresponds to the air-film, and the wet paper to the moisture-film in the ordinary Volta-condenser experiment. The film of moisture on the zine plate is thus shown to have a + charge, and that on the copper a negative. If it be objected that the better the plates fit, the better the manifes- tation of contact HE, it is to be replied that it is not to be sup- posed that there is no air between them anyhow (says Brown). Probably, he says, gas produces the difference of potential only so far as it forms a film on the surface. When a metal and a liquid are experimented on, it is probably really a two- fluid cell, the other fluid being that condensed on the surface of the metal. Brown thus goes strongly for the activity of the films, or condensed air-sheets, which certainly exist on the surface of solids, and which may play an important part in the matter; but he supposes that these films act by corroding or attacking the plates, and that such a film is necessarily existent between surfaces nominally in contact if any Volta effect is to be pro- duced ; so that if the metal faces really and truly touched all over, they would show no charge when separated. Moreover, he lays it down that the potential difference is only observed while chemical action is going on; but that so soon as it ceases, from any cause, at once the Volta effect ceases too. In all this I entirely differ from him; but his experiments are very interesting and much to the point. They cannot, however, be regarded as settling the question —the very important and fundamental question—as to whether the Volta effect depends on the atmosphere or medium sur- rounding the plates, or whether it is an absolute effect depending on contact alone. Hxperiments on this point are absolutely discordant; and it seems to be one of those points Electromotive Forces in the Voltaic Cell. 169 which it is very difficult to settle by direct experiment. For if by using a chemically active gas instead of air, you get a positive result or change in the Volta effect, the answer from the other side is: “ Yes, of course, because your plates are corroded and coated with sulphide or chloride, or something whose contact-forces come in and modify everything.” Ii, on the other hand, you get a negative result when you substi- tute some inert gas like hydrogen for air, then it is objected that you have not removed the air-film which the plates had contracted from long standing in the air; and if you answer indignantly that you did, and that your hydrogen was per- fectly pure, it is replied with a sneer, ‘Oh yes, it is not so easy to get pure hydrogen as you seem to think.” Moreover, suppose a positive effect on changing the gas was established ; what then? Nothing is settled except that the metal /air contact-force is proved to be somewhat different from the metal / gas contact-force. There seems to be really no way of knocking contact-force on the head experimentally, and this probably because it is a reality: there really is a contact-force at every junction of dissimilar substances ; and the H.M.F. of a circuit, whether it be inductive or conductive, is always the sum of such contact-forces. I do not say that the contact-force at any given locality has the value ordinarily assigned to it as the result of experiment. The earliest attempt made to examine the question as to whether the Volta effect depended on the atmosphere was made by Pfaff* in 1829, who used dry and damp air, oxygen, nitrogen, hydrogen, carburetted hydrogen, and carbonic acid, _and he found that there was no difference so long as no visible chemical action occurred; butit must be noted that the oppo- sing faces of his plates were varnished. De la Rive, on the other hand, asserted that there was no Volta effect in the slightly rarefied air then known as “‘ vacuum.” In recent times Pellat has investigated the subject, and has come to a conclusion in agreement with Pfaff, viz. that the differences are very small. The metals used by Pellat were copper and zinc, and the gases were air dry and damp, dry oxygen, dry nitrogen, dry and pure hydrogen, dry and pure carbonic acid. He finds slight variations, but exceedingly slight, and such as Pfaff, Hxner,and Brown could hardly have detected. He says :—‘Au surplus il est fort probable que, si quelgues-uns des auteurs précédents avaient tenté les expé- riences que j’ai faites au sujet des gaz, ils auraient trouvé des résultats négatifs ; les faibles variations produites par le changement des propriétés du gaz que j’ai pu mettre nette- * Pfaff, Ann. de Chim. 2 ser. xli. p. 236. The metals he employed were copper, tin, and zinc. Phil. Mag. 8. 5. Vol. 19. No. 118. March 1885. N 170 Prof. Oliver Lodge on the Seat of the ment en évidence, grace a la précision des mesures, sont au-dessous des erreurs expérimentales de leurs méthodes, ou a peine supérieures dans les cas les plus favorables.”’ Fig. 9.—Pellat’s Apparatus for experimenting in different Gases and at different Pressures. The movable plate is now the lower one, and it is pulled down by an electromagnet, H, a little way against the springs, B, which tend to drive it up against the screw-tops,C. Contact is automatically broken at g the instant before separation. The bell-jar has 35 litres capacity, the diameter of each plate being 15 centimetres. It must be impossible to employ anything like pure gases in a bell-jar enclosing such a bulky mass of heterogeneous material; and the pressure was found not to go below 2 or 3 centimetres of mercury. However, he has since made a smaller arrangement of 1 litre capacity, with plates 9 centimetres diameter, and, what is more important, with the electromagnet out- side, and nothing inside but glass, mica,and metal. In this the pressure goes down to a millimetre. But even this is not all that could be wished. Moreover the experiments described had been made with the larger apparatus. Electromotive Forces in the Voltaic Cell. 171 In all the above gases he has also studied the effect of varying the pressure. Lowering the pressure slightly increases the observed difference of potential; but the change lags a little behind the pressure-variation. Damp and dry air behave in the same way. In oxygen the effects of pressure are rather betier marked. Nitrogen gives nearly the same numbers as air; but after it has been in for some time, the numbers are slightly lower than at first. Hydrogen gives a little greater effect than even rarefied air; rarefying hydrogen does not alter it much. Carbonicacid gives the same numbers as rare air or dense hydrogen. As for liquids, plates wetted with alcohol give the same result as if immersed in plain air. Von Zahn* also tried a condenser in various gases, and found no difference; but when he tried a platinum-zinc con- denser in the highly rarefied air now known as vacuum with some melted sodium in a branch tube to absorb all the oxygen, the Volta effect was diminished, and only represented a po- tential difference of half a Daniell. Iam not clear whether sodium can be trusted to ultimately absorb every trace of oxygen; but I should judge it would take a very long time: and as to rarefaction, dividing the numbers of molecules in a vessel by a million or two leaves them quite numerous enough to accomplish anything they want. Sir W. Thomson has also made experiments in different gases with negative results}. These experiments are not de- scribed in detail, but they were made with the apparatus shown in fig. 10. The views of Ayrton and Perry on the subject of the effects of atmosphere underwent modification between their first paper and their third. In their first paper they say they have good reason to believe that there is no great difference of potential between a metallic or liquid surface and the air in contact with it Clerk Maxwell, in a letter to the ‘ Electrician,’ { pokes fun at them for this, saying:—“‘A statement like this, coming from men whose scientific energy is threatening to displace the centre of electrical development, and to carry it quite out of Hurope and America to a point much nearer Japan, is worthy of all attention, even without an explicit statement of their ‘ good reason.” But Mr. J. Brown has shown (Phil. Mag. August 1878) by the divided-ring method of Sir W. Thomson, that whereas copper is negative with respect to iron in air, it is positive with respect to iron in H,S. It would * Memoir quoted below. + Thomson, Brit. Assoc., Trans. of Sect., Swansea (1880), p. 494. _ ‘Electrician,’ April 26, a : and used in 1859, published in 1880. Fig. 10,—Sir William Thomson's Compensation arrangement for measuring Volta-force in Air and Gases by a null method, devised 172 Prof. Oliver Lodge on the Seat of the \\ \ Y == oe | ELS ul 7 ; Z diz ) 20 ak Ee oe / A & = SS LN 7 \ | \\ : “ \! The upper plate of the condenser is uninsulated, and slides u p and down from one fiftieth to a quarter or half an inch from the lower the position of the slide being adjusted till no deflection ensues. © ed to the electrometer. The upper plate is put in communication with the lower one and is then raised, ated plate, which is permanently join momentarily through the,slide resistance, | insu Electromotive Forces in the Voltaic Cell. 173 appear, therefore, that the reason why the results of metals by the ordinary ‘ contact-force’ experiments harmonize so well with the comparison by dipping beth metals in water or an oxidizing electrolyte, is not because the H.M.I. between a metal and a gas or an electrolyte is small, but because the pro- perties of air agree to a certain extent with those of ordinary electrolytes. Tor if the active component of the electrolyte is sulphur, the results are quite different ; and the same kind of difference occurs when hydrogen sulphide is substituted for air.”’ In their third paper*, therefore, we find Ayrton and Perry’s views changed, and they clearly state that their experiments, like all those based on inductive methods, leave the question of air-contacts quite undecided. They then go on to say :—‘ One way of determining the H.M.F. of contact in volts between a substance and air, and a way we hope shortly to employ, is to repeat all these exact contact-experiments in different gases [it is not quite true that this would give the results required, because it would only give differential effects ; very important to observe, no doubt, but not the same as observing the actual contact-force of air or of gas]. . . . We shall thus ascertain whether the contact-difference of potentials of a substance and a gas differs much for different gases. Qualitative experiments in this direction have already been made with very interesting results by Mr. Brown of Belfast, but his experiments differ from ours in not being quantitative.” [Only, as their ex- periments do not yet exist, Mr. Brown’s have still some value. In a xii. of Wiedemann’s Annalen t I find some in- teresting experiments by Schulze-Berge on contact-force between metals and gases. He uses a condenser and differ- ent gases, but the plates of his condenser are both of the same metal, and he coats one of the plates with a film of the gas, say chlorine, or hydrogen, or ozone, and leaves the other covered with air. To measure the potential-difference he employs the compensation method of Pellat, and his arrange- ment seems fairly satisfactory. But he does not explicitly enter on the question as to the seat of H.M.F. in the Volta experiment (except in a controversy with Professor Exner). He assumes that a contact-force between metals and metals and between metals and liquids has been established, and he wishes to extend it to the contact of a metal and a gas. * Phil. Trans. 1880. Oe + Schulze-Berge, “Ueber die Elektricitatserregung beim Contact von Metallen und Gasen,” Ann. der Phys. u. Chem. xii. p. 298 (1881). 174 Prof. Oliver Lodge on the Seat of the Believing firmly in the existence of films of condensed gas at the surface of a solid, which films require time for their formation or removal, he deems it sufficient to soak one of the plates of his condenser in the gas to be examined, and then to take it out and measure the difference of potential between it and the other plate coated only with a film of air. Tried thus, ozone rendered gold, platinum, and brass negative as against the corresponding air-covered plate. Hydrogen rendered its platinum strongly positive ; but its influence on gold was slight, and on brass uncertain. Chlorine and bromine made platinum negative, and ammonia made brass positive. It may be readily objected that what the soaking with gas accomplished was not the formation of a film of gas, but a film of actual chloride, oxide, or other combination. Against this is to be urged the fact that after removal from the gas the effect diminished with time, and the plates gradually re- turned to nearly their former state. He tried if he could remove the gas film from one of the plates by exhaustion under an air-pump, and the plate so treated exhibited a dif- ference when taken out and compared with an ordinary plate; but he was cautious enough to repeat the experiment, leaving — the plate under the bell-jar for the same time and not ex- hausting. The same difference appeared, so he attributes it to possible grease. This is the right sort of way to make experiments ; and if everybody experimented with proper care there would be vastly fewer papers published, and science would progress on the whole faster. At present it feels to me overladen with a mass of publi- cation, mostly of necessity by men of not absolutely the first order, much of it with no sort of clearness or insight, but rough, crude, and ill-digested. A man makes a number of experiments ; he does not stop to critically examine and weigh them, and deduce from them their meaning, nor indeed does he often take the trouble to examine whether any definite meaning can in their then shape be drawn from them ; but he rushes with them into print, producing a memoir of weari- some length and sometimes extreme illiterateness of style. Some one else then has the trouble of wading through the heap to see whether any fragments of value may perchance be imbedded in it, and probably he is unable to come to much definite conclusion, because he cannot be in so good a position for criticism of the experiments as the original author was. He therefore writes a paper pointing out defects and errors in the communication. Others take up the same line, Electromotive Forces in the Voltaie Cell. ~ the original man replies, and so there is a controversy, and nothing is really settled at all. Finally, some one else in- dependently goes over the whole ground from some distinct point of view, makes a few well-planned, clear, and decisive experiments, describes them in a compact and readable form, and there results a definite gain to science. But how much better would it have been if this last paper had been the only one published! Unless a man is an experimental genius of the highest order, it is necessary for him to think for far more time than he experiments, if he wishes to advance and not to lumber his science. If it be objected, as indeed it may with great truth be, that one man’s life and capacity are not sufficient for this in the present state of knowledge, the ob- jection constitutes a strong argument in favour of the pro- position that the time has come for an organization of science and a more definite division of labour. To return to the experiments of Herr Schulze-Berge, one is not able to say after all that they are very satisfactory, for they do not distinctly settle any question. The general con- clusion he draws from them is the apparently safe one that the contact-force between a metal and a gas is not in general the same as between a metal and air. LHven this is not ab- solutely safe, however, because it might conceivably be that an airjgas contact-force caused all the difference. Granting that this is unlikely, the experiments are in favour of a con- tact-force between metals and air or gas; but they do not establish the fact any more strongly than, if so strongly as, Mr. Brown’s experiments had already done. ‘The weak point in both is the possible corrosion of the plates and formation of films of alloys or compounds, which may be the real source of the observed difference of potential. And against the existence of a contact-force between metals and various gases, the experiments of Pellat and others are to be remembered, which resulted in the conclusion that a con- denser made of two different metals showed nearly the same Volta effect, whether the atmosphere surrounding the plates was air or hydrogen. If it be assumed that the experiments of Brown and Schulze- Berge establish their point, and that Pellat’s apparatus for dif- ferent gases (fig. 9) is satisfactory (rather a large assumption), Iam unable to reconcile the discrepancy, except by suggesting that Pellat did not take sufficient pains to remove the con- densed-air sheet originally on both his plates. It is of course ' just possible that the difference between the potentials of the two metals might be the same in two gases though the absolute potential of both was different, but it is improbable. 196° ~ Prof. Oliver Lodge on the Seat of the In this connection I must notice also a rather long memoir* by Dr. W. von Zahn, published in 1882, which reviews the whole subject, and describes an elaborate series of measure- ments made with an apparatus something like what one might suppose Ayrton and Perry’s to become if it were arranged for use in different gases and in vacuo. He refers with admira- tion to Pellat’s work in the preface ; and I do not suppose imagines that his own numerical determinations can compare with Pellat’s for accuracy where they overlap, seeing that he only makes use of a sort of combination of Kohlrausch’s and Hankel’s methods, with a Hankel electrometer as a measuring instrument t. He has tried, however, a large number of sub- stances as well as ordinary metals, such as powdered antimony, iron and nickel reduced by hydrogen, many kinds of carbon, Fe,0,, manganite, pyrolusite, copper oxide, lead “ hyper- oxide,” iron glance, and other minerals. He has measured the Volta effect in various gases and at different pressures, and finds, like Pellat, that it does not appreciably vary. He has also examined the effect of temperature on the Volta effect, though he appears to think that this ought to bear some. close relation to the phenomenon of Seebeck, a natural mistake many years ago when made by Avenarius, whom it led most happily, though fortuitously, to the true, and by him experi- mentally verified, law of H.M.F. in a thermoelectric circuit f. However, Zahn finds that experiment lends no support to this view, and says that a larger series of results must be obtained before basing a theory on them. Von Zahn is a confirmed contact theorist, and he victoriously assails several experiments supposed to be distinctly in favour of a chemical view of the Volta effect. He says he publishes his results because of the extraordinary discoveries being propounded by Professor Hxner (such as that a thermopile will not work ina vacuum)§, * Untersuchungen tiber Contactelektricitét, von Dr. W. y. Zahn : Leipzig, Teubner, 1882. + A Hankel electrometer is a modification of Bohnenberger’s, in which a battery with middle to earth is substituted for the dry pile; the plates on either side of the gold leaf are minutely adjustable, and the motions of the gold leaf are read by a microscope. It is sometimes preferred to a quadrant for its small capacity and dead quick motion; it can be made very sensitive, but it can hardly be a satisfactory measuring instrument. Pellat used it, but only as an electroscope. { Avenarius, ‘4Die Thermoelektricitat, ihrem Ursprunge nach, als identisch mit der Contactelektricitat betrachtet,” Pogge. Ann. cxix. 1863. See also Pogg. Ann. cxxii., where he proceeds to calculate Volta effects from thermoelectric data. § I have been unable to find this extraordinary statement in Exner’s works, but it is quoted again by Ayrton and Perry, Phil. Mag. 1881, p. 49. Exner seems to have said that the thermoelectric power of bismuth- Electromotive Forces in the Voltaic Cell. by and because of the vague and unsatisfactory views of phy- sicists in general on the matter (e. g. of Hart); but I am bound to say that, so far as I can judge, Dr. von Zahn’s own ex- periments are not of that conclusive and decided character that one had hoped for from his start, and he signally fails to sum up the facts in a neat and crisp manner. He adheres to the contact view, but his adhesion scarcely seems to me to be based on strong evidence ; and in fact his theoretical views seem a little superficial considering the date at which he writes ; so that one may admit pretty well all he says about contact and not chemical action as the cause of the Volta effect without being deeply committed to any specially true or specially false position *. His best experiment, and a very crucial one if only it could be perfectly performed, is the attempt to measure the Volta effect in an absolute vacuum. A pair of zinc and platinum plates are sealed up in a brass and glass vessel in such a way that one of them is capable of moving up and down, and thus of varying its distance from the other. Gravity is employed to separate the plates, the whole vessel being inverted. The vessel is filled with dry nitrogen and exhausted for some days, occasional heat, P,O;, and melted sodium, being employed to improve the vacuum. The result is that the Volta effect is very decidedly “‘ too small,’ going down to half a Daniell, so far as the measure- ments made by his not entirely unobjectionable method can be trusted ; but he does not seem to think that this is much of an argument either way, and, not finding any further change after some days, he did not pursue the investigation further by letting in some air and seeing whether the old value is restored, though he perceives clearly that this would be a crucial experiment. This abstinence is so remarkable that it antimony is destroyed by immersing the pile in pure nitrogen ; and Young of Princetown takes the trouble to examine whether it is so experimentally (see Phil. Mag. x. 1880, p. 450), and finds the thermoelectric power of metals the same at one millionth atmosphere as at 1. This, however would be altogether inconclusive if experiment were needed to settle it. * T am afraid this is not peculiar to Dr. von Zann. It may be that the German writers on the subject are too busy accumulating facts to care much about their precise theoretical bearing; but I notice a very loose and unsatisfactory way of putting forward secondary matters as 1f they were the real points at issue, and of never really getting to the heart of the matter. It is singular that the four questions or heads under which that eminent writer, Professor Wiedemann, proceeds to discuss the attempts which have been made to settle the question of the seat of E.M.F. are such that if a categorical answer to each were, by supernatural means, -vouchsafed to us, we should be, I believe, none the wiser (Wiedemann, Elek, vol. ii. p. 985, new edition). 178 Prof. Oliver Lodge-on the Seat of the seems necessary to quote his own grounds for it, and I do so in a footnote”. Fig. 11.—Von Zahn’s Apparatus for experimenting in different Gases at different Pressures and Temperatures, and also in high Vacua. The upper plate, M, is attached by glass rods to a sledge, H, which slides on vertical steel rods, G, being pulled up by a string. On reaching its highest point it comes into contact with an insulated platinum wire, 8, which communicates with a Hankel electrometer through one of the insulated exits, R. The bottom plate is supported on the ring, HE. T is the stopcock for exhaustion and change of gas. Fig. 2 shows the appendage to the bottom plate for warming it by a current of steam. Fig. 3 shows the apparatus used for high vacua. The two plates are zinc and platinum, and the platinum is arranged to fall by its own weight when the whole thing is inverted. The diagram shows it in its highest position, and just going to fall back into its dotted position. The friction of its guide-rod seems not wholly satisfactory. * “ Andere etwas bessere Beobachtungsreihen gaben ahnliche Werthe. Bei allen war die Kleinheit von C. (the apparent Volta effect Zn/Pt) auffallend. Nun stellt ja dieser Werth, wie oben besprochen, nicht die Potentialdifferenz Zink-Platin dar, fiir seine Kleinheit muss aber eine anderweite Ursache vorliegen. Dieselbe kann ich zunichst nur darin finden, dass die Zinkplatte bei Anfertigung und weiterer Behandlung des Apparates sichtbar angelaufen ist (auf der einen Hilfte sogar blaue Far- bung angenommen hat). ‘His liesse sich allerdings vermuthen, dass diese offenbar zu geringe Electromotive Forces in the Voltaic Cell. 179 Zahn goes on to describe an experiment with bright sodium in vacuo instead of zine, the sodium having been long kept melted in a laterally connected bulb before being introduced into position. He finds the sodium strongly positive to copper; but there can be nothing crucial about this experiment, I imagine, for metal in contact with glass may so easily give rise to disturbing electrifications. I believe he must have employed the best vacuum of any experimenter on this subject, and that he has therefore gone most near to the proof of what I cannot help believing will be found to be the truth, viz. that the Volta effect in an abso- lute vacuum or perfectly inert gas (old air-sheets et hoc genus omne having been thoroughly removed) is very small. But if it be the case, as I believe it is, that the effect is almost independent of the guantity of oxygen present, so long as it is present, the difficulty of making the experiment so as to be sure of the absence of even the last few thousand or million oxygen moiecules is almost overwhelming. The question of the dependence of Volta force on atmosphere remains thus undecided; and all the evidence which I can adduce in favour of such dependence is this incipient decrease observed by von Zahn, the little too-mixed-up observation of Mr. Hart (de- scribed later), the measurements of Schulze-Berge, and the more decided experiments of Brown. It may indeed be readily held that the weight of experimental evidence tends the other way, since most experimenters on the subject (Pellat, Schultze-Berge, von Zahn, and I may add Sir W. ee have left off just as pure contact theorists as they began. would attempt an experiment myself, save that I am so pro- foundly impressed with the difficulty of making one in which no fault or loophole can be found, and which will by every one be deemed satistactory and final ; so I prefer to base my views on a general survey and on fairly conclusive reasoning, rather than on a crucial but almost impossible experiment. 5. Perhaps this is now the place to refer to the somewhat erratic series of papers by Professor Franz Exner, of Vienna*. Differenz in der wirklich wesentlichen Verminderung von Feuchtigkeit und Sauerstoff gesucht werden musste,so dass der Apparat nach dem Oeffnen eine starkere Spannung zeigen wiirde. Dies ware dann wirklich ein experimentum crucis zu Gunsten der chemischen Theorie. Diese Entscheidung vorzunehmen wird aber erst dann nothwendig sein, wenn nach laingerer Zeit, wo das eingeschmolzene Natrium noch mehr alle Reste von Sauerstoff beseitigt haben wird, eventuell noch Wiederhitzen und dergl. der jetzige Zustand des Apparates unverdndert wieder gefunden sein wird.”—Von Zahn’s Memorr, p. 48. * Exner, Sitzb. der Akad. der Wissensch. Wien: July 1878, “On the Nature of Galvanic Polarization;” July 1879, “On the Cause of the Production 180 Prof. Oliver Lodge on the Seat of the” He sets himself to disprove the existence of contact-force in the most straightforward and obvious manner, and to establish the fact that there is no electrical evolution without definite and actual chemical action. To this end he announces the following propositions :—(1) that two metals in a chemically indifferent medium show no electricity; (2) that the potential- difference of two connected metals in air is exactly half the difference of their heat-combustion energies; and (3) that two pieces of the same metal produce contact-electricity as soon as they are put into chemically different atmospheres. The experiments by which he supports these assertions have, every one of them, been elaborately and severely criticised by Beetz, Hoorweg, Julius, Schulze-Berge, Von Zahn, Ayrton and Perry, Pellat,and Wiedemann ; and his numerical deter- minations of contact-force appear to be unique*. It is not necessary for me to enter into a discussion on the merit of his experiments, inasmuch as the mere fact of the existence of so great a body of hostile opinion is sufficient to show that they are not of a kind best qualified to produce conviction. The theoretical views which led Professor Exner to formulate his second statement above, that the potential- difference of two connected metals is equal to half the differ- ence of their heats of combustion per equivalent, are, I am sorry to say, quite unintelligible to me. They depend on the hypothetically necessary existence of films of oxide, between which and the metal there is supposed to be a considerable difference of potential. Perhaps a few quotations from Pro- fessor Hixner’s first paper on contact-electricity will render his position clearer. His views are but little really different of Electricity by the Contact of Heterogeneous Metals ;” December 1879, “Qn the Theory of Inconstant Galvanic Elements;” May 1880, “On the Theory of Volta’s Fundamental Experiment ;” July 1880, ‘On the Theory of Galvanic Elements;” November 1880, “On the Nature of Galvanic Polarization ;” July 1882, “On some Experiments relating to Contact Theory.” * sete, Wiedemann’s Annalen, xii. p. 290; Hoorweg, cbed. xi. p. 138 (1880), and xii. p. 90; Julius, zbzd. xiii. pp. 276 and 296; Schulze-Berge, bid. xv. p. 440, as well as xii. pp. 3807 and 3819; Von Zahn, p. 41 and Preface, of his Memoir; Ayrton and Perry, Phil. Mag. 1881, p. 438; Pellat, Paris Theses, No. 461, p. 17; Wiedemann, Elektricitat, ii. pp. 992-995. : : + I quote from Mr. J. Brown’s translation (Phil. Mag. Oct. 1880) of a paper in Wiedemann’s Annalen of the same year, with some abbrevia- tions :—“ An investigation concerning the nature of galvanic polarization has led me to a quite distinct view of the origin of the so-called contact- electricity, a view which will be supported by experiments following. I have shown that the original cause of the polarization-current is to be sought for, not at the contact of the electrodes with ions liberated on Electromotive Forces in the Voltaic Cell. 181 from those of De la Rive and other older “ chemical theorists;”’ but they are (especially in later papers) expressed in so defi- nite and decided a manner that they have excited a sharper controversy than vaguer and more hesitating writings could. This indeed may be regarded as their special merit. The main objection which can be taken to them relates to the quantitative statements: these are vigorously made, but they seem unwarranted by facts accumulated by all other observers, though indeed some of his own experiments certainly seem to support them. It has also been objected that he misinterprets some of his experiments. He has got hold of the notion that the heat of combustion has some sort of relation to the Volta effect, and there I am heterodox enough to agree with him. But what the relation is, and how it acts, and what sort of potential-difference you ought to expect in accordance with theory, concerning all these things I am utterly at variance with him; and I deem it prudent not to attempt to represent views which I am unable to understand, because it is unlikely that I should do them justice. them, but in the recombination of the latter; and the E.M.F. of the cur- rent so produced is measured by the heat-value of this combination, just as the E.M.F. of any galvanic cell is measured by the heat-value of the chemical process going on in it. With a so-called contact-action the existence of the polarization-current, and obviously of every other cur- rent, has nothing whatever to do. The idea then suggested itself to seek for the cause of the production of electricity in the experiment of Volta, not in the contact of two metals, but in previous chemical actions of the surrounding media on their surfaces. I have expressed the opinion that so-called contact-electricity is produced by the oxidation of the metal in contact by the oxygen of the air, just as in galvanic cells it is evolved by oxidation of zinc. Ifthe supposition prove true, and it has proved true, the E.M.F. of his metal in contact in air must be measured and expressed. by their heats of combustion.” He then points out how all Volta tension series are in oxidation order, and relates approvingly De la Rive’s view that metalsin air were attacked not only by water-vapour but by dry oxygen, and that electricity is pro- duced by any kind of chemical action in proportion to the intensity of the chemical affinity. Then he gives his numerical theory and supporting experiments ; and finally concludes :-—“I believe we are entitled to say that no Scheidungskraft exists at the contact of two metals.” The fol- lowing must take the place of Volta’s law of the evolution of electricity :— “The difference of electric potential between two metals in contact is measured by the algebraic sum of the heat-value of the chemical action going on at each.” In his theory and experiments, and all through the rest of the paper, he considers the difference of potential equal to half the difference of heat- values, so the above last statement must be a slight numerical slip. The above extracts are among the most favourable. It would be easy to select passages from this, and from his other memoirs on the subject, of a more surprising character. 182 Prof. Oliver Lodge on the Seat of the Professor Exner, to strengthen his position, adduces a large number of very simple experiments (such as connecting first one Daniell and then two Daniells to an electrometer, and observing that in the second case the deflection is double the first), and from them i obtains equations proving algebrai- cally that Zn/Cu=0. Considered as conundrums these equations are ingenious, but it is a waste of time seriously to discuss them as Herr Julius has done in an elaborate manner. To suppose that such everyday experiments as these are in direct contradiction of the contact theory is scarcely compli- mentary to the great men who have held, and who still hold, that view. Dr. C. G. Knott, in 1879*, examined the contact-force between plates of the same metal at different temperatures, using the condenser or Kohlrausch method. He found that iron, copper, zine, and probably tin, were negative when hot to the same metals cold ; and the effect. increases uniformly with temperature. But it is permanent, remaining after the hot plates have cooled down; hence it must be due to oxidation. A slow oxidation proceeds with time alone. Time-curves are logarithmic like cooling-curves, and the most oxidizable metal varies most quickly both for time-variation and tempe- rature-variation. ‘There seems to be a surface-condition of a metal proper to each temperature which no polishing can change, for it establishes itself in a few seconds after cleaning, and only changes with temperature. Mr. 8. Lavington Hart, in 18517, describes a mercury- dropper where the mercury is contained in a funnel, and is connected with an electrometer by an iron rod dipping into it. The drops form inside an iron inductor, and they fall negatively charged. Mr. Hart so far ignores any Volta force that he considers the arrangement as an inversion of Lipp- mann’s electrometer, the advancing drops being oxidized. It can plainly be regarded, however, as a mere Fe / Hg contact arrangement; and that is what I suppose it to be. He makes two interesting modifications : the first is to replace the air round the dropping mercury by coal-gas ; the electrical effect is then zero. ‘This is interesting, because the exuding drops of mercury, unlike most pieces of metal, expose to the coal-gas a virgin surface which has probably contracted no condensed air-sheet: only coal-gas is a rather sophisticated substance for * Knott, Proc. R. 8. Edinb. 1879-80, No. 105, p. 362. + Hart, Brit. Assoc. York, p.555; and Phil. Mag. November 1881, ser. 5, xil. p. 524, Electromotive Forces in the Voltaic Cell. 183 it to be first exposed to. If the experiment is regarded as sufficiently direct and simple, this fact lends support to the view that Volta forces depend on the medium surrounding the metals. The second modification is to bring an earth-connected iron bar close to the drops, and to show that it reduces the deflec- tion. Mr. Hart thinks it reduces the oxidation by proximity; and certainly, provided the obvious action of a mere electro- static screen has been considered and provided against, the action by proximity is very remarkable. A similar effect has been observed and more fully worked out by Pellat, in a paper published in 1882*. Pellat says that if he places two metallic surfaces parallel to one another and very close together (say half a millimetre more or less, variations from 12 to ‘1), each metal undergoes a slight alteration of the properties of its superficial coat. The alteration takes some minutes to pro- duce, increases with time, but tends to a limit. When the influencing metal is removed, the other returns gradually to its primitive state. Lead and iron produce the largest influ- ence effects; copper, gold, and platinum give smaller but distinct effects ; zinc produces hardly any, unless it be put within a hundredth of a millimetre or so. Pellat does not attempt to account for this interesting phenomenon further than by suggesting some possible connection with the smell of metals. Mr. Hart’s theoretical views are at first sight somewhat analogous to my own, though they are by no means the same. He considers the case of two metals immersed in liquid elec- trolytes, and dismisses air by calling it a gaseous electrolyte. He believes zinc and copper in contact to be at the same potential, and throws the variation of potential on the air between them}. He considers the electrical effect brought about by the electro-negative ion oxygen combining with the zinc and charging it negatively, while some electro-positive ion combines with the copper and charges it positively, “though not unless the two metals are in sufficient proximity to over- come electrolytic diffusion”? (whatever that may mean as applied to this case). He thinks his mercury-dropping expe- riment in coal-gas is conclusive as to the equality of potential of metals in contact. This, I fear, is rather rapid induction. * Comptes Rendus, xciv. (1882) p. 1247: “Influence of Metals on one another at a Distance.” + The diagrams of potential which Mr. Hart gives of cells were given . more fully by Prof. Exner in his paper on the Theory of Galvanic Elements (1880). Mr. Hart’s views are, in fact, rather similar to some of the more reasonable ones of Prof. Exner. 184 Prof. Oliver Lodge on the Seat of the I do not see how it follows Fig. 12.—Thomson’s Gravitation on his own hypothesis that Voltaic Cell. his arrangement is virtually a reversed Lippman electro- meter. : Sir W. Thomson’s dropping arrangements, or voltaic cells, in which gravity does the work instead of chemical action, are so well known that it is scarcely necessary to do more than refer to them. Mr. Hart’s mercury-dropper is scarcely a modificaton of the copper-filing dropper shown in fig. 12. Sir William also = shows how to couple up such copper filings. ¢ receiver. cells in series*, and how to 6 inductor—zine. d copper funnel. construct a mechanical re- The copper filings drop negatively . . charged against electrical forces. plenisher on the Volta prin- jp you join ¢ and @ by a copper ciple (fig. 13). wire, you can get a current flowing wholly through and with copper. Fig. 18.—Thomson’s Voltaic Induction Machine. HY [ One of the inductors, T, is lined with one metal, the other with another, and the two connected. The carrier-wheel is rotated, and the contact- springs, A, A’, become oppositely charged. By afterwards charging the inductors with a Daniell cell, and comparing the deflection now produced in an electrometer connected to A, A’ with what it was before, measurements of Volta effect can be obtained ; or of course it can be made a null method. 6. In order to give this historical sketch more complete- ness, it may be as well to record rapidly such other memoirs as I have been able to get acquainted with: it is in the highest degree probable that several are omitted, but I hope no very important ones. Prof. Wiedemann’s collection of views and memoirs bearing on the subject is at the end of the second volume of the new edition of his Hlektricitat, — * Electrostatic Reprints, p. 325. Electromotive Forces in the Voltaic Cell. 185 Hdlund has published a long paper* in which he investi- gates experimentally the Peltier effect; he points out clearly at the end that there is no relation between the Peltier and Voltaeffects; and he suggests that this is because of the contact- force between the metals and the gas or air in which they are, the fact of such contact-force being, he thinks, sufficiently established by gas-batteries and galvanic polarization f. Majocchi, in a paper printed in Phil. Mag. xxx. p. 97, regards the H.M.F. of contact as due to the “adhesion”’ of the two metals for each other: pretty much the same idea as Sir W. Thomson’s chemical action ata distance, an idea which makes the energy of the Volta effect Zn /Cu depend on, and be calculable from, the combination-heat of zinc and copper in making brass. I must return to this matter later, because it is important in itself and crucial as regards theory. (yassiot | made an experiment intended to show that there could be a difference of potential excited between metals by proximity without actual contact, or at any rate without metallic contact. Grove§ also made a similar experiment. Hoorweg |, and also Nobili4], have a theory that all galvanic currents are really thermoelectric. In the article “ Electricity” in the Encyc. Brit. p. 99, Professor Chrystal gives some clear general considerations regarding the seat of H.M.F. and the opposing views which are held with regard to it. He is judicial in his attitude with regard to them; but the mere statement of the position in so * Edlund: Pogg. Ann. cxxxvil. p. 474; cxl. p. 435; exliil. pp. 404, 534. See also Phil. Mag. [4] xxxvii. p. 268; xl. pp. 81, 218, 264, especially p. 273. + Sundell investigates the E.M.F. of alloys in contact with copper, employing Edlund’s method, and finds, like him, that for alloys as well as for simple metals the Peltier corresponds with the Seebeck force. The peculiar language used in this and the preceding paper may easily cause it to be imagined that they have found Volta force to agree with Peltier. In fact, Sundell is so quoted in Watts’s 8rd Suppl. p. 708, Von Zahn . quotes Edlund in the same sense; and indeed it is probable that Edlund himself at first thought he was investigating Volta forces thermoelectrically (Pogg. Ann. exlix. p. 144). { Gassiot, Phil. Mag. xxv. 1844, p. 283. § Grove, ‘ Literary Gazette,’ Jan. 21, 1843 ; Wiedemann, E/ek. 11. p. 988. || Hoorweg, Wied. Ann. ix. p. 552, 1880; xi. p. 233; and xii. p. 75. q Prof. Wiedemann notes as interesting that in 1828 Nobili held a notion that all galvanic currents are thermoelectric, thus vaguely antici- pating the modern thermodynamic theory of E.M.F. See Wied. Elek- tricitit, ii. p. 985, and Nobili, Bibl. Univ. de Geneve, xxxvii.p.118. But Prof. Hoorweg seems bitten with the same idea in recent times, and in 1879-80 writes long papers in proof that all current-energy is due to absorption of heat at junctions! Phil. Mag. 8. 5. Vol. 19. No. 118. March 1885. O 186 Prof. Oliver Lodge on the Seat of the clear a form is in itself a powerful argument for the views held by Maxwell *. Prof. Fleeming Jenkin, in the last edition of his ‘ Electricity and Magnetism,’ p. 216, endeavours to reconcile the contact and chemical theories. Acccrding to the chemical theory, the H.M.F. ofa cell ==(J@e); according to the contact-theory itis C/L+L/Z+Z/C. On these undoubted facts he pro- ceeds to found a number of statements which are true, though scarcely simple; in fact they perhaps rather tend to compli- cate what may be held to be a simple matter. Schonbein, in a letter to Faraday published in the Philoso- phical Magazine for 1838, throws out a remarkable sugges- * Although this article is, or ought to be, easily accessible to everybody, there is one important suggestion in it which it is as well to quote, viz. that contained in the following sentence :—“ We are so ignorant of the nature of the motion which is the essence of the electric current that the very form in which we have put the question [as to the locality of E.M.F. | may be misleading. If this motion be in the surrounding medium, as there is great reason to believe it to be, it would not be-surprising to find that speculations as to the exact locality of the E.M.F. i the circuit were utterly wide of the mark.” Prof. Willard Gibbs suggested something of the same sort at Montreal, though in a rather vaguer form. I do not myself feel any doubt that a precise location can be given to the H.M.F., notwithstanding that much of the current energy exists in the medium. The most complete attention to the distribution of energy in circuits which has yet been bestowed on the subject has been given by Prof. Poynting in his remarkable memoir (Phil. Trans, 1884), and he therein locates the E.M.F. of a battery exactly where I do myself. + Except, indeed, a doubtful statement at the end of Number 2 and an erroneous bit of reasoning at the end of Number 4, though the conclusion drawn is correct. t Schdnbein, Phil. Mag. vol. xii. pp. 225 and 311. The two most striking sentences are here extracted :— ‘‘ Before closing my letter, allow me to communicate to you in a general manner the view which I have taken of the subject in question. In the first place, I must tell you that I am by no means inclined to consider mere contact in any case as the cause of the excitement of even the most feeble current, I maintain, on the contrary, in accordance with the prin- ciples of the chemical theory, that any current produced in a hydro- electric voltaic circle is always due to some chemical action. But as to the idea which I attach to the term ‘chemical action,’ I go further than you and M. de la Rive seem to go; for I maintain that any tendency of two different substances to unite chemically with one another must be considered as a chemical action, be that tendency followed up by the actual combination of those substances, or be it not; and that sucha tendency is capable of putting electricity into circulation.” And on page 314 he explains this last phrase, which he has elsewhere called a “current of tendency,” thus :— “As what I term a current of tendency is no doubt in some cases nothing but that electrical state which the Voltaists consider to be the effect of their ‘force electromotive,’ or of contact, it appears to me that, from some of the facts above stated, a specific and most important con- clusion regarding the theory of the pile can be drawn, Even if we Electromotive Forces in the Voltaic Cell. 187 tion with regard to “chemical tendency” as the possible source of a current, or rather of “ force electromotive.” His language and ideas are in many respects old-fashioned and erroneous ; he uses such phrases as “a current of tendency,” he supposes currents with no electrolytic power to exist, and of course is not troubled about energy considerations. But I feel little doubt that, had he lived later, he would have held that while currents were due to chemical action, electromotive force was due to “chemical tendency;” and this is pretty exactly my own view of the matter. I have only just discovered this Schénbein letter; and I have also found some paragraphs in Faraday which more in detail and with fair distinctness express what I believe to be the true view. (See §§ 893-900, Exp. Res. vol. i.*) grant to the Voltaists our current of tendency to be the effect of mere contact, the facts alluded to prove that such a current does not possess a sensible degree of electrolyzing-power; consequently that the chemical effects of the common voltaic arrangements have nothing to do with current-electricity excited by contact.” * Extract from Faraday’s ‘ Experimental Researches,’ vol. i. :— “ (893) The use of metallic contact in a single pair of plates and the cause ofits great superiority above contact made by other kinds of matter, become now very evident. When an amalgamated zinc plate is dipped into dilute sulphuric acid, the force of chemical affinity exerted between the metal and the fluid is not sufficiently powerful to cause sensible action at the surfaces of contact, and occasion the decomposition of water by the oxidation of the metal, although it is sufficient to produce such a condition of the electricity (or the power upon which chemical affinity depends), as would produce a current if there were a path open for it; and that con- tact would complete the conditions necessary, under the circumstances, for the decomposition of water. “ (894) Now the presence of a piece of platina touching both the zinc and the fluid to be decomposed opens the path required for the electricity. Its direct communication with the zinc is effectual, far beyond any commu- nication made between it and that metal (7. e. between the platina and zinc) by means of decomposable conducting bodies, or, in other words, electrolytes, as in the experiment already described [that of decomposing iodide of potassium without metallic contact by interposing it on blotting- paper between the platinum and the zinc of a simple voltaic cell], because, when they are used, the chemical affinities between them and the zinc produce a contrary and opposing action to that which is influential in the dilute sulphuric acid; or if that action be but small, still the affinity of their component parts for each other has to be overcome, for they cannot conduct without suffering decomposition ; and this decomposition is found experimentally to react back upon the forces which in the acid tend to produce the current, and in numerous cases entirely to neutralize them Where direct contact of the zinc and platina occurs, these obstructing forces are not brought into action, and therefore the production and the circulation of the electric current, and the concomitant action of decom- osition are then highly favoured. “ (895) It is evident, however, that one of these opposing actions may be dismissed and yet an electrolyte be used for the purpose of completing © O2 188 Prof. Oliver Lodge on the Seat of the Various observations regarding the E.M.F. of different cells are made in the series of papers still appearing in the Philo- sophical Magazine by Dr. Alder Wright and Mr. C. Thompson, “On the Determination of Chemical Affinity in terms of H.M.F.” For much discussion of contact-electricity and for some interesting statements of the views of Marianini, Davy, and others, refer to ‘ Experimental Researches,’ vol. ii. p. 20 &e. From what is there said, it appears that Karsten and Marianini held a modified contact theory, placing the E.M.F. at the metal-fluid junction; and that Becquerel admitted as a possi- bility the efficiency of chemical attraction, as distinct from combination, something in the same way as Schonbein. Professor Tait in his ‘ Thermodynamics’ lends his powerful support to the contact view of the activity of the pile as taught by Sir W. Thomson. Some work has been done in the direction of observing reversible heat-effects at metal-liquid junctions, notably by Joule, Thomson, and Bosscha. We shall have occasion to refer to this work later. Joule in 1841 sent currents through several dilute acid voltameters with different electrodes, and measured the excess or reversible heat H— RC? generated in the whole cell ; with the result that the excess of heat observed is that due to the observed back E.M.F. of the cell, minus that concerned in the decomposition of water. A table of his results is given by Chrystal, Hincyc. Brit. p. 91. For Maxwell on the same subject see ‘ Hlementary Electricity,’ p. 146. Thomson (Math. and Phys. Papers, pp. 496, 503) says that, of two decomposition-cells, one with zine cathode, the other with platinum cathode, the former showed the most heat when the same current was sent through both. Separa- the circuit between the zine and platina immersed separately into the dilute acid; for if in the above experiment the platina wire be retained in metallic contact with the zinc plate, and a division of the platina be made elsewhere, then the solution of iodide placed there, being in contact with platina at both surfaces, exerts no chemical affinities for that metal; or, if it does, they are equal on both sides. Its power, therefore, of forming a current in opposition to that dependent upon the action of the acid in the vessel is removed, and only its resistance to decomposition remains as the obstacle to be overcome by the affinities exerted in the dilute sul- huric acid. (896) This becomes the condition of a single pair of active plates where metallic contact is allowed. In such cases, only one set of opposing affinities are to be overcome by those which are dominant in the vessel ; whereas, when metallic contact is not allowed, two sets of opposing affinities must be conquered (894).” Electromotive Forces in the Voltaic Cell. 189 ting the electrodes by a porous cell, zinc cathode showed more heat than zine anode, but platinum anode more heat than platinum cathode*. He speaks of the local heat developed at a tin surface, and shows that it is greater where hydrogen is liberated than where tin is dissolved ; and suggests thermal observations on four dilute-acid voltameters in one circuit with zine and platinum electrodes, arranged according to the permutations—zinc-zine, zinc-platinum, platinum-zine, and platinum-platinum. Thomson attributes the extra heat at an electrode to opposing chemical affinities which have to be overcome—a doctrine of “ chemical resistance.”’ Bosscha examines and develops all these matters in a series of interesting papers published about 1857}. He attributes the development of local heat, at a cathode against which hydrogen is liberated, to the change of hydrogen from the nascent condition to the ordinary one—in other words, to the energy of the molecular combination H, H. He finds the electromotive forces exhibited by this local generation of heat at the surface of different metals in acid to have the following yalues in volts :— Pt Fe Cu Sn He Zn "45 “49 "64 36 12 1:2 One more memoir I must mention before closing this his- torical sketch and discussion thereon, a valuable communication by Bouty to the Journal de Physique t, “On Thermoelectric Force at Contact of Metals and Liquids, and on the Peltier Effect thereat.” He finds the Peltier coefficient at a junction of copper with salts of copper eighty times as great as at an iron-zine junction, and eleven times as great as bismuth- copper. He also measures the metal-liquid thermoelectric i.M.F. at different temperatures, and shows that Thomson’s thermodynamic formula | 7 Tdi oilih = aT is perfectly true and in agreement with experiment in these eases also. He endeavours to see if this Peltier, or, as we had better call it for distinction, Joule or Bouty effect, can be calculated from the energies of combination. After tabu- lating his results alongside of heats of oxidation and heats * Showing, I suppose, that while zinc attracts oxygen much and hydrogen not at all, platinum attracts hydrogen more than oxygen. + Bosscha, Poge. Ann. vols. ci., ciil., ev., cviil. ~{ Bouty, Journal de Physique, 1879, viii. p. 341; ix. pp. 229 and 306, especially p. 306. 190 Dr. P. EH. Chase on some Principles of solution, he decides that it is hopeless, and that we must give up trying to establish a relation between these quantities. Chemical action, he concludes, only disturbs the effect by altering the surfaces, and by developing parasitic heats. They may mask, but they do not produce, the true Bouty pheno- menon, which he believes is probably physical. The difficulties of making these measurements are exceed- ingly great; and, notwithstanding the ingenuity and skill dis- played, it seems to me possible that some error or unexpected source of disturbance may have modified the results. So far as | know, they have not yet been repeated; and I can hardly regard the experimental method used as perfectly safe*. [To be continued. ] XXI. Some Principles and Results of Harmonie Motion. By Pury Hare Cuase, LL.D. AWoEN two bodies, in relative motion, come into con- tact, pressure begins to act between them to prevent any parts of them from jointly occupying the same space. .... Any force in a constant direction acting in any circumstances, for any time great or small, may be reckoned on the same principle ; so that what we may call its whole amount during any time, or its ‘ ¢ime-integral,’ will measure, or be measured by, the whole momentum which it generates in the time in question?’ (Thomson and Tait, ‘ Natural Philosophy,’ i. sec- tions 294, 297). No relative motions can be more important, and no contact more complete, than those which exist between the all- pervading luminiferous zether and the sun. In the conversion of tangential luminous waves into spherical vibrations, gravity is acting In a constant direction towards the sun’s centre. The amount of its activity upon each ethereal particle, y, or its time-integral during each cyclical period, ¢, is measured _ * T find that a method exactly like that used by Bouty was suggested by Clerk Maxwell, ‘ Elementary Electricity,’ p. 146. + From the Journal of the Franklin Institute, January 1885. Com- municated by the Author. This paper has been written, in part, to meet a desire which has been expressed by some members of the Royal Astronomical Society for an introduction to the article on “Harmonic Motion in Stellar Systems” (Phil. Mag. Sept. 1884). The author will feel under obligation to any meade who will inform him of other points which need further eluci- ation, and Results of Harmonic Motion. 191 by wot. The study of the various correlations which flow from this integral involves the following considerations:— (1) The principle of Galileo, that the total effort is equiva- lent to the effective sum of the causes which are operating. This is illustrated at sun’s surface, which is the region of greatest energy in our system, by the cyclic equation Sedu. (2) The equality of pressures or resistances to opposing forces, in all equilibrating tendencies. In consequence of this equality, every interruption or prevention of the free action of any force may be measured as a rate of change of momentum ~ in the opposite sense. (3) The invariability of the sum of kinetic and potential energies. (4) The maximum of kinetic energy in all cyclical motions, at the point of the trajectory which is nearest to the centre of force, and the maximum of potential energy at the point . which is most remote from that centre. At the origin of luminous radiation, where }y=vy, the reaction of gravitating resistance is all kinetic; after a haif-rotation it becomes all potential, but it is then combined with a new reaction which is all kinetic. (5) The evidences of local ethereal stress, which is opera- tive in various forms of gravitating, thermal, electromagnetic, and chemical attraction and repulsion. (6) The indestructibility of energy, which requires, as Maxwell has stated, that energy must exist in the ether during the interval of its transfer from one body to another. (7) The strong reasons for believing that the media for luminous, gravitating, thermal, electromagnetic, and chemical interactions, occupying the same space and represented by the same cyclical velocities, are identical. (8) The counteraction of stress by obvious elasticity, as in a spring, or by probable intermolecular elasticity and orbital motion, as in the resistance of solids. (9) The principle of Fourier, that any complex periodic motion must be compounded of a definite number of simple harmonic motions, of definite periods, definite amplitudes, and definite phases. (10) The application of “ Laplace’s Coefficients,” or sphe- rical harmonic analysis, to the explanation of cyclical waves and vibrations in spherical elastic masses. (11) Cumulative and progressive undulating tendencies, resulting in complex harmonic motions of various kinds. The evidences and consequences of harmonic motion in 192 Dr. P. H. Chase on some Principles stellar systems flow simply and naturally from the two fol- lowing important FACTS:— (1) The fundamental velocity in the solar system is the velocity of light. _ (2) This is not a merely accidental and temporary coinci- dence, but, according to the first proposition of Newton’s Principia, it must have existed, and must continue to exist, during all past and future stages of solar condensation. The first of these facts was discovered by investigating the tendencies to oscillatory nodal harmony in elastic media. It appears to be still regarded by some persons as merely curious ‘ and without important significance. ‘This is, perhaps, because attention has been so often directed to the angular velocities in different orbits, which vary inversely as the 3 power of the mean distance, that the synchronous variability of angular velocity with the inverse square of the radius, in all the par- ticles of an expanding or contracting nebular nucleus, is forgotten or overlooked. We find in our stellar system three stages of material aggregation :—(1) A nucleus, probably consisting chiefly, if not entirely, of condensed gas, rotating in about 25°5 days. (2) An atmosphere of lighter gas, rotating synchronously with the nucleus, and therefore extending no further than Kant’s limit (p, = 36°35, py being Sun’s semidiameter). (3) A luminiferous ether which, if infinitely elastic, may be of infinite extent, but which would reach, if made homo- geneous, to 2210-74 times Earth’s mean distance from the Sun. If the Sun were homogeneous and unresisting, a particle would fall to its centre from its surface, or from any point within its surface, in 41°87 minutes, or in + of the time of free revolution at the surface (4 of ama | j = se / 7 The relation of radial oscillation to orbital revolution is therefore that of simple harmonic motion. ‘The velocity acquired by falling from the surface to the centre would be »/gr ; which is the same as would be acquired in falling from an infinite distance to 27, or from 2r to r, or in virtual fall through 47, or through one half the length of a cycloidal pendulum which would oscillate synchronously with circular orbital revolution at 7. It is also the velocity of wave-propagation in a homo- geneous elastic atmosphere of a depth equivalent to +. At all points within the nucleus the velocity acquired by fall to the centre would be preportional to the distance from the centre. Let us apply the principles which are here indi- cated to a stellar system like our own, with a nucleus so and Results of Harmonic Motion. 193 preponderating that its oscillatory tendencies are not mate- rially modified by the perturbations of attendant planets or companion stars. Within our solar nucleus all the tendencies to orbital revo- lution have been converted into constrained rotation, which shows a retardation by collision, subsidence-oscillations, &c., such that the velocity of every particle is only about =}, as great as that of free and self-sustained revolution. The con- tinual violent agitation of Sun’s mass indicates the probability of synchronous radial and tangential oscillations, which are dependent upon simple harmonic motions. The measure of gravitating acceleration for the oscillatory unit of time being — ua f , (& being the distance from the point of suspension to the centre of oscillation in a linear pendulum /), we have Sun’s semidiameter ( and the quotient of circular aim 2 orbital velocity by equatorial velocity of rotation 2\ 2 ee = (+) = 219-17. The principle of conservation of areas requires that the angular velocity should vary inversely as the square of radius, without the nucleus as well as within it, provided we look merely at the orbit of any given mass or particle, It is only when we compare different extra-nucleal orbits in the same system, each of which has its own original force of projection, that we find angular velocities varying inversely as the 3 power of the mean distance. If the nucleus is expanding or Eemeuciing. the Kantian radius, p,, should, accordingly, vary as the 4 power of the nucleal radius, so that 3 pe= (FF a ) Po= 36°39 po. The free undulatory velocity at po, both radially and tan- gentially, is »/go79 The mean harmonic radial velocity of 1 BOP): rotary exiation at the same point is — a of 33 "= as 2 great, or Ga 6885 fT as great as the fundamental velocity, or the gravitating acceleration in the fundamental Vet ak unit of time. As the idea of “ fundamental velocity ” will be new to many readers it may be well to explain it. In whatever way g may 194 Dr. P. EH. Chase on some Principles act, whether by constant, successive, or undulatory pressures, thrusts or pulls, all of its results may be accounted for on the hypothesis of successive instantaneous impulses. The entire accelerating force gt is always exerted, but a portion is usually counteracted by opposing resistances or momenta, Suppose, for example, three bodies in a vacuum—A falling freely for a second, B suspended from a string between cycloidal arcs so that its centre of oscillation is 3 of 32°08 feet from the point of suspension, C sliding on a frictionless plane in which h:l::1:a*. A will fall 16°04 feet, while B swings once and C slides 16:04 feet, falling through a height equivalent to one half the length of the pendulum. The choice of a second as the unit of time is altogether arbitrary. The desirability of a natural unit has often been felt and expressed. Maxwell suggested, as a suitable unit, the interval of some particular luminous wave-length. At the surface of a stellar nucleus, where gravity is a maximum, where the time of rotary oscillation can be linked with all possible times of revolution by simple formulas of harmonic vibration, and where a universal gravitating unit can be readily framed from the units of mass and density, the velo- city gt, which is indicated both by the gravitating and by the ethereal unit*, may properly be regarded as a fundamental velocity. It is at present impossible to test the oscillatcry velocities in remote stellar systems ; but as the considerations on which they are based are universal, there are good grounds for believing that their influence is equally universal, so that gt=, at every stellar surface. In the solar system we find t= 1101227 sec. = oscillatory unit of time = one half solar rotation. 2 4 0,1 pp (F) r0 = unit of gravitating acceleration in unit of time at px. 2\ 4 = n(=) po = unit of gravitating acceleration at pp in oscillatory unit of time = y, in oscillatory unit of time = solar modulus of light (=185505 miles per sec.) = 185505 x 1101227 miles = (688°54)"pp. * The time of virtual fall through one half homogeneous ethereal atmosphere. and Results of Harmonic Motion. 195 3 erst go+n(=-) = V7 9opo = Yo = radial velocity acquired by falling from p, to the centre of a homogeneous nebular sphere = self-sustained velocity at surface of the sphere (= 269-42 miles per sec. at Sun’s surface) =269°42 x 11011227 miles in ¢,. ete (Om: \ P : d es 5(s-) =v,= simple harmonic radial component of stellar equatorial velocity of rotation (=*7826 mile per sec. for our Sun) =2p)+7 in &. The cumulative influence of mean luminous undulation and solar action is shown by the proportions ° 48 ee ripall Up e Vo ee Vo e 2VdAy CO ae In the second of these proportions v, is parabolic velocity, or velocity acquired by infinite fall, at Sun’s surface. In studying planetary harmonies, regard should be paid to the following cyclical tendencies:— _ t, oc (d)? in simple oscillation under a constant force. t, a d in cyclical motions which are immediately determined by luminous undulation, or by other constant velocities. t; oc d? in different orbits, under different original forces of projection but with the same central force. t, « d” in arotating and uniformly expanding or contracting nucleus. If d in each instance is equivalent to the Kantian limit (p,), and if the mean density of the rotating mass is represented by 64, Ii, 1\3 eth | Seb), 1\3 1\3 to «(5) 3 ty (5) ° If the mean density of Harth’s Kantian rotation is taken as the unit, the corresponding reciprocals of density for Sun and for the several planets, except Neptune, are nearly as follows:— SIH cede cesacees 649°800 Mars tescceaee 1:053 Mercury ..... ele 20 Jupiter ...... “L271 IPOH US: Sceicces ce 1:031 SPhaligal | eeBeee 182 196 Some Principles and Results of Harmonie Motion. The influence of luminous undulation. upon the actions and reactions between the chief centre of nucleation and the chief centre of condensation (Sun and Earth) seems to be indicated by the following tendencies :-— t, in the conversion of circular motion into simple harmonic :; 2 2 motion, « ace d; representing such conversion, «(= d. The radius of mean condensation (46) is 2* times the radius 2\3 of actual condensation ; 365°256 x (=) = 95-9) 4°54 ge apparent solar semidiameter which corresponds to this value is 961/43, which differs by less than 5!5 of 1 per cent. from the British Nautical Almanac estimate, 961/82. Dr. Fuhg’s estimate (Astron. Nachr. 