iy awa van Cow ae « X acy ea sak i +H) 42 AES ORS NaC eran ee * 4 ib! ie, oe Sha sc a on sit geaet ee ota: + aA) i "i ot a a tert rash 280 Rie Greliraty . - nik Na pcb os te COP ab Rea bia ME Friar ae ey Cente Yes ~ THE LONDON, EDINBURGH, aynp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY SIR ROBERT KANH, 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. Lres. Polit. lib.i. cap. 1. Not. VOL. XIV.—FIFTH SERIES. J ULY—DECEMBER 1882. TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, SOLD BY LONGMANS, GREEN, READER, AND DYER; KENT AND CO.; SIMPKIN, MARSHALL, AND CO.; AND WHITTAKER AND CO. ;—AND BY ADAM AND CHARLES BLACK, AND THOMAS CLARK, EDINBURGH ; SMITH AND SON, GLASGOW ;— HODGES, FOSTER, AND CO., DUBLIN ;—PUTNAM, NEW YORK ;—AND ASHER AND CO., BERLIN. “ Meditationis est perscrutari occulta; contemplationis est admirari perspicua..... Admiratio generat queestionem, questio 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. Pinelli ad Mazonium. CONTENTS OF VOL. XIV. (FIFTH SERIES). NUMBER LXXXV.—JULY 1882. Dr. E. J. Mills’s Researches on Melting-point ............ Mr. C. V. Boys on Measurement of Curvature and Refractive ererememenlelaels ete hey oe Cosa. ee bases « pelo miad Professors Ayrton and Perry’s Experiments on the Faure Ag SEGED COL ANICISSG Rie ae eae aR SFE Professors Ayrton and Perry on a Simplified Dispersion- MDC gi RAs c tN as dls Gs Be 8 4ichs g)~ HAG eS sew ee MM. Warburg and v. Babo on the Connexion between Vis- cosity and Density in Fluids, especially Gaseous Fluids Mr. F. D. Brown’s Notes on Thermometry. (Plate Il.) .... Notices respecting New Books :— Geological and Natural-History Survey of Canada, Di- Mecrons Heporb tor lO 9280 re, § asd. be, sodas Dr. Geikie’s Geological Sketches at Home and Abroad. . Proceedings of the Geological Society :— Prof. J. W. Judd on the Relations ofthe Hocene and Oligocene Strata in the Hampshire Basin ..... bial a Science and Metaphysic, by Wyndham R. Dunstan, Vice- President of the Aristotelian Society, Demonstrator of Che- mistry in the Laboratories of the Pharmaceutical Society . . On the Depression of the Zero-point in Mercurial Thermome- SpSnSPEDY aE MEMO ratbst a SMe sposonenle sisarted ete whee Soe On the Oscillations of the Plane of Polarization produced by the Discharge of a Battery: Simultaneity of the Electrical and Optical Phenomena, by D. Bichat and R. Blondlot NUMBER LXXXVI—AUGUST. M. A. F. Sundell on Absolute Systems of Physical Units.... Major Allan Cunningham on Moseley’s Theory of Steady Flow Mr. T. C. Mendenhall on the Influence of Time on the Change in the Resistance of the Carbon Disk of Edison’s Tasimeter 45 81 110 115 iv CONTENTS OF VOL. XIV.— FIFTH SERIES. Mr. W. J. Lewis’s Crystallographic Notes. (Plate IIL.)...... Prof. R. Clausius on the Dimensions of a Unit of Magnetism in the Electrostatic System of Measures .............. _ M. 4H. Brongersma on Double Refraction, produced by Elec- trical Influence,in Glass and Bisulphide of Carbon. (Plate IV. HS. OG=h.) oo. wees cee hte tne se ie ee Notices respecting New Books :— (i) Mathematical Papers by William Kingdon Clifford ; (11) Mathematical Fragments, being Facsimiles of his unfinished Papers relating to the Theory of Graphs, by the late W. K. Clifford ...........2)seeeen Mr. T. Muir’s Treatise on the Theory of Determinants, with graduated sets of Exercises for use in Colleges and Schools’ 224.) wa... 2c as | one ees Proceedings of the Geological Society :— Mr. H. J. Johnston-Lavis on the Comparative Specific Gravities of Molten and Solidified Vesuvian Lavas .. Mr. G. Attwood on the Geology of Costa Rica ........ Mr. 8. V. Wood on the Newer Pliocene Period in England Don M. F. de Castro on the Discovery of Triassic Fossils in the Sierra de Gador, Province of Almeria, Spain .. Prof. C. Lapworth on the Girvan Succession.—Part I. Stratigraphical 4... 060.600 V 6 +s noe Mr. E. Wilson on the Rhetics of Nottinghamshire .. Dr. F. Schmidt on the Silurian and Cambrian Strata of the Baltic Provinces of Russia..........0). sss ee Mr. T. F. Jamieson on the Cause of the Depression and Re-elevation of the Land during the Glacial Period . . On some Explosive Alloys of Zinc and the Platinum Metals, byH. Sainte-Claire Deville and H. Debray.............. On the Reaction-current of the Electric Arc, by M. Jamin, with the assistance of M. G. Maneuvrier ...............+.. On the Motion of a Spherical Atom in an Ideal Gas, by G.Litbeck oi. ts ee es 1 NUMBER LXXXVII.—SEPTEMBER. MM. Elster and Geitel on the Electricity of Flame. (Plate IV. ies -4) 2 ee ee Lord Rayleigh on the Equilibrium of Liquid Conducting Masses charged with Electricity ..-............5seseue Lord Rayleigh on an Instrument capable of Measuring the Intensity of Aerial Vibrations ......|. ...5).2. 52 aeeeee Dr. C. R. A. Wright on the Determination of Chemical Affinity in terms of Electromotive Force.—Part VI. ............ Mr. W. Baily on an Integrating Anemometer. (Plate V.) . Rey. O. Fisher on the Effect upon the Ocean-tides of a Liquid Substratum beneath the Harth’s Crust............ Page 119 124 127 135 140 141 141 142 146 147 . 149 150 151 “152 154 157 161 213 CONTENTS OF VOL. XIV.—FIFTH SERIES. Wi 1y Mr. J. J. Thomson on the Dimensions of a Magnetic Pole in the Electrostatic System of Units. .................... 225 Mr. F. J. Smith on a new Form of Magnetic Torsion-balance REMMI TPUHE VOICED © och tenn: sicfe-cie seis «Gs weed «6 2 a8 aorerd 227 Notices respecting New Books:— Dr. G. Lunge’s Treatise on the Distillation of Coal-Tar nee ATM OMIACALAQUOL = 8.4 sca 'ece: 3, or ohet asain 6-b o areres 228 Mr. F. E. Hulme’s Worked Examination Questions in iBiane Geometrical: Drawing 2 0 cee ee ee eee 230 On the Duration of the Perception of Light in Direct and In- airccimvsion, by Aug. Charpentier... 0.0.0.4. c02a ce 230 On an Air-Thermometer whose Indications are independent of the Barometric Pressure, by Albert A. Michelson ........ 233 On a Property of the Isentropic Curve for a Perfect Gas as drawn upon the Thermodynamic Surface of Pressure, Volume, and Temperature, by Francis HE. Nipher ........ 233 On the Influence of the Quantity of Gas dissolved in a Liquid upon its Surface-tension, by 8S. Wroblewski ............ 236 On the Structure and Movement of Glaciers, by M. F.-A. Forel. 238 NUMBER LXXXVIII.—OCTOBER. Mr. R. H. M. Bosanquet’s Notes on Practical Electricity .... 241 Prof. G. Wiedemann on the Methods employed for determin- SOLE Ce, OTT as ge re a Pc 258 Mr. L. Fletcher’s Crystallographic Notes ................ 276 Mr. E. Vansittart Neale on the Tails of Comets............ 292 Mr. Silas W. Holman on a Simple Method for Calibrating Ther- 22 PENGUINS) Sign eee CCRT DER Di: ee eae ee nee 294 On Boltzmann’s Theorem on the average Distribution of Energy in a System of Material Points ................ 299 Mr. W. Le Conte Stevens’s Notes on Physiological Optics .. 312 Notices respecting New Books :— Mr. Latimer Clarke’s Treatise on the Transit Instrument as applied to the Determination of Time .......... 319 Geology of Wisconsin. Survey of 1873-79. Vol. III... 319 Dr. J. H. W.Stuckenberg’s Life of Immanuel Kant.... 322 On the Conservation of Solar Energy, by Pliny Earle Chase, . [Lilie DEA se eyo re eae MNS Sn Oe oe EE OER 322 On the Appearances of the Electric Arc in the Vapour of Bisul- phide of Carbon, by M. Jamin, with the assistance of M. G. IIE ACHIMIIEL: , 1) (i .psis 5 Pa ee late a ach ee Ea 324 On the Electric Resistance of Glass at Low Temperatures, by Gis BOWSsereall, ©. occa.5/ 5 <5 oo Garr eile ee Metelg Ge ae Ee hore 325 On the Surface-tension of some Liquids in contact with Car- hontesAcid, by S-.W roblewski'.. .. salen dees 327 vi CONTENTS OF VOL. XIV.—FIFTH SERIES. NUMBER LXXXIX.—NOVEMBER. Page Lord Rayleigh’s Comparison of Methods for the Determination of Resistances in Absolute Measure .........-2++ee00> 329 Messrs. C. F. Cross and E. J. Bevan on the Correlation of the Chemistry of the Carbon Compounds a the Phenomena of Mite of. y.2 as 59 acs 22 v9ieie 9 Oot» wie 346 Dr. O. J. Lodge on the Dimensions of a "Ngee Pole in the Electrostatic System of Units ...........--eeee-seeees 357 Dr. Eugen Goldstein on the Electric Diacharag in Rarefied GARBER of oc es ne ss sian 001d a op = + eben 366 Mr. Ernest H. Cook on Carbon Dioxide as a Constituent of the Atmosphere... ... 504+ ee0s0-*> ng) nn 387 Mr. E. B. Sargant on the Dimensions of the Magneti¢ Pole in Hilectrostatic Measure -.. ....: «4+ it 32 40 40 50 “41 3 40 38 53 4] 39 47 45 50 48 46 51 40 27 4376 41 51 3l 42 2511 4] 51 26 42 58 dH 49 24 45 46 On 38 ae le | 51 2 “31 e303), US eee *32 Wears cette 111-34 | 111-45 | 111-46 | 111-41 111°43 Probable error ... 014 017 ‘016 012 014 Thermometer ... 3 2 3 3 3. « Dinitrophenol.—« dinitrophenol appears to have been first observed by Armstrong, who, however, did not obtain it in a state of purity ; the exacter definition of the substance is due to Hiibner and Schneider (Zeit. Chem. xiv. p. 524). In preparing it, I followed the method recommended by the last- named chemists, depending more especially on the insolubility of the baric derivative in boiling spirit of 90 per cent. When the baric derivative was dissolved in water and treated with aqueous hydric chloride, the hydric salt was precipitated: this was afterwards dissolved and crystallized. a dinitrophenol has an extremely pale yellow colour when crystallized from naphtha or spirit ; the powder has a deeper shade; and the solution imparts a dark-orange tint to a tissue on which it has been dried. A, B, C, D, E were distinct preparations. A and B had been crystallized thrice from naphtha and thrice from spirit ; C had been crystallized from water, aqueous potassic chloride, and twice from spirit; D had been made from a baric salt twice extracted with spirit, after which it was crystallized once from naphtha and four times from spirit*; E was formed by uniting the remainders of A, B, and C, extracting the barie salt thrice with alcohol, and crystallizing the resulting a dini- trophenol once from naphtha and once from spirit. * The hot alcoholic solution was poured off from a red, quite insoluble foréign substance. ae Dr. EH. J. Mills’s Researches on Melting-point. 23 a dinitrophenol melts sharply, the pasty stage being short. According to Hiibner and Schneider its melting-point is 63—64°. TABLE XX. A. A. B. B. C. D. K. Oo (2) Oo ie} (2) (e} fe} 61-89 | 61°79 | 61-85 |61°82 | 61-78 | 61:82 | 61-79 “80 ‘79 i nelle | “79 85 74 Wighiay Wes = eomreee 61:79 | 61-82 | 61-79 | 61:76 | 61-75 | 61-79 | 61:77 Probable error ...| °013} -010) -006; -009} -007) :009} -007 Thermometer ...| 4 2 2 4 2 2 4 4. B Dinitrophenol.—Z. The crude compound was pre- pared by Griiner’s method, from crystalline phenol. A con- siderable amount of its baric salt was crystallized repeatedly from a large volume of water, and the cooled and filtered mother-liquid precipitated with hydric chloride. Z. was the tenth precipitate; it was crystallized thrice from water. Zz was the eleventh precipitate ; it was crystallized once from water. Z,, was the twelfth precipitate; it was crystallized once from water. Preliminary determinations of melting-point were made with the nine preceding fractions ; but the numbers were not sufficiently satisfactory to warrant proceeding with purification. Y was made by Dr. Armstrong from trinitrophenol, by way of amido-dinitrophenol; it was crystallized thrice from water. T. For this also I am indebted to Dr. Armstrong: he had prepared it by acting with ordinary hydric nitrate on phenol. It was crystallized once from naphtha, once from alcohol, and four times from water. 4 24 Dr. E. J. Mills’s Researches on Melting-point. In determining the melting-points of Z,, Z;, and Y, the thermometers were protected by two glass cylinders ; in the other three cases the cylinders were not used. Crystallization, powdering, desiccation, and filling of eapil- lary tubes had to be effected either in total darkness or ina deep shade. £ dinitrophenol is very nearly white; but by two hours’ exposure to a somewhat gloomy atmosphere it becomes deep turmeric yellow. 8 dinitrophenol melts with moderate sharpness. TABLE XXI. Diy. Ze. Y. T, Ze. Ze, fe} ° ° ° fe) (9) 11660 | 11163 | 111-46 | 111-57 | 111-66 | 1131-65 * . . 4 60 63 “57 57 6 ‘DD “46 49 63 49 61 “65 52 58 68 “60 61 58 55 63 *82 57 64 DS 63 60 60 “60 80 63 46 58 “49 “57 61 60 43 68 457f 52 66 58 52 52 ‘60 "BA 53 53 63 55 57 D4 66 65 1 ey es a 111:54 | 111°59 | 111°60 | 111°56 | 111-64 | 111-59 Probable error ... 015 012 “020 ‘007 014 ‘010 Thermometer ... 2 2 2 2 2 3 5. Trinitrophenol—Sample A was a commercial specimen. It was crystallized twice from water, once from alcohol, and again from water. Z was prepared from dinitrophenol made by Griiner’s pro- cess (v. supra); the material employed was very pure, having been precipitated from a 12th (Z,) cold aqueous extract of the crude basic salt. This was evaporated to dryness on the water-bath with a very large excess of hydric nitrate, and crys- tallized once from naphtha, once from ethylic alcohol, and twice from water. O was made from phenol, containing minute amounts of the two modifications of dinitruphenol, by evaporation, as with Z. It was crystallized thrice from water, once from alcohol, and a first (O,), second (O,), and third (O;) time from water. M was similarly prepared from sodic « nitrophenate (B under « nitrophenol), and was crystallized thrice from water. F was derived from sodic 8 nitrophenate (the analysis is J ‘Ad ‘t Mean Dr. E. J. Mills’s Researches on Melting-point. 25 given under 8 mononitrophenol); it was crystallized once from water, once from alcvhol, and again from water. N was prepared from some e (Hiibner’s) dinitrophenol, for which I am indebted to Prof. Armstrong. This was purified by Hiibner’s two processes, and can have contained at most mere traces of its isomer. The trinitro-compound was crys- tallized thrice from water. Trinitrophenol is a nearly white substance when in crystals; if very finely divided by any means, it appears a pale yellow. The powdered crystals, if exposed for two hours to indirect light on a dull morning, acquire a deep mustard-yellow colour. The crystals of the substance termed N were almost perfectly white. The melting-point of trinitrophenol is, on the whole, not difficult to observe. TABLE XXII. A. Zee Oa 0. (ah Ole Mao BY gee 120-97 {121-00 09 ‘11 06 16 {120-98 hace — | $< ———— | —_ _ Thermometer... 2 2 2 2 2 2 2 2 F. Naphthalin Derivatives. Naphthalin.—Commercial pure naphthalin, which had been twice sublimed, was digested for a few hours with strong oil of vitriol in the water-bath. After washing with water, it was distilled from caustic soda in a current of steam. The first portion of the distillate is termed A, the second B. These portions were crystallized twice from naphtha and thrice (A; &c.) from alcoho]. Before naphthalin melts it exhibits a de- cided pasty stage; yet the melting-point is sufficiently sharp. The powdered substance is highly electric. ° fo) o fe} fe) ° fe) te} 121-11 |120-95 {121-04 [121-14 [121-03 120-99 |121-20 |121-20 [121-09 06 {120-92 O07 {121-11 |120-98 |121-:13 {121-17 |120°98 |120-89 O08 {121-03 “Ol {120-97 |120:98 16 {120-98 |121-09 |121-09 ‘11 {120-95 15 |121-714 {121-08 18 {121-14 "12 |120°94 703 |121-06 18 |120:97 00 “10 09 12 121-11 706 {121-00 12 {121-06 08 16 “O1 15 |121-11 03. {120-98 23 “14 06 “19 “12 12 /121-14 06 {121-20 09 09 “14 07 04 12 120-94 24 (121-00 12 ‘09 ‘ll 19 14 15 {120-99 sce eee 121-07 {121-01 |121-11 |121-08 |121-05 |121-:13 |121-09 |121:12 |121-04 Probable error. 014 016 7013 013 ‘O11 “013 016 “012 9 018 3 26 Dr. E. J. Mills’s Researches on Melting-point. TaBLeE XXIII. °o ° ° oO 80-06 | 80:03 | 80-01 | 80:03 |80-05 80:05 |80-06 7998| -06| -06| 08} 05| 08 | -14 80-01! -08| 091 -00| -05| 05 | -09 7995 | -00| 06] -08! -05| 02 | 09 8003 | 00] -09| -08| 05) 08 | -09 30061! -00.| -06| -08| -07| -05.| -09 30-09 | -08| 12) -08| -07| 08 | -03 80-06 | -06| -12/ -11| -05| -08 | -09 80-03} -11| -06| -11| -07| -05 | -09 7998 | -03| -09| -06| -07| -05 | -09 30-06 | -11| -06| o6| 07| 10] tl 8003! vo! -o1/ 08! -07| -05 | 03 Mente 80:03 | 80:05 | 80:07 | 80:07 |80-06 30-06 | 80-08 Probable error ...| ‘008, 008} -007) 006] 002, 004} -006 Thermometer ..| 2 | 2 | 2/2 | 2 | @ | 2 | Nitronaphthalin.—A was a sample which had been in my collection for some years, and the details of its preparation are unknown. It was distilled in steam, and crystallized twice from naphtha and thrice &. (A; &.) from alcohol. B was a similar sample from the same source. It was purified and fractionated exactly in the same way as A. Nitronaphthalin becomes sensibly yellowed by continued exposure to light. It melts with considerable sharpness. TABLE XXIV. 56-17 |5616 156-17 | 56-21 56-15 | 56-24 |56-17 | 5610 +15 | 24) gt eee VEG STI sce a cscs: ses 56°19 | 56°18 | 56:18 | 56:18 | 56-16 56:19 | 56°14 | 56°11 Probable error ...} 004) -006} -007| -006 009) O07) ‘006 -010 Thermometer ...) 2 2 2 2 2 2 2D ees Dr. H. J. Mills’s Researches on Melting-point. 27 TasLe XXV. Summary of Results. k After : Substance, | Weight | Preble | poggendon| set a 5 correction. ; Toluidine .............+- 49-765 004 42-700 42-890 Nitrophenol (@)......... 44-270 003 44-205 44-392 Witrotoluol <.....:..... 51:305 005 51:239 | 51-407 Dichlorobenzol ......... 52-723 ‘002 52°657 52°821 Nitronaphthalin ...... 56°175 002 56°110 56°261 Dinitrophenol (¢)...... 61-778 003 61-714 61-843 Monobromaniline ...... 61-806 “003 61:°742 61:871 Dinitrotoluol (a) ...... 69-211 “004 69-154 69-252 _ Chie (eres 69:571 “O04 69-514 69-610 Monochloraniline ...... 69-667 003 69-610 69°706 Dinitrobromobenzol...| 70-598 “004 70°542 70°634 Trichloraniline......... 77-052 ‘001 77-004 77-068 Dibromaniline ......... 78821 004 78776 78°833 Trinitrotoluol ......... 78-841 004 78°796 78853 Naphthalin ..:...... .. 80-061 002 80-018 80:070 Trinitrotoluol (M) ...| 80°524 003 80-481 80:532 Nitrodibromobenzol...| 83°:490 “002 83-452 83-492 Dibromobenzol ......... 87:037 “002 87:007 87:035 Dinitrobenzol ......... 89-718 ‘003 89-693 89:712 Nitrophenol ........... 111-413 006 111-448 111-455 Dinitrophenol ......... 111-579 “004 111-614 111-621 Tribromaniline......... 116-247 ‘005 116-298 116°319 TrinitrophenoL......... 121-082 005 121-151 121-194 Discussion. The determinations of melting-point which have been recorded in the preceding tables, and the results of which are summarized in Table XXV., show a very small probable error in connexion with their weighted means. The probable error of a weighted mean has ranged from 0°-001 to 0°:006, its average value being less than 0°:004. So far, then, as regards the actual process of ascertaining melting-point, con- siderable accuracy has doubtless been attained. The preliminary operation of calibrating the thermometers was so conducted as not to have introduced material error, as indeed is obvious from a comparison of the results obtained with different thermometers on melting the same substance*. Regnault was of opinion that the height of the barometer cannot be ascertained with a less error than about 0-1 millim. Such an error would correspond to about 0°:0037 on 100°; and the error would be still less on the mean, as in the present case, of several readings. The small errors in the determina- tion of the exposure-corrections could not sensibly affect the * See, for instance, Table VIL. 28 Dr. E. J. Mills’s Researches on Melting-point. final results. It is to comparison with the air-thermometer that we have to look for any important source of error. All observers who have made an extended range of such compari- sons have found noteworthy errors, though they have in no case stated probable error. The probable error of the result of my own comparisons of thermometer 2 with the air-ther- mometer is 0°-085 for a single set of comparisons, or 0°-085 —/33=0° 015 for the results of the thirty-three sets. This number is the measure of probable error of the equation em- ployed in the final reductions. Compounding, then, the mean probable error of the melting-point (-004) with that of the comparison (‘015) with the air-thermometer, we may consider the melting-points in Table XXYV. ascertained, in terms of the air-thermometer, with a probable error of o/ (004)? + (015)? =0°015. The relation of the chemical symbol to the physical proper- ties of a substance is a matter of such great interest that I have sought for it in melting-point, although other investigators of the general subject, working with less definite data, have not arrived at very encouraging results. It is very easy to show that, in some cases, there is a very simple connexion between the formula and the melting-point of a substance in the centigrade scale. Thus, dichlorobenzol, bromaniline, and trinitrotoluol forma group in which melting- point =¢x numerical value of formula. Substance. Formula. Melting-point. p- Dichlorobenzol . C,H,Cl, =147 52°821 *35933 Bromaniline . . C,H, BrN =172 61°742 “39971 Trinitrotoluol . C,H; N;0O,=227 80°532 35477 In the first of these two instances the values of ¢ are almost exactly the same ; in the last, however, the limits of probable error are exceeded, though a close approximation is very evident. The following comparison furnishes another practical iden- tity :-— Melting-point. Melting-point. Trinitrotoluol ._78°853 — Dinitrotoluol . 69-252=9-601 Trinitrophenol. 121-194 — Dinitrophenol. 111:621=9-573 In the next instance there is an approximation:— Melting-point. Melting-point. Dinitrotoluol . 69:252 — Nitrotoluol . 51-407=17°845 Dinitrophenol. 61°843 — Nitrophenol, 44:392=17-451 Dr. E. J. Mills’s Researches on Melting-point. 29 Such illustrations may be of service in enabling us to detect, with more or less probability, the parallelism of chemical series, and to enable us to decide whether a function—nitra- tion, for example—has or has not the same value in different parts of a series. Other groups in which a similar but less intimate relation prevails, might be adduced from the list ; and a glance at Table XXV. will show that, on the whole, melting-point and formula grow together. It may not im- probably prove to be the case that, when the whole subject of melting-point has been successfully investigated, this simple relation is the limiting condition of the real law. The data, however, hitherto adduced are far from adequate to a discus- sion of numerical relations among melting-points: for such an object it would be a fruitless task to examine them further. Some negative results of this investigation are worthy of attention. Thus e and 6 nitrophenol have the same additive formula, and yet differ by 67°-063 in their melting-point. It is clear then, as already well known, that melting-point may, in cases of isomerism, be related to something else than for- mula. The melting-point of naphthalin is actually lowered in the first stage of nitration. Considerations such as these may perhaps serve as suggestions for future work. An accurate method of determining melting-point places it within our power to detect far more delicate shades of isomeric differences than have hitherto been regarded as possible. Thus strong presumptive evidence has been adduced (p. 14) that dinitrotoluol, when prepared directly from toluol or from liquid (meta-) nitrotoluol, or from solid (para-) nitrotoluol by gentle nitration, melts at 69°-252; but that when paranitro- toluol is energeticaly nitrated, the product melts at 69°610. There are consequently two modifications of dinitrotoluol ob- tainable very directly from toluol—the melting-point of these substances differing by 0°-358, a quantity far beyond the range of error of the method. In like manner, it can be shown that two parallel modifications of trinitrotoluol exist— one of which melts at 78°-853, the other at 80°-532 *. [| For a complete account of the thermometers referred to in this memoir the reader is referred to the Transactions of thé Royal Society of Edinburgh, 1881, p. 567; for the method of determining melting-point, to the Proceedings of the Royal Society, vol. xxxiii. p. 203.] * Compare Phil. Mag. 1875, 1. p. 17. [ 30 ] II. Measurement of Curvature and Refractive Index. By C. Vernon Boys, A.R.S.IL, Demonstrator of Physics at the Normal School of Science, South Kensington*. [Plate I.] F the methods best known for measuring the curvature of surfaces, that depending on the spherometer is both accurate and convenient in the case of surfaces of sufficient diameter and where the curvature is not too small. The reflection-test, depending on the observation with a telescope of two images projected ona scale, is certainly not convenient, nor is it capable of giving very accurate results. While endeavouring to find some more satisfactory way of exa- mining the curvature of the surfaces of lenses that would be both accurate and simple, I discovered the method which I am about to describe. Though, from its great simplicity, I can hardly expect it to be new to every one, yet I have never heard of its being employed, nor do those to whom I have shown it remember to have seen it before. Therefore, even if it should be shown that this method is not new, it is certainly so little known that I think it worthy of attention. The centre-of-curvature test known as Foucault’s test, which is used to examine the figure of the mirrors of re- flecting telescopes, gives, perhaps, the most delicate means of examining form that exists. By its means the expansion by heat of a portion of the surface produced by touching it with the finger is rendered evident, as an apparent mountain standing out of the glass, which takes from five to fifteen minutes to disappear ; and the warm air leaving a hand held between the centre of curvature and the surface has the appearance of flames of fire. In each of these cases no other system of observation could show in so striking and conspi- cuous a manner effects depending on so slight a cause. The examination at the centre of curvature is carried out in this way:—The mirror is placed in a convenient support so that its surface is vertical; and in front of it is placed a lamp with an opaque chimney, through which some pin-holes have been made. If one of these holes is near the centre of cur- vature, the light leaving it and reflected by the surface is brought to a focus on the other side of the centre. This focus is then found; and the lamp is moved till the focus is as near the chimney as will allow of its observation. A piece of thin sheet metal, with a straight edge, is then placed so that it may be moved to or from the mirror or laterally. Now, if the edge of this is sufficiently on one side to let the light * Communicated by the Author. Measurement of Curvature and Refractive Index. 31 pass the focus, an eye immediately behind the focus will see the mirror filled with light; but if it is gradually moved across while the eye still watches the mirror, the illumination of the latter will appear to die away in the same direction as, or in the opposite direction to, the movement of the edge, or uniformly, according as the edge is between the mirror and the focus, or between the eye and the focus, or at the focus. By this means, and by this means only, can the different radii of curvature of the successive zones of a parabolic mirror whose radius of curvature is twenty times its diameter be accurately measured. The close contact between the para- bola and the circle is due to the fact that it is one of the third order. I think it worth mentioning that the formula given by Dr. Draper in the ‘ Smithsonian Contributions to Know- ledge,’ vol. xiv. (1865), for testing the true parabolic form, gives only half the deviation from the sphere, as was pointed out by a correspondent of the ‘ English Mechanic’ who signs himself “ Orderic Vital,’ and was confirmed by Mr. H. H. Liveing and myself*. I have gone thus fully into the Fou- cault test, as my method involves the same general principle, viz. making the rays return along the path whence they came. Before considering the general case applicable to any kind of lens, I think it best first to show the simplicity of the method in a particular and common case—that of a thin equi- convex lens. Tix an ordinary spectacle-lens in a clip, with its principal plane vertical ; in front of it place a card with a small hole in it; and illuminate the hole with a candle-flame. It will be found that, when the lens is at a certain distance from the card, there is an inverted image of the hole formed on the card. When this is the case, the light leaving the hole and meeting the front surface of the lens is refracted and meets the back surface normally: most of the light passes through; but a small portion is reflected back along the path whence it came, and is sufficient to produce an image easily visible in the day. This distance of the card from the lens, which is the apparent radius of curvature of the back surface seen through the front surface, is throughout this paper called 7 The true focal length F of the same lens may be observed in the usual way; but it is more conveniently found by fixing a plane sur- face of glass behind the lens, when it will be found that another image may be produced when the lens is about twice as far from the card as it was before. Since an image is pro- duced, the light must have returned along the path whence it came, and must therefore have struck the plane surface nor- * English Mechanic, vol. xxxi. pp. 89, 184, 207. 32 Mr. C. V. Boys on Measurement of mally—that is, have left the lens and returned to it as a parallel beam; therefore the card is at the principal focus. For a plane glass surface a piece of plate glass blacked at the back, or the surface of a prism may be used. The observations of the distances F and / can be easily and accurately made ; then the radius of curvature may be found from the formula as I shall presently show. Before doing so, however, I think if well to describe the most accurate method of observing the distances F and f. The card with the pin-hole is convenient; but it is difficult to find the place with great accuracy where the focus is most sharply defined, and to measure the distance when found. All diffi- culty is completely avoided by the following plan:—Take a piece of thin sheet metal, of the size and shape shown in Pl. I. fig. 1, and fix in front of it, in the position shown by the dotted line, a small reflecting-prism, so that, when a small bright flame is placed on one side of the prism, a beam of light leaves the slit in the plate. Replace the card by this plate and prism, and move the lens till the aerial image of the slit is formed in the corner, close by the edge of the prism. To examine the position of the image with greater precision, an ordinary positive eyepiece will be found convenient. When the image and the slit are equally distant from the lens, there will be no relative movement on moving the eye ; if there is relative movement, the distance between the lens and the plate must be increased or diminished according as the plate or the image appears to move with the eye. When the distance has been properly adjusted, it is easily measured by resting a scale on the continuation of the lower edge of the slit, and moving it till it touches the surface of the lens. The position of the edge of the prism or of the slit may then be read with great accuracy; and it will be found that, on repeating the obser- vations several times, a discrepancy more than a tenth of a millimetre between any of the measures need not occur. Instead of observing the position with an eyepiece, the Foucault plan may be adopted. Place the eye immediately behind the edge of the prism, so that all the light forming the image enters the eye. Move the prism laterally towards the image, which of course moves to meet it, and observe whether the light which fills the lens dies away uniformly, or whether it seems to retreat from one edge of the lens. If the retreat is in the same direction as the movement of the prism-plate, the distance is too small; if in the opposite direction, too Curvature and Refractive Index. 33 great. Hither of these systems will give accurate results ; I prefer the first, as tiring the eye less and being, especially with small lenses, the more accurate. A conyenient support for the lens is made by boring a hole, with a less diameter than the lens, in a piece of thin parallel- sided wood. The lens may be slipped under two clips, so as to rest against the edge of the hole on one side of the wood. On the other side a piece of plate glass, blacked at the back, is cemented or held in a similar way by clips. If this piece of wood is fixed vertically on a horizontal slide, it may be moved away from the prism-plate, and the distances 7 and F determined in a few minutes. Fig. 2 is a horizontal section of the arrangement when the principal focus F is being deter- mined. The dotted line shows the position for 7. By If instead of a lens a single surface only is to be measured, there is of course no difficulty in the case of a concave sur- face ; but a convex surface may have its curvature determined in the following way:—Arrange the prism-plate and flame as before. Ata distance in front of the prism-plate more than its focal length fix a converging iens, preferably achromatic. Observe the position of the aerial image on the other side of the lens, and make it coincident with the edge of a plate of metal, m. The positions must be so adjusted that the distance of m from the lens is greater than the radius of curvature of the given surface. Now place this surface between the metal plate and the lens, and move it till an image is formed accurately by the side of the prism. Then the light impinging on the convex surface has been reflected back along the path whence it came, and has therefore struck that surface normally; therefore the place m, where those rays would have met had they not been intercepted, is the centre of curvature of the convex surface. Its radius of curvature can therefore be measured by suitably- formed callipers. Fig. 3 is a horizontal section of the arrangement. Kf I have stated above that R=p5 _in the case of a thin equi- convex lens. This must now be proved, and the more general case of any kind of lens treated next. First, consider that the jens is so thin that any normal to either surface cuts each at points appreciably equally distant from the axis. Since the image which is produced is partly formed of rays which are near the axis, these rays meet the axis at angles so small that the tangent, the sine, and the arc are convertible terms. If the lens is large and not of very long focus, this will not be true of rays from near the edge of the lens; but as these rays are not necessary for the image, the central ones alone may be Phil. Mag. 8. 5. Vol. 14. No. 85. July 1882. D 34 Mr. C. V. Boys on Measurement of employed, and by them the curvature of the whole surface, if spherical, determined. On the front surface take any point p, and through it draw a radius mR of the back surface. Join p with f, the apparent centre of curvature of the back as seen through the front sur- face. Draw also through p a radius ab of the front surface and a line de parallel to the axis. Then the angles mpd, dpb, ape are equal to one another. Call these angles @. The angle apf=x angle mpb=p20; therefore the angle cpf= u20—0. But the angle epR=8@; R R+ Fai ex or pane By the property of equiconvex lenses, poet L; RR un sg oF = OF and R = F-f 5 or, in a thin equiconvex lens, the radius is equal to the product divided by the difference of the principal focal length and the apparent radius of the back as seen through the front surface. It might be expected that, as this formula has been deduced from a specially simple case, a more complicated one would be necessary if the two sides of the lens were not equally curved, or if one surface were plane or concave. But such is not the case ; the same formula applies in every possible case though, as will be shown, experimental difficulty occurs in the case of a diverging meniscus. The proof of the formula in the case of a thin lens which is not equiconvex is similar to that already given. Make the same construction as before, and let Ry, Ry be the centres of the surfaces 1 and 2, and 7, the apparent centre of 1 seen through 2.. Also let R.=nR,. Call each of the angles mpd cpR,, 9; then the angles dpR, and ape will each equal nO. As the angle apj;=y x angle mpR,= (1 +7)0, .*. angle epfj= w(1+n)@—né. But angle cpR,\=@; sealed eee Ry i Substitute R. for n, and it will be found that 2 _ Ri( A+R) ne OR ES 2 Curvature and Refractive Index. 35 A similar proof will show that Ro(fot+ Ri) SS eS i Fo( Ry + Re) @) By the property of lenses, <2 el aay des Wa Leona erat a CS) where F is the principal focal length. By combining (1) and (38), 1 hoe Solaagl ald BA Bo , ol se eas ne (4) By combining (2) and (3), tad Pee ee ih Ey 5 Rep Pav ae iO) By combining (1) and (2), 1 sf sted Siaeea | sp 6 R, R, Ji Je Tt is not a little surprising that, whatever the refractive index of the material of the glass, or the curvature of the front surface, the curvature of the back surface can always be ob- tained ‘from an expression in which both apparently are omitted. They are both of course involved in each observa- tion, F and /, which accounts for the possibility of their being eliminated. Tt is interesting to follow the changes which occur between the two extreme limits of form—a double convex and a double concave lens. Take a double conyex lens, and suppose one of the surfaces to be gradually pushed in; when it has become plane we have the first particular case—a plano-convex lens. Call the flat surface 1 and the convex surface 2 ; then, by (4), gran “. Ai=F, or the apparent centre of curvature of the flat sur- face seen through the round surface is at the principal focus. By (5), _ since F= — ; «. R,=y/fo, or the apparent radius of 2 is less than the true radius in the ratio of yw to 1. If the pushing-in process is continued, the surface 1 will become concave. Four observations can then be made—F, Ji; fz, and R, ; therefore R, may be found by either of the D2 36 Mr. C. V. Boys on Measurement of equations (5) or (6). As the surface 1 becomes more con- cave, its apparent centre on the other side of the lens will retreat to an infinite distance ; and then the concave side will appear flat when viewed through the convex surface. This is the case when R,= —F, as may be shown by making 7, = in (4), or as is obvious from a diagram. When R, becomes less than this, 7; becomes an imaginary point on the other side of the lens, such that, if rays were sent so as to converge upon it, they would return as though they had come from it. _ Its position could be determined experimentally by the method given for a convex surface on p. 33; but as the true radius can be determined directly, there is no necessity to find this imaginary apparent radius. Let the concavity of surface 1 increase ; the next particular case is that of a watch-glass, where R,=—R,. Then F be- comes infinite, and the two points 7, and R, become coinci- dent. When the surface 1 becomes still more concave, F becomes negative and virtual, and R, and /, pass one another. The experimental determination now becomes more difficult; for neither can F or f, be observed directly; but still the equations (5) and (6) hold. They may each be found by the method for a convex surface, which is less convenient than the direct method. If the concavity of the surface 1 continues to increase, another limit will be reached, at which /, becomes infinite. This is obviously the case when R,=—F; that is, when the focal length has been so shortened by the increasing concavity as to be equal to the radius of the convex surface. When this is the case, the surface 1 seen through 2 appears plane. When the concavity passes this limit, 7, becomes negative and imaginary, and the experimental difficulty is still further increased, for R,; only can be directly observed ; but still the equations (4), (5), and (6) are true. No further increase in the concavity of 1 will produce any new conditions. Now, the curvature of 1 remaining constant, let 2 become flatter ; when it has become plane, there is no occasion to observe F’, f,, or f, to determine the form of the surfaces. When 2 becomes concave also, the curvature of each surface can be directly measured; and all difficulty is removed. Every possible case has now been considered ; and though the equations are always true, experimental difficulty only occurs in the two classes of diverging meniscus. If a parallel beam of light falls on the lens, it will be refracted at the front surface, partly reflected from the back, and again refracted at the back surface, and be brought to a focus at a distance from the lens equal to half the apparent radius. Curvature and Refractive Index. 37 As the light, in its passage to and from the apparent centre ji, is twice refracted by 2 and once reflected by 1, it would seem at first sight that the value of 7, might be obtained by combining in the usual way the expression for twice the focal length of an equiconyvex lens with surfaces having the same curyature as 2 and the radius of 1 ; thus gee . 1 Pia a: Bey But this operation, depending on a false assumption, leads to an erroneous result. It makes gi a , instead of R R p—1R, +R, 1? ___ The error arises in this way:—When a double p—1R, +R, convex lens is employed, either to bring or to hurry light to a focus, the bending-powers of the two surfaces depend on the angles they make with the ray in the lens. Now, if one of these angles is great, the other must be small; so that, as a combination, they have the same focus-shortening power, how- ever the light falls on them. But when a ray passing from and returning to the apparent centre 7 strikes the front sur- face, that surface makes an angle with the ray in the lens which is greater than the mean in the ordinary way; there- fore the surface produces a greater diverting effect; and hence the distance 7 is less than it would be if the supposition made were correct. All that has been shown at present is only true when the thickness of the lens is inappreciable. When this is not the case, rays, whether from the principal focus F or from an apparent centre 7, will not cut the two surfaces at points equidistant from the axis. First, consider the case of an equiconyex lens. Let fig. 5 represent a portion of a thick equiconvex lens. As before, since the central rays are sufficient to give an image, arcs, sines, and tangents may be considered identical, On one surface take any point p. Through it draw a radius pR, and the line pbe parallel to the axis. Nowa ray of light parallel to the axis, meeting the surface in the point p with an angle of incidence equal to @, will be refracted so that the angle dpe is equal to os therefore the angle bpd= pas Therefore the line pd continued will ~ meet the axis in a point a such that R ja ee Me ac 1) But this ray is diverted at the point d, and bent down so as to 38 Mr. 0. V. Boys on Measurement of meet the axis at the principal focus F. It is required to find the length dF, or, shortly, F—that is, the distance of the principle focus from the surface.- Since the line pa has cut the front surface at a point d nearer the axis than p, the in- clination of the normal, bs, at d will be less than 6, and will equal m@ if a—t mee Tee ie (2) t being the thickness of the lens. Now the angle pds = the angle dbp +the angle bpd =A(m +=") ; therefore the angle bdF = w0( m+ = *), and the angle gd B= pO m+ "= *) — m= 61 mp—1). «eee Since the lines dF and da leave the same point d with different inclinations, they will meet the axis at distances which are inversely as these angles. Therefore T < ae =pl+m; be therefore pa—t (AE 2) Tw itm) > eR by (1) and (2). This is the distance of the principal focus from the surface of the lens. The distance ef of the apparent centre from the surface may be found in a similar way. The normal at e makes an angle nO less than 0, such that R—t = F By . . . ° . . . . (5) The angle pet=(n+1)6; the angle cef=p(n+1)0; and the angle kef=@[u(n+1)—n]. Therefore of 1 ; RR-t ae ia =>, andi. Boe w(n+1)—n’ gna (u—1)(R—t)+uR (6) This is the distance of the apparent centre from the surface. By (6), pa R+f(R—0 J(2R—-t) * Substitute this value of w in (4); on simplifying, it will be — ee — Curvature and Refractive Index. 39 found that zo ope g ee EP Bene. R fo t*)=F > Eg anety, hatte iC2) from which R may be found if F, 7, and ¢ are given. If ¢ is made equal to 0, equation (7) gives Rape, or —/. The first result is the same as that already found for a thin lens ; while the value —/ seems to have no physical meaning. If the thick lens is not equiconvex, there are five observa- tions possible—the distances of the two apparent centres from the surfaces, the distances of the two principle foci from the surfaces, and the thickness ; but there are only three things to be determined—the two real radii and the refractive index: therefore the equations for R,, R,, and ~ must be capable of solution. The following are the expressions which may be found by a similar treatment of fig. 5 to that already employed in the case of the equiconvex lens, if it be remembered that all the angles made by surface 1 are Re times those made by surface 2 at the same distance from the axis. They are ie Bip _ ae alge gaRnoese 1 7u( Ry + R,—2) +0 F(R, + Rt) +0? R,-t R,—t at R,—7)—(B,—2y 7? The first two of these equations give PF, e—-RiG@—l), FL p—Rt(u¢—1)’ and the second two give Pe R,+fAi Ri-t Ri +fe Rowe Ay _ R, —6) 2( Ry ~~ R,—t) By these » may be eliminated. The solution for R, and R, I haye not obtained ; but Ido not think there is any difficulty. The following application to the case of liquids of the prin- ciple of making the rays return along the path whence they came, forms a neat though impracticable method of deter- mining their refractive index when greater than V 2 :—Re- place the cross-wires of a telescope by a prism-plate, as already described, but in which the slit is longer and adjustable. Fix opposite the object-glass a piece of parallel-sided plate-glass, with its plane at right angles to the optical axis. The cor- 1u(B, + By—)— (at) and p= 40 On Measurement of Curvature and Refractive Index. rectness of this adjustment may obviously be determined at the eyepiece. Let the glass plate form the bottom of a trough in which the liquid may be placed, and let there be under this a dish containing mercury. Now, there is a certain inclination of the telescope at which the beam from the illuminated slit, rendered parallel by the object-glass, is refracted at the free surface of the liquid, and again at the surfaces of the glass plate, so as to leave the latter vertically; then, striking the mercury, it returns along the path whence it came, and may be viewed by the eyepiece. Under these conditions the beam of light on either side of the prism is at right angles to the opposite side; therefore they make equal angles with the adjacent sides, and the prism is at minimum deviation. Calling the inclination of the telescope 0, we have sinOd=p i he ; therefore w= V2(1+cos@). The telescope may be first in- clined on one side and then on the other, and half the angle moved over taken as 6. I have found it utterly impossible to get the sodium-line to keep still for a moment, or to be even fairly defined, as every movement in the neighbourhood pro- duces a tremor on the surface of the liquids, which, in the Science Schools at Kensington at any rate, is so continuous as to make it impossible to observe with accuracy. I should have said that the top of the prism must be covered in with a glass plate, to prevent the evaporation and consequent super- ficial cooling of the liquid forming the prism, which causes strize in the liquid, spoiling definition even more than the con- tinuous tremor. Helmholtz and others have shown that, during accommoda- tion of the eye for near objects, the cornea does not change in curvature, the front surface of the lens becomes more curved and advances, and the back surface does not appreciably change. The proof given is that the images of a light pro- duced by reflection from ihe cornea and from the back surface of the lens do not change, while that produced by the front surface of the lens advances and becomes smaller. Now it would appear at first sight that these observations prove a flattening of the back surface of the lens during accommodation ; for if it did not change in curvature, the rays of light passing twice through the more curved front surface would sooner come to a focus; but since they do not apparently sooner come to a focus, it would seem that a flattening of the back surface must have occurred to counteract the shortening influence of the more curved front surface. In the case of ordinary lenses this would be so; but it so happens that in the crystalline lens the focus by reflection is formed Experiments on the Faure Accumulator. 41 within it, and so the more curved front surface magnifies the smaller image, which therefore appears unchanged. While on the subject of reflection in lenses, I think it worth while to mention that convex lenses silvered at the back make excellent and easily constructed concave mirrors. Since both surfaces conduce to bring light to a focus, flatter curves may be used than are necessary for a plain concave reflector of the same focal length; also, since the two surfaces are not parallel, false images are not produced ; so that the advantage of glass silyered at the back remains, without the usual disadvantage. A spectacle-lens of about five inches focal length, silvered at the back and mounted, forms an eye-glass (I mean a glass for examining the eye) which every one who works in metal should possess. I have found by its means specks of metal, thrown from the lathe, which were utterly invisible by other means, but which were nevertheless exceedingly painful. Ill. ELeperiments on the Faure Accumulator. By Professors W. H. Ayrton and JoHN PERRY*. ANS made, at the request of the Faure Accumulator Company, a series of experiments on some of their cells, we have thought that a short account of some of the results obtained may not be uninteresting to the members of the Physical Society. The object of the experiments was to ascertain, first, the efficiency of a cell—that is, the ratio of the energy given out by it to the energy put into it; secondly, the storing-power of a cell; and, lastly, whether or not there was a deterioration in its working-powers. To measure the energy put into any electric circuit, we have merely, of course, to take time- readings of the current flowing through the circuit, as well as the difference of potentials between its two extremities. The current in ampéres multiplied by the electromotive force in volts and by 44°25, gives the number of foot-pounds per minute that is being put into that part of the circuit as elec- tric energy. For measuring the current we have used through- out our ammeters (short for ampeére-meters), and for measuring electromotive force our voltmeters, the latter being employed of course in a shunt circuit. Of the total electric energy put into the circuit, and which is measured, in foot-pounds per minute, by 44:25 AV, a por- tion will be employed simply in heating the circuit, and the * Communicated by the Physical Society, having been read at the Meeting on February 25, 1882, 42 Professors Ayrton and Perry’s Experiments remainder may be utilized in producing useful work. For example, ifa time-curve be drawn for 44:25 AV when charging a Faure accumulator, the area of the curve will measure the total energy put into the accumulator in foot-pounds ; but of this some portion has been wasted in heating the cell, due to the charging having been more rapid than was absolutely necessary. It was, of course, of considerable importance in our experiments to ascertain what portion of the energy put into the cell was really thus wasted; and to measure this the following experiments were made. Occasionally the main current was stopped, the shunt cur- rent through the voltmeter being left completed. The reading now on the voltmeter gives the difference of potentials pro- duced by the cell itself, whereas the previous reading was the combined difference of potentials produced by the cell and the dynamo-machine charging it. Jf now a new time-curve be drawn in which the ordinates represent the product of 44:25 AV’, where V’ is the electromotive force of the cell measured on the circuit being broken, and A is the mean value of the current flowing just before breaking and just after closing the circuit, the area of the new curve will represent that portion of the energy put into the cell which is usefully employed in chemical decomposition. The difference between the areas of these two curves represents, then, the amount of energy wasted in heating the cell in foot-pounds. Again, on discharging the cell, experiments of a similar nature have to be made. The product 44:25 AV represents the number of foot-pounds of work per minute the cell is pro- ducing in the external circuit, V being the difference of poten- tials between the two poles of the cell while it is discharging; but, in addition, there is a certain amount of energy which is being expended in heating the cell itself during discharge. This, as before, may be ascertained by breaking the main circuit, leaving the shunt-voltmeter circuit completed. The reading on the voltmeter V’ now indicates the real electro- motive force of the accumulator during discharge; whereas the previous reading, obtained just before breaking the circuit, represents merely the fraction of the total electromotive force employed in sending the current through the external resist- ance. Ifa time-curve be drawn with its ordinates propor- tional to 44:25 AV’, where A is the mean value of the current just before breaking and just after closing the circuit, its area will represent the total number of foot-pounds of energy per minute being given out by the cell; and the difference between the areas of the last two curves will represent the number of foot-pounds of energy employed in heating the cell itself. It EE on the Faure Accumulator. 43 is to be noticed that during charging V’ is less than V, whereas on discharging V’ is greater than V. An examination of thirty-five sheets of time-curves, which we have drawn from the experiments we made, shows that, in charging, the curve for AV rises at first; and as it rises more rapidly than that for AV’, this means an increase in the resistance of the accumulator. E.M.F. x Current. As the charging continues, the two curves for AV and AY’ approach one another, showing that the internal resistance of the accumulator diminishesagain. On the other hand, at the end of a long discharge the curve for AV falls more rapidly than that for AV’, due to an increase in the internal resistance. Now our experiments show a great constancy in the electro- motive force of a Faure cell, and that the falling-off in dis- charging which occurs during a very rapid discharge, or at the end of a long discharge, is due more to an increase in the internal resistance of the accumulator than to a diminution in the electromotive force, which our methods of experimenting above described enable us to separate and measure inde- pendently. But, whether discharging rapidly or whether discharging slowly, there is a most curious resuscitating- power in the cell, which, if disregarded, will cause totally erro- neous underestimates to be made of the efficiency of the cell. This resuscitating-power is more marked for rapid discharges than for slower ones. In the case, for example, of an ex- tremely rapid discharge, we found that when the flow had become apparently so feeble that the cell appeared totally dis- charged, leaving the poles of the cells insulated caused three times as much electric energy to be given out all together in the second discharge as had been given out in the first. And even when several days are taken to discharge the cell—and we may mention that we have had continuous observations made day and night for several days in certain cases—this 44 Experiments on the Faure Accumulator. resuscitating-power is wonderfully marked. An insulation of a few hours will cause the energy given off per minute on redischarging to be eight to ten times as great as it was before insulation. Indeed on one occasion, after a cell had apparently nearly discharged itself, it was left shortcircuited with a thick wire for half an hour, then insulated all night, when the num- ber of foot-pounds of work per minute given off at the com- mencement of the discharge the following morning was found to be ten times as great as it was on the previous evening, and a greater amount of energy was actually taken from it in the second discharge than in the first. This phenomenon gives the Faure accumulators a great value for tramcar propul- sion, since, as is well known, it is just on starting after stop- ping that the strain on the horses is so great. Lifficiency—To determine the efficiency of cells we com- mence with them empty, or at least as empty as many hours’ shortcircuiting with a thick wire could make them. We then measured the total amount of energy put in and the total amount subsequently given out, and we found that, for charges up to a million foot-pounds put into the cell and dis- charged with an average current of 17 ampéres, the loss in charging and discharging combined may not exceed 18 per cent. Indeed, for very slow discharges the loss in charging and discharging combined in some of our experiments has been as low as 10 per cent. Storing-power.—lIt is a little difficult to measure the maxi- mum storing-capacity of the cell at the same time that mea- surements are made of its efficiency, because in the latter case we must take care that we do not put in more electric energy than the cell can hold; on the other hand, if precautions are taken to avoid overcharging, it is a little difficult to ensure that the full charge has been put in. We have therefore separated our experiments for measuring the efficiency from those em- ployed to ascertain the storing-power. Let us take a single example of the storing-capacity. A certain cell containing 81 lb. of lead and red lead was charged and then discharged, the discharge lasting eighteen hours— six hours on three successive days; and it was found that the total discharge represented an amount of electric energy ex- ceeding 1,440,000 foot-pounds of work. This is equivalent to one horse-power for three quarters of an hour, or 18,000 foot- pounds of work stored per pound weight of lead and red lead. The curve shows graphically the results of the discharge. Horizontal distances represent time in minutes, and vertical distances foot-pounds per minute of energy given out by the cell, and the area of the curve therefore the total work given On a Simplified Dispersion-Photometer. 45 out. On the second day we made it give out energy more rapidly than the first, and on the third more rapidly than on 1000 Foot-pounds per minute. 500 Time in hours. the second, this being done of course by diminishing the total resistance in circuit, During the last day we were discharging with a current of about 25 amperes. And this cell, like the others, showed, on being insulated after having been apparently totally discharged, that there was still a large charge stored up; hence the numbers given above for the capacity are probably under the total value. Deterioration.—As to deterioration, two months constant charging and discharging of the two accumulators under test showed no signs of deterioration. _ LV. A Simplijied Dispersion-P hotometer. By Professors W. E. Ayrton and JoHN PERRY*. T will be in the recollection of the Members that in 1879 we described to the Society a dispersion-photometer which enabled measurements to be made of the intensity of the strongest electric light in a small room and for the rays coming from the electric light at any angle—two essentials which appeared to us necessary in an electric-light photometer. The principle of this photometer consisted in our use of a con- cave lens to weaken the strength of the light, so as to make the illumination of a screen comparable with the illumination ofa standard candle, instead of keeping the lamp a distance of * Communicated by the Physical Society, having been read at the Meeting on February 25, 1882. 46 Professors Ayrton and Perry on a 50 or 100 feet away, which was the plan in use until that time. We exhibit now five successive forms of the instrument, which illustrate the history of its development to the present time. 1. The first of these is very nearly the same as that described in our former paper, with the exception that we discarded the use of a long screw (shown in our original figure) for adjusting the position of the lens—as we found that a very easy adjust- ment might be effected with the fingers, the tension of the bellows part making an automatic clutch which fixed the lens- slide in any position. 2. The second specimen is on the same principle, only that telescope-tubes are used instead of a wooden frame and a bel- lows. Instead of the lens part alone tilting when the elevated or depressed light has to be examined, the candle-box is here made to tilt also, the candle being supported in gimbals so that it may remain vertical for every angle of elevation. 3. The third specimen is on pretty much the same principle; but as we found a difficulty in comparing two illuminated disks whose centres were some distance apart, we arranged in front of these disks two mirrors, which enable us to make the comparison between two illuminated semicircles having the — same diameter. The difficulty of adjusting the lens and making a comparison of the illuminations, and reading the scale, without moving one’s head, in all these early instru- ments led us to the 4th form, which is probably familiar to the Members, as it was exhibited at Paris and largely used there for measure- ments. In this the candle-box and the lens-box are placed end to end, the lens is fixed in a wooden piston which moves in its hollow square box, which is lined with velvet; and the lens shows its position by a pointer moving over the scale | outside. The pointer projects from the inside of the wooden cylinder at any point of a long slot, whose sides are made of india-rubber tubing, so that no extraneous light can reach the illuminated screen. A little handle working a rack and pinion enables the lens to be placed inany position. Through a hole at the side the two screens can be viewed reflected in two mirrors, inclined to one another in the space between the candle-box and the lens-cylinder; and the illuminated papers are viewed as two semicircles having a common diameter. In front of this hole we have slides of red and green glass ; so that, as our custom has always been, we make two measurements— one a comparison of the ruby-red light of the lamp examined with the red light of the candle, and another of the green lights. This instrument differed from the earlier forms in not requiring any calculation to be made of the strength of the OQ Simplified Dispersion-Photometer. 