2040), 961/495, is still closer. Tendencies to solar equatorial acceleration and polar retar- dation, such as are shown by the sun-spots, are indicated by the following approximations to the period of solar rota- tion :— t, ca/d3; (36°3514 x 430891)+(6°6 x 3962°8) = (24-472), 2 d; 430891 (3962'8 x 3°92295)= 27-7174. ts x/5; (36°3514+6'6)? x 392295 = (25°602)?, t, ocd’; (36°3514+-6-6)? =30°336. The secular influence of the chief centres of nucleation and nebulosity (Sun and Jupiter) on the chief centre of conden- sation (Harth), as well as the cyclical actions and reactions between Harth and Jupiter, are shown by the equation Os Psp 9p Psa= bata In this equation 6;, 6) are the mean Kantian densities of Jupiter, Sun; pg, Psa, the nearest secular approaches of Harth to Jupiter, Sun; ¢,, orbital period of Jupiter ; ¢,, Kantian or rotational period of Harth. The secular eccentricity of Harth which satisfies this equation is ‘06543. Stockwell’s estimate is (06774. eRe Y See XXII. On the Determination of Chemical Affinity in terms of Electromotive Force-—Part IX. By C. R. AupER WRIGHT, D.Sc. (Lond.), F.RS., Lecturer on Chemistry and Physics, and C. THompson, #.C.S., Demonstrator of Chemistry, in St. Mary’s Hospital Medical School*. [Concluded from p. 124.] D. Voltaic and Thermovoltaic Constants of Metals immersed in Solutions of their Acetates. I. Copper. 194. A NUMBER of cells were set up with amalgamated- zine and electro-copper plates immersed in solu- tions of their respective acetates, the constant molecular strength being -25 M(C,H;0,), H,O*. ‘The following values were obtained :— Wire ss gy er OA WEI ge a ee LOWS pegeraselr Ore Se ae VOT Enobable error: “..).« ».. "0029 Julius Thomsen’s thermochemical data lead to the values Zn, O, 2C,H,0,a9.= 100710, and Cu, O, 2 C.H,O,aq. =50340; whence Hy=1-'111, corresponding with 50370 gramme- degrees. Hence H—Ey=—-020 for electro-copper in contact with copper-acetate solution of strength °25 Cu(C,H30.), 100 H,0. Il. Lead. 195. Two series of cells set up with electro-lead opposed to amalgamated zinc and electro copper respectively, with acetate solutions uniformly of strength ‘25 M(C,H;0,), 100 H,0, gave the following results ; the differences observed between the values obtained for different cells set up in the same way being notably greater than with most of the other com- binations examined :— Zinc-Lead. Lead-Copper. ——SE—_ O———— eS —— Mia ximiimny Ss cae auenaen ‘616 503 Miniiniam sees 587 ‘471 PAVING O) ore temas Beach 608 "485 Probable error ......... +:0048 +:0044 * The acetate solutions employed were prepared by dissolving the freshly-precipitated, well-wasked carbonates of the metals in boiling dilute acetic acid somewhat stronger than that required, filtering alter cooling, and diluting to the proper extent, 198 Messrs. Wright and Thompson on the Determination of From these average values the following valuations result for the voltaic constant for lead in acetate solution of strength °25 Pb(C,H30,)2 100 H,O :— Yane-lead ts sy Me MR es i 3 oe 1-091) _. Zinc-copper—Copper-lead . « 4 49 5 ¢ = 606 Mean. «©, . = oum Hence, since Thomsen finds that Pb, O, 2C0,H,O,aq.= 65770, the value of Hy is ‘770, corresponding with 34940 gramme-degrees, whence H—HEy=—'163; 2. e. the thermovoltaic constant for lead in acetate solution is negative, and of nearly the same magnitude as in nitrate solution, or in contact with lead sulphate suspended in zine or cadmium-sulphate solution of corresponding strength, ‘25 PbX 100 H,O. In consequence the actual H.M.F. ofa lead-copper-acetate cell exceeds that due to the net chemical change taking place therein, just as in lead-copper-sulphate and lead-copper-nitrate cells. Some observations were made on the rate of depreciation in E.M.F. with increasing current-density in zinc-lead-acetate cells, with the result of showing that the average rate of fall is indicated by a curve lying between the analogous curves obtained with zinc-silver-sulphate and iron-copper-sulphate cells (§§ 130 and 176), being below the former and above the latter, which, as already shown, overlie the analogous curves obtained with zinc-copper-sulphate and zinc- cadmium-sulphate cells. It is remarkable, in this connection, that the thermo- voltaic constants for the metals silver, lead, iron, copper, and cadmium in these solutions respectively follow in the same order as regards numerical magnitude, though not as regards sign:— @ Silver (in sulphate solution). . =°351 Lead (in acetate solution) . . —'168 Iron (in sulphate solution) +:113 to +°148 Copper (in sulphate solution) . +°009 Cadmium (in sulphate solution) +°005 to —:010 Tif. Silver. 196. The following values were obtained with cells contain- ing electro-silver immersed in saturated silver-acetate solution opposed to amalgamated zinc and electro-copper immersed in their respective acetate solutions, the constant strength being ‘OD 7 M(C,H;30,). 100 eG < Chemical Affinity in terms of Electromotive Force. 199 Zinc-Silver. | Copper-Silver. PPD nc ccascuc es - 1501 404 J 1°486 389 PPE RRO 205 vse van 1-490 397 Probable error ......... +0024 +-0021 From these figures the following concordant valuations are deduced for the voltaic constant of electro-silver immersed in saturated silver-acetate solution :— Zinc-silver . . bia eA OO *Zinc-copper ee inc, . f 108 091 =1°488 Weare soo = YES O9 The heat of formation of silver acetate not being known, the value of Ey cannot be calculated. Admitting that this value is the same as in the case of nitrate cells of the same molecular solution-strength, viz. near to 1°890, the value of E—Eg would be —:°401 ; whence it is at least evident that the thermovoltaic constant for electro-silver in acetate solution is a large negative quantity, comparable in magnitude with the corresponding constants found for sulphate and nitrate solutions. It is noteworthy that the E.M.F. of lead-silver-acetate cells deduced from the foregoing experiments is 1:489 —°607 = -882 volt. On setting up a number of such cells, however, fluctu- ating and inconstant figures were obtained, usually averaging during the first half-hour after setting up vale from ‘02 to -12 volt below this amount; these cells therefore resembled in this respect the lead-copper- chloride cells above described (§ 184). HK. Voltaic and Thermovoltaic Constants of Metals immersed in Solutions of their Bromides. 197. The experiments above described indicate that the sign and magnitude of the thermovoltaic constant for a given metal does not vary widely, whether the metal be in contact with its sulphate, nitrate, or acetate, whereas the values obtained under these circumstances are often considerably different from those obtained when in contact with its chloride. In order to * Assumed to be the same as the value found for solution-strength 25 M(C,H,0,), 100 H,0. 200 Messrs. Wright and Thompson on the Determination of trace out whether the different halogen salts exhibit analogy with these oxygen-acid salts, or whether they differ materially amongst themselves, a number of cells were examined con- taining various metals immersed in solutions of their respective bromides of constant strength °25MBr, 100 H,0, or in magmas of their bromides immersed in zinc-bromide solution of this strength (saving in the case of lead bromide, where the sparing solubility necessitated the use of weaker solutions). I. Cadmium. The following values were obtained with zinc-cadmium- bromide cells :— Maximinnt, sei men 2. rolls Manian eile ese bonal: Wyeramed 6520 hme he oe a odes Probable error 29). 5 0014 Julius Thomsen finds the values Zn, Br, aq. = 90960, and Cd, Br, aq.=75640; whence Eg=-338, corresponding with 15320 gramme-degrees. Hence E —Hy= — 023 3 that is, the thermovoltaic constant for electro-cadmium in bromide solution of strength :25CdBr, 100 H,O is a small negative quantity, not quite so large numerically as that for the corresponding chloride solution (viz. —-036). II. Silver. 198. The following values were obtained with cells set up with amalgamated zinc opposed to electro-silver immersed in a magma of freshly precipitated well-washed silver bromide suspended in zinc-bromide solution, the solution-strength throughout being °25ZnBr, 100 H,0. Maximus 5.2 eaten ie ae ee Noinimunat sere ee Om AWerave: eis ie a tay SOO Probable error. . . .+:0012 Julius Thomsen finds Ag,, Br, = 45400; whence Eg=1-005, corresponding with 45560 gramme-degrees. Hence Py He 090) that is, the thermovoltaic constant for silver in contact with silver bromide suspended in zinc-bromide solution is a notable negative quantity, slightly less numerically than the corre- sponding value for silver chloride suspended in equally strong zinc-chloride solution (viz. — 112). Chemical Affinity in terms of Electromotive Force. 201 III. Lead. 199. Two sets of cells were examined containing electro- lead immersed in saturated solution of lead bromide of strength ‘037 PbBr, 100 H,O opposed to amalgamated zinc and electro- cadmium immersed in their respective bromide solutions of the same strength. The following values were obtained :— Zine-Lead. Cadmium-Lead. i foc) 5 fad) ‘257 i D607 "255 BYMEEMTO) oe 2sssoc..1i.ss. ‘571 256 Probable error ......... +:0014 +:0001 These figures lead to the following valuations for the vol- taic constant of lead in saturated lead-bromide solution :— _Picclendl, oe seen nai wen naan mmE tty ct ier ys 715) oe S150 a Zinc-cadmium* + Cadmium-lead . 4 4.956 ‘ = 571 Meany ae ere 571 Julius Thomsen finds Pb, Br, aq. =54410; whence Ey =806, corresponding with 36550 gramme-degrees. Hence H—Ey = —:235; 1. e. the thermovoltaic constant for electro-lead in saturated lead-bromide solution is a large negative quantity, slightly greater numerically than that for lead in saturated lead- chloride solution, viz. —°222. IV. Mercury. 200. When mercuric-bromide solution is agitated with metallic mercury, mercurous bromide is rapidly formed, so that in a very short time practically all mercury and bromine are removed from solution, just as is the case with mercuric chloride (§ 183). Cells were therefore set up containing mercury in contact with a magma of mercurous bromide (freshly precipitated and well washed), suspended in zinc- bromide solution, and opposed, firstly, to amalgamated zine immersed in zinc-bromide solution, and, secondly, to electro- * Zinc-cadmium assumed to give the same value for this solution- streneth as that found above for the somewhat stronger solution °25CdBr, 100 H,0. Phil. Mag. 8. 5. Vol. 19. No. 118. March 1884. je 202 Messrs. Wright and Thompson on the Determination of silver in contact with a magma of silver bromide suspended in zinc-bromide solution, the solution-strength being :25ZnBr, 100 H,O throughout. The following values were obtained, the current passing, in the latter case, in the direction oppo- site to that predicable from the relative heats of formation of mercurous and silver bromides :— Zinc-Mercury. Mercury-Silver. Wiaxamannin yo-ea-ceeaceecee ‘O74 — 062 Mirmaimauan: 2ceeesnce aeacee ‘969 — 073 MVEA Ce ie orien ine tanec ‘972 — 066 Probable error ......... +0006 +0019 These figures lead to the following valuations for the voltaic constant of mercury in contact with mercurous bromide sus- pended in *-25ZnBr, 100 H,O :— PANCAMMCT OOTY. re ye eee eek ee serie aes 972 es a "906 ; Zine-silver—Mercury-silver . . { 4-066 (= 972 Mean 2° ae 979 Julius Thomsen finds Hg,,Br,=68290; whence Hy=*500 volt, corresponding with 22670 gramme-degrees. Hence K—-—Ey= + “472 5 that is, the thermovoltaic constant for mercury in contact with this bromide magma is a large positive quantity, somewhat greater than that observed with the corresponding chloride magma, viz. +°498. It is noticeable that the heat of formation of mercurous bromide exceeds that of lead-bromide solution (Hg,, Bry = 68290, Pb, Br, aq.=54410, difference 13880, corresponding with *306 volt); whilst the value of 4,—k, for lead-mereury- bromide cells is —'235—(+°472)=—-707 ; so that Eq+’,—, 1s negative relatively to Hy, being =—'401. On examining various such cells (solution-strength ='037MBr, 100 HO), the E.M.F. was found to be actually of negative sign, the average observed value being —-402. V. Iron. 201. A series of cells was examined containing plates of nearly pure sheet iron (bright) opposed to amalgamated zinc Chemical Affinity in terms of Electromotive Force. 203 and electro-cadmium with bromide solutions of the respective metals of strength :25MBr,100H,O (the ferrous-bromide solutions being prepared by agitating together pure spongy iron in excess and weighed quantities of bromine and water in a stoppered bottle, filtering and using immediately). The following numbers were obtained :— Zinc-Iron. Tron-Cadmium. i 44] — 086 (oli ohiat)) cr 40] —°126 LG CG are “417 —'103 Probable error ......... +:005 +:005 As with the cadmium-iron sulphate and chloride cells, the current passed in the second case in the direction opposite to that predicable from the relative heats of formations of iron- and cadmium-bromide solutions ; while the H.M.F’. actually set up in the first case notably eaceeded that similarly calculable from the heats of formation of zinc- and iron-bromide solutions. These numbers lead to the following valuations for the voltaic constant for bright iron in solution of strength -25 FeBr, 100 H,O :— op CSC ed a? ae A ren penny 6 Pisce Pay abi Zinc-cadmium — Cadmium-iron e0s = 418 Mean ie" S408 Julius Thomsen finds Fe, Br.aqg.=78070; whence Hy= "284 volt, corresponding with 12890 gramme-degrees. Hence EK —Ey = +°134 3 i. e. the thermovoltaic constant is a notable positive quantity, less, however, in magnitude than the corresponding value for ferrous-chloride solution of the same strength, viz. + ‘204. VI. Aluminium. 202. A number of cells were set up with bright aluminium plates opposed to amalgamated zine and electro-cadmium, immersed in their respective bromide solutions of strength °25MBr, 100 H,O. The readings exhibited the same fluc- tuations as were observed with the sulphate and chloride cells previously examined (§ 178 and § 186). The following readings were obtained, the current passing in the opposite direction to that calculable from the relative heats of forma~ P2 204. Messrs. Wright and Thompson on the Determination of tion of zinc- and aluminium-bromide solutions in the first case, but in the normal direction in the second case :— Zinc-Aluminium. |Cadmium-Aluminium. ees Mascaras sesecnraeeeeee — "323 + -037 Mirman eee e ee — ‘278 +0138 Average i tcanenacnabee — ‘296 +022 Probable error ......... me OT +:005 These numbers lead to the following valuations for the voltaic constant for bright aluminium in bromide solution 25 Al,Br, 100 H,0 :— ZmG-aluminiin 62.09. eee eel Fn ees ene Zine-cadmium — Aluminium-cadmium 4 ee } = +'293 Mean:-°)- «"“d)) 55 ee=220 the constant being of + sign, since aluminium actually acquires the higher potential, although it might @ prior: be expected to acquire the lower potential. Julius Thomsen’s thermochemical data lead to the value Al,, Br. aq.= 136680; whence Hy=—1-008 volt, corre- sponding with 45720 gramme-degrees. Consequently H—EHy= + '295—(—1:008) = +1°303 ; 1. e. the thermovoltaic constant for bright aluminium in bromide solution *25 AlzBr, 100H,O is a large positive quantity, slightly greater than that found with the corre- sponding chloride solution, viz. + 1°288. EF. Voltaic and Thermovoltaic Constants of Metals immersed in Solutions of their Lodides. I. Cadmium. 203. The following values were obtained with a number of cells set up with amalgamated zinc and electro-cadmium immersed in solutions of their iodides of strength *25 MI, 100 H,O :— Mia xamanenaas aS Re en Se ea ao Minimum? 60%." } Cea Averages) Shek i Eee Probable error . . . +°0008 Chemical Affinity in terms of Electromotive Force. 205 Julius Thomsen finds the heat-values for this strength of solution are Zn, I,,aq.=60540, and Cd, I,,aq.=47870; whence Ey= "279 volt, corresponding with 12670 gramme-degrees. Hence H—HEy= +:'048; 7. e. the thermovoltaic constant for cadmium in iodide solution of strength :25 CdI, 100 H,O is positive in sign but not large numerically. It is noteworthy that, with the corresponding bromide and chloride solutions, the values were negative, viz. —'023 and —-086 respectively; the bromide value being thus intermediate between the chloride and iodide values. II. Silver. 204. The following numbers were obtained with cells set up with electro-silver immersed in a magma of freshly preci- pitated well-washed silver iodide suspended in zine iodide solution, and opposed to amalgamated zinc or electro-cadmium in their respective iodide solutions, the solution-strength being uniformly °25 MI, 100 H,0. Zinc-Silver. Cadmium-Silver. oSco ee 713 393 MUR RGNANATHS |... 25s wouesiese -696 374 BEVERAGE .2 62.5 ..002 + eee "7055 "384 Probable error ......... +0028 +0030 These values lead to the following valuations of the voltaic constant for electro-silver in contact with this magma :— Zine-silver . Siete Meee res Fo oan eh grat ROE) Zine-cadmium + Cadmium-silver ‘ iB es = ae Means i cviiai 2606 Since Thomsen finds Ag», 1,=27600, the value of Hy is *726 volt, corresponding with 32940 gramme-degrees : hence H— Eg = —:020. On comparing this value with those found for silver bromide suspended in zinc-bromide solution and for silver chloride suspended in zinc-chloride solution, all of the same strength *25 Zn X, 100 H,O, viz. —-099 and —:112 volt respectively, it is noticeable that the direction of variation is the same as that observed in the analogous cases for cadmium, the bromide value being intermediate between the chloride and iodide values, the last being algebraically the greatest. 206 Messrs. Wright and Thompson on the Determination of III. Mercury. 205. Cells were set up with mercury in contact with freshly precipitated mercurous iodide suspended in zinc-iodide solu- tion, and opposed, firstly, to amalgamated zine in zinc-iodide solution, and, secondly, to electro-silver immersed in a magma of freshly precipitated silver-iodide and zinc-iodide solution, the solution-strength being uniformly °25 ZnI, 100 H,0. The following values were obtained :— Zine-Mercury. | Mercury-Silver. Wilbobaribhiie Sqgeesegn sess 806 — ‘092 Muniimimma te) dea. ase 797 — 101 INV ELAR OM OR EI Asante a ‘800 — ‘096 Probable error ......... +:00138 +:0014 the current passing in the latter case in the direction opposite to that predicable from the relative heats of formation of silver and mercurous iodides. From these values the following valuations result for the voltaic constant of mercury m contact with mercurous iodide suspended in *25 ZnI, 100 H,O :— eee See try ol) Zinc-silver — Mercury-silver J Me "802 y +096 Mean OU Julius Thomsen finds that Hg, 1,=48440; whence Hy= 267 volt, corresponding with 12100 gramme-degrees. Hence K—Hy= +°584; 2. e. the thermovoltaic constant for mercury in contact with a magma of mercurous iodide suspended in ‘25 ZnI, 100 H,O is a large positive quantity, as similarly found for mercury in. contact with mercurous-bromide and zinc-bromide solution and with mercurous-chloride and zinc- chloride solution of the same solution-strength, these latter two values being respectively +°472 and +:458. So that the bromide value is intermediate between the values for chloride and iodide; whilst the direction of variation with the three halogens is the same as that observed both with cadmium and with silver, viz. that the iodide value is algebraically the greatest. ZiAG-MCLCULY — . Ante IV. Lead. 206. The very sparing solubility of lead iodide rendered it impracticable to obtain good readings with cells set up with Chemical Affinity in terms of Electromotive Force. 207 aqueous solutions of that salt. Accordingly a magma of lead- iodide and zinc-iodide solution of strength 25 ZnI, 100 H,O was employed to surround the electro-lead plates used, opposed in one set of experiments to amalgamated zinc in the same zinc-iodide solution, and in another set to mercury immersed in a magma of mercurous iodide suspended in the same zinc- iodide solution. The following values were obtained, the degree of concordance being distinctly less than with most of the other combinations examined :— Zinc-Lead. Lead-Mercury. [Sc “489 — 317 | Minimum ............... ‘418 —'379 | Average .........ccceccses A455 — 347 Probable error ......... +:009 +:008 The lead-mercury cells gave a current in the direction opposite to that deducible from the relative heats of formation of zinc and mercurous iodides. - From these numbers the following valuations of the voltaic constant result :— _ 1 2:1. S21 eine i eae one eran aera igy 594) Zinc-mercury + Mercury-lead { ee == "454 Mica ons. 6a. oye ie OD Julius Thomsen finds Pb, l,=39800 ; whence Ey=°457. Hence the thermovoltaic constant for electro-lead immersed in a magma of lead iodide suspended in ‘25 ZnI, 100 H,O is a minute negative quantity, viz. —‘002. This value and those above found for electro-lead in contact with saturated-chloride and bromide-of-lead solutions respec- tively, viz. —°222 and —-°235, are not strictly comparable, since the solution-strength was not the same throughout ; whilst a magma containing zinc-iodide solution was used for the iodide cells and pure lead-salts for the others, which, moreover, had respectively the strengths ‘05 PbCl, 100 H,O, and ‘037 PbBr, 100 H,O. Probably from these causes the bromide value is not intermediate between the chloride and iodide values, as might have been anticipated ; but the last 208 Messrs. Wright and Thompson on the Determination of value is algebraically the greatest,-as was found with cadmium- silver and mercury. It is hence evident that whilst the thermovoltaic constants of metals in contact with their oxy salts (sulphates, nitrates, and acetates) do not vary widely, the same remark is not true for their halogen salts (chlorides, bromides, iodides). In general the thermovoltaic constant is decreased (algebraically) by substitution of bromide for iodide or of chloride for bromide ; although this rule is not without exception, e. g. in the case of iron, where the values for :25 FeX, 100 H,O are +°204 and +:°134, where X represents chlorine and bromine respectively, the substitution of chlorine for bromine thus causing a notable increase. Summary of Results. 207. The experiments above described lead to the general conclusion that electromotors, consisting of voltaic cells in which two different metals are surrounded by solutions of corresponding salts respectively, are capable of generating electromotive forces which (when not depreciated sensibly below their maximum value by giving rise to currents of densities greater than certain small limiting values) usually stand in no simple relationship to the chenucal action taking place in the cell during the passage of the currrent, or to the heat-evolution taking place during that passage, or to the heats of formation of the two solutions electrolyzed. The values of the maximum H.M.F’.’s thus generated may, however, be deduced within very close limits of accuracy by taking the algebraic difference between certain numerical values or voltaic constants assigned to each metal in contact with each given solution, these values varying slightly according to the surface-nature of the immersed metal, and being also depen- dent on the nature and strength of the solution of metallic salt in contact with the metal, and probably also varying with the temperature, but being otherwise actually constant. Further, these maximum H.M.F. values may be connected with the difference in heat of formation between the two solutions electrolyzed by supposing that the total difference of potential set wp is due to two superposed causes:—one, the heat- evolution due to the difference in heat of formation of the two solutions, which tends to make the metal immersed in the electrolyte of lesser formation-heat acquire the higher potential (like the copper plate of a Daniell cell) ; the other, a thermo- voltaic action akin to the medus operandi of an ordinary Chemical Affinity in terms of Electromotive Force. 209 thermovoltaic couple, in virtue of which a difference of potential is set up expressible by the algebraic difference between two numerical values, or thermovoltaic constants, assignable to each metal respectively, the which values vary pari passu with the variations in the corresponding voltaic con- stants. This thermovoltaic action being expressible by k,— kz, and the first source of potential-difference being indicated by Hn, the total difference of potential set up is H=Hyt+hk,—hky, where, if k;—k, be materially different from zero (which is most frequently the case), the value of H will differ materially from that of Hy, exceeding or falling short of it according as ky — ky is positive or negative in sign wath respect to Hy. In the latter case, if Eh, be numerically greater than Hy, the direction of the current actually generated is the reverse of that predi- cable from the relative heats of formation of the electrolytes. 208. The following Table furnishes a brief epitome of the mean values of the voltaic and thermovoltaic constants deduced above for various metals and fluids at a temperature within a very few degrees above or below 18° C.; the solutions surround- ing both plates being of equal str ength (m zine-salt molecules per 100 water molecules), the plate-surfaces being freshly amal- gamated ones for zinc (standard), bright fused metal for iron, magnesium, and aluminium, and freshly electro-coated plates in all other cases. . . Voltaic Thermovoltaic Metal. Surrounding Fluid. mM. Pe tag 13 constines °1:114 inva-/|1°105 inva- } 4-009 MOPrPER ...... SPU MIATC Say. ss aacnnswee's "1 to 2:25 : riable. riable. INSEL NOM ciate Ree Asian sicais ss -25 to 8:0 |1:066 to 1:109,1:105 to 1:100) —-039 to +005 PROP EALON si oteasn on 95 50/afo seis "25 1-091 (SDE — ‘020 Chloride: Cu,Cl, suspen- ded in CuCl, solution ; or CuCl, solution alone ‘25 1-099 ( +°061 Chloride : Cu,Cl, suspen- | ded in CdCl, solution. "25 1-001 1038 + —°037 Chloride : Cu,Cl, suspen- | ded in ZnCl, solution. Ay) 988 y —°050 SAmMEUM ...| Sulphate ...........0e0.00 "1 to50 | 362 to 357 | -357 to 367 |+°005 to —-010) INGLE: ©. o0..e reser. clesdaaoens 25 "B52 307 —°005 Chilorides02)..5 Ane -25 to 8:0 | °330 to -262 | °366 to 240 |—-036 to +°045 Bromides 4. .i.coeaewere. "25 "315 "338 —°023 ode «.dcan ht arecseasek ‘20 —‘701 —1-634 + °933 Atuminium...| Sulphate..................5- 5 +°537 — ‘982 +1:519 Chiloriden essa toones deere "25 +°280 — 1-008 +1:288 IBVONMIGE st paren: ee ccoe eee "25 +295 -- 1-008 +1:303 Chemical Affinity in terms of Electromotive Force. 211 209. The following is a list of the cells examined, in which the value of k,—, is opposite in sign to, and numerically greater than, Ey; so that the current actually generated flows in the direction opposite to that predicable from the rela- tive heats of formation of the electrolytes :— Combination. ™m. E. Ex: EK-— E, =k,—,,. Iron-cadmium-sulphate .... Ol tol0 |—-073 to —:035) + °075 |—-110 to —-148 Tron-cadmium-chloride "25 — 157 + -082 — ‘239 lron-cadmium-bromide ...| "25 —'103 + :054 — ‘157 Zinc-aluminium-sulphate ...| a +537 — ‘982 +1:519 Zinc-aluminium-chloride... 25 +280 — 1-008 +1:288 Zine-aluminium-bromide... “25 +°296 —1-008 +1:304 _ Copper-silver-chloride. AgCl suspended a "25 —-020 — 174 ZnCl, solution ...... : ) Copper-silver-chloride. A ites AgCl suspended in “25 — 010 — 164 CdCl, solution ...... _Mercury-silver-nitrate ...... 25 | — ‘004 + '688 — ‘692 _Mercury-silver-chloride. Be : pee 5 _ Both suspended in ZnCl, = wee Fs 920 =7 2a _Mercury-silver-bromide. : : “<7 Ke _ Both suspendedin ZnBe, j = ee: Estar etd 'Mercury-silver-iodide. OF : E _ Both suspended in ZnI, } =i ek ieee aoe _Mercury-silver-chloride. _ AgCl suspended in ZnCl, | ‘25 — “058 \ (— °583 | Hg,Cl, Ps CdCl, | _Mercury-silver-chloride. _ AgCl suspended in cad} “25 — 038 | | — 563 | Hg,Cl, x ZnCl, b+ -525 4 _Mercury-silver- chloride. . te See Both suspended in caci, |} 2 pia | ~ 8 | Mercury-silver-chloride. _ AgCl suspended in Zn} "25 —‘167 y, — 692 | Hg.Cl, > HgCl, Lead-mercury-chloride. _ Hg,Cl, suspended mf 05 — 549 | — “694 | J) See : Lead-mercury-chloride. | + 145 Hg.Cl, suspended i} ‘05 —*539 — ‘684 pee eee Lead-mercury-bromide. _ Hg,Br, suspended in ‘037 — “402 + 306 — “708 | oe ie -Lead-mercury-iodide. a: Cay. : é | Both Sepaded in ZnI, \ 025 at + “190 on ae 210. The following is a list of the cells examined in which the value of k,—k, is of the same sign as Ey; so that the H.M.F. actually set up eaceeds in numerical value that pre- dicable from the relative heats of formation of the electro- lytes ; only those cells are named where the excess is somewhat considerable, 7. ¢. 0°1 volt or upwards. 212 Messrs. Wright and Thompson on the Determination of Combination. Lead-copper-sulphate. | PbSO, suspended inZnSO, solution Lead-copper-sulphate. PbSO, suspended CdSO, solution Lead-copper-nitrate Lead-copper-acetate eoerestesacseseese ses coscesccocos ee eecteccees eeceosecccas Lead-copper-chloride Zinc-iron-sulphate Zine-iron chloride Zinc-iron-bromide eecpeeescees e@veeccescaroe eeevecscyooe Zine-mercury-sulphate Zinc-mercury-nitrate Zine-mercury-chloride. Hg.Cl, suspended HegCl, solution Zine-mercury-chioride. Hg,Cl, suspended in CdCl, solution Zinc-mercury-chloride. Hg,Cl, suspendedin ZnCl, solution Zine-mercury-bromide. »Br, suspended Zn Br, solution Zine-mercury-iodide. Heg.I, suspended in ZnI, ecevectes eeoer es caceccs see e es cers esses cosces eoeeosesecectecesneces SON WENO Sek Nadia obonsoeodonone Cadmium-mercury- chloride. Hg,Cl, suspended in ie Cl solution cecescare: Cadmium-mercury-chloride. Hg,Cl, suspended mf CdCl, solution ............ Cadmium-mercury-chloride. Hg,Cl, suspended in ZnCl, solution Copper-mercury-nitrate Lead-mercury-nitrate Lead-silver-chloride. AgCl suspended in ZnCl, | solution Lead-silver-chloride. | AgCl suspended in PbCl, ; solution J eeceescccresseseorees mM. EK. Le Excess. 0-1 to 2:0| °577 to ‘611 | -+'184 to +:217 393 to °394 0-1 to 2:0) -564 to -596 +171 to +°202 ‘25 to 2:0) -486 to 519 | -345 to 3888 | +141 to +:128 25 ‘ -485 341 4144 : rrecular, ‘ 3 05 { Bee at 295 About tae 0-1 to 1:0} -445 to °399 284 +161 to +°115 25 “490 "284 +206 25 417 "284 aes ‘1 to 5°75/1-514 to 1-457 ? (ane about 25 1-500 1-202 +:298 iy 1:256 +588 668 "25 1-140 +°572 25 to 9:5) 1123 to -988 °668 to -5386 | +452 to +°481 25 ‘972 ‘500 4-472 25 -800 267 +533 25 -929 | (4627 25 812 | 302 «|4 4 510 25 7709 unl) ee o7 25 433 097 +336 25 ‘917 443 4-474 05 -489 +110 L 879 05 | 480 | +101 211. The following is a list of the cells examined in which the value of k;—f, is of the opposite sign to, but not greater in magnitude than, Eq; so thatthe E.M.F. actually set up is less in numerical value than that predicable from the relative heats of formation of the electrolytes ; only those cells are Chemical Affinity in terms of Electromotive Force. 213 named where the deficiency is somewhat considerable, viz. 0-1 volt and upwards. Combination. mM. E. Zinc-silver-sulphate .............-- 042 1-536 Zinc-silver-nitrate ............--- 25 to 2°0/1°495 to 1°556 ‘057 1-490 Zinc-silver-acetate Zinc-silver-chloride. Ey. Deficiency. 1-890 "B04 1-890 395 to °364 ? Probably near -40 AgCl suspended in ZnCl, | ‘25 to 6:0|1:080 to 1014/1192 to 1076; 116 to -062 solution Zine-silver-chloride. AgCl suspended in CdCl, "25 1-088 <3 LST” a eee Copper-silver-sulphate............ ‘042 4235 Copper-silver-nitrate ............ ‘25 to 2:0) -429 to -446 Copper-silver-acetate ..... ...... ‘057 397 Copper-silver-cbloride. 7} AgCl suspended in CuCl, "25 035 ReMeintenite niet eens .-2..02--00 Cadmium-silver-sulphate...... 042 1°1805 Zinc-lead-sulphate. PbSO, suspended in ZnSO, | | *1 to 5:0 solution Zinc-lead-sulphate. ‘D37 to ‘487 sere ee reeeetssessetee PbSO, suspended in CdSO, } | “1 to 5:0} -550 to 505 100 EO ee Zane-lead-nitrate ..... ............ 25 to 2:0} -580 to 591 Zine-lead-acetate .................. "29 608 Zinc-lead-chloride ............... nes) ‘O91 Zine-lead-bromide ............... ‘037 ‘O71 Cadmium-Jead-sulphate ......... 1 to 3:0} 173 to -133 Cadmium-lead-chloride ......... ‘05 “260 Cadmium-lead-bromide ......... 037 "296 Lead-silver-sulphate. , aie EEE G1 AnSO, solution... | ae ele Lead-silver-nitrate ............... ‘25 to 2:0) .914 to -965 , Irregular, Lead-silver-acetate ............... 037 { eee 0:8 Tron-lead-sulphate. PbSO, suspended in ZnSO, } | -1 to 1:0; -120 to -112 52 S17 ee Tron-copper-sulphate ......... .. ‘1 to 1:0} ‘685 to -715 Tron-silver-sulphate............... 042 1108 Sron-silyer-chloride. ae Lae AgCl in ZnCl, solution...... } = fe Zine-magnesium-sulphate ...... 1:0 “724 Zine-magnesium-nitrate ......... 25 ‘O51 Zine-magnesium-chloride ...... ‘25 ‘702 Copper-magnesium-sulphate ...| 1-0 1-840 Copper-magnesium-nitrate ...... "25 1595 Cadmium-magnesium-chloride .| -25 1-030 Aluminium-copper-sulphate ...) ‘5 078 Aluminium-cadmium-chloride . 25 "050 Aluminium-cadmium-bromide .| ‘25 "022 1-192 104 ‘785 3515 ‘785 to °786 356 to -340 5 Probably about e 39 154 119 1-533 "3925 \ apes! | [oe “Later are ; 712 to 704 { | -162 to -199 at \ ¢ ‘759 to °716 179 to 125 ‘770 162 "E13 ‘222 "806 "235 355 to 345 "182 to 212 “447 187 468 "212 11775 1745 1:131 to 1:174| 217 to ‘207 ? Probably about 3 “428 308 to ‘316 "821 "136 to :106 1605 ‘502 ‘908 316 1-634 910 1631 1-100 1-634 "932 2°739 "899 2°736 1-141 2-000 ‘970 2-087 1-509 1374 1-324 1-346 1-324 214 On the Determination of Chemical Affinity. 212. The following is a list of the cells examined in which the value of k,—k, 13 not numerically greater than Hy, and lies witbin the limits +0°l volt. Itis evident that the number of cells coming into this category is only a fraction of the total number of combinations examined. Combination. mM. 1 Dea Ey. Differences. Zinc-copper-sulphate ......... ‘25to 2°25 eile sek. +:009 Zinc-copper-nitrate ............ ‘25 to 8:0|1-066 to 1-091/1°105 to 1-100) +005 to —-059 Zinc-copper-acetate ............ 25 1-091 1111 — 020 Zine-copper-chloride. ( Cu,Cl, suspended in CuCl, "25 10885 | +:061 sol., or CuCl sol. alone... Zinc-copper-chloride. | Cu,Cl, suspended in CdCl, "25 1001 \ 1-038 { — 037 ROMIGIOM se. sco ceres sone | Zinc-copper-chloride. | Cu, Cl, suspended in ZnCl, "25 —°050 BOlutlont es. soos oe eae ) Zinc-cadmium-sulphate ....., ‘1 to 5:0} 362 to °357 | -357 to °367 | +°005 to —-010 Zine-cadmium-nitrate ......... "25 B51 357 — ‘006 Zine-cadmium-chloride ...... ‘25 to 8:0) -330 to -262 | 3866 to 240 | —-036 to +045 | Zinc-cadmium-bromide .. ... *25 315 338 — "023 Zine-cadmium-iodide ......... "25 "322 "279 +043 Copper-cadmium-sulphate ...|°1 to 20} °752 to ‘755 | °748 to "748 | +°009 to +-007 Copper-cadmium-nitrate...... ‘25 713 “748 —"0aa Copper-cadmium-chloride. Cu,Cl, in CuCl, sol., or ‘25 “769 +:°097 CuCl, sol. alone ......... Copper-cadmium-chloride. 3 : tr. 642 4 : Cu,CL, in CdCl, solution | oe Be | | mee Copper-cadmium-chloride. ee Cu,Cl, in ZnCl, solution . i = ey ] a a“ Finc-silver- chloride. : AgCl in CuCl, solution ... | #0 ree ii eae Zinc-silver-bromide. 4 AgBr in ZnBr, cae 20 ave BOVE a Zine-silver-iodide. : G AgI in ZnI, solution ...... \ =o WOES is — 0205 Cadmium-silver-chloride. ; é ( : MeClan! Gul, gol. «5c. }] 2 oui | ete ee Cadmium-silver-chloride. : q ea : AgCl in OdCl, solution ... | ae (OE ey icee 1 — 1065 Cadmium-silver-chloride, a y | ees AgCl in ZnCl, solution ... } ae (ol ey (i ae Cadmium-silver iodide. E ; : aves AglI in ZnI, solution ...... } ae 208 fel — 068 Zinc-lead-iodide. . ‘ a f PbI, in ZnI, solution...... } ap ane | i res XXIII. On some Electromagnetic Experiments, continued.— No. Il. Diverse views of Faraday, Ampere, and Weber. By 8. Totver PREsTon*. N Poggendorff’s Annalen (1841, Bd. lii.) is a remarkable paper by Prof. W. Weber, entitled “ Die unipolare Induction,” which refers of course to the well-known fact of the induction of continuous currents by the influence of the single pole of a rotating magnet. In spite of the comparatively old date of this paper, it is well known and referred to in the present day. This paper has some relation to the subject of my last communica- tion to the Philosophical Magazine (February 1885) ; but I wish to point out that it does not alter or affect the conclu- sions there arrived at, but, on the contrary, tends to confirm them. The paper of Prof. Weber appears to open out a new ques- tion, distinct from the phenomena dealt with in my commu- nication ; and I would call attention to the fact that Prof. Weber’s idea would appear to involve one theoretie conclusion which appears at first sight improbable, but which, if true, would seem to render an experimental determination possible which might be capable of throwing some light on the phy- sical nature of the electric “current.”” Iam not aware that the subject has been considered from this point of view, and of course anything I submit will be open to criticism. I will remark, first, that Prof. Weber agrees with my view (which accords with that of Ampére, and is opposite to that of Faraday), viz. that the “ lines of force,”’ or field of force, about a magnet must be considered in that sense fixed or dependent on the magnet, that this field of force rotates when the mag- net rotates on its axis, or, otherwise put—When a magnet rotates on its axis, the field of force must (in regard to the inductive effect) be considered as moving with the magnet and intersecting external conductors, in the same selse as it would do if the magnet were bodily translated. The chief point which I wish to notice in Prof. Weber’s paper is his view as to the cause of the rotation of a magnet * Communicated by the Author. + I may mention that the object of my last paper was to point out an apparent ambiguous case (involving an oversight) in Faraday’s experi- ments, which caused him to take the opposite of the above view as to the rotation of the field of force with the magnet, whereby Faraday contradicted _ Ampére’s theory in this respect, although he speaks in approving terms of the theory in other respects. 216 Mr. 8. Tolver Preston on some Electromagnetic on its axis, when one terminal of a voltaic battery is main- tained in sliding contact with the equatorial part of the magnet, the other terminal in sliding contact with the pole of the magnet (a perfectly well-known experiment). Prof. Weber thinks that, because in this case the current flows during part of its course within the body of the magnet, the explanation of the rotation afforded by Ampere’s theory is “not at all” (keineswegs) applicable*. Prof. Weber says (translation):—“ The two effects (2. e. the rotation of a magnet on its axis, and the converse case of the rotation of a conductor about the magnet), which Ampere here endeavours to explain from like causes, are, however, in reality of different nature; and each demands its own expla- nation. The explanation given by him (Ampere) only applies to the rotation of the conductor about the magnet, discovered by Faraday, and not at all to the rotation of the magnet on its axis discovered by himself.” { But now I would call attention to the fact that the rotation of the magnet is found to take place apparently equally well when the current does not enter the body of the magnet at all, such as when the magnet is coated with a metallic sheath or cylinder, insulated from the body of the magnet by intervening cement or paper, so that the current flows along the sheath instead of entering the body of the magnet. If, then, the magnet rotates in this case (when no current enters its body), how, it may be asked, can it be said that Ampéere’s explanation of the rotation when the body of the magnet (instead of the metallic sheath) is used to conduct the current, is “ not at all”’ (keineswegs) applicable ? For Ampere’s theory, when the magnet is coated with the sheath, admittedly accounts for a force of rotation of the magnet (on its axis) equal to that with which (conversely) the external loop—cealled for brevity ‘‘ conductor ”-——would rotate about the magnet if it (the loop or “ conductor’) were free to move. Ampere’s theory therefore accounts for a force of rotation in the magnet equal to the opposite force of * Ampére, as is known, considered the rotation of the magnet on its axis to be due to the same cause as the (converse) rotation of the “con- ductor” (or external loop of wire) about the magnet, or he considered the effect to be a simple case of “ action and reaction” between the movable parts of the circuit ; ¢. e. whether the conductor revolved about the mag- net, or (conversely) the magnet rotated on its axis, depended simply on which was free to move. The movement (on Ampére’s view) depended on the reaction between the current in the conductor and the external magnetic field of the magnet, whereby the two tended to be twisted or to rotate in opposite directions. t+ Pogg. Ann. 1841, Bd. lit. S. 354. EHexperiments of Faraday, Ampére, and Weber. 217 rotation of the conductor about the magnet. What more, may I ask, do we want, or is not this sufficient? Is it to be supposed that when the body of the magnet conducts the current instead of the insulated sheath, the force of rotation of the magnet is then (by some action of the portion of the current within the magnet) greater than in the former case, i. €. greater than the (converse) force of rotation of the con- ductor about the magnet? In other words, when (in the first case) the magnet is coated with a sheath (simply to prevent the current from entering its body) the rotative forces of the magnet and conductor are equal: then (in the second case), when the sheath is removed, is it to be assumed, or does Prof. Weber’s theory imply, that the opposite rotative forces are unequal (so that the magnet and the conductor now tend to revolve in opposite directions about each other with unequal forces)? It appears that Ampére’s theory is sufficient to account for equal rotative forces in magnet and conductor in opposite directions. Does Prof. Weber’s view imply that unequal forces of torsion—or of tendency to rotation—in opposite directions have to be accounted for, or exist when the current flows into the body of the magnet ? If so, a curious result would appear to follow, viz. (the opposite moments of torsion being assumed unequal, or the moment of torsion of the magnet on its axis being assumed greater than that of the conductor about the magnet) a re- sultant moment of torsion must exist inthe system ending to turn it about its centre of gravity. Or otherwise expressed, it would follow apparently that if the whole system, with a small voltaic battery fixed in it, were all delicately suspended as one whole, it would tend to rotate about its centre of gravity by the action of forces within itself without any external visible support or point of reaction. I would call attention to this improbable result, which appears to follow from Prof. Weber’s view. But l am not prepared to contend that this result might not be possible under certain conceptions. If found to be true on trying the experiment, the result would be highly interesting, as its analysis would probably be capable of throwing a light on the physical nature of the electric “ current.” Another way of trying the experiment might suggest itself. The moment of torsion of the magnet on its axis might be exactly measured, first with the insulated sheath, and, secondly, without it. If in the last case (4. e. without the sheath), the moment of torsion were found to be greater, this would (as stated) appear to indicate the existence of a resultant moment of torsion which, when the sheath is removed, tends to twist Phil. Mag. 8. 5. Vol. 19. No. 118. March 1885. Q 218 Is a Vacuum a Conductor of Electricity ? the whole system—conductor, magnet, battery and all—about a common centre of gravity. This result (as remarked) will appear improbable at first sight at least. If found to be con- firmed on making the experiment, it would not, as it seems to me (and I would put this as a query) necessarily invalidate Ampére’s theory, which accounts for equal forces of rotation in opposite directions. It would rather add an additional or new experimental fact to knowledge. P.S. The conditions stated in the above paper are, I think, capable of settling this question ; and in this I am confirmed by a letter recently received from Prof. Wilhelm Weber, of Gottingen, to whom the present manuscript was previously sent. I quote the following remark from Prof. Weber’s letter (dated February 15, 1885) :— “Ich habe sie (2. e. the present manuscript) mit groésstem Interesse gelesen und mich gefreut, dass die Frage iiber wni- polare Induction dadurch endlich zu definitiver Hrledigung gelangen werde.”’ I may say I had, some time ago, received a letter from Lord Rayleigh, in which he spoke favourably of my view in the last paper (Phil. Mag., Feb.), which was in opposition to that of Faraday. I pointed out in my last paper that the experiment on which Faraday founded his view was capable of a double meaning. The subject appears an extremely interesting one to follow out experimentally, as there are conditions in the inquiry which would seem, if investigated, to be capable of throwing a light on the physical nature of the electric “current,” aid even of magnetism. Paris, February 1885. XXIV. On Prof. Hdlund’s Theory that a Vacuum is a Conductor of Electricity. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, SHOULD like to call the attention of Prof. Hdlund to an objection to his view that a discharge-resisting vacuum is nevertheless a conductor of electricity. The objection is one that I urged in a letter to ‘ Nature’ in the spring of 1883, and, so far as I am aware, it has not yet been answered. i refer to the fact that a body surrounded by such a vacuum is acted upon inductively by another electrified body near it, and not screened from the action as it would be if surrounded by a conductor. Determination of the Mean Density of the Earth. 219 Although there was probably when I wrote already sufficient experimental evidence to show that induction took place across such a vacuum, yet I thought it worth while to make the experiment described in my letter, in which a platinum ball suspended in such a vacuum is shown to be strongly attracted towards a neighbouring electrified platinum sheath, precisely as if suspended in any other fluid dielectric, while a minute sp’rk was ceen at the moment when the two attracting bodies carie into contact. This tube and others that I experimented with exhibited the luminous effects described by Prof. Edlund when moved in the neighbourhood of an electrified body or influenced by the passage of currents in the neighbourhood; but 1 do not think that this luminosity is necessarily the proof of a current in the ordinary sense. It may be due to the increase or diminution of induction within the medium, some of the energy of the induction-tubes being absorbed in transit. It would be interesting to make the experiment of passing a stroug current through a stout wire surrounded by such a vacuum, and to observe whether the transit of energy across the vacuum ™* was attended by any luminous effect. If it were, then the vacuum might be regarded as a conductor in so far as the inductive energy entering is transformed into the lumi- nous form. If no effect were observed, we should infer that this transformation did not take place when a steady flow was reached, but only accompanied variations in the flow. I am your obedient servant, Montreux, February 14, 1885. A. M. WortTHINGTON. XXV. On the Application of the Pendulum to the Determi- nation of the Mean Density of the Earth. By Dr. J. Witsine, of Potsdam ft. » ae first experimental determination of the mean density of the Harth which Maskelyne and Hutton carried out depends on the observation of deflection of the plumb-line in the neighbourhood of Schehallien. It is limited by the uncer- tainty arising from our imperfect knowledge of the mass and density of the deflecting mountain, an error which also affects the results deduced by Carlini and Airy from oscillations of the pendulum. Accordingly the use of the pendulum has been abandoned in favour of the torsion-balance, as it is not sensi- * See Prof. Poynting’s paper “On the Transfer of Hnergy in the Electromagnetic Field,” Phil. Trans., Part IT. 1884. + Translated from the Sttzwngsberichte der Berliner Akad. der Wissen- schaften, January 1885. Q 2 220 Dr. J. Wilsing on the Application of the Pendulum to tive enough to be appreciably influenced by smaller masses which are capable of accurate determination. The necessary degree of sensitiveness may be obtained by adjusting the centre of gravity of the pendulum close under the axis of oscillation. With an experimental apparatus, which was intended to get some indications as to the practical execu- tion of this modification, experiments were made in September of last year in the observatory. ‘This consisted of a prismatic rod of thin sheet-iron, at the ends of which were fixed lead balls, each weighing 300 grammes. The steel knife-edge, which worked on agate, was fixed in the middle of the rod. The apparatus was so arranged that, when in equilibrium, its axis was almost vertical. The motion was read off by reflection. When the position of equilibrium was found and the attracting masses were placed near the lead spheres, from the deflection of the pendulum, the ratio of their attraction to the constant of gravitation can be determined. By reversing the direction of the deflecting forces, the action of the force can be doubled. This method may be regarded as a combination of the two oldest methods. In comparison with the method used by Prof. von Jolly with such distinguished success, it has the advantage that the sensitiveness of the pendulum is consider- ably greater. Although the crude construction of the experimental instru- ment made it very difficult to introduce the needful corrections, —it being mounted on a wooden support, and not sufficiently protected against currents of air,—a time of oscillation of 150 seconds could be attained without the occurrence of irregula- rities which could be regarded as essential. This may be explained by the fact that partial oscillations are excluded as completely as possible, and the axis of the pendulum de- flects but a little on each side of the vertical, so that the bending of the rod is only a very slight amount. The degree of delicacy corresponding to the above-mentioned time of oscillation would be sufficient to measure the attraction of spheres of a few hundredweight, as is possible by using a torsion-balance. The sensitiveness of the apparatus was ascertained from the observation of oscillation by the addition of weights, which were placed at known distances from the knife-edge at the lower end of the pendulum. If gm is the weight of the piece added, d the distance of its centre of gravity from the knife- edge, the time of vibration for infinitely small oscillations is Gap MK? + mk? + md? g( Ms + md) the Determination of the Mean Density of the Earth. 221 From this, in connection with the time of vibration of the unloaded pendulum, we get the magnitude gMs, which forms the denominator in the Gepecesion for the angle of deflection, tan d= ae ‘ where g’ is the attraction of the ALGHa mass, m the mass of the pendulum-bob, / the distance of its centre from the knife-edge. Closer consideration shows that the use of this method is even allowable if a correction is made for the buoy- ancy of the air, Bessel’s correction for the moment of inertia, and for a possible blunting of the knife-edge ; for the form of the equation does not alter, and only the ‘magnitudes gMs and MK? acquire a different ‘signification, As an example of the determination I may here give the results of two series of observations. In the first the duration of the free oscillation was :— T, = 59-20 lixtra weight 1 gr. . . T, = 22:00 ” De Olea T; = 10°46 9 ” 10 PO ac ara Tro ==) (46 Expressed in grammes and millimetres, we have for gMs the values SELIG: we Sle 2b S189: In the second series the time of the free oscillation was:— T, = 145-20 Hxtra weight 1 gr. . . T, = 23°64 » OL Ot ab etre ley =o 13766 ABM theron ol We eas a and for gMs, ‘ 13°75, 18°50, 13°50. The concordance between these numbers, which are inde- pendent of each other, is also somewhat limited by the error of the extra weight, the amount of which was not known. The experiments show, however, with certainty that the value of the reduction may be determined with great accuracy with an apparatus of convenient construction. Besides the calculation of the gravitation of the pendulum- bob towards the attracting masses which is common to all methods, two measurements are necessary—the distance of the extra weight, and of the centre of the pendulum-bobs from the knife- edge. These measurements, however, require no other appliances than those which are in use with the reversion-pendulum. 222 Notices respecting New Books. The result of the experiments hitherto made renders it scarcely doubtful that the pendulum, which does such excel- lent service in all problems bearing on the determination of gravity, will also give useful results for our present purpose ; and in the immediate future I hope, by means of an apparatus constructed by Repsold, of Hamburg, to continue these observations in the astrophysical observatory ard to bring them to a conclusion. XXXVI. Notices respecting New Books. A Treatise on the Principles of Chemistry. By M. M. Parrison Moir, V.A., F.RS.E., Fellow, and Prelector in Chemistry, of Gon- ville and Caius College, Cambridge. Cambridge: The University Press. R. MUIR’S book is certainly one of the most important con- tributions which have been made to general English Chemical literature for many years, and will, we feel sure, be heartily welcomed by all who are engaged in teaching chemical science in this country. A text-book of a like scope to Lothar Meyer’s well- known Moderne Theorien der Chemie has long been a desidera- tum ; and it is surprising that a translation of the latter into the English language has not been published long ere this. Such a translation will, however, not be in such request now that Mr. Muir has brought out a book similar in kind, and, as we think, of equal merit, and probably more suitable for Eng’’ Ampere ampere. ampere. ampere. ampere. 0-01 800 800 195 195 1095 1095 140 #140 0:03 3150 =1175 650 227 4800 1852 430 145 0:05 6250 1550 | 1125 237 10500 2850 750 160 007 (10500 2125 | 1640 257 20500 5000 | 1100 175 0:09 {15500 2500 | 2165 262 33000 6200 | 1410 155 O-1 18350 2850 | 2400 235 36200 38200 | 1570 160 015 {37000 3730 | 3700 260 Pee ae 2390 164 0-2 ee BAe 4830 226 ae a3 3100 =142 0:25 ae gs 6000 234 = Ais 3900 160 0:3 50 bbe 7100 220 ube Ag 4700 160 0-4 ae Be 9600 250 a5 a 6200 150 0-5 see oe 12250 8 265 ote te T9008 — 170 The foregoing Table gives in the first column the observed current-strength, in the first column of each succeeding series the corresponding deflection, and in the second the increase of magnetic moment calculated from it for an increase in current-strength of 0-01 ampere, both in the open condition and when closed. ‘The result is, that in the closed horseshoe the magnetism at first increases in more rapid ratio than the current-strength. With the open magnet for feeble currents (0°05 ampere) the magnetism is about one fifth of the mag- netism produced by the like magnetizing force in the closed magnet; for the double current-strength (0-1 ampere) about one eighth. The increase of magnetism, on the other hand, is nearly constant with the open magnet, 7. e. the magnetism was nearly proportional to the current-strength up to the limit which the wire-coils permitted without too great heating. Next I cut 20 millim. off the projecting poles of the electro- magnet and repeated the experiments. As is seen in the third and fourth columns of the above Table, the magnetism of the closed magnet was much increased by this shortening of the poles ; whilst the magnetism of the open magnet de- creased in a still greater ratio, so that now for a current of 0:05 ampere the above ratio has decreased to 7; and for 0-1 ampere to ss. This disproportionately large decrease is evi- dently to be ascribed to the circumstance that not only has Theory of Magnetism. 243 the resistance to the magnetic disturbance of the surrounding space been increased by the shortening of the magnet, but the magnetizing force has also been decreased, since the coils of wire exerted some magnetic force upon the portions cut off. I endeavoured to determine the length for which the mag- netism of the open magnet would, with a constant current, become doubled, by lengthening the poles with pieces of iron of the same diameter and 10 millim. in height. This con- dition, according to the following Table, was exceeded when five pieces had been added to the poles, corresponding to an increase in length of the original magnet by something more than half. Tasye II. Current 0°1 ampere. Magnetism. Increase. Without addition ......... 1950 if 1 piece on each side......... 2430 480 2 pieces on each side ...... 2805 465 3 a5 Ses ea rCOre 3330 435 4 i rte ere 3750 420 5 5 PA MY asissets 4125 375 We see from the increase in magnetism for each lengthening of the magnet by 10 millim. that there is a considerable falling off in this increase with the number of pieces added. This is, partly at any rate, a consequence of the stronger direct action of the coils upon those of the added pieces which were nearer to the coils, which also explains the too rapid doubling of the magnetism with increased length. Nevertheless these expe- riments render it in the highest degree probable that the magnetism produced by a magnetizing force in an open mag- net is a function of its surface. This was further confirmed by the observation that the magnetism was increased just as much by placing on the magnet-legs pieces of thin-walled iron tube as by using solid cylinders of equal diameter. Closing the tubes by means of iron covers made no perceptible difference if there was no increase in length produced by doing so. To determine the resistance opposed to the production of magnetism by the nonmagnetic surrounding space, it was necessary to compare the resistance offered to magnetic dis- turbance by a space filled with air, or empty, with that of iron. This ratio cannot be constant, since the specific 244 M. Werner Siemens on the magnetic resistance of iron varies with the strength of its magnetization. As is known, and as we may also see from the above expe- riments, the magnetism in a closed electromagnet increases at first more rapidly than the current-strength. The increase of magnetism then soon attains a maximum, and with further increase of current-strength sinks slowly down to a very small amount. In this behaviour of magnetic substances the initial increasing action of the magnetizing force to a maximum is very striking. The position of this maximum is dependent upon the properties of the iron. With softiron the maximum is sooner attained with equal magnetizing force than with harder iron. It is therefore not improbable that this initial feebler action of the magnetizing force is always only a con- sequence of the imperfect softness of the iron. In order to examine this more closely I had two similar rings made, the one of the softest iron rod possible, the other of soft steel. The external diameter was 50 millim. and the internal dia- meter 35 millim.; and they were similarly wound each with two coils, the lower one of 350 turns of wire 0-2 millim. thick, the upper one of 190 turns of wire 0°75 millim. thick. The second coil served for the magnetizing current, the first as induction-coil. The first column of Table III. gives the current-strengths as measured ; the second the corresponding magnetic moments of the iron ring as measured by the de- flection of the reflecting-galvanometer; the third the increase in magnetism for an increase in current-strength of 0-001 ampere calculated from these numbers; the fourth and fifth columns give the same values for the steel ring. TABLE III, Iron.| Iron. | Steel.| Steel. Iron.| Iron. | Steel. | Steel. Ourrent- Increase Increase |; Current- Increase Increase strength.|Deflec | for zo'55|Deflec-| for yo'gq/| strength | Deflec-| for z¢55 |Deflec-| for ;355 tion, | ampere. | tion. | ampere. tion. | ampere. | tion. | ampere. 0:001 3:2 3°2 35 35 0-100 | 1810} 65 430 5:0 0-002 7 3°25 GZ, 37 0:15 4520} 54 760 6°6 0:004 15 4 15 34 0-2 6880} 47:2 1120 72 0:008 36 5:2 29 3°5 0:25 8640] 35:2 1640} 10:4 0-01 46 5 35 30 0-3 9900} 25:2 2500| 17-2 0:02 114 68 wi a7 0-4 11500! 16 4950| 24:5 0:03 196 81 112 4:0 05 12400 9 7000} 380°5 0:04 300 10°5 155 4°3 06 13150 75 8750} 17:5 0:05 410 tel 195 4:0 0-7 13750 6 10000; 12°5 0:06 550 14 245 5:0 08 14250 5 11000} 10:0 0:07 710 16 290 4:5 0:9 14600 3°5 | 11900 9°0 0:08 895 18°5 340 5:0 1:00 =| 15000 4 12550 6:5 0:085 {1015 24 360 4-0 iil 15250 2°5 | 13150 6:0 0:090 |1160 29 380 4-0 1:2 15500 2°5 | 18600 4:5 0-095 aut at 405 5:0 15 16150 2-1 15000 4:6 Theory of Magnetism. 245 It results from these experiments that the maximum increase of magnetism in the case of the iron ring was attained for a current of 0:1 ampere, whilst with the ring of soft steel the maximum was not reached until the current rose to 0°5 ampere ; and, further, that this latter maximum amounted to only one half of the maximum increase in the case of the iron ring. Since the direction of the current is reversed in each measurement, the residual magnetism could exert no direct influence upon the results of the measurement; but the in- ternal friction, which opposed itself to the rotation of the hypothetical circular currents, must no doubt produce a de- crease in magnetization which would be smaller in the ring of soft steel than the iron ring. It hence appears very probable that, with absolutely soft iron, the maximum action would be attained even with the feeblest currents. We may therefore regard this anomaly which appears in the magnetization of iron as a consequence of the frictional resistance, which hin- ders the rotation of the Amperian circular currents. This resistance will be so much the more peréeptible the smaller the angles of rotation; sincé the work done by friction must be proportional to the angle of rotation itself, and not to the magnetic moment produced by the rotation. The following Table gives the results obtained when, instead of a closed ring, a straight iron bar of equal length and thickness was subjected to magnetization by means of a current of in- creasing strength. ‘The iron bar was provided in the middle with an induction-coil, and, together with this, was pushed into the middle of a magnetizing-coil of nearly double length. In the deflections of the mirror-galvanometer the direct action of the coils upon each other is allowed for. TABLE IV. Current- é Increase for || Current- ; Tnerease for strength. 2 LSUTES tooo ampere. || strength. Des econ: tooo ampere. 0-001 1 12 0:08 1160 16 0-002 22 10 0:09 1320 16 0-004. 44 it 0°10 1480 16 0-008 88 il 0:20 2900 14:2 0:01 109 10°5 0°30 4600 ive 0:02 233 12-4 _ 0:40 6240 16-4 0:03 365 13°2 | 0°50 8000 17-6 0:04 524 15:9 0:60 9720 L7:2, 0:05 688 16-4 i 070 11560 18-4 0-06 844 15°6 | 0°80 13200 16°4 0:07 1000 15°6 1:00 16800 18 246 M. Werner Siemens on the The increases in magnetism, calculated for 0:001 ampere, show here also a small increase with increase of current- strength. The maximum increase could not be attained with- out unduly heating the coil. If the assumption is correct, that nonmagnetic material, in the same manner as magnetic material, is filled with pre- existing molecular circular currents, it is to be assumed that in it, as in magnetic material, there exists a maximum of magnetism. An approach to a maximum of magnetization must then become perceptible with very great magnetic moments of a magnetic field, as in iron. In order to investigate this, I placed two prismatic pieces of iron on the poles of the horseshoe-magnet described, which could be made to approach each other closely. The parallel surfaces opposed were reduced to one square centimetre. The increase in magnetic moment of the magnetic circuit was measured for increasing current-strength. The results are given in the following Table :— TABLE V. _ || Horseshoe closed || Poles fitted with prismatic pieces of iron. Their a by iron plate. distances apart :— 2 BS Tecra 0-1 mm. 1 mm. 35 mm. ne Deflec- k 1 ||\Deflec-| Increase || Deflec-| Increase ||Deflec-| Increase = tion. 7 - oe tion. | per z3_ || tion. | per z3q || tion. | per z35 a Poe alnpere. ampere. ampere. a Bok St SN ES | ie 2. 3. 4, O11) 219 19:9 80 72 49 4:4 37 34 O2U (20) b0z1 193 | 11:3 107 58 78 4-1 0:°53|| 1708 | -380°9 620 | 13:3 313 6-4 217 4:3 0-85)| 2124 13:0 1020 | 12:5 524. 6:6 362 4:5 1:06|| 2292 8-0 1276 | 12:2 680 TA 460 4:7 2°12|| 2640 3'3 2028 fal 1344 6:3 942 4:5 3°18]| 2760 ileil 2400 3°5 1908 53 1380 4-1 4:24|| 2840 0-7 2620 21 2340 4°] 1820 4°2 5:30]; 2870 05 2728 10 2576 2:2 2172 33 6°36|| 2980 0-4 2800 0°7 2700 | 1-2 2440 2°5 The pole-pieces were placed at. distances of 0:1, 1, and 3°5 millim. apart. The current-strength was increased to the highest possible value, 2. e. 6 amperes. As seen from column 1, with a closed magnet the maximum increase occurred with a current of only 0°2 ampere. It is remarkable that with approximated pole-pieces the turning-point for each distance Theory of Magnetism. 247 apart fell nearly at the same current-strength of about 1 am- pere. ‘The increases themselves cannot be in proportion to the distances apart of the parallel faces, since the side faces of the pole-pieces must take so much the more part in the magnetic action the further the parallel faces were separated, and consequently so much the greater must be the magnetic resistance of the interval. That a maximum increase takes place with all distances apart, and that with increasing current- strength this uniformly decreases to a small amount, is a consequence of the large moment of the electromagnet itself, which, in consequence of the small magnetic resistance of the entire circuit, with strong currents approaches its maximum of magnetization. The experiments certainly seem to indicate an increase in the resistance and magnetic disturbance of the nonmagnetic material for very high magnetic moments, but not decisively. For such experiments we must employ electro- magnets of small length and so large section that the resistance of the iron to magnetic disturbance may remain very small in comparison with that of the surrounding medium. The experiments show, however, that a maximum of mag- netization does not occur sooner with atmospheric air than with iron. It follows from this that the strength of a mag- netic field is limited only by the maximum of magnetism in the iron, and that the magnetic conductivity of nonmagnetic material may be taken as constant. Since this value for iron is very variable and the law is not yet known of its dependence upon the magnetic moment of the mass of iron, there is no possibility of comparing the magnetic conductivity of the two in general. Since, however, in the construction of mag- netic machines it is always precisely that magnetic condition of the iron for which the increase of magnetism with increas- ing current-strength is a maximum which is of the most im- portance, we must make this point the starting-point of the inquiry. To investigate this point I had two square iron plates made, A millim. thick and 80 millim. square, which could be screwed on sideways to the prismatic movable pole-pieces of the pre- viously described horseshoe-magnets. At a distance of 5 millim. from each other, with a current-strength of 0:1 ampere the plates gave the same increase of magnetism as a piece of sheet-iron of 1 square millim. section which, after screwing off the plates, was made to connect the pole-pieces through a distance of 5 millim. With feeble magnetizing-forces the iron was the more _ powerful, with stronger currents the plates. This shows a magnetic conductivity for iron in its condition of greatest 248 M. Werner Siemens on the magnetic susceptibility of 480 to 500, when that of air is taken equal to 1. The experiment was repeated with greater dis- tances apart of the plates, and further with iron wire, sheet- iron, and prismatic rods of iron, and the same ratio was obtained. The question next presented itself whether this resistance of the air, amounting to some 500 times the resistance of iron, was not in part to be ascribed to the magnetic oxygen contained inthe air. In order to investigate this, | connected two round iron plates of 8 millim. diameter by means of a ring of brass — soldered to them. By means of tubes closed by taps fitting into two openings in the brass ring, it was possible to fill the space between the metal plates, which were 5 millim. apart, with any desired gas or to exhaust the chamber. The iron plates thus connected were fastened to the pole-pieces of the electromagnet, and the magnetic moment of the magnetic circuit measured for different current-strengths. Not the smallest difference could be observed whether the space between the plates was filled with air, oxygen, or hydrogen, or whether it was exhausted as completely as possible by means of the mercury-pump. It follows therefore that the magnetic properties of oxygen, and in general the influence of matter, with the exception of iron and the other so-called magnetic metals, upon the magne- tization only become of influence with very great magnetic moments, such as those with which diamagnetic phenomena occur, and that for nonmagnetic substances, only the geo- metrical conditions of space need to be taken into account in magnetic phenomena. Whether this will not lead us, in ac- cordance with the views of Secchi and Hdlund, to replace the Amperian molecular circuits by ether-vortices which fill all space, but are present in magnetic substances only in greater number or of greater intensity, may remain here undiscussed. The striking fact that a vacuum permits magnetic distribution and attraction like nonmagnetic matter would, however, be explained by it. That space filled with nonmagnetic material as well as a vacuum is affected by electric currents quantitatively exactly in the same way as iron in its condition of greatest magnetic susceptibility, but some 500 times less energetically, is seen from the following experiment. I had two coils made of insulated wire 1 millim. thick, of 87 millim. diameter, and 100 millim. length, and placed them with axes parallel and at a distance apart of 131 millim. The pole-surfaces of these solenoids opposite each other were each covered by an iron plate, which was wound between the solenoids, with an Theory of Magnetism. 