47 light; that is, the reading of the pointer was not merely a reading of its distance from the screen, but it was a reading in standard candles of the power of the light. Three such scales were placed on the instrument; and there were three certain distances at which the lamp had to be placed for examination. The tilting-arrangement was of course different from that of the earlier forms. As the instrument had by this time (the end of last year) come into a rather extensive practical use, we had opportu- nities of seeing that, as an instrument to be used by unscien- tific persons, it was not yet in a perfect condition, in spite of the many changes that had been made in its construction. The most important difficulty was due to the fact that a slight lateral change in the position of the observer’s eye caused the apparent illumination of the screens to vary. Being aware of this fact ourselves, we maintained a certain fixed position of the eye when making observations; but the instrument could not at once be used by persons not accustomed to make deli- cate experiments. 5. The fifth form, which we now present to the Society, is the outcome of our labours on this subject. We have all along seen the disadvantage of using the Bouguer’s two- screen method, since, when lights are examined that have passed through tissue or tracing-paper, a very slight change in the position of the observer’s eye makes a very great differ- ence in the apparent illumination, whereas, using Rumford’s method, when a sheet of white blotting-paper is employed as a screen very considerable changes in the. position of the eye produce no change in the apparent illumination—a result, however, which is not attainable when ordinary drawing-paper is used as the screen. If, however, Rumford’s method is to be used to measure the rays coming at different angles from an electric light, a mirror must be employed to reflect them successively onto the same screen; and if used in the ordinary way, the angle of incidence of the rays on the mirror will be different in different cases. Now the difficulty that always met us arose from the inequality of the reflecting-power of an ordinary mirror for rays falling on it at different angles of incidence. We have, however, completely overcome this dif- ficulty in an extremely simple way, by causing the mirror to turn about a horizontal axis inclined at 45° to its plane, and the whole photometer to turn about a vertical axis. With this arrangement the angle of incidence, and consequently the proportional absorption, is the same whatever be the inclina- tion of the rays coming from the lamp to the mirror; and, further, the angle being 45°, the amount of rotation of the 48 Professors Ayrton and Perry on a mirror about its horizontal axis necessary to enable measure- ments to be made of rays coming at any angle, after measure- ments have been made of the horizontal beam, is exactly equal to the inclination of the beam in question. i Using Rumford’s method in this latest form of our photo- meter, we are to a great extent independent of the presence of other sources of illumination of the screen, so that the appa- ratus need not be enclosed in a box. At the same time, how- ever, the sensibility of the test is much increased by placing a shade to prevent the electric light shining directly onto the screen. On this screen of blotting-paper, B, is thrown the shadow of a black rod, A, placed in front of it, by a candle in the candle-holder, D. = Vee Now it is well known that if an electric light is also allowed to illuminate this screen, and to throw a second shadow of the rod A on the paper, and if the candle is adjusted at such a distance that the two shadows are of equal intensity, the strength of the light is to that of the candle in the ratio of the squares of their distances from their respective shadows. But instead of allowing the strong light to pass directly to the screen, we cause it to pass through the concave lens in the sliding wooden frame C. A pointer on this slide tells the distance of the lens from the screen. As you are all aware, the weakening of light-intensity produced by the lens enables us to leave our electric lamp within a few feet of the instru- ment. We have experimentally found that there is no appre- ciable loss of light in passing through the lens. The candle slides on the bar J; and its distance from its shadow is shown by a pointer on a scale. If is the focal length of the lens, D the distance of the electric light from the paper-screen, d Simplified Dispersion-Photometer. 49 the distance of the centre of the lens from the screen, and c that of the candle when the shadows show equal illumination, then, if L is the strength of the examined source of light in standard candles, : eis = {ira poa)} L= 51 D+ ae Ce i For our own use we prefer to employ the formula; but as all the common instruments which have hitherto been manufac- tured have lenses whose focal length is 4 inches, we have pre- pared a table, a copy of which is sent out along with each instrument, in which the value of L is given “for various values of D, d, and c. Using this table, it is necessar y to have the lamp. at either 60, 120, or 300 inches from the screen; the candle is either at 10, 14: 14, or 20 inches from the screen; and the table is made out for ever y half inch of the lens-scale. But inasmuch as we find that the improved arrangement of the mirror already referred to constitutes perhaps the most useful part of the instrument, and as the use of this improve- ment involves many alterations of D, the manufacturer pro- poses in future not to furnish any table of values of L unless specially asked for. H is the plane silvered-glass mirror which makes the angle of 45° with the axis of the lens, and with the axis about which the mirror itself is free to revolve. As already explained, a ray of light reflected from the mirror and passing through the centre of the lens must, for any position of the mirror, have an angle of incidence of 45°, and so must experience the same amount of absorption, from whatever direction it may have come to the mirror. Further, .this angle being 45°, a fixed pointer marks on the graduated circle G, which moves with the mirror, the angle which any ray we may be examining makes with the horizontal. In this instrument we find that from 380 to 34 per cent. of the incident light at 45° is absorbed, whether this light is of ruby-red or sional-preen colour ; so that we have the easy practical rule for all cases—add one half to the measured intensity of light reflected. We need not here refer to the fact that, when investigating the efficiency of an electric lamp, we always measure the horse-power given electrically to the lamp simultaneously with the photometric measurement. The lamp is suspended in such a way that it can readily be Phil. Mag. 8. 5. Vol. 14. No. 85. July 1882. aD or 50 On a Simplified Dispersion-Photometer. placed at any elevation. The frame of the tripod-stand is first levelled. A pin at F, directly underneath the ceutre of the mirror, passes through the base of the photometer and fits into a hole in the top of the tripod-stand. The photometer, by turning round this pin, can, without producing any change in the distance of the centre of the mirror from the lamp, and therefore without changing the distance from the screen to the lamp, receive the small horizontal motion necessary for the adjustment of a new inclination of the rays coming from the electric light, without any alteration of the distance of the centre of the mirror fromthe lamp. The divided circle is clamped with the index at 0°; the lamp is lowered or raised till the illuminated disk formed by the reflected light, passing afterwards through the jens, is in the middle of the paper screen. A little sliding shutter with a fine hole in its centre, seen in the figure, enables a very exact adjustment to be made; but in practice we find that we get sufficient accuracy without the use of the shutter. We now measure the distance from lamp to centre of mirror in inches. Equalizing the intensities of the two shadows by adjusting the lens-slide when looking at them through red or green glass, we now note the lens- and candle-readings ; and we repeat these operations, changing from red to green and green to red about five times in a minute, The lamp is now raised or lowered and fixed in any position ; a few seconds suffice to turn the mirror so that it sends its centre ray exactly through the centre of the lens. The dis- tance from screen to mirror in this instrument being 22 inches, if 6 is the distance from centre of mirror to vertical from lamp, Connexion between Viscosity and Density in Fluids. 51 and if @ is the angle of elevation, then D=22+6sec @. Using this value of D in the formula above, and adding one half to the strength of the light to make up for absorption, the true intensity of the light in standard candles can be ascertained. We find in practice that, if an electric light is moderately steady, ten measurements may be made, with some confidence in their accuracy, in two minutes ; and the light may be measured in ten different positions, from an angle of depression of 60° to an angle of elevation of 60°, 100 observa- tions being taken, in less than half an hour. We may mention one very important result we have been led to by the systematic employment of a photometer which can be used close to the electric light ; and that is the large amount of absorption that occurs on certain days when the rays from strong electric lights, and especially the green rays, pass through the air which appears to the eye perfectly clear. At first we were inclined to think the higher results for the candle-power of a lamp obtained with our dispersion-photo-' meter than those obtained with an ordinary distance-photo- meter were due to some error in our photometer itself; but we have since ascertained that this is due to the absorption of the air—because we find that, if simultaneous measurements are made with ordinary Rumford’s photometers, each without lens or mirror, placed at different distances from the lamp in the same azimuth and in the same horizontal plane, the nearer one gives, as a rule, the highest readings ; and the difference is the greater the stronger the light, and is greater if the light be examined at each photometer with green glass. V. On the Connexion between Viscosity and Density in Fluids, especially Gaseous Fluids. By EH. Warsure and L. v. Bazo*. “en laws according to which the elasticity and viscosity of a body are connected with its density are of great sim- plicity in the case of gaseous bodies. The elasticity of these, a. e. the reciprocal of their compressibility, is given, according to Boyle and Mariotte’s law, by the pressure, and is propor- tional to the density; the viscosity, measured by the coefficient of friction, is, according to Maxwell’s law, independent of the density. It is known that the first of these laws, that which refers to * Translated from the Sttzwngsberichte der K. Preuss. Akademie der Wissenschaften zu Berlin, May 4, 1882, pp. 509-514. KR? ad 52 MM. Warburg and vy. Babo on the Connexion elasticity, holds only approximately, and even that only at moderate degrees of density; at higher densities, according to the investigations of Natterer, Andrews, Cailletet, and others, the connexion between elasticity and density is not even approximately given by Boyle’s law, but is apparently more complicated. It can, however, according to van der Waals*, be explained from the kinetic theory of gases, if the volume of the molecules and the attraction between them be taken into account. Corresponding investigations in relation to the viscosity of gases have hitherto been carried out only so far as Kundt and one of ust have studied the deviations of Maxwell’s law at very slight densities. For higher degrees of density the con- nexion between viscosity and density has not yet been inves- tigated. Tor the solution of this problem (treated in the pre- sent paper for one substance, viz. carbonic acid) the corre- sponding values at constant temperatures of the coefticient of friction, the density, and, for many reasons, the pressure must be determined. We employ as the measure of the pressure the inverse value of the volume of a mass of nitrogen at constant tempe- rature of the apartment, the volume of that mass at the pres- sure of one atmosphere being put =1. ‘To measure the pres- sure according to this definition a nitrogen-manometer was employed, which was always attached to the principal appa- ratus, and permitted pressures between 30 and 120 atmo- spheres to be evaluated. The density of the substance heated above the critical tem- perature we determined by a volumetric measurement of the carbonic acid, which at each transition from a greater toa less density was liberated from our apparatus, the volume of which was known to us; the density of the mass in the appa- ratus after the conclusion ofa series of experiments we calcu- lated from the pressure, which then amounted to about 30 atmospheres, by Clausius’s formulat, which at so small a pressure is sufficiently accordant with the observations. At the temperature 32°°6 our experiments comprise the interval of densities between 0-1 and 0°8. For the determination of the friction-coefficient we em- ployed the method of flow through capillary tubes. The capillary, placed vertical, ended below in a measuring-tube which dipped in mercury, above in a space A, which could from time to time be shut off from the rest of the space by a cock, and in which a diminution of pressure could then be * Dissertation: Leyden, 1873. — + Berlin Monatsberichte, 1875, p.160. { Wiedemann’s Amalen, ix. p. 348. | between Viscosity and Density in Fluids. 53 produced by discharging carbonic acid. After the mercury had been thereby raised in the measuring-tube, the spaces A and B were again put into communication. From the time occupied by the mercury in the measuring-tube in descend- ing from one mark to another, the coefficient of friction was calculated by means of the constants of the apparatus. Three capillaries were employed, from 6 to 7 centim. in length, and of which the radii amounted to 0:005162, 0:003601, and 0:002847 centim. The validity of Poiseuille’s law was controlled ; but an equation cannot be deduced from the expe- riments. The results obtained are contained in the following Table, in which ¢ denotes the temperature measured by the air-ther- mometer, s and w the density and the friction-coefficient in the gramme-centimetre-second system, and p the pressure in the measure above-mentioned; 2 is the air-content of the sub- stance, in parts of a volume, as given by analysis. The den- sity of the liquid carbonic acid is taken from Andreef’s expe- riments*. t =32°°6. ¢ =40°'3. | A\=0:00074. A=0-00085. Ss. p. pehOX Dp. pe. 10°. 0:800 107°3 677 0-730 88:5 574 1146 580 0-660 80:7 493 101°6 499 0:590 78:2 414 94:9 426 0:520 776 351 91:7 366 0:450 77-2 304 89:2 316 0:380 766 270 868 275 0-310 74-6 239 82°7 243 0:240 69-9 213 799 218 0:170 60:3 188 64:3 196 0-100 431 | =n 45:3 180 ¢ =25°-1 4=0:00044 P- s pe. 108 105 0-896 800 95 0-875 | 741 85 0:858 703 "5 0:27 ~ | 665 | 70 0809 628 * Annalen der Chemie und Pharmacie, 1859, ex. p. 1, 54 MM. Warburg and v. Babo on the Conneaion % | Viscosity of liquid carbonic acid under the pressure of | its saturated vapour. A=0°0018. t | 8 pw. 10% oO 5 / 0-922 925 10 | 0:895 852 15 0-864 784 20 0°827 712 25 0-783 625 | 7: Nia tables a Pee 555 539 9 50 700 Density. The figure gives a graphic representation of the results— namely, the isotherms* of viscosity and tension, the latter in dotted lines, noted according to the Table. Andreef’s values of the pressure t exceed ours but little— at 32°6, on an average, about one atmosphere. This may arise from the air-content of the carbonic acid being in Andreef’s experiments somewhat less than in ours. The values of p calculated by Clausius’s formula, however, are not inconsiderably higher than those observed by us; the differ- ences increase with the density, and reach the value of 10-12 atmospheres. On account of the agreement of our results * We thus name lines the abscissee of which are proportional to the densities, and the ordinates to the friction-coefticients and pressures respec- tively. + Pogg. Ann, Erg. Bd. v. p. 79 —|> 2 between Viscosity and Density in Fluids. > 5S with those of Andreef, found by a quite different method, it is not likely that the differences are due to errors of observation. Respecting the viscosity, especially its connexion with the density, the results are as follows: I. Above the critical temperature, Gaseous Carbonic Acid. 1. To the maximum of compressibility (=) , 2. e. to the s | ds ef ore d : i minimum of elasticity (s A) , given by observation corresponds no minimum of viscosity, which much rather increases in a constantly increasing ratio with increasing density. Pp ds ds” At the density 0-1, about 500 times the normal, the Daiiciont of friction exceeds the normal (0:000165 for 40°-3) by only about 9 per cent. of the latter. 3. At the temperatures 32°°6 and 40°-3 the substance shows, at equal density, slightly different values of w, very different values of p. According to this the viscosity appears to be much more simply connected with the density than with the pressure. 4, The influence of the temperature upon the viscosity, at constant density, is so small that it cannot be inferred with perfect certainty from observations embracing a temperature- interval of only 8°. Since, however, the isotherm for 40°3 runs entirely above that corresponding to 32°°6, the viscosity appears to increase slowly with the temperature when the pressure is constant. Il. Liquid Carbonic Acid. 5. Liquid carbonic acid showed far less viscosity than any other liquid hitherto examined. The friction-coefficient of water, for example, at 15° is 14:6 times that of liquid carbonic acid under the pressure of its saturated vapour. Hvyen the appearance of liquid carbonic acid enclosed in a glass tube which is shaken excites the supposition that this substance possesses very little viscosity. 6. The viscosity of liquid carbonic acid at the temperature of 25°-1 increases with the density. By further extending this investigation, and especially to other liquids also, we pur- pose to ascertain the influence of temperature upon the visco- sity of liquids at constant density—that is, the specific influ- ence of temperature. 7. At densities in the vicinity of 0°$ the isotherm correspond- are always positive. ) = 1of 7 . 56 On the Connexion between Viscosity and Density in Fluids. ing to 25°1 runs below both that corresponding to 32°°6 and those corresponding to 15° and 20°. From this follows that carbonic acid of such density, heated from 15° upward, must show a minimum of viscosity between 20° and 326. Poisson* has given a theory of liquid-friction which starts from the representation that, with respect to a system of simultaneous impacts, a liquid behaves, at the first moment after the expiration of them, like an isotropic solid body. Hence we can speak of the constants of instantaneous elas- ticity of a liquid. For the coefficient of friction in Poisson’s theory we get the expression p— KT. where K is the coefficient of instantaneous rigidityt, and Ta quantity of time which Maxwell has named the modulus of the relaxation-period. For an ideal gas, Maxwell findst K=p, and hence T, at constant temperature, proportional to the mean length of path. In a first approximation let us assume that T still has this property when the volume of the molecules and the attraction between them is taken into account; then we get for wa theoretical expression in which K alone remains unknown— namely K s bus p= mop @(1- 5"); where for the temperature to which yp refers, wy and sy denote the values of yw and s for the pressure P of one atmosphere. A is the normal density of carbonic acid, and 6 van der Waal’s constant, namely four times the molecular volume, the yolume of the substance at 0° and the pressure of one atmosphere being taken as the unit of volume. The equation holds so long as s<2b—that is, for carbonic acid, approximately as long as s<0°4. According to this equation, the occupation of space by the molecules produces a diminution of friction with increasing density, and consequently the opposite deviation from Max- well’s law to that produced by the attraction between the molecules. From the same equation, according to our expe- riments, for carbonic acid of density 0°38 at 32°°6, K comes to 7-2 kilograms upon the square millimetre—that is, about 3h 5 of its amount for glass, and somewhat more than for tallow$. * Journal de V Ecole Polytechnique, 1831, t. xiii. p. 139, T In Kirchhoff’s notation (Vorlesungen, p. 400). { Phil. Mag. [4] xxxy, p. 211 (1868). § Pogg. Ann. exxxyi. p. 295 (1869). es al VI. Notes on Thermometry. By F. D. Brown, B.Sce., Demonstrator of Chemistry at the University Museum, Oxford*. [Plate IT.] Sore years ago, when I determined to try and find out something about the attractive forces which the atoms and molecules seem to possess, by studying the effects of heat upon chemical substances and upon mixtures of such sub- _ stances, I was led to the conviction that, if the work which I proposed to do was to be of any permanent use, I should be obliged to take many and minute precautions regarding the -measurement of temperatures—a measurement which, owing to the peculiarities of mercurial and other thermometers, is so liable to error. In order to learn how best to use my thermo- meters, and how to refer their readings to a satisfactory standard, I made a considerable number of experiments. At the time when these experiments were made I imagined that the subject of thermometry, although presenting many diffi- culties to my mind, had been thoroughly worked out by others, and therefore that a printed record of my observations would be generally deemed to be of little utility. The recent publication of a paper by Dr. H. J. Mills (Hdin. Roy. Soe. Trans. 1880), of one by Professors T. H. Thorpe and Riicker (Phil. Mag. [5] xii. p. 1), and more especially of a report by M. Pernet (Mém. et Travaux du Bur. inter. des poids et mes. i. 1881, pp. 1-52), has led me to change my opinion, and to think that there still remain many points connected with thermometers about which not only I, but others also, would be glad to have more certain information. Acting upon this belief, I have put together in the following pages some of the results of my experiments. The Mercurial Thermometer as a Standard. I was soon convinced that any attempt to express tempera- tures in degrees of an ideal absolute thermometer, or even to refer them correctly to the readings of an air-thermometer, would involve a most extensive and wearisome investigation, which would postpone indefinitely the work I wished to do. To avoid this substitution of the means for the end, I decided to construct a mercurial thermometer and to use it as a stan- dard, keeping it until such time as the progress of our know- ledge should render its comparison with the air-thermometer a matter of less difficulty. As a mercurial thermometer is very liable to be broken, I first wanted to know whether this instrument fulfilled the primary condition of a true standard, of being capable of * Communicated by the Physical Society. 58 Mr. F. D. Brown’s Wotes on Thermometry. reproduction when lost or destroyed. With this end in view, I made two thermometers at different times, and wholly independently one of the other, and compared their readings, To those who may wish at any time to construct a mercurial - thermometer without the elaborate appliances ordinarily em- ployed, but in which absolute confidence may be placed, the following details may be of interest:— A capillary tube of medium bore, about 800 millimetres long, free from all flaws, and having as uniform a section as possible, is provided with a millimetre-scale of 600 divisions. The etching of this scale is a matter of great consequence : it very frequently happens that the divisions on glass tubes are not of exactly equal length, but that, owing to some defect in the dividing-engine or some movement of the tube while un- dergoing the process of division, some of the divisions are so much longer or shorter than the rest as seriously to interfere with the subsequent process of calibration. yen when all the lines are equidistant, they are often so thick, and present so irregular an outline when viewed through a telescope, that it is impossible to fix upon any particular point as that repre- sented by the dividing-line. The tubes I employed were selected and divided with special care by Mr. Casella, the lines being perfectly straight, less than 0-4 millim. in thickness, and in all cases equidistant. As a glass tube, however carefully selected, is never of uniform bore, it is necessary to ascertain the relative capacities of the several divisions of the tube, or, in other words, to “calibrate ’’ it. As is well known, this is easily done by placing a thread of mercury in successive positions along the tube and observing its length, the mean capacity of the diyi- sions occupied by the thread being, of course, inversely pro- portional to that length. In this way, and by adopting the plan of correcting the position of the thread suggested by Dr. Mills in the paper above referred to, which plan he had been kind enough previously to communicate to me privately, a table is readily constructed showing the volume of the tube from the line marked 0 to any line marked x, and also the value of the succeeding division. The only difficulty connected with this process is the accurate measurement of the length of the thread of mercury in its several positions. It is true that this may easily be done witha dividing-engine or some similar instrument, such as a cathetometer provided with a micrometer eyepiece and placed horizontally. As, however, reliable instru- ments of this class are exceedingly costly, I designed a small piece of apparatus for the purpose, which has proved so con- yenient and useful that I venture to describe it here, Mr. F. D. Brown’s Notes on Thermometry. 59 A mahogany board, B B (PI. I. fig. 1), about 18 inches long and 4 inches wide, is provided with a groove, G G, of the shape shown in the section (fig. 1a); a piece of gun-metal, about 5 inches long and + inch thick, slides in this groove with some little difficulty—the friction, which is produced by the spring jf; being necessary to retain the plate rigidly in any given position. The plate, D, is provided with a slot, e e, and a milli- metre-scale, 8 §, the dividing lines of which must, like those of the tube to be calibrated, be very fine and truly equidistant. The piece of gun-metal, EH, which is provided with a vernier, carries the reading-microscope, M, and can be moved along SS by means of the rack and pinion p; the movement is rendered smooth and free from lateral displacement by the spring c, which causes the ends of HK to remain always in contact with the straight edge of the slot. The thermometer-tube is fixed with suitable screws under the path of the microscope, so that the length of a thread of mercury can be easily measured by placing the microscope so that its cross wire coincides first with one end of the thread and then with the other, and noting on the scale the distance between the two positions. The millimetres of the brass scale and those of the tube, if marked off by different makers, will often differ a little in length ; hence it is generally more satisfactory to obtain from the glass scale the number of whole divisions occupied by the thread, and to measure the terminal fractions only by the microscope. Since the line on the outside of the tube is nearer the eye than the thread of mercury inside the tube, it is clear that when the microscope is adjusted to view the end of the thread, and is then moved along until the cross wire coincides with the nearest line, this last will be out of focus, and either the whole microscope must be raised up or the distance between the object-glass and eyepiece altered. Now, unless the in- strument be constructed with great solidity, and much care be taken to fit accurately all the moving parts, this adjustment will probably alter the position of the optical axis, and so render the measurements inaccurate. To avoid this diffi- culty, I added a half-lens, L, fitted in the ordinary way on a brass tube sliding on the end of the microscope. This lens of course brings the focus of half the field nearer the object-glass ; so that, by properly adjusting it, the divisions are seen through the half-lens at the same time that the mereury is observed through the unprotected part of the object-glass. In this way all disturbance of the microscope is avoided throughout the calibration, which is thus carried out with much greater comfort and accuracy. oo See 60 Mr. F. D. Brown’s Notes on Thermometry. Two tubes were calibrated with this apparatus, and tables of their volumes from the first division compiled ; they were then furnished with bulbs, filled with mercury, and sealed up in such a manner that they formed thermometers capable . of indicating temperatures between 0° and 150° C. The fixed points of the two thermometers having been determined . with the precautions indicated below, tables showing the temperatures corresponding to the readings of the scale were made in the usual manner; the two instruments were then compared together, either in a large tank of water which was kept well stirred, or in the steam-apparatus which I de- scribed to the Physical Society at the time when these expe- riments were made. Before a series of readings were taken, both thermometers were heated for at least half an hour in steam, while their zero-points were observed after the series was completed. The numbers given in the following table show that the two thermometers gave practically identical readings. It would seem, therefore, that the mercurial ther- mometer, when carefully made and systematically heated, does really possess that valuable property of a standard, of being | capable of exact reproduction. | | | | Reading of AS, Reading of BS, Corresponding | Corresponding corrected for | corrected for value of AS, value of BS, | Difference. index-error. | index-error. in degrees. in degrees. 58°55 | 70°64 14:30 14-29 —01 134:33 | 150-11 33°69 33°71 +02 179°69 | 197°20 45:29 45°30 +01 321-97 | 345°96 81°88 81°88 00 23°42 33°74 5°28 5°28 ‘00 26°33 36°85 6:03 6-04 +01 30:07 40°63 6-99 6:97 _" 33°76 44:57 794 7-93 —01 43°32 54:70 10°40 10-40 ‘00 47-98 | 59°60 11:59 11:59 00 69°42 82°13 17-09 17:09 ‘00 91°61 / 105°52 22°78 22°79 +01 Determination of the Zero-point. In most books on physics it is stated that, in order to obtain the zero-point of a thermometer, the instrument should be placed in a vessel filled with broken ice and provided with holes at the bottom, through which the water formed by the melting of the ice may escape. In order to learn whether this method is the best possible, the following experiments were made:—A number of tin pots, about 7 inches high and 4 inches in diameter, were obtained, and holes made in the bottoms of two or three of them. A large block of ice was Mr. F. D. Brown’s Notes on Thermometry. 61 broken up into small fragments, which were well mixed up, so as to render the whole perfectly uniform in character. One of the tin pots, which we will call A, was filled with some of this ice, which had been washed in a funnel with ordinary water; A was then filled up with water, so as to form a mixture in which the ice largely predominated. .-AdnAps..-dpa . . (10) The number of systems which, at time 0, have the phase (p’q’), 2. €. for which the variables at this time lie between the limits (8), will consequently be denoted by ON G6. On, P'o> > p'n0) dq'y...dqndp's..adp'n. + (I) But, in accordance with the signification already given to Qi---Pn and g’;..- p/n, exactly the same systems have the phase (pq) at the time t which had the phase (p’q’) at the time 0. The expressions (10) and (11) are therefore equal; whence, referring to equation (7), we have GF (Ga+ + + Yns Pa ++ Pat )= VF's ++ U'ny p'a + ++ Pad). » (12) Maxwell calls the distribution of the system stationary when the number of systems having any given phase, e. g. (p’q'), does not change with the time—when, therefore, for any Bee 9 iP a- > - Pn, FQ 1-6 Om Pla + + PuT)=LD 1 F'n p'g+ + p'nO) (18) Since in equation (12) g’,...p’ are also any initial values Phil. Mag. 8. 5. Vol. 14. No. 88. Oct. 1882. x « ah 306 On Boltzmann’s Theorem on the average Distribution of the variables whatever, equations (12) and (13) may be at once combined with each other, and give UAC oss Qny Po +++PunT =F (7 1-+- Yn, Po-+-f nt) Since f no longer contains the time 7, it is better to omit 7 from under the functional sign and to write DFG ++ Gry Pa ++ Pr) =D SPs ++ Pn; p'2+++P'n)» « (1A) Here g/;..-Qnjp’o...p' are any initial values whatever ; Qi +++Qn; P2-++pn are the values of coordinates and momenta which a system starting from these initial values attains after a time 7, in other respects unfixed. Let us therefore imagine a system starting from any initial values of coordinates and momenta; then in course of the motion it will assume continually new and new values of co- ordinates and momenta. The coordinates and momenta are therefore functions of the initial values and of the time. But there will be in general certain functions of coordinates and momenta which have constant values during the whole motion, as in a free system the component velocities of the centre of gra- vity, or the sums of angular momenta, are invariable. Let us therefore imagine in the expression g; f (41 .-+ ny Po+++Pn) first of all those optional initial values from which each system started, then continuously the values in order which coordi- nates and momenta assume for that system as the time increases; then for the existence of stationary distribution it is necessary and sufficient that the value g,f shall remain unaltered, or, in other words, ¢,;/ must contain only such functions of 7,...p, as remain constant during the whole motion of a system from any initial values whatever, and con- sequently are dependent on the initial values, but not on the time which has elapsed. Ifthe system is so constituted that its coordinates and momenta, starting from given initial values, assume in the course of a sufficiently long time all possible values consistent with the equation of energy, then g,/ must in general have the same value for all coordinates and momenta consistent with the equation of energy—must therefore be a constant. I will now mention some other terms employed by Max- well. If one of the systems 8 starting from a given initial condition moyes, all the conditions through which it passes in consequence of its motion as time increases, constitute the * This or the identical equation (14) is necessary that the distribution may be stationary. It is also sufficient; for from it and equation (12) equation (15) follows at once for any g',...p'n whatever, which is exactly the mathematical expression for a stationary distribution. of Energy in a System of Material Points. 507 path of the system, each separate condition of motion a phase of this path. All the functions of coordinates and momenta which remain constant during the whole path he calls the parameter characteristic of the nature of the path, whilst all other functions of coordinates and momenta depend also on the phase. In order that the distribution of the systems shall be a stationary one, it is necessary and sufficient that / shall be equal to z , multiplied by an arbitrary function of the para- meters characteristic of the nature of the paths. Maxwell considers the simplest case when this function isa constant, and therefore /= 7 then if NCdq, ...ddn Ups « x3 dpn (15) a em nat ates is always the number of systems for which coordinates and momenta lie between the limits (9), whilst p,; is determined by the equation of energy. This is, then, the simplest possible stationary distribution. If the g’s denote the rectangular coordinates of material points, then the products of the component velocities into the corresponding masses my, 1v,... are the corresponding momenta; then the kinetic energy 2 2 Dy p2 T= bm t...)= ei + eee... tai ) 2m, 2m, ; 2 : myth « ae J where evidently —-— is the kinetic energy resulting from the motion of the first atom in the direction of the axis of x, and soon. In like manner, generalized coordinates can always be so transformed that 2 2 Ts +... where the ys contain simply the coordinates. Maxwell calls 2 ue the “ kinetic energy resulting from the 7th momentum,” or simply the “kinetic energy of the rth momentum” The mean kinetic energy of any one of the momenta, say of the 7th momentum, is therefore expressed by il Yr Dr AQr +» -dpn . \J- : a a Dn 21 71 x 2 308 On Boltzmann’s Theorem on the average Distribution Here the integration is effected with reference to all the other p's before that with reference to p,. I will here show only how the integration with reference to pn is to be effected when 7 is not equal ton. For gq, is to be substituted its value . 2 2 o =nn=ViA/ B-V— Pa (16) dp, 2 2 If we consider that, in the integration with reference to p,, the quantities g,...Qn;2-+-Pn—1, and therefore also y--- Yn; V, and p, are to be considered as constant, we may put 2 InP 2 E-V— vate a ae =a, and then, in integrating with reference to pp, all up to g comes before the sign of the integral, and ae reduces to 1 1 +a dx * Jato: Baten which, as is well known, can be easily calculated. The inte- gration can be equally easily performed with reference to the remaining p’s, and lastly to p,. Since V is a given function of the coordinates, the mean kinetic energy may be found simply by repeated integration. The symmetry of the formula (16) shows at once that it has the same value for all momenta, consequently also for all atoms in the case of material points. The number Z, of the systems for which the values of coordinates lie between q, and Atdq...d, and gn+dqn, and the kinetic energy of the mo- mentum p,between £ and k+dk, whilst all the other momenta have all possible values, is found by integrating the expression (15) with reference to those other momenta, but putting / 2k dh 7 WV Qhey which, whilst keeping the conditions for the coordinates, the last momentum may be any we like, by integrating also with reference to p, or k over all possible values. The integration, after using the substitution (16), offers no difficulty, and gives and for p, and dp,; the number Z, of the systems for of Energy in a System of Material Points. 309 n—2 Zp= NC [TGV 1192 «+ Yn(QH—2V) ? dq... ddn « nv 4 rG yz, (-V-HFar(; 2 (@e-v)? ver@r(s) This number, and consequently the law of distribution of kinetic energy, has the same value for all momenta. For large values of n, : Z, __e@ dk Le e kW/ 9 is the mean value of the kinetic energy of a nearly, where K= momentum corresponding to these values of coordinates, and the same for all momenta. In order to apply these equations to the theory of Heat, Maxwell imagines amongst the systems § precisely similarly constituted warm bodies enclosed in absolutely rigid envelopes impermeable to heat, which are completely mdependent of each other, and all possess the same energy H. The systems S therefore now represent to us very many similarly consti- tuted real bodies of equal temperature and under equal external conditions. The condition of motion of each of these bodies is to be determined by the coordinates and momenta q,.../n formerly employed. ‘The different bodies are to have started from very different initial conditions; and the number of systems for which, at the commencement of the time, coordi- nates and momenta lay between the limits (9), is to be given by the formula (15). We know that then the distribution is a stationary one. The systems which had the phase (pq) at the commencement of the time, it is true, soon pass out of this phase; but exactly as many systems enter on this phase to replace them, and thus it continues for all times. The equa- - tions obtained above hold, therefore, for all bodies. The mean kinetic energy must have the same value for each of the momenta, viz. the value calculated above. The case might, of course, occur that the equations should not hold good for each n—2 * When V is small with reference to E, and n is large, (H—Y) 2 u—2 approaches to the limit E 2 e 2) andthe hydrostatic differential equa- tion for polyatomic gases follows from the equation in the text. 310 On Boltzmann’s Theorem on the average Distribution single body—that, for example, the mean kinetic energy of a momentum should be greater in one body than that calculated above, in which case it must of course be smaller again in other bodies, so that we may have the true mean value for all bodies. But it is to be remembered that all our bodies are found similarly constituted, of equal temperature, and under similar external conditions. In the case just spoken of, therefore, the behaviour of bodies of that kind would be different according to the initial condition from which they started. But this is not confirmed by experience. As often as one and the same body is left to itself with the same energy of motion and under the same external conditions, it assumes with time the same thermal condition, the stationary condition corresponding to that temperature and those external conditions. We are therefore justified in maintaining that our equations hold not simply for the above-defined conceptions of bodies, but also for the stationary final condition of each single warm body. That the condition of equality of temperature between warm bodies has a very simple mechanical meaning independent of their initial conditions, follows also from the fact that it is not influenced by the compression, turning, or displace- ment of particular parts. If we substitute for the system § two different gases sepa- rated by a solid division-wall permeable to heat, then there follows the equality of the mean kinetic energy of progressive motion of the molecules of both gases, or Avogadro’s law ; the proof of which, hitherto resting on the equality of this mean kinetic energy in mixtures of gases, is unreliable, since we are not able to show that the mean kinetic energy of pro- gressive motion is the same in mixtures as in separate gases at the same temperature. The second case discussed by Maxwell is very interesting, but cannot be here reproduced in full. In this g,...qn are the rectangular coordinates 2,...2,, therefore p,...p, the velocity-components multiplied by the masses my ...77n Wn of a free system of atoms 8’ with any internal forces but without external forces. Maxwell introduces into equation (5), instead of duty dvy dw, duz dvzdw dug, the product dU dV dW dF d6dH dB; where U, V, and W are the velocity-components of the centre of gravity, F', G, and H the constant sums of angular momenta of the elements of motion of the system S’. Equation (5), dU dV dW dF dG dH dE therefore, after dividing by ) assumes 33 ee eed m3 m3 m, da’, ... den dv'3...dw'n _ day... din Avg... dwn LT Gal a 7! 4 arr & of Energy in a System of Material Points. all ; é SEH a hee where 7 is the distance of the atoms m, and m., r= gs #18 ad the double of the projection of the triangle m,m,m 3 on the yz-plane. If we have again an infinitely great number of similarly constituted systems 8’ given for which the magni- iudes E, U, V, W, F, G, H have equal values throughout, we find, exactly as before, that the distribution of these systems is stationary when the number of those for which a, ... zn, v3.-- Wn lie between the limits x, and #,+dx,...w, and watdwn, is Cdx,...dw” arr former case, the number of systems for which, with any velo- cities, the coordinates of the atoms lie between infinitely close limits, and, further, the number of those for which the velocity-components of an atom also lie between infinitely close limits, the mean kinetic energy of an atom, &e. I quote two only of the results. 1. If &,, € be the velocity-components of an atom of mass m referred to new axes of coordinates, of which, at the instant in question, the z-axis passes through the atom, but the two others are axes of the section of the momental ellipsoid by their plane, whose origin at each instant is the centre of gravity of the system, and which revolve with the angular velocities which the system acquired in suddenly becoming solid through the operation of internal forces, then the mean values of the 2, 2 m m g 5) a , are the same for all atoms. —aye” 1—byz" In particular, the law according to which these magnitudes are distributed amongst the atoms is the same as that accordin pees ares ote 8 to which mz”, mv’, mw? were distributed in the former case. equal to Maxwell calculates, exactly as in the magnitudes m6”, i / / a if M is the total mass of the system, < is the distance of the centre of gravity of the system from a straight line passing through the atoms whose direc- tion-cosine, with reference to the new axes of coordinates, are BC-—L? , AC—M’ 1 ae ies ne 2. if A, B, C are the moments of inertia of the system with refer- ence to the new axes of coordinates, L, M, N the sums 2myz, =mez, Sme«y with reference to the system of coordinates, and At the same time y= proportional to &,7,andé. Lastly, a= ee ow Deseo N ted SA Bela a 8 If the number of atoms is very large, then still le Rane), 312 Mr. W. Le Conte Stevens’s Wotes consequently the mean kinetic energy of internal motion (7. e. of that relative to the new axes of coordinates), is the same for the atoms. 2. A gaseous mixture distributes itself in a horizontal tube rotating about a vertical axis, exactly as if each of its consti- tuents were present alone in equilibrium under the action of gravity and of centrifugal force. A tube 1 metre (/) long, with one end in the axis of rotation, must make about ten (7) revolutions per second in order that a mixture of hydrogen and carbon dioxide shall contain at one end 1 per cent. ( p) carbon dioxide more than at the other. The rotation must last about two hours in order that the previous deviations from a stationary distribution shall become about one hundred times smaller ; p is proportional to the square of the velocity of the moving end of the tube, and therefore to Pn’. XXXV. Notes on Physiological Optics. By W. Le Conte StEvEns*. N the ‘ Philosophical Magazine’ for May 1882 the present writer discussed certain phenomena of vision under yari- able physiological conditions. Among these was stereoscopy, attained from a pair of perfectly similar diagrams, with paral- lelism or slight divergence of visual lines, the binocular re- sultant image being caused to appear concave, convex, or plane at will, by properly adjusting the cards in position so that the two retinal images from them could be made either slightly dissimilar or alike. A geometric discussion of this was given in connexion with the record of other experiments that illus- trated the important effect of muscular action in modifying our unconscious interpretation of retinal sensations. This discussion was preceded by a consideration of the current theory of corresponding retinal points, which was accepted only in a modified sense, and not mathematically. It was assumed that, in examining the binocular resultant, freedom of motion is allowed the eyes—a condition that has usually been found necessary when stereoscopy by this method is performed for the first time by any one who is not skilled in binocular experiments. Hven at that date the writer was convinced that play of the eyes was not indispensable, however effective it might be in confirming the visual judgment. The geometric discussion, though correct so far as it extends, was not deemed capable of covering all the facts; but to test the extent to * An Abstract from two Papers read before the American Association for the Advancement of Science at the Montreal meeting in August 1882, Communicated by the Author, on Physiological Opties. 313 which it was possible to attain such results without motion of the eyes, it was important to employ the electric spark as a means of illumination. The opportunity of doing so was then wanting, but has since been secured. Vision by the Light of the Electric Spark. The apparatus employed for the production of momentary illumination was a large induction-coil belonging to the Phy- sical Laboratory of Columbia College (New York), and loaned for the purpose by Professor O. N. Rood. The stereoscope used was the reflecting instrument described in a former paper *, which had been so constructed as to give for registra- tion the angle, positive or negative, between the observer’s visual lines, the distance of each card from the eye that receives its image, and the angle which the plane of this card makes with the visual line, assuming the latter to be horizontal and the axis of rotation of the card to be vertical. The writer was fortunate in securing the cooperation of Mr. W. W. Share, Assistant in Physics in Columbia College, who soon acquired more than usual skill in the control of his eyes for binocular experiments. In the dark room the stereoscope was first so arranged that parallelism between the two visual lines was necessitated, in obtaining binocular vision of the pair of pictures at the moment these were equally illuminated by the passing of a spark The plane of each card being perpendicularly across the support- ing arm of the reflector, the binocular resultant presented the appearance of a series of concentric circles on a flat surface. By rotating each card through a known angle on its vertical axis, the binocular resultant couid be made to assume at will the form of a convex or concave elliptic shield. The observer was seated with closed eyes in front of the stereoscope while the manipulator of the apparatus arranged the cards. The observer, not knowing whether this arrangement would pro- duce planeness, convexity, or concavity, was then invited to open his eyes and interpret the binocular retinal sensation attained by the illumination of the cards with a single spark. It was found possible, nearly always, to make a correct inter- pretation at the first trial. Mr. Share and the writer acted each alternately as observer and manipulator; and the result attained was confirmed by the experience of Professor Rood, who tried the same experiments independently. The distance and diameter of the circle on each card being known, and also the angle of rotation on its vertical axis, it becomes possible to calculate the maximum retinal displace- * Philosophical Magazine, Decemher 1881, 314 Mr. W. Le Conte Stevens’s Votes ment of images which would have corresponded retinally if the angle of rotation, ¢, were zero. The attention being spe- cially given to the centre of the binocular concave or convex resultant, the illusion of binocular unity and depth in the pic- ture remained possible when the retinal displacement cor- responding to marginal portions of the combined image was as great as ‘39 millim., or more than 80 times the diameter corresponding to what has been estimated to be the minimum visibile. By giving attention, through indirect vision, to the marginal portions, the illusion of binocular unity was easily destroyed, and double images at once became detectable. The result was confusion and loss of the third dimension in space at these marginal portions, while the perception remained clear for central portions where no duplication could be perceived. These effects were noticed by both Mr. Share and the writer. The pictures found best in these experiments were concen- tric circles consisting of broad black bands on a white ground, or of white bands on a black ground. Various other stereo- graphs were employed, many of them constructed for the pro- duction of stereoscopic relief, which could be reversed or totally suppressed by appropriate arrangement of the cards on the arms of the stereoscope. The peculiar nature of the relief, whether direct or reversed, was what the observer was re- quested to ascertain, and with satisfactory results, usually without delay. The most difficult case was that in which one picture consisted of a red diagram ona green ground, the other a green diagram of the same size on a red ground. A series of experiments, continued through many days, was tried under illumination with the electric spark, by Mr. Share and the writer jointly, to test still further the effect of mus- cular strain in modifying the unconscious interpretation of the binocular retinal image as discussed ina former papert. The optic angle was varied from 3° of divergence to 50° of con- vergence of visual lines, while the stereograph of the moon was again employed, being kept ata fixed distance on the arms of the stereoscope while the observer, under the abnor- mal conditions imposed, was requested to form an estimate of apparent distance and diameter. Hach acted as manipulator and recorder for the other, the observer being kept ignorant of his own record until the whole series of experiments was completed. The result was in each case quite similar to that formerly obtained with vision by continuous light; but the limit of error was much wider, showing that under such un- usual conditions no single visual judgment is worthy of any confidence. The general effect on each, however, was that * Philosophical Magazine, December 1881, on Physiological Optics. 315 strain of the internal rectus and ciliary muscles produces the illusion that the object perceived is smaller and nearer. The above is a mere statement of facts. Any discussion they may suggest is reserved for a future paragraph. The Binocular Union of Spectral Images. If a sharply defined object be momentarily illuminated by the intense light of the electric spark, a positive after-image - is perceived and quickly followed by a negative image of short duration. If the gaze be very steadily fixed upon one point of an object that is strongly illuminated by the direct rays of the sun, the eyes being at the same time protected from the glare proceeding from surrounding objects, a negative after- image is obtained that lasts several minutes. Since its exist- ence is due to fatigue of the retina in certain parts while others remain unfatigued, such an image appears always in the direc- tion of the visual line, changing in apparent position with every motion of the eye. The late Professor W. B. Rogers, of Boston, published in 1860* some experiments on the binocular union of after- images from illuminated lines so arranged as to produce the appearance of relief. Perspective after-images were likewise obtained by Wheatstone and by Wundt ; but an objection to conclusions drawn from such perceptions as these consists in the fact that the observer knows what effects would result in direct vision under the conditions imposed; indeed he simply retains a subjective perception of what he has just seen binocu- larly. It is difficult to determine how far the perception may be due to imagination rather than to immediate retinal sensa- tion. Professor Rogers succeeded in attaining perspective after-images even when the luminous lines were regarded suc- cessively instead of together; but thus far no one else seems to have confirmed this result; and the experiment is still liable to the objection that the visual judgment is warped by antici- pation and association. Hxperiments therefore have lately been made with a view to testing these results, and at the same time to ascertain whether any modification would be im- posed by varying the muscular conditions under which the spectral images are seen. 1. Across the median plane of vision was held a card with the upper edge more remote than the centre, so that a white band from top to bottom on a dark background was inclined about 40°. This was fixedly regarded with each eye sepa- * Proceedings of the American Association for the Advancement of Science, 1860, p. 187 et seg. 316 Mr. W. Le Conte Stevens’s Votes rately in succession, while held in direct sunlight, until both retinas were fatigued. On going then into aslightly darkened room, the inclined spectral image was easily perceived, appa- rently in mid-air, On making the visual lines parallel, it became projected on the wall, but without losing its obliquity. On strongly contracting the internal rectus muscles, it ap- peared still directly in front, but much smaller and nearer. The experiment was repeated many times, and varied, but with uniform results. 2. On separate cards a pair of diagrams were constructed in such a manner as to produce an image in relief when bin- ocularly viewed, in the stereoscope or otherwise. These were separately and successively regarded in sunlight, each with the appropriate eye. In the dark room the resultant after- image appeared in mid-air in clear relief. On shutting one eye, the component image that remained visible to the other was at once projected upon the wall as a flat picture. Strongly contracting the ciliary muscle of the eye remaining open, with- out sensibly contracting the rectus muscles, the picture was made to approach and grow apparently smaller, in almost as marked a degree as by the previous experiment. 3. A series of concentric black and white circular bands was constructed on a card, which was held in a vertical plane obliquely crossing the horizontal visual line of the left eye. After the retina had become fatigued, the same card was held across that of the right eye, but with opposite obliquity, so that the distortions of the elliptic images on the two retinas should be opposite in sense. Hach eye was closed while the other was receiving light from the card. The resultant spec- tral image was concave instead of plane, and presented the same variations with change of muscular conditions as in pre- vious experiments. 4, To ascertain whether these perspective stereoscopic effects were due to imagination and association, or whether they were the immediate outcome of retinal sensation, from the existence of dissimilar images remaining through fatigue in the two eyes, it was necessary to test some one whose eyes were normal, but who was ignorant regarding the nature of the visual effects to be produced, and who therefore could not be influenced by anticipation. It was found possible to enlist the interest of a youth of good general intelligence, who was entirely unac- quainted with even the elementary principles of binocular vision. He submitted to be trained until he could secure monocular after-images successfully with either eye at will. Without granting him the slightest clue by which results could be anticipated, the writer employed a pair of cards on on Physiological Optics. 317 which were diagrams so arranged that the binocular resultant could be made either a raised cone, a flat picture, or a hollow cone, according to the mode of combination selected. These cards were viewed in sunlight, never binocularly, but always separately and in succession, the relation between the pictures being varied in successive experiments. As soon as the retinas were fatigued, the observer was led into a perfectly dark room, and requested to describe the resultant spectral images per- ceived. Without allowing him ever to know whether his visual judgments were right or wrong, these experiments were repeated day after day, until the youth’s own conclusions were definitely formed by repeated interpretation of his retinal sensations. His judgments were in the majority of cases cor- rect, during the latter part of the time invariably so; and by spectral images alone he learned what should be the proper arrangement of pictures to produce a binocular resultant that was concave or convex at will. The cards with concentric circular bands were then substituted ; and in like manner he soon learned what kind of obliquity should be given the plane of each card in order to produce a concave or convex spectral binocular image immediately afterwards. His eyes were not sufficiently trained to enable him to test the effect of varying the tension in either ciliary or rectus muscles, nor was he able to perceive duplication in any part of any binocular spectral image. 5. A pair of diagrams were constructed in such manner as to show very plainly the binocular duplication of central parts in the background when the foreground was regarded and the gaze was monocularly directed to the centre of each in suc- cession, with the usual precautions. The spectral image pre- sented the appearance of relief. By an effort of special attention the duplication of the background became percep- tible; but at the same moment the appearance of relief was lost. Results from the Haperiments just described. These experiments, in conjunction with those made by the light of the electric spark, show that in the new mode of ste- reoscopy play of the eyes is by no means necessary, although it constitutes an important aid in all cases where a clear visual judgment is not attainable at the first glance. They show also very conclusively that the conscious perception of double images in the binocular field of view, on which so much stress was laid by Sir David Brewster”, far from being conducive to clearness of binocular perception, tends rather to interfere * Brewster, ‘The Stereoscope,’ p. 76 et seg. 318 Notes on Physiological Optics. with it. If it be said that we unconsciously perceive them and intuitively distinguish between the two kinds, homony- mous and heteronymous, this conclusion cannot be confirmed or disproven, except so far as experiments like those just detailed may be accepted as having some bearing upon the subject. The writer’s disposition is to discard intuition entirely, and, with Helmholtz*, to regard the degree of atten- tion bestowed upon objects pictured at the same moment on different parts of the two retinas as an element of more import- ance than either play of the eyes or the perception of double images. The point in the field of view to which most atten- tion is habitually given is that pictured upon corresponding — retinal parts; but the attention is at the same moment divided, being given in less degree to many other parts of the field of view as simultaneously perceived with each eye. The mental suggestion due to the impression of non-corresponding parts is that of the third dimension in space. If this be called the perception of double images, their effect seems to be dependent upon their not emerging into consciousness. Add to this the fact that the gradation between single and double vision is wholly imperceptible, and hence that for infinitesimal depar- tures from single vision there can be no demonstrable distine- tion between the two kinds of double images. In the inter- pretation of our sensations we are certain that experience is our habitual guide, though by no means always a reliable one. Whether intuition can be accepted as an additional guide at all, it is not easy to pronounce. The debate between the advocates of the empiristic and nativistic theories is doubtless like the well-known quarrel about a certain shield, and may be continued indefinitely. The domain of intuition is certainly far more limited than was thought a few generations ago ; whether it can be reduced to zero may perhaps be decided a few generations hence. In all ordinary cases of binocular vision the effect is cumulative. The judgment quickly reached is a product not only of difference in the degree of attention given at the same moment to objects seen by direct and by indirect vision respectively, but also of variation in attention to different points directly viewed in succession, of the mus- cular sense while free play is given to the eyes, and of all the elements available in monocular vision, which have been grouped together under the name of physical in contrast with physiological perspective. * Helmholtz, Optique Physiologique, p. 1009. weer chag XXXVI. Notices respecting New Books. A Treatise on the Transit Instrument as applied to the Determination of Time. For the use of Country Gentlemen. By Latimer CLARK, M.TI.C.E. §¢. (Published by the author, 6 Westminster Chambers, London.) 72 pages text, with 29 pages Transit Tables. = object of this little work is to popularize the use of the portable Transit for finding correct time among amateurs of small means. About half the work, describing the instrument and its use, is written in a thoroughly popular style, as free as is possible from technical terms. Simple modes of adjusting in position are given; and the instrument is supposed to be used only in correct position, so that no “corrections” have to be computed. This is an admirable mode of use for a beginner: some preliminary personal instruction would, however, be required; the detail given is not enough for a person quite unused to instruments. The second part is intended for more advanced amateurs. In this some astrono- mical terms and usages are explained, and the mode of computing the “corrections” to transits observed with an instrument not in perfect adjustment are fully entered into. The Tables (72 pages) contain the data for transits of the sun and certain stars for six months in a simple form very suitable for beginners ; they form an appendix to the text, and are to be pub- lished anew yearly, thus saving the need of mastering the Nautical Almanac (itself rather a formidable work). There is a misprint of 8° 46’ 28” for 88 46™ 28° on p. 42, which may confuse a beginner. The accounts of the Polestar on p. 26 and p. 48 do not agree: on p. 26 it is said that it “is very close to the North Pole, and revolves round it daily at a distance of about 13 degree ;” whilst on p. 48 it is said, ‘let us imagine ourselves at the North Pole. We should see the Polestar directly overhead remaining motionless.” On the whole, however, the work may be said to fulfil well the purpose for which it was written, and will help to supply an amateur’s wants. To meet the case of amateurs of small means, it is stated (in an advertisement) that an excellent portable transit with 14” telescope and 13” aperture can now be had for £8. ALLAN CunnineHamM, Major RE. Geology of Wisconsin. Survey of 1873-79. Vol. III. Large 8vo, 763 pages. With numerous Plates and other Illustrations, and an Atlas of Maps. Published under the Direction of the Chief Geologist [T. C. Chamberlin] by the Commissioners of Public Printing, in accordance with Legislative Enactment. { Madison. ] 1880. Votume II. of this excellent Survey, published in 1877, and noticed in this Journal for April 1880, p. 302, treated of the geo- logy of the eastern, central, and south-western portions of the State of Wisconsin. In the volume before us the extreme north- western and north-eastern portions of the State are described. The 520 Notices respecting New Books. former area is bordered by Lake Superior, between Minnesota and Michigan ; the latter, with a part of the iron district of Michigan annexed, is traversed by the Menoninee River and some of its affluents. Part I. of this volume consists of valuable observations by Pro- fessor Roland D. Irving on the “General Geology of the Lake- Superior Region,” which is estimated at 70,000 square miles in area, with strata, probably more than 100,000 feet in thickness, including four great unconformable systems; and the whole is coated with enormous deposits of glacial drift, besides lake-alluviums. I. The Laurentian. gneiss forms the crystalline nucleus of the region, and is continuous with that of Canada. With some associated and often gneissoid granite, these altered strata are greatly folded, and have a general southerly dip, with an EW. strike, and an enormous thickness. II. The Huronian rocks are 12,800 feet thick, and consist of (from below upwards) :—1. crystalline tremo- litic limestone and a partial quartzite, 130 feet; 2. quartz-schist, mica-schist, and some noyaculite, 410 feet; 3. tremolitic magnetite- schists and irony quartzites (Penokee fron Range), 780 feet; 4. black mica-slates, with diorite and schistose quartzites, &c., 3495 feet ; 5. dark-grey mica-schists, with intrusive granite, 7985 feet. The dip is northward, and the strike is oblique to that of underlying Lau- rentians. III. The Keweenawan or Copper-bearing series succeeds, seven miles in thickness, and consists of distinctly stratified igneous rocks like great flows and ash-beds. The lower rocks, from 10,000 to 30,000 feet, are almost wholly augite-plagioclase—namely, dia~ base, melaphyr, and gabbro (Rosenbusch). Shales, sandstones, and conglomerates then come in, and, becoming more and more frequent, nearly exclude the igneous rocks for the uppermost 15,000 feet of the series. IV. Lying on the eroded surface of the Keweenawan strata is a great horizontal set of sandstones, defined as the “ Lake- Superior Sandstone,” and regarded as equivalent to the Potsdam Sandstone of the Mississippi valley. In Part I. Professor Raphael Pumpelly gives the “ Lithology of the Keweenawan System,” specimens of which were sent to him, and represented Diabase, Melaphyr, Gabbro, Uralitie Gabbro, Uralitic Diabase, Augite-diorite, and Felsitic Porphyries. Part IIL., by Prof. R. D. Irving, describes the ‘‘ Geology of the Eastern Lake-Superior District” of Wisconsin, premising its Topo- graphy, with Altitudes, Drainage-system, Vegetation, and Soils. The lithology, stratification, and economics of each of the great systems are given in detail according to locality; also an account — of the Glacial Drift and Lacustrine Clays (Champlain Series). Part IV., by Mr. C. E. Wright, treats of the “ Huronian Series West of Penokee Gap.” The Penokee Iron Range is here espe- cially described, with the details of method of examination. The magnetic bands being covered by Drift, their breadth and extent were defined by the use of the solar dial-compass and the dipping needle, both of which are succinctly described. The iron-ores are, it seems, nearly all poor or “lean,” the good ore being probably high up in the series. Notices respecting New Books. 321 Part V., by Mr. E. T. Sweet, gives the topography, natural- history, geology, lithology, and economics of the ‘“‘ Western Lake- Superior District” of the State. Among the Quaternary deposits occur the Moraines and Pot-holes of the Kettle Range, similar to that of Eastern Wisconsin, described in the previous volume. In the Glacial Drift occur not unfrequently nuggets and boulders of native copper. Some of the granitic and gneissic boulders must haye crossed Lake Superior and travelled at least 200 miles. Part VI. consists of an account of the ‘Geology of the Upper Saint-Croix District,” based on the Notes of the late Mr. Moses Strong, edited by Mr. C. T. Chamberlin. It treats of the Surface- features, the Quaternary formations, and the Older formations, both generally and in detail. This area is inland and south of the “Western Lake-Superior District.” The Menominee Region, including parts of both Wisconsin and Michigan, is described geologically and lithologically in Parts VII. and VIII. by Major Thomas Benton Brooks and Mr. E. T. Street. This being an important iron-district, overrunning the boundary of the two contiguous States, and Wisconsin not supplying any money for the Survey beyond its own border, Major Brooks com- pleted the work at his own expense, and suffered serious illness also from his labours. Besides the Superficial Deposits of Drift &c., the country has:—1. The Caiciferous sand-rock and limestone and the Saint-Mary’s (Potsdam) sandstone, of the Lower Silurian; 2. None of the Copper-series; 3. The Upper-Huronian granite, gneiss, schists (hornblende, actinolite, mica, chlorite, and quartz), iron-ores, clay-slate, carbonaceous slate or graphitic shale, quartzite, and conglomerate. 4. Middle-Huronian clay-slate and quartzite. 5. Lower-Huronian dolomite, iron-ore, and quartzite. 6. Lauren- tian granite, gneiss, and crystalline schists. Three elaborate Tables of the rocks and their component minerals in the Menominee and Marquette Regions present a summary of the lithological characters of the several systems and series of rocks and of their relative abundance and stratigraphical order. The descriptive lithology of the Menominee rocks and of the Huronian rocks south of Lake Superior form two interesting chapters (Chapters 3 and 4) of Part VII.; and are followed by Dr. Arthur Wichmann’s microscopical investigations in the Huronian rocks, prefaced with a technical account of the minerals composing the said rocks. Besides this eminent lithologist of Leipsic, others have aided in the microscopical lithology of Wisconsin as treated in this volume, namely HE. Tornebohm, F. Zirkel, Herr Wapler, 8. Allport, Frank Rutley, G. J. Brush, J. D. Dana, G. W. Hawes, A. A. Julien, T. Sterry Hunt, Prof. R. Pumpelly, T. B. Brooks, and C. E. Wright. Nine coloured plates of microscopic sections of rocks occur in the volume, and enhance the value of the lithological descriptions. The lithographic and chromolithographic views, maps, and sections, illustrating the topography, geology, and mining, are numerous (44); there are also 23 woodcuts, chiefly sections of strata. Above all, the magnficent Atlas of Plates XVII. to XXX. inclusive, giving Phil. Mag. 8. 5. Vol. 14. No. 88. Oct. 1882. Vi 322 Intelligence and Miscellaneous Articles. many sections besides the coloured geological maps, is to be noticed as a most useful adjunct to this liberally published Report on the geological structure and capabilities of important parts of the great State of Wisconsin. The Life of Immanuel Kant. By J. H. W. Sruckenpere, D.D., late Professor in Wittenberg College, Ohio. London: Macmillan and Co. 1882. Tue work before us does not answer completely to its title. Our notion of a Life involves in its essence the being written chrono- logically. To put every thing in its proper place with respect to time may be difficult in the case of a philosopher who flourished one hundred years ago and whose life was remarkably uniform ; but the task so accomplished would be more interesting to the general reader and more valuable toa philosopher. For example, at the end of Chap. XI. we are landed in the “return” to Kant’s philosophy, while in Chap. XIII. we are led back to consider the old age and death of the philosopher himself. Our author is in consequence apt to fall into redundancy, a danger of which he is himself conscious ; for he says at the beginning of Chap. XII., devoted to Correspond- ence and Correspondents, “ Kant’s letters have already been so extensively used in this biography, that little more need be said of them.” In all other respects the workmanship of the volume seems to us most praiseworthy. Our author in his Preface says, “If Kant’s works throw light on his life, it will also be found that his life aids materially in understanding his works.” In the thirteen following chapters he aims at giving all the data which can by any possibility throw light on the views of the philosopher—scientific, moral, and religious. There are data given, however, which one would think cannot throw much light; for example, an account given of his method of retiring (p. 435), the nature of which may be inferred from the following specimen : :—‘‘ In summer one, in winter two nightcaps were worn.’ With this book before him, the sciéntific man will be able to appreciate the qualifications, natural and acquired, which Kant brought to the task undertaken in the ‘ Critique of Pure Reason.’ XXXVII. Lntelligence and Miscellaneous Articles. CONSERVATION OF SOLAR ENERGY. BY PLINY EARLE CHASE, LL.D.* LL forms of solar energy are due to solar radiation. The main-~— tenance of the energy depends on the maintenance of the radiations. In investigating the relations of centripetal and centri- fugal action and reaction, it seems desirable to consider the following — hypotheses and conclusions :— * Abstract of a Paper read before the Americau Association at —_ ' treal, August 25, 1882, Communicated by the Author. Intelligence and Miscellaneous Articles. 523 1. Laplace’s estimate that the velocity of transmission, in gravi- tating acceleration, if finite, must be at least 100,000,¢ 100 times as creat as the velocity of light. 2. Le Sage’s hypothesis that gravitation and luminous radiation represent equal actions and reactions. 3. Faraday’s search for a gravitating constant. 4, Herschel’s comparison of the mean vis viva of light with that of sound. 5. Weber’s identification of the velocity of light (v,) with the “ electromagnetic ratio” (v,). 6. Berthelot’s “explosive waves,” and their action upon sound- waves. 7. The inquiries of Siemens into the combined influence of rota- tion, centrifugal action, gravitating fall, and chemical affinity. a these considerations the following may be added :— . Lf there is a natural unit of force, we may look for a natural his of velocity. 9. Oscillations may be orbital, pendulous, or wave. 10. Different transformations of similar oscillations are harmonic. 11. Rotation may be regarded as a pendulous motion, due to retarded and modified revolution. 12. The resemblance of Le Sage’s theory to the kinetic theory of gases points to a probability that the natural unit of velocity is oscillatory. This probability is strengthened if we assume the ex- istence ot molecular and intermolecular elasticity. 13. In looking to the activities of the principal mass in our system for indications of a natural unit of velocity, we find that erayitating velocities may be represented by gt. 14. In order that gi may be constant, ¢ must vary inversely as g, and therefore directly as r*. This variation is found in the rotation of a nebulous sphere, where it holds good for all stages of expansion or contraction which are not affected by external influence. 15. Gravitating acceleration should do its whole work in stellar rotation as well as in planetary revolution. 16. Particles exposed to solar superficial gravitating acceleration, during a single oscillation of half-rotation, would acquire a velocity which is equivalent to the velocity of light. If we designate this acquired velocity by v,, we have v,=gt=v, as a gravitating con- stant, which gives the following extension to Weber’s analogy: V,=vU.=vy. In other words, the unit of velocity which is indicated by solar gravitation is the same as is indicated by light and by electricity. 17. The velocity of light, like the velocity of sound, thus repre- sents an elastic atmosphere whose height, if homogeneous, would be twice the virtual fall which would give the velocity in question, and whose elasticity is in harmonic accordance with solar rotation and planetary revolution. 18. Subsidence, from Laplace’s limit of synchronous rotation and revolution to the poles, gives a mechanical equivalent of 76,000,000 J for each pound of subsiding matter. The spiral character of the 524 Intelligence and Miscellaneous Articles. subsidence produces solenoidal currents, which may help to explain the equality of v,, v., and v,. ON THE APPEARANCES OF THE ELECTRIC ARC IN THE VAPOUR OF BISULPHIDE OF CARBON. BY M. JAMIN, WITH THE ASSISTANCE OF M, G. MANEUVRIER. ; At the meeting of the 19th June I made known to the Academy the modifications undergone by the electrie are in the vacuum of an air-pump when the arc is produced by a Gramme machine with alternating currents of high tension. I soon perceived that the appearances are modified if gases or vapours are introduced into the glass vessel in which the experiment is made. In the vapour of bisulphide of carbon they are very remarkable. The burner is formed by two parallel vertical carbons fixed at their bases; the upper extremities, which face each other, can by a simple mechanisin be joined or separated. The apparatus is placed under a large receiver of an air-pump, in which a vacuum as com- plete as possible is produced. It is known that then the arc is not — formed ; it is replaced by the gleams of a Geissler tube; but when a few drops of bisulphide of carbon are introduced, so as to obtain an increase of pressure of 5 or 6 centim., the arc is seen to kindle between the points when they touch, and to persist after they are separated. At that moment there is as it were an explosion of light, so vivid as to be insupportable, incomparably superior to the usual bright- ness of the arc. On looking at it through a dark-coloured glass, one sees a brilliant arc 5 or 6 centim. in height, resembling a horse- shoe or a capital omega. The two extremities are at the two carbon points. Besides this a long flame is seen like that of a hearth, which overhangs the arc, escapes from it, and ascends yer- tically. The points of the carbons appear red and very brilliant; but the arc is pale green; and as its light dominates that of the carbons, the whole room is illuminated with that tint, as it would be by a Bengal light with copper. The brightness increases with the increase of tension of the vapour, until it becomes intolerable; but as the resistance of the medium is augmented at the same time, the arc often goes out, and it is necessary to relight it every moment by joining the two carbons. Examined with the spectroscope this light presents all the lines of carburetted gases in combustion, but more complete and sharper. They are those described by M. Thollon at the meeting on August 1, 1881. The spectrum is very discontinuous. At its red end a grooved region was seen—first a very bright line followed by several others thinner and close, then a broader line a repetition of the first and likewise followed by fine lines; these appearances were repeated in going towards the orange, but growing weaker till they _ disappeared. After a dark interval the same appearances were seen again in the yellow and the beginning of the green; then there Intelligence and Miscellaneous Articles. 325 was a dark interval, then the repetition of the same effects in the green, and finally in the violet. In brief, the spectrum is composed of four grooved portions, in the red, yellow, green, and violet, so identical that they might be taken, except the colouring, for one and the same design which had travelled from the red to the violet. It is quite probable that they obey one and the same harmonic law, which remains to be discovered. Of these four regions the green is the most luminous; it is that which gives the special tint taken by the are and colouring all objects green. During the manifestation of these appearances a chemical action takes place. If any air has been left in the receiver, or if the appa- ratus is not quite closed, the bisulphide of carbon undergoes incom- plete combustion, a mist of sulphur fills the space and is deposited on the sides; the carbon burns alone. If the air has been well purified, the mist does not form; a brown deposit settles on the sides, becomes black, sticks to the glass, and tarnishes it. This deposit is volatile; its odour reminds one of that of sulphur. It is evidently a compound of sulphur and carbon, perhaps a protosulphide corresponding to the oxide of carbon, perhaps an isomeric modification of the ordinary sulphide. In fact, neither a deposit of sulphur nor one of carbon is seen, and the carbons of the burner have neither lost nor gained any thing. It is probable that the bisulphide of carbon is dissociated, the sulphur volatilized, the carbon in vapour disseminated in the arc, and that this carbon and this sulphur recombine in the flame to reconstitute a combination under different conditions. But this is only a conjecture, no ana- lysis having yet been made. To recapitulate, this experiment is remarkable for the extraordi- nary quantity of light produced, the magnitude of the are, its colour, the composition of its spectrum, and the chemical actions which take place. It is not likely that it can ever be turned to account for lighting, on account of its colour, unless perhaps for light-houses or distant signals.—Comptes Rendus de UV Académie des Sciences, July 3, 1882, t. xcv. pp. 6, 7. ON THE ELECTRIC RESISTANCE OF GLASS AT LOW TEMPERATURES. BY G. FOUSSEREAU. The method employed consists in passing the electricity supplied by a Volta’s pile of from 1 to 100 elements across a reaction-tube of 1-2 centim. diameter and very regular thickness, closed at one end. The electricity is collected in a condenser of known capacity, the two armatures of which are connected with the two mercuries of a Lippmann electrometer of measured capacity. The time ne- cessary for communicating to the mercurial column of the electro- meter a displacement corresponding to a determined difference of potential is observed. : The reaction-tube dips into a wider test-tube; and its two faces 326 Intelligence and Miscellaneous Articles. are bathed, up to a known height, by two conducting masses of concentrated sulphuric acid, into which dip some platinum wires carefully insulated from the sides above the level of the liquid. This apparatus is surrounded by a glass “ muff,” the air of which is dried by sulphuric acid before commencing the experiments. In order to obtain a uniform and slowly variable temperature, the base of the apparatus is inserted, up to a level considerably above that of the acid, in an oil-bath, which is itself surrounded by a sand-bath which can be heated progressively. or the sand-bath a refrigerating mixture can be substituted. The observations were extended to —17° C. If E designates the electromotive force of the pile, p, and p, the internal and external radii of the tube, / the height of the liquid, 7 the specific resistance of glass per cubic centimetre, C the sum of the capacities of the condenser and electrometer, and e the differ- ence of potential communicated to the electrometer (always very small in proportion to E), we have, expressing that the quantity of electricity transmitted through the glass in the time @ has been employed in charging the condenser, jm _2chE x @. Celogn 2 Pr Several experiments, made with different heights of sulphuric acid, permit the elimination of the influence of the bottom of the tube, the thickness of which is not the same as that of the sides. At the instant of the completion of the circuit the glass tube is at first charged like a condenser. Its interior layers afterwards gradually absorb a certain charge of electricity, necessary for bring- ing them into the definitive state corresponding to the fall of poten- tial established between the surfaces. During this variable state, more or less prolonged according to the nature of the glass, the effects of the charge of the glass are superposed to those of the conductivity. The observations are commenced when the time occupied in charging the glass has assumed a constant value. I have also observed that rapid heating determines an apparent increase of conductivity greater than the normal increase; in like manner a rapid lowering of the temperature gives rise to an exag- gerated resistance: but these phenomena quickly disappear, to give place to the normal resistance; and they are not again produced when the variations of temperature are slow *. My observations have hitherto been made on three kinds of glass —common glass (with a base of soda and lime), Bohemian glass, and crystal. In all three, raising the temperature produces a rapid increase of conductivity ; the resistance can be expressed by exponential func- * These phenomena appear to be due to variations in the dielectric power of glass under the influence of temperature, Intelligence and Miscellaneous Articles. 327 tions of the form log x=a—bt+ct’. (1) For common glass, of density 2°539, expressing the resist- ances per cubic centim. in millions of megohms, we get the following results :— Temperatures. Resistances. =EiGHEs re Die Ny os Suan Wek. £4). 0°705 shit tits Acie. AEC al ats te 91:0 1 ae PSE Pee arses ee 7970-0 In order to form an idea of the magnitude of this last resistance, it may be remarked that it represents nearly twice the resistance of a copper wire, of 1 square millim. section, reaching from the earth to Sirius. The whole of the results obtained upon common glass are ex- pressed by the formula log #=3'00507 — 0052664 x ¢+0:00000373 x f°... The term of the second order being very small, the values of logw are represented by a line which differs but little from a straight line. The resistance varies nearly 4 of its value for each degree of temperature. (2) Bohemian glass of density 2°431, upon which I worked, has from 10 to 15 times the conductivity of common glass at the same temperatures. Its resistance is given by the formula log e=1°78300—0°049530 x ¢4+ 0-0000711 x #. (8) The crystal tried has for its density 2-933; and it, contrary to Bohemian glass, has from 1000 to 1500 times the insulating- power of ordinary glass at the same temperatures. Its conductivity only begins to be manifest at above 40°. At 40°-2 its resistance is equal to...... 6182 At 105° - S50 Mt ish tere oe 11°6 The results are represented by the formula log 4 = 7-22370—0:088014 x t+ 0:00028072 x ¢*. —Oomptes Rendus de? Académie des Scrences, July 31, 1882, t. xev. pp. 216-818. ON THE SURFACE-TENSION OF SOME LIQUIDS IN CONTACT WITH CARBONIC ACID}. NOTE BY S. WROBLEWSEIf. Tf instead of water we take a liquid which mixes in all propor- tions with liquid carbonic acid—for instance, alcohol, essential oil * The experiments were made in M. Jamin’s laboratory at the Sor- bonne. + Abstract by the Author. { See the preceding Note, Phil. Mag. Sept. 1882, p. 236. 328 Intelligence and Miscellaneous Articles. of turpentine, ether, chloroform—the phenomena assume the fol- lowing form :— : The surface-tension also diminishes with the increase of the pressure under which the gas is placed; the velocity of the dimi- nution is also much greater at a low than at a higher temperature ; but the surface-tension, instead of stopping at a minimum which would be something characteristic of the liquid, falls rapidly; and at 0° C., under the pressure at which carbonic acid is liquefied, all the liquids above mentioned, without distinction, have the aie yne centimetre” But can they in this state be regarded as the same liquids? Not atall. Let us take water as anexample. When it is saturated with carbonic acid under the pressure of one atmosphere only, has it the properties of pure water? It has a different density, a different coefficient of expansion by heat; even the temperature of its maximum density is changed. The changes which take place in the liquids mentioned are much more considerable: we need only observe what takes place with ether when it absorbs carbonic acid under pressure. Its volume increases with such rapidity that, although my method enables me to measure the surface-tension of a liquid in a much shorter time than a minute, it is almost impos- sible to take exact measurements in this case. It follows from all these facts that the phenomena described in these Notes have absolutely nothing to do with pressure. The diminution of the surface-tension of the liquids depends solely on the circumstance that the surface-tension of carbonic acid, with which they are compressed, is parr slight. While the surface- yne centimetre other liquids examined, with the exception of ether, lie between 32 ~ dyne : a ee, 3 .@ dyne and 25 ge the tension of carbonic acid is only 4-6 ae Capillary phenomena depend only on the molecular forces acting at the surface of the liquid. Therefore it is not surprising that the presence of a body which possesses so feeble a tension among the particles of the liquid of which that surface-layer is composed exerts an influence upon the resultant of all those forces—that is to say, upon the surface-tension. The same mode of reasoning applies to the case of a liquid being compressed with a much less liquefiable gas than carbonic acid— such as oxygen, nitrogen, or hydrogen; for the more difficult it is to liquefy those gases the less must be their surface-tension. The effect of the compression will depend only on the value of that ten- sion and on that of the solubility of the gas.—Comptes Rendus de PAcadémie des Sciences, August 14, 1882, t. xcv. pp. 342, 343. ‘tension of carbonic acid—that is, a tension equal to 4-6 tension of water is equal to 80 nearly, and those of the 4 THE LONDON, EDINBURGH, ano DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIBS.] NOVEMBER 1882. XXXVIII. Comparison of Methods for the Determination of Resistances in Absolute Measure. By Lorp RAYLEIGH, F.RS., Professor of Experimental Physics in the University of Cambridge*. pA. the present time, and in view of the projected confer- ence at Paris, the subject of the present paper is enga- ging a large share of attention; and Prof. G. Wiedemann { has published an interesting discussion of some of the methods that have been employed. Ihave thought it might be of ser- vice if I also were to place upon record the views that I have been led to entertain, and which are the result of a good deal of experience. Resistance being of the dimensions of velocity, its absolute measurement involves the absolute measurement of a length and of atime. ‘The latter is usually the time of a vibration of a suspended magnet, and can be determined without much difficulty. In the B.A. method it is the time of rotation of the revolving coil, and can be obtained with all desirable accu- racy. In this respect there is not much to choose between one method and another; but when we come to consider the man- ner in which the linear measurement enters, important differ- ences reveal themselves. These will be discussed in detail presently; but for the moment it will be sufficient to say that * Communicated by the Author. + “ Ueber die bisherigen Methoden zur Feststellung des Ohm.” Se- paratabdruck aus der Electrotechnischen Zeitschrift, July 1882. [Phil. Mag. for October, p. 258. ] Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. Z 330 = Lord Rayleigh’s Comparison of Methods for the the presumption is in favour of any method which requires only a single linear measurement. It is true that this ques- tion cannot be decided without regard to the subject of the measurement; but, with scarcely an exception, it is necessary to know the mean radius of a coil of several layers of insulated wire. This is apparently the measurement which fixes the limit of final accuracy; and, in comparison with it, determi- nations of the distances of mirrors and scales &e. are of secondary difficulty. It will be convenient now to enumerate the principal methods which have been proposed for determining absolute resistances. Minor details, which are not likely to influence the final value of the results, will in general be passed over. I. Kirchhoft’s Method, Maxwell’s Electricity and Magnetism, § 759. The magnitude of a continuous battery-current in a pri- mary coil-is compared with that of the transient current induced in a secondary coil when the primary circuit is re- moved. Rowland* effected an important improvement by simply reversing the battery-current without motion of the primary coil. The time of vibration of the ballistic galvano- meter employed for the transient current is the principal time- measurement. In Rowland’s investigation a second galvano- meter was employed for the battery-current, and the ratio of constants had to be found by auxiliary experiments. In Glaze~ brook’st recent determination by this method only one galva- nometer was used, the battery-current being reduced in a known manner by shunting. It is shown that the evaluation of the resistance-ratios presents no serious difficulty. Let / denote the ratio in which the primary current is re- duced when it produces a deflection « upon the galvanometer, @ the throw from rest due to the induction-current when the battery is reversed, T the time of vibration of the needle mea- sured from rest to rest, M the coefficient of induction; then the resistance of the secondary circuit in absolute measure is given by _mtanaM _ , TO emee Whenever, as in this method, the conductor whose resistance in absolute measure is first determined is composed of copper, frequent comparisons are necessary with standards of German silver or platinum-silver. Otherwise a variation of tempera- ture of about ¢ of a degree Cent., which can hardly be detected * American Journal, xy. 1878. + Proc. Roy. Soc. June 1882. Determination of Resistances in Absolute Measure. 331 with certainty by thermometers, would influence the result by as much as one part in a thousand. If it be granted that the comparison of currents and the reference to the standard of resistance can be effected satis- factorily, we have only to consider the amount of error involved in the determination of M, the coefficient of mutual induction between the two circuits, which is the fundamental linear measurement. If the two coils are of very nearly the same size, it appears from symmetry that the result is practically a function of the mean of the mean radii only, and not of the two mean radii separately. It is also of course a function of the distance between the mean planes 6. Leaving out of con- sideration the small corrections necessary for the finite size of the sections, we consider M as equal to 474/ Aa multiplied by the function of y, given in tables appended to the second edition of Maxwell’s ‘ Electricity,’ where 2/ Aa J Atar rey or, if we identify A and a with their mean (Ag), sin y= tan y= ze The error in M will depend upon the errors committed in the estimates of A,and 0. If we write dM dAy db > Sh, sed a Aaa then, since M is linear, A+p= +1. Thus, if 6 were great relatively to Ag, A=4, p=—3, a very unfavourable arrangement, even if it did not involve a great loss of sensitiveness. The object must be so to arrange matters that the errors in A, and 6 do not multiply themselves unnecessarily in M. But since pw is always negative, \ must inevitably be greater than unity. The other extreme case, in which 0 is very small relatively to A,, may also be considered independently of the general tables; for we may then take approximately (Maxwell’s ‘ Hlec- tricity,’ § 705) 8A M=4rA, log] ot 2 , whence 1 te ~ Tog (8A,/B) —2” Z2 332 Lord Rayleigh’s Comparison of Methods for the showing that as b diminishes ~ approaches zero, and accord= ingly \ approaches unity, as is indeed otherwise evident. But when 0 is small, it is the absolute error db which we must regard as given rather than the relative error db/b; and thus we are directed to stop at a moderate value of b, even if the in- creased correction necessary for the size of the section were not an argument in the same direction. The following intermediate cases, calculated by the tables, will give an idea of the actual conditions suitable for a deter- mination by this method:— y: b/2A,. A. [ M. 60 ‘577 9:61. |-t-6i 316 70 364 2-18 | —1-18 597 75 -268 1:98 | — -98 +829 80 176 1-76 | — -76 | sae We may say that the error in the distance of mean planes will reproduce itself something like proportionally in the final result, and that the error of mean radius will be doubled. Any uncertainty in the actual position of the mean planes relatively to the rings on which the wire is wound may be eliminated, as Glazebrook has shown, by reversing the rings relatively to the distance-pieces. This method is subject to whatever uncertainty attaches to the use of a ballistic galvanometer*. In its favour it may be said that the apparatus and adjustments are simple, and that no measurements of distances between mirrors and scales is necessary for the principal elements. It should be noticed also that the error due to faulty determination of the distance of mean planes can be eliminated in great measure by varying this quantity, which can be done over a considerable range without much difficulty or expense. With reference to the capabilities of the method for giving results of the highest accuracy when carried out in the most ambitious manner, it is important to consider the effect of in- creasing the size of the coils. The coils used by Glazebrook have a mean radius of about 26 centim.; the axial and radial breadths of the section are each about 2 centim. If we sup- pose the mean radius and the sides of the section to be doubled, the number of turns (about 800) remaining unaltered, the sensitiveness would be increased both by the doubling of M and by the diminished resistances of the coils, while at the * See Phil. Trans. 1882, p. 669. eae yw? ~ = Determination of Resistances in Absolute Measure. 333 same time the subjects of the linear measurements would be of more favourable magnitudes. To enhance the latter advan- tage, it would probably be an improvement to diminish the radial breadth of the section, on which much of the uncertainty of mean radius depends. In either case it is clear that the limit of accuracy obtainable by this method has not yet been reached. Il. Weber’s Method by Transient Currents, Maxwell § 760. “A coil of considerable size is mounted on an axle so as to be capable of revolving about a vertical diameter. The wire of this coil is connected with that of a tangent-galvanometer so as to form a single circuit. Let the resistance of this circuit be R. Let the large coil be placed with its positive face perpendicular to the magnetic meridian, and let it be quickly turned round half a revolution. There will be an induced current due to the earth’s magnetic force; and the total quantity of electricity in this current in electro-magnetic measure will be o= eu where g, is the magnetic moment of the coil for unit current, which in the case of a large coil may be determined directly by measuring the dimensions. of the coil and calculating the sum of the areas of its windings; His the horizontal compo- nent of terrestrial magnetism; and R is the resistance of the circuit formed by the coil and galvanometer together. This current sets the magnet of the galvanometer in motion.” “‘ If the magnet is. originally at rest, and if the motion of. the coil occupies but a small fraction of the time of a vibra= tion of the magnet, then, if we neglect the resistance to the, motion of the magnet, we have, by § 748,, soy 2 ell Ges where G is the constant of the galvanometer, T is the time of* vibration of the magnet, and @ is the observed elongation. From these equations we obtain R Sem IL 2 sin: 48, =7Gq Tango The value of H does not appear in this result, provided it is the same at the’ position of the coil and at that of the galva- nometer. This should not be assumed to be the case, but should be tested by comparing the time of vibration of the 334 Lord Rayleigh’s Comparison of Methods for the ¢ same magnet, first at one of these places, and then at the other.” If a be the mean radius of the coil of the inductor and A that of the galvanometer, we may write, neglecting the cor- rections for the finite sizes of the sections, =a" = I= bf A s so that — 2 a gG=2n"-- This is the linear quantity of the method. With respect to the chances of error in determining it, we see that the error of the mean radius of the inductor enters doubly, and that of the mean radius of the galvanometer enters singly. Probably in this respect there is not much to choose between this method and the use in method I. of the same coils placed at a mode- rate distance apart. A colossal apparatus for the use of the present method has been constructed and tested by MM. W. Weber and F. Zollner*, the coils of which are as much as 1 metre in diameter. The principal difficulty arises in connexion with the galyanometer- magnet. Two magnets were used whose lengths were respec- tively 200 millim. and 100 millim.; and the results obtained in the two cases differed by as much as 2 per cent. The dis- crepancy is doubtless due to the influence of the finite length of the magnets causing the magnetic poles to be sensibly dis- tant from the centre of the coil, for which point the effects are calculated ; and the disturbance will be proportional to the square of the distance between the poles, or more properly to the “ radius of gyration” of the ideal magnetic matter about the axis of rotation. But to assume that the disturbance from this source was exactly four times as great in the one case as in the other, and thence to deduce the result corresponding to an infinitely short magnet, appears to me to be a procedure scarcely consistent with the degree of accuracy aimed at. If this method is to give results capable of competing with those obtainable in other ways, it will be necessary to use a much shorter magnet; or, if that is not practicable, to devise some method by which the distance of the poles can be determined and a suitable correction calculated. In carrying out the observations in the usual manner, it is necessary to measure the distance between a mirror and a scale. By using a double mirror with two scales and tele- scopes, MM. Weber and Zéllner avoid the principal cause of * Ber. d. Kon. Sachs, Ges, zu Leipzig, 1880, ii. p. 77. o Determination of Resistances in Absolute Measure. 385 difficulty, 7. e. the unsteadiness of the suspended mirror, all that is then necessary to know with accuracy being the dis- tance between the two scales. In using this and the three following methods great pains must be taken with the levelling of the earth inductor, since the deviation of the axis of rotation from the vertical (at least in the plane of the meridian) gives rise to an error of the first order with (in these latitudes) a high coefficient. In this respect it would be a decided advantage to carry out the experiments in a locality nearer to the magnetic equator (see “Account of Experiments to determine the value of the B.A. Unit in Absolute Measure,” Phil. Trans. for 1882, p. 684). It is to be hoped that the measurements commenced by Weber and Zéllner will be carried to a successful issue, as it is only by the coincidence of results obtained by various methods that the question can be satisfactorily settled. At present no value in absolute measure of the B.A. unit or of the Siemens unit has been published as the result of their work. Ill. Method of Revolving Coil. This method, first, it would appear, suggested by Weber, was carried into execution by the celebrated Hlectrical Com- mittee of the British Association*, and more recently by myself with the assistance of Dr. Schuster and others+. The greater part of what I have to say upon this subject has been put forward already in the papers referred to, from which alone the reader can form a complete opinion on the merits or demerits of the method as hitherto practised. On the pre- sent occasion I must take many of the conclusions there arrived at for granted, or at most give a mere indication of the nature of the arguments by which they may be supported. Method III. differs from II. mainly in the fact that in III. the earth-inductor is, so to speak, its own galvanometer, the needle whose deflections measure the currents being suspended at the centre of the revolving coil itself instead of at the centre of another galvanometer-coil forming part of the same circuit. If, asin Il., the inductor-coil were simply twisted through 180° when the needle passes its position of equilibrium, the disadvantages of the simplification would probably prepon- derate over the advantages. The diminution of effect due to the oblique position of the coil relatively to the needle (except at the moment of passing the magnetic meridian) would indeed be compensated by the diminished resistance of the complete circuit, and, as will presently appear, considerable advantage * Brit. Assoc. Reports, 1862-1867. Reprint, Spon, 1873. + Proc, Roy. Soc, May 1881, Feb. 1882; Phil. Trans. 1882. 336 Lord Rayleigh’s Comparison of Methods for the would arise in respect of errors in the measurement of the coil ;_ but an almost fatal uncertainty would be introduced from the influence of self-induction. : The important advantage of III., obtained, as I believe, without any really important sacrifice, arises only when the inductor is set into uniform rotation. In IL., if the connexions were maintained without a commutator, the current in the galvanometer-coil would be alternating, and therefore unsuit- able for measurement with a magnetic needle; but in IIL, although the current in the coil itself alternates, the reversal of the coil relatively to the needle causes all the impulses to operate finally in the same direction. When, therefore, the coil is caused to revolve in a periodic time small relatively to that of the free vibration of the needle, a steady deflection is obtained which varies inversely with the absolute resistance of the coil. 3 If we omit for the moment all secondary considerations, although some of them may not be without importance, the formula by which the resistance (R) of the revolving circuit is given in terms of the mean radius (a), the number of turns (7), the angular velocity of rotation (w), and the angle of deflection (¢), runs R=77°n’ao cot $; from which it appears that, in respect of errors arising from the measurements of the coil, this method is much superior to those hitherto discussed. There is only one linear quantity concerned; and the error committed in its determination enters but singly into the final result. Indeed we may say that in this respect no improvement is possible, unless it be in the direction of substituting for the mean radius of a coil of several layers some other kind of linear quantity more easy to deal with. In requiring the absolute measurement of angle, II. and III. stand precisely upon a level. The time of vibration in the experiments of MM. Weber and Zéllner was 17 seconds or 80 seconds—none too long relatively to the time (2 seconds) occupied in turning the inductor. If we suppose the coil to be uniformly rotated at the rate of, say, 2 revolutions per second, there would be 68 or 120 impulses upon the needle in the time of 1 vibration. It would no doubt be a great exaggeration to represent the increase of sensitiveness as being in any thing like this pro- portion, since by the method of recoil it is possible to make several observations of impulses during the time required for one observation of steady deflection. Nevertheless it cannot * Determination of Resistances in Absolute Measure. 337 be doubted that the advantage of III. in respect of sensitive- ness is very considerable. Hxperience has shown that there is no difficulty in controlling and measuring the rotation of the coil; but of course some auxiliary apparatus is required for the purpose. Against this may be set the escape from observations of the time of vibra- tion, and from any uncertainty which may attach to the bal- listic use of a galvanometer-needle. The suspended magnet may easily be made of such dimensions that no appreciable error can arise from supposing it to be infinitely small. On the other hand, some new complications enter in method III. which I desire to state in full. In the first place we have to take account of the fact that the inductor moves in a field of force due not only to the earth, but also to the suspended magnet itself. Ido not think that the correction thus ren- dered necessary (about 4 parts per thousand in my experi- ments) adds in any appreciable degree to the uncertainty of the final result; but we may take note of the fact that an auxiliary determination must be made of the ratio of the mag- netic moment of the suspended magnet to the earth’s hori- zontal force. If the metal ring on which the wire is wound be ona large scale and sufficiently massive for strength, currents may be developed in it, even although it is divided into two parts by ebonite insulation. In my experiments the effect of these currents was very sensible, and had to be allowed for by careful observations of the deflection produced when the ring was rotated with wire circuit open. In any future repetition it will be worthy of consideration whether the ring should not be formed of less conducting material. It does not appear, however, that the final result can be prejudicially influenced ; and the effect produced by secondary closed circuits allows us to verify the insulation of contiguous layers or turns of the wire by comparing the deflections obtained before the wire is wound with those obtained after winding, but with main cir- cuit open, any difference being due to leakage. But the most serious complication in method III., and one which in the eyes of some good judges weighs strongly against it, is the disturbing influence of self-induction. With respect to this, the first point to be noticed is that the action is per- fectly regular, and that the only question which arises is whether.its magnitude can be determined with such accuracy that the final result does not suffer. Now the operation of self-induction is readily submitted to calculation if a certain coefficient (L) be known. We find R=a'n’aw cot d{1—U tan’ ¢—U? tan* $}, 338 Lord Rayleigh’s Comparison of Methods for the where U is a numerical quantity dependent upon L, so that the influence of self-induction is approximately proportional to the square of the speed of rotation. The same law applies also to any disturbances depending upon mutual induction between the wire circuit and subordinate circuits in the ring. It will be seen that, if the law of squares may be depended upon, the influence of self-induction (and mutual induction) can be satisfactorily eliminated by combining observations taken at different speeds. In my experiments four speeds were used, of which the greatest and the least were in the ratio of 2:1. The effect of self-induction was therefore four times as great at the high speed as at the low speed. In other words, the quantity (about 1 per cent.) by which the low-speed result is to be corrected in order to eliminate the influence of self- induction is only one third of the discrepancy between the uncorrected results of the extreme speeds. If, therefore, the observations are good for any thing at all, they are good enough to determine this correction with all desirable preci- sion. If a check be considered necessary, it is supplied by the results of the intermediate speeds. . The above reasoning proceeds upon the supposition that we have no independent knowledge of the magnitude of the coeffi- cient U. In point of fact, this coefficient can be calculated with considerable accuracy from the data of construction, so that the empirical correction is applied only to a small outstand- ing residue. In considering the disadvantageous influence of self-induc- tion as an argument in favour of II. as against ILL, we must remember that the magnitude of the influence can be greatly attenuated by simply diminishing the speed of rotation. At half the lowest speed above spoken of, for which the correction for self-induction would be reduced to + per cent., the deflee- tion (over 100 millim. at a distance of 2670 millim.) would probably correspond to a much greater sensitiveness than it is possible to obtain under II. Ifwe prefer the higher speed, it is because we estimate the advantage of doubled sensitive- ness as outweighing the disadvantage of a fourfold correction for self-induction. The fourth objection which may be taken to this method, and it is one from which II. is free, lies in the necessary crea- tion of mechanical disturbance in the neighbourhood of the suspended magnet. How far these complications may be supposed to prejudice the result of carefully conducted experiments must be left to the estimation of the reader of my paper, in which yery full data fora judgment are given. My own opinionis, that while Determination of Resistances in Absolute Measure. 339 in the aggregate they must be allowed to have some weight, they are far from preponderating over the advantages which the method possesses in comparison with II. If we take the view that the method itself is trustworthy, the principal error will arise in connexion with the mean radius of the coil; and it becomes an interesting question to consider whether advantage may be expected from a further increase in the dimensions of the apparatus. For this purpose we may regard tang as given. The total resistance R will be proportional to n’a/S, where 8 denotes the aggregate section of the copper, from which it follows that oS may be regarded as given, while a is left undetermined by the consideration of sensitiveness. Thus, if we retain w and 8 unaltered in a mag- nified apparatus, we shall have the same sensitiveness as before, while the increased diameter of the coil and the relatively de- creased dimensions of the section will conduce to amore accu- rate determination of the mean radius. The angular deflection being given, the correction for self- induction is nearly constant whatever may be the proportions of the coil. If we are of opinion that there is danger in the operation of self-induction, the case becomes strong for the introduction of a second coil ina plane perpendicular to that of the first*. By this means the relative correction for self-induction would be reduced to one quarter, while the deflection remained unaltered. It searcely needs to be remarked that this use of a second coil would not, as in II., increase the uncertainty depending upon the linear measurements, the two mean radii entering into the result as parts, and not as factors. : This combination would lend itself especially well to low speeds of rotation; for the deflecting force, being uniform in respect to time, would not give rise to forced vibrations of the needle. The latter would have nothing further to do than to indicate the direction of a constant field of force. LV’. This method, which was proposed by Foster t,and more re- cently by Lippmann, and to a certain extent executed by the former, is a modification of III., in which the electromotive force generated during the rotation of the inductor is balanced by an external electromotive force, and thus not allowed to produce a current. The external electromotive force is due to the passage of a battery-current through certain resistance- coils; and the current is compared with the earth’s horizontal * Proc. Roy. Soc. May 1881, p. 123. + Brit. Assoc. Report, 1881. 340 Lord Rayleigh’s Comparison of Methods for the intensity (H) by an absolute tangent-galvanometer. The dif- ference of potential at the two points of derivation is thus known in terms of the included absolute resistance (R) and H. The circuit is continued through a sensitive galvanometer and the coil of the inductor, and is closed only when the latter coil is nearly in the plane of the meridian. When balance is obtained, the electromotive force of induction n.7a?.H .@ is equal to RH tan «/G, where G is the constant of the tangent-galvano- meter and « the angle of deflection, The result, from which H disappears, if it may be assumed to be the same in the two places, is thus R=n7rd’G. w cota, or, if A be the mean radius of the galvanometer-coil, 2 R=2nm7’o cot « = from which the value of the resistance-coils is obtained in abso- lute measure. One advantage of this method, which it shares with VI. below, is that the resistance immediately expressed may be that of well-constructed coils of German silver or of platinum-silver at a known temperature. This method is nearly free from the secondary objections to III. discussed above. The self-induction of the revolving wire- circuit does not enter, as no appreciable current is allowed to form itself; but there would appear to be a possibility of dis- turbance from mutual induction between the wire-circuit and secondary circuits in the ring. It would certainly be neces- sary to prevent the flow of currents round the ring by the insertion of an insulating layer; and even with this precaution some control in the way of a variation of speed would almost be necessary. Again, it is a question whether disturbance, from thermo-electricity for instance, may not arise at the place where the contacts are made and broken. _ It is to be hoped that a complete series of observations may be made by this method, which certainly possesses considerable merits; but at best it remains open to the objection mentioned under II., with which in this respect it stands upon a level, 7. e. that errors may enter from the measurements of both coils, the error of A entering singly into the result, and that of a enter- ing doubly. In respect of requiring absolute measurements of angle, there is nothing to choose between II., II]., IV., and V. V. Weber’s Method by Damping. This is the method followed by Kohlrausch * in his inyesti- * Pogg. Ann. Erganzungsband vi.; Phil. Mag. 1874, April and May. Determination of Resistances in Absolute Measure. 341 gations upon this subject. It is founded upon II.; but in order to avoid the difficulty arising from the necessity of using a magnet small relatively to the coil in which it is suspended, no attempt is made to determine the constant from the data of construction. The inductor is connected with a sensitive gal- vyanometer, and the constant of the latter is deduced from observations of the logarithmic decrement of the vibrations of the magnet when ths circuit is closed (1), and when it is open (A,). The result, however, involves H the horizontal inten- sity, K the moment of inertia of the needle, as well as the time of vibration T. Expressed roughly, in the notation previously employed, it is Free 32a*H?TX AB ae Ke >? By? where R is the resistance of the circuit composed of the in- ductor and galvanometer, A and B are the arcs of vibration in the method of recoil. Interesting as this method is in some respects, I cannot but agree with Rowland in thinking that the final formula is enough to show that it cannot compete with others on equal terms, if the object be to obtain a result of high accuracy. The horizontal intensity itself is perhaps nearly as difficult to determine as absolute resistance; and the error thence arising doubles itself in the result. There is in addition the error of K. But even if H and K were not subject to error at all, I believe that the occurrence of the fourth power of the radius of the inductor is a fatal defect, and tends to explain the dis- erepant result obtained by Kohlrausch*. It is also worthy of note that the error of levelling enters twice as much asin IL., IIl., and IV. VI. Lorentz’s Method. This method, which, with the introduction of certain modi- fications not affecting its essential character, I am disposed to consider the best of all, was proposed and executed by Lorentz, of Copenhagen, in 18737. A circular disk of metal, main- tained in rotation about an axis passing through its centre at a uniform and known rate, is placed in the magnetic field due * Oct. 1882.—It is very satisfactory to note that Kohlrausch (Gétt. Ges. Sept. 1882) has recently detected an error in the value of the area of the windings of the inductor assumed in his previous calculations. Introdu- cing the new value, obtained by an electrical process analogous to that described in Maxwell's ‘ Electricity,’ § 754, he finds 1 B.A. unit = -990x 10°. Tt Poge. Ann. cxlix. p. 251, 342 Lord Rayleigh’s Comparison of Methods for the to a battery-current which circulates through a coaxal coil of many turns. The revolving disk is touched near its centre and circumference by two wires. If the circuit were simply closed through a galvanometer, the instrument would indicate the current due to the electromotive force of induction acting against the resistance of the circuit. The electromotive force corresponding to each revolution is the same as would be generated in a single turn of wire coincident with the cireum- ference of the disk by the formation or cessation of the battery- current. If this be called y, and M be the coefficient of induc- tion between the coil and the cireumeference, m the number of revolutions per second, the electromotive force is mMy. For the present purpose, however, the circuit is not simply closed, but its terminals are connected with the extremities of a resistance R through which the battery-current flows, and the variable quantities are so adjusted that the electromotive force Ry exactly balances that of induction. When the gal- vanometer indicates no current, the following relation, inde- pendent, it will be observed, of the magnitude of the battery- current, must be satisfied, R=mM; and from this, M being known from the data of construction, the absolute resistance R of the conductor is determined. Tt will be seen that this method has pretty close affinity to I. The secondary circuit is here, in a sense, reduced to a single turn, or rather to as many turns as the disk makes revolutions in a time comparable with the time of swing of the ballistic galvanometer; but the disadvantage of a reduced number of turns is probably more than compensated for by the continuous character of the induced current, which allows of its being brought into direct opposition to that of the battery. During the months from April to August of the present year I have been occupied in carrying out a determination by this method. Space will not permit of a detailed consideration of the various questions which presented themselves; and I must content myself with a brief statement of the procedure, and with such a discussion of the sources of error as will allow a comparison of this method with others. I hope shortly to communicate a detailed paper upon the subject to the Royal Society. One of the principal difficulties to be overcome arises from the exceeding smallness of the resistance R, less than 3}, B.A. in my experiments. Lorentz employed an actual column of mercury of known dimensions, so that the result is given at once in terms of mercury. I had intended to follow the same course, but, after some trials, came to the conclusion that there would be difficulties in the way of thus obtaining the Determination of Resistances in Absolute Measure. 348 degree of accuracy aimed at, and ultimately adopted a method of shunting. The main current from the battery was divided into two parts, the larger of which passed through a resistance of half a unit, formed by combining two singles in multiple ares. ‘The resistance traversed by the other part of the main current was much larger (from 10 to 20); and it was to two points on this branch distant +15 that the wires of the derived circuit were connected. With proper precautions this arrange- ment was found satisfactory, and the equivalent resistance R could be accurately expressed in terms of the standard B.A. units. The adjustment for obtaining the balance was effected by varying a large resistance placed in multiple arc with one of the others ; or rather two effective resistances were used, one on either side of that required for balance, the latter being finally calculated by interpolation from the indications of the galvanometer. By observing only the effect of reversing the battery-cur- rent the results are freed from the influence of terrestrial magnetism, and from the very sensible thermoelectric force having its seat at the slidmg contact. These contacts were made by means of brushes of copper wire. One brush pressed against the cylindrical edge of the disk, which was about + inch broad; and the other pressed against the shaft on which the whole turned. The area included by the secondary circuit was therefore not exactly that of the disk, but required a small correction, as to which, however, there is no difficulty. The arrangements for driving the disk and for observing the speed were the same as for the revolving coil of method III. The results, which in the same arrangement have not differed - by so much as 7,495 on different days, show that the sensitive- ness was sufficient. After these explanations I come to the main subject of the present remarks, viz. the degree of accuracy likely to be attained in the fundamental linear measurement. In the pre- sent case the quantity to be determined is M; and so far there is no difference between this method and I. But the fact that the secondary circuit is here represented’by a disk whose dia- meter can be measured much more accurately than that of a coil introduces a certain modification. It is necessary also that the arrangements be symmetrical with respect to the middle plane of the disk, as, on account of the width of the brush, the place of contact cannot be considered as well defined. The necessary condition can be satisfied with a single coil by placing it so that its mean plane coincides with that of the disk. In this position slight errors of adjustment produce effects of the second order only, and every thing depends upon the radii. 