249 induction-coil. The iron plates were held fast together by thin brass bolts which traversed the axes of the solenoids. The two solenoids and the two iron plates formed together a closed horseshoe-magnet, whose magnetic moment was to be mea- sured by means of the induction-coil on the iron plates. In the following Table VI. these measures are brought together. It will be seen from the table that all the phenomena were exactly the same as if the iron plates had been connected by iron cylinders instead of brass bolts. On actually making the experiment with iron cylinders of 4 millim. thickness (which had therefore =}, of the section of the solenoid*), the magnetic moment was, in fact, nearly twice as great as before with a current-strength 0:2 ampere, as shown in the sixth column of the table, which gives the quotients of the deflections with and without iron cylinders. That with feeble currents the quotients are not greatly different from unity, but then rise rapidly to the double value, and then slowly decrease, is due to the property possessed by the keepers of this air-magnet, and the iron cylinder of opposing a great resistance to mag- netization, both with very feeble magnetic moments and with very powerful ones. TaBLE VI. . | As closed | Closed and Ratio of Inten-| Solenoid { As open horseshoe. with iron bolts.) deflections | sity. alone. | horseshoe. Mi B cenee Defi. Incr. | Defl. Incr. | Defi. Incr. | Defi. Incr. 0-01 Sy <5 Bye ar be & 65 65 1:18 0:05 270 855 295 61 380 79 1-27 Pere oe. 52 580 ~=62 640 68 | 1000 124 1:56 0-15 900 64 | 1020 76 | 1920 184 1:88 0-20 1236 67 13892 74 2864 189 2-06 0°30 $928) 018.0) 2160. | 77 4480 162 2:07 0°40 2616 69 | 2960 80 5850 31387 1:97 W507) 258 8 85°2° | 3360. 76 1 3800 84 7200 185 1:89 0°75 ZION) | GOTS. OO! 10250 122 1:68 1:00 7240 78 | 8400 93° | 12880 105 1:53 As a direct proof of the correctness of the assumption that in an iron bar round which electric currents circulate only so much magnetism can be produced as is connected with the sum of the magnetic moments of the air or space in contact with its surface, the following considerations may be men- * If we take the diameter of the active air-cylinder as extending to the middle of the coils, then the ratio of sectional areas aban 2G air 9560 250 M. Werner Siemens on the tioned :—If an iron cylinder of radius 7, regarded as of infinite length, is, anywhere sufficiently far from the ends, encircled by a coil of wire, and if we denote by y the magnetic moment which a current flowing through this coil gives to the unit section at any desired distance « from the centre of the coil, then the magnetic moment of this section is 7°my. This magnetic moment must become smaller as w increases, and, if our theory is correct, by so much as is connected with the moment of the layer of air in contact with it, or the increment dz. Hence the differential equation —rndy=2rrdzy, Bila Oo ® lid yy? e log y Te Nees holds good if ¢ denote the interval for which integration is to be performed, or Uae log ag C, and for equal displacement, with rods of different diameters 2r and 2p, loo” : loo =p: r. OSG oS Te These equations show, first, that for the same iron cylinder the ratio of the magnetic moments of two sections equally distant from each other is constant upon the whole halt- cylinder ; that therefore also equal displacements of a test coil must always result in equal percentage decrease in magnetic moment. They show, further, that with rods of different thick- ness, and for equal displacement of the test-coil, the logarithms of the ratio of moments vary inversely as the diameter of the rods. In writing the differential equation, however, the as- sumption is made that the moment of the layer of air in con- tact with the surface of the rod depends only on the moment of the unit section of the rod at the point in question. ‘This would mean that the resistance to magnetic disturbance of all external magnetic circuits was the same. But in fact the disturbing action takes place between each element of the surface of one half of the rod and all the oppositely magnetic points of the other half. It is therefore also dependent on the distance from the centre of the rod. This source of error will become so much the more important the less the distance from Theory of Magnetism. 251 the middle of the rod to the point at which the displacement through the distance c takes place. TABLE VII. | Tebbaiide @ 9 millim. | @ 6 millim. @ 3 millim. _ | SS ea | centre ofl! Deflee- | Y% | Deflee- | Y. || Deflee-| ¥ © FOC || tion y. ¥, ‘|| tony. Yn tion y Ue millim, | | 90 4268 0032 || 4054 0:057 290 0-112 100 3960 0-037 || 3558 0052 222) |, OFEG 110 3640 0:035 | 38160 0°052 168 | 0121 120 3360 0-035 2800 0059 130 Orit 130 3100 0-038 2440 0:053 100 0-114 140 2840 0:032 || 2160 0°056 80 0-097 150 2640 0-038 || 1900 0-048 60 0°125 160 2420 0-037 || 1700 0:058 170 2220 0:028 | 1488 0°052 180 2080 0-039 1320 0:056 190 1900 0-033 1160 0-058 200 1760 0-040 1016 0-060 210 1605 0-040 884 0-059 220 1465 0-032 772 0-052 230 1360 0-035 684 0-051 240 1260 0:036 608 0-061 Mean value........- GON. Me feces. (Oy Oats taal ae a toe 0114 | Mean value <1) ,4ar 3 , Es, of cod $0105 AMA | OTTO Ne sees 0-114 The above experiments confirm the assumption that there is no such thing as free magnetism, but only bound magnetism, and that a magnetic force can produce in magnetic bodies only so much magnetism as is bound in them and in the sur- rounding medium by magnetic distribution in the form of closed attraction-curves with equal magnetic moment in each section. This mode of regarding the matter is exactly analo- gous to the theory of electric molecular distribution; and hence the laws which hold good for this may be applied to magnetic distribution; and, by the aid of the coefficient 480, which ex- presses the ratio of the resistance of air to that of iron, the ‘influence of the mass and form of iron to be employed in the construction of a magnetic field may be determined. If an iron bar, upon the middle of which a magnetizing force acts, may not be regarded as endless, the formula calcu- lated for the endless bar, 252 M. Werner Siemens on the s not directly applicable on account of the magnetism of the end-surfaces. : The distribution of magnetism in a bar of definite length is quite different if the magnetizing force acts equally on all parts of the bar. The decrease in magnetic moment from the middle of the bar towards the ends loses then its logarithmic character, and assumes the form of a catenary (as already shown by Rees), or nearly that of a parabola. In a rod 150 millim. long and 7:70 millim. diameter, which was enclosed in a glass tube of double length uniformly wrapped with a magnetizing-coil, the magnetic moment of each section could be determined by means of an induction-coil wound over the middle of the tube, when the direction of the magnetizing- current was reversed. In the following Table the magnetic moments are given for the same rod at distances of from 20 to 70 millim. from the centre when the bar was uniformly magnetized, and when magnetized at the centre. The current-strengths were so chosen that the magnetism at the end of the rod was nearly the same in both cases. Distance x of the secondary coil from the centre of Deflection when | Deflection when magnetized uni- | magnetized at the ana formly. middle. millim millim. millim 2 287 463 30 263 378 40 233 302 50 195 229 60 145 160 70 87 92 Calculating from the equation to the parabola 22 Yy a 2p, the deflections of the second column for uniform magnetization give for 2p the values 23, 22, 22, 23, 23, 22. Calculating from the numbers of the third column by means of the for- mula 2 loo a3 oy ae the quotients 7 for a constant displacement of the induction- 1 Theory of Magnetism. 253 coil of 10 millim., we obtain the numbers 1°25, 1°25, 1°32, 1:4, 14. The ratio of the magnetic moments of points of the rod equidistant from each other is therefore not constant, as in the case of the endless rod, but increases as we approach the end of the rod, as indeed was to be expected. Van Rees found that in a homogeneous prismatic magnet the magnetic moments of the sections decrease parabolically, as with the uniformly magnetized iron bar. This, however, holds good only for those magnetic bars to which, in the process of magnetization, a uniform moment has been com- municated through the entire length. As soon as the magne- tizing force has ceased to act, all the molecular magnets have the same tendency to return again to the unmagnetized con- dition, whence at last the same condition of magnetic equili- brium results, as with the uniformly magnetized iron bar. Lastly, I should like to make a few further remarks on a previous communication of mine *. I proposed the theory at that time, that the molecular mag- nets assumed in the Ampére-Weber theory must consist each of two elementary magnets or solenoids close together with opposed poles, capable of free rotation together in any direc- tion without meeting with resistance, but directed by external magnetizing forces, and separately rotated, as would be the case with astatic pairs of needles capable of free and independent rotation. I did not then know that Stephan had already ex- pressed the same view, and accompanied it by important mathematical considerations. Now, in accordance with the theory explained above, the Amperian theory must be extended as already mentioned, by supposing all space to be filled with paired molecular solenoids, or, if we adopt Hdlund’s view that the electric current consists in ether in forward motion, filled with ether vortices, and that these are present in magnetic material in greater numbers than in nonmagnetic material. Since, now, a magnetizing force acting upon the mole- cular magnets only exerts a perceptible influence on the rota- tion apart from each other of the paired elementary magnets when all the neighbours in the magnetic circuit follow the motion,and so are able to produce a closedsystem of equilibrium capable of mutual attraction, it follows that the rotation di- rectly produced by the magnetizing force must be very small in comparison with the mutual strengthening of the rotation in the closed magnetic circuit. The magnetic moment pro- duced must thus be essentially the product of the mutual strengthening of rotation of which the magnetizing force is the cause. Here the difficulty is presented that the rotation * Loe. cit. p. 703. Phil. Mag. 8. 5. Vol. 19. No. 119. April 1885. fi 254 Prof. Oliver Lodge on the Seat of the ceases again, in the absence of coercitive force, as soon as the magnetizing force ceases to act. Such a condition of equili- brium cannot be imagined as produced otherwise than by the simultaneous action of attractive and repulsive forces. There must then be produced a nearly, but not quite, unstable equi- librium of the elementary magnets by the mutual action of all the neighbouring attractive and repulsive molecular forces, if the assumptions of Ampére’s theory are to correspond to facts. That a combination of molecular forces fulfilling this necessary requirement can be shown to be possible I do not venture to assert. XXX. On the Seat of the Electromotive Forces in the Voltaic Cell. By Professor Ouiver J. Lopex, D.Sc. [Continued from p. 190.*] TABLE OF CONTENTS. Chapter Il. Argumentative. Page 7. Summary of the theoretical views which can be agreed to, and of the remaining points mm dispute!) 3. e522). 1. 2 eles eee 254 8. Viewsof Clerk, Maxwell :ic:.aciesiaue os bores a ee 256 9. Views of Bellats 0c. Oe oe ed eri oa are esa ee 257 10. Argument that the Peltier effect does not necessarily measure Electromotive Force at junctions ........0010..s0eeeneee 259 11. Hydraulic illustrations of the difference between Peltier and Volta forces, according to the views of the writer .......... 260 12. Summary of condensed statements embodying orthodox views.. 263 7. f ae result of the survey in regard to our special sub- ject of discussion may be summed up thus:—(1) that there is certainly an H.M.F. at the junction of two different substances, or even of the same substance in two different states ; and (2) that the total H.M.I’. of a circuit is the alge- braic sum of all such contact-forces at every junction in the circuit. Ido not know that these two propositions could be passed nem. con., but I believe that, provided they are properly understood, the dissenting minority would be a very small one. Itis probable that Professor Hxner would be in the minority, but I am unable to be sure of any one else. We can also make a negative proposition which will com- mand almost universal assent—viz. that if in the above second proposition, instead of the sum of the contact-forces at every junction, we attend only to the contact-forces at the metallic junctions, the proposition will no longer be true. This fact, that the metallic junctions are insufficient to account for all the E.M.F., was established by Becquerel, De la Rive, and * Scarcely any of this portion was read at Montreal, but it was given in substance to the Society of Telegraph Kngineers on March 26th. Electromotive Forces in the Voltate Cell. 255 others, and still more thoroughly and exhaustively by Fara- day. It is the easiest possible thing to make a number of batteries which shall give a. current without any metallic junction whatever. Faraday gives some thirty of them*. One more certain proposition we can lay down—viz. that whenever a current is produced, the energy of the current must be maintained by absorption of heat, or by chemical action, or by gravity, or by some other such agent, not by mere contact. So much being agreed to, what remains as subject-matter for controversy? This: A voltaic circuit contains at least _ three junctions ; what is the value of the contact force at each of them ? and especially to which junction is the major part of the observed H.M.F. due? Is it the zinc-acid ? or is it the copper-acid ? or is it the zinc-copper? ‘There is no other question. The old chemical and contact controversy has died out, but another controversy remains. Most physicists pro- bably would say today that the major part of the H.M.I’. of the cell resides at the zinc-copper junction. This was Volta’s view, and this is the view of the text-book writers taught by Sir William Thomson. Some few would say at the zinc-acid junction, and among them | must confess myself. It is no question between contact and something else ; it is a question between a feeble energy-less metal-metal con- tact, and an active energetic metal-fluid contact with poten- tialities of chemical action straining across the junction. What is there to distinguish between the two? Hlectrostatic experiments with air-condensers prove nothing. They add up three H.M.F\s, air/M+ M/M’+M’/air, and give you the sum. ‘The experimenters usually assume that M/M’ is what they are measuring, but there is no proof to be given in sup- port of the assumption, except that if you substitute water for air the effect remains almost unaltered ; but then water con- tains oxygen as the active element the same as air does. Well, then, it may be urged, the effect is the same in vacuo and in hydrogen as in air ; and to this I answer, Not proven. Can any further assertions be made with reference to elec- troscopic experiments as bearing on voltaic theory? Yes, it can be asserted that by adding up the Volta effects for A/B, * Exp. Res. ii. 2020. Dr. J. A. Fleming describes another of taese batteries in Phil. Mag. June 1874, and gives some very cogent and read- able arguments in favour of the ‘‘ chemical theory ” of battery E.M.F., sug- gesting that the difference of potential between the terminals of a battery on open circuit is due to potential chemical combination of the metals _ and electrolytes. He does not, however, explain the old Volta experi- ment; and, as Prof. Chrystal has pointed out (Encye. Brit., “ Electricity,” p. 99), upholders of the chemical theory are bound to explain this. 256 Prof. Oliver Lodge on the Seat of the for B/C, for C/D. . . and for Z/A, you arrive at the total H.M.F. of the circuit A, B, C....A. True, but what then? The Volta effect you call A/B is really 3 air/A + A/B + B/air ; that you call B/C is air/B + B/C + C/air ; and that you call Z/A is 3 air/Z+ Z/A + A/air. Add them up, and you get A/B+B/C+. ..4+Z/A, which must be the H.M.F. of a circuit by common sense—. e. without violent experimental disproof, which no one has ever attempted to give. This fact, that the sum of the Volta effects equals the sum of the true forces, in a closed circuit of any . conducting materials, has nevertheless caused persons to sup- pose that air/metal forces are negligibly small. But it is clear that they may have any value they like without affect- ing the truth of the law. They could only affect it if air/M were not equalto —M/air. The experimental proof of the summation law, therefore, establishes that air/M is equal to —M/air, as well as the important fact that the contact-force at each junction is independent of all other junctions of what kind soever. 8. Leaving electrostatic determinations as without bearing on the point at issue, let us ask, Is there no direct and straight- forward way of measuring the actual H.M.F’. at a particular junction without disturbance from other junctions? The answer is most clearly given by Clerk Maxwell*, thus :— “Sir W. Thomson has shown that if [I is the coefficient of Peltier effect or the heat absorbed at the junction by unit current in unit time, then JII is the E.M.F. at that junction acting with the current. This is of great importance, as it is the only method of measuring a local H.M.F. ; the ordinary method of connecting up by wires to an electrometer being useless. This Peltier measurement is quite independent of the effect of contact-forces in other parts of the circuit. But the H.M.F. so measured does not account for Volta’s force, which is far greater and often opposite. Hence the assump- tion that the potential of a metal is to be measured by that of the air in contact with it must be erroneous, and the greater part of Volta’s H.M.F. must be sought for, not at the junc- tion of the two metals, but at one or both of the surfaces * ‘Hlectricity and Magnetism,’ vol. i. art. 249. Abbreviated here, because so easy of reierence. Electromotive Forces in the Voltae Cell. 257 which separate the metals from the air or other medium which forms the third element in the circuit.” And in another place he says* :-— “Tn a voltaic circuit the sum of the H.M.F.’s from zinc to electrolyte, from electrolyte to copper, and from copper to zinc, is not zero, but is what is called the E.M.F. of the cir- cuit—a measurable quantity. Of these three E.M.F.’s only one can be measured by a legitimate process, that namely from copper to zine. If we cause an electric current to pass from copper to zinc, the heat generated in the conductor per unit of electricity is a measure of the work done by the cur- rent, for no chemical or other change is effected. Part of this heat arises from the work done in overcoming ordinary re- sistance within the copper and the zinc. This part may be diminished indefinitely by letting the electricity pass very slowly. The remainder of the heat arises from the work done in overcoming the H.M.F. from the zinc to the copper, and the amount of this heat per unit of electricity is a measure of the H.M.F. Now it is found by thermoelectric experiments that this H.M.F. is exceedingly small at ordinary temperature, being less than a microvolt, and that it is from zinc to copperf. Hence the statement, deduced from experiments in which air is the third medium, that the H.M.F’. from copper to zine is °75 volt, cannot be correct. In fact, what is really mea- sured is the difference between the potential in air near the - surface of copper, and the potential in air near the surface of zinc, the zinc and copper being in contact. The number °75 is therefore the H.M.F., in volts, of the circuit copper, zine, air, copper, and is the sum of three E.M.F.’s, only one of which has yet been measured.” With every word of Maxwell I cordially agree. 9. While on the theoretical aspect of the subject, it may be well to see what Pellat, as one of the best experimenters on it, has to say. Pellat substantially observes as follows :— “ Does the apparent difference of potential between two metals in contact indicate a real difference of potential be- tween them? In all rigour, No! but the slight variation of its value when different gases or even liquids are used renders it extremely probable that there is such a real difference of potential, and that it is very nearly what is measured in elec- troscopic experiments.” As to difficulties connected with energy considerations * Maxwell: Letter to the ‘ Electrician,’ April 26, 1879. Also ‘ Elem, _ Electricity,’ p. 149. + Further on (sect. 23) I point out that this statement is not quite true, but it does not affect the main argument. 258 Prof. Oliver Lodge on the Seat of the and mere contact, he refers to Helmholtz* and Clausiusf, who, he says, relieve him of all responsibility on this head. The fact that the voltaic order of the metals is much the same as their order of oxidizability must have struck nearly everybody, and must also have been felt as a difficulty by the upholders of the efficacy of mere contact. Pellat considers he disposes of it thus :—‘ Since the H.M.F. of a pile is that represented by chemical action, and since by experiment vol- taic contact-forces have much the same values as the H.M.F. of piles, it follows that there is some vague relation between A/B and the heats of combination, say of substitution of one metal for another in a salt (as in a Daniell).” ; He sums up his experimental conclusions as follows :— (1) “Two different metals united metallically are covered, in the state of equilibrium, with electric coats of unequal potential.” (2) “This difference of potential only depends on the superficial coat of metal. It changes notably when the sur- face is mechanically scratched, becoming always more positive. As the scratching effect disappears with time, so does the extra difference of potential. The state of polish of the sur- face is immaterial, but traces of foreign substances, forming a coat so thin as to be invisible, are able to modify the value of the observed effect enormously.” (3) “ The effect depends somewhat on temperature.” (4) “The pressure and nature of the gas surrounding the metals have a very distinct but extremely feeble influence, but, since the effect produced is a lagging one, it is probably due to some secondary cause, and it is probable that the difference of potential is really independent of the gaseous dielectric.” (5) “ The difference of potential between the electric coats on two metals united metallically has the same value as the H.M.F. of an element of a liquid pile formed by these two * Die Erhaltung der Kraft, p. 47, where Helmholtz develops Volta’s original hypothesis about an attraction of matter for electricity, of an amount depending on the kind of matter, so that it gets pulled one way or another across a junction of two dissimilar substances. He points out that the Volta effect is explained if zinc be granted a stronger attraction for electricity than copper has. This view he returns to in his Faraday Lecture 1881, where also he refers to Berzelius’s electrical theory of che- mical affinity. The opinions of Professor Helmholtz are too weighty to be merely referred to in a footnote, but we may have occasion to consider them later. } Die mechanische Behandlung der Elektricitat, chap. vii. §§ 2 and 38, where Prof. Clausius follows up the above idea by considering the réle which heat plays in the matter, and thus hypothetically explains the Peltier effect also. Electromotive Forces in the Voltaic Cell. 259 metals, provided that the E.M.F. is determined before any alteration of the metallic surface wetted by the liquid has occurred ; but these alterations produce themselves very rapidly.” Pellat’s theoretical conclusions being short may also be here quoted, and I will number them on with the others. (6) “ It is extremely probable that the difference of poten- tial between the electric coats which cover two metals con- nected metallically represents the true difference of potential which exists between them. No reason, either theoretical or experimental, can be invoked against the existence of a dif- ference of potential between two metals in contact.” (7) “This last quantity has no connection with the thermo- electric H.M.F. measured by the Peltier phenomenon.” (8) “It has only a vague and distant connection with the difference of oxidizability of the metals.” Concerning these propositions, I may remark that while number 2 is likely to annoy contact theorists (though I know they have methods of explaining it away), numbers 4 and 5 are calculated to restore their equanimity. The five experimental conclusions I accept as in duty bound, only per- mitting myself to doubt the perfect generality of numbers 4 and 5 under all circumstances; but the three theoretical ones I am unable to wholly accept. Thus with respect to the second part of number 6, I beg entirely to differ from M. Pellat if Lam called on to simultaneously admit number 7. Whether one is prepared to accept any of his theoretical con- clusions or to reject them all, depends upon how one regards them. Ifin the way he himself intended, then I reject them all. If with one’s own interpretation, then I say that the second part of 6 and 8 are true (though for “ only a vague and distant ” I would substitute ‘no’’) ; and 7 is also true if it be held to refer to the quantity first mentioned in number 6, while number 8 refers to the other quantity. Number 6 I should also consider true if the prefix “im ”’ be made to the fourth word. 10. Pellat then proceeds to explain why he considers the Peltier effect to be quite distinct from, and have no relation to, the true H.M.F’. of contact. In explaining this he makes use of a piece of unpleasantly plausible reasoning, which I myself have heard Professor Ayrton use, and which, when unexpectedly suggested, is so painfully benumbing that it is worth while to quote it, and to indicate its weak point. Pel- lat’s statement of the argument is rather long; perhaps it can with advantage be abbreviated. Two metals A and B put into contact are at different poten- tials, the difference A/B being due to and equal to the E.M.F. 260 Prof. Oliver Lodge on the Seat of the of contact. There is, then, at the junction not only the con- tact-force H, but also the equal opposite force —dV, due to the difference of potential established. Hither of these forces alone would resist or aid the passage of electricity across the junction and so give rise to a Peltier effect, but both together will do nothing of the sort; and so if there be any Peltier effect, it must be some small residual phenomenon, or it must be due to some other and totally distinct cause*. Professor Ayrton’s way of putting the argument, which I think he said he got from Sir William Thomson, was some- thing like this. When Q units of electricity are transmitted against a force H, work EQ isdone ; also when they are trans- mitted up a difference of potential V'—V, work Q(V’—V) is done; but, in an open circuit containing an electromotive junction, V—V'is produced by and is equal to H. Hence, at an electromotive junction no work need be done by a cur- rent ; in other words, the existence or non-existence of a Peltier effect has nothing to do with the existence or non- existence of a local H.M.F. The fallacy of the argument, in either form, lies in over- precise specification of locality ; it gratuitously asserts as true for the junction what is only proved to be true for the whole circuit. It assumes that there can be no work done at a junction if it be perfectly easy to drive electricity either way across it—2. e. if there be no work done on the whole. 11. To exhibit the fallacy, consider a hydrostatic analogy. Two vessels of water connected by a pipe in which is a motor of some kind, which, without leakage, exerts a specified force on the water and maintains a constant difference of potentials, but then remains stationary, doing no further work. We typify it feebly in the diagram by an impracticable close- fitting water-wheel driven by a weight without friction. V—V’ is the equivalent of the force exerted at the junction, and everything is in equilibrium. It is pertectly easy for water to flow from one vessel into the other under the influ- ence of the slightest extra force, for W helps the water up the hill V—V’, when the flow is in that direction ; and, when- ever the flow is reversed, it lets the water gently down again, taking all its energy out of it. If water is made to flow from A to B, say by pouring more into A, the weight W is lowered, or energy disappears (heat absorbed) at the junction ; if it is made to flow from B to A the weight is raised, or energy * Thus it may be, suggests Pellat, due to‘ a slight difference between E and —dV produced by the mere fact of a current passing ; 7. ¢. contact E.M.F. with electricity at rest may be slightly different from what it is with electricity in motion. Electromotive Forces in the Voltaic Cell. 261 (say heat) is generated atthe junction. Thus there is a true Peltier effect at the junction despite the existence of V—V’ and its equality to the junction force, and yet no resistance 1s offered to the flow of water either way. Thus is the first form of the argument controverted. Fig. 14, Hydrostatic analogue of the true contact or Seebeck force, and of the real though small difference of potential which it maintains between two metals in contact. A and Brepresent the two metals, C their junction ; W is a weight driving a water-tight wheel until stopped by the dif- ference of potential set up. The hydraulic raising or lowering of the weight represents the Peltier effect. To pump water from A to B by any other pipe would need work to be done equal to Q(V—V’), and to pump water against the force of W, acting alone, would also need work EQ; but when the water goes from A to B wid W, or vice versa, no work is done on the whole. Quite true: but the conclusion that no work is done at the junction by no means follows. Work must be done at the junction in proportion to the force there (by inspection of the diagram); and accordingly the existence or non-existence of a Peltier effect has everything to do with the existence or non-existence of alocal E.M.F. This controverts the second form of the argument. If the argument be now considered upset, are we to pro- ceed to assert that the difference of potential, or force, con- cerned in the Volta effect, and the heat-destruction or gene- ration concerned in the Peltier effect, are closely connected, and in fact different ways of observing the same thing ? By no means. All we have proved is that the Peltier effect accurately and necessarily represents and measures the true contact-force at a junction. True we have considered a difference of potential V — V’ as produced by this contact-force in an incomplete circuit ; and so it is. But nothing has been said to imply that this difference of potential has anything to do with what is observed in electrostatic experiments as the Volta effect. So far from this, I will assert that what is 262 Prof. Oliver Lodge on the Seat of the usually observed when two metals are touched and separated is not primarily a difference of potential between the metals at all. They are at different potentials when separated, no doubt, because they are oppositely charged; but they may have been at the same potential until separated. The real Volta effect is almost independent of the true contact-force, and of the dif- ference of potential which it produces. In other words, a ood Volta effect can be observed when there was no difference of potential whatever between the metals when in contact. According to my view the Volta effect is produced, not by a contact-force at the junction of the two metais, but by a Fig. 15. ae Hydrostatic analogue of the Volta effect, or apparent difference of poten- tial produced by metallic contact, and of the opposite charges but uniform potential which it maintains between two metals in contact. The vessels are covered by air-tight elastic bags differently stretched. contact-force at their free surfaces, between the metals and the air or other medium surrounding them. To represent this hypothesis by a hydrostatic model, we shall have to maintain the difference of level in the two connected vessels, not by a force at the junction, but by a force at the surfaces ; say by using closed vessels and compressed air, or more pictorially by differently stretched elastic membranes or bladders tied over the tops of the vessels. Note that the difference of level in this case implies no dif- ference of potential; and, as before, no work is required to transfer water between A and B. Hence it is not easy to distinguish this case from the former; and this difficulty of distinguishing between the two cases is what has given rise to most of the confusion. The only easy criterion is the non- existence in the second case of any Peltier effect at the junc- tion C. Naturally it is possible and common for the two effects to be superposed, but they are essentially independent. Since the two vessels in the second case are at the same potential, the way to observe the effect is to cut and seal the . Electromotive Forces in the Voltaic Cell. 263 pipe at C, and then show that the vessels are differently charged ; which is what Volta did. The model does not indeed represent the gradual change of potential induced as the distance between the condenser-plates increases; and it is scarcely worth while to complicate the matter by making a more elaborate model. The thickening of the dielectric layer of a condenser, when its plates are separated, corresponds exactly to the thickening and strengthening of an elastic membrane ; and rise of potential in the one case is accurately representable by increase of pressure in the other ; but such considerations belong to general electrostatics, and have no special bearing on our present subject. 12. This is perhaps the most convenient place to introduce the notes or condensed statements which I drew up and dis- tributed at the meeting before the discussion. They were intended to be critically exact (allowing of course for mistakes and possible slips) so as to bear analysis; and hence it is probably worth while to reproduce them here with notes and comments. I. Orthodox Statements believed by the writer to be true in the form here set down. A. Volta. i. Two metalsin contact ordinarily acquire opposite charges”; for instance, clean zinc receives a positive charge by contact with copper, of such a magnitude as would be otherwise pro- duced under the same circumstances by an E.M.F. of about 8 volt. ii. This apparent contact H.M.F. or “ Volta force ”’ is inde- pendent of all other metallic contacts wheresoever arranged; hence the metals can be arranged in a numerical series such that the “ contact-force ’’ of any two is equal to the difference of the numbers attached to them, whether the contact be direct or through intermediate metals. But whether this series changes when the atmosphere, or medium surrounding the metal, changes, is an open question : on the one side are ex- periments of De la Rive, Brown, Schulze-Berge; on the other side, of Pfaff, Pellat, Thomson, Von Zahn }. It certainly changes when the free metallic surfaces are in the slightest degree oxidized or otherwise dirty. And in general this “Volta force’’ is very dependent on all non-metallic contacts. iii. In a closed chain of any substances whatever, the * Observe that it is not said that two metals in contact acquire different potentials. Such difference of potential I believe to be only apparent. Compare figs. 14 and 15. + I put Von Zahn on that side because he himself considers himself there, and because the great bulk of his experiments lean decidedly that way. 264 Prof. Oliver Lodge on the Seat of the resultant H.M.F. is the algebraic sum of the Volta forces measured electrostatically in air for every junction in the chain : neglecting magnetic or impressed H.M.F. [| Verified most completely by Ayrton and Perry. | B. Thomson. iv. The H.M.F. in any closed circuit is equal to the energy conferred on unit electricity as it flows round it. [Neglect magnetic or impressed H.M.F. in what follows. | vy. At the junction of two metals any energy conferred on, or withdrawn from, the current, must be in the form of heat. At the junction of any substance with an electrolyte, energy may be conveyed to or from the current at the expense of chemical action as well as of heat. vi. Ina circuit of uniform temperature: if metallic, the sum of the E.M.F.’s is zero by the second law of thermo- dynamics ; if partly electrolytic, the sum of the E.M.F.’s is equal to the sum of the energies of chemical action going on per unit current per second. vii. In any closed conducting circuit the total intrinsic H.M.F. is equal to the dynamical value of the sum of the chemical actions going on per unit of electricity conveyed (3J6e), diminished by the energy expended in algebraically generating reversible heat. viii. The locality of any E.M.F’. may be detected, and its amount measured, by observing the reversible heat or other form of energy there produced or absorbed per unit current per second. [This is held by Maxwell but possibly not by Thomson *, though its establishment is due to him. | II. Statements believed by the writer to be false though orthodox. ix. Two metals in air or water or dilute acid, but not in contact, are practically at the same potentialf. [Sir William Thomson, Clifton, Pellat. | * The only reason which I can think of as likely to have caused Sir William to doubt or deny the validity of this proposition is given and, I hope, refuted at sections 10 and 11. + The truth or falsity of this statement may be held to depend on a question of words, viz. the definition of potential. Sir William at the meeting said he had always defined potential as the work done in bring- ing a unit charge close up to, but not eto, the body. This definition explains some apparent inconsistency in one or two of his utterances which I had never quite understood. But seeing that there is no difficulty what- ever in giving a charge up to a metal body, but rather the contrary, why not define its potential in the more simple manner which followers of his have unconsciously, and I believe universally, adopted, not knowing that they were thus putting themselves out of harmony with him? Given his definition, so that the potential of a body means really not its potential Electromotive Forces in the Voltaic Cell. 265 x. Two metals in contact are at seriously different potentials (i. e. differences of potential greater than such millivolts as are concerned in thermoelectricity). [This is held by nearly everybody™. | xi. The contact-force between a metal and a dielectric, or between a metal and an electrolyte such as water and dilute acid, is small}. [Ayrton and Perry, Clifton, Pellat, and probably Sir William Thomson. | Chapter III. Theoretical. Page do, Statement of the writer’s OWN VIEWS .....cescce es eeneeenes 265 14, Example of the calculation of a Volta-effect ........ ... ese 267 15. Attempt to mentally represent the action of atmosphere on metals at the instant of contact. Mode in which two Volta plates may Peed AGA CONGONSED, oo. ew kc cine eset ence ee t 268 16. Qualifications and doubts respecting the precise calculation of Volta-effects even for absolutely clean pure metals .......... 270 17. Calculation of a series of metal-air contact-forces ; 2. e, of an abso- eem Oki SOMICS IN, AIT OF Wate? «6. .js0 ee eure es vale we eee ewes 272 18. Calculation of Volta series in other media, such as chlorine and SLL br BiegW a sted Sea einaee tr Sama neta we taenrer 275 PREM MM EMMBING ECM is os oe sls ak esse Ree bes Abie ta cae kk eben es 279 13. Before proceeding to the statements embodying my own views, it will be more interesting if I try to explain in a fuller and more connected manner what they are tf. Let us regard the air as a dielectric bath of oxygen, in which metals are immersed, and picture a piece of zinc sur- rounded by oxygen molecules which are straining at it, and but the potential of the medium close to it, statements Nos. ix. and x. are undoubtedly true; and No. xi. is also true, I suppose, for it then only means that there is not much E.M.F. between the medium close to a metal and that at a little distance. * It is much more natural to suppose that the potential of a metallic conductor is uniform, whether it is homogeneous or not. Indeed, it is not only more natural, but it is true, that two parts of a conductor can only differ in potential by reason of an E.M.F. located at the junction. Now there usually isan E.M.F. ata junction, but itis only of such a magnitude as is concerned in thermoelectricity. This, indeed, does produce a difference of potential between the metals, but nothing else can. N.B. Always provided that by “the potential of a metal” is meant that potential, and not the potential of air near it. ; + The experiments supposed to establish this, really prove only that there is very little difference between the air and the water in which a metal is partially immersed. I do not quite know how to understand, on Sir William’s plan, the potential of a metal which is half in one medium and half in another. { The reason I set them forth at length is because I had no time at the meeting both to open the discussion and also to properly express my own ideas, and Sir William Thomson was kind enough to tell me to write out the paper completely, and to explain the position I took up fully. This, therefore, I have endeavoured to do. , 266 Prof. Oliver Lodge on the Seat of the endeavouring to combine with it. They may indeed partially succeed ; but suppose they do not, we have here a strong potential chemical action or chemical strain, which must pro- bably be accompanied by some physical phenomenon. Now remember that oxygen is an electro-negative element; and without endeavouring to examine too precisely what significa- tion is involved in that statement, it will be not out of accord with orthodox views if we assume that it means that at least any dissociated oxygen atoms are negatively charged, each with the characteristic charge of a freedyad atom. Granting something equivalent to this, without pressing the form of expression too closely, we perceive that the strain of the oxygen towards the zine will result in what I metaphorically call a slackening up, or attempted compression, of the nega- tive electricity in it; 2. e. in a rise of negative potential. We may therefore say that zinc is at a lower potential than the air surrounding it, and that the step of potential in crossing the boundary from zine to air is closely connected with the chemical affinity between zinc and oxygen. Observe that this step of potential does not obviously nor probably depend on the amount of oxygen present. It is possible that a few million molecules may be as effective as a large number. Note also that the step of potential is by no means caused by actual oxidation : in so far as the zinc surface is tarnished by oxidation the strain will be diminished and the step of poten- tial become less. Nothing is said here about the possible effect of the nitro- gen, because it is simplest in the first instance to ignore it, though whether experiment will justify this simplicity or not, I do not yet know. 7 We may go further and assert that if in general the chemical] affinity of two substances can be measured by their energies of combination, then the step of potential in the present case may perhaps be calculable from the heat of com- bustion of zinc. And one may justify this assertion thus. Let an atom of oxygen combine with an atom of zinc; it will generate an amount of heat h, and its characteristic charge, g, will be given up to the zine and will thereby fall down the step of potential, v, which separates the zinc from the air. Mow if — we suppose that the heat h is the representative and equivalent of the fall of energy q v, it follows of course that Jh =. qg Make the hypothesis and see what comes of it. Electromotive Forces in the Voltaic Cell. 267 14. The oxidation energy of zinc per gramme-equivalent (2. e. 65 grammes of zine or 16 of oxygen) is, according to the determinations of Julius Thomsen, Andrews, and Favre and Silbermann, 85,430, 84,825, and 83,915 respectively.. The amount of electricity needed to deposit a gramme- equivalent of zinc, or of any dyad- element, is, according to the modern determination of Lord Rayleigh *, 19,320 units. Hence the value of " which is a ratio evidently independent of the number of atoms dealt with, lies between $2498 and $4000 probably. Let us say it is $399° or 4:4. Now J in absolute measure is 42 x 10°; so the value of »v, which is (—) according to the above hypothesis, comes out 1°85 x 108, that is 1°85 volt. This then, I say, is the step of potential between zinc and air. (To avoid circumlocution I will henceforward speak as if the above hypothesis were admittedly true, and all I now say stands or falls with it.) All clean bright zinc is thus about 1°8 volt below the potential of the air near it; tarnished or oxidized zine will exhibit less difference; and it is perhaps possible that perfectly oxidized zinc need show no difference of potential at all be- tween itself and the air. The step of potential by no means therefore depends upon the occurrence of oxidation ; it is the oxidation tendency which causes it, but so far as oxidation actually takes place the step diminishes. Proceed to consider a piece of copper similarly. Oxygen molecules are straining at it also, but with less force. The combustion energy of copper per gramme-equivalent is given by the three authorities already quoted as 37,160, 38,290, and 43,770 respectively. These do not agree well, and it is difficult to know which to take ; but Thomsen’s results are, I believe, generally relied on; so, assuming his, the step of potential "42 x 37200 19320 8 yolt. This then is the amount by which clean bright copper differs from the air. Oxidized copper will differ less. Com- paring this value for copper with that just obtained for zinc, we perceive that a piece of zinc and a piece of copper are, when separate, not at the same potential ; they differ by about a volt from each other. If the zinc is oxidized, they differ less : if the copper is oxidized, they differ more. between copper and air will be volts, that is about * “4-025 ovammes of silver are deposited by an Ampére current in an hour” (Montreal Address). This gives the electrochemical equivalent of silver ‘01118, and of hydrogen ‘00010352. 268 Prof. Oliver Lodge on the Seat of the Now put the zine and copper into direct metallic contact, and neglect for the present the third of a millivolt of H.M.F. developed at the junction, which acts so as to drive positive electricity from copper to zinc. A rush of electricity must take place from the copper to the zinc to equalize their potential ; it is impossible that they can remain at different potentials when directly united : all parts of a conductor must be at a uniform potential, and the rush has taken place because they were not so when put into contact. 15. Picturing to ourselves the effect as produced by the straining oxygen atoms, we shall perceive that they could not get at either metal when separate: first, because they sur- rounded it everywhere, and strained equally on all sides ; and second, because, being all charged with negative electricity, they could not move in on all sides at once without, so to speak, compressing the electricity in the body and giving it an absolute charge. But directly the copper touched the zinc the oxygen atoms were cleared away at the point of contact, and the stress of those at the rest of its surface was no longer counterbalanced. Moreover, they can now all move nearer to the zinc because a way of escape for electricity is provided into the copper, whose surrounding oxygen atoms will be thus driven back somewhat further from the surface, until the dielectric strain, assisting the chemical strain on the copper surface and opposing it on the zinc surface, prevents further displacement, and equilibrium is again attained. The electri- city which escaped from the zinc to the copper was negative electricity (oxygen being essentially an electro-negative ele- ment), the negatively charged oxygen atoms have moved a little nearer to the zine than their normal distance: 2. e. the thickness of its layer of negative electricity is reduced, or its surface is positively charged; the negative layer on the copper has been slightly thickened—its surface is negatively charged. This is a pictorial way of representing the process, and may be regarded as somewhat fanciful; it is, however, the way in which the theory originally occurred to me, and it permits more insight into the processes than a mere statement in terms of potential can ; though it may well be that the imagined processes are but distant likenesses of the real ones. The oxygen atoms have moved nearer to the zinc; itis now more easily oxidized than before. ‘The copper, on the other hand, is by contact with zinc somewhat protected. Observe that the contact has not developed any force ; it has only, by sweeping away the oxygen from the point of contact, enabled previously existing forces to do work and produce their effect. Electromotive Forces in the Voltaic Cell. 269 The air surrounding the metals in contact is in a state of slight dielectric strain, such as would be produced by two pieces of any one metal of similar size and position, charged so as to differ in potential from each other by a volt. Zinc and copper plates in contact may therefore be regarded as the plates of a condenser, but they form a peculiar con- denser, for they are not really at different potentials ; the whole step of potential which throws the air into its state of dielectric strain is located on their bounding surfaces. Let s and s' be the electrostatic capacity of the zinc and the copper respectively ; think of them as two independent spheres united by a fine wire; and let x be their common potential ; then the zinc has, by the fact of contact, gone up 1°8+.«, and the copper has gone down #—°8; and, since the quantity of electricity which left the one went to the other, it follows that— s(1'8—2z)=s! (x—°8) os os pr ere There is no necessary relation between s and s’ in general, but in the ordinary form of the Volta experiment the two plates are of equal size and shape; in which case s=s', and x=1°3 volt below the potential of the unconstrained air. All this is wholly unlike a condenser investigation. To treat it as a condenser we must consider the air-surfaces close to the two metals as the plates of the condenser, and we can then speak of its electrostatic capacity S in the ordinary way, and say that it is in the present case charged with the H.M.F. of a volt. The quantity of electricity on either plate of such a con- denser is § (1°8—°8) or §; hence s (1°8—wx)=s' (v—'8)=S (1°8—'8). And the general relation between the three 8’s is like that of two Leyden jars in cascade, viz., or me Re ~ sts! If the two pieces of metal are circular disks each of radius 7, 2 and at a distance z apart, the value of S is of course - 5 In Volta’s form of the experiment, two plates are put near each other, connected for an instant, then removed from each other, and the potential of one of them observed. This Phil. Mag. 8. 5. Vol. 19. No. 119. April 1885. U 270 Prof. Oliver Lodge on the Seat of the S (1°8—:8) StH measures , where 2 is the capacity of the electro- meter used. In Pellat’s form the charges acquired by contact are neutralized, and the oxygen atoms driven back to their normal distance, by an extraneous Hi.M.F. carefully adjusted until the plates, after separation, exhibit no charge. This measures 1:8—°8 directly. : 16. So far I have spoken as if I were sure that (granting the hypothesis) the potential of clean zinc is 1°8 volt below the air; but I am not really sure that this is anything better than an approximation. The fact that no actual combination occurs makes the matter perhaps a little indefinite. If an oxygen atom unites with a zinc atom, one has a right to say distinctly that g has stepped down v; but suppose they are only facing one another, and wishing to combine, are we justified then in asserting that the step v is ready for ¢ to go down, and that it is the same v as before? It almost seems to depend on whether chemical attraction becomes greater as two atoms approach one another, or becomes less. Suppose, first, it becomes greater, which is the natural hypothesis, then the v calculated from data obtained by per- mitting the combination to occur will be too large for the step of potential caused by the attraction of metal for oxygen over a standard distance. On the other hand, the differential force urging electricity across a junction of two metals, which is observed in the Volta effect, may be somewhat greater than simply the differences in their pull reckoned at standard distances, because the approach of atoms to the zine will increase it on this side, and the recession of atoms from the copper will decrease it on that. Hence the Volta effect may perhaps be expected to agree better with calculation than the air /metal potential-difference does, if this latter could be experimentally observed, which it never yet has been. Next, suppose that chemical attraction becomes less as atoms approach: the step of potential between a metal and air will now be greater than that calculated from chemical data ; nevertheless the Volta effect will be somewhat less than that due to the differences of such steps for two metals, and may thus possibly agree pretty well with calculation. The agreement or non-agreement of Volta effects with calculation does not therefore quite establish the accuracy of our calculated metal-air contact-forces. But we have no right to assume that even Volta effects will agree with calculation particularly well so long as our data are so slender. They have no chance of accurately agreeing unless the metals used Electromotive Forces in the Voltaic Cell. 271 are pure and perfectly clean—a most difficult condition to attain for even a few seconds. Before leaving this subject it may be well to point out that, whereas the calculation of a Volta effect depends on data obtained by allowing oxygen atoms to approach the metal so as completely and actually to combine, the experimental determi- nation by Kohlrausch’s and similar methods depends on letting the atoms approach somewhat nearer to one metal and recede somewhat further from another ; while the compensation form of the experiment employed by Pellat and others depends upon forcing back and restoring the atoms to their original or standard positions. Now if the views here just expressed have any sense or signification whatever in actual fact, it would be very natural to suppose that the numbers obtained in these three ways might be slightly different. But to specify the direction in which we should expect the differences, if any, to lie would require us to have made up our minds as to the probable variation of chemical attraction with distance. Assuming an inverse variation, the Pellat method should give the least, the Volta or Kohlrausch method the next, and the calculation method the greatest, value for the Volta effect. But all these ideas complicate the matter somewhat, and they are quite possibly unnecessary. If it be considered that we have no data at present, it may be permitted to work on the simplest hypothesis, viz. that the step v is independent of how nearly chemical action has occurred—that it is the same for atoms straining at one another at their normal distance as for atoms on the verge of combination. And it may be argued in favour of this view that we really have some data, viz. these. If it were not true, results obtained by Pellat’s method could not be expected to agree exactly with those obtained by Kohlrausch’s (of which Ayrton and Perry’s or Clifton’s may be taken as the best examples). Now results obtained by these different methods do agree very fairly well; exact agreement cannot be predicated, for the most trifling circum- stances cause large variations in the Volta effect, but no decided disagreement is observable. Again, if it were not true, the Volta effect observed when two metals far apart in the series (e.g. zine and platinum) were employed would be inconsistent with the results obtained by using metals nearer together, say zinc and tin, or tin and platinum ; and if this were so, the metals could not be arranged in the linear series which eighty years ago Volta showed they could be. These arguments throw no light on what may happen just before actual combination, still they a encouraging as far as they go. 2 272 Prof. Oliver Lodge on the Seat of the 17. Let us therefore endeavour to suppress further qualms, and calculate a series of metal-air contact-forces from the heats of combustion ; remembering that all we have to do, in order to convert heats of combustion per dyad gramme- 8 equivalent into volts, is to divide by ee that is by 46,000. But the decision as to what numbers we shall take to repre- sent heats of combustion is a matter of some difficulty, for not only do the numbers obtained by different observers for the same reaction differ, sometimes considerably, but it is not obvious when different oxides are formed which of them we are to consider as most applicable to the case of the Volta experiment. Perhaps one should take the most common or stable oxide ; perhaps, seeing that no combination is supposed actually to occur, and since the metal is, so to speak, in excess, it is most reasonable to take the lowest oxide which the sub- stance will form. It may be that the data are not known for this ; it may even be that they have only been obtained for the hydrate instead of for the oxide. I must therefore do the best I can, and quote several numbers wherever there is obvious doubt. I imagine that J. Thomsen’s are the most reliable when they are available. But it must be remembered all through, that since it is only the tendency to chemical action which is the cause of the Volta effect, whereas combination-heats are obtained by permitting or causing the combination to actually occur, the numbers obtained by calculation are not likely to be quite right; and they may be expected to err on the side of excess, the calcu- lated number being higher than the actual value if directly observed. Energy of Combination of Metals with Oxygen. The Mean ; Heat of} come Ex- ee Metal. Molecule. Authority. forma- | seduced! treme probable | tion. io Volts. values. | value. Thomsen ....-..-. 85430 | 1-85 Joule serene a 77000 | 1:66 VAIL enters ic Zn,O Andrews: (sac. stecn 84825 | 1:84 Favre and Sil- Jee tatty ad } 83915 | 1:82 Zn,O,H,O Thomsen ..seceo-- 82600 Sn,O Andrews.......... 67100 | 1:46 Ti Sn,O,H,O Thomsen ......... 68090 eres 3(Sn,0,) Andrews.........++. 67680 nO,O BY bao iwtnmnasnte ns 69584 Mercury...... Silver Hydrogen ... Potassium ... Calcium Barium Strontium ... Magnesium . Palladium ... Cadmium ... Thallium ... Manganese... Aluminium . Lithium Arsenic eeetereer eocee eres Bismuth...... Electromotive Forces in the Voltaic Cell. Table (continued). Molecule. Authority. Fe,O ean Sicicaceceoes Fe,0,H,O Thomsen ......... 3(Fe,,0,) Be RT ee des 4(Fe,,0, AMOTOW At cnos acess <> Ni,O,H,O Thomsen ......... Co,0,H,O pn ere peer are Cu,O He hasan . ANGTEWS i vee dnoades a EU PBEGS eo Saae vs co Cu,,O Phonasen 1.9. baa- Cu,O DOUIEN dances tse ces ] Hg,O MPHOMIGEN: *).-5.0 5. { Hg,,0 batt oA Scwamiacee Ag., SSS Wine) seen, ree { - de 000 Is ae ee gas Thomsen ’...-..... f os 1 Ria pine atte Fel: 4 Dulong, Hess, he Grassi, Joule, | | Berthelot 2(K,H,O) Thomsen .........13 2(K,H,O,aq.) pe A tes eke K,,O,aq. cg aR RR a WWondsyia2, scesoce:: ( 2(Na,H,O) Mhomsenl? shc/s5ec | 2(Na,H,O,aq.) it: Ciba Ae care < Na,,O,aq. saa Snel a | a,,0 WOOGS® tiscciess0: \ 33 Hypothetical...... Ca,O PROMISE) sgsueci0e: Ca,O,H,O me Ca,O,aq. be Ba,O 5 Ba,O,H,O y Ba,O,aq. a Sr,O rf Sr,0,H,O Et Sr,O,aq 9 Mg,O 9 { Mg,0,H,O %9 Pd,O,H,O 9 Cd,0,H,O Fe 10 5 Mn,0,H,O as 3(Al,,0,,3 H,O) M Li,,O,aq. - 3(As,,0,) ” 4(Bi,,O,) Widods: 2. eins: .: 51530 13200 reduce to Volts. values. e q treme 273 Mean or probable value. * This number for sodic oxide agrees with Thomsen’s value for the hydrated oxide, whereas for K, Ba, Sr, Ca the oxide is distinctly below the hydrate. By analogy, one would expect to have to subtract some 25,000 from the hydrated oxide Na,,O,aq., and this gives the 180,000 which I put down as a hypothetical number for Na,,O. 274 Prof. Oliver Lodge on the Seat of the Numbers obtained from unsatisfactory oxides and hydrates like those of aluminium, arsenic, and bismuth, are not likely to be useful for our present purpose. J know of no better data yet available however. It is now easy to write down a Volta series obtained by pure calculation from heats of combustion. We can then see how far it agrees with the results of direct experiment. The principle on which I determine which of the preceding numbers to select is simply to choose Thomsen’s when it refers to the simplest oxide, and in other cases to take what one can get. Metals about which there is obvious uncertainty, as for instance sodium, aluminium, bismuth, &ec., are omitted. Calculated Volta Series. Lithium and waaae 3°0 Nickel . |. 0 4 p= Bale Potassium. = 2°95 Lead Meer eS Calemm, Ge: 2 ss 284 Thallium’ “> aoe AMO Pepihice: WOae aati eO. Copper .. >“)sieaagel! Tron. 2.4 Oe Eee aot: Mercury. <2 geeaaa BPs) ken. Ree (he) Ceal eet eee Palladium: <2 canes Cadmium) “2 oe. (sales Silver .< . Selle Cobaltse te owe 1°38 To compare this series with those obtained by experiment, we may as well take zinc as the metal of reference, and write down the Volta effect between it and the other metals, first as abstracted from the above table, and then as found by different observers. Strictly, one ought first to subtract Peltier forces from the observed numbers before comparing them with theory; but these forces are too small to make any appreciable difference. hole a Volta Effects in Air. Comparison between Theory and Experiment. Observed by Calculated Pellat. Ayrton and Perry.| Clifton. Metal pair. | from heats of oxidation. Udine Using Clean.) Scratched.| commer- mal- 5 eamated cial zinc ine. Zine :— a 4 Bihar ee eee, See 0 39 25 3h) 28 46 ead .22.020.. “70 or °65 “15 “aul 20 35 Irons es. il er |) -4 56 ‘70 60 74 75 Nickel « ...... 53 47. 63 Copper trn..e 1:04 or fl 86 75 89 "85 Mercury 1:18 aif 1:06 1-20 1:07 Silver cess. PT L-oralb8)|. ol 1-12 Ma IP Latinum ee oa keene ae rs -98 11S Electromotive Forces in the Voltaic Cell. 975 The alternative calculated number sometimes given is merely to show the kind of variation probable in those cases from uncertainty of data. In each case of agreement the calculated number is a little higher than the observed, as was to be expected. No reason occurs to me for the breakdown and apparent interchange, in the case of lead and iron, but such vague guesses as may occur to every one. Measurements of the H.M.F. between clean metals plunged into distilled water or weak acid, have been made by Clifton and by Beetz*. I suppose one is justified in calling them:— Volta Effects in Water. Observed by . Calculated from Metal pair. GHD Or OM GanOs ee Beetz. Clifton. Zine :— WepPer) sic. .c..-s. 1-0 ‘98 82 to 92 ReMRED Rs naan ccna irs 1-23 Pinkinnm _....... 18 or less. 1°52 1-3 (Smee). Sodium amalgam :— Te eee 1-0 ‘78 MRMRCE seccac.s, «. 2:0 1-79 VET occa ta ce esds. 26 2°05 Plating -.......- 2°8 2°31 I do not wish to blink the fact that some of the numbers in the former of the above tables afford a rather poor support to my theory ; but it must be remembered, on the other hand, that they are not relative numbers only that we have calcu- lated, but absolute ; and the fact that the heats of combus- tion reduced to volts are numbers of the same order of magnitude as the Volta effects, is of itself a strong confirma- tion of the belief that chemical strain at the air-contacts is the real cause of the apparent contact-force at the junction of two metals. The agreement of the numbers, though not exact, seems to me too close to be the result of accident. One may, I think, claim that the hypothesis whence the calculated numbers are obtained is justified by the figures as far as they go. It is not put forward as a completed theory, but only asa first step to such a theory. I believe it to be a step in the direction of the truth, but it requires working out and elaborating by a scientific chemist. 18. Not many measurements of metal pairs have been made, even in air; for mere permutations such as copper-tin, tin- silver, &c. follow at once from the numbers given above by Volta’s series-law ; but in gases other than air one has at * Ann. der Physik, x. p. 348 (1880). 276 Prof. Oliver Lodge on the Seat of the present no experimental guidance beyond the barest qualita- tive one given by Mr. Brown, that copper-nickel reverses its sign when changed from air to hydrochloric acid, and that copper-iron is reversed in sulphuretted hydrogen. But satis- factory observation in these gases is difficult, because they not only tend to attack the plates, but they do attack them ; and so a film is formed and everything is rendered uncertain. Another complication results from the fact that, when metals are taken out of air and put into a foreign gas, they are already coated with a film of oxygen, and it is not clear in what way this will affect the action of the new gas. It may have to be replaced almost by substitution ; the affinity to be considered in chlorine, for instance, being something like M, Cl,—M, 0. Ina compound like HCl, the hydrogen also may have to be provided for, the resulting chemical strain being, for instance, M, Clh—M, Cl+ H,, O—2(H, Cl); but the consideration of the hydrogen affinities will not affect dijffer- ences, and therefore will leave comparisons with experiment unaffected. Taking the metals as clean, however, and without air-films, we must suppose the following series to be right. Energies of Combination of Metals with Chlorine ; and Calculated Volta Series in that Gas. Calculated Metal. Molecule. Authority. Ce Volta series, "| in Volts. Zu, Cl, Thomsen, 97210 21 TENG sBonncdee : F. and 8. 100592 . Andrews. 101316 Lead Pb, Cl, Thomsen. 82770 18 nse ho { y F. and 8. 89450 | Fe,Cl, Thomsen. 82050 1:78 Tron je.5.%-- | a F. and &. 99302 BNC OL Ghee cect | Um eeaeeee No data. Cu,Cl, Thomsen, 51630 1:12 Copper ...... a F. and S. 59048 Fe Andrews. 60988 Mercury ...... Hg,Cl, Thomsen. 63160 1:38 Sil 2(Ag,Cl) ” 58760 1-28 ee arcre: af F. and 8S. 69600 2(H, Cl) Thomsen. 44000 96 Hyd 2(H,Cl,aq.) " 78640 Re sh gry 2(H,C1) F. and &, 47566 2(H,Cl) Alvia. 48174 2(K,Cl) Thomsen. 211220 4-62 Potassium... a F. and §, 201920 . Andrews. 208952 Sodium: eee we: 2(Na,Cl) Thomsen. 195380 4°24 This series will hold, as far as differences are concerned, for hydrochloric acid also ; because, whatever effect the hydrogen Electromotive Forces in the Voltaie Cell. 277 affinity may have in changing the numbers, it will have the same effect on all. It is easy to write down the hypothetical series in bromine and iodine in the same way:— Calculated Volta Series in Bromine and Iodine. Metal. In Bromine. In Iodine. Potassium ......... oo 3°50 Zine... 1:74 we aie 2 5 55. o's 3°40 87 RORVE. no x~ ence 1:10 “60 LT “89 23 Hydrogen ......... “40 —13 All this supposes the metals to be perfectly clean, and not covered with a film of foreign gas like oxygen. On the hypothesis that the metal has been taken recently out of air, and that the film of oxygen with which it is covered has to be torn from the metal, though it was not actually combined with it, the Volta series in chlorine or hydrochloric acid would be quite different, and more like this. Hypothetical Volta Series of Air-coated Metals in Chlorine or HCl SS Aes ee eee 1°8 1 ra2 7 gals Senne Sane i=? Wr Gite cs ces des sancwastes cos Tt Copper. .s-.- Solace Shei 9 TSE Grd Se A eae 85 Unfortunately I can get no data for the heat of chlorination of nickel ; but assuming it not very different from iron, the above series gives copper and nickel in the right order, as observed by Mr. Brown, whereas the other one did not. I have no experiments with which to compare the numbers. Calculated Volta Series of Clean Metals in Sulphur or Sulphuretted Hydrogen. Heat of Sulphuri- Metal. zation per gramme Volts. equivalent. Potassium ......... 91276 1:95 ATT See Se ee 41880 ‘87 Pras. 2: sens: anaes 35506 76 Mead st. Se eee 19112 “41 Copper. 4 se..5 18266 39 ERVOR . scxfoee dee faves 11048 34 Hydrogen ......... 5482 12 278 Prof. Oliver Lodge on the Seat of the But it will be observed that this is nothing like the order to be expected in sulphuretted hydrogen ; for it is popularly known that copper is more easily sulphurized in this gas than iron. Now assuming that the metal had been covered with an air-film, and that the oxygen of this has to be replaced by sulphur, the chemical tendency, instead of being M,§S, is something more like M, S—M, O, or possibly M, S—M, O+ H,, O—H,, 8; and either of these will give a quite different order. Data are given on p. 624 of Naumann’s G'melin-Kraut, vol. i., for the neutralization-heats of various bases by H, 8, such as CuO+ H, 8, &e. These are something like what we want, and from them we reckon the following :— Hypothetical Volta Series, in Sulphur or Sulphuretted Hy- drogen, of Metallic Oxides, and possibly of Air-coated Metals. Heat of reaction, Metal. MO-++H,S—MS8+H,0. Volts Silverson Mecesecses 55800 1:20 Mieneuinya =e. 41700 1:04 Copper kaasent.: 31600 68 CAC owes s auras 26600 57 DANO? Soe Pe 19200 ‘Al PPOs eee en hoes 14600 Ol Sodaumalc.:ee- 42 7700 16 The series so obtained gives copper and iron in their proper order ; but it is scarcely likely to be really correct, because it assumes that the oxides of the metals are exposed to the gas rather than the metals themselves. It is quite possible that it is not very incorrect for tarnished metals, 7. ¢. metals coated with a film of oxide ; but for ordinarily clean metals, coated, not with a film of oxide, but with a film of oxygen, it is nothing but a rough approximation, given because we have no better data. It is to be noted that, as the film of oxygen diffuses away, the Volta-effect depending on it must diminish ; until at length the active affinity causing the chemical strain is nothing more than M,S or perhaps M,S—H,,8. A gradual falling off and ultimate even reversal of sign was observed by Mr. Brown in both HCl and H,8. In so far as actual chemical action occurs and a film of chloride or sulphide forms, so far of course also will the effect diminish ; because it depends essen- tially on the unsatisfied chemical strain, not on the accom- plished chemical action. Electromotive Forces in the Voltaic Cell. 279 Additional Note, March 13th, 1885. On page 176 of the March Number of the Philosophical Magazine I quote from Von Zahn and others an extraordinary statement, ascribed to Professor Exner, that a thermopile ceases to work ina vacuum; saying at the same time that I had been unable to find the statement myself in Hxner’s writings. For a sufficient reason as it now turns out, because it is not there. Turning over some back volumes of ‘ Nature’ recently, I accidentally came across a letter from Prof. Exner in vol. xxii. p- 170, December 1880, denying that he had ever said sucha thing, and maintaining that his memoirs were quite clear on the subject of the relation, or rather want of relation, between voltaic and thermoelectric phenomena. This is perfectly true ; Prof. Hxner has expressed himself on this subject with decision, and finds fault with Prof. Edlund for ever confusing the two distinct. things together. In the same volume of ‘ Nature,’ on page 312, appears a note from Professor Young acknowledging that he ought to have been more careful to refer to the original statement, and giving one of the “ Physical Notes” of ‘ Nature,’ p. 156, vol. xxil., as his authority. This “ Physical Note’’ quotes from /’ Hlectricité ; and so the error, however originally manu- factured, gets handed on from one paper to another. One of the memoirs which I have unfortunately overlooked in my historical sketch of the experimental work done in connection with the subject has come to hand this morning, through the kindness of the authors, MM. H. Bichat and R. Blondlot, of Nancy. It was published in the Comptes Rendus (1883), t. xe. pp. 1202 et 1293, and in the Journal de Physique, 2° série, li. p. 533, and is an attempt to measure the Volta- effect for two liquids. The method employed involves the use of three vessels, A, B, C, of which A and C contain one liquid and B the other. A and B are then connected by a liquid siphon with porous diaphragm | the capillary H.M.F. possibly excited by this diaphragm is bad]; and the potential of the air between B and C is then rendered uniform |or, commonly speaking, the potentials of B and C are equalized | by making one of the liquids drip inside a cavity kept moist with the other. A and C are connected by platinum electrodes through a compensation resistance-box and battery to a quadrant- electrometer, and the difference of potential between them measured. The arrangement is highly ingenious, but the difficulties of definite and certain measurement must be considerable. 280 Miss Sarah Marks on the The same physicists have quite recently made a determina- tion, not of the Volta-effect, but of the true contact-force between two liquids, by the use of mercury electrodes ; em- ploying for this purpose a theorem of Helmholtz, that if by judicious polarization the capillary constant of a mercury- liquid surface be made a maximum, then between the mercury and the liquid there is no difference of potential*. Their account of this last determination has not yet been published, but it will appear shortly (before this is printed probably) in the Comptes Rendus. The theorem gives evidently an admirably simple method of measuring liquid / liquid contact-force, if it can be made to work practically. MM. Bichat and Blondlot apparently hope, by a comparison of the two methods, the results of which are quite different (in accordance with the views expressed in the present com- munication), to be able to obtain values for air / liquid contacts. This would be a most important and useful piece of work : the only difficulty in accomplishing it is the difficulty of getting both sets of measurements thoroughly dependable. I hope they may succeed in overcoming all obstacles. [To be continued. | XXXI. The Uses of a Line-Divider. By Miss Saran Marxsf. are ordinary method of dividing a given straight line AB into any number of equal parts (fig. 1), without using a special instrument, is to draw a line AC at any angle to it, to cut off from AC the given number of equal parts AD’, D/H’, &c., to join M, the last of the points so taken, to B, and from D’, Hi’, &c. to draw lines parallel to MB, meeting AB in D, EH, &e. These points D, H, &. divide AB into the required number of equal parts. This is exactly the method adopted in using the line-divider. It consists of a hinged rule with a firm joint, having the left-hand limb fitted to slide in an undercut groove upon the plain rule. Both limbs are bevelled on their inner edges, and the left one is divided both on the bevel and on the top into eighths, quarters, half-inches, and inches, which are consecu- tively numbered, beginning at the hinged end, so that any * Monatsberichte der Berliner Akad. November 3, 1881. + Communicated by the Physical Society. Read February 14, 1885, Uses of a Line-Divider. 281 set may be used. The plain rule has two needle-points on its underside to prevent it from slipping when placed in any Fig. 1. position, and on the top has a single line drawn perpendicular to its longer edges. To divide the line AB into any number of equal parts, say seven (fig. 2): slide the plain rule along the divided limb till its Fig. 2. line coincides with one of the lines of this limb against which the number 7 is marked (it is generally best to use the largest possible divisions), place the corresponding line on the bevel 282 Miss Sarah Marks on the of the limb on the point A, and open or close the rule till the bevel of the undivided limb is on the point B. Now press the plain rule down so that the needle-points enter the paper, and keep it in position. Slide the hinged rule up till the line numbered 6 on the line of reference is coincident with the line on the plain rule, and mark the point where the bevel of the undivided limb meets the line AB. Continue to move the hinged rule up one division at a time till the whole line is divided. It is evident that the ordinary method has been used ; for the divided limb forms a line at some angle to AB, and is divided into seven equal parts, and against the undivided limb I can draw parallel lines through the points of section of the divided limb cutting AB in points equidistant from one another. This is the first method of using the instrument, and is useful in many ways :—to artists, for squaring out their can- vases when they wish to enlarge or diminish their drawings, although the second method would perhaps be best for this if a very large divider were used ; to decorators, who frequently find it necessary to divide lines into given numbers of equal parts in order to get patterns into a certain space; it would also be useful for finding the divisions on the scales of ther- mometers, as the distance between the freezing- and boiling- points is always an unknown length. The second method of using the instrument is this :—Let ABCD be an area to be divided into any number of parts, say five, by equidistant lines parallel to AD or BC. Produce AD both ways: place the bevelled edge of the undivided limb along BC, open or close the rule till the end of one of the lines marked 5 on the bevel of the divided limb is on the line AD. Slide the plain rule up, taking care that it is held high enough for its points not to tear the paper, till its line coin- cides with the 5-line, and press the points firmly into the paper. Now slide the hinged rule up till the division marked 4 coincides with the line on the plain rule, and draw a line along the undivided limb cutting AB and CD. Bring each of the other three divisions against the line on the plain rule, and draw lines as before. These are the lines required. It is evident that, since the angle ABC may be any angle, it may be a right angle, so that lines can be drawn perpendi- cular to AB, dividing it into any given number of equal parts. This method is used in finding the mean pressure in gas- and steam-engines by means of an indicator-diagram. Let A BC D (fig. 3) be an indicator -diagram, H F the atmo- spheric line; GH, HC, tangents at the extremities of the diagram perpendicular to HI’. To find the length of the line Uses of a Line-Divider. 283 which represents the mean pressure of the engine, divide the area EK H C G into ten parts by lines parallel to HC and HB, and equidistant from one another ; bisect each of the areas thus obtained by lines parallel to the last. Let the points where these last lines meet the diagram be aa’, bb’, &e..... Add together the lengths aa’, bb’, &., and divide by 10; the result will give the line representing the mean pressure of the engine. This process of dividing the diagram, first by ten equidistant lines and then bisecting the spaces between these lines, is generally a very troublesome one, effected by means of a system of parallel rulers and a T-square. In the figure the dotted lines are those not required when the line-divider is used. To divide the diagram by means of the rule, place the rule as if for dividing the area by 20 equidistant lines parallel to HC. Draw the first of these lines, and then every alternate one, and the diagram is divided as required. This method of dividing areas is also convenient for draw- ing treads and rises of stairs, joists, roof-timbers. In the third method the divider is used simply as a parallel ruler. As such it has the advantage of having a wide range, and of being firmly fixed at the same time. In graphical statics, where it is often necessary to draw a line parallel to another ata considerable distance from it, set squares have often to be placed and replaced five or six times before the necessary line can be drawn. This instrument will at once draw the line. The range as a parallel ruler may be still _ further increased by having the plain rule considerably longer than the hinged one. 284. Miss Sarah Marks on the The special advantages of this instrument as a parallel ruler may best be seen by drawing what surveyors call the “ give and take line.” When two fields are divided by a curved boundary, it is often required to find a straight boundary which will divide the fields in the same proportions as before. This straight boundary is what is called the “ give and take” line. In order to understand the method of finding it, it will be necessary to recall the method of finding a rectangle which shall be equal to a given polygon. Fig. 4, A Let ABC DE (fig. 4) be the given polygon: produce C D both ways, and join A D and AC. Draw HF || to AD, and BG || to AC, and join AG, AF. Then AAFG is equal in area to the polygon ABCDH. For :.. A’s AF D and AED are on the same base A D and between the same ||’s A D, EF, .. they are equal. Similarly A AGC=A ABC. Having this triangle, it is easy to draw a rectangle equal to it. Now let A1234B (fig. 5) be the curved boundary of a field of which AC, BD are fixed boundaries; it is required to find a straight boundary to replace the curved one through A and B. Place the divided limb roughly parallel to AC, with its bevelled edge nearest to AC, and at a distance about equal to the breadth of either limb from it, and fix the points firmly in the paper. Now move the undivided limb till it cuts AC at A and 1 2 at 2; slide it along till it is on the point 1, and mark the point a where it meets AC. Move it till it is against a and 3, and slide it along till it is against 2, mark- ing the point 6 where it meets AC produced, if necessary. Move it till it is on 6 and 4, slide it till it is on 3, and mark ¢, Uses of a Line-Divider. 285 the point where it meets AC. Move it on to cB, slide back to 4, and mark point d where it meets AC; joindB. dB is the line required, as may easily be seen by comparing the portions given and taken by the respective fields. This line would only divide the fields perfectly accurately as before, if A12, 234, &., were rectilineal angles ; butit is the nearest approximation possible, and the one always used. The divider would also be useful on board ships for drawing lines on charts parallel to other lines at some distance. It would be much better for this purpose than an ordinary parallel ruler on account of its very large range and capability of being fixed. Of course the line-divider can be used in all cases in which parallel rulers are ordinarily used. In summing up, the advantages of the line-divider appear to be these :— 1. Lines of division can be drawn at any angle to the line to be divided. 2, Areas can be divided by equidistant lines parallel to any given line. 3. Since the divisions on the instrument are all equal, they may conveniently be made inches and parts of an inch; and 4, consequently the number of divisions may be made as great as we like without materially increasing the cost. 5. Lastly, the cost of the instrument is small, and it is made by Messrs. Stanley in three sizes—6, 12, and 24 inches in length. Phil. Mag. 8. 5. Vol. 19. No. 119. April 1885. Xx [ 286 ] XXXII. The Logical Spectrum. By A. Macrariane, I.A., D.Sc., RS E.* ie my work on the Algebra of Logic I investigated the meaning of Boole’s analysis by the aid of diagrams. In this paper I propose to make a further use of the same method. When the class of things considered (that is, the universe) is subdivided by not more than three qualities, a modified use of Huler’s circles is sufficient. Let a square represent the universe of objects considered, and let a circle separate those having a particular quality. Diagram 1 represents the two classes formed by the presence and absence of the mark a ; and diagram 2 represents each of the four classes ab, ab’, a/b, Diagram 1. Diagram 2. a’b’ formed by the presence or absence of each of the two marks a and 6. Here the dash is used to denote non, as a’ for non-a. It is a contraction for the complementary expression 1—a. The diagram 38 is quite general, because it represents each of the eight classes abc, abe’, ab/c, ab’, a’be, abe’, a’b’c, a'b’c’ formed by the three marks a, 6, and c. But if we Diagram 3. Diagram 4. attempt by means of four circles to represent each one of the sixteen possible classes formed by four marks a, b, c, d, we shall find that it is impossible. For example, in diagram 4 * Communicated by the Author. On the Logical Spectrum. 287 two possible classes are not represented ; hence the diagram is not general. Another method, which I propose to call the logical spectrum, is capable of representing quite generally the universe sub- divided by any number of marks. Let the universe be represented by a rectangular strip, as in diagrams 5 to 8. Diagram 5. Diagram 6. Diagram 7. a | ~ Ss r SS AES te S = lhe |+| [=|]: S = : a'b’ abe' ab'e a'be abc! a'b'c a'b'c! Diagram 8. By subdividing into two we represent the possible classes formed by one mark a; by subdividing each of these parts again we represent the four possible classes formed by two marks a and ); and by subdividing each of these four parts again we represent the eight possible classes formed by the three marks a, b,c; and so on. This method aliows all the a part to be contiguous ; but the 6 part is broken up into two portions, the c part into four portions, the d part into eight portions. However, the regularity of the spectrum enables us easily to find all the portions belonging to any one mark. I shall apply this method to verify the solution of the logical equations Ufar+by=c}, Ufdz—ey=f} ‘ Here U is the symbol for the whole of the objects considered; it corresponds to the strip of paper in the diagram. The letters a, b, c, d, e, f represent known marks. There are two unknown marks denoted by x and y, which are such that the part of U having the marks a and «, together with the part having the marks b and y, is identical with the part having the mark c; and the part having the marks d and z, excepting the part having the marks e and y, is identical with the part having the mark f. It is required to select the part of U which has the mark wz, and ae the part which has the mark y. 2 288 Dr. A. Macfarlane on the By the ordinary process of solution of simultaneous equa- tions we get : _ cetbf cd—af = ae+bd ae+bd and y = Now, according to Boole’s method, - - _ = A,abedef + A,abedef’ + A;abcde/f + A,abedelf’ + ~ + + + A,a’b'c'd/ef + Agsa’b'c'd’ ef” + Agza'b'c'd' elf +Agsa’b’e'd'ef’; where the coefficients A,, A,,...Ag, are numerical. The coefficient for any term is found by supposing that term coextensive with the universe, and substituting 1 or 0, as the ce + bf RE If U abcdef is identical with the universe, then a, 0, c, d, e, fare each 1, and : case may be, for each of the letters in goggle sl AG ee If U abcdef’ = U, then f is 0 and all the others 1, and A.= According to Boole, these coefficients are susceptible of one or other of four interpretations: 1 means all, 0 means none, ble 9 Means none or a portion or all, and every other coefficient shows that the term is impossible. When I sought to determine the coefficients for # and y by the above method, I found that many coefficients assumed the indeterminate form ; and I found, on verifying the solution by means of the logical spectrum, that some of those terms could not be really indeterminate. Hventually I discovered a simpler method of finding the coefficients ; and the solution obtained by it may be verified by the spectrum. It consists in substituting the special values of a, b, c, d, e, f (due to sup- posing a particular term identical with the universe) in the original equations, and then solving for z and y. The values so found are the coefficients for the terms. 3 For the first term abedef we get ety=l, z—-y=1; Logical Spectrum. 289 from which 2—1 pnd 7—0; hence A, =Ieand, B,=0. For the second term abcdef’ we get aty=1, #2—y=0; hence y is complementary to w and also identical with 2, which is impossible unless the term abcdef’ is null. For the fifth term abcd’ef we get TOY et but y cannot be negative unless abcd’ef is null. For the seventh term, re — to but the latter equation is impossible unless the term vanish. For the eighth term, 2ru—1, -0—O; hence wz and y are indeterminate, but complementary to one another. In the case of the 58th term, we get x and y both indeterminate but identical with one another. These are interpretations which are not conceived of by Boole. For the nineteenth term, 2p t=1; hence Aj is 1 and By, is indeterminate, that is may have any value between 0 and 1. In a similar manner, by solving each of the sixty-four sets of equations the several coefficients are found. In the last case only are both coefficients inde- terminate and independent of one another. I have exhibited the solution obtained by this analysis in the accompanying spectrum (diagram 9). Hach null term is shaded ; each term which is wholly included is white; each term which is totally excluded is black ; and each term which is indeterminate is partly black and partly white. The two complementary indeterminates have complementary parts white, and the two identical indeterminates have the same parts white. The solution is verified by finding whether the az together with the by is identical with the c, and whether the dz, ex- cepting the ey, is identical with the /; and by testing whether any other solution not comprehended as a particular case of that obtained would satisfy the conditions. 290 On the Logical Spectrum. (4 fif' | WG da! é fit f\f e! }! ravanana a é FPS é PIAL e! | al a' vavahaba e' é ralanara e’ MWG ————" Pe Aw \\ WW FIA e! Diagram 9, ALES e’ o’ FSIS £' e! é flelelr e’ é vabahaba e' é ff os SS d e | e ple lelelele e’ a’ é vananana WG e! é tf = peeeer 7 XXXII. On the Quadrant-Electrometer. By J. Horxinson, D.Sc., F.R.S.* N Professor Clerk Maxwell’s ‘ Electricity’ (vol. i. p. 273) it is proved that the deflection of the needle of a vaver 2 C is the potential of the needle, and A and B of the two pairs of quadrants. Desiring to ascertain the value of the standard charge of my instrument, I endeavoured to do so by the aid of this formula, and also by a more direct method. ‘The results were quite discordant. Setting aside the special reasoning by which the formula is attained, we should confidently expect that the sensibility of a quadrant-electrometer would increase continuously as the charge of the jar is increased, until at last a disruptive discharge occurs. In my instrument this is not the fact. As the charge was steadily increased by means of the replenisher, the deflection of the needle due to three Daniell’s elements at first increased, then attained a maximum, and with further increase of charge actually diminished. On turning the replenisher in the inverse direction the sensibility at first increased, attained the maximum previously observed, and only on further reduction of charge diminished. Before giving the experimental results, it may be worth while to briefly examine the theory of the quadrant-electrometer. Let A, B, C, D be the potentials of the quadrants, the needle, and the inductor which is used for measuring high potentials (see Reprint of Sir W. Thomson’s papers, p. 278). Let Q,, Q., Q3, Q, be the quantities of electricity on these bodies respectively, and @ the angle of deflection of the needle, mea- sured in terms of divisions of the scale, on which the image of the lamp-flame is projected. We have the equations Qi= ee ee Qo= —q2A + Go2B—Go3C —quD, 3= —GisA— qosB + qs2C — ga.D, | Q.= — uA —qzaB—GouC ae guD. ) , where quadrant-electrometer varies as (A—B) (c — (1) gx, &c. are the coefficients of capacity and induction. They are independent of A, B, C, D, and are functions of @ only. As above written, they are all positive. Let the energy of electrification be W:— -* Communicated by the Physical Society, having been read at the Meeting on March 14th, 1885. 292 Dr. J. Hopkinson on the 2W = gu’ + Job? + 330” + 44D?” ) — 291,AB = 29;3AC = 2¢u4AD t Ry (2) —2q23BC —29.4BD | — 29340 D Equations (1) and (2) are perfectly general, true whatever be the form of the four bodies. If the four quadrants completely surround the needle, qu=0, O14) Qoay aNd Quy are independent of | ee J33= 913 + Jo3 Now when the electrometer is properly adjusted, the needle will not be deflected when A=B, whatever C and A may be. Hence A—B isa factor of gil , and we have dqu Ades ea 9 tgs dé d6 ~~ ~dé» Aqs3__ i Fae | ) whence adW | dqu Adee dqis 279 =A BY AGg Bag — C8): This should be true of any electrometer having the above adjustment correctly made. But by suitably forming the three bodies A, B, C, further relations between the coefficients may be obtained. The condition of symmetry would give us ae =— ae ; but it is not necessary to assume symmetry. If the circumferential termination of the needle be a circle centre in the axis of suspension (at least near the division of the quadrants), if the needle turn in its own plane, if the quadrants are each approximately a surface of revolution about the axis, and if the radial terminations of the needle be not within the electrical influence of the quadrants within which they are not, conditions closely satisfied in Sir W. Thomson’s electrometer, dqu _ 1 @9s Hoe 8 ale) dgog _ _ 1 4913 de = dO p) Quadrant-Electrometer. 293 If 6 be small, we obtain dW A+B gt =a(A—BY0-=**), the formula in Maxwell. Returning now to our original equation, we have 2W= gyA?+ qo2B? + qe3C? + GagD? —2q,,AB—q3;3AC—2¢,AD — ¢3BC—2q2,.BD +06(4—B)(o—4 3%) 3 2 involving in all eight constants, g,, &c. being now regarded as representing the values of the coefficients in the zero position. Q= gquA— WB—$¢33;0—gquD+a0(C—A), ) = — Q12A+ 922B —4933C — Qo4D —a26(C—B), | Q3= —4933A—$93sB + Y33C + a6(A—B), s=— GuA— GB + 44D. ) ‘We may now discuss a variety of important particular cases. (a) B is put to earth; A then is connected to a condenser, capacity a, charged to potential V: we want to know V from the reading of the electrometer. Here aV —$9330= (a+ qu JA—$G330 +26(C—A), VH=As Mar af(C—A) a a Neglecting A compared with C, and assuming @=(A-B)(C— 5 peeve ve {14214 o}. The apparent capacity of A increases with C. (6) Bisagain zero. A is connected to a source, but is disconnected and insulated when the deflection of the needle is @’; the final deflection is 0: required the potential V of the ane gu V — 39330 + a0/(C—V) = GyA—$q33C +a6(C—A), V=A+ a(@—@')C qu a! ar(1—5) ee Sate saan |. Gi 294 Dr. J. Hopkinson on the We may now consider the methods of varying the sensibility of the instrument (see Reprint of Sir W. Thomson’s papers, p- 280). The methods dealt with are those of Sir W. Thomson, somewhat generalized. (c) The quadrant B is connected with an insulated con- denser, capacity 5, whilst A is connected to a source of elec- tricity :— O=—G2A+ (b+ Yo) B—a8C, aN CAE) therefore 7 p= GA eae) A-3q)—26C; so asl Pye : "6+ du) =a If b=0, we have the first reduced sensibility given by Sir W. Thomson. (d) All methods of using the inductor may be treated under one general form. Let the quadrants A and B be connected with insulated condensers, capacities a and 6; then connect the inductor to a source, potential V; | @) = (gi + a)A— 2B — G14V + afC, O= —gA + (G22 +b) B—quV —abC, 0=r(A—B)O; (+ 9y1922— 924 + 1900 + bu + ab) (A—B) + Gia G12— Y22— 8) — Goal G2 G11 — 2) }V + {29+ Geet qitb+afalC=0 ; whence we have an expression for V proportional to @. Bya proper choice of a and 6, we can make the sensibility as low us we please. Now the whole of these formulze rest on the same reasoning as the equation A+ ] 9) I have mentioned that, in my instrument at least, this equation quite fails to represent the facts when C is considerable. It be- comes a matter of interest to ascertain when the formula begins to err toa sensible extent. Ifa constant battery of a large num- ber of elements were available, this would be soon accomplished. I have at present set up only 18 Daniells. I have therefore been content to use the electrometer to ascertain its own charge 6—r(A—B) (o- Quadrant-Electrometer. 295 by the aid of the inductor, using the 18 Daniells as a standard potential. As the charges range as high as 2600 Daniell’s elements, the higher numbers can only be regarded as very rough approximations; sufficiently near, however, to indicate the sort of result which would be obtained if more precise methods were used. The first column in the following Table gives the ascertained or estimated charge of the jar of my electrometer in Daniell’s elements; the second the deflection in scale divisions caused by three elements ; the third, the coefficient A, deduced by the formula 92=AAC: this coefficient ought theoretically to be constant. I II. IIT 72 (i) 0°35 112 118 0:35 136 140 0-35 178 190 0°35 238 239 0°34 303 288 0°32 383 336 0:30 512 391 0:26 616 409 0°22 813 432 0-18 1080 424 0:13 1312 402 0-10 1728 360 0-07 2124 320 0:05 2634 296 0-037 1704. 353 0:07 1436 304 0:09 1284 412 O-11 876 436 0-17 684 427 0-21 By connecting the jar and one quadrant to 18 elements and the other quadrant to earth, I obtained 0°356 as the value of d, making use of the complete equation @=.(A—B)(o—4+*). It will be seen that this equation may be trusted until C is over 200 Daniell’s elements potential, but that when C exceeds 250 a quite different law rules. The foregoing was read before the Physical Society a few years ago, but I stopped its publication after the type was set up, because I was not satisfied that my appliances for experi- ment were satisfactory, or that I could give any satisfactory explanation of the anomaly. _ The electrometer had been many times adjusted for various purposes before further experiments were made, so that those 296 Dr. J. Hopkinson on the which I shall now describe cannot be directly compared with what goes before. The old experiment was first repeated, and the existence of a maximum sensibility again found. On examination, it was found that the needle hung a little low so that it was nearer to the part of the quadrant below it than to that above. It is easy to see that this would produce the anomalous result observed, though there is reason for thinking it is not the sole cause. The effect of the needle being low is that it will be on the whole attracted downwards; and so the apparent weight hanging on the fibre-suspension and the con- sequent tension of the fibres will be increased. The increase of the tension will be as the square of the potential C; and hence the formula for the deflection will be modified to r A+B io; (c- x) where & is a constant depending upon the extent to which the position of the needle deviates from its true position of midway between the upper and lower parts of the quadrants. By a proper choice of &, the results I previously obtained are found to agree well with this formula. The electrometer was next adjusted in the following way:— The needle was raised by taking up the fibres of the suspen- sion and adjusting them to equal tension in the usual way, and the proportionality of sensibility to charge was tested, the charge being now determined in arbitrary units by discharging the jar of the instrument through a ballistic galvanometer. The operation was repeated until the sensibility, so far as this method of testing goes, was proportional to the charge of the jar over a very long range. It was then found that the needle was slightly above the median position within the quadrants. Increased tension of the fibres from electrical attraction does not therefore account for the whole of the facts, although it does play the principal part. The sensibility of the instrument being now at least approximately propor- tional to the charge of the jar, I proceeded to determine accurately the potential of the jar when charged to the standard as indicated by the idiostatic gauge. In what follows the quadrants, one of which is under the induction-plate, are denoted by B, the others by A. The quadrants B are connected to the case, A are insulated. The jar is connected to the induction-plate, and the reading on the scale noted ; the connection is broken, and the induction- plate is connected to the case, and the reading on the scale again noted; the difference is the deflection due to the charge in the jar. It is necessary to read the scale for zero-charge j= Quadrant-Electrometer. 297 on induction-plate last, because the charging of the in- duction-plate slightly diminishes the charge of the jar, and considerably displaces the zero-reading by giving an induc- tive charge to the quadrant A. It is also necessary to begin with the charge of the jar minutely too high, so that after sepa- rating the induction-plate from the interior of the jar, the latter shall have exactly the correct charge as indicated by the gauge. The deflection thus obtained was precisely 2984, repeated in many experiments. The double deflection given by seventy Daniell cells was 43°6 scale-divisions. By comparison with two Clark’s cells, the value of which I know, the potential of the seventy Daniells was found to be 74°2 volts; hence the potential of the jar is 1016 volts, when charged to the poten- tial indicated by the gauge. The constant » of the instrument was next determined by the formula g=(A—B)(C-AS* ) Four modes of connecting are available for this :-— mw—O—(4-2 yolts, b=: B=C=74:2 volts, A=0 ; a—C—(0, b= 74:2 volte ; B=C=0, A=74:2 volts. In each ease the deflection was 253°5 if the charge on the needle was positive in relation to the quadrant with which it was not connected; and was 247 when the needle was nega- tive. This at first appeared anomalous; but the explanation is very simple. The needle is aluminium, the quadrants are either brass or brass-gilded, I am not sure which. There is therefore a contact-difference of potential between the needle 2 and the quadrants; call it z. Thus, instead of o=—, we have = +rA(F +0) and d=N(—A) (- t)3 this gives 6? fo ON A The result was verified by using fourteen cells instead of seventy: the deflections were 10:0 and 88, which gives the same value toz. It is worth noting that the same cause =0°482 volt. 298 ' Dr. J. Hopkinson on the affects the idiostatic gauge in the same way. Let the jar be charged till the gauge comes to the mark. Call P the differ- ence of potential between the aluminium lever of the idiostatic gauge and the brass disk below which attracts it. The dit- ference of potential between the brass of the case and the brass work of the interior is P+, and between the case and the alu- minium needle within the quadrantsit is P+2«. If, however, the charge is negative, the difference is —P+2z. Hence the sensibility will be different from two causes, according as the jar is charged positively or negatively, till the idiostatic gauge is at its standard. For determining the constant \ we must take the mean of the two results 2535 and 247, that is 250°25. Comparing this with the actual standard charge of the jar, and the double deflection given by one volt 172°4, when charged to the standard, we see that the irregularity has not been wholly eliminated. It appeared desirable to determine the — sensibility of the instrument for a lower known charge. The charge was determined exactly as described above, and was found to be 609 volts; whilst 1 volt gave 107:1 scale-divisions double deflection ; whence in the equation p—A—B)C eee we have, if | Ne OMsla G7 the following as the calculated and observed deflections :-— Calculated 27.0.5 e200 705. NO (ete legos Observed #9. 4. 2002) | LO alge which is well within errors of observation. This deviation from proportionality of sensibility did not appear to be worth correcting, as | was not sure that other small irregularities might not be introduced by raising the needle above the middle position within the quadrants. It appears probable that the small deviation still remaining does not arise from the attraction of the quadrants on the needle increasing the tension of the suspension, but from some cause of a quite different nature, for if it were so caused the capacity- equations would be O,=quA—q12B — 9336 —gu.D + «dC, &c., where » o> ae (A—B) (c-*+*) Now the experiments I have tried for determining 911, qi, Quadrant-Electrometer. 299 &c., are not in accord within the limits of errors of observa- tion, using these equations of capacity; but they are in better adC TRC i have no explanation of this to offer; but in what follows it is assumed that the equations expressing the facts are AC ?=p(A—B), where P= EGP ] Q= guA—gqueB—gquD + bye, Qo= — GA + J22B—924D — Bud, Qu=— quA—quB+ quD. | We are now in a position to determine the various coeffi- cients of capacity : in doing so it is necessary to distinguish the values of g;; and g. when the posts by which contact with the quadrants is made are down and in contact with the quadrants, and when they are raised up out of contact ; the former are denoted by q4,+4 and qo.+ O'o800 accord if, in lieu of the term «9C, we write and hence Bp2=1, Bu2=0°648, Bu? =0°342. Suppose quadrant A be insulated, and potential B be applied to quadrant B; then we have, if @ be deflection which potential B would cause with standard charge, if quadrant A were con- nected to the case, and @ the observed deflection, 0=qiA— B+ Bud 5 o=-(A—B); o= — 3B 3 sop ee Sen Ge ame Ps ut Be” In the calculated values of @ given below, 911; 0°502, Jog = 0°548 Qig=0°293, a=0-°200 for B, = (0-193 for A. whence 300 Dr. J. Hopkinson on the A closer approximation to observation is obtained byassuming the two contact-posts to be of slightly different capacities; the difference given above is no more than might be expected to exist. The jar being charged to standard potential, B was insu- lated, and its post raised,and A was connected to 10 Daniells, for which 0=1808 :— Deflection observed = 293°2, 5» calculated = 293-0. The post of B was lowered to contact :— Deflection observed =467:0, » calculated =466°8. A was now insulated and post raised, B was connected to the same battery:— Deflection observed = 251:0, 5 calculated =251;6, The post of A was lowered to contact :— Deflection observed = 429-0, 5 calculated =428°8. The jar was now charged to a lower potential, for which //= py with B insulated and post raised, and A connected to 30 Daniells, for which 0=5468 :— Deflection observed =925:°0, » calculated=924-0. The post of B was lowered to contact, and A connected to 10 Daniells, for which 6=1808 :— Deflection observed =470°5, » calculated =470°85. A was now insulated and post raised, B was connected to ~ a battery of 30 Daniells, for which 6=5468 :— Deflection observed =798:0, 5 calculated = 800-0. The post of A was lowered to contact, and B was connected to 10 Daniells ; @=1808 :— Deflection observed =437°0, », calculated =435°7. The jar was then charged to a still lower potential, for which #=/4, with B insulated and post raised, and A con- nected to 30 Daniells, for which 02=5468 :— Deflection observed =901°0, » calculated =903°6. The post of B was lowered to contact and A connected to Quadrant-Electrometer. 301 10 Daniells ; 8=1808 :— Deflection observed = 437°0, » calculated =438°7. A was now insulated and post raised, and B was connected to 30 Daniells ; 6=5468 :— Deflection observed =785, » calculated =792. The post of A was lowered to contact and B connected to 10 Daniells ; 2=1808 :-— Deflection observed = 408, » calculated=410. The next experiment was similar, excepting only that the insulated quadrant B was connected to a condenser ; this con- denser consisted merely of a brass tube insulated within a larger tube—its capacity is about 0°00009 microfarad. The jar was at its standard charge. Calling the capacity of the condenser 6, in terms of our temporary unit, we have, as before, age ae gaol tatia—t (yt). b+at 722 +1 When @=1259, @ was observed to be 927, whence b=3°159. We are now in a position to obtain independent verifica- tion of the values already obtained for the constants. Suppose A be connected to the case, that condenser } is charged trom a battery of known potential, such that it would give deflec- tion @ if connected to B, and the charged condenser is then connected to B. Suppose W be the deflection before con- nection is made, ¢ after. Then b(O—b)={92+at1}(p—y). When 6=1439 and w=0, it was found that 6=915. The value of ¢, calculated from the values of the constants already obtained, is 928. When @=1439 and w=—676, it was found that @= +676; the calculated value is 688. A further experiment of verification, involving only the capacity of the quadrant, is the following. The quadrant A being connected to the case, B was charged by contact in- stantaneously made and broken with a battery of known potential, and the resulting deflection was noted. ‘The in- stantaneous contact being made by hand, no very great accuracy could be expected. Let W and ¢ be the readings on the scale before and after the instantaneous contact; then 6—¢ 1 3 ——_ = = |-345: P—-F Q2ta Phil. Mag. 8. 5. Vol. 19. No. 119. April 1885. ¥ 302 Dr. J. Hopkinson on the The following results were obtained :— 6. pr. @ observed. ¢ calculated. 1796 0 763 765 1796 —A93 493 482 We next determine the coefficients q,, and go, of induction of the induction-plate on the quadrants. This is easily done from the deflections obtained with the induction-plate, one or both pairs of quadrants being insulated. First, suppose one pair, say B, are insulated whilst A is connected to the case :— 0O=+ G2 B—qu D—fpd, o= — pB, d= p,D 2 whence ha, iy Ps oot Bu? @ being the deflection actually observed, and 6 that which the battery used would give if connected direct to the quad- rants, the needle having the standard charge. When @ was 12,800 and w=ps, d was 418, whence go,=0°0504. In the same way A being insulated but B connected to the case, @ was found to be 43°6, whence g,,=0°00508. Again, when both quadrants are insulated we have O0= gquA—gqeB—quD+ Bp, O= —qpA + Go2B—guD —Bud, p=(A—B), d=p;D. From the first two equations, (911923 — 9}2)(A—B) —{(G22— G12) 914 — (Gu — 912) 924} D + (922+ Gu—2412)Bub=0 ; ¢= ott. (G22 — 912) 1a — (911 — G12) Goa Mg (911902 =O) + (Goo+ 91 — 2012) Be? In the case when w=ps, substituting the values already determined, we have whence b=8x 0°0142; it was observed with 6=12,800 that 6=183 ; the calculated value would be 182. With a lower charge on the jar, viz. when p=p; x 0°805, with B insulated, A connected to the case, and 6=12,800, it was found that 6=437°5 ; the calculated value is 441. The capacity qi, of the induction-plate is of no use; its value, however, is about 0-004, in the same unit as has been so far used. Quadrant-LElectrometer. 303 The capacity 93; of the needle and the coefficient of in- duction of the needle on either quadrant 4¢33 are also of no use, but the method by which they may be obtained is worth noting. Let quadrants A be connected to the case, and let B be insulated, diminish the charge of the jar slightly by the replenisher, and suppose the consequent deflection be ¢. Let py. and yw’ be the values of w before and after the diminution of charge, as ascertained by applying a known potential-dif- ference between the two pairs of quadrants; we have — 9330 = + 932B —q330’ —Bu'd, where o=—p'B, 933, C—O") = (Gan + Bu”) B, which determine g33, since C and ©’ are known from pand p’. Of course the values of the constants of an electrometer are of no value for any instrument except that for which they are determined in the state of adjustment at the time. Tor any particular use of the instrument it is best to determine exactly that combination of constants which will be needed. Nor is there anything new in principle in the discussion or expe- riments here given; they are merely for the most part the application of well-known principles to methods of using the electrometer given by Sir William Thomson himself. The method of determining the capacity of a condenser by charging it and connecting it to an insulated quadrant has been used by Boltzmann. But the invention of the quadrant-electrometer by Sir W. Thomson may be said to have marked an epoch in Electrostatics, and the instrument from time to time finds new uses. It therefore seems well worth while to make known observations made upon it in which the instrument itself has been the only object studied. Some practical conclusions may, however, be drawn from the preceding experiments. Before using the formula g=(A—B)(0—* 55) it is necessary to verify that it is sufficiently nearly true, or to determine its variation from accuracy. Unless it be sufficiently accurate through the range experimented upon, the electrometer cannot be applied by the methods well known for determining alternating potentials and the work done by alternating currents. ~My pupil, Mr. Paul Dimier, has very efficiently helped me in the execution of the experiments of verification. Y2 [ 304 ] XXXIV. The most Economical Potential-difference to employ with Incandescent Lamps. By Professors W. H. AyRTon, F.R.S., and JOHN Parry, M/.E.* f oes subject in connection with which the accompanying paper is a small contribution is one of considerable commercial importance. It has long been known that the luminous power of an electric lamp increased much more rapidly than the power electrically expended on it; or, that the number of candles per horse-power increased as the lamp was made to become brighter and brighter. Perhaps the earliest experiments on the subject were those published by Sir William Thomson in 1881, and those made by our students in 1880. Since that time (that is, during the last five years) tests of the efficiency of various types of incandescent lamps have been made over and over again by various persons, without perhaps its being clearly realized that such efficiency- experiments by themselves gave us no idea of the commercial value of any particular lamp. It is not sufficient to know that when a lamp is giving out a certain number of candles it absorbs so much power per candle, and when giving out a much larger number of candles it absorbs so much less power per candle; but what must be known in addition is the life of the lamp at each of these two candle-powers, before we can decide whether it is more eco- nomical to use the lamp with the filament at not much more than a dull red or when brilliantly luminous with a bluish tint. For with the filament at a comparatively low temperature, although the efficiency of the lamp is low, its life will be great ; whereas if the temperature of the filament be high, the large efficiency will be to some extent balanced by its short life and the consequent large cost due to lamp renewals. In the ‘ Electrician’ for January 31st of this year M. Foussat gives a table of values of the life ofa 100-volt Edison lamp for different potential-differences; and M. Foussat has assured us that these numbers were obtained experimentally, and not from calculation according to any theory. ‘That the results should lie so nearly in a curve is undoubtedly at first sight a little striking ; but if it be remembered that they are stated to represent the results obtained from the averages of a very extended series of tests, their great regularity is not more striking than is a curve showing graphically the result of mortality tables. We asked M. Foussat whether he had also the results of experiments on the efficiency of the same type of 100-volt lamps, as our own experiments on the efficiency * Communicated by the Physical Society, having been read at the Meeting on February 28th, 1886. Potential-difference to employ with Incandescent Lamps. 3095 of Edison lamps had been made with 55-, 108-, and 110-volt lamps. As, however, he had no such results, and as his tests of lives are the only ones that we now have, and possibly may have, until the completion of the excellent work at present being carried out by the Hlectric-Lighting Jury of the Health Exhibition, we commenced this investigation by endeavouring to combine the lives given by M. Foussat with the results previously published for efficiency. ‘To enable us to do this, we assumed that the life of 1000 hours given by M. Foussat for his 100-volt lamps when used with a potential-difference of 100 volts would be the same as that for our 108-volt lamp when employed with a potential-difference of 108 volts ; or, in other words, we regarded lives given by him as applicable to our 108-volt Edison lamps when each of his potential-differ- ences was multiplied by mae To ascertain the most economic potential-differences, we must proceed as follows :—Let /(v) be the life in hours as a function of the number of volts constantly kept on the lamps, @(v) the number of candles emitted by one lamp as a function of the potential-difference in volts employed, let p be the price in pounds paid for one lamp, and n the number of hours per year that a lamp is kept burning ; then pxn Fe) x Hv) stands for the cost per year per candle, as far as the renewal of lamps is concerned. Next, let H stand for the cost in pounds of an electric horse-power per year for the number of hours an electric horse-power is employed. It is often assumed that H is pro- portional to the number of hours per day that the power is used, or that the yearly bill for power should be based on the horse-power hours, or total energy consumed ; but this idea, which runs even through the Hlectric Lighting Act, is quite an erroneous one. H will be of the form 4+F(n), where A is a constant independent of the number of hours and depending on the rent of the site, capital expended upon engines, dynamos, leads, &c.; and F(7) is some function of the number of hours during which electric power is required,and depends on the cost of coal, superintendence, &c. If the light were only required for one or two hours in a district where rent was very high, h would be the all-important term and F(7) would be unim- portant; whereas if the electric power were required for various _ purposes, for, say, 15 or 20 hours out of the 24, in a place where rent was low but coal dear, (7) would be the important item in the yearly bill for electric power supplied. 306 Professors Ayrton and Perry on the most Economical Let 6(v) be the watts per candie, expressed as a function of the number of volts employed at the terminals of a lamp; then H 7a * PC) represents the cost per year per candle as far as the production of electric power is concerned. The total cost, therefore, per year per candle is xn H Foy x (6) + ag $() pounds, saga and we must find the value of v that makes this a minimum. There are two ways in which such a problem can be solved: the one a graphical method, the other an analytical method. The former may be used by even elementary students, and will be given first. It consists in drawing curves to represent, Lst, J(v) in terms of v, 2nd, O(v) in terms of v, and 3rd, d(v) in terms of v ; and from these the values of /(v), @(v), and o(v) are each determined graphically for many values of v, and the value of A calculated for each of these values. A fourth curve is then drawn, connecting the values of A with those of v, when it is easy to see by inspection for what value of » the expression A has a minimum value. The following is the result so obtained for the 108-volt Edison lamps used for lighting the Finsbury Technical College :— : p is taken at 5s., or £0°25 ; n as 560 hours, the time per year, approximately, during which the lamps are lighted ; H as £5: this is perhaps a rather high estimate for the cost of power, considering that the interest on the steam-engine, dynamos, &c., price of coal burnt, wages of the engine-driver and stoker have to be mainly debited to the driving of the College workshops, sup- plying power for the dynamos worked for experimental purposes; but itwill be accurate enough to take the sum of £5 per year as representing yearly interest on extra plant and the yearly interest on the extra cost of sup- plying one electric horse-power during the 560 hours. Then the value of v which makes A a minimum turns out to be about 106 volts; and on account of the flatness of the curve connecting the expression A with v, we see that in this particular case the annual cost of supplying light is only in- creased by 3°5 per cent., if the potential-difference between the mains be kept diminished to about 104°8 or kept up to about 108 volts. Also, that keeping the potential-difference dimi- nished to about 1045, or increased to about 108°5 volts, increases our total annual cost of lighting by 5 per cent. Potential-difference to employ with Incandescent Lamps. 307 More recently one of our students, Mr. Robertson, has been making efficiency-experiments on some Edison lamps obtained from France ; and by trial he has found some that give 16 candles at about 100 volts, and are therefore pre- sumably of the same type as those employed in the life- experiments given by M. Foussat in the ‘ Hlectrician’ for January 31st. Mr. Robertson’s results from one such lamp are as follow :-— TABLE I. Candles, or 6(v). ee | Volisiorn |. . Watt. 4) or v. Watts. 3 84 56°62 4 87 63°51 5 87°83 66°03 6 90:5 69:05 7 93°d 73°74 10 96°75 79°34 11 97°61 81-01 12 98:04 82°35 14 98-9 85°55 16 100-6 90°54 18 | 101-5 92°37 20 103-6 96°66 22 105-4 100:10 24 107-5 104-28 26 109:2 108-11 28 110 111:10 30 111-4 11363 35 114 118-56 40 115-2 122-11 We are therefore now in a position to take up the problem in a more direct manner, without making any assumption beyond this—that Mr. Robertson’s 16-candle 100-volt French Edison lamp is of the same kind as M. Foussat’s 16-candle 100-volt French Edison lamp. Solving the problem graphically, in the way previously described, and using the same values of p, n, and H—viz. cost of a lamp 5s., number of hours of burning per year 560, and annual cost of an electric horse-power for those 560 hours £5,—we obtain the curve AAA to represent the cost per candle per year as regards renewal of lamps, B B B the cost per candle per year as regards power, and the resultant curve CCC as the total cost per candle per year. The minimum value of this cost appears from the curve CCC to be at about 101°4 volts, and to equal about 11d. per candle per year. If the potential-difference be maintained constantly down at 98:7 volts, or up at 104 volts, then the cost becomes ls. per candle per year. It. will also be seen from the curves that the yearly cost for renewals of lamps is 3808 Professors Avrton and Perry on the most Econonucal Diagram for a. 16-candle 100-volt Edison Lamp. 103 104 lua 106 but a small fraction of the total yearly cost, as long as we are using potential-differences of not more than about 100 volts ; so that when using, with these lamps, this or a lower potential- difference, the actual sum paid for the lamps is not so very serious an item in the yearly lighting bill. But if, on the other hand, we maintain a potential-difference of, say, 104 Potential-difference to employ with Incandescent Lamps. 309 volts constantly at the terminals, then the lamp renewals represent, in our particular case, nearly one third of the yearly expenditure, and consequently any change in the price of lamps becomes extremely important. We find that the simplest expression for the candle-power of this incandescent lamp in terms of volts is ej (O— 8) eS ACE) Thus, for example, it will be found that if the cube roots of the values of @(v), given in the preceding table, are plotted with the corresponding values of v as coordinates of points on squared paper, the points lie in no regular curve so nearly as in a straight line, discrepancies being apparently due to errors of observation, and these errors of observation follow a periodic law which may be of interest physiologically. Or it may be that there really is a point of inflexion in the curve. For the particular lamp in question we find that a=0-0002621, b=62'12 ; or, if the law remains true for a less number of volts than 84, the lowest used in this experiment, then when v=62°12, the candle-power is zero. We do not, however, find that the cube roots of the candle- owers of all sorts of incandescent lamps follow a line-function of the difference of potential at their terminals ; for on exami- ning the results of experiments that have been made with various types of lamps, we find that with the first five of the following set of lamps the law V7 O(v) xv—b is very nearly true. 1. A Lane-Fox lamp . .. . . from 50 to 80 volts. 2. A British Electric Light Co.’s lamp ,, 50 to 68 8. An Edison “7B” 8-candle lamp. ,, 45 to 63 eam ald Swanlamp. .. .. «= sj; 40 to 64_,,, 5. A low-resistance 8-candle Swan lamp ,, 16 to 40_,, Whereas with the next five lamps it is not so true, although for half the range the law might be regarded as true in all the cases. oo Maan lamp... . . |. from 42 to 57 volts: 7. A Maxim lamp . eee tee) Ny yy Oho ROR 8. An old form Swan lamp . 37 20 to 54 9. A high-resistance Swan lamp » 45 t0 90° ,, 10. An Kdison B 8-candle lamp . . ,, 36 to 85 ,, We may here mention that we have found the following plan very useful in helping us to draw correctly a curve at a place ” oP) ) 310 Professors Ayrton and Perry on the most Economical | where there is a sudden bend and an absence of points, deter- mined from experiments to guide us in drawing the curve. Instead of plotting w and y, and obtaining a curve which it would be very difficult to draw correctly, we may by using some simple function of y obtain points which obviously lie in a curve which it is easy to draw. ‘Thus we may plot Vy and x, or “Wy and 2, or logy and w. When the curve connecting y and & is not roughly asymptotic to the axis of a, but to some line parallel to this axis, it is obvious that there is a greater likelihood of obtaining simple curves by plotting Vy--eand x, or Wy+aand 2, or log (y+) and 2, where ais some constant obtainable by inspection, than by simply plotting the function of y alone. The following table gives M. Foussat’s lives in terms of v and the corresponding values which we have calculated of log f(v), log @(v), and of log f(v)@(v) from the values of @(v) given in the previous table. TABLE IT, v. f(v). log f(2). log 6(v). log f(v)A(w). 95 | 3595 3:5557 0-9729 4-5286 96 2751 3-4395 1:0119 4-4514 97 2135 3:3294 1:0485 43779 98 | 1645 32161 1-0851 43012 | 99 1277 31062 1:1199 4-261 100 1000 3-0000 11556 41556 101 785 2:8949 1:1898 4-0847 102 601 2:7789 1:2216 4-0005 103 ATT 2-6785 1:2531 39316 104 375 2-5740 1:2852 83-8592 105 284 9-4533 13152 3°7685 | When log f(v) @(v), and v are plotted as coordinates of points, these points are found to lie so nearly on a straight line that the formula if He)Ae) is found to be true with considerable accuracy, and such a formula lends itself with great ease to calculation. It is quite true that we might have obtained a still more accurate formula than (2) since, as published by Mr. Wright, one of the members of our class, in the ‘ Electrician’ for February 21st, the logarithm of the life of a lamp is shown to be a line-function of the difference of potentials at which it is worked. We may in fact with this particular type of lamp put I(r) =]0'4-Olle Sg al aie aa os with very great accuracy indeed. — LOG ge v—11-697 , : : i : (2) (3) 311 Combining this with (1), we obtain as a more accurate formula, Potential-difference to employ with Incandescent Lamps. ayaa On OB) eree (8) But unfortunately this more accurate formula does not lend itself to mathematical calculation, whereas that given in (2) is very suitable for this, and has a sufficient degree of accuracy for our purpose. In using (2) we are really using for the candle-power O(v) = 1008455 0—2'303 (5) instead of (1). It will be also found that from 95 to 105 volts, the range of volts given in Table II., the values of ¢(v), or watts per candle-power, when corrected for errors of observation, satisfy with considerable accuracy the equation d(v) —3-7 + 1 (Q8:007—0°07667 o (6) If, however, we take the whole range of values given in Table I., then it will be found that the equation b(v) = 2 + 104424008798 » is better satisfied than (6). The following Table III. gives the numbers we have actually employed in making these calculations. TABLE III. | sya | Waits per v. V/ (0). a(v) Watts candle-power| log {¢(v)—2}. corrected. | corrected. | corrected. 4(0) 84 1-4 2°744 56 20-408 1:2650 86 ia 3°582 60°15 16°79 1:1700 88 1:66 4-574 64°25 14:27 1:0888 90 1-786 Sef 68°4 12:0 1:0000 92 1-914 70 726 10°37 °9227 94 2:044 8°55 76°85 9-0 *8451 96 2-75 10°28 81 7882 "7695 98 23 12-167 85°15 70 6990 100 2°428 14:24 89:3 6271 *6305 102 2°556 16°69 93°5 56 "5563 104 2°682 19:29 97°8 5:07 ‘4871 106 2°81 22°188 101-9 4°593 ‘4138 108 2°94 25°412 106 4°172 3369 110 3°065 28°79 110-1 3°824 -2610 112 3195 32°61 114:25 3°504 1772 114 3°32 36°594 . | 118°3 3°233 0910 Using (6) and (2), the total cost of one candle per year is é H 0°07545 p—11697 7 8-007 —0-07667 v prio + agg (8-7 +10 \s 312 Potential-difference to employ with Incandescent Lamps. This is a minimum when pe eOG 571 lees pn Hence taking p=0°25, n=560, H=£5, we find v=101°15 volts. Using (7) and (2), we should find in the same way that the minimum is obtained when : v=101°46 volts ; and these minimum values of v agree very closely with that previously determined graphically. One very important problem in connection with incandescent lamps, and one that cannot yet be regarded as solved, is the determination of the life of a lamp for any given number of volts, from experiments made either on the efficiencies at several different potentials, or from experiments on the life made at so high a potential-difference that the life will be short, and the experiment made therefore in a comparatively short time. If, however, an expression of the form fe) =10-" can be regarded as representing with sufficient accuracy the law of life for all types of incandescent lamps, then if sufficient experiments be made with a number of lamps at each of two different potential-differences to enable us to determine the average life at each of these potential-differences, the constants a and 6 can be calculated from the equation, and hence the value of /(v), the life, calculated for any other potential- difference. In connection with this investigation we have endeavoured, with the aid of one of our Assistants, Mr. Walmsley, to ascer- tain whether some form of ordinary cheap candle could be used, at any rate for rough photometric measurements, in place of the much dearer standard-candles, and, as far as the following results obtained with seven candles selected at random from a packet of No. 8 sperm-candles go, it would seem that these candles do not differ so very much more in intensity from one another than standard candles are said to do. Of course many more experiments on this subject must be made before the possibility of using cheap candles as a rough standard can be decided on, but in the meantime the following experiments may be interesting. This particular type of candle, No. 8 sperm, and costing 11d. per pound, was selected, because such candles were found to resemble in thickness the standard candles that we have been accustomed to use, and which cost 2s. 9d. per pound. Intelligence and Miscellaneous Articles. 313 TABLE IV. Light in terms of Name of candle. fe Esa that emitted by the burnt per hour. Standard candle. Standard candle ... 7°82 1:00 1st Sperm ,, ide Doubtful 1-14 (?) 2nd. _,, ds a0) 6°102 1:00 ord_s,, 7 on 7-188 1:00 4th _,, be He 7°29 1:02 oe 2 ie al 1:02 Gh. .,, ps aie 6°84 1-05 idle Fa ee 6:66 0-99 These tests of candle-power were not made with any very high degree of accuracy; but the comparison of these No. 8 sperm-candles with the standard was carried out with probably quite as much accuracy as is employed in making ordinary 22 experiments on the luminosity of incandescent amps. ——————————— XXXV. Intelligence and Miscellaneous Articles. ON THE LIMIT OF THE DENSITY AND ON THE ATOMIC VOLUME OF GASES, AND PARTICULARLY OXYGEN AND HYDROGEN. BY EK. H. AMAGAT. (ee recent researches on the density of liquid oxygen by . MM. Cailletet and Hautefeuille, Pictet, and by Wroblewski, have led to values all of which are less than unity, in the different conditions in which this density has been determined. It has been concluded from this that, in agreement with the previsions of Dumas, it will be equal to unity under a sufficiently powerful pressure, or a sufficiently low temperature, and that accordingly the quotient of the atomic weight by the density, or the atomic volume, would be virtually the same for oxygen, sulphur, selenium, and tellurium. . In my second memoir on the compressibility of gases under strong pressures (Annales de Chimie et de Physique, 5th series, vol. xxi. 1881), I showed that at sufficiently high temperatures the law of the compressibility of gases is ultimately represented by straight lines which correspond to the ratio p=(v—a@)=constant, which at once gives the limiting volume a tor p equal to infinity, and therefore the limiting density ; and that for lower pressures the curves, starting from a considerable pressure, exhibit a portion which is virtually rectilinear, and by which we can calculate, though with less certainty, the limiting volume™*. * In this memoir I have used the term atomic volume to denote the value of a in reference to one litre of gas at zero, and under a pressure of 76 centims. I make this observation to avoid any confusion. 314 Intelligence and Miscellaneous Articles. For oxygen and nitrogen the direction of the rectilinear parts is not yet sufficiently marked, and to obtain it far higher pressures must be obtained than has hitherto been the case. With this view I have constructed apparatus in which I have been able to compress gas to about 4000 atms. ‘Two accidents in succession have hitherto prevented me from making regular numerical determinations; but I may already announce the following result :— I have frequently reduced oxygen to the nine-hundredth of its volume ; in these conditions its density was far higher than that of water; with the greatest pressure I could produce, density was higher than 1°25, and this when the surrounding temperature was 17°; we must therefore abandon the idea of unity as a limiting density. Compared with hydrogen, numbers are given as the density of this body in the liquid state which present such extraordinary differences that I shall not attempt to discuss them. The limiting density, as deduced from my own experiments, is very nearly equal to 0:12. Referring to the curve of L. Meyer, it follows that the top of the ordinate which represents the atomic volume of hydrogen will be on the prolongation of the curve, passing through the tops of lithium, of sodium, and of potassium. ‘This would enable us, in conformity with the ideas of Dumas, to assume between this body and lithium a period analogous to those which succeed, but in which, it is true, no known body could be placed. The two accidents mentioned above appear to me to present sufficient interest to be noticed. In one of the experiments the gas-manometer was contained in a cylinder of cast steel with very thick sides, and with mercury in the bottom. All at once a screeching sound was heard, and a jet of pulverized mercury was shot through the right section of the breach, striking the base of the apparatus, and bounding off to more than 1 metre in all directions, producing the same sound as steam escaping from a high-pressure boiler ; the section showed no defect when seen under the micro- scope. We have therefore before us the classical experiment of the mercurial rain in the form of a true jet of mercury passing through the pores of steel through a thickness of 0°08 metre. The pressure was certainly at least 4000 atmospheres; the same appa- ratus under the same pressure does not allow a drop of glycerine to pass; this is probably the case also for water and other liquids. Another apparatus, a solid block of steel with a closer grain, weighing 116 kilog., was split parallel to the axes of the cylinder, and although there was neither projection, nor even separation of the parts any more than a sudden entrance of the gas, the fracture took place with extreme violence ; the mercury escaped through the crack, as I had time to observe, i in the form of a bright plane vertical metallic sheet of 0:06 to 0-07 metre in breadth, Among other apparatus which I have used for measuring pressure, I may mention a manometer of Desgoffe’s, in which I have introduced the improvement already pointed out by M. Meraud Deprey for piston-manometers. This apparatus should give ex- Intelligence and Miscellaneous Articles. 315 cellent results; I do not know within what limits of pressure it can be employed. The measurement of the volumes of gas has been made by various methods, one of which, based on the use of electrical currents, was communicated to me by Professor Tait of Edinburgh; I shall fee it in my next communication.— Comptes Rendus, March 2, 1885. ON THE ELECTROMOTIVE ACTION OF ILLUMINATED SELENIUM, DISCOVERED BY MR. FRITTS OF NEW YORK. BY WERNER SIEMENS. Mr. Fritts, of New York, sent me last summer a description of his method of preparing selenium plates sensitive to light, which differs from mine in many essential points, and he also sent some of the plates he had prepared. Unlike mine *, they do not consist of parallel platinum wires which are imbedded in a thin layer of selenium, but of a thin homogeneous layer of selenium which is spread on a metal plate, and after being heated, to convert the amorphous into crystalline selenium, is coated with fine gold-leaf. Mr. Fritts found that the green light which has passed through the gold leaf increases the electrical conductivity of the selenium which it traverses. In fact the conductivity of the selenium plate between the gold-leaf and the metal base is increased from 20 to 200 times as much, when the sun’s rays fall vertically upon it. And even when illuminated by diffused light, the action is greater with Mr. Fritts’s preparation than with my own. One of the plates sent exhibited no sensitiveness to light, but had another and highly remarkable property, namely, that a galvanometer interposed between the gold-leaf and the base plate indicates the existence of an electrical current in the same direction as the motion of the light, as long as the gold-leaf is illuminated. I imagined at first that this current was not permanent, but resem- bled a polarization=current which only continued until the molecular modification of the selenium by the illumination was complete; and my first experiment appeared to support this assumption. More recent and more thorough experiments have convinced me that this supposition was erroneous. We are here dealing with a phenomenon which is of the greatest scientific importance. My experiments have shown that when the gold-leaf is illuminated, a difference of potential is established, which apparently is propor- tional to the light and which lasts as long as the illumination. Obscure thermal rays do not act as electromotors, and accordingly the assumption that the action is thermoelectric is excluded. Mr. Fritts assumes that the waves of light which penetrate the selenium are directly converted into electrical currents, and this view is * Monatsber. der Berl. Akad. der Wissenschaften, May 13, 1876, and Jun 7, 1877. 316 Intelligence and Miscellaneous Articles. favoured by the proportionality of the strength of the current to the intensity of light. This resulted approximately from the experi- ments collated in the following table :— Intensity of light in } . , : standard candles ... } 6-4 99 | 12:8 | 168 Strength of current ..