344 Lord Rayleigh’s Comparison of Methods for the Preparatory to the design of the apparatus for my experi- ments, I made some calculations of the values of the induction- coefficient and of its rates of variation for various ratios of the radius of the coil (A) to that of the disk (a). The angle y (see method I.) is here (b=0) determined by tan?}-y=a/A. If we write éM _ 2 5A oa iN aes a ae the sum of % and vy will be unity. The following are the values found. Those under M are proportional only, and relate to the case in which A is constant. a/A. r. v M az) —12 4+2°2 4°37 6 —1°36 | +2°36 6°65 a, —15 +2°9 9°80 8 —2:0 +3°0 14:4 In Lorentz’s apparatus the value of a/A was even larger than the last in the table, and the radial dimension of the coil was no small fraction of (A—a). On this account, as has already been pointed out by Rowland, no very accurate result could be expected. In my experiments two similar coils were used whose radius (A) = about 26 centim., and in two distinct arrangements. In the first arrangement the two cells were placed close together; so that the case corresponded pretty closely with that just spoken of. The radius of the disk is about 16 centim.; _ and thus the proportions are nearly those of the second ex- ample in the table. It will be seen that the circumstances are not unfavourable to accuracy, the error of mean radius of the coil entering into the result to a less extent than in any of the methods hitherto described, except III. and IV. The disk is so much more easily measured, that the larger coefficient 2°36, applicable to it, should not lead to much error in the result. This arrangement was worked at two speeds of rotation in the proportion of 10: 16, and gave with close accordance 1 B.A. unit =°9867 x 10° C.G.8. In the other arrangement the two coils were separated to a considerable distance, and the induction-coefficient depended not only upon the mean radii of the coils (and of the disk), but also upon the distance of their mean planes. The pecu- liarity of this arrangement, to which I wish to draw special Determination of Resistances in Absolute Measures. 345 attention, is that it is possible so to proportion the quantities that the error of mean radius of the coil does not affect the result, which accordingly depends only upon the diameter of the disk and the distance of the coil’s mean planes. How this may come about will be readily understood by considering the de- pendence of M upon A when a and bare given. It is clear that M vanishes, both when A is very small and when it is very large ; from which it follows that there must be some value of A for which the effect is a maximum and therefore independent of small variations of A. In carrying out this idea it is not necessary to approach the above-defined state of things very closely; for of course we have in reality a good approximate knowledge of the value of A. In my apparatus the distance of mean planes was about 30 centim., so that 6 = about 15 centim. With the actual proportions a calculation of the effects of the various errors shows that oM oA ob on , M7 a 967-+18— 3 so that the error of A enters in quite a subordinate degree. The positive coefficient of 5A shows that with the given coils and disk the separation was somewhat too great to secure the greatest independence of 6A. The success of this arrangement depends principally upon the degree of accuracy with which } can be determined. The two rings on which the wire is coiled are separated by distance- pieces; and, as in I., by reversing the rings relatively to the distance-pieces the result may be made to depend upon the mean length of these pieces and the mean thicknesses of the rings at the places of contact. The three distance-pieces were held together in one length and measured under microscopes; and the thicknesses of the rings were taken with verified cal- lipers. There can hardly be a doubt but that this determina- tion is much more accurate than that of the mean radius of a coil; and, what is also of some importance, it admits of repe- tition at pleasure with comparatively little trouble. The value of the B.A. unit resulting from the measurement with this arrangement was 9869 x 10° C.G.S.* There seems no reason why a further increase of accuracy should not be obtainable by enlarging the scale of the appa- ratus. If we suppose the scale doubled, the number of turns in the coil and the angular speed of the disk being unaltered, the value of M would be doubled; and thus with the same * The reductions not being yet finally completed, these numbers are liable to a change of one or two units in the fourth place of decimals. Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2A 346 Messrs. Cross and Bevan on the Correlation of battery-current the sensitiveness would be improved. Or, if we suppose the circumferential linear speed of the disk rather than its angular speed to be constant, the sensitiveness would be unchanged. If the larger coil were made of the same kind of wire as the smaller, its resistance would be augmented; but if the dimensions of the section were also doubled, so as to keep the proportions throughout, the advantage in this respect would lie with the larger apparatus. On the whole, I am of opinion that if it is desirable at the present time to construct apparatus on the most favourable scale, so as to reach the highest attainable accuracy, the modi- fication of Lorentz’s method last described is the one which offers the best prospect of success. Before this is done, how- ever, it appears to me important that the value now three times obtained in the Cavendish Laboratory by distinct me- thods should be approximately verified (or disproved) by other physicists. To distinguish between this value and those ob- tained, for instance, by Kohlrausch, by Lorentz, or by the first B.A. Committee, should not require the construction of unusually costly apparatus. Until the larger question is dis- posed of, it appears premature to discuss the details of arrange- ments from which the highest degree of precision is to be expected. XXXIX. On the Correlation of the Chemistry of the Carbon Compounds with the Phenomena of Life. By C. F. Cross and K. J. BEvAN*. T is not for us to dilate upon the marvellous progress of Organic Chemistry during this century, nor to find fault with the inevitably specializing tendency of research in the province of the carbon compounds ; and we certainly owe an apology for entering upon a subject of such magnitude as the correlations of chemical with biological science. That which we offer is derived not so much from the consciousness of being able to originate views of these correlations which shall be more productive than certain which appear to prevail, as from the practical necessities of the investigations in which we find ourselves engaged, the paucity of the landmarks to which we have to look for guidance, and the misleading character of certain of the recognized principles and methods which has become manifest in the results of their application. In fine, there are numerous points in that portion of Biochemical Science the study of which we are prosecuting which call for critical discussion; and the existence of the imperfections * Communicated by the Authors. ~ . Curbon Chemastry with Vital Phenomena. 347 which it shall be our aim to expose we can only account for by the influence of the specializing tendency preventing che- mists generally from following up the science in its wider relations. Ii is certainly the ideal issue of organic chemistry to co-or- dinate the multitudinous facts already and to be amassed con- cerning the carbon compounds, with the genesis, changes, and ultimate fate of the substances which go to build up the tissues of living organisms. Beyond this, indeed, many chemists do not hesitate to indulge in expectations as to the possible achievements of synthesis, which know no limits short of the. inconceivable. The special “vital force” of a previous age they dismiss as an ancient cloke of ignorance long since dis- earded, under the genial influence of the sun of knowledge, even by those who most tenaciously opposed its sheltering folds to the stormy blast of “‘ unbelief ;’’ and thus by removing the great barrier, the whole universe of matter and force is opened out to the “conquering progress of man.” In the words of an authoritative modern text-book, ‘At the present day the belief in a special vital force has ceased to encumber scientific progress. We now know that the same laws of com- bination regulate the formation of chemical compounds in animate and inanimate nature’”*. The authors of this mani- festo, however, leave us in doubtas to whether they regard the belief in question as itself obsolete, or, by being modified in accordance with the invincible array of facts by which their second dogma has been established, as brought within the pale of natural truth, and thus to have become an aid, and not an encumbrance, to scientific progress. The two propositions are certainly not equivalent unless this latter interpretation be allowed ; and as equivalence is evidently intended, we take it that the authors, leaving the mystery of life to vindicate itself, also intended this interpretation, and would allow the chemical phenomena of life to be as special, say, as the phenomena of heat. But it is difficult to rest satisfied with the isolated and phy- sical interpretation of the passage; the generalizing tendency of modern physical science impels us to give it a wider con- sideration. Thus, to develop our parallel, we have long ceased to regard heat as having any special objective existence ; and although its phenomena are, in relation to our perceptions, still sufficiently special to admit of classification apart, we no longer allow the exigencies of science to impede our progress towards a better understanding of the unity of nature, but recognize in heat ‘a manifestation of energy as a mode of molecular motion,” a definition which is sufficiently exclusive * Roscoe and Schorlemmer, ‘ Treatise on Chemistry,’ iii. p. 10. 348 Messrs. Cross and Bevan on the Correlation of of subjective impressions. Further, chemists are in the habit of referring the phenomena of their science to the existence of a force of chemical affinity, and that without any justification more or less elaborate, in deference to its conditional character or to the metaphysical questionings which underlie all our natural science. And when we examine into the grounds upon which our belief in a vital force may be said to be dis- missed, we find that we have in them only the basis of a truer knowledge than heretofore of what the vital force is and what it is not. Since the dismissal of the hypothesis of spontaneous generation, the distinction of matter into animate and inani- mate has assumed a very sharp character. In the animate world we have a province of distinct phenomena ; into this - world, matter is coerced and is made to manifest properties distinct from those which it otherwise possesses ; and in this world force is distributed and co-ordinated in such a way as to compel the acknowledgment of agency. Speaking physically, we admit that life is one of the narrowest—i. e. most exten- sively conditioned of phenomena; but this does not lessen our belief in the working, under these conditions, of a special agency. The minutely intimate correlation of life with its chemical phenomena doubtless leaves in the minds of many but a very narrow margin for the operation of the special agency in question, and makes its assumption appear propor- tionately gratuitous. At the same time we have no proof that the science of “‘energy”’ affords the ultimate criterion of natural truth; and we cannot recognize that it has done more than modify the belief in a special vital force, though the modification has been so deep as to convert it from being an encumbrance to an effective aid to scientific progress. How far our progress, thus emancipated from a serious impediment, may be expected to go, is a question which must be relegated to metaphysics ; at the same time we hold that the results of physical inquiry have as yet given no warrant for anticipating, as the realizable ideal, that our science will ever overleap the barrier of structural organization. The limi- tation herein expressed seems to us so obviously to define the natural attitude of the chemist towards living matter, that not without the strongest proofs will he change it for the extreme of conceivable ideals; and in the practical work of investiga- ting the products of life and growth he will find such abun- dant confirmation of his natural impressions as to remain convinced that the distinction of the material universe into animate and inanimate is real and transcendental*. * This subject will be found exhaustively discussed in ‘ Chemical Ditti- culties of Evolution,’ by J. J. McLaren (1877). | | | a tt i vo, a Carbon Chemistry with Vital Phenomena. 349 Chemistry and biology occupy to one another an antithetic relation as_regards their subject-matter : the goal of the one is the starting-point of the other; the protoplasm as yet undif- ferentiated, to which the biologist complacently refers the origin of life, is to the chemist a perfect microcosm, and its syn- thesis perhaps the highest possible achievement of his science. With regard to the supervening phenomenon of organization —the entrance of life—there is also a distinction of attitude. To the biologist it is axiomatic—beyond that, a fact without the range of observation, and one of which we venture to say, therefore, he can give no account. Now the chemist finds his attention challenged, and his work of speculative investigation begin, at an earlier point in the history of the planet, when as yet life was impossible ; his speculations moreover have a certain basis in observation and analogy; and having initiated his career, why break off and affect to view with veiled eyes a change merely in the disposition of the matter and force already existent and active? Why, further, should we attach to the entrance of structural organization a mystic signifi- cance, when not only are we familiar with the inverse change from the organized to the amorphous condition, but find it in many cases to involve no change in the inner subsensible molecular structure, or at least no deeper change than can be included within the province of isomerism? Cellulose, for instance (in the form of cotton), is dissolved by the ammonio- cupric reagent, and on adding excess of acid is reprecipitated, and may be recovered without loss of weight; the change undergone cannot, therefore, be more than morphological. Furthei, the amorphous cellulose behaves towards reagents so similarly to the original, that the change in question appears to have affected merely the external structure. Add to these considerations many others of a similar character, which need not be here specified, togecher with the numerous syntheses of the products of life and growth which have been achieved in the laboratory, and lastly the narrow range of physical con- ditions under which life is possible, and we have a fair con- ception of the intellectual position from which might emanate the dogma, “we have ceased to believe in a special vital force.” We, speaking personally, see no more reason, in these teach- ings of molecular philosophy, for ceasing to believe in life as resulting from special agency, than for ceasing to recognize the living individuality of our English language or constitu- tion, and the agency of Englishmen in their establishment and development, because they are originally a rearrangement of materials and forces once the possession of now obsolete or effete nationalities. We are not aware that in any philosophy, 350 Messrs. Cross and Bevan on the Correlation of worthy the name, life was or is regarded as any thing more than a rearrangement and special disposition of the preex- isting: it cannot be doubted that life, as known on this planet, had a beginning ; nor, further, that the whole analogy of the origin of subsequently derived life points to it as an indivyi- dual and special phenomenon. In a word, the doctrine of Spontaneous Generation has been expunged from biological science; and a revival of its analogue from the point of view of chemical science we hold to be groundless. Not only so, but, to give a more practical expression to these views, a loose adoption of the non-belief in a special vital force will materially impede progress in the domain of biological che- mistry. We cannot find a stronger proof of the want of recognition of the special and peculiar nature of the chemical phenomena of life than in the prevalence of empirical methods for the resolution of plant substances, their empiricism con- sisting chiefly in their unreasoned foundations upon the me- thods of separation of inorganic substances. To this portion of the science our attention has been specially directed; and we proceed to discuss it in certain of its bearings upon the main subject of this paper. The work of the plant, considered in its intrinsic results, is to grow, to form tissues and organs ; a side issue of growth is the elaboration of substances which subserve future growth; and a subsidiary result is the formation of certain substances which we may regard as excreta, as unavailable for the main end. These excreta are often bodies of well-defined physical properties, of more or less simple molecular structure, whose constitution is so far comprehended as to allow of their syn- thetical production in the laboratory. For the isolation of such bodies, methods founded upon the fixity of their consti- tution are general and satisfactory. But, on the other hand, substances whose essential condition is that of continual dif- ferentiation, whose constitution is but little understood even when viewed statically, whose relationship to the former group is probably of a parental character, should be treated with due regard to these distinctions : indeed it seems hopeless to attempt to comprehend their chemical functions in disregard of these their special biological correlations. The neglect of these considerations has led to the adoption of empirical and, to that extent, arbitrary methods of analysis and classification; names have been multiplied to individualize bodies which, occurring in a developmental series, should have received a corresponding general or group definition; and much time and capability have been spent in establishing facts before their probable and relative value had been taken into consideration, : es! AD Carbon Chemistry with Vital Phenomena. dol The chemistry of cellulose is a case in point. This substance will be found, even to this day, treated by chemists as a well- defined body, of intrinsically fixed characteristics ; whereas physiologists, with special regard to its functions in the living plant, have long since observed it to be capable of many modi- fications, more or Jess profound, and have not hesitated to regard it as the parent substance of that large class of aro- matic bodies of which tannin is the type. Geology had made us acquainted with the very profound modification of cellulosic structures which are seen in coal; and the chemical study of coal in its various forms had revealed a progressive increase in aromatic potentiality ; and yet the obvious generalization of these several results has been widely ignored, the genetic connexion suggested by this large group of naturally occurring substances has been practically neglected, and chemists have remained satisfied with a purely empirical treatment. Taking this connexion as a working hypothesis and investigating the essential relations therein suggested, we feel assured that a much more productive field of inquiry is opened out. The essential difference between coal and cellu- lose is measured by the difference of their products of decom- position by dry distillation: in coal we have the source of the vast series of aromatic compounds which constitute the sub- ject matter of the most important development of our science. Although the constitution of coal is still unsolved, and we cannot yet say to what extent it might be made to yield aromatic bodies by less drastic processes of resolution than that of destructive distillation, yet the general fact that in relation to cellulose it possesses an increased (immediate) aromatic potentiality has been sufficiently established.. The nitrogen, further, derived from the proteid matters of the parent tissues exhibits a progressive diminution; and the che- mistry of the formation and decomposition of coal may be considered independently of this element*. It remains there- fore to investigate the conversion of cellulose into substances of the aromatic group of compounds. The first link in the chain of development would appear, from the researches of physiologists, to be contained in the phenomenon of the lignification of cellulose structures. In the life of the plant, extreme processes of reduction and oxi- dation, of synthesis and resolution occur simultaneously and continuously. The formation of cellulose and its lignification have been ranged by physiologists on the basis of this anti- thesis. The connexion between lignin and the great group of * W. A. Miller, ‘Elements of Chemistry,’ iii. p. 145, by whom this subject appears to be developed more consequently than by most writers. 352 Messrs. Cross and Bevan on the Correlation of astringent substances has been already established*; and the latter have been assumed by physiologists to be residues of the oxidation of carbohydrates. In regard to the lignifica- tion of structures originally consisting of pure cellulose, we have two alternative hypotheses to account for the change:— (1) that it results from an intrinsic modification of the cellu- lose itself effected in situ; and (2) that it is the result of com- bination of cellulose with aromatic bodies formed elsewhere in the plant, and probably as residues from the oxidation of carbohydrates. There is perhaps more negative evidence on the subject of the second than there is positive in favour of the first hypothesis; and the difficulties which beset the eluci- dation of the question are an apt illustration of the limitations which impede the solution of the chemical phenomena of life. If the cellulose combine with astringent substances presented in solution, to form insoluble products, these may be assumed to resemble those compounds which form the basis of the dyeing of the cellulose fibres. A superficial study of any of the non-cellulose or lignified fibres will satisfy the observer that they behave rather as modified celluloses than as a com- pound of the above weak order. In the first place, the reso- lution vf the fibre-substance of lignified fibres can only be effected by means of drastic reagents, whereas a compound of cellulose with a body that it has merely removed from solution (that is to say, in what we may term adhesive combination) is always easily decomposed. We have further made a series of observations upon seedlings, which show that the astringent substances formed during germination are present in the juices and yet absent from the substance of the fibro-vascular bundles. Again, if lignification followed the course in ques- tion, it is difficult to account for the comparatively invariable composition of bast-fibres. Not only are they remarkably uniform in composition from end to end, but they may be obtained white and lustrous by a process of bleaching which occasions a minimum loss of weight ; they may be converted into explosive nitro-compounds, an examination of which shows them to be homogeneous; they are soluble in the ammonio-cupric reagent, a property which has been denied to them by certain observers; and the precipitate obtained on adding an acid is simply the amorphous modification of the originally organized fibre-substance. The characteristic yel- low coloration moreover which lignified fibres give when treated with a solution of aniline sulphate, and upon which much stress has been laid as distinguishing them from the * Sachs, Handb. der exper. Phys. (1865) pp. 361-369 ; Sachse, Farbstoffe &e. (1877), p. 113; Cross and Bevan, Chem. Soc, Journ. xli. p. 90, Carbon Chemistry with Vital Phenomena. 353 cellulose fibres, we have found to be so considerably weakened by previously boiling the fibre in a solution of acid sodium sulphite as to be afterwards in many cases quite undistinguish- able. As the loss in weight due to this treatment is imper- ceptible, and the lignin substance remains practically un- changed, the colour-reaction in question is referable to the presence of some body resulting from a superficial decompo- sition (oxidation) of the lignin substance. These observations are a strong confirmation of the view enunciated with much emphasis by Sachs* many years ago, that the only inference to be drawn from the biochemical facts then established is that lignin and cellulose are genetically connected. In our early work on bast-fibres, we were led to regard the jute-fibre as typical of a class of bodies analogous to the glucosides, and which we termed cellulides, a name which suffi- ciently explains our views. Subsequently to this, we found that Hlasiwetzt had arrived at similar conclusions in discussing the chemico-physiological relationships of the tannins, phloba- phenes, resins, and glucosides. He not only regards cellu- lose, tannins, and resins as genetically connected, but is con- vineed of the a priori probability of the existence of series of gummides and mannides parallel with the glucosides. We take this as an additional warrant for the correctness of our view; and in conformity with these conclusions and subse- quent experience, we may state our hypothesis with more emphasis to be, that the fibre substance of lignified fibres is, in its chemical constitution, dominated by the cellulose mole- eule, upon which aromatic molecules, resulting from intrinsic modification of the cellulose itself, have been built. Whether the aromatic molecule is of the nature of a quinone, as would seem to be indicated by the products of the action of chlorine, we have some hesitation in affirming, recognizing more clearly than we then did the difficulty of reasoning from the pro- ducts of decomposition of once living substances back to the condition under which they are formed. The celluloses, which constitute the framework upon which the plant world is developed, being regarded thus as capable of modification, and lignification as the first of the series of changes through which they pass from the group of carbo- hydrates, to which they originally belong, to the extended yrange of naturally occurring substances of aromatic character included in the large group of astringents, in the several varieties of coal, and probably also of other important groups, * Sachs, ibid. Cf Koroll, Quant. Chem., unters. Zstg. Kork, Bast &e.: Diss., Dorpat (1880). + Chem. Soc. Journ. xxxviii. p. 666; Ann. Chem. Pharm. cxliii. p. 40, 354 Messrs. Cross and Bevan on the Correlation of such as the resins, it is surely incumbent upon chemists to recognize the call to investigate the natural origin and history of the carbon compounds, and first of all in their relation to cellulose. We know the objection in the minds of many to forsake the familiar landmarks of positive physical definition, such as crystallization and molecular volume, for a province where the absence of the criteria hitherto regarded as al] im- portant makes the results to be obtained appear to that extent conjectural; we know indeed that the objection in many cases takes the more active form of almost refusing credence to any results obtained with substances that are amorphous and essen- tially transitional; and against this attitude a most emphatic protest is to be lodged. Arithmetic cannot cope with the physics of living matter; and we shall need to promote our equations and constants several degrees before we can include its chemical phenomena. Moreover the purity of substances, as the only condition in which to be approached by the che- mist, will need a very elastic interpretation in presence of matter undergoing differentiation; and such properties as have hitherto been regarded as affording the only guarantees of purity will have no place in a vast amount of research that requires to be done. We clearly recognize the large amount of work already accomplished by isolated effort in this depart- ment of chemical science ; but these remain for the most part uncorrelated, and, as a glance at the text-books will show, in a great measure unrecognized. Not only have the suggestions of physiologists in regard to the probable origin of aromatic substances in the plant been but little developed by chemists, but the equally important correlation of the carbohydrates with the fats, which follows from their physiological equivalence, still lies without our science. Here also a transformation in series is suggested, the intermediate terms of which are probably to be found in cutin and analogous bodies, constituents of cork structures. The changes through which the transition is accomplished are probably very profound, more so than in the conversion of cellulose into lignin. Of the mechanism of the conversion we are as yet entirely ignorant; but we have the conviction, in this as in every other case, that the vital force of the plant operates through the same materials and forces which lie at our disposition, and that its results can therefore be studied and in some measure reproduced. The study of these transformations must, in the first instance, of course be analytical; and most important correla- tions will follow from a comparative examination of the pro- ducts of resolution of plant-substances, Take, for instance, Carbon Chemistry with Vital Phenomena. 355 mucic acid, and represent its connexions by a diagram, and we find a large number of very important correlations implicated, thus:— Cellulose. Gums. Mucic acid. We SS (Dichloro-muconic acid) (Pyromucic acid). Adipic acid. Furfuraldehyde. aS ee ee —_—, rm ! pitas ; Cork tissues. Fats. Lignin. Astringents. A quantification of these relationships, and a multiplication of investigations according tv such a priori correlations, could not fail to establish important truths concerning the genetic connexions of the carbon compounds. A further illustration of the want of correlation of chemical with biological investigation is to be found in the prevalence of empirical and statistical analyses of plant-substances in agricultural work. To a certain extent it is evident that statistical must prevail over molecular methods where the complex substances and mixtures of substances which are elaborated in the plant world are the subject of inquiry; but we contend that these may be ordered on a much more rational basis than is at present adopted. The somewhat arbitrary choice of reagents, such as Schulze’s for the isolation of cellulose, of boiling dilute sulphuric acid and alkali successively applied to plant-substances for the determination of their so-called crude fibre, the dismissal of whole groups of bodies as ‘extractive matters”? or as “ in- crusting and intercellular substances,” and the general absence of the recognition of the genetic connexion of these substances with those from which they are separated—in fine, the almost exclusive choice of the indirect and statistical before direct methods of observation, argues a certain misapplication of time and capability, and sufficiently accounts for the indiffer- ent, if not critical, attitude of the greater number of chemists towards Biochemical science. We may cite the literature on the subject of chlorophyll, the proteids, the carbohydrates, including cellulose, the group of pectous substances, and, until the recent work of O’Sullivan and Brown and Heron, starch. A more special illustration is to be found in the work of Meissner and Shephard on the origin of hippuric acid in the urine of Herbivora. In order to identify the parent substance—that constituent of grasses which could yield the necessary benzoic 356 Correlation of Carbon Chemistry with Vital Phenomena. residue—the authors, adopting the statistical method of exclu~ sive separation, arrived at length at the substance in question —a body which Foster*, in quoting their work, terms a form of cellulose. This substance was found to differ from cellulose, on the result of an aggregate elementary analysis, by a some- what higher carbon percentage, such as, according to the reasoning of these authors, would be due to the presence of a body of the composition of quinic acid; and this they regard as a constituent of this substance, and as converted. during the process of digestion, into hippuric acid. Pushing then the statistical method of inquiry beyond its limits, and evi- dently for the purpose of confirming @ priori views, the authors appear to us to have missed the most important development of their otherwise valuable work. Had they examined the “form of cellulose ”’ at which they arrived by a direct method of proximate resolution, they would have obtained the aromatic substances, allied to the astringents and phenols, which we have obtained from lignified fibres. That they are digested by the Herbivora has been established by numerous observerst; that they are the source of the benzoic residue necessary to form hippuric acid is &@ priori very probable: in fact it must be regarded as first in the order of the probabilities to be inves- tigated. As such, indeed, it is occupying our attention ; and whatever be the result it will be more valuable, because more definite, than any conclusion arrived at by means of the in- direct method. We refrain from extending our discussion of these subjects in anticipation of the more detailed publication of our re- searches. We think we have shown grounds for our state- ment that there is a general want of correlation of chemical with biological research, especially in the hesitation on the part of chemists to adopt, as working hypotheses, the wider- reaching conclusions of physiologists as to the natural origin and history of the carbon compounds. We have also endea- voured to show that, while our conception of the vital force has been modified so as to have entirely lost the significance that belonged to it in a previous age, we have no ground for dismissing it for the alternative view of life as immanent in the universe of matter and force. We have expunged an error that was partial, and are in danger of generalizing the nega- tive by which it needed to be met. Postscript.—Since writing the above, our researches have * Die Hippursdure (Hannover, 1866) ; ‘Text-book of Physiology,’ 2nd edit. p. 354. Cf. Weiske, Zeitschr. Biol. xii. p. 241. + Weende, Berichte. established a connexion of the closest order between the aro- matic portion of the molecule of lignin (bastose) and the tri- atomic phenols—a fact which considerably strengthens the views advanced by physiologists as to the correlations of the carbohydrates with the aromatic group, and the reasoning by . which we have sought to emphasize them. The researches in question, on this point, will be published in due course. On the Dimensions of a Magnetic Pole. 357 XL. On the Dimensions of a Magnetic Pole in the Electrostatic System of Units. By Outver J. Lopez, D.Sc. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, VHE discussion which has been carried on in your pages* respecting the dimensions of a magnetic pole serves to illustrate the divergency of thought between those in this country who have been brought up, “electrically, ander Faraday and Maxwell, and the continental philosophers so eminently represented by Prof. Clausius. From one point of view the discussion may be said to have been roused by a simple mare’s nest constructed by dropping a factor out of one side of an equation (as was pointed out at once by Prof. Fitzgerald and by Mr. J. J. Thomson); but from another point of view it is the natural and inevitable consequence of the different aspects from which these matters can be regarded:—the English standpoint, in which the medium is recognized as the active agent, and is continually present both in the mind and in the formule; and the continental standpoint, from which the medium is perceived as so much empty space, and is taken account of as such in the formule. Both these aspects of the subject are worth consideration; and it may be conducive to future clearness to discuss them at moderate length. Coulomb’s measurements provisionally established the fact that in air the mechanical force between two electrically charged bodies was proportional to ee’/r?; but the subsequent researches of Faraday proved that this proportionality only holds so long as the medium enveloping the bodies is un- changed, and that the above quotient must be multiplied by different factors in order to give the force exerted in different media. Thus if the same two charged bodies were immersed in bisulphide of carbon, they would repel one another with much less vigour than they do in air. Introducing therefore as a factor the electric inductive * Phil. Mag. [5] vol. xiii. pp. 376, 381, 427, 429, 431, 530; and vol. xiv. pp. 124 & 225. 358 Dr. O. J. Lodge on the Dimensions of a Magnetic a capacity K, we have the general equation ee Now all that is solemnly essential with respect to the dimen- sions of the quantities here involved is that e?/K must be a force into an area, or that (e]=[L][KF}’. If we proceed to define the unit of electricity so as to make K of no dimensions and to equal 1 for air, that is a convention, and it is the basis of the electrostatic system ; but the above statement is no convention, but a natural truth. Precisely the same kind of thing is true in magnetism; and we now know that the force between two magnetic poles is not independent of the medium surrounding them, but that if the torsion-balance were full of, say, ferric chloride, the force between the two poles would be measurably less than if it were full of mere air. Thus we again need a factor for com- pleteness ; and the real law is that mim’ or that [m]=(L] [pF }. The conventional magnetic system of units is based on the definition of m in such a way that w, the magnetic inductive capacity of the medium, shall be of no dimensions, and shall for air be simply 1. All then that is objectively and physically fixed about the matter is that the dimensions of ¢/./K and of m//p are absolutely and mechanically definite, being each of them a length into the square root of a force, or MLiT”. But observe that the two system of units, the electrostatic and the magnetic, the arbitrary definition of e and the arbi- trary definition of m, are in their origin utterly independent ; not that they are wnrelated, but their relation must be a matter for future and experimental investigation. All we can so far say about them is, that,in every possible consistent system that can be adopted, [eK7*] = [mp] =[LF**]= [Me-4). . . (1) (The last term of this triple identity is added for the sake of | completeness, though it does not directly belong to the present Pole in the Electrostatic System of Units. 309 subject : the letter & is intended for the gravitation-constant as determined by the Cavendish experiment. Jam not aware whether the question of the possible dependence of this con- stant on the optical density of the medium surrounding the attracting masses has ever been considered; but I feel sure that a direct experimental attack on this question would not be uninteresting, and it might lead to important results. ) We now come to the Cirsted-Ampeére discovery of the con- nexion between m and e—the form of the connexion being that an electric current flowing in a closed circuit can pro- duce a magnetic potential, and therefore of course can act on magnets, precisely as if it itself were a magnet of a certain strength and form. The potential so caused at any point in air is found to be simply proportional to the strength of the current and to the solid angle which the circuit subtends as seen from that point; or, in other words, the moment of the magnet which is equivalent to the current is simply pro- portional to the strength of the current and to the area of the contour round which it flows. The unit of current most simply and directly applicable to these electromagnetic phenomena is not the old electrostatic © unit at all, but a new unit which may be defined in many ways—as, for instance, these :—- The electromagnetic unit of current is that which produces unit magnetic potential at a point whence its circuit subtends unit solid angle; Ii is also that which produces unit magnetic intensity, in a given direction, at a point whence the solid angle sub- tended by its circuit is changing at unit rate, per unit displacement, in that direction; And, again, it is that current which when flowing round a contour of unit area is equivalent to a magnet of unit moment,— all these statements being derived directly from the unit mag- netic pole thus :— Unit magnetic potential is defined to exist wherever a soli- tary and stationary unit pole would possess unit energy ; Unit magnetic intensity exists wherever unit pole would experience unit force ; and Unit magnetic moment is that possessed by two unit poles of opposite sign rigidly connected by a bar of unit length. (The connexion between the old electrostatic unit and this new electrical unit thus magnetically defined may be ex- pressed, if | am not mistaken, by saying that a ring charged with the electrostatic unit of electricity would have to revolve in its own plane with an angular velocity of about 3x 10" 360 Dr. O. J. Lodge on the Dimensions of a Magnetic radians per second in order to produce the same magnetic effects as the electromagnetic unit of current flowing in the same ring. Or, conversely, the electrostatic unit magnetic pole would be that which would experience unit force if placed at the centre of a circle of unit radius in which the electrostatic unit of electricity was moving with unit velocity. This definition I believe to hold equally well in any homo- geneous medium; for it is pointed out below that the electro- magnetic effect of a current is independent of w; while as regards K, a quantity which we might perhaps think would be likely to affect the result, we must remember that electric displacement is totally independent of any such circumstance. So, corresponding to the common electrokinetic equation, Cds Force =f =? Ye we shall have, for a moving charge, mev Force = 7? whence [me]=[ML’T""}. . 2 ow If statements like these are in the main correct, and after the experiments of Rowland we are bound, I suppose, to believe in the truth of something of the kind, they ought to remove Dr. Everett’s objection (Phil. Mag. June 1882, p. 481) as to the introduction of electrostatic units into magnetism ; unless indeed he maintains the thesis—no doubt a tenable one —that directly you begin to carry a charged body about, the discussion of its performances no longer belongs to electro- statics. Bonen from this digression, we have now to ask whether the statements above made are really definite and independent of the magnetic properties of the mecium surrounding the circuits, or must we introduce a factor to express the influ- ence of this medium when it is other than air? Mr. J. J. Thomson has instructively raised this question (Phil. Mag. for June); and he and others at Cambridge consider it a matter to be settled by experiment; and they further con- sider that, in order to agree with Maxwell’s view, experiment ought to make the magnetic effect of a solenoid and its air- equivalent magnetic shell differ, as soon as they are both intro- duced into some medium for which w is not unity. Now, though agreeing with this as far as it goes, | venture with diffidence to think that Maxwell would have drawn a distine- ‘? Pole in the Electrostatic System of Units. 361 tion between the medium inside the region of the solenoid corresponding to the substance of the magnetic shell, and that outside. He over and over again lays stress upon the fact that artificial solenoids can only be compared with magnetic shells for the space outside the shells, and that the line of integration must never be allowed to thread the circuits. Let us follow this out and see what it means when applied to the above question. I will assume it possible (for it certainly is theoretically possible) to imitate any steel magnet whatever by a proper arrangement of electric circuits, both being at present im- mersed in a non-magnetic (7. e. non-magnetizable or w=1) medium. The two arrangements are completely equivalent for all the region outside both—the region outside both being defined by the shape of the steel. For the comparison is not to be urged within the steel, because of the magnetized surfaces, which would have to be cut through, a circumstance which would completely alter all the conditions ; and it is not to be urged within the region of space near the solenoid which is the counterpart of the steel-occupied region, simply because here there are no magnetized surfaces to be cut through, and there- ‘fore the conditions will be continuous. Now take some non-magnetic medium, which for shortness T will call “clay,” mould it into the shape of the steel, and place it in or around the solenoid so as to mechanically define the limits of the “‘outer region.”” And now immerse both magnet and solidified solenoid in any medium for which yu differs from unity: I venture to assert that the equivalence which existed in air will be entirely maintained in the mag- netic medium—even though that medium be iron or bismuth, —and that, for both, the magnetic intensity at any point will be its air-value divided by pu. Still keeping both the things in the magnetic medium, remove the clay from the solenoid and permit the medium to. flow into the space it occupied. If what I said before is true, the solenoid will now be too strong for the magnet, for the mag- netic permeability of the interior will increase its effect u times, while that of the exterior will, as before, diminish it wth 3 SO that the effect of the solenoid completely immersed in the medium is precisely the same as it was when in air, while the effect of the magnet, from whose interior the magnetic sub- stance is of necessity excluded, is still 1h of what it was in air. This latter seems to be the kind of experiment which Mr. J. J. Thomson suggests in his June letter (p. 429), and Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2B 362 Dr. O. J. Lodge on the Dimensions of a Magnetic which, he says, Mr. Sargant then intended (and I hope still intends) to carry out. The solenoid being now completely surrounded with homo- geneous magnetic substance, wall a portion of it in with paper or glass to the shape of the steel of the magnet, and then pull both magnet and solenoid out into the air again. Naturally the solenoid will still be ~ times too strong for the magnet, but no further discrepancy need be expected; and if the cur- rent of the solenoid has been weakened when inside the mag- netic medium so as to restore the disturbed equivalence, they will remain equivalent when the region external to both is again filled with common air. These statements, if in their essence granted, require to make them complete certain provisos about the boundary of the vessel containing the magnetic medium, unless it be infi- nitely large, and also a discussion of what happens in the case of more than one magnetic medium, But the magnetization of bounding surfaces, and the accidents which happen to lines cutting surfaces of discontinuity, are perfectly understood and need not be here entered into. Moreover, in making these statements I am merely saying what one would expect to happen without evidence to the con- trary; but Iam not for an instant implying that direct experi- mental investigation is unnecessary and would not be highly desirable. On the contrary, I think it would be most desirable and satisfactory to have the matter thoroughly sifted. Supposing, then, that I have so far made no mistake, we can make the general statement of the equivalence of a cur- rent and a magnet thus— The magnetic moment of a circuit is equal to the strength of its current multiplied by tts effectwe area and again multiplied by the magnetic inductive capacity (or permeability) of the medium in the interior of the region enclosed by the contour (which region for a simple plane circuit is a mere shell), but is wholly inde- pendent of the magnetic properties of all the rest of the sur- rounding medium. The corresponding dimensional equation is [m]=[LpeT~}. Substituting in this the value of [m] from (1), we obtain the relation ib [-K]=5, - Mer whence nl=L Jose a 4 _ ; Pole in the Electrostatic System of Units. 363 These relations must all hold in any consistent system of units, since they express physical truths ; but of course they are not all independent. The number of independent relations must be limited by the number of fundamental experiments, viz. three—Coulomb, Coulomb, and Oersted ; and the short- est way of writing the independent relations is this :— [we? |=[Km?]=[ML] i [wKe?]=1. ; and (5) The electrostatic convention makes [K]=1; the electromag- netic convention makes [w|=1. So far every thing being pretty clear and straightforward, we have now to ask how it was that Prof. Clausius should have jumped to the conclusion that Maxwell had fallen into error™, or else that he held a theory of magnetism different from (and not merely an amplification of) Ampére’s and Weber’st. With this latter horn of the dilemma, by the way, he is half allowed by Mr. J. J. Thomson (September) to have succeeded in transfixing Maxwell; and Dr. Hverett (June) is not extremely energetic in his repudiation even of the alterna- tive of the first. Now itis perfectly true that Maxwell, in stating the current theory of magnetism, says without any kind of retraction or hesitation that “the magnetic action of a small plane circuit at distances which are great compared with the dimensions of the circuit is the same as that of a magnet whose axis is normal to the plane of the circuit, and whose magnetic moment is equal to the area of the circuit multiplied by the strength of the current..... and if a magnetic shell.... &. be substi- tuted .... then the magnetic action of the shell on all distant points will be identical with that of the current.”’ And in dis- cussing Ampére’s theory, he ignores the existence of magnetic media whose u does not equal 1 as completely as Prof. Clausius could wish. But then, according to Weber’s extension of Ampére’s theory (an extension I suppose universally accepted), the pro- perties of magnetic substances of all kinds are explained by molecular electric currents, and no magnets or magnetic sub- stances other than those consisting of current-conveying molecules exist. [And with reference to a remark of Mr. * Phil. Mag. June, pp. 3887 & 392. + Ibid. August, p. 126. 2B 2 364 Dr. O. J. Lodge on the Dimensions of a Magnetic Thomson’s in the September number, p. 225, I may say in pass- ing that it seems to me that Maxwell held, though no doubt tentatively and hypothetically, the view that electric currents and small magnets are identical and not only equivalent. | The coefficient » is thus foreign to Ampére’s theory applied universally; and this is how it has happened that Prof. Clausius has failed to recognize its existence and has been led intoerror*. A system dealing with Ampérian magnets in media for which » does not equal 1 is a mongrel combination which may no doubt be occasionally convenient but which never can be thoroughly satisfactory. We may accept then without hesitation Clausius’s presen- tation of Maxwell’s views, viz. both that a small magnet zs an electric current, and that magnetic moment ALWAYS equals simply integral current x area—remembering, however, that there exist currents in molecules besides the gross and arti- ficial currents in our copper wires, that these are directed by our artificial currents and add to their effects, and that in all cases they are most distinctly to be taken into account. In air, so far as it is non-magnetic, these molecular currents are zero, and the magnetic induction and the magnetic force are everywhere equal ; but in media consisting of Amperian * Very many errors,I now find; for he has also ignored K, Faraday’s simple old electrostatic constant; and accordingly his equations (1), (2), (4), &c. express mere conventions (if they were any thing more, then truly m, would have to equal m4, and e,=ea, as he begins to perceive in his August letter); while his general equation (3), which is the foundation of his reasoning, is quite wrong, and is indeed at the bottom of the whole con- fusion. In using the term “error” here, I would be understood to mean rather “divergency from opinions commonly held in this country” than absolute incorrectness as to matter of fact. For it would not be becomi to apply the latter term to views held by Prof. Clausius when the experi- mental foundation of opposing views is confessedly incomplete. The views held by Prof. Clausius are no doubt perfectly consistent, and would probably be in accord with fact if only the medium produced no effect such as it is here commonly supposed to produce; and whether the me- dium does or does not produce such an effect appears to some extent at present a subject of legitimate debate and a matter for experimental investigation. It will be understood therefore, that in stating one side strongly I have been influenced by the wish to be clear, rather than with the desire to dogmatize. Since the above letter was in type Dr. Francis has kindly called my attention to a paper by Prof. Helmholtz in Wiedemann’s Annalen, No. 9, 1882, to which I might have further referred if I had known of it in time. As far as I can hurriedly understand his position, Prof. Helmholtz in part endeavours to reconcile the views of Maxwell and of Clausius b throwing a doubt upon the Weber-Ampére theory ; and in fact he pat: to pure physicists not to abandon the old electrostatic for the more cum- brous and less surely founded electromagnetic system. [A translation of Professor Helmholtz’s paper will appear in our next number.—Ep. Phil. Mag. ] ¢ Pole in the Electrostatic System of Units. 365 molecules there is an extra magnetic induction, due to the pointing of these along the lines of force, which is 47 times the magnetization, and which has to be added to the other, thus making the total magnetic induction at any point pu times the magnetic force there. The effect of the medium is a physical fact; and no theory can presume really to dispense with the constant wu. All that the Ampérian theory does is to give a physical interpretation to it, and to render one independent of it so soon as one takes account of every current-conveying circuit, whether molecular or other, existing in the field, and does not arbitrarily elect to deal only with those gross solenoids which we can excite and immediately control by batteries. There can be no doubt, I think, that the mind of Maxwell on this subject, as on most others, was as clear as daylight ; and so far from falling into the least suspicion of an error, he expresses himself in art. 615 (1st edit.) almost as if he were joining in the present discussion, saying :— “There is one result . . . . whichis of very great importance. If we suppose that no magnets exist in the field except in the form of electric circuits, the distinction which we have hitherto maintained between the magnetic force and the magnetic induction [and therefore also the difference ~—1] vanishes, because it is only in magnetized matter that these quantities differ from each other. According to Ampére’s hypothesis ee the properties of what we call magnetized matter are due to molecular electric currents, so that it is only when we regard the substance in large masses that our theory of mag- netization is applicable ; and if our mathematical methods are supposed! capable of taking account of what goes on within the individual molecules they will discover nothing but elec- tric circuits, and we shall find the magnetic force and the magnetic induction everywhere identical. In order, however, [N.B.] to be able to make use of the electrostatic or of the electromagnetic system of measurement at pleasure we shall retain the coefficient u, remembering that its value is unity in the electromagnetic system.” I am, Gentlemen, Your obedient servant, University College, Liverpool, OxtvER J. Lopes, September 28, 1882. [ 366 ] XLI. On the Electric Discharge in Rarefied Gases. By Dr. EucEN GOLDSTEIN*. | HAVE shown in two former papers{, and more com- pletely in my book ‘A New Form of Electrical Repul- sion’ (published by Springer, Berlin), that the discharge cannot be effected by the actual projection of gas-particles. The same considerations which oppose the theory of the pro- pagation of electricity by projected gas-particles, also at once exclude the assumption that other ponderable particles, having access to the space in which the discharge takes place, play any essential part as carriers of electricity in the discharge. Such particles might consist of disintegrated portions of the substance of the electrodes, particles of the wall of the vessel, or of dust. The theory that the kathode-rays at any rate are produced by projected particles of the substance of the electrodes has been recently defended by Gintl§ and Puluj||. Numerous arguments] may be urged against it, over and above those which are at the same time opposed to a special convection by the particles of the gas. I will briefly mention one or two points. I have mentioned on a former occasion** that a system of pores in an insulator, or a single opening of relatively small dimensions, sends out rays whose properties are equivalent to those of the rays which issue from a metallic kathode. The rays of narrow openings, for example, possess the property of rectilinear radiation, and of exciting phosphorescence, which cannot here be explained by a projection of the substance of the pole. Kathodes imitated by systems of pores represent special cases of the phenomenon of secondary negative light, which is * Translated from the Annalen der Physik und Chemie, 1881, new series, vol. xiii. Communicated by the Author. + The readers of this Magazine will find that some observations and conclusions in the first chapter of the above paper, concerning the conduc- tivity of vacuum, do not differ from the views expressed by Prof. Edlund in a paper reprinted in the January number of the Philosophical Magazine for 1882. I beg to mention therefore, that my paper appeared in print in the February number (1881) of Wiedemann’s Annalen, and that Prof. Edlund presented his to the Royal Swedish Academy, April 23, 1881. ¢ Phil. Mag. [5] x. pp. 173 & 234. § Gintl, ‘Studies of ‘ene Radiant Matter’ (Prague, 1880). || Puluj, Sitzungsberichte Wien. Akad. 1880, p. 864. | E.Wiedemann( Wied. Ann. x. p. 252, 1880, Phil. Mag. x. p. 418) thinks it possible to conclude from Zahn’s experiments (Wied. Ann. viii. p. 675, 1879) that the view of Gintl and Puluj is untenable. = *4P tl. Mag, xp. 1/5. On the Electric Discharge in Rarefied Gases. 367 produced with the properties of rectilinear propagation, exci- tation of phosphorescence, &c., at openings of any width, if these openings occur in diaphragms or in tubes connecting vessels or introduced into them, the area of which is consider- able in comparison with the diameter of the opening. A con- sideration of these bundles of rays possessing the properties of the kathode-light issuing from wide openings also protects the experiments on narrow openings against the objection that the coincidence of their rays with the kathode-rays depends on a conductive action of particles of the insulating substance which might possibly be torn off from the edges of the opening. It has further been shown* that the positive light also pos- sesses the property of rectilinear propagation, and of exciting phosphorescence when the exhaustion has been carried far ; it does not seem to be reasonable to adopt an explanation for the phenomena of the kathode-light the principle of which is not applicable to the exactly similar properties of the positive light. “The most convincing proof, however, is given by the fol- lowing observation, which I have made in experiments on the kathodic deflection. This last name was proposed in the book referred to above for the deflection of the electric rays there described, of which I have made usef in determining the velocity with which the electricity propagates itself. I may assume it to be known that a kathode of aluminium pro- duces no deposit on the walls of the tube even after several hours’ use, whilst a kathode of platinum of no great thickness soon produces a completely opaque metallic deposit on the part of the tube played upon by the kathode-light. Two straight smooth wire electrodes, a and b, are inserted in the end of a cylindrical discharge-tube parallel to the axis of the tube. If both are made at the same time kathodes of the same discharge, then each of the two wires causes a deflection, in the rays of the other which pass by near to it, of the nature of a repulsion. We have then, as already described, two sharply- bounded surfaces, of which the one receives no rays from a, whilst none of the electric rays emitted by 0 fall upon the other. At the density of gas favourable to the production of phosphorescence, both surfaces are distinctly seen upon the surrounding brilliantly phosphorescing surface. This pheno- menon is also observed when one of the kathodes a is of pla- tinum, until the increasing thickness .of the platinum-deposit prevents the phosphorescence of the wall. According to the-view of Gintl and Puluj, that portion of the glass wall on which no rays fell from the platinum elec- * Phil. Mag. x. p. 236. + Ibid. p. 246. 