| 18 30 40 48 Quotient “4.ssscccree 28 3 371 2°8 The luminosity was determined by means of a Bunsen’s photo- meter, and the strength of the current was determined by the deflection of a delicate reflecting-galvanometer. When the gold-leaf was exposed to illumination from the south- east side of the unclouded sky, while the sun itself was hidden by adjacent high buildings, the measurements given in the following table were obtained. h mihm Boe hm /hm; hm /hm{jhm/hm\thm{hm Time of ob- 9 37/10 510 30.11 0,11 35) 12 |12 30/1 O}1 20/2 0/2 30:3 0 servation... Deflection of the 1901196; 209 | 223] 250 |250] 244 | 245 | 249 | 228) 188 | 173 galvanometer. Mirite eee. 3'30| 4 Deflection ...} 172/108 It follows from this that the electromotive force of the selenium plate increased pretty regularly from the morning at 9.30 to mid- day at 11.35, and then remained constant with some variations, after which it decreased pretty regularly to 3 o’clock. Mr. Fritts is unable to offer any explenation as to the reason why some plates become better conductors, and some act as elec= tromotors ; he complains of the uncertainty in the preparation of the selenium plates, the properties of which cannot be foreseen, and he gives various methods of dealing with them, by which plates which are often inactive maybe used. More thorough investi- gations will therefore be necessary to establish what is due to the electromotive action of ight on many selenium plates. Neverthe- less the existence of a single selenium plate with the properties described is a fact of the greatest scientific importance, for here we meet for the first time with an instance of the direct conversion of the energy of light into electrical energy.—Sitzungsberichte der Akad. der Wissen. zu Berlin, Feb. 12, 1885. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] MAY 1885. XXXVI. Notes on the Use of Nicol’s Prism. By Jamus C. M‘CoynEL, B.A., Assistant Demonstrator at the Cavendish Laboratory, Cambridge*. 1. On the Error in the Measurement of a Rotation of the Plane of Polarization caused by the Axis, about which the Nicol turns, not being parallel to the Incident Light. By eer O8E we have a beam of parallel light traversing a Nicol’s prism mounted in a graduated circle. Unless we have taken special precautions, we shall find that, when the Nicol is rotated, the plane of polarization of the emergent light turns through an angle somewhat different from that measured by the circle. For instance, if the axis of rotation of the Nicol is inclined 3° to the direction of the incident or emergent light, as large an error as 1° may be made in mea- suring a rotation of 60°. It is, however, tolerably well known that, as far as this error is proportional to the first power of the small angle of deviation, it may be eliminated by taking the mean of the readings in the two opposite positions of the Nicol circle separated from one another by nearly two right angles. It is of course only to a first approximation that this propor- tionality can be considered to hold good. And the main object of the present investigation is to determine, what is- the out- standing error we are liable to in assuming this proportionality ; or, in other words, with what accuracy we must adjust the Nicol circle, that this first approximation may be sufficient. * Communicated by the Physical Society. Read February 28, 1885. Phil. Mag. 8. 5. Vol. 19. No. 120. May 1885. Z 318 Mr. J. C. M‘Connel’s Notes on The phenomenon in its simplest form may be described thus:—If the emergent ray be parallel to the long edges of the prism it is polarized in a plane perpendicular to the prin- cipal plane of the prism, 7. e. to the plane containing the optic axis and the normal to the face. If the ray be inclined to this position but still lie in the principal plane, then the new plane of polarization is as nearly parallel to the old one as is con- sistent with its containing the new ray. This indeed is obvious from symmetry. But now let the ray lean out of the principal plane: there is a marked change in the plane of polarization. It has been twisted about the ray, and the angle of twist is nearly one third of the angle of deviation. From this explanation it is easy to see in a general way how the error arises, and also how it may be eliminated by taking readings in the two opposite positions of the Nicol. There is another important point that is apparent on the face of the matter. If the direction of the ray coincide with the axis of rotation, the ray will not move relatively to the prism when the prism is turned, and the rotation measured by the circle will be identical with the actual rotation of the plane of polarization. We shall find, moreover, that to the second order of approximation the final error depends entirely on the angle between these two directions (see equation 8). It is independent of any reasonably small errors in the adjust- ment of the Nicol in the circle. In a Nicol’s prism used as a po- Fig. 1. x larizer, it is the second half of the | prism that determines the plane of | polarization of the emergent light. | If the optic axis of the spar in the | first half be not accurately parallel to the axis in the second half, the effect | is not to turn the plane of polariza- | tion, but merely to mix a little ordi- / nary light with the emergent polarized ) light. The figure represents a portion of [Ss the sphere of unit radius. X is the optic axis. N the normal to the face. So XN is the principal plane. P’ is the wave-normal of the emer- gent light. FP ()’ is the wave-normal of the inter- xX nally incident light. Draw Q’Q, P’P perpendicular to XN produced. Join XQ’. x P the Use of Nicol’s Prism. 319 Let P’x be the plane of polarization of P’ and PP’x=y. Then y is a function of P’P and PN. The exact function would be a very complicated expression, so we shall content ourselves with an approximation. P’P is always small, and P lies near some fixed point, Po say, in the plane XN. Let eek hr We shall reject the cubes and higher powers of « and 8 and limit ourselves to expanding y as far as the squares. We know that when «@ is zero, y is zero; so our expression can only contain the terms @, a’, and a8. In a Nicol’s prism it is the extraordinary ray which emerges, so the plane of polarization of Q’ is perpendicular to Q’X. Let us assume for the present that the plane of polarization of P’ makes the same angle with the plane of incidence P’Q’N as does the plane of polarization of Q’. The plane of polari- zation of Q’ makes with P’Q’N anangle 90°—NQ’X. Hence eH NOX NEP ee a ey) But in the triangle NP’P, P is a right angle ; so we have sin P’P a tan (90°—NP’P)= cot NP’P= tan NP == tan NP” ° (2) neglecting cubes. It remains to find NQ’X. NQYX=XQY'Q-NYQ | ~=90°—NP/P+ NQ’'Q—XQ’Q. . . . (8) By spherical ee Fine tan (90°— XQ’Q) = a. tan (90°—NQ'Q)= peer Also sin Q’/Q= sin Q/N sin N, sin P’P=sin P’N sin N.- But sin P’N=wpsin Q’/N, where p» is the extraordinary index of refraction for that wave, which we may take to be constant. .. sin Q’Q = : sin P’ Pas to our order of approximation. pe Hence 3 ee ee tan (90°— XQ’Q) = ey ? of OrO\— oa tan (90° —NQ’Q) = eee Z2 (4) 320 Mr. J. C. M‘Connel’s Notes on Since tan XQ and tan NQ occur in small terms, we may reject squares in finding their values. In NQ let us take a point Qo such that sin NPp>=p sin NQp. Then, since sin(NP)+ 8)=p sin (NQ) + QQo), 8 cos NPp>=pQQ) cos NQo, and deg te Pdi epee... Vn eee tan XQ tan XQ, sin? XQ, tan XQ, pcos NQ sin?XQo 1 il QQ, 1 B cos NP» tan NQ ~ tan NQ, sin? N Q, tanNQ, pcos NQ sin?NQ,” Now in the expansion of the tangent of a small angle the squares of the angle do not appear. So we have by (3), (2), and (4), 3 ee a 1 a 1 Xan ptan XQ p tan NQ’ while ake 1 B tan NP tan NPy _ sin? NP, So by (5), 1 i 1 oS ome (ar, + ptanXQo ptan = 1 cos NP 1 Ih ae { 7 sin2 NP) 2 cos NOQ, Ge xO; ee } (6) =la—map say. In Nicol’s prism, as it is usually cut, x = ao Wey = AES, iS aut NQ, = 14°. Substituting these values, we obtain 32) an — 154, y= d2a— 84a8. 82 1 ae In the foregoing we have assumed that there is no rotation of the plane of polarization on refraction out of the spar, or, in other words, that the angle between the plane of polariza- tion and the plane of incidence remains unchanged. There is of course a change, but it is merely due to the disturbing effect of reflection and is very small. If we treat the spar as the Use of Nicol’s Prism. 321 a homogeneous medium and use Fresnel’s formule, we find the rotation is about ‘005 in the case of an ordinary Nicol. I have calculated from Neumann’s theoretical formule for refraction at the surface of crystals what the rotation would be in the case of light entering the Nicol and exciting only the extraordinary wave, and find it is less than with a homo- geneous medium. In the case of light leaving the Nicol there are two reflected waves, so the formule would pro- bably be very complicated. I think we may safely assume that the rotation is less than ‘Ola, and may therefore be neglected. In the case of a flat-ended Nicol the incidence is nearly direct, and the rotation may obviously be neglected. Owing to the circumstance that this rotation is negligible, the whole of this investigation applies without alteration to the case when the Nicol is used as an analyzer, and the light is consequently incident on the spar. In this case we have to find the position of the plane of polarization that only the ordinary wave may be excited, and the formula for the rotation is the same as in an isotropic medium. Weare nowin possession of a convenient formula for ex- pressing the position of the plane of polarization in terms of the direction of the emergent light relative to fixed planes in the Nicol. We shall apply this formula to the discussion of the error in measuring arotation. This part of the investiga- tion would be very short if we confined ourselves to the first ap- proximation. A number of com- Fig. 2. plications are introduced by the necessity of retaining the syuares and products of small quantities. The figure represents a portion of the sphere of unit radius. Let A be the axis of rotation, N P the principal plane, P’ the emergent wave-normal, P’« the plane of polarization. Draw AP, and P’P perpen- dicular to the principal plane. This fixes Py, which has hitherto been arbitrary within certain limits. A and P’ are fixed in space, while N and P> are ro- tated round A. For simplicity, suppose the circle-reading is zero when P’ K lies on AP,. Then 6=P AP” is the reading at any time. Produce A P’ to meet N Py in K, 322 Mr. J. C. M‘Connel’s Notes on What we want to measure is the rotation of P’z round P’; so let eP/K=. As before, let P’/P=a, PPo>=£, and let AP,)=a, AP’=r. Then a, 8, a, 7 are all small. Since the figure A Py P P’ is small, we have to our order of approxi- mation ae =a—Pr COS ere B=r sin (W+ x). Let us now find the difference between 0 anday+y=PP’K. By spherical triangles, cos K=sin (+) cos PP’, t cos K=sin @ cos a; *, sin (r+) cos PP’=sin @ cosa, 2 2 sin O=sin (W+y) (ig + ) sin (P4x) + O—Y—x) cos (P+ A =sin'+y)(1-F +9) oe Bet 2. 0pm y= 9S tan (+x) a* — a? sae tan yr, neglecting cubes. But : a* —a’=2ar cos p—71’ cos’ Wp, and v= la—maB =l(a—r cos +x) —mr sin ¥re(a—r cos p) =l{a—rcosy + lr sin (a—r cos )}—mr sin yr(a—?7 cos wr) =la—lr cos +(?—m)r sin W(a—r cos Wr); 6 0=W+la—Ilr cos p+ (?—m+1)arsinw —(?—m-+4)r’ sin w cos w. Now let the plane of polarization be turned through 180° and the new reading of the Nicol circle be 180°+6,. Instead of y we must write in the last formula 180+. So 6,=W+latlr cos — (?—m-+1)ar sin p | —(?—m+4)r’ sin p cos; AO) ig gd a oe 5 = +la—(?—m-+ })r’ sin cos yp, 6,—6 2 =lr cos y—(l?—m-+1)ar sin wp. the Use of Nicol’s Prism. 323 Inserting numerical values, we have mae ihe W='32a+‘24r? sinoosy, . . . (8) @,—0="64r cos , approximately... . . . (9) To render these formule intelligible to one who has not read through the investigation, we may remark that we have to deal with one plane fixed in space, viz. the plane con- taining the axis of rotation of the Nicol circle and the direction of the emergent light. 6 and 180°+6@, are the readings of the circle in the two opposite positions, and @=0 when the principal plane of the Nicol is at right angles to the fixed plane. av is the angle between the plane of polarization and the fixed plane. :; ais the angle between the axis of rotation and the principal lane. . r is the angle between the axis of rotation and the emergent light. “The angles are supposed to be expressed in circular measure in these as in all the other formule. The first term on the right-hand side of equation (8) is a constant, and is therefore of no consequence in measuring a change of y. ‘The second term is a measure of the out- standing error. Let us suppose fo i Ol). Then "247? sin vr cos = 1’; but if w= —30°, the same=—1’. So in measuring a rotation of 60° we may be subject to an error of 2’ if the axis of rotation be inclined to the emergent light at an angle of 3°. To make sure that the error shall be less than 1’, the last-mentioned angle must be kept within 2°. Hquation (9) affords the means of deducing the value of r from the difference of readings in the two opposite positions. The second term of (8) is due to two main causes. One is that the rotation of the plane of polarization takes place about one axis, while the rotation is measured about another. The effect of this appears in the coefficient —4. The other part of the error is due to the values of y in the two opposite posi- tions not exactly neutralizing each other. This appears in the coefficient m—l. If these two causes had reinforced instead of counteracting one another, the resultant error would have been five times as large. 324. Mr. J. C. M‘Connel’s Notes on If the arrangements permit of taking readings when the plane of polarization is inclined at 90° to its two first positions, we can, by taking the mean of all four readings, get rid of the error depending on the squares of small quantities, as is evident from (8). This is what Lord Rayleigh has done in his recent measurements of the electromagnetic rotation in bisulphide of carbon. Fig. 3. The formula (6) applies to almost every mode of cutting a Nicol, ex- cept the important case when the ends are cut off square to the length, the case of the so-called “ flat-ended Nicol.” This case requires the in- vestigation to be modified. The peculiarity consists in N lying very close to P’. v= 90°—NP’P+NQ’Q—XQ’Q, as before ; and by (4) and (5), tan (90°—XQ’Q) _ 4 i aS igen wo) aveine If we take N as the point from which to measure 8, P, and Q, will coincide with N. We have now to find NP’P—NQ’Q. The process is pre- cisely similar to one already performed in finding equation (8) ; and we obtain >. PpPp2— QQ” NP’P—NQ’/Q= 5 tan NP’/P 2 —] F “Fa a ; a ap w— =la—meB, say. Taking XN =63°, w=1'52, we obtain [=°33,; -m='83. So the numbers are almost exactly the same as in the case of the ordinary Nicol. As a test of the accuracy of the above calculations, I made a few observations on a flat-ended Nicol. 1 found that, turn- ing the Nicol through 30’, about an axis in the principal plane ee the Use of Nicol’s Prism. 325 and at right angles to the incident light, turned the plane of polarization through 11/+1’. In a paper on Polarizing Prisms (Phil. Mag. 1883) Mr. Glazebrook has suggested a new form of flat-ended prism in which the axis of the spar is at right angles to the length of the prism. In this case XN=90°, and w=1°49. lO =" 0, palates bE So instead of equation (8) we have 6+ 8, 9 —p='237" sin W cos yr, and the outstanding error is substantially the same as before. Hquation (9) appears to be inconsistent with a result ob- tained by Mr. Glazebrook (Phil. Mag. Oct. 1880, p. 252). For the sake of simplicity, he supposed the ordinary ray only to emerge from the crystal. He examined two positions of the Nicol. First the emergent ray lay in the principal plane, so that the plane of polarization coincided with the principal plane. Next he supposed the Nicol to be turned through 90° about an axis, lying in the principal plane, but inclined at 5° to the emergent ray, and he found that now the plane of polarization was inclined at 5° 3/ to the principal plane. But this does not show that the plane of polarization has been turned through 90°+5° 3/ about the direction of the ray, as is evident on examination of the annexed figure. Fig. 4, P’ is, as before, the emergent light ; N, N’, X, X’ are the two positions of the normal to the face and the axis. 326 Mr. J. C. M‘Connel’s Notes on In the first position the plane of polarization is P’ AN X. In the second position let it be P’ K. Mr. Glazebrook finds P/KA=5° 3’. The angle, however, that we wish to find, is the angle through which the plane of polarization has been turned about the direction of the ray, viz. AP’ K, and this, of course, is not equal to 90°—P’ K A. After I had written the greater part of this paper, I found that the ground had been already traversed by Sande Bak- huyzen (Pogg. Ann. exlv. p. 259, 1872). His investigation is considerably longer than mine, and he only examines the case of the ordinary Nicol. He obtains results of the same general form; but he falls into at least one serious error; so his numerical values are quite different. Instead of assuming, as I have done, that the rotation of the plane of polarization on refraction out of the crystal is negligible, he uses a com- plicated formula, giving directly the position of the plane of polarization of the incident ray in which only the extraordinary ray is excited in the crystal. This formula he has apparently deduced from a formula given by Neumann (Pogg. Ann. xli. p- 11). And itis here that the error occurs. He has not paid sufficient attention to Neumann’s explanation of how the quantities in the formula are to be measured. He puts 8 for w; whereas he should put @—a for w. Making this cor- rection in his equation (5), we find all the terms in the deno- minator are of one sign, and the value of tan A is consider- ably diminished. We find, too, that 90°—A is practically the same as the angle between the plane of incidence and the plane of polarization in the crystal, which is what I have assumed. In this very same operation Bakhuyzen falls into another mistake. He is considering the case of light emerging from the Nicol, while he uses the formula for light entering the crystal. Hven with glass this would have been wrong; but with crystal the cases are totally distinct, for when light is refracted out of the crystal there are two reflected rays instead of only one. It may not be out of place here to describe a simple method for testing the necessary adjustment, which I lately found convenient. In my arrangement (fig. 5) the source of light was an illuminated slit A, whence the light passed through a lens B, placed so that the slit was at its principal focus. Thus a parallel beam of Jight fell on the polarizing Nicol C. To the Nicol circle I attached a plane mirror D as nearly as possible at right angles to the axis of rotation. Between B and D, I interposed a lens EH at a distance of half its focal length from D. An image of the slit is thus formed at a on the surface —_——_— the Use of Nicol’s Prism. 327 of the lens HK, or rather on a scrap of paper attached to it. The image a of course remains at the same point on the paper, however the lens E is moved laterally in its own plane. On rotating the Nicol circle I found that a did not move ; so I knew that the mirror was at right angles to the axis of rota- tion. I then adjusted the Nicol circle till the middle point of the image of the slit fell on the optical centre of the lens, which | had previously marked on the paper. If I had chosen a wrong point as the optical centre, the error would have been at once evident on turning the lens E through 180° in its own plane. This method gave without much difficulty an accuracy of 1°, with a lens E of only 4 inches focal length. 2. On anew Method of obtaining the Zero-reading of a Nicol Cirele. In a large class of experiments on polarized light, it is necessary to know the reading of the Nicol circle when the plane of polarization is parallel to the axis of rotation of some part of the apparatus, e. g. of the table of a spectrometer. The usual method of obtaining this reading depends on the pola- rizing power of a glass reflecting surface. It is easy to fix the surface on the spectrometer-table parallel to the axis of rotation. Ifthe angle of incidence be made that of maximum polarization, and the Nicol turned till the reflected light is reduced to a minimum, the plane of polarization is then per- pendicular to the plane of incidence. This method is simple, but it is not very sensitive. Hven with poor illumination the minimum reflecied light is, with glass at any rate, by no means evanescent; and as the Nicol is turned the intensity remains sensibly constant for some distance on either side of the minimum point. The sensitiveness, too, does not increase, but rather falls off with a more powerful light. The method I am about to describe is nearly as simple ; and, as it depends on the crossing of two Nicols, its sensi- tiveness is only limited by the power of the source of light. In its simplest form the process is as follows :—An auxiliary Nicol is fixed on the table of the spectrometer, the polarizer turned till the light is quenched, and the reading taken. 328 Mr. J. C. M‘Connel’s Notes on Then the table of the spectrometer is turned through two right angles—the axis of rotation having been previously set perpendicular to the incident light—the light quenched, and the reading taken again. The plane of polarization now leans as much to one side of the axis as it did before to the other. So the mean of the two readings is the reading when the plane of polarization is parallel to the axis of rotation of the table. The above is of course only a general explanation. The statement in italics requires fuller examination, and we shall find that it is only strictly true when the Nicol 1s symmetrical. Let us, then, first suppose that the Nicol is perfectly symme- trical—that is, that the two faces are parallel and the optic axes of the two halves coincident. We shall assume through- out the investigation that the axis of rotation is accurately perpendicular to the incident light. In the previous note we have carefully determined the position of the plane of pola- rization in terms of the direction of the emergent light, and we have shown that, to a very close approximation, it is at right angles to that position of the plane of polarization of light incident along the same path which gives complete extinction in the Nicol. The discrepancy was shown to be negligible. So there is no ambiguity in speaking of the plane of polarization of either half of the Nicol for a particular direction of the light. In the first position of our Nicol on the spectrometer, the emergent light is parallel to the incident, and the planes of polarization of the two halves are also parallel. The axis of rotation, too, is at right angles to the incident light. Imagine, then, a line fixed relatively to the Nicol to be drawn from the second face parallel to the emergent light. When the Nicol has been rotated through two right angles, this line becomes again parallel to the incident light, and the plane of polari- zation of the second half of the Nicol now leans exactly as much to one side of the axis of rotation as the plane of pola- rization of the first half leant before to the other. The process therefore is so far strictly accurate. Secondly, let us suppose that the Nicol, though not sym- metrical, yet produces no angular deviation on light traversing it. We have seen in the previous note that the plane of pola- rization of a Nicol is nearly at right angles to the principal plane, and that to a first approximation the small deviation is proportional to the angle between the external light and the principal plane. Let Xn, X,n, be the principal planes of the two halves. B, B, their poles. P the direction of incident and emergent light. the Use of Nicol’s Prism. 329 Draw Bm at right angles to B P and Bym at right angles to Bm. We may assume that BB, is very small and BP Fig. 6, a B 1 B in nearly a right angle. The angle between the planes of polarization of the two halves is composed of two parts, of which one, B P B,, is approximately equal to Bm, and the other is approximately proportional to the difference between Pn, and Pn and therefore to Bym.’ So the angle is independent of small variations in the position of P, and is therefore a constant for each particular Nicol. In some Nicols, as we go from one half to the other, the plane of polarization is turned in the direction of a right-handed screw. These we may call right-handed Nicols with a certain rotation-angle. Supposing, then, our auxiliary Nicol is right-handed, the plane of the second half leans at first too much to the right, but, when the Nicol has been rotated through 180°, it leans too much to the left. The correct reading in the case of a right-handed Nicol is therefore that obtained by turning the Nicol circle from the mean reading through half the rotation-angle in the right- handed direction. The question now arises, how we are to determine the rota- tion-angle. The following process explains itself. Place the auxiliary Nicol B on the path of the light from the polarizer A, which is mounted in a graduated circle. Turn A till the light is quenched and take a reading. Then turn A so as to allow the light to pass through B, and place in the path of the light from B a third Nicol C. Adjust C till the light _ from B is quenched. Remove B, cross C with A, and read again. 330 Mr. J. ©. M‘Connel’s Notes on So far the matter is tolerably simple, but if the Nicol produce deviation of the light complications are introduced. Fig. 7. B The figure represents a flat-ended Nicol B traversed by a ray of light PL MP,. The argument, however, is perfectly general. A small error is due to the Nicol C having to deal first with light parallel to MP, and afterwards with light parallel to PP’. This may be eliminated by taking two readings, the Nicol B in the interval having been turned through two right angles or thereabouts about LM. The mean thus found gives us the position of the plane of polari- zation of P L, which is most nearly parallel to the plane of polarization of MP,. We know nothing about the plane of polarization of light which issues parallel to MP’. Clearly _ therefore, when our Nicol is mounted on the spectrometer- table, we ought not to turn it exactly through 180°, but we ought to turn it till the incident light is related to the face M in the same way as P, M was at first. We have then this practical rule. Place the auxiliary Nicol on the spectrometer in such a position that the deviation Jies wholly in the plane of rotation. To get the second reading, turn the table in the direction of the deviation through an angle equal to 150° less the deviation. Correct the mean of the two readings by half the rotation-angle as before. Thus we are able to get an accurate value of the zero- reading in spite of the dissymmetry of the Nicol and the deviation of the light, provided only the two faces of the Nicol are good planes. We have been compelled, however, to limit ourselves to first approximations. On this point it is to be noticed that the outstanding error is due to two causes, the inaccuracy of adjustment of the auxiliary Nicol, and the dissymmetry of the Nicol itself. The latter we may assume to be very small; while the former has very slight eftect. It only comes in as a secondary cause, for if the dissymmetry were removed the outstanding error would be zero. Hence it is not necessary in general to take elaborate precautions about the setting of the Nicol in the determination either of the zero-reading or of the rotation-angle. If great accuracy be the Use of Nicol’s Prism. 331 required, it will be sufficient to attach permanently to the Nicol a small reflecting surface, and make this always perpen- dicular to the incident light. The planes of polarization of both halves will then be perfectly definite. 7 I have treated the method as applied to a Nicol used as polarizer, but it is by no means restricted to this case. The polarizer may be any kind of polarimeter, or if necessary the polarimeter may be the analyzer, while the auxiliary Nicol is used as polarizer. The method occurred to me when I was engaged on some observations on the refraction of polarized light at the surface of Iceland spar. I will describe the arrangements in so far as they bear on the matter in hand ; for, as it happened, they gave a very high degree of accuracy in the determination of the zero-reading. As my source of light I employed part of the filament of a Swan incandescent lamp. I selected a straight piece, and cut off the light from the rest of the filament with a diaphragm placed immediately in front of the lamp. The filament was placed at the principal focus of a lens, from which the light passed to the polarizing Nicol. Then came the spectrometer, from which the collimator had been dismounted ; so only the telescope remained. When the telescope was focussed for infinity and directed towards the light, a sharply defined image of the selected portion of the filament was seen. The top and bottom limits of the image were not hard lines, owing to the diaphragm not being quite at the principal focus of the collimating lens. They were, however, sufficiently definite for practical purposes. lt was necessary for my other observations that the axis of rotation of the spectrometer should be set at right angles to the light coming from the middle of the filament. I accom- plished this in the following manner. I first mounted a reflecting surface on the table of the spectrometer, and ad- justed it to be parallel to the axis of rotation. This may be done with accuracy although the telescope be tilted. Next I adjusted the axis of the telescope to be at right angles to this surface, by getting the cross wires to coincide with their image formed by reflection at the surface. Then I removed the reflecting surface, directed the telescope towards the light, and tilted the spectrometer till the cross wires coincided with the middle of the image. When the auxiliary Nicol was mounted on the spectrometer- table and the polarizer turned past the crossed position, the image of the filament by no means entirely disappeared ; but a patch of nearly complete extinction moved down the image _ from the top to the bottom. This was of course to be expected, since different positions of the image correspond to different 332 On the Use of Nicol’s Prism. directions through the Nicols, and therefore to different posi- tions of the two planes of polarization. The reading was taken when the patch was halfway down the slit. This method of reading proved to be very sensitive. Without any special care I could get a number of successive readings whose greatest difference was 1'. This was quite sufficient for my purposes. Indeed my verniers were only graduated to 1’. But I am convinced that a far higher degree of sensi- tiveness could be reached if desired, by proceeding on the same lines. In securing great accuracy two precautions become very important. The source of light should be of uniform bright- ness. Here a well-made carbon filament is nearly perfect. Again, as much light should reach the eye from the top of the filament as from the bottom, abstraction being made of course of what is stopped by the polarizing properties of the Nicols. or this it is convenient that the lateral throw of the Nicols should be as small as possible. Flat-ended Nicols are therefore to be preferred. But if a pair of Nicols were made for the purpose, it would be easy so to slant the faces that the extraordinary ray should go straight through, and there should be no lateral throw. The incandescent lamp is a more powerful source of light for this purpose than is perhaps at first sight apparent. For it may be shown that with a given slit and object-glass the intensity of the illumination of the surface of the first Nicol depends solely on the intrinsic brightness of the source of light. The filament is practically a slit with the source of light brought into contact with it, so there is no difficulty about the whole of the surface of the Nicol being illuminated, and the illumination is just as powerful as would be given by a glowing sheet of the same brightness half an inch broad placed a little distance behind a slit. The intrinsic brightness of the filament of a Swan lamp is many times greater than that of a good gas-flame viewed edgeways. Besides, even if the gas-flame be placed very close to the slit, it is only the nearer portion of the flame that illuminates the whole surface of the Nicol. The further portion only lights up a narrow strip in the middle of the surface. I used two flat-ended Nicols, belonging to Mr. Glazebrook, of about half an inch aperture. One of these, which gave an angular throw of 15’, had a left-handed rotation-angle of 38). I find that the plan of reading by means of the motion of the patch of extinction has been the subject of an elaborate paper by Lippich (Sitzb. der kais. Akad. der Wissensch. Wien, Febr. 1882). 838) XXXVI. Electromagnets—II1. Lron and Steel. New Theory of Magnetism. By R. OH. M. Bosanquet, St. John’s College, Oxford. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, N the February number of the Philosophical Magazine (p. 73) I gave a number of experiments on the Perme- ability (w) of Iron and Steel, with empirical formule founded on Fourier’s Series. I also gave the elements of a new theory leading to equations of the form p=A(G, —B) cos 8, o= 0, k 60°—o0 Bias Simignen | and gave the comparison of this theory with experiment in the cases of Crown (soft bar) Iron ring H, and Steel ring J (first soft state). I propose now to communicate the com- parisons of all the remaining experiments of the former paper, and of three additional sets on J. For clearness I will recapitulate shortly the bearing of the formule. Hach molecule has one, and only one, axis of transmission (like* a bead with a hole in it). The axis is capable of trans- mitting %, lines of force and no more, and the molecular permeability is proportional to %3%,,—%, or to the defect of saturation. (lf we pack the hole in the bead with thin wires, the aperture remaining is represented by the number of wires that remain to be got in.) A is the molecular permeability per unit defect of satu- ration. 6 is an auxiliary angle representing the obliquity of a zigzag which would augment the resistance to the amount actually observed. @ is the average inclination of the axes of the molecules to the direction of magnetization ; initially it is always 60°. w is the unit angle. f is the factor connecting @ and 6. — represents the force of molecular torsion which is in equi- librium with the tendency of the lines of force further to deflect the average molecule. _ * These statements are not to be taken as actual hypotheses, but as geometrical analogies of the distribution. Phil. Mag. 8. 5. Vol. 19. No. 120. May 1885. 2A 334 Mr. R. H. M. Bosanquet on a The inferences as to these constants to be drawn from the numerous experiments now discussed are not so clear as they appeared to be from the two cases treated in the last paper. The first of the following Tables contains the constants from all the experiments that have been reduced, finishing with those obtained from Rowland’s Table I. The remaining Tables contain the detailed comparison of the theory with experiment in all the cases, except ring H, and J first soft state, which two were given in the last paper. The last column but one of the first Table gives the product of A, the reciprocal of ~,andaconstant. This quantity may be compared with the maximum observed value of wu in the last column. A has been spoken of as the molecular permeability for a certain unit. Regarding magnetism as a motion or displace- ment, whether dynamic or static, we may thus speak of A as a coeflicient of freedom within the molecule. = being the coefficient of the forces which tend to prevent the rotation of the molecule as a whole, we may speak of its reciprocal as a coefficient of freedom without the molecule. The last column but one may be therefore regarded as the product of coefficients of intra-molecular and extra-molecular freedom, and a constant. : This product (¢ x intra- x extra-molecular freedom) is a characteristic of a given approximate state of a given piece of metal. It runs generally with the maximum of yw; but is liable to be depressed with respect to w where 7 has high values, as in the first, second, and fourth entries. As between the hard steel and the iron, the product of the coefficients of freedom is proportional to the maximum permeability. The further general conclusions, so far as these data go, are as follows:— In soft steel the molecular forces are chiefly extra-molecular, the freedom intra-molecular. In hard steel the molecular forces are chiefly intra-molecular, the freedom extra-molecular. In soft iron the average intra-molecular freedom is much greater than in hard steel, the extra-molecular freedom about the same. In soft steel the extra-molecular freedom is much dimi- nished, the intra-molecular freedom is moderate or high. The distribution of the freedom between intra- and extra- molecular conditions depends minutely on the condition of the piece of iron or steel. New Theory of Magnetism. 339 The variations thus arising are comparatively moderate in iron, considerable in hard steel, and enormous in soft steel. In one or two cases the equations do not represent the values quite so well; in G two sets of constants are given. The dimensions of the rings and details of the experiments are given in my paper of February last. Steel ring J was examined first soft, then hard. then soft again, then hard again. Its saturation-point is taken to be 20,000 throughout. It was wound with about 4000 turns in the hard states. P.S.—From the above conclusions we can deduce the out- line of a chemical theory of the hardening and tempering of steel. In hard steel the additional constraint, as compared with iron, is wholly intra-molecular, 7. e. due to chemical combi- nation with a steeling element. This combination must exist naturally at a red heat, and be stereotyped by sudden cooling. in soft steel the intra-molecular constraint is much dimi- nished, and the extra-molecular constraint increased. Hence in slow cooling dissociation of the steeling element takes place. This requires time. At any point in the slow cooling the condition of partial dissociation can be stereotyped by completing the cooling suddenly. This constitutes tempering. Scheme of the Constants of the Rings. J. Steel—BE, F, G, H, K. Soft Iron(Crown). I. Lowmoor. Rowland’s J., “ Burden’s Best.” kK Ap xC Maximum Ring. A. log -. log f. m observed . log C=6'1000. | value of p. J. First soft state...) 11: 4°78936 | 17595 225 461 ,, second soft state) 129 | 2°82178]| °16552 245 423 ,, First hard state... -01735) 2°16327 | -18925 150 157 », second hard state] °0236 | 246312] °15340 102 145 ie ees A cs sds ese °3856 | 2:32208 | °16153 2312 2234 Ge See a 189 | 201524) -16151 pl 1895 313) 2°23407 | °15778 57 2 eae { Se ake call dene aes 2501 Tet. Ss eee 25 2-24075 | -15325 1808 SF i LSS eres ees) 2°30682 | 15973 2422 2070 lo Loca eee 217 ~+| 2:06175| 16046 2370 2173 | Rowland’s Table I. 348 =| 2°14941| -16079 2666 2472 | 2A 2 336 Mr. R. H. M. Bosanquet on a J. First Hard State. A=-01735, log? =2'16327, log f="13925. J. Second Soft State. w= 20,000. é. Caic fo} | 82 39 45 82 11 47 81 41 50 81 18 52 80 31 56 79 38 62 78 19 68 77 38 72 67 4 120 55 18 153 47 45 157 40 47 145 31 35 91 28 23 57 24 48 Gi a I+++ 4+4+4++ $!44+ | Reo wampormHron A=-129, log = =2'82178, log f="16552. 46. eS ee 44 348 1110 1464 1640 2377 3701 6734 9957 10029 18252 14470 16118 19198 0. oO i 1 59 56 30 59 32 52 58 35 58 7 57 55 57 0 55 24 52 0 48 43 48 40 45 42 44 40 45 20 41 0 33 ., = 20,000. é. Cale. re) 1 87 45 101 87 10 125 85 46 180 85 5 205 84 47 215 83 27 259 81 6 325 (6% 7 411 alee 415 7115 413 66 54 341 65 23 295 63 26 294 60 1 52 + H He GO © © pa [fee 1 bits New Theory of Magnetism. 337, J. Second Hard State. A=-0236. log~ =2°46312, log f=15340. % ., = 20,000. pL. 8 Q é. Diffs Cale. Obs | (o} i il 43 | 595220 | 85 14 39 39 0 204 | 593340 | 84 33 44. 39 TER 538 | 58 26 83 1] 54. 46 + 8 821 | 57 36 82 0 63 58 45 923 | 57 20 81 37 66 59 #2 77 1308 | 56 15 80 5 76 72 aie: 1489 | 55 46 79 24 80 17 423 1572 | 55 32 "9 4 82 78 +4 1767.) 55. 1 78 18 87 Sl iG 2186 | 53 55 76 46 96 106 S108. | 2477 | 53 10 "5 Al 102 113 el 3655 | 50 20 71 39 121 130 25,9 | 4305 | 48 50 69 31 130 133 =) Sus | 4468 | 48 30 69 8 131 136 oy 4892 | 47 43 67 56 134 142 24 (ey | | 5442 | 46 26 66 6 | 139 [aah | ed 6255 | 44 50 63 50 14 143 Oa 7351 | 42 48 60 56 145 145 0 | 8793 | 40 24 57 31 142 142 Gar 11128 | 36 58 52 38 124 123 aaa 1263 35 2 49 52 112 97 415 | 14093 | 33 20 AT 27 94 86 aeatal 15515 | 31 50 45 19 74 66 nen eva| 18276 | 29 16 41 40 3 48 me F, K ~ A='189, log = = 201524, log f="16151. % ., = 20,000. | Hs Bb. é. é. [eS NE Dili: | Cale. Obs, fe) i il oO i 15 | 595230 | 86 51 208 208 0 143 | 58 49 85 19 306 360 — 54 513. | 55 49 80 45 592 587 Sige 2784 | 42 0 60 55 | 1582 1592 240 3616 | 38 22 55 89 | 1747 1784 Lea 4283 | 35 48 5156 | 1832 1869 eow 5747 | 31 15 45 20 | 1894 1895 tail 6438 | 29 27 42 48 | 1883 1825 4+. 58 7655 | 26 45 38 48 | 1818 1704 4104 10767 | 21 40 31 26 | 1489 1581 — 92 12537 | 19 34 98 93 | 1241 1252 MBE 13900 | 18 10 26 21 1033 1000 3s 15035 | 17 11 2455 | 853 692 +161 18884 | 14 31 £20. 3.1 206 150 + 56 338 Mr. R. H. M. Bosanquet on a G. Aaa: A=31, log =2:23407, log f="15778. log =2:11959, log f=:15572. p 33, = 18,000. 33, =18,000. | pe pb. , eB. 0. 62: > (eS Diffs.) | We ee ee Cale. | Obs Cale. | Obs Bi | 59 44 40 | 8555 | 447 | 4el) — 14 |i 446 | 4¢ie\eeeme 448| 57 48 83 7| 736| 765| — 29 || 778| 765) + 13 1972| 51 3 73 95 | 1601 | 1615 | — 14 || 17388 | 1615 | +123 6364.| 37 26 3 50 | 2403 | 2501 | — 98 || 2423 | 2501 | — 78 9003| 33. 6 47 36 | 2123 | 9241 | —118 || 2136 | 2241 | —105 11090| 28 50 41 28 | 1812 | 1763 | + 49 || 1745 | 1763 | — 18 11970| 27 38 39 44 | 1623 | 1555 | + 68 || 1558 | 1555 | — 2 13710| 25 30 86 40 | 1904 | 1199) 4 19 || 1140 | 11923 eee 14426 | 24 46 35 37 | 1017 | 8382 | +185 || 974| 832) +142 15505 | 23 41 34 3| 7241 664| + 60 || 680| 664] + 16 16042| 23 11 31 54 | 562) 395 | £167 | 537 | S0oqeueeiee 17536 | 21 53 3128 | 188°] 145) = 7 || (oo | taj ceeeeats H. A='25, log) =2'24075, log f="15325. %_ = 18,000. _ #-p- 5 Ie] 4) 0. a Diffs Cale. | _ Obs. (e) 1 (e) 1 34 59 50 85 9 380 395 = 1X 287 58 36 83 24 509 418 + 91 1079 54 56 78 11 866 817 + 49 6025 38 29 54 56 1727 1797 — 70 7705 34 46 49 19 1678 1717 — 39 8436 3 47 29 1616 1710 — 94 9740 Bal 6G 44 16 1479 1354 +125 11261 28 50 AY 2 1271 1134 +137 13355 26 10 37 14 903 885 + 18 14501 24 55 35 28 712 630 + 82 14718 24 40 35 1 672 502 +170 15409 24 O 34 9 536 254 +282 17642 22 O 31 18 76 | 97 — 21 New Theory of Magnetism. 339 Ke: K (ees NO log = 230682, log f='15973. %_ =15,500. }L.- 13 0 o. Diffs. Cale | Obs lo) i al o) 67 59 42 45 86 16 391 422 — 3l 293 58 46 84 53 529 428 +101 2175 51 36 74 32 1386 1288 + 98 2337 Hie 2 73 43 1439 1176 +263 3949 46 0O 66 27 1800 1766 + 354 4710 43 53 63 23 1982 1885 + 97 5720 41 21 30 59 45 1922 2070 —148 8677 39 17 50 58 1676 1914 = 515: 8890 34 54 50: 25 1643 1775 — 132 9598 33 43 48 42 1519 1557 — 38 10413 32 27 46 52 1356 1531 —175 115tt 30 52 30 44 36 1107 1104 + 8 12148 30 1 43 22 950 799 +151 13246 28 40 41 25 659 666 — 7 13104 28 50 41 39 698 505 +193 13671 23 10 40 41 541 358 +183 15053 26 40 38 31 136 oD + 1 if K A=-217, looX=2:06175, log f='16046. p 33, =20,000. | eB 7) é. Diffs Cale. Obs O° i i O° ‘ 33 59 45 86 27 268 271 — 3 499 56 52 30 82 18 569 617 — 48 13822 bly 5 73 55 1123 1024 + 99 1624 49 20 Ci ee 1273 1427 — 154 2395 45 15 65 29 1585 1558 + 27 4541 36 33 52 53 2024. 2072 — 48 6324 31 25 45° 27 2082 2080 + 2 6712 30 29 44 6 2071 1993 + 78 6700 30 30 44 8 2071 2033 + 38 7091 29 37 42 51 2054. 2173 —119 8194 2 2k 30 39 35 1974 1935 + 39 9691 24 47 35 52 1813 1842 — 29 10400 23 43 30 34 20 1720 1483 4237 13159 20 20 29 25 1293 1188 +105 15050 18 382 26 49 958 818 +140 16309 Re 80 25 19 724 592 +1382 16939 Ke 0 24 36 604 444 +160 340 Prof. Oliver Lodge on the Seat of the Rowland’s Table I. A='343, log? = 214941, log f=16079. 93, =17,500. 16. 0. tole aR Mey, Cale. Obs. fe) 1 715 | 5634 | 8615 | 301 | 391 0 6005 | 5627 | Sl 44 gg | 8601|, «= ab 966-7 | 5427 | 7851 | 1007 | 1129 | — 382 2460 47.12 | 368 21. dy 1903. | 1986, |. = Samet 2923 45.17 |. 65 34. 112068 | 2078) | =a 3082 44 38 | 64 38 .) DIS | 2194) aaa 4959 3815 | 5523 | 2444 | 2433 | 4 11 | 5482 36.45 | 5313 | 2468-| 9470 | — 2 5782 3556 | 52 2 | 9473. | 9479 | 4 at 6651 33 47 | 4855 | 2445 | 2448 | — 8 7473 31 58 | 46 (7 | 2871! | 2367 | ae 8943 29 8 | 4211 | 2175 | 2208 | — 33 10080 2716 | 3929 | 1964 | 1899 | + 65 12270 2416 | 35 8 | 1467 | 1448 | sae 12970 9324 | 3353 | 1290 | 1269 | +4 21 13630 92.42. | 3959)» 1s | - Lister) | = 22 14540 2145 | 31 30 g66 | 824. | +4 42 15770 2037 | 29 51 Bib | 462~| 4eaue 16270 2012 | 29 15 368 | 354 | +4 14 16600 1949 | 28 42 OF1> |: 258eh) Sees XXXVIII. On the Seat of the Electromotive Forces in the Voltaic Cell. By Professor Ottver J. Lope, D.Se. { Concluded. from p. 280. | TABLE OF CONTENTS. Chapter IV. Discursive*. Page 19. Discussion and hypothetical explanation of true (or thermo- electric) contact-force, and reason why for insulators it is large, and for metals small .2\)* wid). fie © om mcd eo eee ee 340 20. Thermoelectric contact-forces between metals and electrolytes, and theory of the common or simple voltaic cell ............ 343 21. Experimental examination of three simple cells used like volta- meters; and dependence of E.M.F. on current .............. 347 22. Summary of condensed statements embodying the writer’s own WIEWS er RA Beebe ie bur erk Cala Se Aut ow oo Rakes chee Reena 300 23. Explanation of the last of the above statements. Example of a Peltier series and of a Thomson series; and question whether thermoelectric contact-force depends upon chemical tendency or whether it 1s purelyplnysicall 54... «<) kosee Sass eee 353 24, Brief summary of the argument eae to the seat of E.M.F. in filer iw. ahe SURE IN EUs ELLs Let 357 19, : AVING now elemed why I believe the main part of the Volta-effect to take its rise at the surface of * Very little of this chapter, and none of Chapter V., has yet been read anywhere. Electromotive Forces in the Voltaic Cell. 341 contact between metal and medium, rather than between metal and metal, it remains to consider whether this belief requires one to assert that there is no true contact-force at all at the junction of two metals. By no means: the existence of such a force is undoubted ; but for metals it is usually very small and may be neglected in comparison with the Volta-force, though, strictly speaking, what is observed electroscopically is a mixture of the two. It is the true contact-force which gives rise to the Peltier effect, and its variation with tempe- rature (assisted by the Thomson effect) causes thermoelectric currents. A contact-force exists, as Thomson has shown, not only at the junction of two different metals, but also between parts of the same metal at different temperatures. In another place* I have endeavoured to gain some insight into the nature of this true contact-force and to suggest its cause. This has been done by many others; but I may be permitted to repeat my own notion, vague and incomplete though it avowedly is. Molecules of matter do not move in independence of electricity ; at any rate the converse is cer- tainly true—electricity does not move independently of matter. Hlectricity, in flowing through a wire, meets with resistance ; there is something analogous to friction between the matter and the electricity, and the opposing force is precisely pro- portional to the strength of the current. This much is expressed by Ohm’s law, H= RQ, which is a carefully verified though empirical statement. But, analyzing R into specific resistance of material (p) and sectional area of conductor, and permitting ourselves to regard ee as proportional to the velocity of electricity in a circuit of different thicknesses, we perceive that Ohm’s law means that ANS): eae dg =P% Velocity. Let us then postulate, between electricity and any given kind of conducting matter, a connection which shows itself as an E.M.F. proportional to the speed of their relative motion and to the specific resistance of the material. Molecules of matter are not at rest, but (say ) vibrating at a rate depending on, or rather itself determining, the temperature. These motions, as we have seen, cannot be independent of electricity, but they result in no force urging it to flow, because their motions are symmetrical. But place two metals in contact—one hot, the other cold ; or one copper, the other iron: at the junction Pea Aehil: Mag. December (Supplement) 1876, “On a Mechanical Dlus- tration of Thermoelectric Phenomena.” 342 Prof. Oliver Lodge on the Seat of the symmetry disappears, there must be constraint and accom- modation ; and, in whatever precise way this acts, it seems probable that it can be conceived of as having the same effect as a layer of molecules moving faster on their outward journey than on their return. If any such dissymmetry of velocity were produced, it would exert a propelling force on electricity* in the direction of the greatest velocity, because the force is proportional to the velocity. This is the crude and tentative way in which I picture to myself the Seebeck or true contact-force—the cause of thermoelectricity and of the Peltier phenomenon. But now, why is this force so small in ordinary metals? Because it depends on p, the specific resistance, and this is small. Choose badly conducting metals like bismuth and antimony, or still better selenium and tellurium, and the force will be greatly increased. Choose so-called nonconductors, like glass and silk and ebonite, and it becomes enormous. But when one uses nonconductors we cannot expect to excite currents flowing in closed circuits ; we can only expect elec- trical displacement and electrostatic phenomena ; and indeed it is no such easy matter for electricity to move in such sub- stances, even though the force urging it be excessive ; and a little mechanical violence (friction) may be necessary to help it to move. But remember that no amount of friction can determine the motion in one direction rather than another : working a pump-piston exhausts no air unless there are valves. Friction may supply some of the energy, but the directing force must be in the substances in contactt. To assist the passage it is customary in electrical machines to touch together a conductor and insulator rather than two insulators. I doubt not that when metal touches glass the surface of contact would become chilled as soon as any transfer of electricity were really produced by the force ; but the heat developed, by the friction apparently necessary to aid the transfer, effectually masks any chilling. Measurement of contact-force between insulators is beset * I do not say necessarily on positive electricity. It seems a complica- tion ; but Sir William’s researches show that it is positive in some metals and negative in others. In the case of lead only does the grip on both electricities seem the same. + Mr. Joseph Thomson (Proc. Roy. Soc. 1876) endeavoured to extend ordinary contact methods to nonconductors. He was hardly likely to get very clear results; but he was able to find some electrical transfer as the result of mere contact, if it be admitted that it is possible to apply mere contact and no sort or kind of violence—a supposition which is probably inadmissible. Yet the least violence destroys all novelty, and sends us back to Thales. Electromotive Forces in the Voltaic Cell. 343 with difficulties, because it is so difficult to make electricity pass across the junction. No limit to the force has at present been observed: whenever an electrical machine reaches its limit, and refuses to charge its prime conductor or a Leyden jar to a higher~potential, it is accounted for by saying that the rate of leakage is now equal to the rate of production (which is undeniably true), but nothing is said about whether the rate of production is the same as it was when the jar was uncharged. It is a difficult matter to settle, because most of the leakage takes place close to the rubber ; and, though it is quite possible, it is unlikely that a limit to the force will be discovered, by finding the activity of a frictional machine less at high potentials than at low. When the substances in con- tact are two metals, it is impossible for them to drive electricity very hard, for it would, so to speak, slip through their fingers ; but when an insulator is concerned, its grip is so great that probably there is no limit to the force until its insulating power is overcome, and through it. also electricity begins to. slip. Certainly any upper limit must be a very high one, for the force can readily pile up a charge till it produces sparks a foot or more long. Whether Volta forces, or contact-forces between substances and the medium surrounding them, exist for insulators also we do not know ; we have no reason whatever to deny their existence ; but whereas in the case of metals these exceeded the forces acting between the substances themselves, here in the case of insulators they are absolutely negligible by com- parison. Tor intermediate substances they may have corre- spondingly important values; and it seems not unlikely that at the junction of metals with electrolytes, and of electrolytes with one another, the total contact-force may be a complex one—partly chemical, and due to the possibilities of chemical action straining across the junction, and partly physical, due to different velocity of the molecules. 20. The preliminary experiments of Bouty have caused him to believe in the existence of physical contact-forces, at the junction of metals with electrolytes, which cannot be brought into harmony with energies of chemical action. And though the subject is too unexplored in this direction to be ripe for discussion, it may be well to point out that these contact-forces are important in the theory of the voltaic cell even in its simplest form. Why is the H.M.F’. of a zinc-copper battery less than that of a zinc-platinum ? _ Why is the H.M.F. of a zine-lead or iron battery smaller than either ? d44 Prof. Oliver Lodge on the Seat of the The same chemical action goes on in each, zinc is dissolved at one end and hydrogen liberated at the other: how, then, can the H.M.F. be different if it is calculable from the chemical reactions ?* If we picture to ourselves the actual forces in action we shall get a kind of answer indicated to us. In a zinc-iron cell the E.M.F. is due to the zine pulling at oxygen harder than the iron does ; but, since the iron does pull too, with no inconsiderable strength, the balance of force is not so great as if the iron were replaced by copper, which pulls less, or by platinum, which barely pulls at all until it is coated and alloyed with hydrogen. This answer cannot be considered as complete, and in order to complete it consider a more precise experiment. Arrange a series of common dilute acid voltameters, with their plates respectively, zinc zinc, zinc iron, zinc copper, and zinc platinum. Pass one current through the series, from zine to the other metal, and measure the differences of potential between the plates in each cell. Now the same chemical action is going on in each. In each, zinc is dissolved at one side and hydrogen evolved at the other—the only difference being that it is liberated from surfaces of zinc, iron, copper, platinum, in the four cases. What is to prevent the H.M.F. between the terminals of each voltameter from being the same? But itis not the same (pace Prof. Exner): the zinc- zinc cell shows the greatest difference of potential between its terminals, the zinc-iron less; and the zinc-platinum may easily show a reverse difference because it helps the current on instead of hindering it. It will be understood that the precise behaviour of the cells is determined by the intensity of the current (7. e. current per area)—if it is weak, even the zinc- iron cell may help it on, but the zinc-platinum will help it on most: if it is very strong, even the zinc-platinum will retard it, but the others will retard it more, and the zinc-zine most. Now why is all this? ‘Take the difference between the heats of formation of Zn, SO, and of H,, SQ,, at the comma, and you will have the total energy assimilated by the current * Professor Exner cuts this knot in characteristic fashion by asserting roundly that the E.M.F. of all such cells is the same, and that it matters nothing what metal is opposed to the zinc of a cell so long as it does not alter the chemical action going on. He further asserts that all batteries are non-polarizable and quite constant, as soon as they have got rid of dissolved air and before sulphate of zinc has accumulated. He verifies these extraordinary statements, to three significant figures, by straight- forward experiment. See his paper “On Inconstant Voltaic Batteries,” cited above. Electromotive Forces in the Voltaic Cell. 345 in each cell. This energy is the same in all the cells, but not in all does it take the same form. In the zinc-platinum cell it mainly results in driving the current forward. In the zinc- zinc cell it wholly results in a Peltier (or Bouty) generation of heat. In going out of the cell by a cathode zinc plate, it has to move hydrogen towards it, and (ipso facto) oxygen away from it, in opposition to the strong chemical attraction ; thus it will do work and liberate energy, which, since there is nothing better to do, must exhibit itself as heat. At an iron surface less heat is generated, and at a copper less still ; but, at any cathode which attracts oxygen, some heat must be generated by a current made to do work in opposition to this attraction. In the zinc-zine cell there is no propulsion of electricity at all by the cell; on one side, where the current enters, zinc is dissolved and the current helped forward with the full energy (or nearly the full energy) of the combination, so that no (or nearly no) waste energy or heat is there produced ; but on the other side, where the current leaves, the same combination is (not exactly undone but) opposed and the current hindered with (probably something less than) the full energy of the combination, and there the heat of combination is generated. Thus, regarding the passage of hydrogen to the cathode as a virtual separation of O (or SQ,) from it, we may say in general that in any one of the above cells used as a volta- meter, the energy available for helping the current on is that represented by the difference between the combination-energies of the substances respectively attacked and liberated ; 7. e. Zn, SO,—H,, SO,; but that besides this, the combination M, SO, is virtually undone ; and, since the energy of this com- bination appears asa generation of heat at the cathode, it is so much to be subtracted from the propelling force available for the current, only the balance being left for this purpose, viz., Zn, S0,—H,, SO,—M, SO,. Whether one ought to write SQ, or O in these expressions I am not sure, but it is not essential to decide this at present. Another way of regarding the matter is to say that the force propelling the current is that due to the difference of energies Zn,O—M,O, but that as soon as a current actually passes and hydrogen is liberated it coats the cathode more or less thickly, and an extra term must be subtracted from the above to represent the opposition force of this hydrogen. The efficacy of this hydrogen as a current-opposer must ~ 346 Prof. Oliver Lodge on the Seat of the depend in some way on the intensity of the current itself, since with a feeble current it will be able to dissipate itself faster than it forms, and with a strong current it will thoroughly coat the plate and the balance will escape. Sup- pose, then, we represent the force exerted by the hydrogen as H,,0 f (C) ; where f (0)=0, and /(o )=1 or something like 1; then the force available for urging the current forward in any of the above cells is, in volts, 45000 { Zn,O—M,0—H;,0 # (C) j. There is an obvious objection to be taken to this last hypothesis, viz. that it supposes the second metal M completely operative, even though it be thoroughly coated with hydrogen. This is hardly reasonable; and a compromise between the two preceding hypotheses is afforded by one of greater generality in which the available force is symbolically represented by Z4n—M ¢$ (C)—H; f (©), where ¢ is a function such perhaps that ¢ (C)=1-+7. fo). On this hypothesis the propelling H.M.F. is e=a5h55 {Zn,0-M,O—(H,,0-+n. M,0) f (C)}. This is too much like miscellaneous guessing, and we will make no more of such hypotheses; but if experiment could fix an empirical formula for this force in any case, we could apparently at once obtain the Joule or Bouty effect,* or rather the difference of two such effects, for that case ; because we should have the E.M.F’. experimentally observed on the one hand, and that calculated from pure energy-considerations on the other, as Zn,O— H,,0 Seclinne ae where the two B’s stand for the Bouty coefficients at the zine and the other metal respectively. The only objection is that in the cells now under discussion M is coated more or less with hydrogen, and hence the Bouty effect obtained is nothing very easily definable. * That is the thermoelectric contact-force at a metal-liquid junction: see section 6, Electromotive Forces in the Voltare Cell. 347 21. To see if the actual behaviour of such cells at all bears out a hypothesis formed on the above plan, I have made some rough experiments on the lines suggested ; that is, I passed the same current through different simple cells. There are so many sources of uncertainty and of variation, that it would be very difficult to get really definite and reliable results. Thus, for instance, the back H.M.F. will depend considerably upon how long the current has been flowing, and so the read- ings will differ according to the time they are taken. The metals I used were zinc-zinc, zinc-copper, and zinc-platinum ; and it was found necessary to put the cathode-plate in a porous cell to avoid deposition of zinc on it. But it was now diffi- cult to compare the cells easily when arranged in series, because different porous pots had different resistances. I therefore ultimately decided to use the same porous pot and the same anode zinc plate, and to substitute the other plates one after the other, making the current as nearly the same each time as convenient (by adjusting resistance) and allowing for outstanding discrepancies. An amperemeter placed in circuit measured the current, and the voltameter used was a reflecting galvanometer with some 380,000 ohms in its circuit. Its indications were interpreted absolutely by tapping off, at the same time as the cells, the difference of potential between the terminals of an ohm (or j or 3 ohm) coil placed in the circuit. Any two values of the strength of current enabled the in- ternal resistance of the cell to be calculated, provided its E.M.F. remained constant. With low currents it did seem to be fairly constant, and a mean value of the internal resistance ry is reckoned from these as } chm. The area of each plate under the liquid was exactly the same, and measured 3 inches by 2? inches. Both faces of each plate were exposed, though naturally one face was more active than the other. The arithmetical reductions are rather long ; the results are all that I give. It will be perceived they are anomalous in places, a great deal of this being dependent on whether the reading of H.M.F’. was taken soon after a current-change or not. As I said before, the plan of experiment is avowedly rough, though the actual readings were carefully taken ; but without understanding more about the circumstances of the case, and what possibilities of variation there are, I do not see how to plan a perfect system of experiment on the subject. I will first give relative numbers, simply comparing the differences of potential between the terminals of the three 348 Prof. Oliver Lodge on the Seat of the cells when the same current is going through each, the resist- ance of each being the same, viz. } ohm; and then I will interpret the observations absolutely, calculating the H.M.F. of the cell under different currents, and seeing what empirical formula will best fit it. Relative Differences of Potential between the Terminals of three Voltameters of the same Resistance, through each of which the same current is driven by an auxiliary battery. Anode of each cell, zine ; cathode—zinc, copper, and pla- tinum respectively. Deflection of Electrometer attached to the terminals of Current flowing through each cell, in amperes.| the Zinc-Zine |the Zine-Copper| the Zinc- cell. Platinum cell. eell. DD —125 +70 to +90 94. —148 + 26 1:88 — 486 — 15 15 —440 + 15 2-4 —535 = oD 2-0 —486 — 8 2°4 —626 —140 1:96 —575 — 77 32 —'700 — 225 2°73 — 630 — 250 4:2 — 800 — 347 3:4 —TAl — 250 In the above Table the difference of potential between the terminals is written negative when it opposes the current, and positive when it helps it on. We will now interpret similar measurements absolutely, reckoning the actual H.M.F. of each cell, and try to fit an empirical formula to it on the plan of those (in sect. 20) already guessed ; assuming /(C) a linear function, for sim- plicity, until forced to try something more complex. It is quite impossible that f(C) can be a linear function really, but it very likely begins by being so, and only for big currents diverges notably. A hyperbolic tangent function, at a guess, would seem most likely to represent the case properly. Electromotive Forces in the Voltaic Cell. 349 Hlectromotive” Force of a Zine-Zinc, Dilute Sulphuric-Acid, Cell, of Resistance 4 ohm, through which the specified currents are driven by two or three Grove’s; each plate exposing 53 square centimetres on each face. Difference of | Observed E.M.F. Ourrent, in 5 of cell (obtained | H.M.F, calculated amperes, eee by adding rC to | from the formula ; eet : the preceding e=—3C. S. column). 552 — 37 — 26 — 276 424 = eee — ‘25 — ‘212 ‘936 — 44 — 25 — 468 “744 — ‘40 — ‘25 — 372 1°88 —1:46 —1:08 — 94 15 —1:32 —1:02 — "75 2°4 —1-61 —1:13 —1-20 1:97 —1-46 —1:07 — ‘99 2:4 —1-'88 —1-40 —1:20 1:94 —1:80 —1-41 — 97 3°22 —2°10 —1°46 —1°61 2°68 —1°88 —1:34 —1:34 3°36 — 2°22 —1:55 —1:68 4:24 — 2°40 —1:55 —2°12 The agreement between the observed and calculated columns is not very bad ; and the polarization H.M.F. does not show decided signs of breaking away from the law of simple pro- portion until a current-strength of 4amperes is reached—say an intensity of ‘04 ampere per square centimetre of total surface. Electromotive Force of a Zine- Copper, Dilute Sulphuric-Acid, Cell, of Resistance £ ohm, through which the specified cur- rents are driven by two or three Grove’s; each plate exposing 53 square centimetres on each face. H.M.F. reckoned positive when it helps the current forward, nega- tive when it opposes it. Difference | Observed H.M.F. H.M.F. cal- Current, in | of potential | of cell (obtained | E.M.F. calculated| culated from amperes, | between ter- | by adding rC to | from the formula | the empirical C. minals, in the preceding e= "8-40. formula volts. column), e='D8—4C. 55 + 24 +°35 +66 =a “94 +. 078 4°27 +54 +°39 ‘76 + °108 +:26 +61 oe 1:88 — ‘045 +°33 +°33 +°20 1-52 + -045 +°35 +42 +27 2°4 — 195 +28 +°20 +10 2:0 — 024 +°38 +°30 +18 2°4. — 42 +°06 +-20 +10 1-98 — 221 +18 +30 +18 3°22 — 675 —°031 —°05 — 06 2-75 — 75 — 2 —‘1l +03 4:16 —1-04 — 21 — 24 — 25 344 — “75 — “06 — ‘06 — ll Phil. Mag. 8. 5. Vol. 19. No. 120. Adfay 1885. 2B 390 Prof. Oliver Lodge on the Seat of the Here two alternative formule are given; it is a matter of opinion which shows the least divergencies from the column of observed values. The first is the one most naturally suggested by the theore- tical considerations of sect. 20, the 8 standing for Zn/O—Cu/O, or what is commonly called Zn/Cu. Electromotive Force of a Zinc-Platinum, Dilute Sulphuric- Acid, Cell, of Resistance 4 ohm, through which the specified currents are driven by two or three Grove’s; each plate exposing 53 square centimetres of surface on either side. H.M.F. reckoned positive when it helps the current on. Difference | Observed H.M.F. | E.M.F. cal- EMF. cal- Current, in | of potential | of cell (obtained | culated from inka amperes, | between ter- | by adding rC to | the empirical ae 2 ain C. minals, in the preceding formula ae volts. column). c= 4— 10. | ee "552 + °26 +°37 +°35 +102 “44 + :30 +39 +°36 +1:05 "936 + :12 +31 +31 + 89 “SEs + 17 +°33 +°32 + 94 1-88 + °15 +52 +°21 + 57 1°52 + °33 +°63 +°25 + ‘69 2-4 + °45 +°93 +°16 + -40 20 + °24 +°64 +20 + °53 2-4 — °30 +:18 +16 + -40 1-96 — 09 +°30 + -20 + ‘55 3°22 | — ‘60 +°04 +08 + 13 2°72 — ‘35 +20 +:13 + :29 4°16 —10 — 17 — 16 — 19 3°36 — 63 +04 +06 + 08 Here also are two alternative formule given, of which the first agrees best with the experimental results. Butit is very strange that the H.M.F. of this cell should be so low when the current is feeble : it is scarcely more than that of the copper cell. The only way I see of accounting for the error (if error it be) is that the platinum was put into the liquid after the copper plate, and it was sometimes found coated with a very thin evanescent film of copper when taken out. Theoretical considerations would suggest something more like the second formula as the probable H.M.F., the 1:2 being what is ordi- narily called Zn/Pt. 22. I can now continue the quotation of the remainder of the preliminary notes with the certainty that they will be at any rate intelligible. I begin with statements intended to be true for substances of every kind, and then specialize them for the case of metals. Electromotive Forces in the Voltaie Cell. aol III. Statements believed by the writer to be true, though not entirely orthodow. xii. A substance immersed in any medium tending to act upon it chemically is (unless it is actually attacked) at a different potential to the medium in contact with it ; positive if the active element in the medium is electro-positive, negative if the active element is electro-negative. xiii. The above difference of potential can be calculated approximately from the potential energy of combination between the substance and the medium; the energy being measured by compelling the combination to occur, and obser- ving the heat produced per amount of substance corresponding to one unit of electricity. xiv. In addition to this contact-force, due to potential chemical action or chemical strain, there is another which is independent of chemical properties but which seems to be greatest for badly-conducting solids, and which is in every case superposed upon the former contact-force, the two being observed together and called the Volta effect. Very little is known about this latter force except in the case of metals ; and in these it varies with temperature, and is small. In the case of non-metals it is often much larger than the chemical contact-force™. xv. The total contact-force at any junction can be expe- rimentally determined by measuring the reversible energy developed or absorbed there per unit quantity of electricity conveyed across the junction (practical difficulties, caused by irreversible disturbances, being supposed overcome). xvi. In a chain of any substances whatever, the resultant ¥).M.F. between any two points is equal to the sum of the true contact-forces acting across every section of the chain between the given points (neglecting magnetic or impressed forces). xvii. In a closed chain the sum of the “ Volta forces,”’ measured electrostatically in any (the same) medium, is equal to the sum of the true contact-forces; whether each individual * T here assume, what I suppose is recognized as true, that what is known as frictional generation of electricity is really due to a contact-force between the substances rubbed—a force which is exceedingly great for insulators (see § 19). Davy seems to have held this view, from a note on p. 50 of his Bakerian lecture in 1806, cited before. + These difficulties are, however, tremendous for most substances except metals. M. Bouty’s is the only attempt I know of to examine junction-energy between metals and solutions of their salts, which is the case next in simplicity to metals. Observe that the statement says energy, not heat only. 2B2 352 Prof. Oliver Lodge on the Seat of the Volta force be equal to each individual true force or not. See section 7. xvill. Wherever a current flows across a seat of E.M.F., there it must gain or lose energy at a rate numerically equal to the H.M.F’. multiplied by the strength of the current*. Development of the above and special application to Metals. xix. A metal is not at the potential of the air touching it, but is always slightly below that potential by an amount roughly proportional to its heat of combustion, and calculable, at any rate approximately, from it. For instance, clean zine is probably about 1:8 volt below the air, copper about °8 volt below, and so on. If an ordinary oxidizing medium be sub- stituted for “air’’ in the above statement it makes but little difference. xx. Two metals put into contact reduce each other instantly to practically the same potential; and consequently the most oxidizable one receives from the other a positive charge, the effect of which can be observed electrostatically. xxi. There is a slight true contact-force at the junction of two metals which prevents their reduction to exactly the same potential; but the outstanding difference is small, and varies with temperature. It can be measured thermoelectrically by the Peltier effect, but in no other known way. It is pro- bably entirely independent of surrounding media, metallic or otherwise}. xxii. If two metals are in contact, the potential of the medium surrounding them is no longer uniform: if a dielectric it is in a state of strain, if an electrolyte it conveys a current. xxiii. In the former case the major part of the total dif- ference of potential is related closely to the difference of the potential energies of combination, and is approximately calculable therefrom. In the latter case the total H.M.F. is calculable accurately from the energy of the chemical * A current gains energy at any junction at which heat is absorbed, or chemical combination permitted, or any other form of energy destroyed, by the passage of the current. The current gains the energy which has in the other form disappeared. A current loses energy at a point where it causes other forms of energy to make their appearance; e. g. generation of heat, decomposition of che- mical compounds, &c. 1 To distinguish between Peltier-force and Volta-force henceforward it will be best to write Bi/Sb or Zn/Cu for the former, and Zn/Air/Cu or Fe /Water / Pt for the latter. The force electroscopically observed is Air/Zn/Cu/Air, but this involves both; the right way of denoting the Volta effect pure and simple is Zn/Air/Cu. Eleetromotive Forces in the Voltaic Cell. 3903 | processes going on, minus or plus the energies concerned in reversible heat-effects*. xxiii a. “The E.M.F. of an electro-chemical apparatus ”’ whose energy is entirely expended in maintaining a current “is equal to the mechanical equivalent of the chemical action on one electro-chemical equivalent of the substance.”’ (Thom- son. xxiii b. “ If the action in a cell consists in part of irreversible processes, such as (1) frictional generation of heat, (2) dif- fusion of primary or secondary products, (3) any other action which is not reversed with the current, there will be a certain dissipation of energy, and the H.M.F. of the circuit will be less than the loss of intrinsic energy corresponding to the electrolysis of one electro-chemical equivalent. It is only the strictly reversible processes that must be taken into account in calculating the H.M.F. of a circuit.” (Maxwell : ‘ Hlemen- tary Electricity,’ p. 148.) xxiv. There are two distinct and independent kinds of series in which metals (and possibly all solids) can be placed : one kind depends on the dielectric or electrolytic medium in which the bodies are immersed, the other kind depends on temperature. The one is the real Volta series, but it is the eommonly observed Volta series minus the Peltier; the other is the Peltier or thermoelectric series. ‘To reckon up the total .M.F . of a circuit, we may take differences of numbers from each series and add them together. 23. It is necessary to illustrate the meaning of this last statement, No. xxiv. By “real Volta series’ I mean such series as we have attempted to calculate from purely che- mical data, because they depend on chemical tendencies. By “ Peltier or thermoelectric series’’ I mean those giving a purely physical H.M.F., produced we know not quite how, whose energy-source is not chemical but thermal. We have on the one hand a number of Volta series, each for a special medium, and on the other a table of thermoelectric powers at different temperatures. The latter can be conveniently repre- sented by a number of curves, because temperature varies continuously ; Volta series, on the other hand, can hardly be represented geometrically, because the transition from one medium to another is probably per saltum; at least, it is not * Such, for instance, as we have been discussing under the head of in- constant or simple voltaic batteries (sects. 19-21). These reversible heat- effects indicate the presence of thermal contact-forces which, wherever they exist, prevent chemical data from giving E.M.F. accurately: they also must be taken into account. We have called them Joule or Bouty effects. 304 Prof. Oliver Lodge on the Seat of the known what is the effect of mixing media, and so passing gradually from one to the next. | We have given several Volta series; and, for the sake of completeness, I will now give some Peltier series for a few substances according to the experiments of Professor Tait at different Centigrade temperatures. Jxpressing each number as a function of the temperature, we are able to give an infi- nite number of Peltier series in one table. The range of temperature over which this table may be interpreted -is from —18° to 400° or so, provided the metals do not begin to melt. Non-metallic substances have not yet been introduced into such series: much experimental work remains to be done before they can be. The metals used by Tait were not chemically pure. True Contact E.M.F. or Peltier Series. (Microvolts.) Metals. At any Temperature 2° C. |At 10° C.) At 100° C. MOM ig aee he eae eeesee hemes —4760— 3-94¢+ 04877? | —4795 | —4667 iardiiPlatimuma. -ecae.ece — 718— ‘54¢+:007527 | — 722 — 697 Sonn elatimumas eee + 168+ 363¢+:0117 + 205 + 641 Vinemesiim, 20). cere sar — 618+ -36¢+°00952? | — 613 | — 487 German Silver ............ +83104+2617¢+ 0512 | +357 +6439 Gadi GL aees Sea - — 73l—1446¢—-0429027 | — 880 | —2606 ZING jes oatres Shisiea aan chars ee — 643— 8957-0247? — 735 —1778 Dilivelesi cee mst aoueeae skeet — 590— 626¢—-015?? — 654 | —13866 AVOAG? pact eees Nees ee scenes: 0 0 0 Copper ssid. seni sase02 — 874— 3:96¢—-00952? | — 415 | — 865 ee lence, Se een erate Soe + 118— 1:08¢—-00552? | + 107 | — 45 PN arMeYANUTTY, ee. eat oer + 211— °31¢—-00392? | + 207 + 141 paleo RSs: +1718+16°15¢+ 0362 | +1883 | +8693 othetical* Mercur Leis y \ +1800+ 46¢ —-0072 | +1845 | +2190 To find the E.M.F. of a junction at a specified temperature we have only to subtract the numbers in the above table, inserting the value of the temperature. Thus a junction of zinc and copper at 10° has an E.M.F’. of 320 microvolts, act- ing from copper to zinc; and a unit current sent across such a junction from copper to zinc, or from zinc to copper, absorbs or generates heat at the rate of 320 microwatts, and the current gains or loses energy at the same rate. Clerk-Maxwell says that the force is one microvolt, and that it acts from zinc to copper (‘ Hlementary Hlectricity,’ p. 149, note) ; but he only means, I suppose, that the H.M.F’. of a zine-copper circuit with one junction a degree hotter than the other is a micro- * This row of numbers is little better than a guess from some curves given in Wiedemann’s Elektriceitdét. A more probable deduction from some quite new experiments of C. L. Weber (Wied. Ann. November 1884), gives, for mercury, 1181+5°68¢+ 00527. (Cf note to sect. 27.) Electromotive Forces in the Voltaic Cell. Shs, volt, and is such as to drive the current from zinc to copper across the cooler junction; at least this is true above —60° or —80°*. Hitherto we have supposed. the circuit to be all at one temperature ; but if different parts are at different tempera- tures, we shall have to use a yet further series, viz. a Thomson series, for the H.M.I. acting in any one substance with a difference of temperature between its ends, or the force acting at a junction of two pieces of the same metal at different temperatures. This series can be deduced from the preceding, using only the coefficient of ¢?, and multiplying it by the difference of the squares of the absolute temperatures of the two ends of the piece of metal. Such a series then stands thus :— Thomson Series, or H.M.F’. in a metal whose ends differ in temperature. (Microvolts.) Pom ee. 0487 (G8) {274 3G Th) German silver . “0512 (4, -&){274+3(4,+%)} Mae s . . "024 (1-8) {2744+ tee) t and so on. Whether a series of this sort can be made to include any non-metallic conductors also, has not yet been discovered. M. Bouty’s experiments provisionally indicate the very inter- esting fact that Sir W. Thomson’s general thermodynamic laws of the thermoelectric circuit apply perfectly to circuits which include some electrolytes as well as metals. Now the meaning of statement No. xxiy. is as follows: Regard zinc and copper in contact as a circuit completed by air or by water, as the case may be, and let the temperature be uniform, and say 10°; to reckon up the total H.M.F. we must look in the proper Volta series for Zn/air (or Zn/water), which we find 1°8 say; for Zn/Cu, which we don’t find, or find zero ; for Cu/air, which we find ‘8. Then we must look in the 10° Peltier series for Zn/air or Zn/water, which at present we shall not find there for want of data (possibly we have no right to put them there if we had data) ; for Zn/Cu, * It is always easy to tell from thermoelectric data which way the force acts at a junction; but it is not always the same way as the current flows, by any means. A current, excited by differences of temperature in a simple metallic circuit, may be urged against the force at both junctions. This is the case, for instance, in a copper-iron circuit with one junction above 275° and the other below it by a greater amount. It is customary to say that the current flows across a hot junction from the metal of higher-to the metal of lower thermoelectric value: this is not necessarily true. The safe statement is to say that the electromotive force acts. from high to low thermoelectric value, at either junction. 356 Prof. Oliver Lodge on the Seat of the which we find about 320 microvolts ; and for Cu/air, which again we don’t find. Add them all up with their proper signs, and we have the total E.M.I’. of the circuit. | Again, consider the case of a Daniell cell at a given tem- perature producing a current; we shall have to look in each series for Zn/ZnSQ,, for ZnSO,/CuSO,, for CuSO,/Cu, and for Cu/Zn, and add them all up. It is true that these tables of numbers have practically yet to be made, for at present they include so few substances ; but that does not affect the question of the existence and independence of these two kinds of series. It is, of course, a question how far all E.M.F. of contact may be found to depend on chemical tendency. For instance, when bismuth and antimony are put into contact, does the H.M.F. developed measure the alloying affinity of these two metals? When sodium is dropped into mercury, does the heat produced represent the thermoelectric power of a sodium- mercury junction? When metal touches glass, does the tremendous H.M.I’. developed represent a tendency of the metal to combine with the glass? These are questions for experiment to decide; but to me it does not seem probable that it will reply in the affirmative. We know that Sir W. Thomson, and Davy before him, con- sidered the apparent contact-force at the junction of zine and copper to be due to the chemical affinity between these two metals, and to be measured by the heat of formation of brass; but this we have seen strong reasons for disbelieving. It sounds more probable that the real contact-force at a junction of bismuth and antimony should be due to the chemical affinity between these metals; but perhaps it is no more true. The greater part of a contact-force of this kind is probably due to a physical difference between the metals, such as difference in atomic velocity, and has no close relation to their chemical affinities for each other. It is, however, just possible that part of a metallic junction-force is due to chemical ten- dency between the two metals in contact. Tor instance, take the case of zinc and copper. ‘There is, I suppose, an undoubted affinity between them, as shown by the formation of brass under proper conditions. [If chemists assume the right to demur to this, on the ground that the two metals mix equally well in any proportions, one can choose any other pair of metals—say, perhaps, copper and tin—for which the statement does not hold.| Now does this affinity result in any H.M.F. between them on making contact? This question, I appre- hend, is to be answered by passing a current for a long time across a copper-zine junction and seeing if any brass does, Electromotive Forces in the Voltaic Cell. 357 after a long time, result. Thermopiles show a curious secular deterioration with use, and it may be that some alloying action goes on, though I have never heard of its being noticed. But if no such alloying goes on during the passage of a current, then I should say that, in whatever ways chemical affinity between two metals is able to show itself, it does not show itself as an H.M.F. Observe, I do not for a moment question the existence of a few hundred microvolts of H.M.F. at a zinc-copper junction. I only ask, is this chemical, or is it physical, or is it a mixture of the two? Statement No. xxiv. is general enough to take into account the possibility of its being a mixture of the two at every kind of junction. It is easy to write one of them zero, if so it turns out. 24. We have been led into a pretty wide discussion of contact- force in general; and, before digressing again on the question of a contact-force-determination of the size of atoms, it may be convenient here to quote the remainder of my preliminary notes, which aim at summarizing, in a compact form, the main argument with respect to the immediate subject of dis- cussion, viz. the seat of electromotive force in a voltaic cell, and in ordinary Volta-condenser experiments. IV. Brief Summary of the Argument. xxv. Wherever a current gains or loses energy, there must be a seat of H.M.F’. ; and conversely, wherever there is a seat of E.M.F. a current must lose or gain energy in passing it*. xxvi. A current gains no appreciable energy in crossing from copper to zinc, hence there is no appreciable E.M.F. there. * Note added January 1885,—My attention has just been called to an article by Mr. Oliver Heaviside in the ‘ Electrician’ of 2nd February, 1884, in which he states views very like those contained in these state- ments. Had I known of this paper earlier I should of course have mentioned it, but I did not know of it. Mr. Sprague also, in his book on ‘ Electricity, its Theory, Sources, and Applications,’ on page 331 expresses his belief in much the same sort of way. Although Mr. Sprague is rather too much occupied in tilting against what he considers the absurdities of orthodox and ‘mathematical ” views to work out his own ideas in a very thorough and clear form, there can be no doubt that he has in his own way arrived at very many of the same conclusions as Clerk-Maxwell, though of course in a far less pro- found and satisfactory manner. He has scarcely received the credit due to him for this, and a cutting review of his bock in ‘Nature’ some years back, though justified im parts by Mr Sprague’s supercilious tore, yet falls. into more important errors regarding electrical facts than Mr. Sprague himself falls into. See ‘Nature,’ June 24, 1875, vol. xii. p 144, 358 Prof. Oliver Lodge on the Seat of the xxvil. When a current flows from zinc to acid, the energy of the combination which occurs is by no means accounted for by the heat there generated, and the balance is gained by the current ; hence at a zine-acid junction there must be a considerable E.M.F. (say at a maximum 2°3 volts). xxvili. A piece of zinc immersed in acid is therefore at a lower potential than the acid, though how much lower it is impossible precisely to say, because no actual chemical action ~ occurs. [If chemical action does occur, it is due to impurities, or at any rate to local currents, and is of the nature of a dis- turbance. | xxix. A piece of zinc, half in air and half in water, causes no great difference of potential between the air and the water (Thomson, Clifton, Ayrton and Perry, &c.); consequently air must behave much like water. xxx. If it makes the air slightly positive to the water, as it does (Hankel), it may mean that the potential-energy of com- bination of air with zinc is slightly greater than that of water, or it may represent a difference in the thermoelectric contact- forces between zine and air and zinc and water, or it may depend on a contact-force between air and water. [If sucha contact-foree between air and water exists, it is obviously of great importance in the theory of atmospheric electricity, for the slow sinking of mist-globules through the air would render them electrical*. | xxxi. Condenser methods of investigating contact-force no more avoid the necessity for unknown contacts than do straightforward electrometer or galvanometer methods; the circuit is completed by air in the one case and by metal in the other, and the H.M.F. of an air-contact is more hopelessly unknown than that of a metal-contact. xxxii. All electrostatic determinations of contact-force are really determinations of the sum of at least three such forces, none of which are knowable separately by this means. xxxiii. The only direct way of investigating contact-force is by the Peltier effect or its analogues. [Maxwell.] xxxiv. Zine and copper in contact are oppositely charged, but are not at very different potentials; they were at different potentials before contact, but the contact has nearly equalized them. xxxv. The potential of the medium surrounding them is, however, not uniform. If a dielectric, it is in a state of strain; if an electrolyte, it 1s conveying a current. * Cf. lecture on “ Dust,” Nature, 22nd January, 1885. Electromotive Forces in the Voltaic Cell. 359 . Chapter V. Suggestive. Page 25. Discussion of Sir William Thomson’s contact-electricity limit to the size of atoms, from the new standpoint.....7.........06. 309 26. Suggested mode of ascertaining the heat of formation of brass or am ON rae tae faa Vues Sins 5) 4.chs) 9 sep etn, Sony ona cup a od otal AIOE ERE 360 27. Attempt to determine size of atoms from heats of amalgamation and thermoelectric data. Possible mode of measuring latent heats of liquefaction for metals at ordinary temperatures...... 361 28. Consideration of limit of thinness of a metal sheet exposed to air, and estimate of molecular dimensions therefrom.......... 3638 Size of Atoms. 25. I may now claim to have accomplished my task, and terminate this long paper; but there are several interesting points which arise in connection with Sir W. Thomson’s deduction of a limit to the smallness of atoms from contact data, and these I may be permitted to indicate. Indeed it evidently becomes a question whether or not his argument remains quite valid if the chemical-strain view be taken of Volta’s force. Let us then inquire whether any modification has to be made in Sir Wm. Thomson’s argument, if the hypothesis set forth in this paper be adopted. He says (virtually), Take a number of plates of zinc and copper of specified thickness, arrange them alternately like the leaves of a book with the covers doubled right back, and then shut the book. Directly they touched at one edge they became oppositely electrified and attracted each other, and therefore did work as they approached. By making the leaves numerous and thin enough, and shutting them up close enough, any required amount of work can be thus done with given quantities of metal, provided the thin plates retain the same properties as masses of metal possess; z. e. provided they are not only a few atoms thick. So far there is no possible objection; but _ Sir William proceeds to consider the attraction as depending on the affinity of zinc for copper, and the work he requires of his plates is that evolved in the formation of brass. But if we regard the attraction as depending on the difference of combustion energies, Zn/O—Cu/O, we must, to keep the charge constant, not only take the plates several atoms thick, but we must suppose films of air of sufficient thickness to preserve their normal activities in the way of chemical strain to be shut up with the plates. Given these, the amount of work he has calculated would certainly be done in shutting the book, and a corresponding amount of heat generated. But would this heat have anything to do with the making of brass? So far as I can see, nothing whatever. — 360 Prof. Oliver Lodge on the Seat of the If we intend to make brass, must we not regard the air surrounding the plates as a simple accident, and imagine all air-films removed before beginning the operation? Work with the zinc and copper plates in absolute vacuum, where (on my hypothesis at any rate) the only difference of potential between them is a minute thermoelectric one; there will be an attraction caused by this difference of potential, and work will be done in shutting the book, but to get any appreciable amount of heat the plates must be terribly thin. How much heat really is produced in the formation of brass I don’t believe any one knows; but if it be enough to warm the metals sixty degrees, the lower limit to the size of atoms becomes greatly depressed. In a note near the end of this paper I show that a rise of from + to 2 degrees is all that is probable, on the usual estimate of atomic dimensions; the smaller evolution of heat being caused by alloying the metals at 10° C., the larger being produced by alloying them at 400 °C. 26. Js there much heat produced in the formation of brass ? Is there any way of attacking the question simply? The only way which has occurred* to me is to dissolve brass in acid, and to see whether one gets appreciably less heat than by dissolving its constituent copper and zinc separately. When an alloy is dissolved, I suppose the affinities of its con- stituents are unloosed, or the combination undone ; hence the heat developed during the solution of an alloy, subtracted from that produced during the solution of its constituent metals and mixing of those solutions, ought to measure the heat of formation of the alloy. Dr. Forster Morley, of University College, London (also on the boat), said he might be willing to undertake this observation, which is doubtless a delicate one, for he was engaged in some thermo-chemieal researches. It may not be practicable for the actual case of brass, because of the complication and uncertainty introduced by secondary © products, but a better pair of metals may no doubt be readily found. Adhering to zine and copper as convenient for explanation, the argument, though obviously not the order of experiment, will stand as follows:—Take definite weights of zinc and copper, dissolve them separately, getting heats H, and H, respectively; then mix the solutions, getting a possible further heat-production 4. ‘This is one plan of passing from separate zinc and copper to a solution of a salt of brass. * It occurred in conversation with Professor 8. P. Thompson and Dr. J. A. Fleming on board the Quebec excursion steamer ‘Canada’, and I am unable to say who suggested it. Electromotive Forces in the Voltaic Cell. 361 Next take the same weights of zinc and copper as before and alloy them, getting heat H; then dissolve the brass in the same acid as before, getting heat H;. This is another plan of passing from separate zinc and copper to a solution of a salt of brass. Now, unless external work and secondary products are different in the two cases, we are justified in writing the heats evolved in the two cases equal :— H,+H,+h=H+ Hs. H is the unknown quantity to be determined, and its determi- nation involves four separate measurements, H,, H., Hs, h. The only one of these at all easy to observe is h, and this my assistant, Mr. Butler, has done. Proportions of zinc and copper sulphate, containing equal weights of zine and copper, are dissolved in as little water as will keep in solution any double salt that may be formed on mixing. The zinc sulphate is enclosed in a thin bulb or tube inside the other solution, and left, sereened from stray heat, for some hours. The bulb is then broken, or the liquid otherwise blown out of it, and the liquids mixed. No certain change of temperature so great as a hundredth of a degree has been observed. 27. In thinking over what metals were more suitable, it struck me that the heat of formation of amalgams was a subject easy of direct attack. I therefore, as a preliminary, have dissolved a little granulated tin in mercury. Of course the latent heat of liquefaction of tin has to be allowed for, and the actually observed result is a cooling; but I hoped that the cooling observed would be less than what the latent heat would account for, and that I might then calculate the real evolution of heat due to combination. Unfortunately the only data I know of with reference to the latent heat of tin relate to its ordinary melting-point, at which point it is given by Rudberg as 13:3, and by Person as 14°25. We have no ground what- ever for believing latent heat to be constant, and Iam therefore utterly in the dark as to what the latent heat of tin at ordi- nary temperatures may be. That liquid tin could be super- cooled to ordinary temperatures without solidification is unlikely. I give, however, the data of my experiment (which was carefully performed) in case better latent-heat data are known to some one else:—2°10 grammes of thin granulated tin at 12°-4 were dropped into 502-00 grammes of mercury at a steady temperature of 10°85, contained in a large thin pro- tected test-tube, of which the part sharing the temperature of the mercury weighed 8 grammes. After solution, which took ten minutes, the resulting temperature was found to be 8°82. a 362 Prof. Oliver Lodge on the Seat of the Three minutes later it had risen to 8°99 from surrounding influences. The thermal capacity of the immersed part of the thermometer was equivalent to ‘48 gramme of water. Working on these data, and taking the specific heat of tin as ‘056, latent heat 14:25, specific heat of glass 19, and of mercury ‘033, we find :— Heat disposed of in cooling and liquefying tin . 30°45 units. Disappearance of heat actually observed . . . 48°07, More than can be accounted for without any combination- heat at all! This is rather depressing; but it only shows how wrong is the estimate of 14:25 for the latent heat of liquid tin at 10°C. - Ignorance of the true latent heat thus effectually prevents our obtaining any information whatever, about the heat of combination of tin and mercury, from the experiment. It seems indeed easier to observe the combination-heat by a process of dissolving the amalgam and the metals separately in acid, as already explained for brass, and then to use the above experiment to calculate latent heat from. One might perhaps thus get the latent heats of fusion at various tempe- ratures for metals soluble in mercury. Another alternative, however, presents itself. Instead of trying to reduce the latent heat to ordinary temperatures, one might form the amalgam at a temperature just below the melting-point of tin, and obtain, if possible, the net evolution of heat then. Suppose the heat of combination of the 2°1 grammes of tin with mercury to be somehow or other determined, we have next to suppose the amalgam made otherwise, bringing the molecules together ina reasoned way. Let the same quantity of tin be brought to within molecular distance of the mercury in successive pieces of very thin foil, first made to touch at one corner and then laid down. It is quite true that each flake would be charged with a Volta H.M.F. of, say, *6 volt, and so would attract the mer- cury and do a certain amount of work in laying itself down. But it is not fair to compare an operation thus conducted in air with the dropping of a solid mass of tin into mercury: to be able to compare the two operations, one must perform the foil experiment in absolute vacuum. This being done, the contact H.M.F. is no longer ‘6 volt, but only about 00015 volt according to the experiments of Matthiessen. Good data for this quantity are, however, wanting. Mercury is not one of the metals included in Professor Tait’s series. It was ob- served by Gaugain; and by rather hypothetical deduction Electromotive Forces in the Voltaic Cell. 363 from his numbers, as given pictorially in Wiedemann’s Lilektricitét, I make the tin-mercury Peltier force 1°75 millivolt at 10°*. Taking one of these numbers (15,000 or 175,000 in C.G.S. units), or a better one when determined, we can calculate how near the given mass of tin must be brought to the mercury in order to generate the actual heat of combination, provided one knows the specific inductive capacity of absolute vacuum f. But I do not know it. Thus the supply of data for this case is distinctly unsatisfactory. 28. Let us try whether we cannot do better with a single metal exposed to air, not troubling about the contact of two metals, which is unnecessary, but simply considering one metal in contact with air. * Since this was in type, a paper by C. L. Weber has appeared in Wiedemann’s Annalen for November 1884, on the thermoelectric pro- perties of amalgams, in which mercury itself was examined ; and from the data there recorded, together with Tait’s value for copper, I reckon the thermoelectric value of mercury at ¢° C. as 431-+-‘d¢ absolute electromagnetic units. Whence the Peltier force at the same temperature is 1181+5-G8¢+ 0052? microvolts. The Peltier force between tin and mercury at 10° is therefore 123,800 absolute units, or 1:24 millivolt, which agrees well enough with the rough estimate above. : + Taking this as 1, and assuming the estimate of molecular dimensions hereafter established, and working backwards, one can show that the Peltier force of tin and mercury at 10° is connected with the heat of com- bination of our 2'1 grammes of tin with the 502 grammes of mercury by the relation JII=3'6 x 10° H. The two rough estimates of JIT deduced from Matthiessen and Gaugain respectively (15,000 and 175,000) thus give H as about 4 and {4 of a unit respectively. Hither of these is too small a quantity to be observed in the process of dissolving tin in mercury; so neglecting it we get, from that experiment, the latent heat of molten tin at 10° C. as 20-4. Another experiment made in a similar way gave 19-6. If the above reasoning be regarded as legitimate, a combination of thermoelectric measurements with observed heats of solution in mercury may furnish a means of estimating latent heats of fusion at various low temperatures in general. - Working back similarly to the heat of combination of 1 gramme of copper with 1 gramme of zinc, we calculate ‘077 unit as the heat developed at ordinary temperatures; only enough to raise the mass of brass formed through three eighths of a degree Centigrade. Ata higher temperature, such as 400° C., the Peltier force for these metals is greater, being 4600 microyvolts, and the calculated heat of combination is then 4 of a unit per _ gramme of each, sufficient to raise the whole mass of metal through nearly 2 degrees Centigrade. This, then, is the sort of elevation of temperature one may expect in making brass at a temperature of 400°. 364 Electromotive Forces in the Voltaie Cell. Take a gramme-equivalent of any metal, say 65 grammes of zinc, and imagine it rolled out into a thin sheet of foil of area A. The difference of potential between it and the air being V in electrostatic units, ;,~ in volts, its charge will be oN 300 — where w is the distance between it and the air, a quan- Ww 9 tity of molecular magnitude. ‘The electrical energy of this s which must therefore have been the electrical Makeat: AV charge 1s 5; work done (2. e. the amount of potential chemical energy trans- muted into electrostatic energy) in spreading out the zine over so much surface. [Capillary tension is part of the mechanical work done. | Now let it be rolled so thin that every atom of it is in con- tact with air, 2. e. let its thickness be also of molecular mag- nitude « We can regard its potential energy in two ways: either as chemical or as electrical. Chemically its energy, measured by heat of combination, is 46,000 VJ, where V is expressed in volts. Hlectrostatically its energy is PME ORE Equating these two values, and writing for the quantity of metal m= Auwp, we have the general relation mu Vi = O20 come ax os whence, taking m=65, p=7, and V=1°8, we get, as our esti- mate of linear molecular dimensions, oi xO The data in this calculation are all very definite; hence if the reasoning is legitimate, this estimate ought to be a pretty good one. It is trae that another metal would give a rather different estimate, unless ne were constant for all; but for ordinary metals—e. g. zinc, iron, copper, mercury, silver—this is not so outrageously far from being the case; though discre- pancies arise with such metals as sodium on the one hand, and platinum on the other. But it is very doubtful whether platinum could be regarded as an oxide, however thin it were beaten ; and sodium would probably take fire long before the proper molecular thinness was reached. ‘The several estimates of Sir William Thomson for the size of atoms were given in ‘ Nature,’ March 1870, and are reproduced Lecture-Eaperiments on Spectrum Analysis. 365 in Thomson and Tait, Part II. Appendix F. Ina lecture on the size of atoms delivered at the Royal Institution in February 1883 he restates these estimates with slight modifications thus :— If atomic dimensions are comparable with 10-® centim., brass would rise 62° C. at the instant of formation; while if atoms are so small as 2°5x10-9, it would rise 1000° C. Hence 10-8 is to be regarded as a limit of smallness. A soap-film so thin as 10-* centim. would raise itself 280° by collapsing ; therefore there are not several molecules in this thickness. The theory of gaseous collision, combined with the density of liquids, suggests a range lying between 7 x 10-9 and Ax 10-9, The dispersion of light seems to require atomic dimensions to lie between 10-7 and 107°. The final estimate made by Sir Wiiliam is something between 2% 10-7 and 10;-%, But if the reasoning in the present paper be admitted as correct, it would seem possible to reduce this range of uncer- tainty, and to make an even more precise estimate. XXXIX. Lecture-Experiments on Spectrum Analysis. By H. Cieminsuaw, IA., £.C.S.* § PROPOSE in the following paper to explain some pro- cesses by which all the phenomena in spectrum analysis, usually shown upon the screen in class-demonsirations, may be exhibited without the use of the electric light, which for various reasons is frequently not available. The methods employed depend upon the use of the limelight and the oxy- hydrogen flame : these of course do not give the same brilliant effects as the electric light, but all the phenomena may be shown upon the screen with much simpler apparatus ; and for some of my methods | think I may claim advantages over the usual method of demonstration. i. Spectra of the Alkalis and Alkaline Earths. Debray (Ann. Ch. Phys. [3] lxv. p. 831) proposed the use of the oxy-hydrogen flame for the volatilization of the alkalis and alkaline earths. By a modification of the ingenious method of Bunsen for procuring a monochromatic flame, the sub- * Communicated by the Physical Society : read March 14, 1885, Piul. Mag. 8. 5. Vol. 19. No. 120. May 1885. 2C 366 Mr. E. Cleminshaw’s Lecture-Hxperiments stances in question may be conveniently introduced into the flame. Bunsen made hydrogen in a bottle containing a strong solution of sodium chloride with zinc and hydrogen sulphate, passed coal-gas into the bottle in order to increase the size of the flame, and to assist in the mechanical carrying-over of the spirtings of the sodium-chloride solution, and burnt the mixed gases in a description of Bunsen burner. Instead of burning the mixed gases in air, I propose to burn them in an atmosphere of oxygen, by which I find a sufficiently bright flame can be obtained to show the spectra on the screen. . The mixed gases are burnt from a jet consisting of two concentric brass tubes, the inner of which passes into the gas- generating apparatus, and the outer is connected with a supply of oxygen; the inner tube is from }—,3, inch diameter, and may with advantage be wider at the bottom. A better result is obtained by passing hydrogen into the bottle, since it is not easy to render the coal-gas perfectly non-luminous by the oxygen. A rapid evolution of hydrogen is necessary for a good result. The lens or lenses should be arranged so as to obtain as bright an image of the slit as possible, even at the expense of some spherical aberration. The light obtained with sodium chloride is perfectly mono- chromatic and very bright. I venture to recommend this - method of obtaining a bright monochromatic flame for lecture- demonstrations. With a strong solution of lithium chloride the red band (Li a) can be shown, and on adding some strong solution of sodium chloride the yellow band of sodium. For showing the spectra of the alkaline earths I use a saturated solution of the chlorides and generate hydrogen with zinc and hydrogen chloride. With two OS,-prism bottles a red, orange (Sra), and blue (Sr 6) can be shown on the screen; and, if the slit is narrow, the yellow band of sodium is clearly shown as soon as some sodium-chloride solution is introduced into the gas-generator. If a strong solution of lithium, sedium, and calcium chlorides are used, with two CS.-prisms five bands can be shown on the screen, including the orange, green, and violet bands of Ca. The above method is applicable for all compounds which can be volatilized in the oxy-hydrogen flame, and which are not reduced by the nascent hydrogen. If hydrogen gas is passed into the bottle, or sufficient oxygen used to destroy the luminosity of the coal-gas, no trace of a continuous spectrum can be seen An occasional addition on Spectrum Analysis. 367 of acid, to maintain the evolution of hydrogen, keeps the flame burning brilliantly for some time ; this method might, therefore, be useful for spectroscopic observations for com- parison. ii. Continuous Spectrum showing Bright Bands. If the slit is narrow, the orange and green bands of calcium may often be seen on the spectrum obtained with the lime- light. If the chlorides of the alkalis or alkaline earths are previously melted upon the surface of the lime-cylinder, the bands of these compounds become very bright. Four different compounds might be melted upon different portions, and the spectra of each shown in turn by turning the cylinder. The lime-cylinder should be a “ hardlime;”’ the softer cylinders are too porous. il. Reversed Spectra. The important fact that the light emitted by incandescent sodium vapour is opaque to light from the same source, is easily shown in a striking manner upon the screen by placing the apparatus used for showing the yellow band of sodium in §i.in the centre of an ordinary optical lantern ; a bright ‘disk of monochromatic sodium-light may be obtained on the screen from 4—5 feet in diameter. A small Bunsen burner is then placed as near as possible to the condensing lens, with the top of the tube projecting $ inch above the edge of the lens, which shows the shadow of the tube at the top of the disk upon the screen. When a platinum wire containing a quantity of sodium chloride is introduced into the flame of the Bunsen burner, the dark appearance of the cooler flame is clearly seen on the screen. Reversal of D line. Mr. Lewis Wright states that this can be done with the limelight by burning sodium in a Bunsen burner placed as close to the slit as possible. I have not been able to obtain very satisfactory results by this method ; the flame is too hot. I have been more successful with the following methods :— The sodium is burnt in a small spoon placed between the lens and prism, just below the focus of the rays from the lens, which must be made as small as possible, so that all the rays are made to pass through the flame where the sodium vapour is densest, and none of the light from the sodium vapour is _ focused on the screen, and a much smaller flame may be used. Or the spoon may be placed a little in front of or beyond the focus in the path of the rays ; a shadow of the spoon is seen 2C 2 368 Dr. J. A. Fleming on the Characteristic Curves across the spectrum, and with a small flame a marked thicken- ing of the dark line is seen just above the spoon. ‘The sodium may be burnt in a Bunsen burner or in the flame of a spirit- lamp. If the sodium-flame is placed between the slit and the lime- light, I have obtained a good result by using a Bunsen burner, the flame of which is cooled down to a proper temperature by a mixture of airand carbon dioxide. Care must be taken not to pass carbon dioxide into the flame to excess, otherwise too great a lowering of its temperature takes place. I have, for instance, obtained in this manner a bluish flame which did not show the slightest trace of sodium in a room where suf- ficient sodium had been burnt to make every gas-flame give a strong sodium reaction. The supply of carbon dioxide to the Bunsen burner may be adjusted in the following manner :—A cork is attached to the movable cover which closes the two holes for admitting air, and two holes made in it opposite the air-holes; to one a glass tube is attached which is connected with a bottle, into which carbon dioxide is passed, fitted with three openings. By opening clamps the carbon dioxide may be all passed into the Bunsen burner, or passed directly out from the bottle. The sodium is first brought into vivid combustion, and then the flame cooled down by admission of the proper supply of carbon dioxide. The reversed line may also be shown by burning sodium in a spirit-lamp with four wicks, in the centre of which is a jet for the admission of oxygen. This is placed between the slit and the limelight. On passing oxygen into the flame, the heat may be raised sufficiently high to produce a bright Na band upon the screen, especially if the light from the incandescent lime is somewhat moderated, and turned into a dark band when the oxygen is shut off, proving that the production of a dark or bright sodium-band depends upon the temperature of the absorbent vapour. XL. On the Characteristic Curves and Surfaces of Incan- descence Lamps. By J. A. Fuemine, M.A., D.Sc. (Lond.), Fellow of St. John’s College, Cambridge*. eee issues of a scientific journal? have contained some interesting letters and notes on the life of incan- descence lamps, and on resulting deductions to be made * Communicated by the Physical Society: read March 14, 1885. + ‘The Electrician, vol. xiv. (1885), pp. 246, 294, 311, 347. and Surfaces of Incandescence Lamps. 369 therefrom. The difficulty of the full and complete discussion of this subject is the absence of sufficiently prolonged experi- ments to give statistics reliable for this purpose. These can only be obtained at great expense and by experiments lasting over a considerable time; but the results to hand make a preliminary investigation interesting on the connection which exists between the life of incandescence lamps and other correlated quantities. The manufacture of incandescence lamps has now advanced to such a condition that the accidents of manufacture are greatly under control. The conditions necessary to get a good lamp are fairly well understood, and the physical actions going on in the lamp are also to a great extent known. We now know that the expectations of earlier investigators of getting an absolutely unalterable carbon incandescence lam are not destined to be fulfilled; but we know that the gradual destruction of the filament is an operation dependent upon several causes, which may be greatly delayed by attention to, and success in, certain operations of manufacture. The gradual destruction of the carbon filament in a vacuum lamp is a kind of erosion taking place at one or more points. Observation seems to show that in a single loop-filament this cutting through takes place most generally near the negative side. The determining cause of breakage is, however, tem- perature ; and carbon filaments which present such inequalities of resistance as to give rise to spots of higher temperature might, other things being equal, be expected to be doomed to a short career. Lamp-filaments are therefore like human lives: some come into the world with a taint of disease upon them, in the shape of irregularity of structure, which pre- disposes to an early death ; but nevertheless, as even in the case of suicide, the great law of averages overrides particular instances, and gives us, in the case of a sufficiently extended series of observations, a law connecting the average behaviour under fixed circumstances. Experience gained during three years of commercial manu- facture and use of incandescence lamps has demonstrated that when a large number of filaments are prepared with identical care, and the lamps made with them sorted out into batches, and worked with varying electromotive force, there is a very constant relation between the average efficiency or candles per horse-power and the average duration or life, and the working potential or volts of the lamp. Now, in a general way we do not know what the form of the function is that connects these three quantities, or any two of them, but there have been a large number of observations on the relation of 370 Dr. J. A. Fleming on the Characteristic Curves certain variables which indicate as a most probable form an exponential function. There are four variables between which a relation is required —electromotive force, resistance, candle-power, and life. The third of these is at present somewhat vague and indeterminate. What we really are concerned with is the total eye-affecting radiation ; and our present methods only allow of a certain more or less imperfect comparison of this as a whole with that of a standard candle, or a calculation of the integral deduced from observation of the relative intensities of certain rays. Accordingly, of these four quantities two alone can be measured with any great accuracy. One is merely an average, and the other is necessarily a somewhat ill-defined quantity. Between any two of these variables we can seek a relation, and having a number of observations we plot down these in what are best called the characteristic curves of the lamp. Now two of the most important of these curves are those connecting the electromotive force and efficiency, or candles per horse-power, and the electromotive force and life; and they may therefore be called the principal characteristic curves of the lamp. Three other useful curves may be obtained by plotting down the curves connecting candle-power and current, candle-power and electromotive force, and electromotive force and resistance. These may be called subsidiary characteristic curves. Since the life and efficiency of a lamp vary together with the electromotive force, we can only properly represent the relation between the three by a surface, which may be called the characteristic surface of the lamp. Take three rectangular axes, «, y, z (fig. 1), and let dis- tances measured outwards represent life, candles per horse- power, and electromotive force. Leta curve be drawn on the y w plane, representing the relation of electromotive force and life, and one on the wz plane representing electromotive force and efficiency; let the ordinates be drawn at various points to both these curves, starting from abscissze, representing certain pressures v1, ve, &c. Complete the rectangles on the ordinates kh, 1, &c.; and we see that these rectangles form the orthogonal sections of a solid bounded respectively by the two planes «y and wz, and two curved surfaces, of which the characteristic curves / and k are the traces on these planes. The surface of this volume may be called the characteristic surface of the lamp. We see that the area of the orthogonal section parallel to yz gradually increases to a maximum, and then decreases. This is obviously because, for zero electro- motive force, life is infinite and candles per horse-power zero; and Surfaces of Incandescence Lamps. 371 whilst for very high electromotive force, life is zero and candles per horse-power or efficiency a maximum. Now the area of cross section which is a maximum for a certain value v3 of electromotive force represents the product of life and candles per horse-power, or the maximum candle-hours per horse-power it is possible to get; and the value of k/ is there- fore a very important quantity. I shall call this maximum vaiue of kl the principal modulus of the lamp, because the value of the lamp for commercial purposes is obtained by dividing the numeric representing this principal modulus by the price of the lamp, taking either the cost of manufacture or the selling-price, according as the question is considered from a manufacturer’s or purchaser’s point of view. Fig. 1, Diagram of the principal Characteristic Curves of a Lamp. = =V Gen, The product k/ is itself a function of the electromotive force, and the value of the electromotive force which makes this quantity a maximum is an important one to determine. It is the pressure at which the lamp should be worked in order to realize the greatest quantity of light for a given expenditure of energy in the lamp. Let us next consider the form of the function which ex- presses these characteristic curves. Take, for instance, the curve of life and electromotive force. We do not know whether this curve is a continuous curve, whether it is asymptotic to axis of y, or, in fact, how it behaves beyond 372 Dr. J. A. Fleming on the Characteristic Curves the limits of the values of electromotive force v, for which lamps are incandescent. We have, however, certain values for / corresponding to values of v not lying far on either side of the ordinary so-called “ marked volts’ of the lamp. When the writer was in America he was shown a large number of observations, made with the view of determining the relation between average life and electromotive force, not far on either side of 100 volts, taken for the Edison 108-volt A lamp. For this lamp the life-pressure curve at or near the working- pressure is approximately a logarithmic curve whose -equa- tion is =e where A and e@ are constants; and for the Edison 16-candle 105-volt lamp « is nearly 25; and, accordingly, life varies inversely as the 25th power, roughly, of the electromotive force. In the figures shown to the writer the life-pressure curve had been drawn for pressures corresponding to lives far in excess of what could actually have been observed during the time filament-lamps have been made, reaching up to 11,793 hours. ‘This is obviously improper: we do not know that « is not itself a function of v, and for pressures departing far from the ordinary working-pressure the variation of average life and pressure is not probably expressed by so simple a relation; and we cannot go fairly beyond the limits of actually observed lives. M. Foussat has recently communi- cated to a scientific journal the results of observations on the life of French Edison lamps. TABLe [. Volts. Life. log, (volts). | log,, (life). 95 3595 197772 3°55570 96 2751 1:98227 3°43949 97 2135 1:98677 332940 98 1645 1:99123 321617 99 1277 1:99564 3°10619 100 1000 200000 300000 101 785 2-00432 2°89487 102 601 2-00860 2°77887 103 477 201284 2°67852 104 375 2°01703 257403 105 284 2°02119 2°45332 Now the figures given by M. G. Foussat on p. 246 of ‘ The Electrician ’ for 1885, stated to be the result of a large number of observations on the relation of average life and pressure at or near 100 volts, conform approximately to the above law. Taking M. Foussat’s numbers for life and electromotive force, and Surfaces of Incandescence Lamps. 373 and taking logarithms of both, we have the figures given in Table I. Writing down the differences between successive values of log v and log /, we get the numbers— Pee ants vas 11621 MVD ie se ain tls 10513 BEEIUET feiss «now 11009 AO sands ee 11600 AAG wrccceeee 11323 ADA Cicse ness 10035 HyH /8r¥=42AT, the = indicating summation through all space. Similarly, the electric energy, if there be no electrification, may be 406 Mr. Oliver Heaviside on the written in the two ways, U=2 Hck /8r@=42ZG. If there be electrification, we have also another term to add, the real electrostatic energy, in terms of the scalar potential and electrification. And if there be impressed electric force in the dielectric, part of G will be imaginary magnetic cur- rent, analogous to the imaginary electric current which may replace a system of intrinsic magnetization. Plane Wave.—Let there be a plane wave in the medium. Tis direction is defined by its normal. Let then N be the vector normal of unit length, and < be distance measured along the normal. If v be the velocity of the wave-front, the rate the disturbance travels along the normal, or the compo- nent parallel to the normal of the actual velocity of propagation of the disturbance, we have H=/(z—2) if the wave be a positive one, as we shall suppose, giving a @ ae) ae = ae ee MOR CR On ee. oO (23) applied to H or H. Next, examine what the operator VY or curl becomes when, as at present, the disturbance is assumed not to change direc- tion, but only magnitude, as we pass along the normal. Apply the theorem of Version (9) to the elementary rectan- gular area bounded by two sides parallel to KE of length a, and fe hs Wave fron€ two sides of length 6 perpendicular to E and in the same plane as E and the normal N. Since its area is ab, and 6=dz sin 0, and the two sides 6 contribute nothing to the line- integral, we find that F curl mails Py AS eae eae z applied to E or H or other vectors, in the case of a plane Electromagnetic Wave-surface. 407 wave. Using this, and (23), in the equations of induction (19), (20), they become dH adi VN DIG my! AD} dH ee = oh Here, since the z differentiation is scalar, and occurs on both sides, it may be dropped, giving us RNS re Bee ti) ea) MOND 2eo/ rc BE 7 ee Mian a 5) The induction and the displacement are therefore necessarily in the wave-front, by the definition of a vector product, being perpendicular to N. Also the displacement is perpendicular to the magnetic force, and the induction is perpendicular to the electric force. Index Surface.—Let ear _ eee Ro Hoary be a vector parallel to the normal, whose length is the reci- procal of the normal velocity v. It is the vector of the index surface. By (25) and (26) we have cH=—VcH, therefore —H=c"'VoH; . . (28) and ge Vol), therefore H=e Vol... (9) Now use the theorem (17). Then, if M= fy Mobs, N=CiCol3 + © «© © (30) be the products of the principal permeabilities and capacities, the theorem gives, applied to (28) and (29), a V CoCr et i Ae ye), Come) Mill NOP Rh Kat ot QOZp) Putting the value of H given by (32) in (28) first, and then the value of E given by (31) in (29), we have Ome ON poplin. |» init oon eh OD —nH=p"VoVeocH. . .. . (84) To these apply the transformation-formula (18), giving —mcH=po(cpH)—pH(opo) . . . (88a) and —npH=co(ocH) —cH(eco), . . . (34a) 408 Mr. Oliver Heaviside on the where the bracketed quantities are scalar products. Put in this form {(cpo)p—me}H=po(ouH),. . . . (89) {(aeo)e =np}H =co(ocH), . . 2 See) and perform on them the inverse operations to those contained in the {}’s, dividing also by the scalar products on the right sides. Then EK peo eS Sa a e e e e 37 op (opo)u—me’ Ce ocH (cco )e— np - Operate by c on (37) and by mw on (38), and transfer all operators to the denominators on the right. Then cl o NE ee matte De IE ERE S £1 -tead op (opo)e1—mp7! Pree (39) poll tee o ocH (aco) u-!—ne™! =, say. «ee [It should be noted that, in thus transferring operators, care should be taken to do it properly, otherwise it had better not be done at all. Thus, we have by (37), po as lage cE or B,=c{(opuo)w—me}—"yo, and the left ¢ and the right p are to go inside the {}. Operate by c~? and then again by {}*?, thus cancelling the { }—, giving po = {(ouo)u—mce}c'6y. Here we can move c™' inside, giving po= {(opo)uc*—m} Ry 3 — and now operating by w—1, it may be moved inside, giving o= { (ope )c~'—mp-"} 6, as in (39). | We can now, by (389) and (40), get as many forms of the index equation as we please. We know that the displacement is perpendicular to the normal, and so is the induction. Hence of,=0, oy oy —i Uy ol bie Cas tore . (41) where ; and 8, are the above vectors, [(39) and (40) ], are two equivalent equations of the index surface. Also, operate on (39) by ouec7'!, and on (40) by acu, and Electromagnetic Wave-surface. 409 the left members become unity, by the conjugate property ; hence userid, cons Bole 2s oe (42) are two other forms of the index equation. (41) and (42) are the simplest forms. More complex forms are created with that surprising ease which is characteristic of these operators; but we do not want any more. When expanded, the different forms look very different, and no one would think they repre- sented the same surface. This is also true of the corresponding Fresnel surface, which is comparatively simple in expression. In any equation we may exchange the operators pw and e. Put c=Nv—' in any form of index equation, and we have the velocity equation, a quadratic in v” giving the two velo- cities of the wave-froni. Andif we put Nv=p, making thus p a vector parallel to the normal of length equal to the velocity, it will be the vector of the surface which is the locus of the - foot of the perpendicular from the origin upon the tangent- plane to the wave-surface. By (83a), remembering that a is parallel to the normal, we see that cH, wH, and uN are in one plane; or, (43) HK, N, and w-'cH are in one plane. And by (84a), 7 #H, cN, and cH are in one plane; or, (44) H, N, and c—'uH are in one plane. These conditions expanded, give us the directions of the elec- tric force and displacement, the magnetic force and induction, for a given normal. We may write the second of (43) thus, NV D D =): e s . e e s (45) cf and the second of (44) thus, & Ly = e e ° 2 . ® (46) Cf and as these differ only in the substitution of B for D, we see that the induction of either ray is parallel to the displacement of the other ; that is, the two directions of induction in the wave-front are the two directions of displacement. The Wave-Surface.—Since the velocity-surface with the ~ vector p=UN is the locus of the foot of the perpendicular on the tangent-plane to the wave-surface, we have, if p be the 410 Mr. Oliver Heaviside on the vector of the wave-surface, PPS=P > sein os een || But o the vector of the index-surface being = Nov-!=pv-?, wii have by (47), dividing it by v’, opal... .:. \si..,, 1 arr To find the wave-surface, we must therefore let o be vari. able and eliminate it between (48) and any one of the index: equations. This is not so easy as it may appear. General considerations may lead us to the conclusion thati the equation to the wave-surface and that to the index- cue 9 may be turned one into the other by the simple process oii) inverting the operators, turning c into ¢~! and p into p—". Although this will be verified later, any form of index equation) giving a corresponding form of wave by inversion of operators, yet it must be admitted that this requires proof. That it is: true when one of the operators c or w is a constant does noti prove that it is also true when we have the inverse compound’ operator {(oco)u-!—nce—!}—! containing both ¢ and p, neither: being constant. I have not found an easy proof. ‘This will not be wondered at when the similar investigations of the Fresnel surface are referred to. Professor Tait, in his ‘ Qua-. ternions,’ gives two methods of finding the wave-surface; one from the velocity equation, the other from the index equation. The latter is rather the easier, but cannot be said to be very obvious, nor does either of them admit of much simplification. . The difficulty is of course considerably multiplied when we: have the two operators to reckon with. I believe the following - transition from index to wave cannot be made more direct, or | shorter, except of course by omission of steps, which is not a real shortenin g. Given ch A . aoe (cuc)e!—mp-” (49) =(39) bos, o8i\=0, . . . « .. OO=@a—— po=l, .... .. . O1l= 4a Eliminate o and get an equation in p. We have also poe Py=1,. . ... O24 which will assist later. By (49) we have o=(cpo)c'Bi—mpB,, . . . «en Multiply by 8, and use (50); then O=(ouc)(Bic-'B,)—m(By-18,). . . « (4) Electromagnetic Wave-surface. 411 _ By differentiation, o being variable, and therefore 8, also, —0=2(douc)(B,e“'8,) + 2(ou0)(dByc—'8,) —2m(dBw-"3,). (55) Also, differentiating (53), do =2(dopo)c~'B, + (ono )de—'!B; —mdpB, ; land, multiplying this by 26,, gives 2B,do =4 (doc) Bic 18, + 2(ouo)(dB,c~!8,) —2m(dB,w-'B;). (56) Subtract (55) from (56) and halve the result ; thus obtaining Bido= (dopo) (Pyc~'B:), —(Pyeo Bi uo do=0e,...), rhe (DO) In the last five equations it will be understood that do and d®, are differential vectors, and that doo is the scalar product of do and wo, &c.; also in getting (56) from the preceding equation we have Byde~"B; =B,c~'d8, = dByc~"By, &c. Equation (57) is the expression of the result of differentiating (50), d(oB,)=dop; + «dp, =0, with d6, eliminated. Now (57) shows that the vector in the {} is perpendicular to do the variation of c. But by (51) we also have, on dif- ferentiation, 4 : | BOC Reka he, (0S he ea ate ta OO) | or Hence p and the {} vector in (57) must be parallel. This | gives Hae B (GC By) MG, 892.0 eee OD) where h isa scalar. If we multiply this by c—18, and use | ° ( (52), we obtain | Pee Sinrehu entrée edhe s (60) vor, by (49), giving 4, in terms of cH, | pi= 0; ° ° e ° 5 ° e ° (61) va very important landmark. The ray is perpendicular to the selectric force. | Similarly, if we had started from, (instead of (49), (50), ov (52)), the Bien ke H equations, viz., | ce Ne | aaa 2 (ceo)! —ne-"” “=, couif,=1, ; with of course the same equation (51) connecting p and o, we | 412 Mr. Oliver Heaviside on the should have arrived at h'p=B.—( Bolts Bo)eo3 3 a iy ae ee h’ being a constant, corresponding to (59); of this no sepa- rate proof is needed, as it amounts to exchanging mw and c and turning E into H, to make (389) become (40). And from (62), multiplying it by 4—’62, we arrive at pp "B,=0; oro =0, 2°. re corresponding to (61). The ray is thus perpendicular both to the electric and to the magnetic force. The first half of the demonstration is now completed, but before giving the second half we may notice some other properties. Thus, to determine the values of the scalar constants h and h’. Multiply (59) by o, and use (50) and (51); then h= — (B,c7'181) (eno) = —m(B,u~"B;), the second form following from (54). Insert in (59), then eG Se yee 64. Py one mee, gives p explicitly in terms of wo and ,, the latter of which is known in terms of the former by (49). Multiply this by —18,, using (50); then | 1 pe'B = — eats 8 Sea (65) Similarly we shall find ies h! = =n Boe: Bs) 5. «, ins 7 giving co Bo = —— —~——; .... (67 P= aca n(Boc"B2) se) and, corresponding to (65), we shall have eke. n Now to resume the argument, stopped at equation (63). Up to equation (59) the work is plain and straightforward, according to rule in fact, being merely the elimination of the differentials, and the getting of an equation between p and oc. What to do next is not at all obvious. From (59), or from (64), the same with hf eliminated, we may obtain all sorts of scalar products containing p and £,, and if we could put B, explicitly in terms of p, (60) or (65) would be forms of the wave-surface equation. From the purely mathematical point of view no direct way presents itself; but (61) and (63), considered physically as well as mathematically, guide us at once to the second half of the transformation from the index Electromagnetic Wave-surface. 413 to the wave equation. As, at the commencement, we found the induction and the displacement to be perpendicular to the normal, so now we find that the corresponding forces are per- pendicular to the ray. There was no difficulty in reaching the index equation before, when we had a single normal with two values of v the normal velocity, and two rays differently inclined to the normal. There should then be no difficulty, by parallel reasoning, in arriving at the wave-surface equation from analogous equations which express that the ray is per- pendicular to the magnetic and electric forces, considering two parallel rays travelling with different ray-velocities with two differently inclined wave-fronts. Now, as we got the index equation from BOING ee Beis we a 5's PE ZO)) OtS Cs Dec ne 71 2 a ie a iba Aran O10) IC we must have two corresponding equations for one ray- direction. Let M be a unit vector defining the direction of the ray, and w be the ray-velocity, so that Cae 12 aie tian Mammen homme L (58) Operate on (25) and (26) by VM, giving VMVNH=—vVMcH, VMVNE= vVMyH. Now use the formula of transformation (18), giving N(HM)—H(MN)=—vVMcH, N(EM)—H(MN) = vVMzeH. But HM=0 and EM=(, as proved before. Also v=w(MN), or the wave-velocity is the normal component of the ray- velocity. Hence Mwy MoM ce! aa) oe ON Fe Se) ceria Re) which are the required analogues of (25) and (26). Or, by (69), levies ee Pea ee ae — HV pill... ab Silay cape be Mare are the analogues of (28) and (29). The rest of the work is plain. Eliminating H and H successively, we obtain O=EK+ Vpe-Vock, 0O=H+VpcVppyH ; Phil. Mag. 8. 5. Vol. 19. No. 121. June 1885. 2E 414 Mr. Oliver Heaviside on the and, using the theorem (17), these give O=H+mVpVpuppu-'cH, 0O=H+nVpVc"'pc- pH ; which, using the transformation-formula (18), become O=E + mp~'p(upcE) —u~'cH(p~"p )m, O= H+ ne7'p(c~!puH) —c—'wH (pe—'p)n; or, rearranging, after operating by mu and ¢ respectively, {(pu—'p)mc—p}H=mp(p~'pcE), {(pe~'p)nu—c} H =np(c~"pyH). Or _i p Sp Gepeoa H p ce cpu (pe—p)u—n—e say.» . « (75) These give us the four simplest forms of equation to the wave. For, since ph=0=pH, we have py=90, pye=O. Also, operating on (74) by wo'pe and on (75) by e—pp we get po pey.=1,. ec pey:=1, -. eee two other forms. 71 and ry, differ from 8, and 8, merely in the change from o to p, and in the inversion of the operators. The two forms of wave (76) are analogous to (41), and the two forms (77) analogous to (42), inverting operators and putting p for o. Similarly, if the wave-surface equation be given and we require that of the index-surface, we must impose the same condition po=1 as before, and eliminate p. This will lead us to ocy,=0, opyjy=—m, ... . (78) corresponding to (60) and (65); and opy,=0, ocy,=—n, . = . ene corresponding to (63) and (68); and the firsts of (78) and (79) are equivalent to ocH=0, opH=0; or the displacement and the induction are perpendicular to the normal. ‘This completes the first half of the process; the second part would be the repetition of the already given investigation of the index equation. Electromagnetic Wave-surface. 