368 Dr. E. Goldstein on the Electric trode ought evidently to remain free from the platinum deposit. If, however, we examine the glass wall, we find that the sur- face from which the kathode-rays are deflected—as determined at high pressures by the visibility of the blue rays themselves, _and at low pressures by means of the phosphorescence which they excite—is just as thickly covered with the platinum as the surrounding portion of the wall, and exactly as we observe to be the case in cylinders where the platinum wire alone acts as kathode while } is not excited. It follows that the rays of the kathode-light are deflected, but not the projected particles of the electrode ; the two cannot therefore be essentially con- nected. The discharge is therefore not to be explained by a projec- tion of material particles, either of the substance of the elec- trodes or of the gas. It follows from the experiments on the order of magnitude of the velocity of propagation of electricity, taken together with the views held on the constitution of gases, that the assumption of oscillations of these particles does not afford a satisfactory explanation, and the assumption of motions of rotation remains equally unfruitful. The wall of the con- taining vessel is not altogether neutral in the passage of elec- tricity through the space enclosed by it; it shows itself phenomena of charge and discharge which appear to be not altogether without influence upon the main discharge between the metallic electrodes. If we wish to go so far as to ascribe to particles possibly torn off from the walls of the vessel when they are discharged the same function which, in the view just considered, gas-particles or electrode-particles were unable to perform, this assumption, quite apart from all new objections, is open to all the objections urged against the previous hypo- thesis. Recent investigations have shown that the dust suspended in gases plays an important and previously unsuspected part in the loss of electricity suffered by feebly-charged conductors in the open air, or in gases not specially purified. In almost all cases in which we have hitherto regarded a mass of gas as a carrier of statical electricity, we must now regard the dust suspended in the gas, in cases where drops of liquid cannot he present, as the only vehicle of the electricity. We might easily imagine an hypothesis ascribing a similar essential func- tion to the dust in gases in the case of current electricity as in the case of statical electricity, but that the objections we have previously considered might easily be employed to refute an assumption of the kind. The discharge cannot then in general be explained by the motions of ponderable particles ; it follows therefore directly CC Discharge in Rarejied Gases. © 369 from the experiments which prove this, that that medium must be essentially concerned in the discharge which, accord- ing to our present views, together with the gas-molecules, the particles of the electrodes of the walls, and any other solid substances which may be present, occupies the space in which the discharge takes place—that is to say, the ether. According to my view, the discharge is a process which takes place in the free ether. I have already indicated this view in the work already several times mentioned, and will now give other evidence supporting the observation made there. Hittorf* found that the resistance of the positive light always decreased as the exhaustion of the gas increased ; on the other hand, he thinks he has shown that the resistance increases with the exhaustion in the kathode-light and at the surface of the kathode. Changes in the form and magnitude of the anode have no influence on the resistance. The great resistance which offers itself to the discharge at an extreme exhaustion, and finally leads to its extinction in a vacuum as perfect as possible, depends therefore altogether upon the resistance at the surface of the kathode and in the space filled by the kathede-light. After I had recognized that the pecu- liarities of the negative light might be produced at any point whatever of the column of positive light by simple changes in the cross section of the discharge-tube, and that each separate stratification of positive light is nothing else than a modified bundle of negative light, this opposition between kathode- light and positive light appeared to me just as doubtful as already a number of other supposed differences between the two, which I had found not to exist. I found in fact that, exactly as with the positive light, the resistance of the kathode-light at small pressures becomes vanish- ingly small in comparison with the total resistance of the dis- charge. Hence, since no specific resistance exists at the anode, and since further, as already mentioned, the resistance of the positive light vanishes in comparison with the total resistance of the discharge, it follows that the resistance to the discharge at very small pressures takes place entirely at the surface of the kathode. My experiments on this subject were not made by means of a galvanometer, like those of Hittorf, but by means of the spark-micrometer, which is here much more efficient. The spark-micrometer was included in a second circuit connecting the electrodes, and the distances of the poles of the micrometer compared for the different densities of gas and lengths of * Hittorf, Poge. Ann, cxxxvi. p. 1 (1869). 370 Dr. E. Goldstein on the Electric kathode-light at which the currents of the inductorium either cease to pass through the exhausted tube or else pass no longer through the micrometer*. * The distances of the balls of the spark-micrometer corresponding to these two alternatives are not exactly identical. The discharges do not pass exclusively through the exhausted tube up to a certain distance of the balls, and then with a certain small decrease of this distance exclu- sively across the air-space between the balls; but between the distances of the balls at which the spark takes one only of the two courses open to it are to be found positions of the micrometer at which both paths are taken —sometimes the one, sometimes the other—and the one path the less fre- quently the nearer we come to the distance at which the other is taken alone. This apparently unstable character of the resistance in the tube does not affect the accuracy of the measurements here in question; we may compare the resistances by comparing the distances of the balls apart at which for a certain fixed time, say two minutes, no spark passes in the tube or between the poles of the micrometer. The distances so measured agree upon repetition to ;'; millim.—that is to say, toa fraction of 1 per cent. of the distance measured. The alternation of the discharges with certain distances of the balls no doubt depends, partly at least, upon the same cause as the following phenomenon, which I have observed in the same experiments, and which, as far as I know, has not been pre- viously described. If we include the spark-micrometer in a branch circuit of an exhausted tube which transmits both the discharge at ‘‘ make” and that at “ break,” then, if the distance between the balls of the micrometer be gradually diminished, the current at “break ” completely leaves the tube and passes altogether in the free air, whilst that at “make” continues to traverse the tube with undiminished light. Consequently we are able to study the discharge of the “ make” current in the exhausted gas separate from that of the “ break” current; whereas hitherto a separation of the two currents has been effected by introducing an air-break in the direct cireuit inclu- ding the tube, with which arrangement the tube is traversed only by the discharge due to the “break” current. The reason of this phenomenon may lie in the different maximum tension of the current on “making” and “breaking” contact, and may correspond to the observation of tele- graphists, that discharges of great tension (as observed in electrical storms) will sooner traverse a short distance through air in the form of a spark than traverse a long metallic circuit in the form of a current. Such phenomena show that in the case of discharge through gases, the division of currents cannot be calculated according to Ohm’s law. This we see from the so-called Holtz’s “funnel-tubes.” If two similar tubes are placed opposite to each other side by side in the same induced currrent, then at suitable pressure of gas the current does not subdivide itself be- tween the two in any definite ratio to the resistances of the tubes, but the one tube remains entirely dark, the current goes altogether through the other. The law according to which currents divide when the discharge takes place in gas must therefore be investigated empirically in the first place. I take this opportunity of remarking that I have made an erroneous assumption on this subject in a series of experiments in my book pre- viously referred to, which, however, does not actually affect the result obtained. I believed myself justified in assuming as the evidence of certain phenomena (p. 146), that if a part of the discharge traverse a me- tallic circuit from the kathode a to an electrode 6, and then the resistance of a moistened thread be introduced between 4 and a wire c, that then the Discharge in Rarefied Gases. 371 One of the experimental tubes is represented in fig. 1. A cylindrical tube is provided with a flat kathode placed at right angles to the axis of the tube, and nearly as large as the section of the tube. The anode is placed close in front of it, or in other cases consists of a very short wire in the plane of the kathode itself. Inside the cylinder is a movable partition c, consisting of a short glass cylinder ter- minated by a plane surface at the end turned towards the kathode. In accordance with what I have noted on former occasions”, the positive light disappears for such an arrange- ment of the electrodes when the exhaustion has reached a certain limit, or it is confined to the immediate neighbourhood of the anode ; the kathode-light, on the other hand, expands to any extent if the exhaustion is sufficient, and the expansion of its rays is limited only by their striking upon a solid wall. Hence, when a sufficient exhaustion has been reached, we can vary the expansion of the kathode-rays within wide limits by sliding the piece ¢ (by inclining the discharge-tube and tap- ping it) along the tube; since its length is always equal to the distance between the kathode and the end-surface of the movable cylinder, which can be moved right up to the anodeft. If now the expansion of the kathode-light is made to vary in the ratio 1 : 30, the total resistance of the discharge at low pressures does not alter so much as in the ratio 1: 1-05. Hence the resistance of the kathode is a vanishing quantity in comparison with the resistance at the surface of the kathode. Hence we see that the resistance of the whole quantity of gas contained in a discharge-tube becomes smaller the more density of the discharge at ais not changed. ‘There is in fact a certain change; but its influence upon the phenomena considered in the place referred to is so small that, upon repetition of these experiments with actual constancy of density at a, results were obtained partly exactly cor- responding, partly nearly corresponding. The examples given on p. 149 for the magnitude of the deflective power in a particular case consequently represent these values at least very nearly. The same method was employed (p. 181) to confirm a result obtained by two other methods; so that the result given there is not affected by the failure of the experiment in question. * Goldstein, Phil. Mag. iv. p. 362; ‘A new Form of Repulsion,’ p. 8. + In order to resist blows without deformation, the anode in these cases was made of strong iron or steel wire. ; 372 Dr. E. Goldstein on the Electric the density of the gas is diminished ; the space in which the discharge takes place conducts better the less gas it contains ; and since this change is always in the same direction while the density is continuously reduced, so far as the experiments can be extended, we must conclude that the greatest conduc- tivity would be obtained after complete removal of the gas. But after complete removal of the gas the discharge-space contains only free ether; and I therefore regard this as the true medium of the discharge. Any gas present seems to act only as a hindrance to the ether. Detailed speculations on the concrete form of the motion of the free zther to which the discharge is due are, in my opinion, premature. We are not justified in regarding the discharge as essen- tially a progressive motion of the ether so long as, on the one hand, we regard Doppler’s principle as valid in optics, and, on the other hand, refuse to attach any considerable value to the progressive motion of gas-particles in the discharge. We must’ then ascribe to the motion of the ether amongst the relatively stationary gas-molecules an optical effect precisely similar to that produced by the motion of gas-molecules in ether at rest. Experiments on the constancy of gaseous spectra when observed in directions parallel and at right angles to that of the electric rays, show at once the absence of progressive motion of the ether (of velocity comparable with the velocity of propagation of the ray-discharge), after we have shown by other experiments* the relatively stationary condition of the gas-molecules. It appears to me safest to characterize the motion of the eetber in discharge as radiant, in accordance with what has been previously statedt. Every particle concerned ina pencil of negative light assumes the same form of motion which is excited at the point of origin of the pencil. The behaviour of the discharge towards magnetic forces has frequently been brought forward in support of the view that the gas-mass forms the medium of the discharge, since this behaviour may obviously be explained by regarding the gas- molecules as carriers of electricity. If the magnet acts upon the positive light of an equatorially-placed cylindrical tube with electrodes at the end, and finally compresses the light which at first filled the width of the tube into a thin thread lying in the equatorial plane against the wall of the tube, itis generally assumed that the gas-molecules are compressed together with the electricity; Ihave not found this confirmed. * Goldstein, ‘A New Form of Electric Repulsion,’ Chap. IV. + Phil. Mag. x. p. 184. Discharge in Rarefied Gases. 373 A piece of metallic sodium was introduced into a cylindrical vessel 4 centim. in width and more than 20 centim. long, having the electrodes at its ends; and the tube was then quickly filled with dry nitrogen. After the tube had been so far exhausted that its positive light filled the section of the tube, the sodium was brought upon a part of the wall of the cylinder, in a hori- zontal position, played upon by the positive light. The sodium was next warmed until no more hydrogen was evolved, the tube was refilled with fresh nitrogen, and exhausted again to the same density as before. The sodium is then heated strongly until it begins to volatilize, and the discharge, which was reddish purple before, assumes a golden-yellow colour in its neighbourhood. If the heating be carefully managed, it is seen that the sodium vapour diffuses itself very slowly; so that the discharge in the upper part of the tube still shows the red colour due to the nitrogen, whilst it is of a golden yellow in the lower part of the tube. If the tube be brought in a hori- zontal and equatorial position near to a strong magnet, whose poles are so placed that the positive light is drawn upwards, the discharge, which at first filled the whole width of the tube, is concentrated into a thread of greater or less tenuity against the upper surface of the tube. But this thread possesses the pure purple colour of the nitrogen discharge without any trace of the sodium-yellow. The sodium vapour is consequently not displaced by the magnet, together with the current, as we are accustomed to see with movable carriers of electricity; the current seems to obey the magnet with- out affecting the gas-molecules. The result is exactly the same in experi- ments ‘made with the Holtz machine instead of the induction-coil. I have further examined whether it is possible to recognize a transport of gas-molecules by means of the magnet, in the local increase of density which must result from the assumed transport in a closed space traversed by the dis- charge. Two discharge-tubes, A and B, fig. 2, were joined together in the man- ner shown by means of a tube in which a stopcock was inserted. A second stop- cock at the end of a short tube shuts B off from the pump during the time oc- cupied by an experiment. The cylin- drical portions of A were sufficiently long to show stratified positive light, at least in the cylinder containing the anode, 374 Dr. E. Goldstein on the Electric when pure dry air was employed. The distance between the similar boundaries of the different layers, or the number of layers in a given distance, is a very delicate test for change of density in the gas. Changes in the residual gas which corre- spond to less than ;4, millim. mercury are shown by very marked changes in the interval between the layers*. The current of a coil was first sent through A, the number of layers in the anode-cylinder determined, and the boundary of each on the kathode-side marked on the tube with ink, thus marking the size of eachlayer. The current was regulated so as to give perfectly steady stratifications. Opening and closing the tap h, before or after turning on the current, did not affect the position of the stratifications. The combination was now brought near to an electromagnet while the current was pass- ing and while the tap h was open, the poles of the magnet being so placed that the discharge appeared compressed towards the side of the tube B furthest from the tube A. If this concentration of the discharge depended upon an increase in density of the gas, then the gas in B outside the column along which the discharge passes must be rarefied, and gas from A would enter and rarefaction in A would result. After a few seconds h was closed, the current of the magnet was interrupted, the tube removed from the neighbourhood of the magnet to guard against the effect of any residual magnetism, and the discharge again sent through A. The number and position of the layers were found to be exactly the same as before the action of the magnet on the discharge. The same result was obtained by operating as follows :— The initial density of the stratified discharge of an induction- coil through A was noted; then, after interrupting the current of the coil, the rapidly following discharges of a powerful Holtz machine were sent through B; and this discharge was subjected to the action of the magnet. On now again pass- ing the current of the coil through A, there was no sign of — any change in density; any change which had taken place must therefore have been less than 745 millim. mercury; on the other hand, the change of density necessary to produce (when possible) effects upon the discharge, similar to those produced by the action of the magnet at constant density, must be measured by centimetres of mercury. The theory which makes the gas molecules the carriers of the current is therefore in no way supported by experiments with the magnet. The view which 1 take of the part played in the dis- * By the interval between two consecutive layers I understand here and elsewhere the distance between the bounding surfaces turned towards the negative pole. ia Discharge in Rarefied Gases. | 375 charge by the free zether is commonly supposed to be refuted (where it is mentioned at all as a possible case, e. g. in text- books) by a reference to the experience of spectrum-analysis. If the zther were the vehicle of the discharge, it is said, all gases would give the same spectrum—the spectrum of zther— when subjected to the discharge. But since each gas has a special characteristic spectrum, the gass mass must be regarded as the conductor of the electricity. But it is well known that the zether itself has no power of emitting light. The fact that it has no “ spectrum ”’ is therefore no evidence that it cannot conduct electricity. With equal justice it might be argued that the phenomena of light and heat due to a current can only be produced in the molecules of the conducting substance; every conductor in whose mass non-conducting particles are embedded proves the contrary. The luminosity of a gas pro- duced by the discharge depends entirely upon its molecules possessing the form and period of oscillation which are neces- sary for the emission of visible rays. That this vibrating * motion is accompanied by motion due to electricity, executed by the particles themselves or their zether-envelopes, does not seem to be necessary; but, as the phenomena of fluorescence and phosphorescence in sunlight show, the molecules of bodies may execute motions of the form and period of the vibrations of light by taking up the vibrations of the surrounding free eether. T assume that a similar process take place when a gas is rendered luminous by the electric discharge. The discharge itself represents a motion of the free ether, and is in itself non-luminous. This motion of the ether disappears, being communicated to the gas-molecules and their constituent atoms; the particles of each molecule then vibrate in accord- ance with their special structure and the conditions as to elasticity of the molecule, and communicate again to the zether the transversal vibrations so produced as such; thus the original motion which the ether possessed as electricity is converted into light, and of course into light whose oscilla- tion-periods depend upon the specific nature of the gas-mole- ecules. The difference in spectrum between chemically dif- ferent gases thus in no way disproves the conduction of elec- tricity by the ether. I thus regard the luminosity of gases traversed by the electric current as a phenomenon of reson- ance. Ishould not be disposed to regard it as a phenomenon of fluorescence or phosphorescence, for two reasons :—(1) Because in fluorescence and phosphorescence the vibrations are transferred from the ether to the atoms, and back again to the zther, without changing their character as transversal 376 Dr. E. Goldstein on the Electric vibrations; here, on the contrary, a motion of the ether which does not consist of transversal vibrations is converted into transversal vibrations. We have, however, a phenome- non analogous to this in acoustic resonance, where we see the longitudinal motions of particles of air transformed into the transverse vibrations of a resounding string. (2) lam dis- posed to reject the name phosphorescence for the phenomena under consideration, because, according to all the ideas which we have so far associated with the name phosphorescence, an hypothesis as to the temperature-conditions of the discharge would be introduced by the choice of this name, since the temperature of a gas is always supposed to be lower than that of a gas of like emissive power rendered luminous by heat. But this, even assuming that the conclusions of E. Wiode. mann as to the temperature of the discharge should be con- firmed by further experiments, is not yet accepted as the true character of the light of the discharge; and my speculations on the nature of the discharge do not in any way prejudice the question of the temperature of the discharge. For the present I leave this entirely out of the discussion. The assumption that a vacuum conducts electricity has con- sequences which are far-reaching, especially in the domain of cosmical physics. The usual fate of attempts to found a cosmo-physical theory upon experimental results is scarcely such as to encourage imitators. At the same time I venture to point out at least so much as this, that certain terrestrial phenomena of an electric or magnetic nature which, because of the coincidence of their periods or epochs with solar changes, have been explained as due to the statical influence, magnetic induction, &c. of the sun’s mass, might possibly be more conveniently referred to electric currents radiating through interplanetary space from the central body. Expe- riment shows no limit to the expansion of that remarkable motion which we observe in the kathode-rays as we eliminate the ponderable medium more and more completely—it is conceivable that the sun radiates electric rays as well as light- rays through space. We see that even when the two poles are placed close together, the kathode-rays stream out into space without limit, without reference to the position of the anode; consequently for electrical communication with the sun, it would not be necessary that the earth should be the source of electricity or pole of the current, but discharges for which both poles are situated on the sun might produce rays radiating from the sun into space. a : | Discharge in Rarefied Gases. 377 IL. _ I consider two processes to be necessary for the production of the discharge:—(1) A change in the condition of the ether, preceding the discharge, which produces a certain condition of unstable equilibrium in the arrangement of its parts: this condition may be called, for shortness, tension of the ether. (2) The restoration of equilibrium: this constitutes the dis- charge itself. The tension which precedes the discharge is not equally great in all cross sections of a discharge-tube, even when the - tube is of equal section throughout; it may even equal zero in certain parts of the tube. ‘The tension has either finite or maximum values at the surface of the metallic poles and at those points which appear as points of issue of the separate positive layers or of the secondary negative pencils. The resultant of the opposing force produced by the tension on each element of the kathode is directed away from it; at the other points of issue also, it is directed at each point towards the side turned away fromthe kathode. When the restoration of equilibrium commences, a motion results in consequence of the finite or maximal tension on the surfaces, which ad- vances to the side of each surface of issue remote from the kathode, and, originally excited in free ether, transforms itself secondarily on its way into transversal vibrations of the ma- terial atoms. The distances in which the tension before the discharge was zero, and in which the, motion excited at the surfaces of issue does not propagate itself, remain dark; such places are the distances between the positive light, on the one hand, and the kathode-light or secondary negative light, on the other hand. The greater the exhaustion becomes, the more do the dis- tances between the surfaces of origin increase, and at the same time also the distances to which the motion excited at the sur- faces of issue extend. This latter increase, however, is com- pleted more rapidly than the increase in the distances between the surfaces of origin; hence it comes that one and the same section of the space occupied by the discharge may be affected by motions which radiate from two or more surfaces of origin. (Penetration of the kathode-light into the positive light or of the stratified pencils into each other.) Experience shows that such motions penetrating each other do not sensibly alter each other when their directions are the same; but when their original directions are inclined to each other at a considerable angle, they show marked phenomena of deviation *. * Goldstein, Wien. Ber. 1876, 23 Nov. Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2C 378 Dr. E. Goldstein on the Electric That the so-called sether-envelopes of the gas-molecules or atoms take part in the emission of light resulting from the dis- charge is a matter of course ; but the part which they play in the processes of charging and discharging must remain for future discussion. The forces exerted by the material particles upon which the formation of the zether-envelopes depends, tend to produce a different disposition of the ether from that which would result from the electrical forces only. Consequently the more gas-molecules are included in the space occupied by the discharge, the greater the electrical forces must be in order to bring about the disposition of the ether which must precede the discharge. Hence we understand how the gas acts as a hindrance to the discharge, and why conduc- tivity of the space occupied by the discharge continually im- proves as the gas is more and more completely removed. In any case, 1am unable to accept EH. Wiedemann’s view%, according to which the zther-envelopes are the real medium of the discharge. If, moreover, the ether-envelopes suffer deformations without the free ether taking any part in the process (and in the case of the kathode-discharge Wiedemann excludes any such participation), then, as regards the velocity of propagation of the discharge, Wiedemann must assume a pure distance-action between the zther-envelopes, since in highly rarefied gases we regard the times during which the zether-envelope and the sphere of action of a molecule are in contact with those of other molecules, or penetrate them, as small in comparison with the times during which the sphere of activity is isolated. The assumption that the direction of the negative current from the kathode is the direction in which the electric dis- charge is propagated in the kathode-light, and also in the secondary negative pencils and positive stratifications, con- trary to the usual view, seems to be justified by numerous experimental results. I would call attention, first of all, to the phenomena of shadows, which, formerly observed only with the kathode-light, have caused this phenomenon to be represented as a motion from the kathode, even by the de- fenders of the convection theory. If a solid body be placed in a pencil of the kathode-light, or of the secondary negative light, then, as may be observed directly, that portion of the pencil falling upon the object which lies between its end turned towards the kathode and the object itself remains in every case intact, but that portion of the in- cident pencil lying on the further side of the space occupied by the object is wanting. The shadows previously described f, * E. Wiedemann, Wied. Ann. x. p, 245, 1880; Phil. Mag. [5] x. p. 419. + Phil. Mag. [5] x. p. 236. sta iat i i a rts ae, - formed in the phosphorescent surfaces excited by the positive light, and their position indicate similar behaviour. If the electric rays in the kathode-light proceeded from its exterior boundary towards the kathode, and in the secondary negative and positive pencils from the side of the anode towards the side of the kathode, then, on introducing an object, the pencil of rays would, on the contrary, remain intact from the exte- - rior boundary up to the object, and the shadows would appear upon the wall upon the kathode side of the object. Another argument for propagation in the direction of the negative current is found in the phenomenon described above, that the properties of secondary negative rays are, even for considerable distances, such as correspond to the conditions which exist at the negative boundary of the pencil of rays— that is, the one nearest to the kathode. The pencil, which with increasing evacuation radiates continually more and more from the mouth of a narrow tube opening into a wider vessel, contains rays possessing the properties of the light of narrow tubes. If the pencil had its origin in the wider vessel and propagated itself from it into the narrower tube, we should expect to find its properties more in accordance with the conditions of discharge offered by wide tubes. The pencil between a narrow cylinder and a wider one following upon this upon the side of the anode would show then the same colour and spectrum as those pencils which have their origin in the wide cylinder and compose the column of its positive stratifications. A further criterion for the direction in which the electric rays propagate themselves is found in their magnetic behaviour as described above for the kathode-rays, in accordance with Hittorf’s conclusions. It is characteristic of this behaviour that if a (sufficiently weak) magnet is allowed to act upon the end of a long kathode-pencil remote from the kathode, only this end is affected by the magnet, whilst those portions of the pencil near the kathode retain their form and position unaltered. Ifthe magnet is brought into the neighbourhood of the kathode itself so as to act upon the portions of the rays nearest the kathode, then the whole pencil is deflected together with these portions even toits furthest point, upon which, in consequence of its great distance, the magnet could exert no action directly. The electric particles (or ‘the electric motion) at the end of the ray remote from the kathode therefore follows the direc- tion impressed upon the particles at the kathode itself; but the particles at the kathode are not influenced by action upon the particles at the further end. Both phenomena agree with 2C 2 Discharge in Rarefied Gases. 379 380 Dr. E. Goldstein on the Electric the theory that the particles at the outer end of the ray were previously at the kathode, and are immediately opposed to the view that the particles nearest to the kathode have already passed through the place occupied by the remote ends; that is, the motion in the kathode-light must propagate itself from the kathode outwards. Exactly correspondent are the phenomena of the rays of the secondary negative pencils, and also of the rays of the sepa- rate positive stratifications, when these are sufficiently expanded by high exhaustion. Hence the discharge propagates itself also in each separate stratification from the bounding surface on the kathode side to the boundary on the side of the anode. The often-mentioned phenomena of deflection are to be inter- preted ina similar manner. If K (fig. 3) be the projection of a plane kathode, K’ that ofa thin wire, quae s the natural direction of an electric ray issuing from K, then the ray through K’ takes the form s K’s’; at K’ it bends round through a considerable angle, and beyond K’ follows again a straight course, which, however, deviates considerably from the direction s K’; 7. e. the portion of the ray beyond K’ obeys the deviation which was exerted upon the electrical particles at K’. Hence the forces which produce motion between the first point and the kathode. This is very simply explained by the hypothesis that the electrical motion in the ray propagates itself from the kathode outwards (in the direc- tion of the arrow). ITI. The velocity and direction of the discharge of a pencil of electrical rays is to be distinguished, a priori, from the velo- city and direction with which the tension that precedes the discharge propagates itself. We are not here further con- cerned with the velocity of this tension, but only with its direction. I believe that the phenomena observed indicate very plainly a propagation of the tension also in the direction of the negative current; that is, the tensions for the separate positive stratifications are developed in the same order of time as that in which they follow each other in space from the kathode towards the anode. I draw this conclusion from the fact that the position and peculiarities of the separate com- pletely formed stratifications, and in particular the position of Discharge in Rarefied Gases. 381 the heads of the stratifications, 7. e. of the points from which the separate discharges formed by the stratifications issue, de- pend altogether upon the positien and peculiarities of the kathode, and not at all upon the conditions of the anode*. Let the discharges pass in a cylinder with terminal elec- trodes which can be moved along the axis of the vessel towards each other by means of an arrangement which need not at pre- sent be further described. If the anode in such a vessel is caused to approach the fixed kathode, no displacement whatever of the stratifications in front of the anode is observed; they remain altogether im- movable and unchanged, so far at least as their continued existence is consistent with the new position of the anode. Since the positive light in every case reaches only to the anode, the layers which were situated in the portion of the tube * The experiments described in what follows are performed with stra- tified discharges in pure dry air or in dry highly exhausted hydrogen, produced from a sufficiently powerful induction-current by regular inter- ruption of the primary current. Under these conditions we obtain thick stratifications which do not vibrate to and fro like the so-called “ saucer” stratifications, but, with a constant pressure of gas, preserve their position unaltered. I think it necessary to mention this, because to many who are still accustomed, upon mention of stratifications, to figure to themselves only the “ saucer ” stratifications and their behaviour, the mention in the following of motionless stratifications with constant intervals between them may appear surprising. The thick stratifications, strange to say, are always treated, sometimes as quasi-pathological developments, as phe- nomena which are disturbances of the normal phenomena of stratification ; sometimes as optical illusions, caused by rapid vibration to and fro of the “saucer” stratifications assumed to exist alone. According to the evi- dence I have given, the meaning and mutual relation of the different forms of stratification are tolerably clear; each separate layer in a cylinder is qualitatively analogous to the discharge at a kathode which occupies the whole section of the cylinder. When the exhaustion is small this kathode-light is only a thin layer, corresponding exactly to the thin “saucer” stratification. If the exhaustion proceeds, the electric rays which make up either structure lengthen and so increase its thickness; and just as the kathode-rays finally lengthen so much as to completely fill the dark space and reach to the first positive layer, so the rays of stra- tifications extend so much as to completely occupy the dark spaces between them. As the density of the gas decreases the thickening proceeds further, the intervals between the heads of the layers continually increasing, and the rays issuing from the heads continually occupying the increasing intervals. When the stratifications appear most plainly in a cylinder with dry air, their thickness is very nearly equal to the diameter of the cylinder, so that with wide vessels they are of considerable thickness. As little as a kathode-discharge with extended rays is a monstrosity or disturbi phenomenon, or consists entirely of a luminous layer vibrating to and fro, so little can we entertain similar views about the thick layers ; and as the laws of the kathode-light may be studied most easily in the longest pen- cils of it which can be obtained, so also it is just the thickest layers which represent the phenomenon most completely developed, which are in the first instance best suited for the study of the stratification. 382 Dr. E. Goldstein on the Electric passed over by the anode in its approach to the kathode dis- appear one after the other, presenting the appearance of the layers being gradually absorbed by the anode. If the anode is caused to move from its original position away from the kathode, then all the layers originally present remain unaltered, whilst new layers appear in the space left by the anode, of which each immediately upon its formation remains completely indifferent to the further motion of the anode. Let us now move the kathode, and first let the motion be an approach to the fixed anode; at once the whole of the layers present begin to move, and are displaced each in the same direction and exactly by the same amount as the kathode itself. (In the distance occupied by the discharge, shortened by the approach of the poles, there is consequently room only for fewer layers than before ; each layer disappears as soon as it is pushed up against the anode by the motion of the kathode.) If the kathode is removed from any initial position whatever further away from the anode, all the layers present follow the kathode, and keep exact time with the motion of the kathode itself; new layers appear in the space between the last of the layers originally present and the anode as the kathode moves further away, and each immediately after its formation follows the motion of the kathode*. ~~ The interval between every two layers in a cylinder is so little different in passing from one pair to another, that in a cylindrical column of stratified light at given density of gas and intensity of discharge, we may speak simply of the stra- tification-interval of the column. The number of layers present is therefore equal to the quo- tient of the length of the column by the stratification-interval. If the distance of the electrodes varies continuously, this quotient will only be a whole number in particular cases. If the division of the space occupied by the discharge into layers advanced from the anode, then in the case when the length of the positive light is not divisible by the stratification-interval without remainder we should expect that the incomplete and abbreviated layer corresponding to this remainder would be found at the negative end of the positive light, whilst at the anode there would be nothing but complete layers. Observation shows exactly the contrary: the positive layer nearest the negative end of the positive light, 7. e. nearest to the kathode, preserves the same constant extension with every distance of electrodes; so also the following layers, only the one directly in contact with the anode shortens or lengthens * Goldstein, Phil. Mag. [5] iv. p. 362. F : | Discharge in Rarefied Gases. 383 exactly in proportion as the excess of the above-mentioned quotient above a whole number changes. The changes of colour are also strikingly characteristic of the influence of the kathode, as explained above. The conse- cutive layers of a column of positive light may show very striking differences of colour, even when no differences in form and magnitude can be perceived; these differences are very marked when hydrogen is employed. The colour of a layer when the difference of electrodes changes is always, ceteris paribus, dependent on its position with refer- ence to the kathode. Suppose, for example, that we observe a cylinder the positive light of which is divisible into five layers, the one next the kathode being blue, and the following ones in order being yellow, red, greyish red, and grey. Next to the anode we have, therefore, a grey layer. If the distance of the electrodes is now diminished by the length of one layer, whether by the motion of the anode or of the kathode, it is the grey layer which disappears, and we have a greyish-red layer next the anode followed by the rose-coloured, yellow, and blue layers in order. If the distance between the electrodes be further diminished by the length of one layer, the greyish-red layer disappears, and the rose-coloured layer is in contact with the anode, followed by the yellow and blue layers in order. When the poles are caused to approach further so as to leave only two layers, the yellow layer is next the anode, and the blue layer tollows it. If, therefore, we count the layers from the anode, then with every change of distance between elec- trodes, the first, second, and every layer change colour; but if we count from the kathode, then the colour of the nth layer is independent of the distance of the electrodes, and each layer present possesses always the same colour. Hence the colour of each layer is regulated by the position of the kathode, and depends on its position in the series, counting from the anode. Lastly, we may vary the size of the anode indefinitely with- out causing any change in the position of the layers present ; but if the magnitude of the kathode be changed, the position of all the positive layers changes. The smaller the kathode becomes, under conditions otherwise similar, the larger becomes the interval between the kathode and the first positive layer, but the interval petween the positive layers is not altered ; so that each single layer lies further from the kathode the smaller the kathode is made. We cannot, however, assume that the kathode, or the phy- sical conditions which obtain at the kathode determine the conditions of tension and discharge of the whole stratified 384 Dr. E. Goldstein on the Electric column; but it appears that the position and properties of each separate layer depend mainly or entirely upon the position and properties of the layer preceding it on the side of the kathode. The influence of the kathode on all the members of a stratified column, which appears so markedly in the experi- ments just described, would then be only an indirect one, inas- much as the properties of the kathode determine the proper- ties of the kathode-light ; this determines the position and properties of the first positive layer, this the position and properties of the second layer, and so on. This conclusion is drawn from experiments on the secondary negative light. We saw that in a cylinder where the kathode is moved, all the layers move in the same direction as the kathode and through an equal distance. If now we introduce into the cylindrical tube C (fig. 4), with movable kathode K, a por- tion of tube R fitting C closely and also movable in it, haying a narrow opening at «, then, as already explained, « acts as a secondary negative pole for the portions of the whole discharge between and the anode A*. If now, whilst R retains the same position in any portion of the discharge-cylinder, the kathode K is moved, all the layers between K and « move as in the previous experiments ; but the layers between x and A remain immovable, in spite of the displacement of the kathode. If, on the other hand, K be fixed and R be displaced, so that the secondary negative pole «© moves with the secondary nega- tive light radiating from it, then all the layers between and A are displaced exactly like the stratifications of a simple cylinder haying a metallic kathode at z. If the separate layers of the discharge show different colours, then we observe further that, when K moves, the colours of all the layers between K and « behave as previously described * A may with advantage be made short, and placed somewhat excen- trically but parallel to the axis of the tube, so that it may not be struck by the movable piece R. goueme bae. Discharge in Rarefied Gases. 385 for the simple cylinder, but the colours of the layers between z and A show no regular relationship to their position in order from K; their colours remain the same however their position in order varies. But if « be moved, the same law holds good for these layers as if z were a metallic kathode—the colour of each depending on its position in order from «, and the colour of every nth layer, counting from 2, remaining the same for every position of x. The dependence of the stratifications upon their secondary negative pole, and the complete analogy with the dependence upon the metallic kathode, is seen, lastly, also in the influence of the magnitude of the secondary pole. If its magnitude be diminished the layers become further apart, as if from a dimi- nished metallic kathode; and the displacement is in both cases more marked when the surface of the pole is diminished in a greater ratio”. If we have now a tube (fig. 5) provided with two secondary poles w and y of this kind, of which only z is movable and y is fixed (the piece RY of which y is the mouth may be conveniently united with the wall of the large vessel by fusion when * The diminution of a secondary negative pole- may be effected in a variety of ways. Fig. 6 shows in one diagram three different simple arrangements for effecting this :— In eylinder I. a glass diaphragm is arranged perforated with two round openings of different sizes; a glass ball is also enclosed in the tube, whose diameter exceeds that of the largest opening. By allowing the glass ball to rest upon the one or the other of the two openings, the dis- charge issues from a larger or smaller secondary pole. (Of course the opening acts on the side towards the ka- thode as a secondary positive pole.) In cylinder II. the opening x of the communicating glass tube is the secondary negative pole; a glass rod, provided at one end with a knob to prevent its falling completely through, is movable to and froin 7». It is clear that by this means the magnitude of the opening x may be varied. Cylinder IiI. shows the simplest arrangement, a glass tap the perforation of which replaces the communicating tube. The magnitude of the secondary pole is a maxi- mum when the tap is completely open. If we gradually turn the tap from this position, and so gradually reduce the magnitude of the secondary negative pole, we see the layers gradually recede from the pole. The adyan- }f tage of this arrangement is found in the power of gradu- ally altering the magnitude of the pole ; its disadvantage |j in the gradual alteration of the quantity of gas contained in the tube, by the evolution of gases produced by the action of the discharge on the substance with which the tap is lubricated. 386 On the Electric Discharge in Rarefied Gases. the apparatus is constructed), w lies between the kathode K and y. Ifthe kathode K is movable, we observe first that its motions only affect the stratifications between it and z, but, on the other hand, all between « and y, as well as those between y and A, are unaffected. If z is moved, we find that the motion of this pole causes a motion only of the stratifications between # and y; the stratifications between y and A remain unmoved. In the same way, when the magnitude of the negative pole varies, it is found that only changes in the pole y affect the position of the stratifications between y and A. Hence the position of each stratification depends on the position and properties of the secondary negative pole, or pencil of secondary negative light nearest to it. But since each separate positive layer, even in a simple cylinder, is, as I have shown%, only a form of the secondary negative pencil (the section of its origin is itself a secondary negative pole), it fol- lows that the position and properties of each separate layer, even in a simple cylinder, do not depend so much upon the kathode and kathode-light as upon the position and properties of the layer immediately near it. If, then, in a simple cylinder all the stratifications are put into motion by displacing the kathode, it follows that the motion of the kathode itself properly causes only a corresponding change in the position of the kathode-light which issues from it; the displacement of the point of origin of this last displaces the surface of origin of the first positive layer; this change displaces the surface of tension for the second layer, and so on. I have mentioned that, in a simple cylinder, the consecutive intervals between the stratified layers of the positive light differ very little from each other; but if we observe also the very stnall differences which present themselves, we find that the intervals graduaily decrease from the kathode towards the anode. If the space in which the discharge takes place be contracted at any point whatever so as to produce a secondary negative pole, then the intervals diminish only up to this pole; beyond it the intervals suddenly increase and a new series of decreasing intervals begins, again increasing beyond a new secondary pole, and soon. We find, then, that the magni- tude of each stratification-interval is determined by the ratio of the secondary negative pencil produced by the change of section which immediately precedes the interval under consi- deration. In passing to infinitely small changes in section when the secondary negative pencil passes into a positive layer, we find that the magnitude of the interval between any two layers * Goldstein, Berl, Monatsber. 1876, p. 280; Phil. Mag. [5] iv. p. 361. ee Carbon Dioxide as a Constituent af the Atmosphere. 387 depends on the properties of the layer forming the component of the pair nearest to the kathode ; or, shortly, each layer, or the conditions existing at its point of origin, always influence the layer following next to it, on the side of the anode, but does not influence the preceding, on the side of the kathode. The conditions under which the nth layer forms seem to stand to the properties of the n+1th layer in the relation of cause and effect ; and hence it seems to me only a verbally different expression of the observed facts if we assume, as above, that the propagation of the electrical tensions, or the produc- tion of the separate layers, takes place in the direction of in- creasing values of n, 2. e. advances from the kathode towards the anode. Berlin, Physical Institute of the University. XLII. Carbon Dioxide as a Constituent ofthe Atmosphere. By Hrnest H. Coox, B.Sc. (Lond.), A.R.C.S., Lecturer upon Chemistry and Physics at the Bristol Mining School*. (*® all the agents which have brought about geologic changes and modified the surface of the earth from time to time, the atmosphere seems to have been the least studied. Nor is this very surprising when we remember the peculiarity of its action. So general and cosmopolitan are its effects that their very abundance causes us to overlook them—and, again, so slowly acting that the changes effected require the employ- ment of long periods of time. The two constituents of the atmosphere which have been most active in producing these changes are the oxygen and the carbon dioxide. The latter substance occurs in the air in such a relatively small amount that we are apt to underrate its influence. But when it is remembered that, were it not for the presence of this sub- stance in the air, no coal and very little limestone could have been formed, we at once see its importance. In fact, to come somewhat nearer home, without carbon dioxide in air no vege- table growth could take place ; and without plant life very little, if any, animal life would occur. Thus this substance, although in itself inimical to most forms of animal life, is absolutely necessary in the atmosphere in order that those animals may exist. In the present paper an attempt is made to consider some of the results arising from the presence of this substance. * Read before the American Association for the Advancement of Science at Montreal, on August 25, 1882. Communicated by the Author, 388 Mr. E. H. Cook on Carbon Dioxide Amount of Carbon Dioxide in the Atmosphere. This question has been made the subject of experiment by many of our leading chemists. In order to calculate the ab- solute amount, we require to know two things—viz. the capa- city or weight of the air, and the percentage of CO, which it contains. Fortunately the data for doing this have been determined with very great accuracy. The lengths of the diameters of the earth have been determined to be very nearly 7899 miles for the polar and 79254 for the equatorial ; “and. in these measures it is pretty certain that there is not an error of a quarter of a mile”’*. Applying the ordinary rule for the cubic content of an oblate spheroid, we obtain 259,026,554,299 cubic miles as the capacity of the earth. Now the height of the homogeneous atmosphere is found to be 26,214 feett, or very nearly 5 miles ; calculating the capacity of the spheroid formed by adding this distance to the lengths of the diameters given above and subtracting the capacity of the earth, we obtain the cubic content of the atmosphere supposed homo- geneous: this is found to be 591,647,337 cubic miles. With regard to the amount of carbon dioxide present in the air, the older experimenters, Dumas and Boussingault (Ann. Ch. Phys. iii. pp. 257, 288), Lowy and Saussure (Pogg. Ann. xix. p. 891), have published results which yield a mean of 4 vols. in 10,000 of air, or 43 parts in 10,000 by weight. Thorpe (Journ. Chem. Soc. vol. xx. p. 189) has shown that over the sea the average is 3 vols. in 10,000 ; while Saussure states that at high altitudes the proportion of dioxide is greater than at lower levels. Without deviating very far from the truth we may take 4 vols. in 10,000 of air; and we thus find (assuming capacity of air to be 592,000,000 cubic miles) 236,800 cubic miles as the amount of CQ, in the atmosphere. Finally, calculating from the specific gravity, we find the weight to be 4287 billions of pounds. Expressed on the metric system these figures become:— Cubic capacity of air... 2,439,987,200,000,000,000 kilolitres. Weight of CO, in air... 1,913,685,903,480,000 kilogrammes. I have given these calculations somewhat in detail because of the great difference between my numbers and those hitherto published. Thus, Dumas and Boussingault (op. cit.) say that the air is equal in weight to 581,000 cubes of copper each havin a side of 1 kilometre: this gives 4,200,000,000,000,000,000 kilolitres as the capacity of the air, or very nearly 40 per cent. * Herschell, ‘ Familiar Lectures,’ p. 53. t+ Maxwell, ‘Theory of Heat,’ p. 228, NN EE EEEEeEeEeEEeEeEeEeEEEEE eG eee eS Sa r,l,l ee as a Constituent of the Atmosphere. 389 too high. Again, Roscoe and Schorlemmer (‘ Chemistry,’ vol. i. p. 449) state that “the amount of CO, in the atmo- sphere reaches to upwards of 3000 billions of kilogrammes,” which is about 33 per cent. in excess of the truth*. Sources whence the Air derives its Carbon Dioxide. These are mostly natural ; but the progress of civilization has added a large artificial supply to those already existing. We may state them as follows:— (1) Combustion of carbonaceous bodies. (2) Respiration of animals. (3) Decomposition of vegetable and animal substances. (4) Volcanos and other subterranean supplies. Under the first heading is included the amount produced by the burning of coal, wood, peat, &c. From the most re- cently issued statistics with regard to the amount of coal raised in the world that I have been able to consultTt, I find that for the last three years at least 280 millions of tons have been raised annually. This is probably a slight underestimate. Assuming that 75 per cent. of this consists of pure carbon, which if completely burnt in air would produce CQ,, and allowing a further 10 per cent. for the carbon thrown away with the ash, we leave 182 millions of tons which are annually converted into carbon dioxide. This will produce 1,800,000 tons per’day, or very nearly 1800 millions of kilogrammes per day. Assuming that by the combustion of wood, peat, oil, &c. there is added one third more, we produce a total of 2400 millions of kilogrammes daily. In the case of the respiration of animals we can only form an approximate estimate. The population of the world is at present about 1500 millions; and it has been shown by experi- ment that each individual produces on an average about a kilogramme of CO, per day of 24 hours. Thus the human race, in respiring, add to the air about 1500 millions of kilo- grammes of carbon dioxide perday. Remembering the large * The above calculations are made on the figures deduced from the results of the experimenters cited above. Recent investigations have, however, thrown some doubt on the correctness of these numbers, the general opinion being that 4 vols. in 10,000 is much too high. Thus, Fittbogen and Hasselbarth (Chem. Centr. 1875, p. 694) give 3:4 vols. in 10,000 as the average; Farsky (Chem. Centr. 1877, p. 198) found 3-4, while more recently Reiset ( Comptes Rendus, lxxxviii. pp. 1007-1011) de- duces 2:942, Taking the mean of these numbers, we have Weight of CO, in air .... 1545 billions of ilogrammes nearly. + Mineral Statistics for Great Britain for 1881; and Smyth’s ‘Coal and Coal-Mining,’ latest edition. ‘ 390 Mr. E. H. Cook on Carbon Dioxide amount of animal life existing on the globe, and also that many of the larger species produce a greater quantity in a given time, we may with asufficiently near approach to accu- racy say that from the lower animals the air receives twice as much daily as from man. Hence from the whole animal kingdom we derive about 4500 millions of kilogrammes. The amount of dioxide which the atmosphere receives from decaying animal and vegetable substances is impossible to esti- mate. Most of it is produced in regions far away from the abode of man. That aconsiderable quantity is produced from this source, however, is evident when we consider the vast quantity of vegetable matter which year after year falls to the ground and undergoes decomposition. In fact, if the estimate of the amount of action exerted by plants given later on in this paper is a correct one, we must conclude that a much greater amount of dioxide is produced by this process than has been hitherto supposed. Although it is evidently impos- sible to give figures, yet, in order to arrive at a numerical estimate, we may assume that the same quantity is yielded as by man, viz. 1500 millions of kilogrammes daily. The last source whence the air receives its supply of carbon is from volcanos and the fumaroles and rents in the ground in volcanic districts. The amount thus supplied is enormous, both active and extinct voleanos joining in increasing the quantity. Considering the area occupied by the volcanic dis- tricts, and the immense quantities of gas which are given off from the craters and fumaroles, we must readily come to the conclusion that from this source by far the greater part of the atmospheric carbon dioxide is derived. In fact Poggendorfft has calculated that at least ten times as much is derived from this source as from all others put together. The numbers given above for the amount yielded by other sources are pro- bably greater than similar numbers deduced by Poggendorff, since the amount of coal used and the population have both increased since his time. Instead, therefore, of taking ten times, if we take five we shall perhaps approach very near to the absolute amount given by Poggendorff. This will give us about 40,000 million kilogrammes daily given to the atmo- sphere from subterranean sources”. Taking the whole of these results together, we have that from all sources there is daily added to the atmosphere the * Supposing this CO, produced according to the equation CaCO,=Ca0+CoO,, we shall have daily decomposed about 90,000 million kilogrammes of limestone. OO — ———— =~ eo r _ Area of Arctic and Antarctic land . 8,200,000 as a Constituent of the Atmosphere. 391 enormous amount of at least 50,000 millions of kilogrammes of carbon dioxide. Dividing the absolute amount given above by this number, we find that the amount of carbon dioxide in the atmosphere would be double what i 1s at present in about one hundred years if there were no means of compensation. In arriving at this estimate no account has been taken of the amount of oxygen used up in producing the dioxide. This obviously affects the first three sources only; but by taking it into account we should reduce the time somewhat; but practi- cally this correction is so slight that it can be neglected. Poggendorff made a similar calculation, and gave 386 years as the period which it would take to double the amount of the dioxide, supposing there were no compensating influences at work. The discrepancy in the two numbers is explained, first, by the absolute amount of CQ, in the air being much less according to my calculations than that previously sup- posed, and also by the circumstance that Poggendorff’s esti- mate of the amount yielded by the combustion of carbonaceous substances was much less, owing to the defective data at his command. Compensating Influences. Having now arrived at an estimate of the amount of carbon dioxide daily added to the atmosphere, let us examine the causes which bring about its decomposition and removal from the air. The known causes which are at work producing this change may be considered under three heads, viz.:— (1) Fixation of carbon by growing plants. (2) Removal of dioxide by zoophytes. (3) Absorption of dioxide by inorganic chemical actions. The first cause here mentioned is one which is essential to almost all forms of vegetable growth. In estimating its mag- nitude we are met by the want of reliable experimental data, making it almost impossible to arrive at any definite conclu- sion. It is, however, the only one which restores the oxygen to the atmosphere, in the other two actions the dioxide being absorbed bodily without being decomposed. Also most, if not all, the decomposition effected by plants will occur during the spring and summer, the most active period of plant-growth. The second and third causes act continuously. Certain expe- riments have shown that a square metre of leaf will decompose in sunlight about a litre of CO,. Also Mr. Trelawny Saun- ders, some years ago, calculated for Sir Charles Lyell the area of the land-surface of the globe. The figures he gives are* :— Total area of land . . . + 97,600,000 square miles. 