415 The vector rate of transfer of energy being VEH/47 in general, when a ray is solitary, its direction is that of the transfer of energy. It seems reasonable, then, to define the direction of a ray, whether the wave is plane or not, as per- pendicular to the electric and the magnetic forces. On this understanding, we do not need the preliminary investigation of the index-surface, but may proceed at once to the wave- surface by the investigation (69) to (77), following equations (25) and (26). The following additional useful relations are easily dedu- cible :-—F rom (25) and (26) we get _ Veo Pen ep) and from (72) and (73), VEH 4 p= Eek * : . . . ° : . (81) Also, from either set, [OVA Die a 97a ieaevencg Dea ome acta be eee Average thickness from above . . . ‘00456 cm. By calipers the thickness appeared to be at one end ‘0046; other end -0044 ; between arms ‘0048; average 0046. Take, then, for true thickness between arms, ‘00476. Equipotential Lines of an Electric Current. 423 The measurement with calipers in this case was not made with great care, and the correction here applied is open to some suspicion. With this strip the space between the brass strips B, B (fig. 1) was about 3:2 millim. B. ..(No..1.) Length of main strip when weighed . 4°58 cm. Width of main strip when weighed. . 1:08cm. Area, including that of thearms . . 5°32 cm. sq. Ben ee ee es. PhS 4 ee Density .. Pita aati fo, Average i fuom fheco! fala 4s 23"°00403em:- From the indications of the calipers I concluded that the thickness between the arms was about 13 per cent. greater than the average thickness. Hence thickness between the arms ‘00409 cm. This value, like that given for A, may be wrong to the extent of several per cent. “Distance between strips B, B about 3°2 cm. Capt No. Es) Length of main strip when weighed . 38°75 cm. Width of main strip when weighed. . 1:08 cm. Area of whole se when Beret . 4°39 cm. sq. Meo ht ..!. . 4502 L085 arma, Density. . 844 Average thickness from these data. . 00292 cm. By calipers, thickness at one end ‘0034 ; at other end -0032; between arms ‘0034; average ‘00333 cm. Take, then, for true thickness between arms, ‘00299 cm. Distance between strips B, B, about 3:2 cm. De 2: (Neel:) Length of main strip when weighed . 3°86cm. Width of main strip when Peer . 1:07 cm. Area of whole stri oe . . 445 cm. sq. vee! . 7. get shen 3. UT OS® mene Density .. See Ore Average thickness from these data. . -00291 cm. _ By calipers, thickness at one end ‘0030 ; at other end ‘0030 ; between arms ‘0032; average ‘00307cm. Take for true _ thickness between arms, ‘00304 cm. Distance between strips B, B, about 3:2 cm. 424 Mr. E. H. Hall on the Rotation of the EY. ¢Nowl -) Length of main strip when weighed . 3°70 cm. Width of main strip when weighed. . 1:06cm. Area of whole strip when weighed . . 4°28cm.sq. Weight he tes EM Sos EE CO lena Detistty\) Aen egies ae alti, Average thickness from the data . . °00934cm. By calipers, thickness at one end ‘0098 ; at other end -0100 ; between arms ‘0100; average ‘(00993 cm. Take for true thick- ness between arms, ‘00941 cm. Distance between strips B, B, about 3°2 cm. G. GNovd:) Length of main strip when weighed . 4:17 cm. Width of main strip when weighed. . 1°09 cm. Area of whole strip when weighed . . 95:03cm.sq. Weight ore 5,0 2e a a eer ore ane Density to GOL00" scree pelt aos Gd, eee Average thickness from these data. . ‘00383 cm. From a somewhat careful use of the calipers it appeared that the thickness between the arms was about 4% per cent greater than the average thickness. Take, then, for thickness between arms, ‘00348 cm. Distance between strips B, B, about 3°2 cm. The main object in the experiments upon these metals and their alloys was to determine whether the alloys would range themselves according to any simple law, so that the magnitude of the rotational power in any alloy might be inferred from its known proportions of copper and zinc. Some attempt was made, moreover, to determine the effect of change of tempe- rature in different specimens. It will be seen that the intensity of the magnetic field was kept nearly the same throughout the experiments of August upon copper, zinc, and their alloys. The strength of the direct current was, moreover, of about the same magnitude in all cases, except the experiments of August 11th on copper. On that day the current used was less than one half as strong as that used later. The same strip of copper was tested again August 29th with a current of the usual strength ; and the agreement between the results obtained under so widely different conditions is quite close. In the following table and throughout this article the C. G.S. system is used wherever no statement is made to the contrary. The following symbols used with the tables need explanation :— C means current along line C D (fig. 1). by the expression D Equipotential Lines of an Electric Current. 425 M means intensity of magnetic field perpendicular to plane of paper in fig. 1. R. P. means rotatory power, which is numerically defined Cx MW’ in which D is the thickness of the metal strip, and E is the electromotive force resulting from C and M which maintains the transverse current*. The R. P. is considered positive when E is of such a character as to send a positive transverse current in that direction in which the conducting strip tends to move under the action of the main current and the magnetic force. The temperatures referred to in the tables are those indi- cated by a thermometer placed in the water-tank containing. the plates when under examination (fig. 2). Copper, Zinc, and their Alloys. Composition | _ Composition, | ace. to Pit ER | &e.t s, | chem. anal. | ies Near | e Date. Temp.| M.| C. 1013 | 24° 0 | 2 | Per | Per | Pe FO a Per “ieee | cent. | cent. cent. | cent. | | Coppr.| Zinc. | Coppr.| Zinc. | | (| 100 | 1888. | °C | | | | | (99-9) | Aug. 11} 8 |5700|-0619 | (—521) | | | 6. a G — — eae 4 ue Bf ae a Z as, o — Z 7 Le! 6 Ts — 4/ — Vig. 5 represents a metal strip, having along its middle a slit longer than the diameter of the magnetic poles, between which the slit is placed, 7 and / being corresponding equi- potential lines when the strip is in its normal unstressed condition. Let a magnetic force act as before. Hach of the lines J, / in fig. 5 is rotated about its centre through the same angle as {in figs. 3 and 4. The result is shown in fig. 6. If now a and b be connected by means of a wire a current will flow from a to 6 through the wire. If a and Jb’ be connected in the same way a current will flow from 0’ to a/ through the wire. To get Mr. Bidwell’s case, imagine a narrow bridge of metal to be left crossing the slit between a’ and U’/. Such a bridge would serve as a shunt to the wire which we have imagined connecting a’ and b’, but would not reverse the relative poten- tials of these two points. The lines U, /, as Sir Wm. Thomson pointed out at the Philadelphia meeting, would now take a form something like that shown in fig. 7. As the bridge across the slit becomes wider such lines as J will become more nearly straight, till, finally, the condition of things represented in fig. 4 will be practically reproduced. On the other hand, if the slit in fig. 5 were short compared with the width of the poles of the magnet, a reversal such as Mr. Bidwell detected should not occur. Mr. Tomlinson’s Suggestion. Tn the ‘ Philosophical Magazine’ for May 1884, Mr. Tom- linson stated that certain relations which he had discovered Equipotential Lines of an Electric Current. 435 indicated that the rotational effect in nickel should be greater at low than at high temperatures. He therefore called in question the conclusion to the contrary which I had drawn from certain hasty and very rough experiments made before the use of the water-tank gave me the means of easily con- trolling the temperature of the metal under examination. I have therefore recently taken up the matter again. I used the same piece of nickel with which the former test was made (Phil. Mag. Sept. 1881, p. 163); but the strip was now so much damaged while being fastened upon glass, that it was necessary to cut its width down a good deal in order to obtain the “arms”’ for the side connections. The following Table shows the results obtained :— No. of Exp. Date. Temp. M. C. digpli Be f. July 28,1884.) 22 1717 | :08074 | 14940x10-% 2. » 28 49 | 1703 | :03135 13760 ,, 3. ys) 20°5 1652 | ‘03140 Lay LO ses 4, 5» oO 2°2 1636 | 03123 T2810" 5; 5. fie 21-2.) 1629 | -03121 15060 __,, 6. Aug. 1 2°8 1671 | :03137 13180 7. ye. 26°1 1691 | 03140 | 15110 ,, 8. Ls ae 4-1 1627 | 03112 13220 _,, Combining the Ist, 3rd, 5th, and 7th, we have Temp. RiP. 22°°5 TAICOS 10: From the 2nd, 4th, 6th, and 8th we have 3°°5. 13240 x 10-°. Decrease for 1° fall of temperature = approximately ‘6 per cent. | It will be noticed that the results obtained at low tempe- ratures do not accord so well as those at high temperatures. - This fact is in all probability due to the difficulty experienced in preventing slight fluctuations of temperature while the colder water was flowing through the tank. Irregularity in the flow of this water causes disturbing thermo-electric currents. The quantity called R. P. in this paper corresponds to the ; = of my 1881 paper divided by the F. of that paper. Cal- culating the R. P. of nickel from the 188 experiments, I find it to be about 12700x10~”, for a field of intensity 1660. 436 Mr. E. H. Hall on the Rotation of the In looking about for an explanation of this disagreement, I found that the thickness of the strip had been called :00104 cm. in 1881, and 0012 cm. in the later experiments. The former estimate was obtained by weight, the latter by measurement with calipers. The difference accounts well enough for the different values obtained for the R. P. Which estimate of the thickness is the more reliable I will not undertake to decide. Summary. 10% R.P. at 20° C. Copper . . . . —820 Zico iis ames 1-820 Four alloys of copper and zine were tested. Ifa series be made beginning with zinc and ending with copper, the four alloys being ranged between according to composition, the series thus formed will be the same as that obtained by ranging these metals and alloys according to the algebraic magnitude of their R. P.’s. In the alloys, however, the R. P.’s are algebraically somewhat nearer that of copper than might be expected from the composition. Troi.) a Mie eicte oes R. P. nearly constant through wide range of magnetic intensity, but apparently decreasing slightly at high inten- sities. No ascertained permanent effect. Steel, soft se eet L20GO: Permanent effect about 5 per cent. of temporary effect. Steel, tempered . +88000. Permanent effect about 1} per cent. of temporary effect. Gold (no new test of magnitude of R. P.) . —660 No ascertained permanent effect. CoWaltacuie mae + 2460. Nickel ane — 14740. Bismuth . . —8580000. Antimony. . +114000. A fall of 1° C. in temperature causes in the R. P. of Iron, a fall of 3 per cent. approx. Steel, soft, x 4 i Steel, temp’d, _,, 4 55 Cobalt, zm dl 3 Nickel, 2 ) 3 7) Non-magnetic metals, apparently a small increase. Equipotential Lines of an Electric Current.. 437 Appendin. At the Philadelphia meeting of the American Association I stated that I had compared the behaviour of a strip of soft steel cemented to a plate of glass with that of a similar strip fastened to a plate by means of a clamp. In preparing the matter for publication, however, I found that the test had not been made so carefully as was desirable ; and I have therefore just repeated the experiment with the assistance of Mr. W. A. Stone, of the Harvard class of 1886. I shall call the cemented strip A. It has been already mentioned as No. 1 in the preceding article. The clamped strip I shall call B. Both strips were cut from the same sheet of soft steel. Hach is about 1:1cm. wide and 3:2 cm. long between the terminals of brass. A is about ‘O11 cm. thick and possibly a tew per cent. thicker than B. A suffered rather more than B in the process of adjustment (fig. 1). A was not only fastened to its plate with the cement of beeswax and resin, but was imbedded in the cement,. the latter covering it with a layer, probably a millimetre or more in thickness. ‘The plate was not placed in water for this test. The bearing of the clamp which fastened B to its plate was of wood, possibly a millimetre wide, and extended nearly from arm to arm of the strip. ‘To prevent any very great bending, each end of the strip was loosely tied to the plate with a piece of twine. Otherwise the strip was free and was exposed to the air. The measurements recorded below were made between five and six o’clock, January 17th. There was an interval of one minute between successive readings of the Thomson galvano- meter. No measurement of the intensity of the magnetic field was made. It is assumed that this intensity during the one trial of A, which was made between the two trials of B, was equal to the mean intensity during these two trials. The signs + and — refer to the direction of magnetization, Rand L to direction from the zero point of the Thomson galvanometer-scale. ‘The zero position of the index in these experiments was a considerable distance to the right of the zero of the scale. The tangent-galvanometer measured the direct current through the strip. Thomson Galyv. Tangent Galyv. 74:0 +- — T3°9 ans ihe 0 iat Strip B ) 52 one Gilesuldetok suas 736 52 — 1:5=50°5 73°8, tan.=3°44 438 Prof. Fitzgerald on the Structure of Mechanical 74-9 74:8 Tea i iat on. 147 Sirip A \s ee 74-7 if ” 746 45 129072 «(4°75 tan. =a700 73-7 73°6 BSR 73:5 Sirip B | 580. gh eat 734 25” Z 733 533 = T2=4G-1 73:5, tan 8-38 From 2nd we have AN. 50°2 + 3°66=13°7. From Ist and 3rd 00°5 +461 , 3:'444+3°38 B, + 2 2 Of course absolute agreement in so rough a test was not to be expected. The difference of about 3 per cent. here observed might easily be accounted for. I think Mr. Bidwell will admit that his theory would have predicted a different result of the comparison. Cambridge, U.S., January 19, 1885. =14°2. XLVI. On the Structure of Mechanical Models illustrating some Properties of the dither. By Prof. Grorce FRANCIS FItzGERALD, /’..S.* HE elements of which the model is constructed consist of pairs of wheels so geared together that when one of them rotates it causes the second to rotate in the same direction. The simplest way of effecting this is to connect them by a band, and this is sufficient for a one-dimensional model. Such a model may be constructed by fixing a number of wheels with their axes parallel and at right angles to a plane, and con- necting each wheel with its neighbours by elastic bands. This represents a nonconducting region of the ether. =0. The conductors p; and p, represent the series- and shunt- coils, and 7, represents the external resistance. A Tz Pp Z Hence | io wee [oh p; E, x = Y In this case Ui == (Una 2) 6 The conductors p, and pz represent the series- and shunt-coils, and 7, represents the external resistance. Hence R4=pi, RB’e=rop./ (2+ 2), Rang, + ae te he Fhe) ale 19 Pa Po + pe Slag Hg Rope gom ro( 8, +82) + Sipe , ToT Pe To + Pg of the Compound Dynamo. A67 whence we get p=- fra alta t prt Pa) + Pa(at Pr) VL, 79( sy + Sp) i SPQ Also, since Go esl ar 1+ Pz i My, rs, OL (rat pit pr) +polreatp:) %o(8, +52) +512 9” which may be written ae Le Qs : Asta, Bz,+a3 if i pee J _ Tat pit po P3= Gay ea) Para ey (05) ‘ie 1 81 + So 1 Q=—-, Batt, » 3" bere Sip. 7 "9 And, as before, ae aa aie 2 Ayta, Bata if pe eee elon’ Wes Palit pr) >: (6) o(7,+pitpe)’ Tat Pi + Po Q.= P2 Be 81 P29 as a (8, +55)’ Smyospee eae , and the sum of the resistances of the armature and series-coil for R,,. If the maximum efficiency is attained when 7, has its usual value, we may put the last expression in a form which will be useful hereafter. Let Y be a quantity which has with regard to > the same meaning as w with regard to 7; 7. e. let it be => or 1/> according as ¢ represents the external current or external electromotive force. Then ; n=(VY¥~ VA)/(S¥+VA) 5 and if the maximum efficiency is attained for the usual value of x, PHVA. Conditions of Maximum Power. Since the power of a dynamo is expressed by either of the formule: e} / 2 or c3r2, it is in all cases given by ¢7z. This has a critical value if d 24 = +6=0 . i.e, if ls Q \ le Qe 8) — crea (aay A ee ee ee dr O.18 Piha) OBLn Gta * Gra Conditions of Self-Regulation. Ee EAS, Oe Boe e Dees 18 BY op ae e eis (A+xz) (B+z2) Hence ¢ has two critical values corresponding to the values of x given by the equation a(/ PE/Q)=—BvPLAVQ. If we take the lower signs, w is necessarily negative unless B is negative ; which can only be the case if some of the indu- cing spirals are wound in the negative direction, 7. e. so that they reduce the strength of the magnetic field. If B is nega- tive, it is evident that ¢ is infinite for a positive value of «. This unintelligible result is explained by reference to the Since 472 Prof. A. W. Riicker on the Self-Regulation general equation in which both & and o are included, viz. (E—nk)(E+R/ocS)=nME /co. For if some of the quantities s,, s,, or s, are negative, and if the value of 7, is such that S=0, then H=nk. The approxi- mate expression which is being discussed fails therefore in this case, but it applies to cases in which one of the spirals is wound in the negative direction but in which B remains positive. Reference to the expressions for B shows that this will be the case in the Short-Shunt Machine if the series-coils are negative and if the number of turns is . 9 a Also Lows aie 20 dz ~ (A+a (B+a)>’ whence, at the critical point, a= —2(VP—VQ)'/(A—BYY PQ. . . (18) Hence if A>B, @ is positive and is a maximum; and if A(BP—AQ) /(Q—P), while in (IIL.) it is negative. Next, taking cases in which A —B is positive, we see that oy ThA) BS i>? / Q, ¢ is negative for all positive values of z. Pee A/S BS PL Q> 1, ¢ is positive for values of e>(AQ—BP) /(P—Q). oe) EP/Q>A/B> vyP/VQ>1, ¢ is positive for all positive values of z. In cases (V.) and (VI.) @ has a maximum yalue corre- ~ sponding to a positive value of w. . aE) 1h./P//Q>A/B>1, is positive for all positive values of 2, and X is negative, so that there is no maximum value of ¢. The physical meaning of these different conditions may be best understood by considering the inequalities fee > or <1 and P/Q> or OF or or < Citar Pat apa, SaP1t $1Pa which is identical with (14). Similarly, in the case of the Long-Shunt Machine, we get for the same condition, nM > or < moh, which is identical with (15). Hence, in these cases, B/S orc 474. Prof. A. W. Riicker on the Self-Requlation according as the speed is greater or less than the critical speed for the resistance of the circuit when the external resistance is Zero. In like manner, it can be shown that if @ represents the external current, the expression P/Q > or < 1 according as the speed is greater or less than the critical speed when the external resistance is infinite. Inasmuch, however, as =1/7, when @¢ is the external electromotive force, and 2=72 when @ is the external current, these results may be briefly expressed by saying that P/Q is > or <1, according as the speed is greater or less than the critical speed when w is infinite. Similarly it may be proved that ~ P/Q> or 1; pi(Ta+ Pa) + Papa Sa Pi ("a+ Pa) + apa or if $4 Ta ee aM!” rte eee Ta Tat Pa 8] i Ps epee Pit, Pa whence it follows that we must have om ey Sa) Vat Pa Similar deductions can be made in the other cases. of the Compound Dynamo. 475 The fact that if P/Q be sufficiently large there is no maxi- mum value of @ for any positive value of 2, means that if the | velocity is so great that the inducing magnets are saturated so that the total electromotive force is constant, any increase in the resistance of the external circuit must be accompanied by a decrease in the current which flows through it and an increase in the electromotive force at its extremities. In the former case #=72, and in the latter e=1/ 7, so that in both cases an increase in w produces a decrease in ¢. ‘This state of things is reached before complete saturation, viz. at the point when the prejudicial effect due to the weakening of the cur- rent produced by an increase in 7, overbalances the advantage gained by the fact that a larger proportion of the whole cur- rent passes through the shunt. This point is reached when VP/VQ=A/B. We are now in a position to discuss the amount of change in @ produced by a given finite change in 2, i. e. the self- regulating power of the dynamo. The treatment of this question must be slightly varied, according as a maximum value of ¢@ does or does not occur for a value of x intermediate to ~ and m, the largest and smallest values of that quantity between which self-regulation is aimed at. If it does not, we may write P rast eee Bema ee | se il gee At+pm Btp 14¢7’ where ¢, is the value of the electromotive force or current to be kept constant, and g is a quantity which will be smaller as the self-regulation is more perfect, and which will be positive or negative according as @ diminishes or increases as « increases. If, on the other hand, X lies between » and m, then the equations corresponding to (16) become. aia ele) Pee Os. ie @ At+m Btm 1+ p” P Q © Rrgeer rete ne (Aly) where © is the maximum value of ¢. If the constants are so chosen that the values of ¢ corre- ‘476 Prof. A. W. Riicker on the Self-Regulation sponding to w and m are equal, then pel igunonied Cees IE Q ® where ® is the maximum value of ¢. If, now, the following quantities are given, viz. :— (1) the value of ¢ which is to be attained (¢, or ®); (2) the extreme values of x (« and m); (3) the percentage variation in the value of @ which can be allowed (100g or 100p); (4) the usual value of w (€), together with the condition that the maximum efficiency shall be attained for that value ; (5) the value of the required maximum efficiency ; then we have four equations, viz. either (16) or (17) and the two equations which connect y and € with A and Y (see p. 471) to be satisfied by the five constants A, Y, B, P, and Q. Of these, A and Y are absolutely determined by the conditions ; but any one of the three P, Q, or B may be given any con- venient value if the maximum value of ® does not lie between wand m. If it does, we have the additional relation d=(/ P—VQ)’/(A—B); and if the values of both p’ and p” are assigned, there are in all five equations by which the five constants are determined. When these five quantities are known, we may equate them to their appropriate values in terms of the resistances &c. of the various parts of the machine; and we thus obtain five equations between eight quantities, viz.:—n, M, o, 81, Sa (OF 8), Ta P1y Pa (OF p,); in the selection of which, therefore, there is considerable range for choice. Although the problem of the Self-Regulation of the Com- pound Dynamo is solved as far as the algebra is concerned, it is possible that the values of P,Q, &c. found for arbitrarily selected values of ¢, w, m, Ke. may be negative, or such as it would be impossible to attain in practice. The question as to what value of g it is physically possible to attain in any given case can only be answered if we have regard to the limitations to the values of A, B, P, and Q which apply to that case. If this be done, it is possible to obtain limits to g, that is to the perfection of self-regulation. I shall add two examples of the use of equations (16) and (18) for this purpose. Case II]. AQ. As the values of ¢@ diminish as w increases, the value of the Compound Dynamo. AT7 which corresponds to » must be less than that which corre- spond to m. Hence meee Atm B+m Puy le Q Py Solving for P and Q, we get pa $i bom—9(B+m) . l+q (A—B)(u—m) Gees in) ee ea—m—qA+m) Be Sg CABG ny OTM, Now since A—B is negative, we must, if P and Q are positive, have q>(u—m)/(A+m), and, a fortiori, > (u—m)/(B+m). Further, since P>Q, {q(B+m)—(u—m)}(A+p)(A +m) > {q(A +m) —(%—m)}(B+p)(B+m); “. gQA+m)(B+m)(B—A) <(#—m){B?—A? +(u+m)(B—A)}; “. g(A+m)(B+m) <(w—m){A+B+p.+4+m)}. Cases V. and VI—A/B> /P//Q>1. Taking next the case in which the values of ¢ corre- sponding to w and m are equal, we deduce from (18) p—_2 (A+e)(At+m) l+p A—B ” ® (B+p)(B+m) 1+p A-B Substituting these values in the equation b= (/ P—/ Q)?/(A—B), & we get (A—BY(1+p)={/ (A+ p)(A4m)—V/ (B+ p)(B+m)}3 Phil. Mag. 8. 5. Vol. 19. No. 121. June 1885. 2K 478 Prof. A. W. Riicker on the Self-Regulation which reduces to {(A—B)p+p—m\*=4p(A+m)(B+ p). Solving for B, we get Bp=Apt+ptm+2A+2/(At+p)A+m)1 +p). Hence, since A> B, Ap must be greater than the right-hand side of the equation. This inequality can only hold if we take the negative sign, and if IV (A+p)(A+m)(1+p)>(A+p)+(A+m), anes alike 4p(A+p)(A+m)>(e—m)’; whence (4 —m)* PT h+py(Atiny Also, since B is positive, Apt+(A+p) +(A+m)>2/(At+p)\(At+m)(1+p); L+p—2/1+p/A+p)Atm)/A +(A+p)(A+m)/A?> pin / A’; {V1 tp—V (At p)y(Atm)/AS? > win /A?, We find, therefore, that in both these cases an inferior limit can be found to p or g, which depends only on pw, m, and A. If, therefore, the latter quantity is determined by considera- tions relative to the efficiency, we implicitly determine at the same time a limit to the perfection of the self-regulation. The last case is probably important practically, and the expression obtained shows that the inferior limit to p varies, if A is large, nearly as the square of the range. It will be less as A is greater; and this statement holds good for all the other cases enumerated above, so that a large value of A is favourable to good self-regulation. On referring to equations (8) and (10), we see that for a given usual value of « a high maximum efliciency is favourable to a large value of A if ¢ is the external electromotive force, and to a small value of A if ¢ is the external current. Hence we conclude that it is more difficult to combine a high efficiency with an approxi- mately constant external current than with an approximately constant external electromotive force. Postscript, April 30, 1885. Since the above paper was read before the Physical Society, of the Compound Dynamo. 479 I have seen a solution of the question with which it deals, published by Dr. Froélich in the current number of the Elek- trotechnische Zeitschrift, April 1885. I should like, there- fore, to add a few words as to the relations between our investigations in respect both of time and result. The method and chief conclusions given in my own paper, including the formule for ¢, g, and the mechod of finding limits to the perfection of the regulation, were given to my Senior Class in Technical Electricity in February last. In March I had several engagements which made special calls upon my time, and partly on this account, partly because I wished to add a discussion of the case when Q or B is nega- tive, I did not publish my results at once. Towards the latter end of March I received my copy of the Eilektrotechnische Zeitschrifé for that month, which contained the first part of Dr. Frolich’s paper. In that he gave the formule for the electromotive force, current, &c. in the cases of the series, shunt, and both forms of compound dynamo, in terms of the external and other resistances. The formule were not reduced to any simple form like the equation in } given by me; and though the paper showed that Dr. Frélich was engaged on the question of self-regulation, it did not afford any indication of his method of attacking the problem. The next day after seeing this paper I sent my own investi- gation to the Secretary of the Physical Society. It was - brought before the Council of the Society on March 28th ; but as it was thought that the matter was of some interest, the reading of the paper was postponed till the first Meeting after the Haster vacation (April 25th), and I was asked to attend for the purpose of giving an account of it myself. In the interval I made some improvements in the statements as to the physical meanings of the inequalities which I de- scribed at the Meeting, and have incorporated these in the text. It is only since the paper was read that I have received the April number of the Elektrotechnische Zeitschrift, from which I learn that Dr. Frolich has “seit dem Abdrucke des. ersten Theiles dieses Vortrages,’ and guided partly by theory, -partly by experiment, arrived at a very satisfactory solution of the problem of obtaining a constant external electromotive force. As far, therefore, as our work is common, I do not wish to question Dr. Frélich’s undoubted right to claim prior publi- cation. The above statement is, however, necessary to show _ that my results were obtained independently. On comparing the two papers, it will be seen that I have throughout considered the ee with reference to the 2K 2 480 Prof. A. W. Riicker on the Self-Regulation efficiency as well as to the self-regulation, and have given the equations amore general form, in which they apply, when the symbols are properly interpreted, either to the external electro- motive force or to the external current. Dr. Frélich has dealt chiefly with the case of a constant electromotive force, in which the conditions of high efficiency and good self- regulation are in accord, and both can be secured together. To obtain the best result, if a constant current is required, will need a careful balancing of opposing requirements. As regards, however, the practical determination of another condition which shall render the problem determinate when a maximum value of @ does not occur between » and m, Dr. Frolich has advanced the question a step beyond where [I left it, and has added very greatly to the interest of his paper. He has shown that when the external electromotive force is in question, and without any reference to the value of the external resistance for which the maximum efficiency occurs, excellent results may be ebtained by taking (in the above notation) A°?Q=B?P. I had previously shown the physical meaning of this condition; geometrically it amounts to choosing the arbitrary constant, so that db /de=0 when «=0. Since, in the case under discussion, «=1/7,, Dr. Fr6- lich’s curves and mine are so related that the product of the abscissee of corresponding ordinates is unity, and the tangent to my curve at the point where it meets the axis of ¢ becomes in Dr. Frélich’s figures an asymptote. As expressed by the curve between e, and 7, (Dr. Frolich’s), good self-regulation can only be obtained in this case for values of 7, greater than that at which the curve may be con- sidered to have become practically parallel to its asymptote. As expressed by the curve between e, and 1/7, (my own), the corresponding condition is that shall be small enough for the curve to be at the corresponding point practically parallel to the tangent at the point for which w=0. Dr, Frolich has shown that these conditions are fulfilled in prac- tice, and has thus added very materially to the importance of his paper. It must, however, be noted that this solution has nothing absolute about it unless the efficiency is considered. If it is left out of account another constant (A) is indeterminate, and may be chosen so as to make ga minimum. For when TANG Ol) pyle _ em | AB(utm) + um(A+B) 1~ (A+m)(B+m) AB+M(A+B) In the case under consideration we may put m=O, and thus of the Compound Dynamo. 481 write q= | {AB+u(A+B) t; which shows that, among the various solutions which satisfy the condition A?Q=B’P, that will give the best self-regulation for which A and B are largest. The condition that A shall be large implies (since A=1/R,,) that the resistance of the machine must be small, the necessity for which could of course be readily foreseen. The condition that B should be large leads to less obvious conclusions. Thus, in the case of the Long-Shunt Machine, B;=(s,+ Sa) / S1P9 5 and to make this as large as possible, we should have s,/s large and p, small. The first of these conditions is always, the second is never, fulfilled in practice. The reason of this is obvious, viz. that the efficiency would be reduced by dimi- nishing the resistance of the shunt. The maximum efliciency is given by the formula n=(Vp2—V Rn) /(V pot / Rm); which diminishes with p,. It is interesting therefore to note that a high shunt-resistance is not in itself conducive to good self-regulation ; and that, within the bounds of Dr. Frélich’s condition, there are still opportunities for choice by which improvements in the efficiency and regulation may be effected. Probably in practice the last adjustments will be best made by some system of experiment like that described by Dr. Frélich. The theory given above will, however, enable much to be done by a few preliminary calculations. Since | read the paper, Prof. Silvanus Thompson has called my attention to the question as to whether my formulz indi- cate the advantage of back winding in the case when a constant external current is desired. Dr. Froélich has constructed a machine on this principle, to which he was led by theory. To discuss this question fully would require an investigation of the problem when B is negative; but it may be remarked that in a case such as that discussed above, when a large value of B is desirable, it may be increased in the case of the Long- Shunt Machine (B,) by taking s, negative and <3). edison LIV. On the Identity of Energy: in connection with Mr. Poynting’s Paper on the Transfer of Energy in an Electro- magnetic Field; and on the two Fundamental Forms of Energy. By Ourver Lover, D.Sc.* [‘ is well known that Prof. Poynting has communicated to the Royal Society a most admirable and important paper, “ On the Transfer of Hnergy in the Hlectromagnetic Field”? t; a paper which cannot but exert a distinct in- fluence on all future writings treating of electric currents. In that paper he introduces the idea of continuity in the existence of energy—a natural though not a necessary conse- quence of its conservation; so that, whenever energy is trans- ferred from one place to another at a distance, it is not to be regarded as destroyed at one place and recreated at another, but it is to be regarded as transferred, just as so much matter would have to be transferred; and accordingly we may seek for it in the intervening space, and may study the paths by which it travels. This notion is, I say, an extension of the principle of the conservation of energy. The conservation of energy was satisfied by the total quantity remaining unaltered; there was no individuality about it: one form might die out, provided another form simultaneously appeared elsewhere in equal quantity. On the new plan we may label a bit of energy and trace its motion and change of form, just as we may ticket a piece of matter so as to identify it in other places under other conditions ; and the route of the energy may be discussed with the same certainty that its existence was continuous as would be felt in discussing the route of some lost luggage which has turned up at a distant station in however battered and transformed a condition. In this new form the doctrine of the conservation of energy is really much simpler and more satisfactory than in its old form ; and the doctrine may be proved rigidly and instanta- neously from two very simple premises, viz. Newton’s law of motion on the one hand, and the denial of action at a distance on the other; as I endeavoured in this Magazine some time ago to showf, and will now repeat. I speak of Newton’s law of motion because I believe it will be admitted that Newton’s three laws of motion, in so far as * Communicated by the Author, + Poynting, Phil. Trans. ii. 1884, p. 348, { Phil. Mag. January 1881, p. 36; and June 1881, p. 531. Also ‘Elementary Mechanics’ (Chambers), § 80. On the Identity of Energy. 483 they are more than definitions, are really three very important aspects of one law*. They may be regarded as (1) a defi- nition of time, (2) a definition of force, (3) a statement of a law of Nature. The law of Nature they embody is capable of various modes of expression, such as these (in brief):— Change of Momentum= Impulse. Resultant force = Action + Reaction=0. Force is always one component of a stress. The last form is perhaps as convenient as any for our present purpose, and is our first lemma. To deny action at a distance is easy; we have only to say, “Tf a stress exist between two bodies they must be in con- tact.”” This constitutes a second lemma. We then only further require the definition of work and energy; for instance, these:—A body does work when it exerts force through a distance; the measure of work being { Fads. Hnergy is that which a body loses when it does work; and it is to be measured as numerically equal to the work done. [The repetition with mere change of sign, about gain of energy when negative work is done by a body, or positive work done upon it, may be understood. | Now at once follows, simply and rigorously, the law of the conservation of energy ; and not only conservation, but conservation in the new form, viz. the identification of energy; thus: If A does work on B it exerts force on it through a certain distance; but (Newton’s law) B exerts an equal opposite force, and (being in contact) through exactly the same distance ; hence B does an equal opposite amount of work, or gains the energy which A loses. The stress between A and B is the means of transferring energy from A to B, directly motion takes place in the sense AB. And the energy cannot jump from A to B, it is tranferred across their point of contact, and by hypothesis their “ contact” is abso- lute: there is no intervening gap, microscopic, molecular, or otherwise. The energy may be watched at every instant. Its existence is continuous; it possesses identity. It is no use objecting that two pieces of ‘‘matter’’ are never in contact—nobody said they were. If they are not, and it seems quite certain that they are not, then evidently one * For argument in support of this view, see ‘The Engineer,’ 1885, March 20, April 24, May 15. 484 Prof. Oliver Lodge on the piece of “ matter’? cannot act immediately on another piece. A and B therefore are not two pieces of ‘‘ matter ’”’ in the ordinary sense. A may be a molecule of matter, M may be the nearest molecule to it, and energy may be transferred from A to M, but not directly ; A cannot act on M, cannot do work on it, because of the intervening gap. A can act on B, transferring its energy to B, B can act on C, C on D, and so on, handing on the energy to L, which is in contact with, and can act on, M, doing work on it and giving up to it the energy lust by A. What B, C, D,....L are, I do not presume to say ; but of course one supposes them to be successive portions of the perfectly continuous space-filling medium Aither, Relation between Potential and Kinetic Energy, from the contact point of view. Reason of the two forms; and Transforma- tion into one another. In the older and more hazy view of conservation of energy the idea of “ potential energy” has always been felt to be a difficulty. It was easy enough to take account of it in the formule, but it was not easy or possible always to form a clear and consistent mental image of what was physically meant by it. | A stone is raised, it gains potential energy ; but how does the stone “‘up”’ differ from the stone “ down”’ ?, and how can an inert and quiet stone be said to possess energy ? Well, then, the stone hasn’t the energy but the earth has, or rather “the system of earth and stone possesses energy in virtue of its con- figuration.” True, but foggy. The usual ideas and language current about potential energy are proper to notions of action at a distance. When universal contact action is admitted, the haze disappears*; the energy is seen to be possessed, not by stone or by earth or by both of them, but by the medium which surrounds both and presses them together; and the foilowing statement may be made. Knergy has two fundamental forms because work has two factors, force and motion, F, s. Work cannot be done except by a body exerting force and in motion. Force without motion is no good. Motion without force is no good. Wither factor separately may be energy, but it is not work. * It is by no means intended that the natures of gravitation, elasticity, cohesion, &c, become clear. What is meant is, that the seat of the energy is Clearly recognized: the season of the stress recognizable in the medium is a much higher and more difficult problem, Identity of Energy. 485 The two forms of energy correspond to the factors in the product work *. “ Potential’’ energy correspond to I’, “ Kinetic ”’ energy correspond to s. But is this quite true and satisfactory? A strained bow is exerting force and possesses energy. A pillar supporting a roof is exerting force, but possesses no energy. What is the difference between the two cases? It is evident that some- thing more is needed than mere force. The difference of course is that the bow can recoil, it has a range or distance through which it will continue to exert a force: not the originai force, but still some force. The pillar is exerting a great force but it has no recoil in it; if released it would at once cease to exert any force; consequently its energy is minute. Thus, then, for a body to possess potential energy we must have two things—the exertion of a force, together with a guarantee that that force shall be exerted over a certain dis- tance; 7.¢. a continuance of the force even after motion is permitted. And this is quite analogous to what may be said of the other form of energy. “‘ A body in motion possesses energy ;” but is it so necessarily ? Cannot a body in motion be conceived as possessing no energy? Suppose it stops the instant you give it work to do—the instant you make it exert force. It is evident you must have not merely motion, you must have a guarantee of persistence of motion, the body must possess inertia; the motion must continue over a certain range even against resistance. Hence we may exhibit the relation be- tween the two forms thus :— Kinetic energy corresponds to motion combined with inertia, so that the motion shall continue even against some force; and Potential energy corresponds to force combined with elasticity (or something like it), so that the force shall continue even though motion be permitted. Both forms of energy are potential work, but, gua energy, one is as real and actual as the other. Hach has a factor missing, which if supplied, work will at once be done. Kinetic energy requires the Force factor todo work. Potential energy requires the Motion factor to do work. An important thing is now evident moreover, a_ thing which I have never seen accepted, though it has been pre- * Of. Lodge on “ Forms of Energy,’ Phil. Mag. October 1879, p. 281, and June 1881, p. 531. Also ‘Elementary Mechanics’ (Chambers), § 84, 486 On the Identity of Energy. viously pointed out*. The statement is in two parts :— (1) Energy cannot be transferred without being transformed ; and (2) it always transforms itself from Kinetic to Potential, or vice versa. When A does work on B energy is transferred from A to B; and I say that if the energy which A lost was kinetic, then what B gains is potential ; if, on the other hand, A loses potential, then B gains kinetic. I may make a converse statement, viz. that energy cannot be transformed without being transferred; cannot take on a different form without being at the same time shifted to a different body. So that the common mode of treating a falling weight, saying that its energy gradually transforms itself from potential to kinetic but remains in the stone all the time, is, strictly speaking, nonsense. The fact is the stone never had any potential energy, no rigid body can have any; the gravitation medium had it however, and kept on transfer- ring it to the stone all the time it was descending. The above statement, that transformation of energy neces- sarily goes on from potential to kinetic or vice versa at every act of transfer, almost proves itself. It follows from the fol- lowing facts:—When a body possessing potential energy does work, its “range ” necessarily diminishes, while the motion of the body on which the work is done increases. On the other hand, when a moving body does work its motion dimi- nishes, and the body which resists the motion, since it yields over a certain distance, gains potential energy. Tor the first case think of a catapult, bow and arrow, orair-gun. Tor the second case think of a bullet fired against a spring and caught by it. "These examples are favourable and easy, but any others will serve equally well to illustrate the matter if regarded from the right point of view. Thus a bullet fired upwards gra- dually transfers its undissipated energy to the gravitation medium, transforming it at the same time into potential. As soon as the highest point is reached, the gravitation medium proceeds to re-transfer and transform it. A pendulum exhibits the alternation of energy from the kinetic to the potential form and the accompanying transfer from matter to medium, at every half-swing. Any vibrating body does the same; but in considering a strained spring we must remember that the energy resides not in the spring as a whole but in its elemen- tary parts. The strain resides not even in the molecules them- selves, perhaps, but in something between those molecules (for * Phil. Mag. October 1879, p. 281, sect. 11, and June 1881, p. 582. And ‘ Elementary Mechanics,’ § 85. On the Paths of Electric Energy in Voltaic Circuits. 487 by hypothesis molecules are incapable of exerting direct force on one another, not being in contact). The medium is exerting the force, and will continue to exert it over a certain range, hence it possesses the potential energy; when released it will do work and transfer its energy to the steel, in the kinetic form. If the spring overshoots its mean position, the energy is re-transferred and transformed. A perfectly elastic boundin ball has all its energy transformed into potential, at the middle of every period of contact with the obstacle from which it rebounds. One case possesses perhaps a little more difficulty, viz. the case of a bullet fired into dough—when the body exhibits no recoil: how can the energy of the bullet be said to be trans- formed into potential now? Only by remembering that heat- motion is a vibration of some kind, and that when a vibration is excited by a blow or by friction, strain is the effect first produced, and afterwards the recoil. Think, for instance, of exciting a tuning-fork or a string by bowing or striking it. Alternations from kinetic to potential may be rapid in some cases, slow in others: no matter; all I have stated is that change of form is necessary and universal whenever energy is transferred, 7.¢. whenever any kind of activity is exhibited by any known kind of material existence. University College, Liverpool, May 16, 1885. LY. On the Paths of Hilectric Energy in Voltaic Circuits Appendix to Paper on the Seat of the Electromotive Forces in the Voltaic Cell. By Prof. OLIVER LopGE*. [Plates IV. & V.] HE main conclusions to which I have been led with regard to the potentials of metals and the seat of H.M.F. may be very briefly stated thus :-— (1) A metal is not in general at the same potential as the air in contact with it; the difference of potential (or contact- force) between any given clean metal and air being calculable, at least approximately, from thermo-chemical data, though there is no known way of experimentally observing it. (2) Putting two metals into contact equalizes their poten- * Communicated by the Author. For the sake of completeness it may be convenient here to mention that a report of a discussion on Seat of E.M.F., at Montreal (Brit. Assoc., Sect. A), is published in the ‘ Electrical Review ’ for Nov. 22, 1884, and that a more elaborate discussion on the same subject, by the Society of Telegraph Engineers and Electricians, will be reported in their volume of ‘ Proceedings’ next issued after the present date. 488 Prof. Oliver Lodge on the Paths of tial, their surfaces becoming charged with the electrostatic charges proper for effecting this equalization of potential. (3) The air surrounding a pair of different metals in contact is therefore in a calculable condition of dielectric strain, espe- cially near the junction of the two metals; in other words, there is in the air a slope of potential which is most rapid in the neighbourhood of the junction, and is there easily observed electroscopically. (4) This slope of potential observed by Volta, measured by Kohlrausch &e. &c., near the junction of any two metals, has caused observers to imagine that the metals themselves differed in potential, and accordingly to postulate an H.M.F’. or contact- force resident at the junction in order to maintain such dif- ference of potential in a conductor. (5) No such force exists at a metallic junction; because, if it did, the passage of a current across such a junction would produce violent reversible thermal effects, and none such are observed. (6) This non-existent force has been imagined, and has been utilized to account for the greater part of the H.M.F. in a voltaic circuit ; in fact, it has itself been considered to be the main H.M.F. in such a circuit ; although it was manifestly unable to account for the energy of the current. (7) The real seat of the H.M.F. in a voltaic or any other circuit must be where conversion of energy, from some other form (chemical, thermal, &c., &c.) into the form known as an electric current, occurs. The object of the present Appendix or Supplement to my paper is to supply an accidental omission in the history of the subject, and more particularly to exhibit and illustrate the mode of regarding conducting circuits which I advocate, by diagrams of energy-paths, or erg-odes for those who like Greek barbarities. The accidental omission from the history of the subject is a notice of Dr. Gore’s communication to the Royal Society of November 1883*, in which he makes an attempt to bring liquids into a thermoelectric series. The contact-force between a metal and a liquid is shown to vary with temperature; and the results indicate that this contact-force is a complex one, not simply depending on the chemical relations of the substances in circuit, 7. e. on the cor- * Gore, Proc. Roy. Soc. No. 238, vol. xxxvil. p. 251: “Some relations of Heat to Voltaic and Thermoelectric Action of Metals in Electrolytes.” See also former papers in Phil. Mag. January 1857; Proc. Roy. Soe, 1878, p. 518, No. 188; 1879, No, 199, and 1880, No. 208. Electric Energy in Voltaic Circuits. 489 rodibility of the metals, but involving some other more purely physical force also:—much as Bouty surmised from his expe- riments on the generation of heat at a metal-liquid junction when a current was driven across it. A number of tables of the order of metals in different solu- tions of different strengths and at different temperatures are given, together with some numerical values. It is possible that by an attentive study of Dr. Gore’s work, and of other work in the same direction, a more com- plete account could be given of the exact relation existing between what may be called the thermal and the chemical contact-forces at metal-liquid junctions ; if indeed any valid distinction can actually be drawn between them. At present, at any rate, I do not attempt this; but proceed to the other matter spoken of, viz. the illustration of my views on the voltaic circuit by a diagram of its energy-paths. Prof. Poynting has taught us, in a paper of the very greatest interest and power”, that modern views of vis a tergo, a3 opposed to action at a distance, lead necessarily to the idea of continuity in the existence of electric, as well as of all other, energy, and hence toa study of the paths along which it moves from one part of the field to another. He has shown that these paths are the intersections of the magnetic and the electro- static equipotential surfaces, and that the rate of flow of energy is proportional to the product of the electrostatic and electro- magnetic intensities at every point. This view of the electromagnetic field, though no doubt implicitly involved in Maxwell’s equations, yet urgently needed to be dragged forth and exhibited ; and it is difficult to imagine how the developing process could have been done better than it is done in Prof. Poynting’s memoir. The special cases by which his memoir is illustrated are not, however, in exact accordance with the views of the electric circuit which I am advocating; and in particular the diagram of the curves for a voltaic current is, in my view, wrong. I cannot say I thought it wrong at the first glance; I was pleased to see that Mr. Poynting held what I consider the correct view, that the main seat of the E.M.F. in a simple pile is at the zinc-acid junction and not at the zinc-copper, and that his diagram embodied this view. But when I came to draw the curves myself for this case, taking account of the step of potential which I believe to exist between a metal and the air, I found the energy-paths refuse to start spreading out from the zinc-acid junction, as we had * Poynting, Phil. Trans. 1884, pt. ii, “On the Transfer of Energy in the Electromagnetic Field.” 490 Prof. Oliver Lodge on the Paths of both at first sight expected them to: they insisted on di- verging from the zinc-copper junction, as a Voltaist would wish them to. This behaviour is really in perfect accord with my theory; though the fact is the cause of Voltaists’ views con- cerning seat of H.M.F. They locate the force at the zinc- copper junction just because the energy-paths diverge thence and appear to start thence. Prof. Poynting’s diagram, therefore, not only differs from my theory, a thing which is natural and unimportant, but it is discrepant with experimental fact. Rigid experimental truth would have led him to spread out his energy-paths from the metallic junction, rot from the acid junction as he has done. ‘True such a proceeding would have | landed him in difficulties and apparent absurdity, and he would have been compelled to ask, “ How can all the energy start from an inert metallic junction?”’ And he might well have considered such a conclusion absurd, as it is. The reconciliation between sense and fact is simple. The lines do, indeed, diverge and spread out from this junction, but they do not start thence. They ail start from the zinc- acid junction; but they at first creep along close to the surface of the zinc, investing it like the coats of an onion; and some continue to creep along the copper too, but some do not. More lines invest the zinc than the copper ; and the lines in excess are given off at the junction, and thence diverge through che air. An electroscopic experimenter seeking the seat of H.M.F. traces these lines, home as he thinks, to the zinc-copper junc- ction, and hence regards this as their origin and the seat of the torce. Itis not. The lines do not start thence ; they start at the real seat of H.M.F’. and source of all the energy, though Lheir close-lying continuations between metallic junction and acid junction are impossible to trace out experimentally. With this preliminary, the diagram of energy-paths for a voltaic circuit in Plate IV. almost explains itself. The lines are loci of constant electrostatic potential ; and I happen to have chosen a circuit whose external resistance is twice its internal. The junction of the two metals is placed at random wherever its peculiarities may be most conveniently observed, The liquid in which the metals are immersed is only faintly indicated by the outline of its trough, and, for simplicity, it is supposed to be one differing in no electrostatic respect from air. Dilute sulphuric acid of a certain strength has been shown by Prof. Clifton to satisfy this condition almost exactly. The particular metals for which the diagram is intended to Electric Energy in Voltaic Circuits. 491 be drawn are zinc and copper. Now thermo-chemical data lead me to conclude that the step of potential between clean zinc and air is 1°8 volt [the exact decimal not being insisted on except for purposes of illustration]; hence, if an equipo- tential line be drawn for every tenth part of a volt, 18 of these lines would closely invest clean zinc always, and form a boundary between it and the air. In the diagram (Pl. IV.) lines are only drawn for every fifth of a volt, and consequently 9 of them envelop the zinc. As for copper, it is probable that the step of potential between it and air is *8 of a volt; and accordingly four lines invest the copper at every point in the diagram. They are not always the same four lines—that is of no consequence ; the essential thing to remember in drawing the diagram is to keep the number constant at every point for the same metal. Such a metal as gold or platinum may be nearly free from lines. It is needless to say that the lines have to be drawn with spaces between them for distinctness, but that in reality the step of potential is of the most sudden description, and all investing lines ought to lie close to the mathematical surface of the metal. Now, since nine lines coat the zinc, and only four the copper, it is manifest that five lines must leave the metallic surface at the junction, and must spread out into the air. These five lines correspond to the one volt* Volta effect observed near a junction of clean zinc and copper, and which has been called a difference of potential between zinc and copper. Of the five lines thus starting to spread out from the junc- tion, some make for points on the external circuit, and others go through the internal circuit. Those which go to the ex- ternal circuit can by no means go through it, or into it, for the potential of the copper differs -by °8 volt from that of the air ; but they can go round it, and leave it on the other side just as if they had gone through it. Moreover, a line does go through, or into, the copper at the very point where the air- line abuts against it, viz. the line of potential °8 volt lower. So the transfer of energy into the conductor of the external * Different observers give different values for this number; from ‘5, Kohlrausch, to between ‘76 and ‘89, Ayrton and Perry and Clifton, up to ‘92, Pellat; but since tarnish or dirt on the zinc surface will certainly lower it, and it is difficult to suppose any zinc surface absolutely clean, I have not thought it necessary to modify the theoretical value of one volt, which at any rate serves well enough for illustration, though it may turn out to be about ten per cent. too high. 492 Prof. Oliver Lodge on the Paths of circuit is complete, except for just the metallic skin, and everything goes on i the outer field as if the energy-paths really started from both sides of the zinc-copper junction, and some of them cut through the metal of the external circuit with degradation into heat. Note, however, that the heat-energy in a wire is not really thus carried through the air: it creeps along the surface of the wire, some of it perpetually diving into the wire, and be- coming converted into heat. The energy which liberates hydrogen from the copper-acid surface, moreover, does not reach it in the way Mr. Poynting has supposed. Some of it crawls over the current the whole distance ; all of it goes some distance with the current. In the electrolyte, however, this 1s not so; and the heat which there makes its appearance is produced at the expense of energy which has arrived via the air from the zine-copper junction. ‘This is on the supposition that no contact-force exists between the electrolyte surrounding the plates and the dielectric medium (air) enveloping the rest of the circuit. In cases where such a contact-force does exist, some energy will creep along the air-liquid surface, just as it does over the surface of a metal. In the diagram one of the five lines here spoken of is doubled back upon itself, so as never to leave the surface of the zinc: the spaces between the lines are the real paths of the energy of course, not the lines themselves; the lines only indicate the directions across which no energy goes. There are five spreading-out energy-paths, then, and it is most instructive to watch the energy arising at the zinc-acid surface flow in its first narrow channels, then broaden out through space, and then cramp itself again into its tube, by which it reaches the copper surface, and is transformed into energy of chemical separation ; or, again, to watch that in the channels touching the copper fritter itself gradually away into heat. Energy-paths in Secondary Circuits. (Plate V.) The four figures in Plate V. are intended to indicate the transfer of energy to a secondary circuit, 7. e. one in which an induced current is being generated. Fig. 1 shows a steady electromagnetic field disturbed by the presence of a stationary copper channel. The energy simply flows round it, as Prof. Poynting has said. Fig. 2 shows a field no longer steady, but with the potential changing: the energy- paths moving, say, toward the right. Hach line, as it comes up, Electric Energy in Voltaic Circuits. 493 folds itself round the circuit, and sends part of one of the pre- viously investing paths to the inside, where it displaces part of one of the original inside paths, which at once begins to close up. Fig. 2 shows it half closed, on the hypothesis of absolute suddenness. Fig. 3 the same thing, on the supposition that energy possesses something like inertia. The induced current is produced by energy flowing along the semi-displaced path through the copper. If the change of field stops, fig. 2 is supposed quickly to revert to fig. 1, with an opposite trans- ference of energy. Three stages in the change of field are shown in fig. 4: or this figure may be regarded as showing three lines in a uniform field disturbed by a moving con- ductor. The arrows are drawn as if the energy flowed right away again without loss, or at least without complete loss. It is easy to reverse one of the arrows, so as to make energy flow up from both sides to the secondary circuit; but it is not easy to see how energy can reach the copper and be dissipated when its path does not pierce the copper atall. The lines have to be thought of as first embracing the circuit, then as moving away, having left a portion enclosing the circuit be- hind, and finally, more lines having come on, as sinking into and through the copper, and shutting themselves up ; and so on perpetually, as long as the field is changing. The energy thus reaches the secondary circuit a little behindhand always, which is not wrong. [If all the energy is dissipated in the act of passing through the copper, arrows ought not to be drawn on the inside paths which are shutting up ; because though they are still paths for energy, it does not follow that they are made use of; in fact, they cannot be, if all the energy is extinct. Probably, however, what all these diagrams better represent is the steady state of a field disturbed by the presence of a perfect conductor in which there is no dissipation whatever— a conductor like the molecules postulated in Ampére’s and Weber’s theory of magnetism and diamagnetism. Voltaic Energy-paths. (Plate IV.) Returning to the Plate showing voltaic-energy path: the diagram seems to me to constitute the most absolute and complete reconciliation between the truth in the opposing views of the voltaic circuit. It not only justifies modern voltaic experimenters in their recognition of the slope of air-potential near a junction, but it partially justifies even the view of old Volta that this Phil. Mag. 8. 5. Vol. 19. No. 121. June 1885. 2 L 494 On the Paths of Electric Energy in Voltaic Cireuits. junction is the source of all the energy. So far as the external circuit is concerned, the metallic junction is the source of the energy ; all the energy does in a manner start thence, though it does not start originally thence. It reaches the junction from another place, its real source, but it travels thither by infinitely unrecognizable paths. Does the diagram, then, justify modern Voltaists altogether? Certainly not. It cuts the ground from under the feet of those who have asserted that there is an H.M.F. at the junction of zinc and copper—a contact-force which is the cause of the observed difference of air-potential in the neighbourhood. And it annihilates those who have seen in this imaginary and non-existent force any means of propelling the current in a voltaic circuit. On the other hand, the diagram of course justifies all those experimenters who have regarded the zinc-acid junction as the main seat of energy-transformation, and therefore of electro- motive force. At the same time it exhibits the crudity of some of their statements ; and, just in so far as it upholds the truth and consistency of the Voltaists with regard to a part of the phenomenon, it contradicts some of the opposing statements made by chemical theorists with regard to the Volta effect. In particular, it lends no support to the customary ‘“ chemical” view, which sets down the whole Volta effect as an accident due to unavoidable chemical action, and so practically ignores it. Imagine the lines investing the metals to be microscopically close to them, and then look at the diagram as truly exhibit- ing the facts of nature: it irresistibly suggests a voltaic or contact theory of the voltaic pile. It was right, therefore, for the first observers of voliaic phenomena to found a contact theory, and to adhere to it tenaciously, as in some sense true. It was also right for later philosophers, imbued with notions of energy, to ieel the doctrine that the metallic junction was the source of power to be absurd and incomprehensible, and to found a chemical theory. In the conflict both sides have made mistakes; but it is the essence of truth in both views which has given them such vitality and endowed their upholders with such energy of persistence. University College, Liverpool, May 17, 1885. [ 495 ] LVI. On the Thermoelectricity of Molten Metals. By F. Braun (Carlsruhe)*. ia Ye a circuit of metallic conductors a current produced by difference in temperature must be the equivalent of heat derived from an external source. If we assume (1) that the process is reversible, (2) that heat is absorbed only at the point of contact of higher temperature, and is given out only at the colder point of contact, then it follows that the thermo- electric force must be proportional to the difference in tem- perature of the junctions for intervals of any magnitude. If we assume a change in potential function at both junctions, the resuli may be expressed thus: that the change in poten- tial is proportional to the absolute temperature of the junc- tion. The electromotive force therefore, expressed as a function of the difference of temperature, ought to be a straight line. But experiment shows that in all the thermo- piles as yet examined this linear relationship does not hold good; in by far the majority of cases the curve is much nearer a parabola. This led Sir W. Thomson to the conclu- sion that even in the interior of one and the same metal unequally heated there must be produced, upon the passage of a current, a quantity of heat proportional to the first power of the current-strength (adopting Le Roux’s term, we may call this ‘“ the Thomson-effect ’’). In fact, if the thermopile works, not between two tempera- tures, but between an infinite number, it follows inversely that its electromotive force can no longer be expressed as a linear function of the greatest temperature-difference which occurs in it. Although, strictly speaking, nothing can be determined as to the locality of the electromotive force, yet we should be disposed to add to the changes in potential assumed to exist in the junctions (of which, however, no proof has yet been given that they occur there) other changes of potential occurring in the interior of the unequally heated metal. : Hitherto, so far as I know, only thermopiles have been examined in which at least one metal has been solid. The explanation is then obvious, that these internal thermo- electric forces are due to changes produced by the heat itself in the solid metal—hot and cold metal behaving like two different substances, or, as we may shortly express it, the heat produces structural changes. In fact, as shown by the * Translated from the Sttzwngsber. der kinigl. Akad. d. Wissensch, of Berlin, of April 9th, 1885. : 212 496 M. F. Braun on the experiments of Magnus, pieces of the same metal but of different temperature produce a thermoelectric current when brought quickly into contact. Only with lead could this re- sult not be observed with certainty. But in lead, as Le Roux showed, the Thomson-effect is nearly or quite zero. In general, those metals which show a large Thomson-effect show also the further peculiarity that, upon heating a single wire the ends of which are kept at a constant temperature, a thermoelectric current is produced, the intensity (and even direction) of which often varies with insignificant changes in the distribution of the temperature or the structure of the wire. These currents, I may at once mention, are so energetic, and especially so variable, particularly if the temperature is raised to a red heat, that I have had to take precautions with my thermopiles that there should not be any great differences of temperature in the solid metal. With lead only have I been unable to observe with certainty any such currents, even when the solid metal was plunged into molten lead. According to an experiment of Magnus’s, often quoted, which for short I will call the Magnus experiment, currents are altogether absent in mercury. It is an obvious explanation to refer the currents, produced on bringing together a cold and hot metal, to differences in structure (although we must then ascribe some influence either to time or to distribution of temperature), and to class them together with the Thomson effect—that is, the deviations which the thermoelectric force shows from proportionality with the temperature-difference. If certain metals give no thermo-current either in the Magnus experiment or when a wire, whose ends are maintained at a constant temperature, is heated, this may be explained in two ways: either changes of potential take place on both sides of the point heated, which, however, must decrease equally in both directions, or no thermoelectric excitation takes place, because, in conse- quence of the nature of the metal, differences in structure are impossible. To this latter, although more special, assumption it seems to me we shall be most inclined. It is to be assumed that other molten metals will behave as mercury does, which, in fact, I have found to be the case (cf. § 7). 2. If we regard the Magnus experiment in this second way, it would follow that the thermoelectric force between molten metals must be proportional to the difference in absolute temperature between their points of contact. But this would show the possibility of measuring absolute tem- Thermoelectricity of Molten Metals. 497 peratures to a very high point by a method presenting many advantages over measurements made with an air-thermo- meter (smaller space of constant temperature, independence of expansion and changes in form of the vessel). We should further, and probably for the first time, obtain numbers which are entirely dependent upon the chemical nature of the substance, and free from uncertainties as to how hard or soft the body is. They would offer us a more ready con- clusion as to the internal processes by which thermoelectric forces are excited. In fact, it appears very remarkable how, under similar external conditions (where any desired quanti- ties of heat are available), large quantities of heat are trans- formed into the form of energy of mechanical work, at the points of contact of many metals, and with others very small quantities *. | Since, further, each molten metal in thermoelectric rela- tionship must be characterized by a single constant (which no doubt may vary with the pressure), this must stand in some relationship to other constants, characterizing the par- ticular metal, and independent of the temperature ; but of such there is only the atomic weight available. 3. These considerations induced me to measure the thermo- electric forces of molten metals against each other between as wide limits of temperature as possible. A linear dependence upon the temperature appeared to me @ priori so probable, that I directed my attention from the first to the utmost possible chemical purity of materials, and, moreover, chose only elements. Alloys were investigated only in the second lace. In the following I give the combinations which were measured, as well as the range of temperature employed ; ¢ denotes the temperature of the colder point of contact, T the highest reached at the warmer point of contact. eon ST Soce ies f= 202% or! 100% 5 :T370?. Bee. 8 ei) en ¢=220°; T= 580°. MOE. 3. \ oheenpd—20?-or 100 s| P—b20". nee) Ga) 2 Wel t= 200s) T= 460°. * That we may regard the Peltierian heat as the equivalent of the work which the electricity does in passing to a lower potential-level at the points of contact, requires no justification. The work lost at the one contact-point can be restored by the equal amount gained at the other, just as the quantities of work in the portions of the two arms of a siphon at equal heights compensate each other. We cannot conclude anything, as Maxwell has done, as to the difference of potential produced, as a result of contact-electricity, from the Peltierian heat at the point of contact of two conductors. 498 M. F. Braun on the Hg(Na+K)* . ¢=20°; T=380°. PbSn:. . (J...) 20°; T=435°; t=424° ie IemST 92) 5 1=508°; T = 882°. He(Hg + Bi+ Pb)tt=20°; P= 5305. A, For the determination of high temperatures in spaces frequently small I employed spirals of platinum wire, whose galvanic resistance had previously been determined as a func- tion of the temperature. I employed for this purpose a large muffle furnace heated by coal, the description of which, as well as of other experiments made with it, I propose to give shortly elsewhere. The vessels for the air-thermometer were made of Meissen porcelain {. The dimensions could be so chosen that, assuming constancy of temperature, temperatures of 1000° C. could be accurately measured to 1° or 2°. 5. The metals were enclosed in glass tubes, wherever glass could be used. Platinum wires melted into the glass served for external connections. With some metals the platinum wire was in direct contact with the metals ; with others this contact was made by means of a pencil of retort-carbon § or graphite, with others by means of an iron-wire. Two glass tubes filled with metal were placed vertically side by side. At the hotter (upper) point of junction the platinum wires were melted together outside the tubes by means of the oxy- hydrogen blowpipe. So far as the wires which serve to make contact with the fluid metal at the hottest and coolest points penetrate the ends of the tubes, uniformity of temperature must be maintained. The cooler (lower) ends of the tubes were plunged into two concentric vessels full of mercury, which were placed in a bath of constant temperature, though not always the temperature of the room. From these mercur vessels wires of lead conducted to a petroleum bath of the temperature of the room, from which the copper connections were made. ‘The leaden wires of course could not be placed directly in contact with the mercury. Their ends were melted intoa glass tube, through the lower closed end of which a short platinum wire passed. I pass over here the precautions found necessary in order to ensure that the * Alloy liquid at ordinary temperatures; about 1 eq. K to 1 eq. Na. + Alloy liquid at ordinary temperatures; 1 part lead, 1 part bismuth, 3 parts mercury. { I wish here to express my obligations to the Royal Saxon Porcelain Manufactory, and especially to M. Bittner, for the great trouble which they have taken in the very difficult manufacture of these vessels. § Platinum at 200° is amalgamated by mercury, and at about 500° is dissolved as energetically by mercury as it would be by boiling aqua regia. Thermoelectricity of Molten Metals. 499 other portions of the circuit should be affected only by slight thermoelectric forces, which remained constant for a con- siderable time and which were separately determined. The electromotive forces were measured by compensation. 6. The temperature of the hotter point of contact was maintained:—(1) Ina bath of mineral oil of high boiling-point, which was kept agitated by a stirrer. In this way a tempe- rature of about 380° C. could be obtained. (2) In an air- bath, consisting of three concentric iron cylinders, surrounded on the outside by a jacket of iron and chamotte, which was constructed according to my designs for another investi- gation, and which Hhrhardt* has recently described. It was heated by means of gas, and permitted the attainment of a temperature of 580°. (38) By a brisk current of vapour of constant boiling-point, sent through a glass vessel protected against external radiation of heat. The substances employed were alcohol 80° C., water, xylol 140°5 C., aniline 183° C., dimethylaniline 192° C., toluidine 198° C., xylidine 214° C. In order to decide with certainty particular questions I re- quired constant temperatures, not differing much from each other. For the control of other measurements, I further employed baths of vapour of benzoic acid 250° C., mercuric iodide 357° C., and sulphur 448° C. For still higher tem- peratures (up to 980° C.) I employed (4) a muffle. The vessels which contained the metal were of earthenware. Imagine an earthenware tube inclined some 10° to the hori- zontal plane, and provided at both ends with vertical pipe- heads. Two such tubes of equal length were placed side by side. Hach contained a molten metal. The upper pipe-heads were within the muffle, and heated to a higher temperature than the lower ones. They were connected by a bridge of thick iron-wire or of retort-carbon, by means of which a wide thick-walled chamotte-neck passed from the muffle through the heating-channel outwards, through which the earthenware tubes passed ; the other two pipe-heads were outside the mufile, surrounded by an iron box, which was heated by coal. The temperature then was maintained as close as possible to the melting-point of the more difficultly fusible metal. In order to carry the circuit from the molten metal outside the muffle, previous experience had shown lead to be the only available metal which permitted the reduction of temperature to that of the room. The following arrangement was adopted in view of its properties :—At the lower end of a thin- walled brass-tube of about 12 millim. diameter an iron tube * Wied, Ann. vol. xxiv. p, 217 (1885). 500 M. F. Braun on the was brazed ; it was closed below by an iron disk screwed on, to the inside of which a piece of platinum foil was soldered. The screw closed against the molten metal in which the iron tube plunged. A platinum wire was in contact with the platinum foil. This was melted through the closed lower end of a glass tube. The bottom of this was filled to a height of about 10 millim. with graphite. Lead wire was pushed slowly into the glass tube, which melted and formed a continuous connection from the molten to the solid lead. The solid lead wire conducts again to points at the temperature of the room. All the different conductors (iron, platinum, and graphite) were completely surrounded by the molten metal in the pipe-head, which stood some 4 centim. above the top of the graphite layer. We may therefore assume equality of temperature in all. This last-described arrangement was employed for the circuits PbSn and SnBi. 7. I pass now to the results obtained. If we take the temperatures as abscissee and the electromotive forces as or- dinates, the following results are obtained. Most, if not all, the curves are not actually straight lines ; they are of such a form that the centre of curvature lies on the side of the curve turned away from the axis of abscisse, i. e. the electro- motive forces increase more rapidly than corresponds to proportionality with the temperature. Only the curve for NaHg, which is almost straight for a considerable distance, seems at higher temperatures to assume a curvature towards the other side. The thermoelectric force of this element is, however, so small that measurements with it offered special difficulties. KHg is almost a straight line, but possesses certain peculiarities (see below). | The curves are certainly not of the second degree, but of the third at least. Tait’s assumption that specific heat of elec- tricity is proportional to the. absolute temperature, which would lead to the equation to a parabola, therefore does not hold good for molten metais. I give here a few numbers from the curve for the element PbHg. It is of especial interest, on ac- count of the property of lead, not to give any Thomson-effect. The first column gives the temperature of the warmer point of contact in Centigrade degrees, the second the same reckoned from absolute zero. ‘The temperature of the other point of contact is throughout 20° C. The third column contains the electromotive force e in micro-volts. If e is a function of 0, represented by a curve of the second degree, then s ought to be a linear function of 9. The fourth column shows the Thermoelectricity of Molten Metals. 501 TABLE I. Lead-Mercury. de 0. p- ao II calculated. | Observed. | Calculated. 200.) 293 | 0 3:4 ‘" 46-2 100 ee sl 340 4-8 te 13:0 200 473 920 70 6:5 153°7 300 573 1710 9-2 83 244-6 400 673 2640 10:2 10:0 318°5 500 773 3790 12°5 11:8 448°3 580 853 4940 19:0 13:2 751-9 observed value of = and the fifth the value calculated from the first two numbers of the fourth column. The differences are far greater than possible errors of observation. The last column gives the quantities of heat in gramme-calories which result at the point of contact of absolute temperature 6, when the quantity of electricity electro-chemically equivalent to 2 grammes hydrogen (193,000 coulombs) passes through. If we conclude from the experiments of Le Roux (who, however, gives no absolute value of the Thomson-effect) that there is no Thomson-effect in lead, there must be such in mercury. Moreover its magnitude must be considerable. This follows from the observations with the couples HgCu, HgPt, HgFe, whose electromotive force I have measured for considerable differences of temperature. The Thomson- effect is very considerable in the metals Cu, Pt, Fe ; in mer- cury it must be at least of equal magnitude according to the results of these measurements. ‘ The wires employed of the three metals when heated in the middle, whilst the ends were maintained at constant temperature, gave very considerable electromotive forces (70 to 200 microvolts) even after they had been repeatedly heated. Mercury on the other hand, as is well known, gives none. This last phenomenon, and the Thomson-effect, cannot therefore stand in any direct connection. In the thermo-element PbHg, the contact-points may have the respective absolute temperatures © and @ (O>@); it may be supposed to remain closed so long that its thermo-current has conveyed the electro-chemical unit of electricity through it. Then at the temperature © the quantity of heat II is ab- sorbed, and at 6 the quantity of heat Hg is given off to sur- rounding objects. The difference Hg—LIg in the present 502 M. F. Brann on the example cannot be completely converted into electrical energy (with an oppositely bent curve it would not be the only equi- valent), but there would be also heat from the interior of the metals themselves converted into work. The following Table II. gives for different intervals of tem- perature the heat Ilg—IIg in gramme-calories. Further, the electrical work L in the same units. The result is that in the most favourable case 47 per cent. of the heat Ig—IIy appears as useful electrical work. The remainder, at least 53 per cent., remains in the metals themselves, in the form of (reversible) heat. It is given in the fourth column. The thermopile absorbs the quantity of heat Io at the highest temperature ©; at least, the pile works with this heat-capital, How much of this heat appears as useful work ? The sixth column shows that it is at the outside 40 per cent. If of the quantity of heat IIe the whole remainder not con- verted into work at the temperature @ were given off, the . O-90 ‘ fraction 6 must be converted into current-energy. The next column shows this fraction, Tasxe II. Elec ‘Temp. Pelle work, II og LOS ea L | 60—@ |Te—Te interval. Jap ey ete el = Uliga malig S) Ile 20-100 36°8 15°8 21:0 0:43 0-19 | 0-21 0°44 20-200 107°5 42-7 64:8 0:40 0:28 | 0:38 0:70 20-300 | 198-4 79°4 119-0 0-40 0:32 | 049 | O81 20-400 | 272'3 128°5 149°8 0:47 0-40 | 0°56 | 0°85 20-500 402-1 174:0 228°1 0-43 0°39 | 0-62 0°89 20-600 | 705°7 229°2 476°5 0°32 0°30 | O66 | 0:94 If we now enquire whether thermo-elements are suitable arrangements for converting heat into work, we obtain the following result :—Elements for which the electromotive force increases greatly with rise of temperature, as is the case for the element HgPb, work with very small useful effect (not regarding the loss of heat by conduction, radiation, &e.). Thermo-elements whose electromotive force decreases with rise of temperature work with more useful effect, but contribute absolutely less towards the work to be done. Other elements with liquid metals give essentially the same results as the PbHg element. The curve for Hg(Hg + Br + Pb) has nearly the same form. In this combination both con- stituents are fluid at ordinary temperatures ; I have examined them for an interval of more than 500°. It appeared to me Thermoelectricity of Molten Metals. 503 of particular interest to repeat Magnus’s experiment with this fluid alloy. Ifa portion of the amalgam was plunged cold into the rest heated to about 300°, no thermo-current was produced the electromotive force of which exceeded 0°5 micro- volts, which was the lowest I was in a position to measure. The curve for this element shows a remarkable peculiarity. At 180° it is convex towards the axis of abscissee, but between 180° and 210° it becomes concave, and then again convex. In this respect it is qualitatively exactly like the curve which platinum-iron elements give, only that in the latter the pecu- liarity is more decided. With a Pte element the curve rises steeply to about 360° and somewhat concave towards the axis of abscissee, then bends rapidly towards the horizontal direction, having a maximum at 420°, then falls from this very little (almost horizontal) to a minimum at 520°, rises then slowly, and then from about 630° ascends again to 1000° as steeply as from 0° to 36°. The element consisting of molten potassium and mercury shows an exactly similar behaviour, the curve rising with oscillations. Consistent results are, however, only obtained with this latter element when vapours of constant boiling- point are employed as source of heat. Using the oil-bath or the air-bath, the values obtained at the same temperature often vary considerably. We shall probably only be able to explain these phenomena . by the assumption that molecular transformations take place also in liquid bodies (as is known to be the case, for example, with sulphur); and these changes appear, at least as far as their velocity is concerned, to depend on the rate of heating. The question then suggests itself whether molten cadmium, which in the form of vapour is monatomic, combined with a thermo- element with the similarly constituted mercury, would show linear dependence of electromotive force upon temperature. The interval of temperature available seemed to be too small to determine this point with certainty; and I considered it beside the mark to employ cadmium amalgam, since we could no longer assume the existence of isolated atoms. 8. Taking all the results together, we may come to the conclusion that in thermoelectricity we are still further from an insight into the true nature of things than most phy- sicists have supposed. We must assume the existence of electromotive forces even in the interior of molten metals of unequal temperature ; and, moreover, these follow no simple laws. It would not be difficult to find formule for the elec- tromotive forces supposed to exist in the interior of metals which should satisfy the observations; but it seems to me 504. Mr. J. W. L. Glaisher on the Complete that we do not thereby come nearer to a representation of the processes which occur. We may say with certainty that fluid unequally-heated metals are electrically charged, and that by simple inequalities of temperature in a conductor the con- ditions for transformation of heat into work are fulfilled, only that we cannot obtain the work in the convenient form of a closed current. Perhaps this excitation of electricity takes place in all fluids, and generally in all substances, 7. e. also in the so-called vacuum ; and the further question, important in principle, may arise, what influence this hitherto disre- garded circumstance has upon physical processes. If we return to the facts detailed above, everything indicates that thermoelectric excitement is an intermolecular process dependent upon the number or arrangement of atoms in the molecule. It is thus suggested that all the rough mechanical changes, which exert so much influence on the thermoelectric behaviour of a solid body, and which consist in drawing, bending, hardening, annealing, &c., are also connected with intermolecular, and thus in a measure chemical, changes. This would be in harmony with the one already known fact, that in steel, upon passage from the soft into the hard con- dition and vice versé (also by simple drawing), the quantity of chemically combined carbon changes. Hard and soft steel give, as is well known, a tolerably powerful thermoelectric action. LVII. On the Expression for the Complete Elliptic Integral of the Second Kind as a Series proceeding by Sines of Mul- tiples of the Modular Angle. By J. W. L. GuatsHER, MOA, LR SS Series for K and Hi, §§ 1-4. Sie iB vol. xix. pp. 51, 52 of Crelle’s Journal, Guder- mann has given the following interesting expres- sion for K in a series proceeding by multiples of the modular angle 0 :— Ke ae lly 3 172830. le. 372152 8 =n 6+ gp sin 5A + 97 geen 0+ oa aa Ge sin 130+ &e. (1) The coefficients are the same as in the well-known fundamental formula 2K Ae a Layne 1? .8 here == —JT+ oy sin? 6+ gz ge Sin’ 0+ S356 sin°@+&e. (2) * Communicated by the Author. Elliptic Integral of the Second Kind. 505 Of course for the actual calculation of the numerical value of K corresponding to a given value of 0, the second formula is much to be preferred ; for the trigonometrical factors dimi- nish rapidly, whereas in ‘the first series they have no tendency to diminish, and the gradual convergence of the series is due solely to the numerical coefficients, Thus in (1) the nth term is of the order z but the corresponding term in (2) is of the order 1 inom20 When @=0, the series in (1) is of the form 0x, the true value being 4; when 0=47, the series is infinite in value, as it should be. § 2. Gudermann’s process is in effect as follows. He shows that the transformation which converts k into e-? converts K into 3e°(K—iK’), where & denotes $7—0@. Starting with (2), he thus finds K—7K/ ike ee lego? mee ot oa from which (1) is immediately deducible by equating the real arts. : At the end of the investigation Gudermann, after referring to the slow convergence of (1), which renders it of no prac- tical value, adds: —“Aus diesem Grunde iibergehen wir auch die Herleitung einer abhnlichen Reihe fiir den Quadranten HE.” The main object of this note is to give the series for which corresponds to (1). It does not admit of quite such simple derivation as the series for K. § 3. Gudermann’s transformation corresponds to the change of qinto ig*; and this change may be supposed to be produced by the change of q into g?, followed by the change of g into —g. By the change of g into 1g?, k’ is changed into e~**, and K’ is changed into 4e(K’—iK). Starting with the series 910" +. &e., 2K’ - 12. 3% be ea-e H1t et orp + op ga ge bt he., we thus find Me as tk WAS an Vad ty as Ht gpet + on gee + on ge ge tee § 4. In order to apply the same process to the series for Ki’, viz. 20’ 1 ere ea oe ee ome Bag) a it is necessary to determine the quantity into which H’ is converted by the change of gq into 2°. 506 Mr. J. W. L. Glaisher on the Complete It can be shown that, by the change of q into q?, ee Lieder} * nd that, by the change of g into —q, Hy’ becomes k becomes _ ” k’(K’—iK), H’—?K’ +7(h— —hPR) 4) kf Thus, by the change of g into ig2, EH’ becomes e~ 4H! — 7K! + kK + i(H—kOK + kk’ K)}. It follows, therefore, that 24H’ —h’?K/ +k K+1(B-k?OK +k’ Kt K/ Hy’ 7 1 1.3135) ese ee =e ea ee whence, equating imaginary parts, 2(B—h?K +4 RK!) _ 3 an 16-2 ke. vi 2 42 sin 0+ sin 30+ 5, The left-hand member of this equation _ 2H—K 3 K’ sin 20—K cos 20° T 1 and therefore the equation itself may be written 2H K is K cos 2€6—K’ sin 26 ire ae T +sin 0+ Sin 30 + — sin 70+ &e. Now * =sind+5 sin Ron ele ee Bee 2 ae sin 130+ &e. TT 97, 42 ae A? G6? e / 2 * 008 0+ 5: 5008 90+ 55 7008 904% Finny 008 130+ do, ae 2?, 4”. Ellliptie Integral of the Second Kind. 507 whence K cos 20—K’ sin 20 TT = —sin 0+ 30 i 70 pests 110+& =— seein ors qzsin +or 2. gz sin + WC. Thus 2H _K 1 ges Bh oS, — == +58 in 30-+ 5 SFT (mae Ez ~; sin 116+ &e.; or, substituting for = its value, yA i gs: Me — =sin 645 sin 30+ 5p sin bes sin 70 T P74 2 2 2 -- aoe = sin 90+ 5E. sia sin 116+ 92. ees S sin 136+ &c., which is the series for E corresponding to (1). Formule for K, E, 1, U, V, W, §§ 5-9. § 5. The results obtained in the previous sections form part of a general system of formule which may be stated as follows :— Consider two quantities I and G defined by the equations I=EK-K, G=H—k’K ; and let U, V, W denote 4+G), 3(G+H), $(H+)) respectively. The values of the six quantities, expressed in terms of HE and K, and of I and K, are therefore H=H =I+K, I =HK-K =, G=H—k?K =1+?K, U=E—-4(14+k”)K =14+4/K, V=H—-$k?K =1+3(1+/)K, W=E-1K =I+iK. 508 Mr. J. W. L. Glaisher on the Complete It can be shown that == 1 ae b-geg BH a3 § 6. Denoting by ea ee the same functions of k? that the unaccented letters are of £?, it can also be shown that, by the change of g into @?, k’ becomes e-”®, | eooamea aah a ICL ce Ve pest! aw): Vv! e~ 9 G +iG); and H’ becomes e~®{G/ +k K+i(G +kk’K’)}, GG, ees Oey —khK+iG —kk’K)}, Wo, eG + WK + (G+ WKY}, Wi ge PEW AW +E K+iG4+W4kh'RK)}. 2K’ 20 2v" § 7. Starting with the series for —— | hel mae in powers of k”, and changing k’ into e—**, we find, by equating the real, and the i imaginary, pe in the ping formule, K 12 a3" roi = = sill cs sin 50+ 5 oF. a a8in 90+ 5 a. sin 130 + &e., K’ 12 Ne tae hae =. ces 6+ 92 CO8dE + 55 92 4208 90+ 52 42, 62 08 130 +&e. ") v= 5 sin 30+ = sin 70+ ee sin 110+ &e., Elliptic Integral of the Second Kind. 509 2W’ 1 ah Sits ee. —— — 5 008 30— ; 97 4 088 70— 5E ge > cos 110—&ce., AS = sin @— = sin 30— 5 a qisin 10— oF ae sys Sin 110—&e., / si oF 5-5 COS 110+ée., i gee Be 10+ 2.6 § 8. It appears from § 5 that the quantities I’ and V’ resemble K’ in being transformable, by the change of modulus from k’ to e—**, into expressions of the form e+%(P’+7P), where P’ is the same function of k” that P is of #?. Perhaps the simplest method of obtaining the sine-series for E is by deducing the sine-series for W from the i/-series for I’ and then adding the sine-series for $K ; and it was in this manner that I was first led to the series for E*. It will be noticed that the process followed in § 4 also gives in the first instance the sine-series for HH —4K or W, and that the series for E is deduced from it by the addition of that for 4K. By the change of k’ into e-?”, kK’ becomes $e—(K’—iK), =cos 0+ 52008 30+ and therefore V’—k’K’ becomes e-®( I’ +7E). if then we start with the 4’-series for I’/—#’K’ and transform k’ into e~*, we obtain directly the sine-series for E by equa- ting the imaginary parts in_the resulting formula. The transformation therefore (of k’ into e~2) which converts K’ into de(K/—iK) converts also K/—EH’+2#’K’ into e~®(K’—H'—iE) ; and we may therefore derive the sine-series for H from the k’-series for K’— Hi’ + k’K’ by a process exactly analogous to that by which the sine-series for K is derivable from the k’-series for K’. The six quantities H, I, G, U, V, W are considered in detail in the Quarterly Journal of Mathematics, vol. xx. pp. 313- 361, and in the Proceedings of the Cambridge Philosophical Society, vol. v. pp. 184-208. The formule in these papers show that E forms one of a triad of corresponding funda- mental quantities of which the other two members are Land G. § 9. It may be remarked that I=—J, where J is the * Proc. Camb. Phil. Soe. vol. v. p. 204. Phil. Mag. 8. 5. Vol. 19. No. 121. June 1885. 2M 510 Notices respecting New Books. quantity so denoted by Weierstrass, atid =K—H. We thus have —_ cin 0+ 5 sin 36+ esin SO + 5 L resin 70 2 ee 2 faiSBee Z 8 Laee BE . my sin 130+ &e, ee = sin 6—5 sin 564. ? sin 59-2 oy. sin 70 2 92 2 ae Bast 99— 52 peaed > sin 116+ tS a >, sin 130— &e. LVIII. Notices respecting New Books. An Elementary Treatise on Dynamics, containing Applications to Thermodynamics. By B. Wiurtamson, M.A., ge, and F. A. Tarzteton, LL.D. London: Longmans, Green, and Co. 459 pp. yale is uuquestionably an important work on Dynamics, com- prising within the compass of 459 pages the Dynamics of a Particle (218 pp.), the Kinematics and Kinetics of a Rigid Body (207 pp ), including two chapters on Energy (40 pp.) and one on Small Oscillations (43 pp.), anda final chapter on Thermodynamics (29 pp.). Except for a few applications to elastic material and some to the thermodynamics of gases (as illustrations of the Theory of Energy), the work is confined to the Motion of Rigid Bodies, and is on the whole a most carefully thought-out treatise on so large a subject. It professes to “ start from the most elementary conceptions, so that any student who is acquainted with the Calculus can commence the Treatise without requiring the previous study of any other work on the subject.” (see preface). It is perhaps a natural result of this that the early parts are easy and in considerable detail, whilst the later parts are difficult from their conciseness. It may, indeed, be doubted whether any student could really read this Treatise through (and work out the examples) without external help in the later parts. The examples have been chosen with great care so as to form excellent illustrations of the text; of a great many, however, it must be said that they are rather mstruc- tive problems which have been solved by accomplished mathema- ticians than exercises for students ; more or less full details of the working of these are given :—e.g. Ex. 15 to 27, on Kinetics of a Rigid Body, are ‘“ the substance of Prof. MacCullagh’s Lectures on Rotation.” It is singular that though the work bears the names of two mathematicians on the titlepage, and seems to have received at least partial revision from a third (see preface), a decided looseness Notices respecting New Books. 511 of expression occurs here and there. Thus the opening lines run :— “We give the name of matter to that which we regard as the permanent cause of any of our sensations.” This definition would surely include heat, light, railway accidents, &e. Again the term velocity nowadays has surely the unique definite meaning of “space described (or capable of description) in a time-unit ;” but the term is used in several places as if it had a simply spatial meaning, e.g. (p.-28) “a velocity of 400 feet,” (p. 29) ‘‘ the velocity per minute,” and similar instances in many other places. AtLan Cunninenam, Major, AL. Energy and Motion. A Textbook of EKlementary Mechanics. By W. Patcr, M.A. Cassell and Co. (Pp. 114.) THIs is one more of the legion of small textbooks of elementary science the razson d’étre of which it is hard to discover. The pre- face states that there “‘ appear to be no good books on the subject which approach it from a sufficiently elementary standpoint ;” but we fear that this book put into the hands of ordinary schoolboys or schoolgirls, unless supplemented by good oral teaching, will make too large demands upon their intelligence. ‘There are a few good points of more or less novelty to be noted, but these are more than counterbalanced by erroneous teaching upon certain important matters. A few instances will suffice. The specification of an acceleration as “23 feet per second per second,” or as ‘‘ 24,000 yards per minute per minute,” is no doubt to be commended; but such unusual accuracy contrasts, unfortunately, with such state- ments as that “‘ 1 horse-power is equal to 550 foot-pounds ” (p. 61) ; or that “to produce a velocity v in m units of mass, or to stop the mass m if moving with a velocity v, would require mv units of force” (p. 44). The author seems to be of opinion that the formula s = 3 ft.’ does not admit of rigorous proof, but always involves some assum p- tion. Certainly he makes an assumption (p. 13); but using the word “therefore,” he gives his readers no hint of this when he says, “When a moving body is uniformly accelerated the increase of velocity is the same throughout for every equal small portion of time, therefore the distance passed over will be the same as if the body moved uniformly with the average velocity for the whole number of small spaces of time—that is, for the whole time.” The statement on p. 39, “Ifa bullet of lead and another of wood of the same size be thrown at the same time with the same velocity, the bullet of lead wili go further than the bullet of wood ” needs no comment; it is sufficient to quote it. The meaning of “mass” is not explained by saying that there is more of ‘“‘ some- thing” in a leaden bullet than in a wooden bullet of equal size; and the statement that there is more “matter” or “stuff” in a cubic inch of gold than in a cubic inch of water has simply no meaning at all. Until it is proved that gold is a compound of hydrogen and oxygen, in the proportions in which they occur in 2M 2 512 Geological Society. . . .. water (which is possible, but extremely improbable), we shall not know which of these two contains most matter; and in the present state of chemical science it is simply idle to pretend to compare the quantities of matter in two things of different chemical nature. We fail to see why a gramme should be called a ‘‘ mass-gramme,” and it is certainly not “ the quantity of matter contained in a cubic centimetre of distilled: water at the temperature and pressure at which water has its greatest density.” Until these and similar errors are corrected no competent teacher will consent to employ this production as a textbook. LIX. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. {Continued from p. 393. | April 29, 1885.—Prof. T. G. Bonney, D.Sc., LL.D., F.B.S., President, in the Chair. (RES following communications were read :— 1. On the Structure of the Ambulacra of some Fossil Genera and Species of Regular Echinoidea.” By Prof. P. Martin Duncan, M.B. (Lond.), F.R.S., V.P. Linn. Soe., F.G.S. 2. “The Glacial Period in Australia.” By R. von Lendenfeld, Ph.D. Communicated by W. T. Blanford, LL.D., F.R.S., Sec. GS. Although several previous writers have suggested that boulders and gravels found in different parts of Australia are of glacial origin, the evidence is vague, and no clear proof of glaciation has been brought forward. During a recent ascent of the highest ranges in Australia, parts of the Australian Alps, the author succeeded in discovering a peak which he: named Mount Clarke, 7256 feet high, and in finding traces of glaciation in the form of roches moutonnées throughout an area of about 100 square miles. The best-preserved of the ice-worn surfaces were found in a valley named by the author the Wilkinson Valley, running from N.E. to 8. W., immediately south of Miller’s Peak and the Abbot Range. No traces of ice-action were found at less than 5800 feet above the sea. The rocks showing ice-action are all granitic, and the fact that the surfaces have been polished by glaciers is said to be proved by the great size of such surfaces, by their occurrence on spurs and projecting points, by many of them being worn down to the same general level, and by their not coinciding in direction with the joints that traverse the rock. In conclusion the author briefly compared the evidence of glacial action in Australia with that in New Zealand. 3. ‘* The Physical Conditions involved in the Injection, Extrusion, and Cooling of Igneous Matter.” By H. J. Johnston-Lavis, M.D., F.G.8., &e. . The great disproportion between the displays of volcanic activity Intelligence and Miscellaneous Articles. 513 in the same volcano at different times, and between the eruptions of different volcanoes, is a subject deserving the most attentive con- sideration. The violence of a volcanic outburst does not bear any relation to the quantity of material ejected. The union of water with lavas may be compared with the solution of a gas in water; but there is reason to believe that in their deep-seated sources lavas con- tain little or no water. If igneous matter be extruded through dry strata the eruption might take place without explosive manifesta- tions. But if igneous matter be extruded through water-bearing beds, a kind of dialysis would take place between the igneous and aqueous masses. In this way the tension of the steam in the fluid rock may at last become so great that a fissure will be formed at the surface and volcanic action will follow. In this way the violence of a volcanic eruption will be determined by the quantity of water contained in the strata through which the lava passes in its passage to the surface, and by the temperature at which it reaches the surface. This theory explains the acknowledged sequence of volcanic out- bursts of different degrees of violence, and the intervals which occur between them. It also explains the differences between the central and lateral eruptions of a great volcano, and the phenomena attend- ing its extinction. The structures of the igneous rocks, whether of basic or acid composition, are greatly modified by the presence in them of volatile ingredients. The succession of events indicated by the structure of Monte Somma and Vesuvius, Roccamonfina, Monte Vulture and Monte Nuovo, show that after a long cessation of volcanic activity we have an extensive production of fragmentary and scoriaceous material, and that this is gradually succeeded by the eruption of lava-streams. The water and other volatile substances, such as sulphates and chlorides, which are given off abundantly in volcanic eruptions, may act as solvents for the various minerals which constitute lavas. LX. Intelligence and Miscellaneous Articles. APPLICATION OF PHOTOGRAPHY TO ELECTRICAL MEASUREMENTS. BY JOHN TROWBRIDGE AND HAMMOND VINTON HAYES, i the study of electromotive force and of voltaic cells it is often desirable to have long-continued observations. The com- plete history of the action, for instance, of the Daniell cell with different strengths of solution extending over hours or days, if it. could be presented to the eye as a curve, would be valuable to those who desire to know the behaviour of such a cell while it is doing work under definite conditions. Such curve could be obtained by patient observation, but it would be unprofitable labour for one to spend his time in watching the excursions of a galvanometer- needle, if the needle can be made to record its movements by any device. 514 Intelligence and Miscellaneous Articles. The method we have used enables one to study the action of a celi at one’s own leisure, the apparatus running at night or during the day when one is occupied with other work. A beam of light from a gas-flame passes through a vertical slit placed in front of the flame, and is reflected from the concave mirror of a tangent-galva- nometer, of few turns of wire, through a horizontal slit, in a dark box, in which a sheet of sensitive paper is placed. By means of this arrangement of a vertical and a horizontal slit, 2 small point of light is obtained. A stationary concave mirror is placed near the needle of the tangent-galvanometer, so that the same beam of light may be reflected by both this mirror and the one attached to the galvanometer-needle. The spot of light given by the stationary mirror serves to mark the zero point of the needle when no current is passing through the galvanometer. The photographic paper is placed in a slide which is lowered uniformly by the unwinding of a string from a little cylinder placed either upon the hour-hand or the minute-hand of a cheap eight-day clock. When the electrical current from the voltaic combination, which is being used, passes through the galvanometer, its changes in strength for different times are indicated by the relations of the two lines drawn upon the sensitive paper. The line drawn by the light from the sta- tionary mirror is a straight one, and serves for the abscissa of times; while the perpendicular distances from the curve drawn by the mirror attached to the needle of the galvanometer to this axis of times give the ordinates of the curve drawn by the latter. Rapid printing-paper was used, and an ordinary gas-flame gaye a sufficiently strong spot of light to produce an actinic effect. Fig. 1 represents the action of a modification of Trouve’s battery. During this experiment, which lasted for thirty minutes, there were five ohms in the external circuit. The right-hand portion of en Fig. 2. ae \J ie the diagram shows the strength of current when the circuit was made, and it will be observed that the battery was not at its best Intelligence and Miscellaneous Articles. 515 until ten or twelve minutes after making the circuit; from this maximum point the strength of the current gradually diminishes. Fig. 2 shows the action of the same battery with ten ohms external resistance. Under these conditions we find at the instant of making circuit a strong current, which rapidly diminishes within the first five minutes to one sixth of its first strength. Knowing the distance of the galvanometer from the sensitive paper, the strength of the current may be calculated by measuring the distance between the two lines at any instant, and proceeding as with an ordinary galvanometer and scale. From a comparison of the two figures the electromotive force may be determined by Ohm’s law, if the distance between the lines is measured at the instant the current is made. Then knowing the electromotive force, current, and external resistance, we can readily find the internal resistance. This resistance will be the liquid resistance of the cell only for the moment that the circuit is made, for afterwards the variation in electromotive force due to polarization, and the change in resistance of the liquid due to electrolytic action will combine to cause changes. Since, however, the changes in electromotive force due to polarization are much more rapid in their action than the changes in battery resistance, a very small error will be introduced if we compare points near each other on those parts of the curve in which the variation in current is greatest: during the small fraction of a minute that is taken, the change in battery-resistance will be infinitesimal and may be neglected. We have selected these photographs as an example of the large variations that some batteries present, and the consequent useful- ness of some such way of studying their action. From measure- ments upon these photographic charts the variations in electro- motive force and internal resistance can be studied by obtaining such charts under different conditions of external resistance. It is evident that the same photographic method can be employed to study the swing of the needle of a short coil-galvanometer, which indicates the gradual heating of a thermopile. In this way the conduction of heat along a bar could be studied.— Silliman’s American Journal, May 1885. Jefferson Physical Laboratory. ON AN INSTRUMENT RESEMBLING THE SEXTANT, BY WHICH ANGLES WITH THE HORIZON CAN BE MEASURED. BY E. H. AMAGAT. Imagine’a sextant of which the optical axis of the telescope, instead of being oblique in reference to the fixed mirror, which I shall call B, is perpendicular to it. Arrange the movable mirror A so that its axis of rotation coincides with one of its edges, and cuts _ the optical axis. Suppose that the mirror B, instead of being fixed, is movable about an axis parallel to the plane of the graduated circle, and perpendicular to the optical axis; in these conditions, 516 Intelligence and Miscellaneous Articles. the image twice reflected from any given point will be displaced in a plane perpendicular to that of the circle, when B turns about its axis. If the circle is placed horizontally, all the objects on the same vertical plane will be seen to pass in succession. Now let us suppress the telescope, and replace it by a simple vertical slit placed between the eye and the axis of rotation of A; suppose, moreover, the mirror is silvered all over. By placing the eye at a convenient height in front of the slit, we can look directly at an object above or below the mirror (according to its height), and we can make it coincide with the image twice reflected of another object which may be at any height, since the movement of B may bring it vertically to the desired height. A reading made as with the sextant will give at once the angle of the two objects projected on the horizon, such as would be obtained with a grapho- meter. It follows from the preceding that the coincidence should be exact with the image of the axis of rotation or vertical edge of A, which would reduce to zero the field of the objects seen in B by double reflection ; but it is easy to see that by slightly inclining the visual ray so as to have a sufficient field, the error produced will be extremely small from the properties of minima, since we move but little from the position m which the error is completely nul= lified ; with a small instrument which is only 7 centimetres in the side, an operator who is but little practised may take, in a few seconds, angles with sufficient accuracy for most ordinary opera- tions; the approximation mainly depends on the horizontality of the instruments. Although the coincidence becomes more difficult and the exactitude less for very large angles, we may work directly up to 140°.—Comptes Rendus, April 27,1885. ON THE PRODUCTION OF ALTERNATING CURRENTS BY MEANS OF A DIRECT-CURRENT DYNAMO-ELECTRIC MACHINE. BY JOHN TROWBRIDGE AND HAMMOND VINTON HAYES. It is often desirable to transform a direct current into an alternating one for the purpose of obtaining electricity of high tension by means of a Ruhmkorff coil, for studying the effects of stratifications in vacuum tubes, or for employing alternating currents in the study of magnetism. The best way is undoubtedly to employ an alternating dynamo-electric machine, as has been done by Spottiswoode. When, however, only a direct-current machine is available, the following method can be employed :— The dynamo machine, if it is not a shunt-wound machine, is shunted by a suitable resistance. We have employed for this pur- pose thin ribbon-steel about 1:5 centim. broad and -01 millim. in thickness. The remaining portion of the current from the machine is conducted to two brass or copper segments a, a’, fig. 2. This current is led to the primary coil, for instance, of a Ruhmkorff coil from two other segments }, 6’. These segments are fixed upon a Intelligence and Miscellaneous Articles. 517 eylindrical shaft A (fig. 1), which is stationary. A belt passing over the pulley B turns the wheel ©, upon the face D of which Fig. 1. Fig. 2. revolve four brushes which connect the adjoining segments. The brushes aa, 66 are made adjustable, the two adjoining brushes being electrically connected, and a small stream of water plays upon the segments of the commutator. The character of the spark produced by a Ruhmkorff coil which is marked by alternating currents has been studied by Spottiswoode. Without condensers in the secondary circuit, a bright yellow glow spans the distance between the two terminals of the coil, which partakes more of the character of a voltaic arc than of the ordinary discharge from a Ruhmkorff coil. The apparatus which we used produced three thousand reversals a minute. This rate was too rapid for the best effects with a Ruhmkorff coil. It enabled us, however, to study the musical note produced in the cores of the electromagnet by rapid reversals of the current in the electromagnet, and also the heating effects which have been so often studied.—Silliman’s American Journal, May 1885. Jefferson Physical Laboratory. THERMO-ELECTRO-PHOTO-BARIC UNIT. BY PLINY EARI.E CHASE, LL.D. The earliest attempt at measurement, with a view to demonstrate the correlation of thermal and electric energies, appears to have been that of Principal Forbes, who found, in 1832 (Phil. Mag. iv. p- 27), that the conductivity of metals for heat and electricity is nearly the same. The dimensions of absolute measure involved were MV, L. In 1843 Joule published his discussion of the calorific effects of magneto-electricity, and his determination of the mechanical equivalent of heat (Phil. Mag. xxii. pp. 263, 347, 485), using the same dimensions, M, L. ~ In 1856 Weber extended the correlation of Forbes (Pogg. Ann. xcix.), by showing the approximate equality of the electro-magnetie ratio to the velocity of light (£ 7'—'). | Wolf’s discovery of the sun-spot period was followed, in 1857, by the investigations of Lamont and Sabine, showing the identity 518 Intelligence and Miscellaneous Articles. of the sun-spot periods with the periods of magnetic perturbation (Mag. and Meteorol. Obs., Toronto, 11. Ixvii.; St. Helena, 11. CXX1.—CXXXV1.). In 1860 Henshall showed the influence upon sun-spots which is produced by Mercury, Venus, and Jupiter, when in conjunction with the same face of the Sun (Cosmos, xvu. p. 578). In 1863 Chase showed (Proc. Amer. Phil. 08 ix. pp. 283-288 ; Phil. Mag. xxvii. pp. 55-59) that the mass of the Sun can be approximately estimated from the influence upon the barometer ot the constrained “relative motions” of the Earth and Sun. In 1864 he showed, by the investigation which received the Magellanic medal (Trans. Amer. Phil. Soc. xii. pp. 117-186; Proc. Amer. Phil. Soc. ix. pp. 425-430 ; Phil. Mag. xxx. pp. 52-57), that the magnetic disturbances of the Sun and Moon are many times greater than simple tidal disturbances, and that they can be very closely represented by the disturbances of gravitating pressure, under constrained and “ coercitive” relative motion. In 1869 he further showed (Proc. Amer. Phil. Soc. xi. pp. 103-107) that the constrained relative motion at Sun’s surface represents a cyclical gravitating and electric disturbance which acts with the velocity of light. i 1873 Maxwell (Electricity and Magnetism) published his theory that light consists of a disturbance in a medium susceptible of dielectric polarization. In 1884 Langley (Researches on Solar Heat) confirmed the identity of thermal, electric, and luminous radiation, for which Chase had suggested probable reasons in 1864 (Proc. Amer. Phil. Soc. ix. p. 408), and Draper in 1872 (Phil. Mag. xlvi. pp. 104-107). All of the foregoing investigations can be coordinated, in the oe of greatest known energy, by means of the kinetic unit SS -, in which p represents an infinitesimal particle, and v, is the velocity of light, the electric ratio, the projectile velocity which represents thermo-dynamic energy at Sun’s surface, and the projectile velocity which represents the maximum energy both of constrained rotation and of free revolution in the solar system. The greatest constant energy of free revolution, which can be 2 iven to uw by solar attraction, is PP v, being the velocity of g He by 5) g aif circular orbital revolution at the Kantian radius r , where solar rotation and orbital revolution are synchronous. The same energy would give synchronous radial or elliptic revolution through or about a major axis 2r,, under gravitating acceleration varying inversely as 7°. The energy which would be required to produce synchronous radial oscillation, under the constant gravitating acceleration g,, perv ne 2 would be z? times as great, or The energy which would be required to produce constant radial oscillation in the region of maximum solar gravitation and coercitive Intelligence and Miscellaneous Articles. 519 force (at Sun’s surface) would be &* times as great, or 4 prrktu,? iat pv. 2 Days k being the ratio of the Kantian radius to the solar radius. The time which would be required to communicate this maximum energy is ¢,, the time of virtual projection against uniform resis- tance, in the region of greatest solar energy, which is also the time of solar half-rotation, as well as the minimum time of synchronous elliptic, circular, and radial oscillation in the solar system. The ordinary thermal and gravitating units may be deduced from the general unit by means of the equations 2 M,7o Vo U Ph Mol tk a 29, In the second of these equations T represents the mass of water which could be heated one degree by p of oscillating lumi- niferous ether, or the number of degrees to which » of water could be heated ; g,, gravitating acceleration at EHarth’s equator ; h, the linear dimension of the mechanical unit of heat. The harmonic values are as follows :— m,=329414 m,, r, = 198-923 r,, 9,=27°765 9 v,=185500 miles per second, 9,=32°033 feet per second, T=10,775,492,000,000° C.—Communicated by the Author, having been read before the American Philosophical Socvety, April 17, 1885. ee THE CHASE-MAXWELL RATIO. BY PLINY EARLE CHASE, LL.D. In 1872 (Proc. Amer. Phil. Soc. xu. p. 394) Chase showed that the tendency of particles, in exploded gases, toward primary and secondary centres of oscillation leads to a permanent vis viva of equilibrium which is 3 of the vis viva of explosive projec- tion, and that the synchronous action of the Sun and the Earth upon the oscillating particles furnishes a ready method for estimating the Sun’s mass and distance. He also showed (ibid. pp- 403-405) that the successive planetary positions in the solar system illustrate the influence of ethereal oscillations of a similar character. In 1875 he showed (op. cit. xiv. p. 651) that the mean velocity of expanding gaseous pressure is = of the corre- sponding constant velocity of revolution; the ratio of wis vwa 520 Intelligence and Miscellaneous Articles. 4 is therefore > = °405285, and we have K 3 is: 405230 8. In 1877, Preston (Phil. Mag. ii. p. 453; iv. p. 209) showed ‘“‘ that a physical relation exists between the velocity of the particles of a medium constituted according to the kinetic theory, and the velocity of propagation of a wave in the medium.” Maxwell calculated the numerical value of this relation at »/3, which repre- sents Chase’s ratio of relative vis viva; but he did not give the method by which he reached that result, and no record of it was found among his papers. The followimg thermodynamic demon- stration may therefore be satisfactory to those who have found any difficulty in accepting the more simple and more general photodynamic proof which is furnished by reference to oscillatory centres. If we represent the density of a gas, ue by p, the fundamental equation of pressure becomes , A Alexander Naumann (Ann. Pharm. 1867, pp. 142, 267; J. B. 1867, p. 62) showed that oni baaae Sis u==5 (yy hcylis ae ae Relic nice (2) pu being the heat of molecular motion, or mean vis viva of a periect gas; y', the specific heat under constant pressure ; y, the specific heat under constant volume; y'—y, the heat of expansion, or vis viva of mean velocity. The total specific heat is therefore’ 6=pt+y at Aa (3) Hence yippee ira Series Percent Sc amererr tracts 5 <0 = (4) PR erate gory come Sommers oS. (5) Prof. d’Auria, in a special investigation relating to the dynamics of direct-acting pumping-engines, not yet published, has found, by analogy, that Vimaewes pelt coraalny sis. 2 Ee (6) Substituting this value in eq. (2) we get Chase’s result :— y¥-y= "A05285y ©. o Weve ip de welusl tame tte ke) Vol letunite (7) y= 1:-405285y, « Solhedorxe Mele gel me lepes lage (8) The exactness of agreement between this @ priort value and the one which was found by Rontgen (1°4053 ; Pogg. Ann. 1873, pp. 148, 603) is very remarkable.— Communicated by the Author, having been read before the American Philosophical Society, April 17, 1885. 521 INDEX to VOL. XIX. AcTINOMETER, on a new, 231. AXther, on the structure of mecha- nical models illustrating some pro- perties of the, 438. Ahrens (C. D.) on a new form of polarizing prism, 69. Alkalis and alkaline earths, on the spectra of the, 365. Amagat (E. H.) on the value of Poisson’s coeflicient for caoutchouc, 66; on some results for use in calculations with manometers with compressed air, 150; on the limit of the density and on the atomic yolume of gases, 313; on an in- strument by which angles with the horizon can be measured, 515. Amalgams, on the thermoelectric properties of, 363. Arctic interglacial periods, on, 30. Atomic arrangement, on the influence of, on the physical properties of compounds, 50. Atoms, on the size of, 359. Ayrton (Prof. W. E.) on gas-engine indicator-diagrams, 152; on the most economical potential-differ- ence to employ with incandescent lamps, 304. Binocular glasses for eyes of unequal focal lengths, on, 461. Books, new :—Geology of Wisconsin, 60; Jukes-Browne’s Handbook of Physical Geology, 61; Gray’s Ab- solute Measurements in Electricity and Magnetism, 141; Day’s Exer- cises in Electrical and Magnetic Measurement, 142; Lupton’s Nu- merical Tables and Constants, 142; Pattison Muir's Principles of Che- mistry, 222; Pendlebury’s Lenses and Systems of Lenses, 888; La- timer Clark’s Transit Tabies for 1885, 389; Wormell’s Electrical Units, 389; Williamson and Tar- leton’s Treatise on Dynamics, 510; Paice’s.Energy and Motion, 511. Bosanquet (R. H. M.) on permanent magnets, 57; on the magnetic permeability of iron and steel, with a new theory of magnetism, 73, 333. Braun (F.) on the thermoelectricity of molten metals, 495. Brown (J.) on the formation of a stalactite by vapour, 395. Cailletet (M.) on the employment of marsh-gas for producing low tem- peratures, 65. Callaway (Dr. C.) on the granitic and schistose rocks of Donegal, 390. Caoutchouc, on the value of Poisson’s coefficient for, 66. Capillary multiplier, on a, 43. Chase (Dr. P. E.) on elementary phyllotaxy, 68; on some principles and results of harmonic motion, 190; on the thermo-electro-photo- baric unit, 517; on the Chase- Maxwell ratio, 519. Chemical affinity, on the determina- tion of, in terms of electromotive force, 1, 102, 197. Cleminshaw (E.) on spectrum ana- lysis, 365. Climate, on the characteristics of in- terglacial, 36. Cole (G. A.J.) on hollow spherulites, 391. Collins (J. H.) on the geology of the Rio Tinto mines, 227. Colouring matters, on combinations of, with silver salts, 229. Compounds, on the influence of atomic arrangement on the phy- sical properties of, 55. Croll (Dr. J.) on Arctic interglacial periods, 30. Dielectric constant of some gases, on the determination of the, 393. 522 Dielectric polarization, on the elec- tromagnetic action of, 385. Drops, on a point in the theory of pendent, 46. Dynamo, on the self-regulation of the compound, 462, Dynamo-electric machine, on the pro- duction of alternating currents by means of a, 516. Earth, on the determination of the mean density of the, 219. Edlund (Prof. E.) cn the behaviour of electricity in rarefied air, 125, 218. Electric current, on the influence of an, in modifying the rate of thin- ning of a liquid film, 94; on the measurement of strong, 396; on the rotation of the equipotential lines of an, by magnetic action, 419. Electrical measurements, on the ap- plication of photography to, 513. Electricity, on the behaviour of, in rarefied air, 125; on Edlund’s theory that a vacuum is a con- ductor of, 218. Electromagnetic action of dielectric polarization, on the, 385. experiments, on some, 13], 215. wave-surface, on the, 397. Electromagnets, on, 73, 333. Electrometer, on the quadrant, 291. Electromotive action of illuminated selenium, on the, 315. force, on the determination of chemical affinity in terms of, 1, 102, 197; on the seat of the, in the voltaic cell, 153, 254, 340. Elliptic integral of the second kind, on the complete, 504. Elsass (Dr. A.) on a new form of monochord, 48. Energy, on the identity of, 482; on the paths of electric, in voltaic cir- cuits, 487. Fitzgerald (Prof. G. F.) on the rota- tion of the plane of polarization of light by reflection from the pole of a magnet, 100; on the structure of mechanical models illustrating some properties of the ther, 488. Fleming (Dr. J. A.) on the charac- teristic curves and surfaces of in- candescence-lamps, 368. Fog, on the theory of illumination in a, 443. Fol (M.) on the penetration of day- INDEX. light in the water of the Lake of Geneva, 70. : Fritts (Mr.) on the electromotive action ofilluminated selenium, 315. Fee rere indicator-diagrams, on, 52. Gases, on the passage of electricity through rarefied, 125; on the limit of the density and on the atomic volume of, 313; on the determi- nation of the dielectric constant of some, 393. Gardner (J. S.) on the Tertiary ba- saltic formation in Iceland, 64. Geological Society, proceedings of the, 63, 143, 225, 389, 512. Glaisher (J. W. L.) on the expression for the complete elliptic integral of the second kind, 504. Gravitation, on a new method of determining the constant of, 148. Green (Prof. A. H.) on a section near Llanberis, 63. Hall (EK. H.) on the rotation of the equipctential lines of an electric current by magnetic action, 419. Harmonic motion, on some principles and results of, 190. Hartley (Prof. W. N.) on the influ- ence of atomic arrangement on the Pol properties of compounds, 5) Hayes (H. V.) on the application of photography to electrical measure- ments, 513; on the production of alternating currents, 516. Heaviside (QO) on the electromagnetic wave-surface, 397. Hopkinson (Dr. J.) on the quadrant- electrometer, 291. Horizon, on an instrument for mea- suring angles with the, 515. Hughes (G.) on some West-Indian phosphate deposits, 144. Hutton (Capt. F'. W.) on the geology of New Zealand, 146. Hydrogen, on the occlusion of, by zine dust, 232; on the limit of the density of, 313. Illumination in a fog, on the theory of, 443. Incandescence lamps, on the most economical potential-difference to employ with, 304; on the charac- teristic curves and surfaces of, 368. Tron, on the magnetic permeability of, 73, 333. INDEX. Irving (Rev. A.) on the Bagshot strata from Aldershot to Woking- ham, 392. Judd (J. W.) on the Tertiary and older Peridotites of Scotland, 228. Jukes-Browne (A. J.) on the boulder- clays of Lincolnshire, 225. Klementic (Dr. I.) on the determi- natiou of the dielectric constant of some gases, 393. Konig (A.) on a new method of de- termining the constant of gravita- tion, 148. Lea (M. C.) on combinations of silver chloride, bromide, and iodide with colouring-matters, 229, Lendenfeld (R. von) on the glacial period in Australia, 512. Light, on the rotation of the plane of polarization of, by reflection from the pole of a magnet, 100; on the action of fog upon, 443. Line-divider, on the uses of a, 280. Liquid film, on the influence of an electric current in modifying the thinning of a, 94. Lodge (Prof. O. J.) on the seat of the electromotive forces in the voltaic cell, 153, 254, 3540; on thermo- electric current-direction, and on a point in thermodynamics, 448; on the identity of energy, 482; on the paths of electric energy in voltaic circuits, 487. Logical spectrum, on the, 286. M‘Connel (J.C.) on the use of Nicol’s prism, 317. Macfarlane (Dr. A.) on the logical spectrum, 286. Magnet, on the rotation of the plane of polarization of light by reflection from the pole of a, 100. Magnetism, on a new theory of, 73, 333; contributions to the theory of, 237. Magnets, on permanent, 57. Malcolm (Col.) on binocular glasses for eyes of unequal focal lengths, 461. Manometers with compressed air, results for use in calculations with, 150. Marks (Miss Sarah) on the uses of a jine-divider, 280. Marsh-gas, on the employment of, for producing low temperatures, 65. 523 Metals, on the thermoelectricity of molten, 495. Monochord, on a new form of, 48. Morgan (Prof. C. L.) on the Clifton fault, 143. Morize (H.) on a selenium-actino- meter, 231. Nicol (Dr. W. W. J.) on supersatu- ration of salt-solutions, 458. Nicol’s prism, on the use of, 317. Oxygen, on the limit of the density of, 313. Pendulum, on the application of the, to the determination of the mean density of the earth, 219. Perry (J.) on gas-engine indicator- diagrams, 152; on the most econo- mical potential-difference to em- ploy with incandescent lamps, 304. Photography, on the application of, to electrical measurements, 513. Phyllotaxy, on elementary, 68. Poisson’s coefficient, on the value of, for caoutchouc, 66. Polarization, on the electromagnetic action of dielectric, 385. Polarizing-prism, on a new form of, 69 Potential-difference, on the most economical, to employ with incan- descent lamps, 304. Preston (S. T.) on some electromag- netic experiments, 131, 215. Pyrrol, on the synthesis of, from coal- gas, 232. Quadrant-electrometer, on the, 291. Rayleigh (Lord) on the theory of illumination in a fog, 448; on a monochromatic telescope, with ap- plication to photometry, 446. Reade (T. M.) on the drift-deposits of Colwyn Bay, 147; on boulders near Festiniog, 229. Reinold (Prof. A. W.) on the influ- ence of an electric current in modi- fying the rate of thinning of a liquid film, 94. Richarz (F.) on a new method of determining the constant of gravi- tation, 148. Rontgen (Prof. W. C.) on the elec- tromagnetic action of dielectric polarization, 385. Rucker (Prof. A. W.) on the influ- ence of an electric current in modi- fying the rate of thinning of a 524 liquid film, 94; on the self-regu- lation of the compound dynamo, 462. Rutley (F.) on fulgurite, 389; on brecciated porfido-rosso-antico,393. Salt-solutions, on supersaturation of, 453. Sarasin (E.) on the penetration of daylight in the water of the Lake of Geneva, 70. Selenium, on the electromotive action of illuminated, 315. Selenium-actinometer, on a, 251. Siemens (W.) on the theory of mag- netism, 237 ; on the electromotive action of illuminated selenium, 316. Silver chloride, bromide, and iodide, on combinations of, with colouring- matters, 229. Spectrum analysis, lecture-experi- ments on, 365. Stalactite, on the formation of a, by vapour, 395. Steel, on the magnetic permeability of, 73, 338. Supersaturation, 453. Teall (J. J. H.) on the metamor- phism of dolerite into hornblende- schist, 145. Telescope, on a monochromatic, 446. Temperatures, on the means of pro- ducing exceedingly low, 65. Thermoelectric circuits, on, 448. properties of amalgams, on the, observations on, Thermoelectricity of molten metals, on the, 495. INDEX. Thermoelectro-photo-baric unit, on the, 517. Thompson (C.) on the determination of chemical affinity in terms of electromotive force, 1, 102, 197. Trimethylamine, on the synthesis of, . from coal-gas, 232. Trowbridge (J.) on the measurement of strong electrical currents, 896 ; on the application of photography to electrical measurements, 513; on the production of alternating currents, 516. Voltaic and thermovoltaic constants, on, l. Voltaic cell, on the seat of the elec- tromotive forces in the, 153, 254, 340. circuits, on the paths of electric energy in, 487. Williams (G.) on the synthesis of trimethylamine and pyrrol from coal-gas; and on the occlusion of hydrogen by zine dust, 232. Wilsing (Dr. J.) on the application of the pendulum to the determina- tion of the mean density of the earth, 219. Worthington (A. M.) on a capillary multiplier, 43; on the theory of pendent drops, 46; on Prof. Edlund’s theory that a vacuum is a conductor of electricity, 218. Wright (Dr. C. R. A.) on the deter- mination of chemical affinity in terms of electromotive force, 1, 102, 197. Zine dust, on the occlusion of hydro- gen by, 282. END OF THE NINETEENTH VOLUME. Printed by Taytor and Francis, Red Lion Court, Fleet Street. Pe ee “YT ' Sug Use yUIpy se ocean ‘TId GL 1A° 9's Sew trug Phil. Mag. S.5.Vol.19 . Pll. Fig. 5. ae ie ee SS I << . j S K ———— a 5 : Sb mm Fue 3) 2 Pig), 4 d a e ~----- m b L--—--------- ra Fig. 4. (bis). n h Ss Fig. 6. Mintern Bros. lith. Phil. Mag.5.5.Vol.19. PI. Ili. w. ls <1 te Sy intern Bres.lith. Pome avietaeneroe Volta ial IV 2 D P 7 NG R S iD - 4 j u Phil.Mag. S.5 Vol 19. Pl. IV . Ne | NN Es Se S WR SS S Ss S WR Mintern/ Bros. lith. Phil. Mas. $5. Val 19- Pl Hi S ears 1 Phil Mag. S 5. Vol 19. Pl. V. omie - JANUARY 1885... - No. 116. Published the First Day of every Month.—Price 2s. 6d. oO \ THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘Philosophical Magazine” * Micholson’s ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’ CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. MRA. F.G.S8, SIR WILLIAM THOMSON, Kyr. LL.D. F.RS. &c.° AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S. F.C.S. - FIFTH SERIES. N° 116.—JANUARY 1885, WITH ONE PLATE. Illustrative of Mr. A. M. Worrateron’s Papers on a Capillary Multiplier, and on the Theory of Pendent Drops. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Sold by Longmans, Green, and Co.; Kent and Co.; Simpkin, Marshall and Co.; and Whittaker and Co.;—and by A. and ©. Black, and T. and T. Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster and Co., Dublin:—Putnam, New York:—Veuve J. Boyveau, Paris :—and Asher and Co., Berlin. a Pee eit , Errata m Vol. XVIII. 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DESCRIPTIVE CATALOGUE OF THE SPECIMENS ILLUSTRATING SURGICAL PATHOLOGY IN THE MUSEUM OF UNIVERSITY COLLEGE, LONDON. Part I. By MARCUS BECK, MS., M.B., F.R.CS., Assistant-Surgeon to University College Hospital, an S. G. SHATTOCK, M.R.CS., . Curator of the Museum. TayLor and Francis, Red Lion Court, Fleet Street, E.C. [ADVERTISEMENTS continued on 3rd page of Cover. i) MAY 1885. No. 120. Published the First Day of every Month.—Price 2s. 6d. THE LONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson's ‘Annals of Philosophy.’ CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Knr. LL.D. F.RS. &e. AND WILLIAM FRANCIS, Puz.D. F.L.S. F.R.A.S. F.C.S. FIFTH SERIES. N° 120.—MAY 1885. 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Published the First Day of every Month. THE LONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE, | AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson's ‘Annals of Philosophy.’ ¥ CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Kyr. LL.D. F.RS. &e. AND WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S. ° FIFTH SERIES. N° 121.—JUNE 1885. ~<-_ WITH THREE PLATES. cae Llustrative of Prof. Ot1ver Lopex’s Papers on Thermoelectric Circuits, . and on the Paths of Electric Energy in Voltaic Circuits. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Sold by Longmans, Green and Co.; Kent and Co.; Simpkin, Marshall and Co. ; and Whittaker and Co.;—and by A. and C. Black, and T. and T. Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster and Co., Dublin :—Putnam, ‘| New York:—Veuve J. Boyveau, Paris :—and Asher and Co., Berlin, 4 Double Number. Price Five Shillings. 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THE SCIENTIFIC PAPERS OF THE LATE SIR CHARLES WHEATSTONE, D.C.L, F.RS., &e. Published by the Physical Society of London, TayLor and Francis, Red Lion Court, Fleet Street, E.C. Royal 8vo, price 2s. DESCRIPTIVE CATALOGUE OF THE SPECIMENS ILLUSTRATING SURGICAL PATHOLOGY IN THE MUSEUM OF UNIVERSITY i EGE, LONDON. Parr 1% @ <4 da. ¢ By MARCUS BECK, MS. MB. FES, Assistant-Surgeon to University College Hospital, and : §. G. SHATTOCK, M.R.CS., f Curator of the Museum. 'TayLor and FRANciIs, Red Lion Court, Fleet Street, E.C. [ADVERTISEMENTS continued on 3rd page of Cover. * ‘ ’ £5 ' : } ’ . : A a > ly — ’) = ‘: ~ = See - ES et : : - me has r = = : f ay , : . ri “ fi ce is if . , r a | mn | | [ ene 3h ye 4 ‘ pays Ps | Pees ee TP et we ai asi 7 oh we Arges PPT ” \ yi 4 tS ea # hee h pares BP DR post he { E Bi Ns Y en a ‘ F yard. 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