3 7 * Ansted’s ‘ Physical Geography,’ p. xxxviii. 392 Mr. E. H. Cook on Carbon Dioxide Thus the land-surface bearing vegetation capable of decom- posing carbon dioxide amounts to 49,400,000 square miles. A large portion of this land, however, is uncovered by vegeta- tion: cities are built on it; barren mountains rise out of it; and large rivers run through it. Hstimating the absolute area of leaf (7. e. chlorophyll-bearing organs) borne by the plant-bearing land of the earth as 50 per cent. of the total area, we find that 24,700,000 square miles of leaf are en- gaged in purifying the atmosphere. This is equal to about 63,973,000,000,000 square metres, which gives the number of litres of CO, decomposed per hour. But sunlight only lasts, on an average, about ten hours a day; consequently the total amount daily decomposed is equal to ten times this amount. Finally, allowing 25 per cent. for the diminution of the action which takes place in winter, we find that the enormous amount of 479,000 millions of kilolitres, or over 900,000 millions of kilogrammes of carbon dioxide are decomposed daily. ‘This amount is much greater than that produced from all sources taken together. Butit must be remembered that a large por- tion of the carbon thus withdrawn by plants during the spring and summer months is returned to the air again by the decom- position of the leaf in autumn. Although we have allowed for this above, yet if plant-action is anything like so powerful as these calculations show, that allowance will have to be consi- derably increased. Again, a reduction, and perhaps a consi- derable one, will have to be made on account of the respiration which has been proved to take place in some plants during the hours of darkness; but I am unable to find an account of any experiments upon this point. The magnitude of this action given by these calculations is astonishing. This paper was commenced under the idea that the action usually attri- buted to plants was greatly overestimated, and that their purifying effect was exaggerated. It will be seen that the vegetable life on the globe is sufficient of itself to keep up the purity of the air. ‘The author wishes this statement to be received with caution, because of the unsatisfactory nature of the fundamental experiment upon which the calculations are based, and also of our total want of knowledge of the amount of plant-respiration. This latter action may be much greater than is usually supposed. The second great action going on in nature is effected by the interposition of animal life. It consists in the removal from.sea-water of the carbon dioxide held by it in solution by certain low forms of animal life. The most important of these are Actinozoa and Foraminifera—the former being concerned in the building of coral reefs, and the latter in forming those as a Constituent of the Atmosphere. 393 immense masses of rock-material of which the chalk and nummulitic limestone may be taken as examples. Certain other forms of animal life, such as Brachiopoda &c., also add their influence to that of these lower forms; but their effects, how- ever, are comparatively insignificant. The immense influence exerted by these minute creatures is evident when we re- member the vast masses of limestone entirely of organic origin occurring in geological formations of all ages. Millions of tons of limestone formed in this way occur in the solid crust of the earth; and every ton of limestone contains about nine hundredweight of dioxide. Nor is this action confined to the past. It is as active now, in all probability, as when engaged in building up those immense deposits of white chalk so abundant in some parts of Hurope. Recent deep-sea sound- ings haye revealed the fact that Foraminiferal life still flou- rishes in the depths of the ocean, while the coral-polypes are still building reefs in the warmer seas. On the other hand, we must not forget that Darwin has shown that these coral- polypes can only exist in water of a certain temperature, which is only;attained in the warmer seas, and at a certain depth below the surface of this water. Their influence, therefore, is limited and confined to a comparatively small area of the globe. Another circumstance which seems to have been overlooked by most writers upon the subject is, that this dioxide fixed in the solid state in this way is contained in the water, and not in the atmosphere. It is generally supposed that all of it has been derived from the air; but a very large portion must have been obtained from submarine volcanic eruptions, and never formed part of the atmosphere at all. Taking all things into consideration, this cause, although very powerful, seems rather to be one whose influence is only felt after the lapse of many years, and, for activity, cannot be equal to the first one. The third action going on in nature effecting the purification of the airis a strictly inorganic one. Included under this head are such processes as the conversion of felspar into kaolin, the decomposition of such silicates as hornblende, pyroxene, &c. The large deposits of kaolin and decomposed felspar which are met with in the earth sufficiently prove the magnitude of this action. Calculations were made many years ago by Ebelmen (see the Recewil des Trav. Scient. de M. Ebelmen, Paris, 1855), and have recently been recalculated and very clearly stated in an excellent paper by Dr. T. Sterry Hunt, F.R.S.* A glance at the numbers given in these memoirs will show the vast and important effect which these processes must have exerted. * « Chemical and Geological Relations of the Atmosphere,” American Journal of Science, May 1880, Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2D 394 Carbon Dioxide as a Constituent of the Atmosphere. Thus, Dr. Hunt says “ that a weight of carbonic dioxide equal to more than twenty-one times that of our present atmosphere would be absorbed in the production from orthoclase of a layer of kaolin extending over the earth’s surface with a thickness of 500 metres, an amount which evidently represents but a small proportion of the results of felspathie decay in the sedi- mentary strata of the globe.”” Hvidently, then, here we have a cause which has removed, and is removing, a vast amount of carbon dioxide from the atmosphere. Any estimate of the rate of its action is obviously impossible. It must not be for- gotten, however, that subaerial felspathic decay is a very slow process, and that therefore the large deposits of decomposed felspar found in the earth seem to point rather to a compara- tively slow process acting through an immense number of years than to a rapid process such as that effected by plants. General Conclusions. It is of course evident that, if the compensating influences are just equal in amount and in rate of action to the producing ones, the amount of carbon dioxide in the air will remain con- stant. Unfortunately an insufficiency of reliable data prevents a definite answer being given to such a question. The fore- going considerations, however, seem to show that in all pro- bability the causes at work removing atmospheric dioxide are more powerful than those producing it. As a consequence, the atmosphere is being robbed of this constituent, the greater part of which is becoming fixed in the solid-earth as carbonate of lime. But this process has already gone on for so long a time, that there is already fixed in this way an immense quan- tity of CO, equal to many hundreds of times the amount con- tained in the existing atmosphere. The question of the source of this large amount naturally arises; but the answer to be given must simply be.an admission of our want of knowledge. The idea that it all at one time formed part of the atmosphere of the globe has been suggested by Brongniart; and Dr. Sterry Hunt considers (Joc. cit.) that a universal atmosphere of the same quality as that of the earth exists, from which the carbon dioxide now fixed in the earth’s crust has been derived. There can be no doubt that, unless we accept the latter of these theories, there must at some antecedent period have been an atmosphere covering the globe much richer in this gas than the present one; but whether such an atmosphere would account for the luxuriant vegetation of the Coal Period is at present an open question. If Dr. Hunt’s hypothesis be a cor- rect one, it is interesting to remember that the carbon which we contain in our bodies may have existed at one time as a | my | Cot On the Dimensions of the Magnetie Pole. 395 portion of the body of an inhabitant of the most distant member of the universe. But whichever way we consider the subject in the light of the facts which we have stated, it is full of unusual difficulty, and is singularly devoid of accurate experimental data. XLII. On the Dimensions of the Magnetic Pole in Electrostatic Measure. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, HAVE had the honour of reading a letter upon the-di- . mensions of the magnetic pole in electrostatic measure which Dr. Lodge addresses to you this month. His sugges- tion seems to me to reconcile the views of Prof. Clausius and Mr. J. J. Thomson on this subject. A model of the magnetic system must be made in a substance of the same magnetic permeability as the medium that is to surround the current- system, and must be substituted in the place of the magnets, before any comparison can be effected: The two systems, current- and magnetic, will then be always equivalent if once equivalent. Dr. Lodge treats this as a suggestion; but I think it is almost susceptible of demonstration. According to Weber’s law, a current flowing in a closed circuit can be replaced by a sumple magnetic shell of which the edge coincides with the eireuit. The shell may be as thin as we please; but its strength must have a definite value. This law we only know to be true for air. Consider any equipotential surface of the positive magnetism on one face of the shell, at a distance from it infi- nitely smaller than the thickness of the shell. It passes through the substance of the shell, issuing at the edges, and covers the positive face. Similarly such an equipotential surface of the negative magnetism on the other face passes through the substance without cutting the former surface, and covers the negative face. If on each of these surfaces we spread a surface-magnetism of which the density is the quotient of the magnetic force by Ar, then for all points outside the pair of surfaces and the shell we may replace the latter, and therefore its equivalent current- system, by the magnetic couts upon the equipotential surfaces. Now consider any diaphragm, 8, completely enclosing these surfaces and the shell. If instead of air we substitute a me- dium of magnetic permeability » throughout space outside 8, a surface-density o is developed upon 8. But the equipoten- tial surfaces and the coats of magnetism thereon are not - affected by this development; for they relate only to the en- 2 D2 396 Notices respecting New Books. closed system. Hence the magnetic and current-systems, if equivalent in air, are equivalent in a medium which does not penetrate through any portion of the space occupied by the magnetic substance. wpe It is particularly to be noticed that, while in air any two of the infinite number of magnetic shells equivalent to two closed currents exercise the same attraction upon one another, this is no longer true when they are immersed in the medium yp. Then each pair exercises the same attraction as the two cur- rents when the corresponding diaphragms S are drawn in the shape of the magnetic shells. An experiment made by me in the Cavendish Laboratory last June confirms, as far as it goes, Dr. Lodge’s view ; but, fearing to make my letter too long for insertion, I must post- pone any account of it for the present. I am, Gentlemen, Your obedient servant, October 20, 1882. ie B. SARGANT. XLIV. Notices respecting New Books. The Concepts and Theories of Modern Physics. By J. B. Svaxo. London: Kegan Paul and Trench. 1882, ope write an adequate criticism of this book would involve writing a book of equal size. In the present review it is intended to make clear the standpoint from which the author speaks, and the general conclusions reached, rather than to enter into a detailed criticism of these conclusions. The failure to appreciate the posi- tion from which the author writes has already led to some mis- understanding and not a little confusion. Itis stated in the preface that the work is intended “as a contribution not to physics, nor certainly to metaphysics, but to the theory of cognition.” There is probably no word which is more quoted and less understood than the word “metaphysics.” It is used by hardly any two writers in the same sense; and it is not too much to say that in many cases it is merely used as a term of abuse without any clear conception of its meaning. As in the present work this word is constantly used, and, moreover, as the author’s main purpose is to show that certain scientific theories are in reality metaphysical, it will be im- portant to understand precisely the signification which he puts upon the word. It is abundantly evident from the whole book that the subject which Mr. Stallo condemns, and rightly condemns, under the name of metaphysics is that which is far better designated by ontology ; and in fact he himself frequently uses these terms as synonymous. The assumption of fictitious entities as causes, the belief that “ the true nature of things can be discovered only by divesting them of their relations—that to be truly known they must be known as they are in themselves in their absolute essence,” and in fact the whole procedure of ontology, is what is meant by Notices respecting New Books. 397 “metaphysics.” Against metaphysics in this sense of the term the author, in common with many other scientific writers, wages un- ceasing war. Admitting the utter futility of the ontological method, it is very questionable whether this has not been overdone, whether this reiteration of abuse against ontology is not mere slaying of the slain. It is far otherwise if, after a man has clearly understood what ontology means and has been convinced of the falsity of its method, he sets himself to see whether these same errors exist in subjects non-metaphysical, and even in the reasoning of those who were loudest with their revilmgs. This is action, not profession, and indeed noble and useful work in the field of criticism. As Prof. Huxley most truly has said, “ It is the business of criticism, not only to keep watch over the vagaries of philosophy, but to do the duty of police in the whole world of thought. Wherever it espies sophistry or superstition they are to be bidden to stand, nay, they are to be followed to their very dens and there apprehended and exterminated, as Othello smothered Desdemona, ‘else she'll betray more men.’” This in truth is the task which Mr. Stallo has un- dertaken in the present volume, having chosen the field of science for his beat. Besides having critical value, it is stated that the work is “in- tended as a contribution to the theory of cognition.” Now this term, which is a translation of the German “ Erkenntniss-Theorie,” is but seldom used in this country in precisely the same sense which is here, in common with modern German usage, adopted. In the present work it is used in a sense very similar, if not identical, with what I have called the “ New Metaphysic” (Phil. Mag. xiv. p- 7))—that is to say, in regard to method. The author, as we have seen, entirely rejects the “old metaphysic,” or ontological method of inquiry—“ all cognition being founded upon a recognition of relations ;” and his theory of cognition seeks to discover these rela- tions. The “thing per se,” the ‘ Ding an sich” or thing-in-itself of Kant, and ‘“‘the absolute,” as well as the assumption of other fic- titious entities as the “fountain and origin of all phenomenal existence,” is distinctly repudiated; and hence these conceptions form no part of his theory of cognition. From this standpoint the author proceeds to examine the validity of the reasoning upon which the mechanical theory and other scientific theories rest. It may fairly be asked, what are the qualifications of the author for this by no means easy undertaking? The title-page of the book affords no information on this point. It will therefore be probably unknown to most readers of the book in this country that the author is an American judge of no small reputation, who (I believe myself to be correct in saying) was formerly a professor of physical science. The book itself bears witness to the author’s wide acquaintance with philosophical and scientific writings. The volume may be divided into two parts. The first, consisting of eight chapters, is devoted to a rigid examination of the atomictheory, the kinetic theory of gases, and the doctrine of the conservation of energy. While ad- mitting the value of the atomic theoryas a “ working hypothesis,” the 398 Notices respecting New Books. author attempts to show that, as a scientific explanation of the con- stitution of matter, it is of little or no value. The kinetic theory of gases is condemned without reservation, as not even satisfying the conditions of a scientific theory and as based upon ontological assumptions. The doctrine of the conservation of energy is con- sidered to be sound ; and the chapter which is devoted to its exami- nation shows an intimate acquaintance at least with the history of the subject. A detailed criticism of the validity of the author’s conclusions (for there is much to be said against them) would be impossible within the limits of a review; and therefore this will not be attempted here; but one or two positive errors and miscon- ceptions will be noticed. In the first place, it is mcorrect to say (p. 23) ‘‘that with few exceptions scientific men of the present day deem the validity of the mechanical explanation of the phenomena of nature to be, not only unquestionable, but absolute, exclusive, and final. They believe that this validity is not conditioned, either by the present state of human intelligence, or by the nature and extent of the phenomena which present themselves as objects of — investigation.” The reverse of this is nearer to the truth. A man of science, in the capacity of a scientific investigator, is logically compelled to consider no explanation or theory as final, but to be prepared at any moment to abandon an explanation which should prove to be insufficient or at variance with facts, im favour of another which more adequately accounts for them. This is what all scientific men hold and are bound to hold, as Liebig expressed it in a passage actually quoted by the author in another part of the book, ‘‘The secret of all those who make discoveries is that they regard nothing as impossible.” Throughout the book the author seems to lose sight of the necessary tentativeness of all scien- tific theories. Under the head of the Atomic Theory the author discusses the doctrine of the indestructibility of matter. In Chap- ter II. he states that the true correlate of motion is not matter, but mass; and hence this term is used where ordinarily the word matter is employed ; but when discussing the indestructibility of matter in Chapter VII. we find that he uses this term,and not indestructibility of mass, which is really what chemists mean. The current doc- trine is first stated, ‘‘ That the constancy of mass is attested by the balance, which shows that neither fusion nor sublimation, neither generation lior corruption, can add to or detract from the weight of a body subjected to experiment. When a pound of carbon is burned, the balance demonstrates the continuing existence of this — pound in the carbonic acid, which is the product of combustion, and from which the original weight of carbou may be recovered. To test the correctness of this interpretation we may be permitted slightly to vary the method of verifyingit. Instead of burning the car- bon, let us simply carry it to the summit of a mountain or remove it to a lower latitude: is its weight still the same? Relatively it is: it will still balance the original counterpoise. But the absolute weight is no longer the same. This appears at once if we give to the balance another form, taking a pendulum instead of a pair of scales.” What the author means by talking about “ absolute et Notices respecting New Books. 399 weight,” when he so rigidly insists “that there is nothing abso- lute or unconditioned in the world of reality,” is by no means clear, especially as we find from the context that what he calls “absolute weight ” is evidently and, indeed, necessarily based upon a relation. In any sense the expression “absolute weight” is a contradiction in terms. From this the author argues that “the ordinary state- ment of the fact is crude and inadequate;” and adds that it is “further necessary to remember that this weight may be infinitely reduced, without any diminution in the mass of the body weighed, by a mere change of its position in reference to the body between which and the body weighed the relation subsists.” Itis this very constancy of mass or quantity of matter amid all changes, of ne- cessity relatively determined, which chemists mean to indicate by the expression “ indestructibility of matter ;” and the author’s criticism merely amounts to a quibble about words; he has mis- taken the letter for the spirit. Of the second half of the volume, Chapters IX. to XII. are devoted to the theory of Cognition, and contain an analysis of scientific ultimates, Matter, Force, Time, and Space—that is, a consideration of how we really know these, to what realities these words correspond. This being not strictly a scientific inquiry, although of much interest and importance, the _results will not be considered here. In Chapters XIII. and XIV. transcendental geometry receives most severe and lengthy treat- ment. Lobatschewsky’s non-Euclidean geometry and Riemann’s doc- trine of the manifoldness of space, which have occupied the attention of the most eminent mathematicians during recent years, are consi- dered to be absurd. The same ontological error “‘ which has given rise to the atomo-mechanical theory in physics, has led to the doc- trine of pangeometry in mathematics.” Even admitting the author’s criticism as to the nature of space, it by no means follows that trans- cendental geometry is not a legitimate department of mathematics. The Nebular Hypothesis is considered in Chap. XV.as the cosmogony of the atomo-mechanical theory. The author rejects the hypothesis, first, because “all speculations respecting the universe as an unli- mited whole” are fundamentally madmissible; and, secondly, the hypothesis has proved to be at variance with a number of impor- tant astronomical facts. The last chapter of the book consists of a summary and forecast, the author concluding that ‘the atomo- mechanical theory cannot be the true basis of modern physics,” and looking to the Conservation of Energy as a basis for the future. On the whole the book deserves careful consideration from all physicists ; for although the author has more than once mistaken the letter for the spirit, which gives some of the criticism a ludi- crous aspect, and, further, has in many cases attributed to Science speculative doctrines and opinions held by individual scientific men, yet there is much acute and careful critical work in the volume. Certainly Science ought to be the first to welcome and the last to reject candid criticism of her methods and theories; for, perhaps even more than other pursuits, Science maintains Magna est veritas et preevalebit. Wynpuam R, Dunstan, [ 400 ] XLV. Intelligence and Miscellaneous Articles. ON DR. C. W. SIEMENS’S NEW THEORY OF THE SUN. BY M. FAYE. [ would appear that this theory has greatly struck our physicists ; for it had scarcely appeared in London when it was translated and published in France in various forms, and especially in the last number of the Annales de Chimie et de Physique. I suppose that the principal object of this haste was the announcement of fresh experiments which have been instituted by the author upon the chemical action of light. It is well known that, under the action of light and with the intervention of the chlorophyll of plants, aqueous vapour and carbonic acid are decomposed at ordinary tem- peratures, and brought back to the combustible form, carbon and hydrogen variously associated. Dr. Siemens has tried whether the action of the light of the Sun alone would not produce this decompo- sition if we submit to it, without any other intermediary, aqueous va- pour and carbonic-acid gas excessively rarefied, brought for example to the vacuum of ;,,,;. His experiments, which, in my opinion, only require a counter-test which it would be easy to institute, have given perfectly affirmative results. Thus, the burnt gases having been brought to such a rarefaction that they no longer ermitted the passage of the induction-spark, a few hours’ exposure to the light of the Sun sufficed to enable the mixture to allow this spark to pass with the well-known coloration that it acquires in hydrocarburetted media *. Regarding these beautiful experiments as decisive, Dr. Siemens has been led to inquire whether this phenomenon does not per- form in the universe a part still more considerable than in yege- table life. Supposing Space to be filled with analogous gases, already burnt, the light of the Sun would revivify the combustibles hydrogen and carbon, which would then be quite ready to furnish the food of a fresh combustion. By drawing them to himself and burning them afresh, the Sun would recuperate a good portion of the enormous heat which one is grieved to see him radiating in pure loss into celestial space. Dr. Siemens has thus been led to put forward the following hypothesis :—Space is filled with burnt gases, aqueous vapour and carbonic acid, mixed with imert gases, nitrogen &c., pretty nearly the same as those of our atmosphere, at a pressure of suzy: These gases are partially converted into combustibles under the action of the solar light; then, by a mechanism like that of the fan of a blower, the Sun draws them to himself, burns them, and sends them back again into space. This immense source of heat would be continually resuscitated ; the only part of its radia- tion lost would be that which is not absorbed by the cosmical medium of a density of 5345. * A vacuum produced in a bell-glass into which a drop of oil of turpentine has previously been introduced, for example. Intelligence and Miscellaneous Articles. 401 It is perfectly true that, for the physicist, air at 5,45) would be an almost absolute vacuum, so much so indeed that in such a vacuum the electric spark would no longer pass. But to the astronomer such a medium would be very dense. When we speak, in Astronomy, of the resistance of a medium or of the wether, and when by the aid of the most delicate observations and the most profound calculations, we seek for traces of this re- sistance, we have to do with a very different thing. Without entering upon these discusions, I will remark that the trajectory of a cannon-ball with a velocity of 500 m. is sufficiently altered at the end of a few seconds to compel artillerists to take into account the resistance of the air in their tables. Tf the air is reduced to 5,5, but the velocity of the projectile becomes that of the celestial movements, 60 times as much for example, these palpable effects will become, for a multitude of celestial projectiles of dimensions comparable to those of our cannon-balls, twice as great as in our firing-grounds, and this not merely at the end of a few years or a few centuries, but at the end of a few seconds. In the second place, it seems to me that the celebrated English physicist has somewhat neglected to examine into the quantity of matter which he adds to the solar system. Under the influence of attraction this matter would go to unite itself with the preexisting stars, with the sun especially, and would continually augment their mass. Nothingis easier than to form an idea of this. A litre of air containing the required proportion of aqueous vapour weighs at least 1 gr. at the ordinary pressure. Ata pressure of 5>),, this will be 0-0005 gr., and a cubic metre will weigh 0-0005 kilog. This being settled, if we restrict the solar system to a sphere including all the planets as far as Neptune, the weight of the excessively rarefied matter added by the hypothesis would be, in kilogrammes, 4 7 (6400000 x 24000 x 30)? x 0:0005 kilog. * The actual weight of the Sun is, in kilogrammes, 4 (64000000)? x 5°6 x 324000 T. The first is 100,000 times as great as the second. It is there- fore 100,000 times the mass of the Sun that this hypothesis adds to those of which celestial mechanics has hitherto kept so minute an account. It is not very probable that the astronomers will adopt such hypotheses. No doubt they wouid be pleased to think that Nature has provided the Sun with resources to make his heat last longer ; but as his final refrigeration is still, under any circumstances, a * The first number is the radius of the earth in metres; the second the distance of our globe from the Sun in terrestrial radii; the third the distance of Neptune in parts of the distance of the Sun. + The first number is the radius of the earth in decimetres; the second the mean density of our globe referred to that of water ; the third the mass of the Sun referred to that of the earth. 402 Intelligence and Miscellaneous Articles. tolerably distant catastrophe, they will console themselves by the thought that the things of this world, even the most beautiful, do not appear to be made to last for ever. As to the fundamental experiments of Dr. Siemens, they will lose none of their importance in their eyes. The business is to surprise a secret of living nature, one of the laws of the organic world ; and their desire will be that Dr. Siemens may pursue the course in which he has commenced so brilliantly, even though they cannot hope to have a very bright light thrown by it upon their own researches.— Comptes Rendus, October 9, 1882, p. 612. ON THE CONNEXION BETWEEN THE GAS-DENSITY AND STRATUM- INTERVAL IN GEISSLER TUBES. BY DR. E. GOLDSTEIN. - Let the total length of a series of immediately consecutive strata of the positive light, of which the first is that which is next to the positive end of the tube, divided by the number of strata, be called the mean interval. The following data respecting this quantity are abstracted from experiments with dry air, hydrogen, and mixtures of the two, under such conditions of the discharge that the strata do not exhibit the to-and-fro vibrating saucer-shapes which escape any precise measurements, but appear in the so-called nebulous forms, which can be brought to a considerably greater degree of stability. In opposition to the generally current view that these clouds represent degenerations and derangements of the proper stratification, I have already* called attention to the far greater probability that they only represent the full development of that phenomenon. The thick cloudy strata stand in precisely the same relation to the thin saucer-like strata as a long-rayed tuft light at the cathode to thin films at first mvesting the cathode, from which, with diminishing density of the gas, the elongated rays are deve- loped. In order to form a clear conception, I wished, further, to be able to presuppose as known that in cylindrical tubes the stratum-interval increases with increasing width of the tube+, so that, in tubes filled with air, the intervals between the individual strata, when the latter are most distinctly formed, are about equal to the diameter of the tubet. If, now, we determine, for cylindrical tubes of different widths inserted in the current-circuit, from an equal number of strata the mean stratum-interval J, J’, J",... for any two pressures of gas d and ¢, we obtain constantly in words :—For cylindrical tubes of different widths, the mean stratum-interval constantly varies in the same ratio between the same gas-pressures. Therefore, if, for example, in one of the tubes * Wied. Ann. xii. p. 272. + Monatsb. der Akad, Berlin, 1876, p. 294; Phil. Mag. [5] iy. p. 853. 1 Wied. Ann. xii, p. 272. Intelligence and Miscellaneous Articles. 403 the stratum-interval has by the rarefaction of the gas been raised to twice or three times its first-measured value, then in all the other tubes the intervals have been doubled or trebled. The tube-diameters in my experiments varied between 2 millim. and 4 centim. The above-mentioned regularity came out, indepen- dently of whether the different cylinders formed separate vessels with two metallic electrodes each, or whether, united into a single ‘tube, they were inserted in a line one behind another in the current. The law is moreover found to hold good equally whether the mean interval be taken from a large or a small number of strata, provided the numbers in the different tubes be equal, although at the same time the absolute value changes. From this it can be concluded that each single interval also increases in accordance with the above-mentioned law. The value of the mean interval is found with great regularity to be, in every tube, as much smaller as the number of strata from which it is derived is greater. Yet the amplitude of the undulation, multiplied by the greatest number of strata employed, never reaches the value of the smallest of the single intervals. Consequently, from the above law it follows that, if in any tube the magnitude of the mean stratum-interval for a series of gas-densities D,, D,... Dn is known, and also, for a number of other tubes, each value of the mean interval that corresponds to any one of those densities, the number of the strata which these tubes can show at all the densities from D, to D, can be calculated. The proportion 7° = a permits us to conclude that the func- 8 tion according to which the mean interval varies with the gas- density is the same for tubes of different widths. Experiments for the purpose of ascertaining that function gave the following result :— If the rarefactions of the gas increase in a geometrical series, the stratum-intervals are augmented also, very nearly, in a geometrical series. But the exponents of the two series are not identical ; that is, the stratum-intervals are not (as was once maintained by the other side) inversely proportional to the pressure of the gas. On the contrary the measurements prove that the intervals increase much more slowly than the rarefactions—approximately at the rate of 4 when the rarefaction is 3. I will defer more definite state- ments until I have determined the exponents with the greatest possible exactness, for which I am at present experimenting ona Toepler pump in the form described by von Hagen*.—Monatsbe- richte der Kon. Akad. der Wissenschafteu zu Berlin, 1881, pp. 876— 878 (separate impression, communicatd by the Author). ON THE ELASTICITY OF RAREFIED GASES. BY E. H. AMAGAT. This subject has already been treated by Mendeleef, Kirpitchoff and Hemilian, by Silgerstrom, and by myself. Those researches * Wied, Ann. xii. p. 425, 404 Intelligence and Miscellaneous Articles, having led to different results, I thought it necessary to resume my experiments, considerably improving my apparatus, especially in what concerns the measurement of the pressures, which is the only difficulty peculiar to this investigation. The method employed having been already described in the Annales de Chimie et de Physique, t. viii. (1876), 1 shall only dwell on the modification which the differential barometer has undergone ; it is the essentially delicate part of the apparatus, all the other parts of which haye also been considerably improved. This barometer consists of a single glass tube bifurcating, at about 70 centim. above the level of the mercury in the cistern, into two wider cylindrical branches, one of which forms the barometric chamber, and the other is put into communication with the space filled with the gas the pressure of which is to be measured. The immediate result of this disposition is that there is no need to attend to the difference of temperature between the two mercurial columns, which are here joined into one at a little distance below the meniscuses. The branches of the bifurcation are prolonged upwards by stems of very small diameter, having each a glass cock, and joining again to form a single stem. The rest of the apparatus is disposed so that the manometer can be charged in place by the process generally adopted nowadays, which consists in first exhausting it with a Sprengel pump; this was worked, moreover, during all the time of the filling, so as to main- tain the vacuum continually dry by the intervention of a tube containing phosphoric acid. All suction of air through the slender point was avoided by covering the surface of the mercury with a layer of sulphuric acid, which remained in the cistern during all the experiments. Above the lower single branch was a glass cock, by closing which the differential barometer could be transformed into an ordinary truncated barometer, and thus the errors due to variations of the atmospheric pressure be eliminated—which is extremely important. In order to avoid as far as possible the errors due to refraction and capillarity, the two branches of the manometer, before being soldered to the single stem, were rounded and polished inside with the same copper mandrel, so as to be rendered perfectly cylindrical ; a plane facet was then cut on the exterior, quite parallel to the generating lines of the interior cylinder. This done, the pieces were soldered, the necessary precautions being taken to keep the plane facets rigorously i in the same plane. These pieces are very difficult to obtain: a Jarge number of them break or split, either during the rounding, or the soldering, or even after these operations are finished. The cylinders were smoothed and cut by M. Lutz; the manometers were afterwards finished by M. Alvergniat ; that is to say, they were made with all the skill and perfection that could be wished for. To eliminate capillarity-errors, an internal diameter of 2 centim. was given to the cylinders; and they were evidently perfectly equal: it was easy to verify that the mercury in them was in per- fect equilibrium under the thread of the cathetometer. et . , ‘ ) Intelligence and Miscellaneous Articles. 405 T shall not dwell upon the precautions which I took with respect to the illumination of the meniscus (by means of a pencil of elec- trie light sifted by passing through a column of water coloured with a little bichromate of potass) in order to be certain of viewing the upper part of it. Here a cause of error exists which is much more frequent than is generally thought, especially when the black sil- houette of the meniscus is projected upon a bright ground. The measurements were performed with a small cathetometer of a peculiar construction, on which 5}, millim. could be read off, and which I had made by M. Benevolo, in my private atelier, spe- cially for these researches. In my first investigation I descended only to 6°5 millim. pres- sure ; this time I have often operated with pressures below 1 mil- lim. I always arrived at the result that the deviation is of the order of magnitude of unavoidable errors. Indeed, for initial pressures of 12 millim. (in round numbers), two series composed of ae pv being sensibly = 2v') the numbers 0-9986 and 1:0020 relative to air; for the initial pressures comprised between 3 and 4 millim. the results varied between 0-9999 and 1-0040; and for pressures near 1 millim. the extremes are 0-999 and 1°015: this divergence corresponds to an error of 15 millim. in the measurement of the pressure. All these numbers are means. In his experiments M. Mendeleef obtained a series of products pv. This appears a more favourable condition for showing how those products vary. According to him, they go on decreasing with the pressure, starting from a certain pressure which would be 6 decim. for air. In order to preyent any delusion in this respect, it is well to observe that every sensibly constant cause of error in the esti- mation of the pressures, taking effect upon smaller and smaller pressures, and consequently giving a relatively greater and greater error, will produce the illusion of a regular augmentation or dimi- nution of the products pv. This is what must result, for example, from the want of absolute vacuum in the barometric chamber, even if it be only on account of the effect produced by the mercury vapour. In short, a minute examination of the possible errors has shown me that, even if one could attain in the readings the precision spoken of by M. Mendeleef (thousandths of a degree, and thou- sandths of a millimetre), that pressure would be illusory in the presence of errors proceeding from manifold causes—such as the refraction- and capillarity-errors (which, even when the precautions I have indicated are taken, are never absolutely cancelled), the error due to the compelled imperfection of the barometric chamber (which, causing all the pressures to appear a little too low, tends to produce the illusion of a negative deviation), that due to condensa- tion of gases on the sides of the vessels or even on the mercury, &e. &e. ; By admitting an error of one or two hundredths of a millimetre, numerous fairly concordant results gave for the value of 406 Intelligence and Miscellaneous Articles. which is no exaggeration, we arrive at divergences of the order of magnitude of the deviations found; it is therefore impossible to ‘ pronounce a decision upon either the direction or even the existence of those deviations. All that we can say is that at the lowest pres- sures at which experiments have been made (1 millim. or even less ; I have experimented at two tenths of a millimetre) no abrupt change in the law of the compressibility of gases appears to be pro- duced ; they still follow Mariotte’s law, with the exception of diver- gences for which the experiments cannot be responsible. It is certainly possible that sufficient rarefaction, acting like a great elevation of temperature, would cause other gases to follow the law p(vu—a)=c, as takes place for hydrogen; but there is a great distance from this to the boundary state spoken of by Mendeleef and Siljerstrém, in which the gases would become infinitely little compressible—a mere hypothesis, to which the numerical results of M. Siljerstro6m do not even appear to lead, as M. Petier has already remarked in the Journal de Physique. The study of carbonic acid has led me to analogous conclusions. For hydrogen the deviations found have varied between —0-0010 and 0-0028 for initial pressures between 3 and 6 millim. in round numbers.— Comptes Rendus de V Académie des Sciences, Aug. 7, 1882, t. xcv. pp. 281-284. ON THE INFLUENCE OF TEMPERATURE UPON THE SPECTRA OF METALLOIDS. BY M. D. VAN MONCKHOVEN. Kirchhoff and Bunsen have shown that the temperature of the flame in which a substance is reduced to vapour has no influence upon thé position of the bright lines of its spectrum. When, for instance, sodium or lithium is volatilized in the flame of a spirit- lamp, or in that of the oxyhydrogen blowpipe, the lines remain the same, but their brilliancy increases with the temperature: most frequently some new thin lines appear at the elevated temperatures ; but it never happens that those which have already been emitted at lower temperatures disappear. If this is always the case as regards the metallic vapours, it is never so with the lines emitted by the metalloids*. Pliicker has in fact shown that oxygen, ni- trogen, sulphur, selenium, &c. give two different spectra which have no line in common, according as the spectral tubes contain- ing these substances are heated by the ordinary spark of the elec- trical machine or by that of a Leyden jar. He admits there- fore, and with him nearly every physicist, that certain elementary bodies give, at a high temperature (Leyden jar), a spectrum different from that given by the same body at a low temperature (ordinary spark). PBut numerous and varied experiments have proved that we can obtain those spectra called those of high temperature at very * Hydrogen is an exception; but this gas is known to be a true metal, not only as to its chemical properties, but also as to its physical. Hydrogen bears, as regards conductivity of heat and electricity, the same relation to other gases as mercury to the other liquids. Intelligence and Miscellaneous Articles. 407 low temperatures, and vice versd. Thus, at very feeble pressures (0-001 metré), with tubes of oxygen or nitrogen and with very small Leyden jars, we obtain the spectrum which Pliicker attributes to high temperatures, while the tube is scarcely warm after the ex- periment has last several minutes, and the brilliancy of the light emitted by the incandescent gas is very feeble. The same tube, traversed by the current of a very powerful induction-coil (without the interposition of a Leyden jar), emits, on the contrary, an ex- tremely bright light, becomes rapidly hot, and nevertheless gives the spectrum which Plicker attributes to low temperatures. But here is a still more decisive experiment. Let us take a tube in the form of an H with four electrodes, and filled with nitrogen*, oxygen, or one of those gases (or vapours) which give two spectra. Through this tube let us pass at the same time the currents of two inducticn-coils, of which one has a Leyden jar interposed. We shall observe the two spectra superposed-—the spectrum assigned to elevated temperatures (Leyden jar), and the spectrum assigned to low temperatures (ordinary spark). According to Pliicker’s hypothesis, the gas would have, at the same physical instant, two different temperatures, which is inad- missible. It may perhaps be objected that, the interrupters of the two coils not working strictly in unison, the perception of the two spectra is due to the persistence of the images upon the retina. But this is not the case, as some tubes, especially with oxygen, give forth light for several tenths of a second after the current has been interrupted. We attribute the change in the spectra given by these metalloids to a vibratory state peculiar to their molecules, directly depending upon the nature of the electricity employed. Thus, a tube of highly rarefied hydrogen gas, submitted to the action of ordinary sparks, presents quite a different aspect from the same tube submitted to the action of the condensed spark. Highly rarefied gases, traversed by the continuous current of the battery, or by a current interrupted by sparks (induction-coil), pre- sent a dynamical state well known under the name of stratification. But this stratification differs entirely, according as we employ the ordinary spark, the condensed spark, or the continuous current of a battery of very high tension. ’ We shall see in further communications that with each different behaviour of an incandescent gas (alteration in the stratification, colour of the light emitted, &c.) there is always a corresponding modification, and often an entire change, in its spectral lmes—an effect assuredly independent of the temperature.— Comptes Rendus, Sept. 18, 1882. ON A THERMOSCOPIC METHOD FOR THE DETERMINATION OF THE OHM. BY G. LIPPMANN. It will be remembered-that Mr. Joulef employed a calorimetric * Nitrogen in the electric are gives a different spectrum from that given by Geissler’s tubes or the spark in air. + Reports of the Committee &c., pp. 175-190 (London, 1873). rr” ’ 408 Intelligence and Miscellaneous Artieles. method for the determination of the ohm. The method which Iam about to describe differs from that of the eminent physicist in not requiring the quantities of heat to be measured or the mechanical equivalent of heat E to be known. This last point is not unim- portant ; for in Joule’s calorimetric method the final approximation is limited by the uncertainty at present existing respecting the exact value of the number E; that is to say, the possible error is near ;1,. The wire of which I wish to know the resistance is placed in the middle of a vessel arranged as a calorimeter in the centre of an en- closure with a constant temperature. An electric current is passed into the wire, and its intensity 7 measured. I wait until, m con- sequence of the heat liberated by the current, the vessel attains a stationary temperature; I leisurely ascertain that it is so by em- ploying a thermometer, or, rather, a sensitive thermoscope, placed inside the vessel. This done, I interrupt the current, and then set in action a motor which produces friction in the midst of the vessel that already contains the wire. The heat evolved by the friction is substituted for that just before evolved by the current. I manage so that the stationary temperature resumes its former value ; I then have r?=T, T being the work expended, whence the value of r. It is scarcely necessary to add that the friction-apparatus must remain in the vessel which contains it, even when it is not in ope- ration, and be furnished with the known arrangements for measu- ring T. It is also more convenient to commence by the friction- experiment, and afterwards to regulate the intensity 7 so as to recover the same stationary temperature. Lastly, it may be advan- tageous, for apparatus of large capacity, to replace the observation of the stationary temperature by that of the velocity of the heating. In the form given to it by Joule in 1867, the calorimetric method of the English physicist rests equally upon the measure- ment of 7 and the measurement of a mechanical work, namely the work done at the time of the determination of E. Moreover, it involves two calorimetric measurements, which are to be mutually eliminated from the final result—namely, the calorimetric measure- ment which accompanies the determination of E, and that which accompanies the passage of the electric current. These imterme- diate determinations bring in their causes of error and their cor- rections, owing to the imperfections of the calorimeters employed in making them. I dispense with them by taking care to expend the work T and the electric energy 777 in one and the same calo- riscopic vessel. It becomes as needless to ascertain the quantity of heat evolved in that vessel as to ascertain the weight of the tare in a double weighing ; and the advantage obtained appears analogous to that which there would be in replacing two successive single weighings, made with different balances and different weights, by a Borda’s double weighing.— Comptes Rendus de ? Académie des Sciences, Oct. 9, 1882, t. xcv. pp. 634, 635. THE LONDON, EDINBURGH, anv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIKS.] DECEMBER 1882. XLVI. On Variations in the Vertical due to Elasticity of the Earth's Surface. By G. H. Darwin, F.R.S., formerly Fellow of Trinity College, Cambridge*. 1. On the Mechanical Effects of Barometric Pressure on the Earth’s Surface. | ig remarks of Signore de Rossi, on the observed con- nexion between barometric storms and the disturbance of the vertical, have led me to make the following investiga- tion of the mechanical effects which are caused by variations of pressure acting on an elastic surface. The results seem to show that the direct measurement of the lunar disturbance of gravity must for ever remain impossible. The practical question is to estimate the amount of distor- tion to which the upper strata of the earth’s mass are sub- jected, when a wave of barometric depression or elevation passes over the surface. The solution of the following problem should give us such an estimate. Let an elastic solid be infinite in one direction, and be bounded in the other direction by an infinite plane. Let the surface of the plane be everywhere acted on by normal pres- sures and tractions, which are expressible as a simple harmonic function of distances measured in some fixed direction along * Appendix to the Second Report of the Committee of the British Association on the Lunar Disturbance of Gravity. Read at the Meeting at Southampton, August 1882. Communicated by the Author. Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 24h 410 Mr.G. H. Darwin on Variations wn the Vertical the plane. It is required to find the form assumed by the surface, and generally the condition of internal strain. : This is clearly equivalent to the problem of finding the dis- tortion of the earth’s surface produced by parallel undulations of barometric elevation and depression. It is but a slight objection to the correctness of a rough estimate of the kind required, that barometric disturbances do not actually occur in parallel bands, but rather in circles. And when we con- sider the magnitude of actual terrestrial storms, it is obvious that the curvature of the earth’s surface may be safely neg- lected. This problem is mathematically identical with that of finding the state of stress produced in the earth by the weight of a series of parallel mountains. ‘The solution of this problem has recently been published in a paper by me in the ‘ Philosophical Transactions’ (part ii. 1882, pp. 187-230); and the solution there found may be adapted to the present case in a few lines. The problem only involves two dimensions. If the origin be taken in the mean horizontal surface, which equally divides the mountains and valleys, and if the axis of z be horizontal and perpendicular to the mountain-chains, and if the axis of « be drawn vertically downwards, then the equation to the mountains and valleys is supposed to be z z= —hcos 3? so that the wave-length from crest to crest of the mountain- ranges is 27b. The solution may easily be found from the analysis of sec- tion 7 of the paper referred to. It is as follows:— Let a, y be the displacements at the point «, < vertically downwards and horizontally (a has here the opposite sign to the « of (44)). Let w be the density of the rocks of which the i are composed, g gravity, v modulus of rigidity ; then 1 dW == |e -W], ] i. dW Y= 5,be—s - 2 where a “Ss z W= —guhe ? Coss J From these we have at once 1 due to Elasticity of the Earth's Surface. 411 a= io + sea cos = | 2u b | y= gemal sine, ( a EA de _—gwh *) a ee =~ (14 5) sing. J The first of these gives the vertical displacement, the second the horizontal, and the third the inclination to the horizon of strata primitively plane. Atthe surface, Z— 7 Coss, y=0, da gwh . z Ae ERO BRNO) dz. 29° b Hence the maximum vertical displacement of the surface is +gwhb/2v, and-the maximum inclination of the surface to the horizon is + cosec 1” x gwh/2vu seconds of arc. Before proceeding further, I shall prove a very remarkable relation between the slope of the surface of an elastic horizontal plane and the deflection of the plumb-line caused by the direct attraction of the weight producing that slope. This relation was pointed out to me by Sir William Thomson, when I told him of the investigation on which I was engaged; but I am alone responsible for the proof as here given. He writes that he finds that it is not confined simply to the case where the solid is incompressible; but in this paper it will only be proved for that case. Let there be positive and negative matter distributed over the horizontal plane according to the law whcos(z/b): this * It is easy to verify that these values of 2 and y, together with the yalue p=guwh e—/* cosz/b for the hydrostatic pressure, satisfy all the con- ditions of the problem, by giving normal pressure gwhcosz/6 at the free surface of the infinite plane, and satisfying the equations of internal equi- librium throughout the solid. I take this opportunity of remarking that the paper from which this investigation is taken contains an error, inas- much as the hydrostatic pressure is erroneously determined in section 1. The term —W should be added to the pressure as determined in (3). This adds W to the normal stresses P,Q, R throughout the paper, but leaves the difference of stresses (which was the thing to be determined) unaffected. If the reader should compare the stresses as determined from the values of «, y in the text above, and from the value of p given in this note, with (38) of the paper referred to, he is warned to remember the missing term W: 2H 2 412 Mr. G. H. Darwin on Variations in the Vertical forms, in fact, harmonic mountains and valleys on the infinite plane. We require to find the potential and attraction of such a distribution of matter. Now the potential of an infinite straight line, of line-density p, at a point distant d from it, is well known to be —2yp log d, where wp is the attraction between unit masses at unit distance apart. Hence the potential V of the supposed distribution of matter at the point 2, z Ai given by V=—2uwh (~* cos? Plog VW {2 + (€—z)dé = —pwhb { [sin : log {27+ (€— 23] avi aia ee dt It is not hard to show that the first term vanishes when taken between the limits. Now put t= -— = * so that sin? = sin . coss + cos sings and we have eat “(sine cos> + cos — tf in’ a b 6 b/14# But it is known* that ** ¢ sin ct dt ae eee ie ee 3 bd 142 i= Therefore V =2arpwhbe-*" cos : If g be gravity, a earth’s radius, and 6 earth’s mean density, 3g 2p = A d 2a6 dqwh z = a be" Coss. . « » « « (A) The deflection of the plumb-line at any point on the surface denoted by «=0, and z, is clearly dV /gdz, when e=0. There- fore i ds Sowhis ae the deflection rig x 5 a5 0; -: nn But from (2) the slope (ora &, when 2 is zero) is * See Todhunter’s ‘ Integ. Cale.’ ; chapter on “ Definite Integrals.” pif ie due to Elasticity of the Earth’s Surface. 413 Therefore deflection bears to slope the same ratio as v/g to 4a0. This ratio is independent of the wave-length 27b of the undulating surface, of the position of the origin, and of the azimuth in the plane of the line normal to the ridges and val- leys. Therefore the proposition is true of any combination whatever of harmonic undulations ; and as any inequality may be built up of harmonic undulations, it is generally true of inequalities of any shape whatever. Now a=6:37 x 10° centim., 8=52; and 4ad=12°03 x 10° grammes per square centimetre. The rigidity of glass in gravitation-units ranges from 1°5 x 10° to 2°-4x 10%. There- fore the slope of a very thick slab of the rigidity of glass, due to a weight placed on its surface, ranges from 8 to 5 times as much as the deflection of the plumb-line due to the attraction of that weight. Hven with rigidity as great as steel (viz. about 8 x 10*), the slope is 14 times as great as the deflection. A practical conclusion from this is that, in observations with an artificial horizon, the disturbance due to the weight of the observer’s body is very far greater than that due to the attraction of his mass. ‘This is in perfect accordance with the observations made by my brother and me with our pendulum in 1881, when we concluded that the warping of the soil by our weight when standing in the observing-room was a very serious disturbance, whilst we were unable to assert positively that the attraction of weights: placed near the pendulum was perceptible. It also gives emphasis to the criticism we have made on M. Plantamour’s observations—namely, that he does not appear to take special precautions against the disturbance due to the weight of the observer’s body. We must now consider the probable numerical values of the quantities involved in the barometric problem, and the mode of transition from the problem of the mountains to that of barometric inequalities. The modulus of rigidity in gravitation-units (say grammes weight per square centimetre) is v/g. In the problem of the mountains, wh is the mass of a column of rock of one square centimetre in section and of length equal to the height of the crests of the mountains above the mean horizontal plane. In the barometric problem, wh must be taken as the mass of a column of mercury of a square centimetre in section and equal in height to a half of the maximum range of the barometer. This maximum range is, I believe, nearly two inches, or, let us say, 9 centim. The specific gravity of mercury is 13°6; and therefore wh=34 grammes. The rigidity of glass is from 150 to 240 million grammes 414 Mr. G.H. Darwin on Variations in the Vertical per square centimetre, that of copper 540, and of steel 843 millions. I will take v/g=3 x 10°; so that the superficial layers of the earth are assuined to be more rigid than the most rigid glass. It will be easy to adjust the results afterwards to any other assumed rigidity. With these data we have fe iO ald Gy a Ee also 648,000 5:67 7 ~ 10 It seems not unreasonable to suppose that 1500 miles (24x 10* centim.) is the distance from the place where the barometer is high (the centre of the anti-cyclone) to that where it is low (the centre of the cyclone). Accordingly the wave-length of the barometric undulation is 4°8 x 10* centim., and b=4°8 x 10°+6-28 centim., or, say, b=*8 x 10* centim. Thus, with these data, ie 2v We thus see that the ground is 9 centim. higher under the barometric depression than under the elevation. If the sea had time to attain its equilibrium slope, it would stand 5 x 13:6, or 68 centim. lower under the high pressure than under the low. Butas the land is itself depressed 9 cen- tim., the sea would apparently only be depressed 59 centim. under the high barometer. It is probable that, in reality, the larger barometric inequa- lities do not linger quite long enough over particular areas to permit the sea to attain everywhere its due slope, and therefore the full difference of water-level can only be attained occa- sionally. On the other hand, the elastic compression of the ground must take place without any sensible delay. Thus it seems probable that the elastic compression of the ground must exer- cise a very sensible effect in modifying the apparent depres- sion or elevation of the sea under high and low barometer. It does not appear absolutely chimerical that at some future time, when both tidal and barometric observations have attained to great accuracy, an estimate might thus be made of the average modulus of rigidity of the upper 500 miles of the earth’s mass. Kyen in the present condition of barometric and tidal infor- =00117. b=4°5 centim. due to Elasticity of the Earth’s Surface. 415 mation, it might be interesting to make a comparison between the computed height of tide and the observed height, in con- nexion with the distribution of barometric pressure. It is probable that India would be the best field for such an attempt, because the knowledge of Indian tides is more complete than that for any other part of the world. On the other hand, we shall see in the following section that tidal observations on coast-lines of continents are liable to disturbance, so that an oceanic island would be a more favourable site. Tt has already been shown that the maximum apparent deflection of the plumb-line, consequent on the elastic com- pression of the earth, amounts to 00117; and this is aug- mented to 0’:0146, when we include the true deflection due to the attraction of the air. It is worthy of remark that this result is independent of the wave-length of the barometric inequality, and thus we get rid of one of the conjectural data. Thus, if we consider the two cases of high pressure to right and low to left, and of low pressure to right and high to left, we see that there will be a difference in the position of the plumb-line relatively to the earth’s surface of 0/0292. Hvyen if the rigidity of the upper strata of the earth were as great as that of steel, there would still be a change of 0-011. A deflection of magnitude such as 0/03 or 0-01 would have been easily observable with our instrument of last year ; for we concluded that a change of 51, of a second could be detected when the change occurred rapidly. It was stated in our previous Report that at Cambridge the ealeulated amplitude of oscillation of the plumb-line due directly to lunar disturbance of gravity amounts to 0/0216. Now, as this is less than the amplitude due jointly to elastic compression and attraction, with the assumed rigidity (3800 millions) of the earth’s strata, and only twice the result if the rigidity be as great as that of steel, it follows almost certainly that from this cause alone the measurement of the lunar dis- turbance of gravity mnst be impossible with any instrument on the earth’s surface. Moreover the removal of the instrument to the bottom of the deepest known mine would scarcely sensibly affect the result, because the flexure of the strata at a depth so small, compared with the wave-length of barometric inequalities, is scarcely different from the flexure of the surface. The diurnal and periodic oscillations of the vertical observed by us were many times as great as those which have just been computed; and therefore it must not be supposed that more than a fraction, say perhaps a tenth, of those oscillations was due to elastic compression of the earth. 416 Mr. G. H. Darwin on Variations in the Vertical The Italian observers could scarcely with their instruments detect deflections amounting to +4, of a second; so that the observed connexion between barometric oscillation and seismic disturbance must be of a different kind. It is not surprising that in a volcanic region the equaliza- tion of pressure, between imprisoned fluids and the external atmosphere, should lead to earthquakes. If there is any place on the earth’s surface free from seismic forces, it might be possible (if the effect of tides as computed in the following section could be eliminated) with some such instrument as ours, placed in a deep mine, to detect the exist- ence of barometric disturbance many hundreds of miles away. It would of course for this purpose be necessary to note the positions of the sun and moon at the times of observation, and to allow for their attraction. 2. On the Disturbance of the Vertical near the Coasts of Continents due to the Rise and Fall of the Tide. Consider the following problem:— On an infinite horizontal plane, which bounds in one direc- tion an infinite incompressible elastic solid, let there be drawn a series of parallel straight lines, distance J apart. Let one of these be the axis of y, let the axis of z be drawn in the plane, perpendicular to the parallel lines, and let the axis of z be drawn vertically downwards through the solid. At every point of the surface of the solid, from z=0 to J, let a normal pressure gwh(1—2z/l) be applied; and from z=( to —/ let the surface be free from forces. Let the same distribution of force be repeated over all the pairs of strips into which the surface is divided by the system of parallel straight lines. It is required to determine the strains caused by these forces. Taking the average over the whole surface, there is neither pressure nor traction, since the total traction on the half-strips subject to traction is equal to the total pressure on the half- strips subject to pressure. The following is the analogy of this system with that which we wish to discuss: the strips subject to no pressure are the continents, the alternate ones are the oceans, g is gravity, w the density of water, and / the height of tide above mean water on the coast-line. We require to find the slope of the surface at every point, and the vertical displacement. It is now necessary to bring this problem within the range of the results used in the last section. In the first place, it is convenient to consider the pressures and tractions as caused by due to Elasticity of the Earth’s Surface. A17 mountains and valleys whose outline is given byz= —h(1—2z2/l) from z=0 to /, and z=0 from z=0 to —/. To utilize the analysis of the last section, it is necessary that the mountains and valleys should present a simple-harmonic outline. Hence the discontinuous function must be expanded by Fourier’s method. Known results of that method render it unnecessary to have recourse to the theorem itself. It is known that +47—30= sin0+4 sin 20+4 sin 30+... —t0=— sin 6+4sin 20—4 sin36+... pea 1 1 37 + 0=— 4 cos@+ 55c0s 30+ =c0s 50+... ¢; 7 3° dD the upper sign being taken for values of @ between the infi- nitely small positive and +77, and the lower for values between the infinitely small negative and —7. Adding these three series together, we have 2{4sin20+4sin40+..} +24 cos @-+ 500s 30+ 200s 5O+.. \ equal to 7—20 from 6=0 to +7, and equal to zero from @=0 to —7. Hence the required expansion of the disconti- nuous function is — = ty sin204+3sin40+...}, Ah 1 1 f a —— cos 8+ 3300s 36+ <=cos50+... by | where Te Deepest ce? ols ty ZN for it vanishes from z= —/ to 0, and is equal to —h(1—22/l) from z=0 to +/. Now, looking back to the analysis of the preceding section, we see that, if the equation to the mountains and valleys had been x= —/sin (z/b), « would have had the same form as in (2), but of course with sine for cosine, and y would have changed its sign and a cosine would have stood for the sine. Applying then the solution (2) to each term of our expansion separately, and only writing down the solution for the surface at which z=0, we have at once that y=0, and ax Uh TY 5 8in20 +7 sin 46+ asin 66+... }, Tt 2 4 6 (8) +o =| cos 8+ $008 30+ 300s 50+... TU 1 418 Mr. G. H. Darwin on Variations in the Vertical . da «wda, The slope of the surface is ET de thus be mp Lz C08 28+ ¢ 608 46 + § cos BO +... .F | gwh 2 1 bi | MR — 22h 2 f in 6+ sin 30+ pysin 56+... }.| The formule (8) and (9) are the required expressions for the vertical depression of the surface and for the slope. _ It is interesting to determine the form of surface denoted by these equations. Let us suppose, then, that the units are so chosen that gwhl/m?v may be equal to one. Then (8) and (9) become = pain 20+ 4 sin40+...+24 5080+ 7008 30+... \ ( 1A =400820+4c0s40+...—=4 Asin + psin 30+... }. 11) When @ is zero or +77, da/d@ becomes infinite, which de- notes that the tangent to the warped horizontal surface is vertical at these points. The verticality of these tangents will have no place in reality, because actual shores shelve, and there is not a vertical wall of water when the tide rises, as is supposed to be the case in the ideal problem. We shall, how- ever, see that in practical numerical application, the strip of sea-shore along which the solution shows a slope of more than 1” is only a small fraction of a millimetre. Thus this depar- ture from reality is of no importance whatever. When 6=0 or +7, ee Ae da ee CS 2 a= ={ ptratpat-- } = 1-052 ="670, (12) being + when 6=0, and — when 0=+7. When 0= +47, « vanishes; and therefore midway in the ocean and on the land there are nodal lines, which always remain in the undisturbed surface, when the tide rises and falls. At these nodal lines, defined by 0= +37, da__ 4) ax 24 Sata } Wis 7102 coh ig 38 ie = — 3466 + °6168= —:9634 and +°2702. Thus the slope is greater at mid-ocean than at mid-land. By assuming @ successively as $7, 4a, 47, and summing arithmetically the strange series which arise, we can, on pay- due to Elasticity of the Earth’s Surface. 419 ing attention to the manner in which the signs of the series occur, obtain the values of « corresponding to 0, +47, +147, tem, +é7, +$7, +37, +82. The resulting values, together with the slopes as obtained above, are amply suffi- ient for drawing a figure, as shown annexed. LOW TIDE. HIGH TIDE, LAND. SEA. LAND SEA. -~ LOW TIDE SOOT TNE Te a aS aE I The straight line is a section of the undisturbed level, the shaded part being land, and the dotted sea. The curve shows the distortion, when warped by high and low tide as indicated. The scale of the figure is a quarter of an inch to }7 for the abscissas, and a quarter of an inch to unity for the ordinates ; it is of course an enormous exaggeration of the flexure actu- ally possibly due to tides. It is interesting to note that the land-regions remain very nearly flat, rotating about the nodal line, but with slight cur- vature near the coasts. It is this curvature, scarcely percep- tible in the figure, which is of most interest for practical application. The series (8) and (9) are not convenient for practical cal- culation in the neighbourhood of the coast, and they must be reduced to other forms. It is easy, by writing the cosines in their exponential form, to show that cos 0+ 4c0s 20+4 0s 30+...=—log,(+2sin}0), . (13) cos 0—£ cos 20+4.c0830—...= log.(2cos30), . . (14) where the upper sign in (13) is to be taken for positive values of 6 and the lower for negative. For the small values of @ with which alone we are at present concerned, the series (13) becomes — log, (+@) and the lower loo; 2! “ee half the difference and half the sum of the two series, we have Lcos20+icos40+..... =—tlog(+0@)—4log2, . (15) cos 0+4 cos 30+4c0s50+ =—tlog(+0)+4log2. . (16) Integrating (16) with regard to 0, and observing that the 420 Mr. G. H. Darwin on Variations in the Vertical constant introduced on integration is zero, we have sin 0+ Les 30+ Emnba: ...= —40[log( +0)—1] + d6log2. 2 La Then, from (15) and (17), 1 cos 20-+4.00840+.. =f mee pein 30+...) 20 oe T Tove =—3(1- log (+0)—3(1 + = log 2— Integrating (15), and observing that the constant is zero, we have & sin 20+ asin 46+...=—46[log( +0)—1] —40 log2. (19) Integrating (17) , and putting in the proper constant to ~ make the left side vanish when 6=0, we have 1 1 1 ata B +.1.— (F005 0+ 5.008 30+...) = —1@ log (+0)+i0 ($4 log2). . . (20) For purposes of practical calculation, @ may be taken as so small that the right-hand side of (18) reduces to —}log (+28), and the right-hand sides of (19) and (20) to zero. Hence, by (8) and (9), we have in the neighbourhood of the coast, _oek ANT) AB Tet gaat ea | wh tt = x — x 21087, f » + (21) da __—gwh Qarz | re =>—_ ones log. 10 logyo T. J I shall now proceed to compute from the formule (21) the depression of the surface and the slope, corresponding to such numerical data as seem most appropriate to the terrestrial oceans and continents. Considering that the tides are undoubtedly augmented by kinetic action, we shall be within the mark in taking h as the semi-range of equilibrium tide. At the equator the lunar tide has a range of about 53 centim., and the solar tide is very nearly half as much. Therefore at spring-tides we may take h=40 centim. It must be noticed that the highness of the tides (say 15 or 20 feet) near the coast is due to the shallow- ing of the water, and it would not be just to take such values due to Elasticity of the Earth's Surface. 421 as representing the tides over large areas ; w, the density of the water, is of course unity. If we suppose it is the Atlantic Ocean and the shores of Hurope with Africa, and of North and South America, which are under consideration, it is not unreasonable to take Las 3900 miles, or 6°28 x 10° centim. Then 27z/l=z~x 10-8. Taking v/g as 3 x 10° (that is to say, assuming a rigidity greater than that of glass), we have for the slope in seconds of are, at a distance z from the sea-shore, 40 Orx3x 108 x log. 10x (8— logyo z) =07-01008 (8—logyz). . . . (22) cosec 1’ x From this the following table may be computed by simple multiplication :— Distance from mean water-mark. Slope. 1 centim. =—elcenhin. eae 6260-0806 iS Aen a= 0): Sapa Maran parr ss 07 (05 Oe, == LMC. ot tty SOOUD 103°, = lOmetres. 25 4 6 o5 2.0504 HOE = OOP RO sare & stk OAMS LO? ;, ae su kiloms she slat oe OS02 HOP, Se (hes 8 ee a at es Oa PeaeOccentms— 20.0) 8k. OLTO em ete DO A OLS 10’ centim. SS UD ea Me? ata el eames O80! On considering the formula (22), it appears that z must be a very small fraction of a millimetre before the slope becomes even as great as 1’. This proves that the rounded nick in the surface, which arises from the discontinuity of pressure at our ideal mean water-mark, is excessively small; and the vertical displacement of the surface is sensibly the same, when mea- sured in centimetres, on each side of the nick, in accordance with the first of (21). The result (5) of section 1 shows that, with rigidity 3 x 108, the true deflection of plumb-line due to attraction of the water is a quarter of the slope. Hence an observer in a gra- vitational observatory at distance z from mean water-mark, would note deflections from the mean position of the vertical 13 times as great as those computed above ; and as high water changes to low, there would be oscillations of the ver- tical 24 times as great. We thus get the practical results in the following table:— 422 Mr. G. H. Darwin on Variations in the Vertical q - Distance of Amplitude of observatory from apparent oscillation mean water-mark. of the vertical. 10 metres’... 2 US. Oras 100) a0 3. 1 ea eo Vkilom. isin 4S ee 10: ,, (5% 01,5 se) OP 90: of) wlezalon, Gea an 50. pe ajodaetes, gin eae” 100° "ee It follows, from the calculations made for tracing the curve, that halfway across the continent (that is to say, 3142 kilo- metres from either coast) the slope is 648,000 gwh vis TU x ‘2708 second of are =0:00237, and the range of apparent oscillation is 0/006. In these calculations the width of the sea is taken as 6283 kilometres. If the sea be narrower, then, to obtain the same deflections of the plumb-line, the observatory must be moved nearer the sea in the same proportion as the sea is narrowed. If, for example, the sea were 3142 kilometres wide, then at 10 kilometres from the coast the apparent amplitude of deflection would be 0-042. If the range of tide is greater than that here assumed (viz. 80 centim.), the results must be aug- mented in the same proportion. And, lastly, if the rigidity of the rock be greater or less than the assumed value (viz. 3x 10°), the part of the apparent deflection depending on slope must be diminished or increased in the inverse propor- tion to the change in rigidity. I think there can be little doubt that in narrow seas the tides are generally much greater than those here assumed ; and it is probable that at a gravitational observatory actually on the sea-shore on the south coast of England, apart from seismic changes, perceptible oscillations of the vertical would be noted. Sir William Thomson has made an entirely independent estimate of the probable deflection of the plumb-line at a sea- side gravitational observatory*. He estimates the attraction of a slab of water 10 feet thick (the range of tide), 50 miles broad perpendicular to the coast, and 100 miles long parallel with coast, on a plummet 100 yards from the low-water mark, and opposite the middle of the 100 miles oflength. He thinks this estimate would very roughly represent the state of things _ * Thomson and Tait’s ‘ Natural Philosophy,’ § 818. due to Elasticity of the Earth's Surface. 423 say at St. Alban’s Head. He finds, then, that the deflection of the plumb-line as high tide changes to low would be zoobo000 Of the unit angle, or 0/050. The general theorem proved above, as to the proportionality of slope to attraction, shows that, with rigidity 3x 10° for the rocks of which the earth is formed, the apparent deflection of the plumb-line would amount to 0°25. Ii is just possible that a way may in this manner be opened for determining the modulus of rigidity of the upper 100 or 200 miles of the earth’s surface, although the process would be excessively laborious. The tides of the British Channel _ are pretty well known; and therefore it would be possible by very laborious quadratures to determine the deflection of the plumb-line due to the attraction of the tide at any time at a- chosen station. If, then, the defiection of the plumb-line could be observed at that station (with corrections applied for the positions of the sun and moon), the ratio of the calculated to the observed and corrected deflection, together with the known value of the earth’s radius and mean density, form the mate- rials for computing the rigidity. But such a scheme would be probably rendered abortive by just such comparatively large and capricious oscillations of the vertical as we, M. d’Abbadie, and others have observed. It is interesting to draw attention to some observations of M. d’Abbadie on the deflections of the vertical due to tides. His observatory (of which an account was given in the Report for 1881) is near Hendaye, in the Pyrenees, and stands 72 metres above and 400 metres distant from the sea. He writes* :— ““ Jai réuni 359 comparaisons d’observations spéciales faites lors du maximum du flot et du jusant ; 243 seulement sont favorables a la théorie de l’attraction exercée par la masse des eaux, et l’ensemble des résultats pour une différence moyenne de marées égale a 2°9 metres donne un résultat moyen de 056 ou 0-18 pour le double de l’attraction angulaire vers le Nord-Ouest. Ceci est conforme a la théorie, car les différences observées doivent étre partagées par moitié, selon la loi de la réflexion ; mais comme il y a toujours de l’inattendu dans les experiences nouvelles, on doit ajouter que sur les 116 compa- raisons restantes il y en a eu 57 ot le flot semble repousser le mercure au lieu de Vattirer. Mes résultats ont été con- firmés pendant Vhiver dernier par M. l’abbé Artus, qui a eu la patience de comparer ainsi 71 flots et 73 jusants consécutifs, de janvier 4 mars 1880. Lui aussi a trouvé un tiers environ * “Recherches sur la Verticale,” Ann. de la Soc, Scient. de Bruxelles, 81. 424 Mr. G. H. Darwin on Variations in the Vertical de cas défavorables 4 nos théories admises. On est done en droit d’affirmer que si la mer haute attire le plus souvent le pied du fil a plomb, il y a une, et peut-étre plusieurs, autres forces en jeu pour faire varier sa position.” We must now consider the vertical displacement of the land near the coast. In (21) it is shown to be _guh_ fl , a x 2°1037, where a indicates the displacement corresponding to z=0. With the assumed values, h=40, v=3 x 10°, 1=6°28 x 10%, I find #,=5°684 centim. Hence the amplitude of vertical displacement is 11°37 centim. As long as Al remains constant this vertical displacement remains the same ; hence the high tides of 10 or 15 feet which are actually observed on the coasts of narrow seas must probably produce vertical oscillations of quite the same order as that computed. If the land falls, the tide of course rises higher on the coast- line than it would do otherwise ; hence the apparent height of tide would be h+a,. But this shows there is more water resting on the earth than according to the estimated value h ; hence the depression of the soil is greater in the proportion 1+4,/h to unity; this again causes more tide, which reacts and causes more depression, and so on. Thus on the whole the augmentation of tide due to elastic yielding is in the ratio of ako Gg\ol! fan’ 1 : 1+ 2+ (2) +(?) = Me! 0) i. jk This investigation is conducted on the equilibrium theory ; and it neglects the curvature of the sea-bed, assuming that there is a uniform slope from mid-ocean to the sea-coast. The figure shows that this is not rigorously the case ; but it is quite near enough for a rough approximation. The phenomena of the short-period tides are so essentially kinetic that the value of this augmentation must remain quite uncertain; but for the long-period tides (the fortnightly and monthly elliptic) the augmentation must correspond approximately with the ratio ie (1- gu 21037). TU The augmentation in narrow seas will be small; but in the Atlantic Ocean the augmenting factor must agree pretty well with that which I now compute*. * Sir William Thomson has pointed out to me, since the meeting of the Association, that this augmentation will only hold true in the cases of certain distributions of land. due to Elasticity of the Earth's Surface. 425 With the previous numerical values we have a) // (which is independent of h) equal to 1421, and 1—«,/h=:8579 =$ very nearly. . Thus the long-period tides may probably undergo an aug- ‘mentation at the coasts of the Atlantic in some such ratio as 6 to 7. The influence of this kind of elastic yielding is antagonistic to that reduction of apparent tide which must result from an elastic vielding of the earth’s mass as a whole. The reader will probably find it difficult to estimate what degree of probability of correctness there is in the conjectural value of the rigidity, which has been used in making the numerical calculations in this paper. The rigidity has not been experimentally determined for many substances; but a great number of experiments have been made to find Young’s modulus. Now, in the stretching of a bar or wire the com- pressibility plays a much less important part than the rigidity; and the formula for Young’s modulus shows that for an in- compressible elastic solid the modulus is equal to three times the rigidity*. Hence a third of Young’s modulus will forma good standard of comparison with the assumed rigidity, namely 3x 10° grammes weight per square centimetre. The follow- ing are a few values of a third of Young’s modulus and of rigidity, taken from the tables in Sir William Thomson’s article on Elasticity+ in the Encyclopedia Britannica:— A third of Young’s modulus and Material. rigidity in terms of 10° grammes weight per square centimetre. BONG. tears A OME L 2 Slate . . . . About 3 to 4. Glass : . . - Rigidity 1°5 to 2°4. Weer a ee AE Copper. . . . 4, and rigidity 4°6 to 5-4. Steel . . . . 7 to 10, and rigidity 8-4. It will be observed that the assumed rigidity 3 is probably a pretty high estimate in comparison with that of the mate- rials of which we know the superficial strata to be formed. It is shown, in another paper read before the Association at this meeting, that the rigidity of the earth as a whole is pro- bably as great as that of steel. That result is not at all incon- sistent with the probability of the assumption that the upper strata have only a rigidity a little greater than that of glass, * Thomson and Tait’s ‘ Natural Philosophy,’ § 683. + Also published separately by Black (Edinburgh). Phil. Mag. 8. 5. Vol. 14. No. 90. Dee. 1882. 2F 496 On Variations in the Vertical. 3. On Gravitational Observatories. In the preceding sections estimates have been made of the amount of distortion which the upper strata of the earth pro- bably undergo from the shifting weights corresponding to barometric and tidal oscillations. These results appear to me to have an important bearing on the utility of gravitational observatories. It is not probable, at least for many years to come, that the state of tidal and barometric pressure, for a radius of 500 miles round any spot on the earth’s surface, will be known with sufficient accuracy to make even a rough approximation to the slope of the surface a possibility. And were these data known, the heterogeneity of geological strata would form a serious obstacle to the possibility of carrying out such a computation. It would do little in relieving us from these difficulties to place the observatory at the bottom of a mine. Accordingly the prospect of determining experimentally the lunar disturbance of gravity appears exceedingly remote; and I am compelled reluctantly to conclude that continuous observations with gravitational instruments of very great delicacy are not likely to lead to results of any great interest. It appears likely that such an instrument, even in the most favourable site, would record incessant variations of which no satisfactory account could be given. Although I do not regard it as probable that such a delicate instrument should be adopted for regular continuous observations, yet, by choosing a site where the flexure of the earth’s surface is likely to be great, it is conceivable that a rough estimate might be made of the average modulus of elasticity of the upper strata of the earth for one or two hundred miles from the surface. These conclusions, which I express with much diffidence, are by no means adverse to the utility of a coarser gravita- tional instrument, capable, let us say, of recording variations of level amounting to 1” or 2”. If barometric pressure, tidal pressure, and the direct action of the sun and moon combine together to make apparent slope in one direction, then, at an observatory remote from the sea-shore, that slope might per- haps amount to a quarter of a second of arc. Such a disturb- ance of level would not be important compared with the minimum deviations which could be recorded by the supposed instrument. It would then be of much value to obtain continuous syste- matic observations, after the manner of the Italians, of the — seismic and slower quasi-seismic variations of level. On the Evolution of the Earth-Moon System. A27 I venture to predict that at some future time practical astro- nomers will no longer be content to eliminate variations of level merely by taking means of results, but will regard cor- rections derived from a special instrument as necessary to each astronomical observation. XLVI. New Views of Mr. George H. Darwin’s Theory of the Evolution of the Earth-Moon System, considered as to its bearing on the question of the Duration of Geological Time. By the Rey. Samurt Haveuton, ID., Fellow of Trinity College, Dublin*. a has- been tacitly assumed, even so far back as the times of Newton and Clairaut, that the earth and planets have passed through a liquid condition (owing to former great heat) before assuming the solid condition which some, at least, of them now possess. Laplace, in his nebular hypothesis, also assumes the former existence of this liquid condition; and it is openly asserted by all geologists who believe that the earth consists of a solid crust (more or less thick), reposing upon a fluid or viscous nucleus. It has been proved by Sir William Thomson, following out the views of the late Mr. Hopkins, that the present condition of the earth, taken as a whole, is such that it must be re- garded as being more rigid than glass or steel, possibly more rigid than any terrestrial substance under the surface-condi- tions of pressure. The following considerations show that it may be fairly doubted whether the earth or any other planet ever existed in a fluid condition. 1. The possibility of the equilibrium of the rings of Saturn, on the supposition that they are either solid or liquid, has been more than doubted, and the most probable hypothesis respect- ing them is, that they consist of swarms of discrete meteoric stones. 2. It is difficult to understand the low specific gravity of Jupiter and the other outer planets, on the supposition that they are either solid or liquid; for we know of no substance light enough to form them f. If the outer planets consist of * From the ‘ American Journal of Science ’ for November 1882. Read before the Mathematical Section of the American Association for the Advancement of Science, at Montreal, August 1882. + The force of this argument could not be felt before the revelations of the spectroscope, because at that time there was no proof that the whole universe was composed of the same simple substances, and those very limited in number. 22 428 Rey. S. Haughton on Mr. G. H. Darwin’s Theory discrete meteoric stones moving around a solid or liquid nucleus, the difficulty respecting their specifie gravity would disappear. 3. The recent researches connecting the November, the August, and other periodic swarms of shooting-stars with comets, tend in the direction of showing that comets in cooling break up into discrete solid particles (each no doubt having passed through the liquid condition), and that probably the solar nebula cooled in like manner into separate fiery tears, which soon solidified by radiation into the cold of space. 4, Mr. Huggins’s recent comparisons of the spectroscopic appearances of comets and incandescent portions of meteoric stones, showing the presence in both of hydrocarbon and nitrogen compounds, confirm the conclusions drawn from the identity of the paths of comets and meteoric periodic shooting- stars. 5. Mr. H. A. Newton, in a remarkable paper read before the Sheffield Meeting of the British Association (1879), showed the possibility (if not probability) of the asteroids being extinct comets, captured and brought into the solar system by the attraction of some one or other of the outer large planets, and permanently confined in the space between Mars and Jupiter, which is the only prison-cell in the solar system large enough to hold permanently such disorderly wanderers. In the same paper Professor Newton threw out the idea that some of the satellites of the large planets might also be of cometary origin. From all these and other considerations it is therefore allowable to suppose that the earth and moon, when they sepa- rated from the solar nebula, did so as a swarm of solid meteoric stones, each of them having the temperature of interstellar space, 7. e. something not much warmer than 460° F. below the freezing-point of water. Mr. George H. Darwin has shown admirably how the earth- moon system may have been developed from the time when the earth-moon formed one planet, revolving on its axis in a few hours, to the present time, when the earth and moon (in consequence of tidal friction) have pushed each other asunder to a distance of sixty times the radius of the earth *. In his paper on the tidal friction of a planet} (supposed viscous and under the influence of bodily tides caused in it by.an external body such as the moon), Mr. Darwin has found a remarkable equation of condition, which may be thus * Proceedings of the Royal Society, 19th June, 1879. + Phil. Trans. 1881, part ii. p. 494. a a ba of the Evolution of the Earth-Moon System. 429 expressed :— a Wdt d(/r) « =e EP Sea eeaue (1) where r=distance between centres of earth and moon, ¢=time elapsed from a fixed point, = p(n—Q) (2 ) 1+ p20)” SWE hy PAG! etl are eaiG n=angular velocity of earth’s rotation, Q=angular velocity of moon’s orbital revolution, p=quantity varying inversely as the viscosity of the planet. The extreme interest of equation (1) consists in the appear- ance of the inverse sixth power of the distance. As the function W varies very slowly, we find by integra- tion, for any portion of time during which VY may be regarded as constant, Ds iN E es oa) i OU LE AO ey a most unexpected and remarkable result. Upon reading Mr. Darwin’s papers, my mind turned to a problem with which I was familiar, viz. the retardation of the earth’s rotation produced by the lunisolar tide exerted upon the ocean supposed collected in an equatorial canal, the moon and sun having no declination; and I readily found an equa- tion to express the evolution of the earth-moon system, on the foregoing hypothesis as to friction. This equation is the following :— HOE et eee Pere where var \n— G o= f4V 2(n—O)? —P}./4n—- OP +7” Fin tee) Ale (5) f=coeficient of friction supposed proportional to relative velocity, k varies inversely as 7°, V,=velocity at earth’s equator. This leads, as in Mr. Darwin’s hypothesis of viscous earth, to the integral Li ENS ae ge ere ae, re AF) The form of the functions VY and © is similar, as both ascend by odd powers of (n—2) and vanish when n=0—that is to say, at the beginning and end of the evolution by friction of the earth-moon_system. = 430 Prof. H. Helmholtz on Systems of Absolute It is quite clear, therefore, that the remarkable expression (1) found by Mr. Darwin is not peculiar to his special hypo- thesis of a viscous earth, but can be deduced equally well from the totally distinct hypothesis of an absolutely rigid earth retarded by the tidal action of a liquid ocean. I was led by this result to consider the case of the earth- moon, separating (as I believe they did) from the central solar mass in the form of a swarm of discrete masses of mete- oric iron and stone, each one having the temperature of the cold of interstellar space, or not much aboveit. Translating this conception into mathematical language, I find that the equation of continuity belonging to the hydrodynamical theory applies equally well to the meteoric theory, viz. vy=y!, s.r where v, v’ are the velocities at any two points, and y, y’ are the depths of the ocean or meteoric swarm at the same points. The depth of the swarm or ocean without jostling or friction will be least under the moon and greatest at right angles to the moon, and the velocities will be inversely. Hence the chances of jostling among the meteorites when disturbed by the moon’s tidal action will be proportional to the velocity, being greatest where the velocity is greatest and the area of passage least, and vice versd. This consideration reduces the meteoric problem to that of the hydrodynamical problem, with a friction proportional to the velocity, and gives equations in all respects similar to those derived by Mr. Darwin from the hypothesis of a viscous earth. On the meteoric hypothesis, if the jostling of the stones be slow they may cool almost as fast as they are heated, and the result will be a cool earth and almost indefinite time at the disposal of geologists. XLVIII. On Systems of Absolute Measures for Electrie and Magnetic Quantities. By Prof. H. Hetmuorrz*. pa have hitherto been obliged to employ two different systems of electrical absolute measures, the electrostatic and electromagnetic ; while for magnetic quantities only one has always been made use of—namely that introduced by Gauss, in which only the parts of the metre and the gramme employed as the units of length and mass have changed. Indeed the employment of those two systems of electrical measures could not be dispensed with, for practical reasons, because the determination of the factor which had to be used * Translated from Wiedemann’s Annalen, 1882, no.9, vol. xvii. pp. 42-54, Measures for Electric and Magnetic Quantities. 431 for the reduction of electrostatic to electromagnetic measures, namely Weber’s critical velocity, could not yet be effected with the same degree of precision that could be attained within the sphere of electromagnetic measurements on the one hand and electrostatic measurements on the other. It was on this account more advantageous to employ in each experimental investigation that system of measures to which the quantities measured could be referred with the greater exactness. To this is to be added the consideration of avoiding excessively large numbers, which will probably induce us to continue to employ for electrostatic and galvanic phenomena two kinds of measures, although reducible to one another. At present the electromagnetic methods of measurement are the most perfect; - they are unmistakably the most important practically for an art that advances with giant strides; and I have therefore considered that the International Congress that met in Paris last year acted quite suitably in endeavouring to establish an electromagnetic system of absolute measures. Had the aim been purely scientific, I should have preferred the electrostatic system hitherto employed, since this, I think, best represents the essential analogies of the phenomena by analogous for- mulz, and gives to them the clearest and most intelligible expression. It was on this system, grounded on Gauss’s principles, that most of the physical-mathematical treatises in this department of science have hitherto been based. Just on this account it would appear to me very undesirable if this system should now entirely fall, and even its name give place to a new one, as proposed by Clausius in his recently published memoir*. I would not at all recommend the mul- tiplication of systems of measures without very urgent reasons; and certainly the transference of a name already in use and frequently employed to a new system would inevitably pro- duce needless and vexatious confusion in physical literature, even apart from any estimate of the relinquished in compa- rison with the new system. Any determination of a new absolute measure must be based on the measuring observation of a natural process or behaviour, just as already, among the three fundamental units, the gramme has been reduced to the two others by means of the density of pure water at 4° C. The measure of magnetic quanta which has hitherto been exclusively employed is founded on the definition laid down by Gauss, according to which the repellent force between two magnetic quanta, m, and m,, which are situated at the distance r from one another, * Clausius, Verhandl. des naturh. Vereims d. preuss. Rheil. u. Westfal. March 6, 1882; Wied, Ann, xvi. p. 529; Phil, Mag. June 1882, xiii, p. 881. 432 Prof. H. Helmholtz on Systems of Absolute is put not merely proportional, but equal to the value of (m,.m,/r°). Since the force and the length r are to be mea- sured by known methods, the value of the product (m, . mg) is thereby determined in absolute measure ; and therefore, if from other facts the ratio (m,/m;) can be determined, m, and m, can each be separately determined. Exactly the same principle is also applied by Gauss, at the commencement of his memoir “ Allgemeine Lehrsatze in Beziehung auf die im verkehrten Verhiltnisse des Quadrats der Entfernung wirkenden Anziehungs- und Abstossungs- kriifte”’*, to electrical quanta and gravitating masses. Al- though he has not in the latter two cases carried the prin- ciple into practical effect, it would be justifiable to designate all three methods by his name as that of their mental author. That which refers to electricity gives the electrostatic system as»it has hitherto been employed. The third, referring to gravitating masses, will probably in future play an important part, when we have succeeded in accomplishing more exact determinations of the force of gravitation. If, like Maxwell, we denote by angular brackets the dimensions of the expres- sion enclosed in them, by M a mass, by L a length, and by T a time, according to Gauss the attraction between two heavy masses m at the distance 7 is ‘i= ae pel fe =| al aig re he TA)” | eee On the left stands a density, on the right a function of the time. If, therefore, as hitherto, we put the absolute density of water equal to unity, while the unit of mass is determined in gravitation-measure, a time-measure is thereby given which is independent of the probably variable rotation of the earth, and only a single measure, the metre, is left to be handed down by tradition. But even this could be absolutely defined if we availed ourselves of an invariable velocity, for instance the velocity of light in free zether. Thus, for example, the period of revolution T of a small satellite revolving close to the surface of a sphere of pure water of normal density D, would, independently of the radius of the sphere, in gravitation-measure be T= %, and the velocity of light foal, Whee af 2B v= a= bh Sa * Resultate aus den Beobachtungen des magnetischen Vereins 1839. Measures for Electrie and Magnetic Quantities. 433 by which latter equation the length L would be given. This system would therefore free us from the handing-down of any traditional measure. In Gauss’s magnetic and electrostatic measure the dimen- sions of the magnetic quantum m and the electrostatic quantum ¢ are determined by the equations [m]=[e]=[M*L?T™”), both based on the phenomenon of repulsion between resting magnetic or resting electric quanta. On the other hand, for electromagnetic determinations the ponderomotive action of a closed electric current upon a pole of a magnet was used, the laws of which have been mainly and completely formulated by Ampere. The components of the magnetic forces produced in its vicinity by an electric current can, like those of a magnet, be represented as differential quotients of a potential-function which satisfies the same differential equations as those of mag- nets, and only differs from those of the latter in that it periodi- cally increases in value by the same quantity as often as only one pole is caused to make a whole reyolution about the con- ductor of the current. As the electromagnetic forces are pto- portional to the current-intensity of the conductor, the period of the potential is also proportional to that intensity, and inde- pendent of the shape of the conductor. Maxwell on this account employs the value of the period of the potential 0 as a measure for the intensity of the current C, and therefore, in § 623 of his Treatise on Electricity and Magnetism, puts the dimensions of the two equal: [O]=[C]. The fixed numerical relation between the two follows from an earlier passage of the above-mentioned work, § 479, where T denotes the magnetic force of a very long straight current- conductor at the small distance r from its axis, and J is put for C:— Tr=2J. Since O=T .2ar, O=47J, by which Maxwell’s determination becomes, when Gauss’s magnetic measure is employed, equal to the electromagnetic measure proposed by W. Weber. In Ampere’s time a complete theory of potential-functions did not yet exist. He has, however, represented quite accu- 434 Prof. H. Helmholtz on Systems of Absolute rately what we can now, in the manner stated, express in con- formity with nature, by a suitably chosen fiction; namely, he imagined a surface bounded by the conductor, dividing the in this case doubly connected space covered with a double mag- netic layer. If the magnetic moment of each unit of surface of the double layer is denoted by pw, according to well-known principles the leap of potential between the two sides must be O=47rp, and therefore ~=J. With this form of expression of Ampére’s law Prof. Clausius stops. Both forms are perfectly equivalent and equally justified, so long as we measure the magnetic quanta according to Gauss’s rule. This Prof. Clausius also admits ; but he thinks an extension of Maxwell’s expression to other systems of mea- sures must be rejected ; he explains this as an oversight on Maxwell’s part, and the equations and determinations of mea- surements derived from it as erroneous. The only reason which, in this respect, he alleges against Maxwell’s definition is the following, in § 3 of the memoir above cited:—“ The force, however, which a current exerts upon a magnetic pole is electrodynamic ; and from this it fol- lows that an equation of which the deduction is based upon this force can be regarded as valid only in the dynamic system founded upon the electrodynamic forces, and not in the static system based on the electrostatic forces.” But even if one, as an adherent of Ampére’s hypothesis, entertained no doubt respecting the first part of this proposi- tion, I do not see why the conclusion should be urged against Maxwell only, and not against the interpretation of Ampére’s law adopted by Clausius himself, since the latter is, after all, nothing but another way of expressing the same facts. Both quantities, Maxwell’s potential-period © as well as Ampére’s magnetic momentum of unit surface, are, in Gauss’s system of measurement, of the dimension [m/L]; both have a physical meaning only in “ the representation of the force which a cur- rent exerts upon a magnetic pole.” The true reason of the difference moreover appears to me to lie in quite another circumstance—namely, in Maxwell’s defi- nition of the magnetic potential Q. This is with him not the form of calculation 2[m/7], but he defines it in this case, as also in the corresponding applications to electrostatics and electrodynamics, by stating that Q.m is a work—which defi- nition also underlies Gauss’s definition of m. The differential quotient —dQ/dz is, corresponding to this, the force which acts upon the unit of magnetism, and therefore Measures for Electric and Magnetie Quantities. 435 (—Q) Jacoby’s force-function. If we introduce for m another measuring unit, and measuring with it obtain m, Oy, J, instead of m, 0, J, then must, according to Maxwell’s defi- nition, mOA=mO,, and therefore mJ =m,J3. The unit of current therefore increases in the inverse propor- tion of the newly chosen unit of magnetism to the old one; but the force which the unit of current exerts upon the unit of magnetism remains constant. With Prof. Clausius, on the contrary, both m and J increase in the same, and not in the inverse ratio, and the force increases as m” or J. According to his determinations, the feigned surface of Ampere always produces one more leap, equal to the momentum of unit of surface, in the function =(m/r); but this function has then no longer the signification of the force-function for the newly chosen magnetic units. In all this I cannot perceive any mistake of Maxwell’s; and his equations, derived from the formulation chosen by him of the fundamental phenomenon, are altogether as consistent with each other and as correct, if understood in the sense of their author, as those of Prof. Clausius. Rather, this case shows that, if we abandon Gauss’s determination of the magnetic unit, we again fall into at least two different and equally jus- tifiable systems of measuring-units; and, for my part, I could, with respect to both Maxwell and Clausius, draw from this the practical conclusion that we ought by no means to forsake the above-mentioned method of Gauss until we have particu- larly important reasons and a definite purpose for such a pro- ceeding, when the choice between the systems of Maxwell and Clausius would probably be decided on positive grounds. Now, although J must vindicate Maxwell from the charge of having, in consequence of an oversight, set up incorrect equations, yet it should be mentioned that in the w ording of the text of § 623 of his work, where he reduces the dimensions of all the rest of the electric and magnetic quantities to the dimensions of any one chosen from among them, an omission occurs which might easily lead the reader into error, if he does not closely examine the connexion of the somewhat com- plicated systems of equations of §§ 622 and 623, and which seems to give to the propositions of § 623 a greater extension than Maxwell himself would probably have given them. For at the beginning of Chapter X., in § 620, he speaks of electro- static and electromagnetic but not of magnetic units, and 436 Prof. H. Helmholtz on Systems of Absolute moreover gives definitions according to which the electro- | kinetic units are determined without any consideration of magnetism. But in § 621 he introduces magnetic quantities without in any way saying expressly that, in all his determi- nations of the ratio between electric and magnetic quantities, the electromagnetic determination discussed in the chapters in question, AnJ =O, will be retained. In this respect Maxwell’s intention in sketching different systems was exactly the same, and as limited, as that more recently carried out by Clausius, although, from the cause above discussed, the manner of carrying it out by the two has turned out different. The matter being so important, I will take leave to give here a summary of the connexion of the equations of the cor- responding paragraphs (621-623) of Maxwell’s Treatise on Electricity and Magnetism. In § 621 he arranges the quan- tities for which the dimensions of the unit are to be determined. I place them here in a somewhat different order, and with the notation of their meaning which is more usual in Germany. There are four electrostatic, namely :— e, electric quantum ; K, electrostatic potential-function ; ®, dielectric polarization, measured by the electric density at the surface of the dielectric ; ©, the electric force in a point, acting upon the unit of s. The four corresponding magnetic quantities he denotes, in the same order, by m, 0, B, H. ; To these are added four more corresponding quantities, namely :— C, the intensity of a current ; ©, current-density ; p, the electrokinetic momentum of a current ; 9, the vector-potential of electric currents. As regards the meaning of the last two quantities, p is Neumann’s electrodynamic potential of the other currents present, referred to the entire conductor (passed through b the unit of current) for which it is calculated ; and %.ds is the same potential referred to a conductor-element ds situated at a determined place. I remark further that the quantities denoted by German capital letters are vectors, 7. e. quantities having direction and resolvable into components according to the law of the paral- lelogram of forces,—and that the selection of them resulted from Maxwell’s endeavour to introduce, as far as possible, only Measures for Electric and Magnetic Quantities. 437 directly observable quantities into the calculation, and to avoid hypotheses. In § 622 Maxwell sets forth dimension-determinations for the products and quotients of these twelve quantities, as given immediately by their meaning. There are fifteen of these determinations, in which those quantities referable to elec- tricity are kept quite separate from those which refer to mag- netism, so that (which is certainly remarkable) from these fifteen determinations no relation between electricity and mag- _netism appears. I arrange them tabularly, retaining Max- well’s above-employed notation of the dimensions. No. | Dimension. Electric quantities. Ae ee Mel tM | fe), [p. 0). [m0] 2 M/(LT’) |[D.€], [C.] [B.H] 3. p [e/C], [p/E}, [UAE] 4 L [E/E], [p/] | /9] 5 UE Le/D], [O/@] Lm/%] The last series of determinations result from the first, if they be divided by the product of the quantities in question of the second and fourth series. The fifth series may therefore be omitted as superfluous; then there remain the following iden- tical equations between the quantities in the first four rows:— fel (eat [eh [el eee [6] al Caan A Lastly, there are left three independent determinations for the four magnetic quantities m, 0, 8, , and seven for the eight electric quantities e, H, p, C,D, ©, €, A. If, therefore, of these two groups one quantity each be defined by other de- -terminations—for example m and e, the quantum of magnetism and the quantum of electricity—all the others are completely defined, namely :— 438 Prof. H. Helmholtz on Systems of Absolute Electric. Electrokinetic. Magnetic. Forces: ...... [¢]= lees [a] = ea [Hl= [ae Densities ...|[D]= ital TCj= al [B]= ka [e]=[CT] These are the determinations which, without any further limiting equations, result from the above fifteen. These can be applied to any definition of the units of m and e, and there- fore also to the electrostatic-magnetic system of Gauss. Now follows, in Maxwell, § 623, “These fifteen equations are not independent of each other; and in order to deduce from them the dimensions of all the twelve units they contain, we require one more equation.” In fact we require two, since e and m must be determined singly by recurring to two facts of observation regarded as fundamental phenomena. The one here wanting, not expressly mentioned by Maxwell, but from the connexion self-evidently presupposed, we can write as above:— [2]=[C]. Clausius has chosen for it the less perspicuous [p]=[~]. But, since one of the fifteen determinations in § 622 reads (m.O]=[p.C], each of the two follows from the other. Just on this account, however, the closing words of § 623, “ All the above-given determinations are correct for any sys- tem of units we may choose,” must be altered, and limited to electromagnetic systems, and, indeed, to such only as are derived from the meaning, as defined by Maxwell, of the fun- damental law of electromagnetism. For that coucluding sen- tence applies neither to the electrostatic system nor to the system set up by Clausius. Of the possibility that another conception of the electromagnetic fundamental law might here lead to other consequences Maxwell probably did not think ; and in this respect Clausius has indeed, in his most recent memoir, given a thankworthy enrichment of our ideas. Finally, we must speak of the reason why Prof. Clausius is Measures for Electric and Magnetic Quantities. 439 willing to drop the electrostatic system, constructed according to Gauss’s principles, hitherto employed. The only thing he says on this subject is contained in § 1 of hismemoir. After mentioning that the forces exerted upon each other by closed electric currents may be regarded as indubitably known, he continues:—* As, further, the small electric currents which according to Ampere are to be assumed as existing in the interior of a magnet are likewise closed, we have in magnetism to do with forces of the same kind.” Thereupon follows an analysis, according to which the forces of two magnetic quanta are to be regarded as dynamic. This reason, however, would be decisive only if it were cer- tainly proved that Ampere’s hypothesis corresponds to the reality, while up to the present it can hardly be said that it has been clearly and consistently worked out for all sorts of diamagnetic and ferromagnetic bodies. In particular, this hypothesis would also require that the hypothetic molecular eurrents of magnetized bodies should show the changes which are to be generated by electrodynamic induction, as they are in fact logically assumed to do by W. Weber in his well- known explanation of diamagnetic polarization. How this ean be reconciled with the properties of ferromagnetic bodies I leave the adherents of this theory to explain. Meanwhile, however interesting this theory may be, we may look upon it as neither verified nor even completely worked out. Among the electrodynamic theories which assume direct action at a distance, its quantity and direction depending on the absolute er relative motions of two electric quanta, stands that of Faraday and Maxwell. It has at least this superiority to those, that it does not violate either the principle of the finiteness and constancy of energy or that of the equality of action and reaction ; and moreover it bases a theory of light, free from many difficulties of the hitherto received undulation theory, upon the identical hypotheses which form the ground- work of electrodynamics. In order to discover the essential character of the forces of electricity and magnetism, Maxwell excludes those processes in which, according to the sort of friction, heat is generated and electric or magnetic energy lost, and founds his theory upon conservative processes only. In particular, he excludes the conduction of electricity in con- ductors, and the coercive force in magnets. Then, however, his fundamental equations present the most complete analogy, not between magnets and moved electricity, but between resting dielectric and resting magnetic polarization. It is precisely to this analogy that Gauss’s electrostatic system of measures perfectly accommodates itself. 440 Messrs. Trowbridge and Penrose on I will make one more remark, that when one seeks to form, after the analogy of Hamilton’s principle, that integral, taken with respect to the time, whose variation gives the equations of motion according to Maxwell in place of the electrodynamie potential of Clausius (Maxwell’s electrokinetic energy), a bilinear function of the components of the electric flow, on the one hand, and of the components of the magnetic momenta, on the other, arises in which the latter have to be dealt with, but not as velocities. This last point I reserve to myself to treat soon in another place. For the present I need only remind physicists that the ground on which Prof. Clausius is inclined to reject the hitherto accepted electrostatic system is a hypothetical assumption, contested between different theories ; and I would beg them not to transfer the name of the electrostatic system pro- ceeding from Gauss, and hitherto employed by preference in mathematical works, to another. In this system the potentials (m?/r) and (e?/r) are quantities of work; their entire physical importance rests upon the fact that they are such. The theory of the potential-functions forms one of the most complex and interesting chapters of mathematical physics, corresponding to well and perfectly known physical processes. If Gauss’s units be changed, then must we accustom ourselves to add factors to all potential-functions, in order that they may remain quan- tities of work and their differential quotients give the forces, On the contrary, whether J? is a force and mJ a work, or whether we must write for them A’J? and AmJ, appears to me much less important, especially as we know well and accurately just a portion of the department of electromagnetic actions, viz. that consisting of closed currents, but in the pro- vince of unclosed currents the most luxuriant flora of hypo- theses still flourishes. XLIX. The Thomson Effect. By Joux TROWBRIDGE and CHARLES BrncHAM PENROSE’. IR WILLIAM THOMSON? first discovered that when an electrical current passes through a piece of metal, the ends of which are of different temperatures, it carries heat with it; the direction depending upon the character of the metal and the direction of the current. This pheno- menon is known as the Thomson Effect. Le Rouxt subse- quently verified Thomson’s results, and gave an incomplete table of the effect in different metals. No especial pains have * From Silliman’s American Journal of Science for November 1882. + Phil. Trans. 1856, vol. iii. p. 661. t Ann. de Chim. et de Phys. 1867, [4] vol. x. p. 258. eS eee ee Le ee a eS ee ee ee es. the Thomson Effect. 441 been taken hitherto in experimenting with pure metals. We have thought it would be valuable to test the effect in as pure a metal as we could obtain by electrolysis. We have also extended Le Roux’s table by the addition of the effect in nickel, which Thomson was unable to obtain, and also in carbon. An endeavour has been made to ascertain if the effect is reversible, and also to discover if it is modified in a magnetic field. The strip of nickel, 45 centim. long, 2°6 wide, and 2 mil- lim. in thickness, was placed with its Hat surface horizontal. One face of a thermopile was placed at a fixed point on the surface of the nickel, separated from it by a thin piece of mica. A weight pressed upon the other surface. The thermopile was connected with a Thomson’s reflecting galvanometer of six ohms resistance. The two extremities of the strip of nickel were connected with a battery of six Grove cells, the wires first passing through a key so that the direction of the eurrent could be reversed. One end of the nickel was kept at the temperature of the air, 15° C.; the other at a constant red heat by means of a Bunsen burner. The metal was heated in this way from 9 a.m. to 3 P.m., until it reached a condition of thermal equilibrium, as shown by the galvanometer. The scale of the galvanometer was then moved until the spot of light came to 0. The current from the Grove cells was then passed for one minute alternately in opposite directions, and the deflections of the galvanometer were read every quarter of a minute. Before the direction of the current was changed, the circuit was each time broken, and the spot of light was allowed to fall to 0. The following table gives the results. The column marked “‘ C-H” gives the deflections when the current was passing from cold to hot. The small numbers show which deflections in each pair were taken first. C-H. H-C. Defiections taken every + minute. Deflections takez every ¢ minute. 1 Deeley e Tees | seo ae |ye ae wakes 2 4-1 42 | 40 | 43 | 44 SOP AON roiO ale oOubaceek 6:3 | 64 | 6:5 | 64.) 6-4 HOME G20 OA SO) 8 6:0 female tO =| 0-0) | 7:2 Hie Gils | OA Ge AO ee | FO. es | ee. Gt | 73 | 65 | 68 | 72 From this table it is obvious that more heat is evolved by a constant current per unit time in passing from the cold to the hot end of the nickel than in passing in the opposite direction. The Thomson Effect in pure nickel is consequently negative ; Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 2G 442 Messrs. Trowbridge and Penrose on i. e. heat is absorbed by a current in passing from hot to cold, and evolved in passing from cold to hot. The above results were confirmed by many similar experiments, as will be seen later. It was next determined to find whether the Thomson Effect was reversible—that is, whether the heat absorbed by a current in passing across a section of temperature ¢ was equal to the heat evolved by the same current when passing in the opposite direction across the same section. This subject has import- ant bearings on the thermodynamical theory of thermoelec- tricity. The following method was pursued:—Both ends of the nickel were at the temperature of the air, 15° C. The current from six Grove cells was passed as before, and the deflections of the galvanometer were observed every half-minute. The apparatus was arranged exactly as before. Column I. of the accompany- ing table gives the deflections. One end of the nickel was now placed in melting ice. After one hour it reached a con- dition of thermal equilibrium, and the current from the Grove cells was passed alternately in opposite directions. The deflec- tions are given in II. and III. If the deflections in IL. and IIL. are subtracted from the cor- responding deflections in I., we get the amount of deflection due to the Thomson Effect. It will be observed that all the deflections in II. are less than those in I., and those in ILI. are greater, as they obviously should be. The only inaccuracy in this determination is due to the fact that we neglected the alteration in electrical resistance of the nickel due to the slight change in temperature. aes TI 7 ae H-CO: C-H. . “ np | Deflections | Deflections Lat ) I.—III. ie atte M every every | 2 ‘ | $ minute. % minute. | / 1:8 18 2:0 0-0 —02 26 2°4 2°8 0-2 —02 29 2°65 3°15 0:25 —0:25 3-1 2°75 3-95 0-35 015 | The numbers in these tables are obviously too small to draw any conclusions. They, however, confirm the preceding results as to the direction of the Thomson Effect; and tend rather to prove than disprove the reversibility of the effect. The experi- ment was repeated several times, but with no better result. Experiments were also made to test the influence of mag- the Thomson Effect. 443 netism on the Thomson Effect. Nothing but negative results, however, were obtained. The strip of nickel was placed horizontally, with its flat sur- face perpendicular to the axis of a large electromagnet, the strip being between the two poles of the magnet. One surface of the nickel was pressed against one pole; on the other sur- face was placed one face of the thermopile, while the opposite face was in contact with the second pole of the magnet. Mica was used, as in the previous experiments, to protect the faces of the pile. The whole was wedged and pressed tightly toge- ther, and clamped by means of wire, the object being to pre- vent any motion of the nickel when the magnet was made. One end of the nickel was heated by a Bunsen burner ; the other was at the temperature of the air. Six hours were re- quired for the apparatus to reach a condition of thermal equi- librium. The electromagnet was connected with thirty-eight freshly set-up bichromate-of-potash cells, with plates of large size. A current from eight Grove cells was now passed along the nickel, with and without the circuit of the magnet being made. The deflections of the galvanometer were exactly the same in each case, showing that in a magnetic field (at least of the strength in the experiment) the Thomson Effect was unaltered. It is unfortunate that the strength of the field could not be accurately obtained, as the batteries had been running about thirty minutes by the time the experiment was completed. The field, however, was very much stronger (as shown by rough tests) than in another experiment, where the minimum value was found to be 184 times the vertical intensity of the earth’s magnetism. The determination of the relative value of the Thomson Hiffect in nickel by the following method gives of course but approximate results. The value, however, is probably as accu- rate as those given by Le Roux for other metals. A strip of copper, of about the same dimensions as the nickel used before, was arranged exactly as the nickel had been. The thermopile was insulated from the strip by the same piece of mica, and the same weights were placed on the upper surface. One end of the copper was heated in boiling water; and when the apparatus had reached a condition of equilibrium, the deflection of the galvanometer was 35 centim. A current from four amalgamated Grove cells was now passed alternately in opposite directions along the bar, the deflections of the spot being taken, in each case, after one minute. The results are given in the left-hand table :— 2G 2 444 Messrs. Trowbridge and Penrose on | Differences Differences C-H. H-O. | between | O-H. H-O. between Deflections Deflections | oh: Deflections | Deflections the same _|taken every | taken every| -condineg | taken every |taken every g ont minute. minute. | Preece hh minute. minute. def jes 120 2 | 130 4 1-0 145) | 138 2 12 1235 (epee le 0-8 Icsh 13.0 10 pp Ee 13°42 30 1:3 14:3 } 1g'4, 2 8) 12:0 2 12-8. 1 | 08 148 ? iss Ib Mean difference =0°97. Mean difference =1°15. The strip of nickel was now substituted for the copper,. every thing else remaining exactly the same. One end of the nickel was heated, and the thermopile was placed on such a spot that the galvanometer gave a deflection of 35 centim. The same current was passed as above. The results are given in the right-hand table. Let d= the mean difference in the first table, and d’= that in the second, d and d’ are then proportional to the elevation of temperature of the part of the bars under the pile on account of the Thomson Effect. Let o= coefficient of Thomson Effect; that is, o is such a quantity that od@ represents the heat absorbed per unit current per unit time in passing from section at temperature 9 to section at temperature 0+d6. The heat evolved in unit section when the temperature is increased by $d. K is }KdSD, where K is a constant depending on the galvanometer, 8 is the specific heat, and D the density of the metal. If we consider the Thomson Effect to be constant under the pile, and @ and @& to represent the temperature of the ends of the space covered by the pile, we have :— o(0—6/)=K SSD; and the similar expression for nickel, d! o'(0—8')=K FSD. eta aie ee » ou (hh) Kiquation (1.) then gives the relative value of the coefficient of the Thomson Effect at any temperature 0. S=-095, §’=:108, D=8-9, D/=8:3, d=0-97, d’=115 o’ = 1°25; .*., o/ =]2ome Co the Thomson Effect. 445 In Le Roux’s table c=2; .*. of =2°50: cand o’, however, are of opposite sign. Introducing nickel, Le Roux’s table becomes :— + = Sb 64 Fe 31 Cd 31 Bi 3l im LE Arg 25 Ag 6 Pits Cee 32 IN ey Al O01 Sn 0-1 The Thomson Effect in carbon was next investigated. The carbon used was the graphite of the common carpenter’s lead- pencil. The pencils which gave the best results were Faber’s. Attempts were first made to measure the direction of the Thomson Effect in the same way as in the case of nickel—that is, by placing a face of the thermopile on one surface of the carbon, the two ends of the carbon being maintained at con- stant temperatures, and passing the electric current alternately in opposite directions. This method was unsuccessful from the tact that one Grove cell heated the carbon to such a degree that in one minute the spot of light was thrown off the gal- vanometer-scale, thus rendering it impossible to measure, with any accuracy, the rate at which the deflection increased. The method of Le Roux was then tried, of using two strips of carbon, each face of the pile being in contact with one strip. This method not only doubles the deflection due to the Thom- son Effect, but also greatly diminishes the deflection due to the heat evolved on account of the electrical resistance of the car- bon. Ifthe two strips of carbon were exactly the same in all their physical properties, and the contacts with the faces of the thermopile were the same on each side, the latter deflec- tions would evidently be entirely eliminated. Two carpenter’s pencils were split longitudinally, the lead being left in one half of the wood. They were then tightly bound, parallel, against each face of the thermopile, and insu- lated from it by thin pieces of mica. Especial care was taken to fasten the carbons firmly, so as to prevent any motion from the passage of the current. The pencils were placed perpen- dicularly, the lower ends in two vessels of mercury, surrounded by melting ice; the upper ends were at the temperature of the air. The upper ends were electrically connected; and the ‘wires from a battery of three Grove cells were placed in the vessels of mercury. The thermopile was connected with a reflecting galvanometer of six ohms resistance. 446 Messrs. Trowbridge and Penrose on When the system had reached a condition of thermal equi- librium, the current from the battery was passed, and the observations were made. The vessels of mercury and the cor- responding pencils are denoted by “a” and “6.” The cur-— rent entered alternately in “a” and “ b,” the deflections of the galvanometer being taken, in each case, every half minute. The deflections showed that the pencil “a”’ was warmer than “b;” but the difference of temperatures was greater in one case than in the other. The following table represents the results of two sets of ex- periments. The smali numbers at top show which column of each pair was taken first. First experiment. | Second experiment. | Current Current | Difference, || Current | Current . Difference, enters enters | proportional enters | enters proportional at “a.” at “5,” to47H. || ata.” at “8.” | to47 EB. Pe (eR, 21-0 208 | 0-2 | 208 20-2 06 3845 324 21 | 347 32'8 19 2 1 | : 2 21:2 21°0 0-2 19-5 18-2 13 345 33°0 15 31:0 293 a r/ 370 342 28 2 ; ry 2 | 21-4 206 | 08 19'8 iso | 18 34:3 32°8 15 318 292 | 26 | 373 340 33 2 ut / ao ie 2 21-7 216 01 20:0 188 12 36:0 34:3 17 382°6 30°4 2-2 42-4 40-0 2-4 38°7 35°7 30 2 1 eis, 2 23-0 21-7 | 13 21:0 19'8 1:2 38'2 350 | 3:2 33'8 Sis: 2-5 45°5 41-2 / 43 39°8 36°3 35 aot 1 / 1 2 23-5 230 | O85 20:0 1990 | 190 39:0 370 —s| 2-0 o22. |) 129 San 2-4 45°8 43°8 2-0 av4 | 343 . ok From this table it appears that the Thomson Effect in ordi- nary a is negative ; that is, heat is apparently evolved when the current passes from cold to hot, or the negative cur- rent carries heat with it. The difference in the last columns are obviously proportional to four times the Thomson Effect, the Thomson Effect. 447 assuming that the effect is reversible. It also appears from the table that the effect increases as the temperature increases, which is in accordance with Tait’s assumption. These experiments were repeated with the graphite from other kinds of pencils; but in no case was the effect nearly as marked as in Faber’s. ven in the case of Faber’s pencils many trials were made before satisfactory results were obtained. Hquations representing the thermal condition of a bar when acting as a conductor of heat and electricity may be deduced as follows:—One end of the bar is supposed to be maintained at-a constant temperature, the other at that of the air ; and the electric current is supposed to be constant. For simplicity, we will assume that the specific electrical resistance of the bar is constant throughout, 7. e. is independent of slight differ- ences of temperature. The quantity of heat, H, evolved by the current in time 64, in the section of the bar Sdwz (8 being the area of a section), is represented by HES PRS8e of, 8 le ea x= distance of the section from heated end. If we assume that the thermal conductivity is unaltered by the slight rise in temperature due to the current, it can easily be seen that the flow of heat due to conduction is unaltered by the current. Hence we can consider that the heat evolved by the current is partly used in raising the temperature of the section Séz, and that all the rest escapes from the surface by radiation. The Thomson Hffect is at present purposely neglected. The bar is supposed to have reached a permanent condition as regards conduction before the current was passed. Let 0 be the temperature of the section of the bar we are considering before the current passes; let h= the exterior conductivity or velocity of cooling ; let p= the rise of temperature above @ when the current passes. Assuming Newton’s law of cooling, the heat radiated on account of the rise of tempe- rature p is proportional to ph; and the quantity radiated from the section in time 6¢ from the same cause is n= phidegoh cece ee oe CE) [= the periphery of the bar. In time 6¢ the increase of temperature p becomes p+ 6p; and the heat developed in the section by this increment is He=OSDSzt Sp. > 1) Ce) As we saw that the heat of the current was expended only 448 On the Thomson Effect. in the ways represented by (II.) and (III.), we have H = H, + EG . . . . . . (IV.) If we now consider the influence of the Thomson Effect, we simply add that a certain quantity of heat is absorbed or evolved by the current in the section Séz, distinct from that represented by [’R. If o = the coefficient of the Thomson Effect, the heat ab- sorbed or evolved due to this effect is, in time 64, H,=I080.5t..... |. Os ee The effect being proportional to the current, and o being de- fined as such a quantity that o6@ represents the heat absorbed or evolved in passing from a point at temperature @ to +60, per unit current per unit time, introducing this effectin (1V.), H — H, + H, -- H,, . . e . Py (V2) as the total value of the excess of heat (due to the current) in the section can be considered as made up of these quantities. Substituting the values in (VI.) from (I.), (II.), (IIL), (V.), and transposing, plhdx . bt= PRSéz . dt—CSD6z . 8p—1068 . dt; dp 56 St —Ic 52’ . phl=PRS—CSD or, at the limit, apis ad : d 2 = capl! RS—phl—Io]. . (VIL) This equation gives the rate at which the temperature rises when the current passes, and will approximately apply to the preceding experiments. When the temperature of the bar becomes permanent, apy: di? and (VII.) becomes Te ede PRS phl=lo— =(); . p= | PRS ie2”] 1 p= [1 RS Io | > so giving the excess of temperature due to the current in the per- manent condition of the bar. The values in (VIII.) are all easily determined except o and h, The differential coefficient a (the rate of change of On the Reflection of Electrical Rays. 449 temperature due to conduction along the bar) can readily be found by experiment; or deduced by analysis, as in the case of an infinite square bar, where 6=aG-” and = —ak@G—™. As p may easily be determined by experiment, the equation can be used to determine o, as PRS—pAhl p= SS SS (IX.) If Tait’s assumption that o = MT (where M is some con- stant and T the absolute temperature) is true, we might obtain two values of o for two points of the bar, the temperature of which was known, eliminate 4 from the two equations, and thus obtain a value for M. If we performed the same opera- tion for two other points, we should get another value for M, and could verify Tait’s assumption if this value was equal to the preceding. The sources of error in the preceding investigation are due to assuming Newton’s law of cooling, to neglecting the change of electrical resistance due to a change of temperature, and to partly neglecting the change of thermal conductivity due to the same cause. L. On the Reflection of Electrical Rays. By Dr. HE. GOLDSTEIN *. [Plate VII. figs. 1-8.] [ has been usually assumed f that the (rectilinear) electrical rays radiating from the kathode of the discharge of an induction-coil terminate where they impinge upon a solid wall, and that beyond the point in which they cut the wall they cannot propagate themselves in any direction{t. The experi- * Monatsber. der Konigl. Akademie der Wissenschaften zu Berlin. Trans- lated from a separate impression communicated by the Author. + Hittorf, Poge. Ann. cxxxyl. { Herr J. Puluj (Ween. Ber. 1880, [2] p. 886) is the only physicist who has assumed a limited power of reflection of the kathode-rays, under the assumption that the kathode-light consists of scattered particles of the electrode, since “it is not intelligible why these should in general suffer no reflection at the wall.” The conditions of an experiment made by Herr Puluj to examine whether reflection takes place were not, in my opinion, such that any possible reflection would have been recognizable. That which Herr Puluj considers phosphorescence produced by reflected rays is partly phosphorescence produced by the positive light of the so- 450 Dr. E. Goldstein on the ments which have led me to reject this assumption were sug- gested by an observation made by Prof. E. Wiedemann*. Prof. Wiedemann, in using a tube of the form of fig. 1 (Plate VII.), where the disk & at right angles to the axis of the vessel C forms the kathode, not only observed green phos- phorescence such as produced by the kathode-rays on the _ sides of the tube up to the point x which could be reached by straight lines from /, but saw also a feeble illumination of the tube 7 beyond the bend, and a brighter phosphorescent sur- face F on the wall C opposite the mouth of the tube 7. The motions of the small surface F under the influence of the magnet showed that it was produced directly by electrical rays, and not simply by optical rays possibly reflected at the glass. Prof. Wiedemann is disposed to explain the appearance as one of the phenomena of deflection discovered by mef, assu- ming that the glass wall at « becomes charged and acts as a weak kathode, causing the deviation of the pencil of rays passing by it out of the direction at right angles to the plane of k, into the direction «F. ~ This explanation seemed improbable to me for two reasons:— (1) Because the surface F is always much more feebly illuminated than would have been the case if the phospho- rescence had been exerted by the direct kathode-rays pene- trating to C. In order to make the comparison, the kathode- rays may be so curved by the influence of a weak magnet as to pass the bend w. The comparison may be more certainly made without the use of a magnet in a vessel of the form shown in fig. 2, where two paths are offered to the kathode- rays—on the one side the path as in fig. 1 through the bent tube 77,, and on the other side the path through the equally long straight tube 7, at right angles to k. (2) Because the surface F totally disappears if the tube rr, has a second bend in it, in whatever direction this second bend is made. This would not happen with the phenomena of deflection, which I have examined, where a ray may be bent any number of times. If now the rays which produce the surface F are not direct rays from the kathode /, then we may suppose either (a) that the portions of the tube about x, upon which the rays from the called reflex currents in the system of tubes, partly phosphorescence pro- duced by direct kathode-rays, which Herr Puluj unintentionally produced by touching the glass with the finger in order to concentrate the light. * E. Wiedemann, Wied. Ann. xi. p. 236; Phil. Mag. [5] x. + Goldstein, Monatsber. d. Konigl. Akad. der Wiss. 1876, p. 285; Phil. Mag. [5] iv. Also ‘A new Form of Electrical Repulsion’ (Berlin, 1880). of Pe — : % Reflection of Electrical Rays. 451 kathode impinge directly, become charged with negative elec- tricity, which reaches such a tension that they themselves form a second kathode and radiate electric rays, which then produce F'; or (6) that the rays which produce F are rays from the kathode £, which suffer reflection when they fall upon the solid wall. In this reflection, either the power of producing phosphorescence of the rays becomes weakened or their density, thus explaining the small intensity of light emitted by F. The hypothesis (a) may be excluded, as shown further on ; for the phenomenon in question is not altered if the surface upon which the kathode-rays impinge directly be metallic, and if this metal surface be made the anode of the discharge. If in accordance with this assumption we suppose that reflection takes place, then again reflection according to the optical law is at once to be excluded, since the position and form of the surface F remain unchanged even when the angle of the bend at « varies from 25° to 80°. Consequently the law of the equality of the angles of incidence and reflection, or the rule that when the reflecting surface is rotated while the inci- dent ray preserves the same direction, the reflected ray rotates through twice the angle, is not obeyed. We may, however, easily make numerous experiments which agree in showing the presence of diffused reflection, in consequence of which each point of the wall on which the rays impinge directly diffuses rays in all directions. If diffuse reflection is proved, we have at once the explana- tion of the small luminosity of F in comparison with portions of the tube reached by the direct rays in the diminution in density of the incident pencil of rays. In the next place, if we employ a vessel such as fig. 3, we obtain phenomena corresponding to the surface F in the cylin- ders C, and C, at the same time. The rays which travel as far as x nearly parallel to each other, therefore, after reflection, follow at least two directions at right angles to each other. The following experiment forms an experimentum crucis:— A chamber B was introduced between the portion of the tube containing the kathode and the bend at 2, which contained a paper diaphragm which could be turned round the axis a, and which had a slit cut in it about 1 millim. broad and parallel toa. Ifthe plane of the diaphragm falls along the axis rr, its edge intercepts no perceptible portion of the pencil of rays _which reaches the tube 7 from the kathode, and which is about 7 millim. across. But if, on the other hand, D is at right angles to the axis of r, then only the portion of this pencil which passes through the narrow slit can reach the bend « 452 Dr. E. Goldstein on the If the reflection were similar to that of a mirror, the form and magnitude of the surface F would change perceptibly. This surface, in all the experiments so far described, and in this one also, resembles an ellipse of small excentricity, where D has the position first mentioned. Its smaller axis, which falls in ~ the plane of 7 7, is about twice as large as the diameter of 7, in the vessel C, which is about 3 centim. in diameter. If now we mark the position, form, and magnitude of F on the out- side of the tube C when the diaphragm presents its edge only to the kathode-rays, and then place the diaphragm at right angles to the rays, we find that the position, form, and magni- tude of F remain unchanged; only its luminosity is now consi- derably diminished. If, instead of the diaphragm with a slit, a plate without openings is introduced into the chamber B capable of free motion, so as to cut off at pleasure either the upper or lower half (and also the right-hand or the left-hand half of the kathode-pencil) by covering the corresponding portion of the mouth of 7, then also the position, form, and magnitude of the surface F remain unchanged; the luminosity only of the whole surface decreases, but most in the half which is opposite to the half that has been intercepted. Thus, for example, the surface is darkest in the upper half when it is the lower half of the kathode-pencil which is intercepted. We easily see how these observations, inconsistent with optical reflection, entirely agree with the assumption of a dif- fuse reflection of the kathode-rays. Tubes of the form of fig. 5 are better adapted for the further study of this diffuse reflection than the vessels employed by Wiedemann. The rays emitted by the kathode & which pass through the connecting tube r into the wider cylinder Z fall then upon the plate P, which is fastened to a wire d insulated with glass inside Z. The cylinder is closed air-tight by the caoutchouc stopper £, by removing which the plate P can be exchanged for another; or other changes in the apparatus can be made. If the plate P consists of phosphorescent glass, then the rays which fall upon it directly produce at the plate s simply an oval very bright green phosphorescent surface. We see, however, distinctly how the diffuse reflection from this surface causes the whole wall of the tube Z lying above the plane of P up to the stopper & to phosphoresce with subdued green light, which is weaker the further the portion of the wall is removed from s. If the plate P be covered with chalk, its surface at s shines with orange-red light, but the wall of Z presents a green Reflection of Electrical Rays. 453 luminosity as before—a proof that this luminosity does not depend upon optical reflection. So also the phosphorescence produced by diffuse reflection remains unaffected if P be con- structed of some material which does not phosphoresce at all. Ii is further a matter of indifference whether P is metallic or consists of an insulator. In the former case P may even be made the anode of the discharge, without the reflection of the rays appearing in any way weakened. The kathode-rays are therefore not absorbed by the anode, even when they play directly upon the surface of the anode. Further we see, as already mentioned above, that the pheno- menon in question cannot be explained by supposing that the surface struck by the direct kathode-rays is itself converted into a kathode. If we bring small objects between the plate P and the phos- phorescent surface of Z, such, for example, as the wire D (fig. 6), whose distance from P can be varied by rotation round the axis D, we can very well recognize the character of the diffuse reflection which the place s causes in the rays which fall directly upon it. For the shadow of the wire D only appears narrow and sharp when the wire is brought close to the wall of the vessel; if D is moved from the wall towards P, its shadow soon becomes bread and indistinct. If we cut off a further portion of the kathode-rays, by means of a small movable plate of mica introduced into Z at the mouth of 7, the space s, directly impinged upon by the rays, of course becomes smaller. ‘The further this decrease proceeds the nar- rower and sharper does the shadow of D become, exactly as we should expect on the theory of diffuse-reflection. I will here cite only one other consequence of this theory which has been experimentally verified. I may take it as known that a pencil of rays emitted by a plane kathode after it has passed, as in fig. 7, through the aperture (supposed cir- cular) of a diaphragm occupying the whole area of the tube, gives on the flat wall W a well-defined circular luminous figure on a dark ground. Upen our assumption of the diffusion of the kathode-rays, this ought not to happen any more if the rays are made to pass through a cylindrical tube open at both ends (fig. 8), in place of the thin diaphragm. For since the different rays of a plane kathode are not altogether parallel to each other, but also diverge somewhat around “the central portion of the kathode, a part of them must play upon the wall of the tube r, and be then diffusely reflected. The portion of the diffuse rays which reach C must then form an extended luminous space round the bright surface resulting from the direct rays. We find 454 On the Reflection of Electrical Rays. this confirmed by experiment ; and if we bring into C a wire § throwing a shadow, we find that its shadow is sharp and nar- row in the region illuminated by the direct rays, but broader and ill defined in the surrounding region. This takes place also when 6 is made the anode. We see from this that the difference in breadth of shadow does not depend upon a stronger deflection which-6, apparently neutral but really act- ing as a weak kathode, causes in the reflected rays*. These last are indeed themselves capable of deflection, as we see if, instead of making 6 an anode, we connect it with the earth, or give to it a small portion of the current from the kathode. The motions of the shadow of 6 under the influence of a magnet, and with other arrangements the motions of the sur- face F under similar influence, show that the reflected rays are deflected, as far as one can observe, in the same way as the direct kathode-rays would be if their course were the same as that of the reflected rays. If r be placed equatorially above a horseshoe magnet of suitable strength, the direct kathode-rays before reaching C are compressed against the upper or under wall of rv, and the phosphorescent surface (@) produced by the direct rays disap- pears ; but the feebly illuminated region remains, occupying now the position of the surface @: this corresponds exactly to Wiedemann’s surface F; its production here is due to the dif- fuse rays which issue from the portions of the straight tube r struck by the magnetized rays. The further the terminal point of the direct rays is forced towards C by the action of the mag- net, the less luminous does the surface F become, since then a continually smaller portion of r is able to reflect rays. On the whole, the foregoing series of experiments leads to the following result, which I propose to describe more fully in a further communication:—A pencil of kathode-rays does not end (at any rate under the conditions suitable for producing phosphorescence) where it strikes upon a solid wall, but elee- tric rays radiate in all directions through the space oceupied by the gas from each point of the wall struck by the direct rays. These rays may be called reflected rays. Any solid wall, no matter what its properties are, may serve as reflecting surface. It is a matter of indifference whether it is capable of becoming phosphorescent or not, whether it consists of a conductor or of an insulator. The reflection is diffuse, equally whether the reflecting surface is dead or as smoothly polished as possible. An anode apparently reflects the kathode-rays, the same as a neutral conducting surface or an insulator. The reflected rays, like the direct kathode-rays, have the property _ * ‘A new Form of Electrical Repulsion,’ p. 124. Influence of the Shape of the Kathode in Geissler’s Tubes. 455 | of exciting phosphorescence at their ends. They are capable of being deflected ; and their ends are bent aside by a magnet in the same direction as the ends of the kathode-rays would be which radiated from the reflecting surface to the points reached by the reflected rays. LI. On the Influence of the Shape of the Kathode on the Dis- tribution of the Phosphorescent Light in Geissler’s Tubes. By Dr. Ei. GoupstEIn*. [Plate VII. figs. 9-35. ] YLINDRICAL wires cut off at right angles have been almost exclusively employed as kathodes in systematic investigations on the discharge of the induction-coil in rarefied gases, or, in particular cases, spherical electrodes or plane circular disks. Kathode-surfaces, which can be divided into two halves of similar shape by an infinite number of cuts, do not give rise to a class of phenomena which I have observed with kathodes of regular surface, in which nevertheless there is no axis of symmetry corresponding to an infinite number of equivalent sections. We are concerned with extremely regular figures, in which the phosphorescent light of the walls illuminated by the raystrom those kathodes arranges itself, which, however, are for the most part altogether unlike the shape of the kathode itself. Reserving a detailed description, | may here give the general characters of the most important types of these figures +. Kathodes of concave spherical form were first examined, constructed of thin soft iron, which was first of all stamped and then ground into the desired form. The kathodes were soldered at the middle points of their convex sides to wires which conveyed the current, and which were insulated by being covered with glass thermometer-tubing between their junction to the kathode and the point at which they entered the vessel. The discharge-tubes were glass bulbs of 4 to 5 centim. radius; the axis of the spherical concave mirror which formed the kathode was placed in a diameter of the bulb. The dis- tance of the kathode from the wall, measured along this dia- meter from the centre of the mirror, could be varied ; in the * Monatsber. der Konigl. Akademie der Wissenschaften zw Berlin, July 1881 Translated from a separate impression communicated by the Author. t A preliminary notice appeared in the Wien. Akad. Anzeiger of the 13th Jan. 1882. The phenomenon of figures in phosphorescent light dis- similar from the kathode was described “by me for the case of a kathode of cylindrical curvature so long ago as 1876 ( Wien. Sttzungsber. xxiv. [2] p. 465). 456 Dr. E. Goldstein on the Influence of the experiments next to be mentioned it was made equal to twice the radius of curvature of the spherical kathode. If we now assume, as for example Crookes does in his well- known memoirs, that from each point of a concave kathode only one rectilinear ray radiates, and that along the normal to the surface, it would follow that the phosphorescent image of a concave kathode on a concave spherical wall, at a distance of twice the radius of curvature of the kathode, would be iden- tical in form and dimensions with the kathode itself, if the radius of the vessel were equal to that of the kathode; it would be coincident in form and nearly in dimensions with the ka- thode itself if, as in my experiments, the radius of the vessel were greater than that of the kathode, without the kathode having any considerable aperture. There will be no essential change in the character of the phenomena to be expected, if we also take into account the feebler phosphorescence caused by the rays* emitted by the elements of the kathode on its edge in variously oblique directions up to the tangential di- rection. But experiments show very different phenomena. 1. Fig. 9a represents a square of the actual size, ground into a spherical surface of 40 millim. diameter; and fig. 9b repre- sents the phosphorescent image, also of the actual size, formed by this kathode in a highly exhausted glass vessel of 8 centim. diameter ; we remarka star of light with four rays, the axes of the rays being at right angles to the sides of the square ka- thode. In the figure representing the luminous star, the edge of the kathode is marked by black dots in order to indicate the relative positions of kathode and image. At extreme exhaus- tions there appear, less distinctly marked, four much shorter rays coming from the centre of the image and corresponding to the directions of the diagonals of the kathodef. An equilateral triangle having the same curvature (fig. 10) produced a star with three rays, whose axes were at right angles to the sides of the triangle. So also polygons of 5, 6, 7, and 8 sides gave stars, with a corresponding number of rays, whose axes appeared to bisect the sides of the polygon at right angles. The position of these figures with reference to the kathode * Eine neue Form electrischer Abstossung, i. p. 11. t In the accompanying figures of portions of the surface of a sphere, the ares of great circles between the centre of the light-figure and the separate points forming the bounding surface of the figures are approxi- mately represented by the chords of these arcs, or in the smaller figures by the corresponding aliquot parts of these chords. This corresponds with the method of measurement employed, in which distances on the spherical surface were determined by the direct distance between the points of a pair of compasses applied to the surface. Shape of the Kathode in Geissler’s Tubes. 457 is worthy of remark, as throwing light upon their mode of production. If we cover up the upper portion of a polygonal kathode by a screen placed between the kathode and the centre of curvature, then the wpper arms of the star are want- ing in theimage. The arms are therefore not produced, as we might have expected, by the radiation from the portions of the kathode diametrically opposite. A four-armed cross, fig. 11 a (actual size), forming a portion of a sphere of 40 millim. diameter, gives fig. 11 on the wail of a vessel 8 centim. in diameter, in which again the position of the kathode is marked by dots. The metallic arms of the kathode thus correspond to the dark arms of the cross in the phosphorescent figure, and the light is concentrated in fields corresponding to the intermediate spaces in the kathode. If, again, the kathode has three arms, with angles of 120° between the arms, we obtain a figure with three dark arms. These again fall upon the metallic arms, and the bright fields upon the intermediate spaces between the metal arms *. The dark arms of the image, however, are much narrower with the four-rayed figure than with the three-rayed one, if the arms of the kathode are of equal width and equal length in the two cases. We obtain analogous figures when the kathode has five or six (uniformly distributed) arms, except that as the number of arms increases the dark fields which correspond to the metallic arms become narrower, not only absolutely but also relatively ee is, in proportion to the width of the bright intermediate fields. These two typical forms—the polygon, and the star consisting of rectangles—may suffice as a preliminary indication of the forms of the images which appear when the exhaustion is sufficient. 2. The images formed by kathodes of this sort alter very much when the density of the gas is altered. The image-forms described above are obtained with den- sities of gas about 7), millim. mercury. We can, however, trace the phosphorescence at pressures only slightly less than 1 millim., or even over this pressure, by including in the dis- charge at the same time sparks in free air. We obtain then, for example, for the four-armed cross-shaped kathode, fig. 11 a (radius of curvature 20 millim.), the images 12a to 12e in * I have made repeated attempts to obtain a result described in Carl’s Repert. 1880, p. 244, where a sort of three-rayed star gave simply an erect image of the kathode, but never with success. Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 2H ail 458 Dr. E. Goldstein on the Influence of the i succession, to which succeeds the image represented in fig. 114 when the exhaustion becomes sufficient. We obtain then at first an image of the kathode itself—a cross having nearly the dimensions of the cylindrical projec- tion of the kathode upon the wall. The arms of the cross in the image grow smaller and become the central lines of a well-defined square, that appears as a luminous background round the cross. As the density decreases, the square be- comes smaller and its luminosity increases. Its sides lengthen beyond the angular points, and form points resting on the sides of the square. The central cross disappears ; only the intersection of its arms remains as the bright centre point of the whole figure. The square now becomes smaller; and the points superposed on the sides become narrower in the same proportion. This takes place in consequence of the concave sides of the contour- lines approaching each other, and passing over each other, 12d and 12¢, As this displacement continues in the same direction while the density of gas decreases, the pair of ares which previously intersected finally pass apart, and leave a dark space between their convex sides: thus finally, at great exhaustion, the dark cross already figured in fig. 115 results, The series of changes thus described is typical also for the successive images given by crosses or stars with other numbers of arms. We obtain in each case at first an image closely resembling the kathode, and of nearly the same dimensions. Observation with three- and four-rayed stars (fig. 13 and fig. 14), shows— what was not evident with the four-rayed star, nor generally — with regular figures with an even number of arms—that these figures are reversed images of the kathode, formed by the rays from the kathode crossing each other. Next, the background round these figures becomes brighter, bounded by as many sides as the kathode-star has rays. The rays of the star- figure form the smaller radii of the polygon so formed. As the exhaustion of the gas continues, this polygonal figure decreases, its surface becoming brighter; and the inserted star disappears, its bright centre point remaining visible the longest. On each side of the polygon appears a point similar to those in fig. 12d. The concave sides of the bounding arcs approach each other more the further the exhaustion proceeds ; and at last, as the result of displacements exactly similar to those of figs. 12 and 12g, there appear dark rays between bright fields, which again correspond to the metallic arms of the kathode. Shape of the Kathode in Geissler’s Tubes. 459 The type of successive changes in decreasing density of gas with polygonal kathodes may be illustrated by the series of images given by a concave spherical square (fig. 15). Figs. cand d, for the sake of greater distinctness, are represented ona scale somewhat larger. If the kathode-polygon possesses an odd number of sides, then the luminous polygonal images corresponding to figures 15 b-d are reversed with reference to the polygonal kathodes, corresponding with the observation made with star-shaped kathodes with an odd number of rays. It is these luminous figures so far described and figured which first strike the observer, in the phosphorescent images of the corresponding kathodes ; upon closer observation we see that the other surfaces of the glass vessel are also not devoid of luminosity, but show phosphorescent surfaces of feeble luminosity at different points. The boundaries of these sur- faces, in the case of star-shaped kathodes, are prolongations of the luminous curves which bound the chief figures; with polygonal kathodes they are extensions of the star-rays observed in the luminous figure. Partly because, from what has been said, a sufficient preliminary account of the way in which these less-luminous portions complete the figures already figured and described is now possible to the reader, and partly to economize space, I abstain from further description of these outlying portions until the separate observations have been completely described. The image obtained in a spherical vessel of about 9 centim. diameter, employing as kathode the cross figured in fig. 11 a, may serve as a good example : it is represented in figs. 16 a and 16¢, in the pointed phase and in the dark-cross phase. 3. Besides the forms obtained by simple variation of the number of sides and arms of polygons and stars composed of rectangles, I have further examined the images given by numerous other forms of kathode—some simpler, some more complex—in order to separate as far as possible that which is general from that which is special. Thus, for example, of simpler forms were examined :—rectangle, rhombus, rhomboid, isosceles right-angled triangle, &c. of compound forms; crosses composed of obliquely compounded rectangles, and crosses formed of isosceles triangles (the latter either with the vertices or with the bases outwards); further, figures such as are obtained by cutting out of squares segments of circles or smaller squares at the four sides. So far as the effect of the form of the kathode, and of the variation in density of gas, manifests itself with these images, I must defer a description of the phenomena observed until I give a more complete explanation of the whole. The 2H 2 460 Dr. E. Goldstein on the Influence of the following general rules (4—7), however, hold good for all the kathode-forms mentioned. 4, At constant density of gas, the forms of the phospho- rescent images (not only their absolute dimensions) alter when the distance of the kathode from the wall of the vessel is made to change; as the distance of the wall decreases, the same figures appear, in the same order, as when the distance of the wall remains constant and the density of gas decreases. Instead of altering the distance of the wall by displacing the kathode, we may, as in the vessel represented in fig. 17, displace the wall which receives the rays with reference to the kathode. If we experiment with varying distance of wall, and also with varying density of gas at the same time, then, in order to pass from one given figure to another of the same series, the wall must be displaced through a greater distance the smaller the density of gas is. This shows that all the figures which a kathode can call forth upon a fixed wall as the density of gas decreases, do at any fixed density of gas already exist in space one behind the other at the same time, and that the different figures are produced by the rays intersecting each other in various ways at different points of space. As the density of gas decreases, the images move further apart and further away from the kathode, no doubt because the rays which first converge become less convergent, and then, when after intersection they diverge, their divergence is decreased. The influence of the distance of wall thus described would lead us to expect that the series of images given in figs. 12 and 15 as examples obtained with a kathode at a distance equal to twice the radius of curvature, would not include all the forms which the particular kathode is capable of producing, but that a diminution of the distance of the wall at the highest obtain- able exhaustion would in general give other figures besides these. This conclusion is found to be confirmed by ex- perience, although the forms thus obtained are not for the most part so striking as those previously described. It may, however, be mentioned at this stage as worthy of consideration further on, that upon diminishing the distance of the wall the dark arms of ihe cross in fig. 1le increase considerably in width. 5. If we take similar plane figures, and then bend them into portions of spheres of different radii, p;, ps2, p3, and place them as kathodes in similar vessels with equal distance of wall, then at equal density their images represent different phases ot the series of figures obtained from a single such ce tethake se tp en Shape of the Kathode in Geissler’s Tubes. 461 kathode with varying distance of wall: and the figure pro- duced by a particular kathode & corresponds to a greater dis- tance of wall from the kathode used to compare with, the greater the curvature of the kathode & is. This result might indeed have been regarded as & priori probable. We might indeed expect to obtain simultaneously like figures from different kathodes (similar in their original plane condition) by making the distance of the wall equal to Np, NPi, NPs, &e. for different radii of curvature p, pj, ps2, Ke. —that is, the distance of the wall in each case the same mul- tiple or submultiple of the radius of curvature—as, for example, by placing each kathode at a distance from the wall equal to twice its radius of curvature. But experiment shows also that in this case the phases are different; and the increased curvature acts in the same way as, ceteris paribus, the increase of the distance of the wall or an increase of the density of gas. This influence goes so far that, with kathodes which are much curved, it has not been found possible by exhausting the gas to produce those forms of the series of figures which, with electrodes of less curvature, correspond to the lowest degrees of the scale of density. Thus, for example, with the four-armed cross fig. lla, of a radius of curvature of 124 millim. instead of 20 millim., and with a distance of wall 2p, we find it impossible by exhausting to reach the phase of the dark cross fig. 116. The figure obtained immediately before the cessation of the current at the greatest exhaustion is the figure with curved points, fig. 12¢. 6. If we leave the general form of the kathode and its cur- vature unaltered, but increase the aperture of the kathode, this increase acts also as an increase of the distance of the wall would do. If, for example, we replace a square of 12 millim. in the side which has been bent to form a spherical surface or 40 mil- lim. diameter by a square of similar curvature, but with sides 30 millim. long, then at the extreme exhaustion we do not advance further than fig. 15d, whilst the small square gives us figures up to 15g. We obtain similar results with the more complicated forms of kathodes—for example, the four-armed cross made up of rectangles, fig. lla. If the length of the cross be increased from 20 to 25 millim. without altering the width of the arms, then at the greatest exhaustion at which the current will pass, the dark cross is just visible ; but it cannot be obtained with arms of any considerable breadth. If the cross is increased to 40 millim. the dark cross is no 462 Dr. E. Goldstein on the Influence of the longer to be obtained, and fig. 12¢ is the last obtained at extreme exhaustion. The results are qualitatively identical if we increase the breadth of the arms in the same proportion*. 7. The experiments mentioned in No. 5 show thatthe phase alters when plane kathodes of similar shape are bent into spherical surfaces of different curvature. Since the same figure, formed to different spheres, will form a mirror of greater aperture the smaller the radius of the sphere is, the result described in No. 5 as to the influence of increased curvature might possibly seem to be only another state- ment of the influence mentioned in No. 6 of increased aper- ture. In that case we should expect that kathodes of like form and different curvature but like aperture, at distances forming the same multiples of their radii of curvature, would give like figures at like densities of gas. To test this I constructed a series of kathodes (e. g. three four-armed crosses, I., IJ., I1I.), whose dimensions were as follows:— Radius of fone Breadth curvature (p). ane of arms. millim. millim. millim. | Pp 121 124 1 Dy, wisnes adits 20 20 + Tide ete 263 263 54 The kathodes thus all covered equal aliquot parts of the spheres from which they were formed. They were placed at a distance 2p from the spherical wall of the similar containing vessels—that is, 25 millim., 40 millim., and 534 millim. re- spectively. Here also the result was obtained that there is no identity of phase for equal density, but the figures given by kathodes IJ. and III. corresponded to the figures which kathode I. would have given if the distance of the wall had been increased. This occurred indifferently, whether the two electrodes of each of the three discharge-vessels were separately connected with the poles of the induction-coil, or whether, in order to secure equal intensity of discharge, the current was sent at the same time through the three vessels, connected together in line. * The changes in curvature and aperture of kathode described in the two preceding paragraphs cannot, in one respect, be always compensated by changes in density of gas or in distance of wall: the last term of the series of figures (corresponding to fig. 15g) for a polygonal kathode shows with kathodes of greater curvature or larger aperture richer differentia- ae ad finer detail. The rougher figure cannot be reproduced with these athodes. . 4 Pas Shape of the Kathode in Geissler’s Tubes. A63 8. The phosphorescent figures which appear when spherical electrodes are employed, as might have been expected, become replaced by others when the originally plane kathodes are formed, not into spherical surfaces, but into cylindrical or conical surfaces. I will content myself in this cursory report with mentioning that, with cylindrical kathodes, the phospho- rescent images are different according to the position which the axis of the cylinder has with reference to the axis of sym- metry of the kathodes. Thus, for example, with a square kathode formed to a cylindrical surface we obtain different figures according as the axis of the cylinder is parallel to a side of the square or to one of its diagonals. In the same way there are marked differences in the images of cross-figures according as the axis of the cylinder is parallel to one of the arms of the cross, or bisects the angle between the arms. 9. With reference to the explanation of the phenomena so far described, it is only wise to maintain a certain reserve towards a class of phenomena as yet very imperfectly known. A doubt as to the success of the attempt to bring a large portion of these phenomena into any simple relationship with known causes, could only be supported by the observations described in No. 10, on the images given by plane kathodes. All that I hope to do is to give some indications, derived from experiment, on the direction in which the explanation of many of the phenomena observed with star-shaped kathodes is to be sought. As to the explanation of most of the phenomena given by the above-mentioned polygonal kathodes, I do not here venture upon any hypothesis. ‘The star-shaped kathodes are of course also polygons with reentrant angles; and their separation from the polygonal surfaces appears unnatural at first sight. Nevertheless the phenomena which we have to ex- plain with star-shaped kathodes are for the most part just those which are closely connected with the presence of reentrant angles, and which may be approximately explained by taking into account only the edges of the kathode. The phenomena due to the surfaces themselves, in those forms of kathode where the surface of the kathode is relatively unimportant as compared with the extent of its bounding edge, are insig- nificant in comparison with the phenomena due to the curves of its circumference ; and the former remain unexplained here just as with the polygons with convex angles, where the phe- nomena of the surface constitute the chief part of the pheno- mena observed. Only the surface-phenomena produced at small exhaustions can be approximately accounted for with both kinds of polygons That the images of a star-shaped kathode which appear at relatively small exhaustions result 464 Dr. E. Goldstein on the Influence of the from the intersection of the rays emitted by one half of the cross with those from the other half, was shown to be probable by the experiments already described with stars of an uneven number of arms. This may, however, be better shown b experiments with screens arranged to throw shadows, whic also prove the same thing for kathodes with an even number of arms. ; If we arrange (fig. 18 a) ascreen of paper or of mica in front ‘of the kathode, and at a distance from its centre less than the radius of curvature, so that, for example, the lower half of the kathode-cross is covered, then in the phosphorescent image it is the upper half of the cross which is wanting (fig. 18 D). . Since at a certain density these images formed on the wall at the distance 2p from the kathode possess nearly the same dimensions as the kathode itself, it follows that the rays which produce the images, at least for the most part, are under these circumstances at right angles to the surface from which they are emitted, assuming, of course, that their course till they strike upon the walls of the tube is rectilinear. (Exactly similar experiments show that the images of ordi- | nary polygonal kathodes observed at small pressures are formed by the intersection of the rays which issue from points situated symmetrically with reference to the centre of the kathode. ) As with the figure of the kathode-cross, so also in the con- tour of the square (fig. 12 6) which appears surrounding the figure of the cross as the density decreases, each side is formed by rays which come from the opposite side of the kathode. We may obtain a more satisfactory explanation of the figures of kathode-crosses which appear at small densities; we only need to place a screen P(fig. 19 a) between two of the arms of a cross, so that it projects beyond the kathode on the con- cave side. The screen may be rectangular, and the edge which faces towards the image may be called its front edge. I anticipated, and the anticipation was verified by experiment, that the figures which correspond to the higher degrees of exhaustion are formed by the rays emitted by one arm of the kathode suffering a repulsion by the neighbouring arm, of the same or a similar kind to that described in my work on ka- thodic deflection, This deflection cannot take place through a solid plate. If now, at high exhaustion, we obtain repeatedly the figure with the dark cross so often mentioned, then, when the plate is introduced, we obtain the figure 194; or, if the plate does not project so far beyond the kathode, we obtain 19 ¢, We have therefore, in the first case, only the left bounding Shape of the Kathode in Geissler’s Tubes _ 465 are of the upper arm of the cross, and only the lower bound- ing arc of the right-hand arm: the two dark arms themselves cannot be perceived; but the space between the bounding arcs mentioned is uniformly illuminated. The two bounding ares, which are now absent, result there- fore from an action between the upper and right-hand arms, prevented or hindered by the presence of the screen. If the plate is withdrawn a little, then, as already men- tioned, the figure 19 ¢ is seen. The dark arms which were wanting in the first image are here seen as very narrow strips, and the corresponding two bound- ary curves are of feeble luminosity. The more the screen is withdrawn towards the kathode the broader do the two dark arms become, and the more closely does the luminosity of the two ‘curves approach to the normal luminosity. The mutual action between each two neighbouring arms, to which the production of the dark cross is due, may be supposed to take place in three different ways :—either (1) as an immediate action of each of the arms of the kathode upon the other, which thus in- directly produces an effect upon the course of the electric rays; or (2) as an action of each arm upon the system of electric rays emitted by the other; or (3) as a mutual action of the two systems of rays. Any further discussion of the utility of the three hypotheses at present would lead us too far away. I will content myself with remarking that the assumption (1), so far asI see, is opposed to the details of the phenomena of kathodic deflection; but it is not possible to decide certainly between (2) and (8). Taking account, however, of the fact that the third assump- tion involves certain accessory assumptions which have not yet been verified by experiment, I shall employ the language of the second hypothesis in seeking for further explanation; which hypothesis, moreover, | have employed throughout in | my research on kathodic deflection, m describing the phe- nomena observed. If now (fig. 20) rays issue from the edge a of the right- hand arm (1) towards 6, then, according to the laws of ka- thodic deflection, these rays will be repelled by the edged and the whole surface of (2). The same holds good for the rays emitted by the left arm atc. Let fig. 21 be a rough repre- sentation of the kathode, turned through 90° from its position in fig. 20, the upper half having moved forwards; and let / and r represent the upper edges of the left and right arms respectively, and o the (fore-shortened) upper arm. The repulsion which o exerts upon the systems of rays emitted by y and J will cause the mutual convergence of these two last 466 Dr. E. Goldstein on the Influence of the to decrease, but so that the two systems of rays still intersect each other (at wz, in fig. 22). If now a plate capable of phosphorescing move at right angles to the plane of the drawing in the space free from rays between the points of intersection # and o, a dark space will be seen on it, bounded by its luminous intersection with the repelled systems of rays; thus the upper arm of the dark cross is bounded by its two luminous curves. ‘As the density of the gas decreases, the repulsion increases; the convergence of the two pencils of rays will therefore be still further di- minished; the point of intersection, 2, moves further away from the kathode; and the plate may now be further off from the kathode and still show the dark cross. As we saw already, in examining deflection, the rays further off from the repelling surface are carried with those which are nearer to it, but are not deflected through so great an angle; the deflected rays are therefore compressed together on the side turned towards the repelling surfaces; hence the greater brilliancy of the narrow contour-line immediately bounding the dark arms. If the phosphorescent plate moves away from o beyond 2, the dark cross on it must of course disappear, since the plate comes into a space occupied by rays. We must therefore have a bright field on the plate opposite o, the outer contour of which is again formed by the intersection of the plate with bounding surface of the deflected system of rays. If we take account of the fact that, according to the form of the dark cross, the curved surfaces of these systems of rays have their convex sides turned towards each other before the intersection, we see that beyond « they will have their concave sides towards each other, and will thus form the “ curved points,”’ which observation shows to exist. Consequently the upper “ curved point” (fig. 23) is not formed, as we should have expected at first, by rays from the upper arm of the kathode, but it is formed by rays from the two horizontal arms of the kathode—the left-hand half, and in particular the contour-line /, being formed by rays from the right-hand arm R, and the right-hand half by rays from the arm L. If this is the right way of regarding the curved points, we ought to find it confirmed by experiments in which shadows are thrown. This is, in fact, the case. If we put a plate as a screen close in front of the kathode, so that, as in fig. 24a, it covers one half of the kathode ob- liquely, then at the density at which the curved points appear we observe the phosphorescent figure 246. The bounding eurves shown in dotted lines are now wanting. The phe- aE Shape of the Kathode in Geissler’s Tubes. 467 nomenon thus agrees most exactly with the explanation given above. If we exhaust up to the density which corresponds to the figure with a dark cross for the uncovered kathode, we obtain the figure 25. By comparison with fig. 246, we see here also very plainly that the bounding curves of the dark cross, with their convex sides turned towards each other, are nothing else than the bounding lines of a “ curved point” with con- cave sides turned towards each other, which have become displaced across each other. 10. The most remarkable phenomena of the kind we are now considering, however, are undoubtedly those produced by plane kathodes. That plane kathodes cut into figures would present pheno- mena similar to those of the dark cross was probable, since rays emitted by one edge of an arm of the figure would be repelled by the other edge. Thus, in fact, a four-armed plane (fig. 26 a) gives a figure resembling fig. 26 b, with a distance of wall from 3 to 4 centim. The figures 12 c, 12 d, &e., observed with the curved cross- shaped kathode, do not appear with the plane kathode, but as the density decreases the first figure recognizable is the dark cross; if the density is still further diminished the arms in- erease in width, and show in the part nearest the centre a nebulous luminosity, with convex contour line (fig. 27). Tf the distance of the wall be made less than 3-4 centim., this nebulous portion increases in brightness, and contracts, be- coming better defined; and with a distance of wall of about 14 millim. we obtain the figure represented in fig. 28. In each of the four arms, which would otherwise be dark, there appears a beautifully forked line of light, the space between the forks being filled with uniform light with convex contour, while each fork is connected with the others by a slightly luminous are of light. In using a concave spherical cross of the same dimensions as kathode, the radius of curvature being, however, greater than 25 millim., we observe in the arms of the dark cross, so often mentioned, which appears at low pressures, this same luminous fork. We have therefore, as was to be expected, a gradual passage from the forms given by the curved kathodes to those of the plane kathodes, the figures given by the plane kathodes regulating those of the spherical kathodes. Inas- much as no explanation of the images produced by the former is possible, so for the present no explanation is to be given for a number of phenomena obtained with the curved surfaces. The dark cross produced by the plane crogs-shaped kathode 468 Dr. E. Goldstein on the Influence of the we might foresee ; but it is not possible to predict, a priori, the phenomena produced by plane kathodes, not cut out, nor having concave edges, and these constitute an pais new class of phenomena. I make here the general remar. that, while it is true that the images given by plane kathodes alter somewhat with decreasing density, they do so much less than the figures obtained with curved kathodes, and often the changes consist only in the acquisition of richer detail and more definite contour, or perhaps somewhat larger dimen- sions. If these images are produced by kathodes of relatively small surfaces (1 to 14 square centimetre), the kathodes must be placed tolerably near to the wall of the vessel. The larger the surface of the kathode is, the greater the distance of wall at which it first appears. If with a given kathode we go further off than a certain distance, we obtain a uniform y illuminated phosphorescent surface, whose luminosity slowly and gradually decreases from the centre outwards. If a plane square be employed as kathode, we obtain fig. 29 on the wall of the spherical discharge-tube of 9 centim. diameter. The relative size and position of the kathode (2% centim. distant from the wall) is marked by the dotted lines. We obtain therefore a star of eight arms, four of whose rays correspond in direction to the diagonals of the-kathode, and the others to its central lines. The centre of the figure is formed by a feebly illuminated square space, upon which the star appears; a luminous zone surrounds the dark central space, formed of four arcs, convex outwards, The four rays corresponding to the central lines of the kathodes have their maxima of light within this outer zone ; the four diagonal rays, which are narrower than the others, are uniformly luminous, except that all eight rays are more luminous at the centre of the whole figure. The whole figure is considerably larger than the kathode-square, the darker central square space being larger than the kathode. The figure given by a rectangle 2 centim. by 1 centim., with its longest sides horizontal, on the wall at a distance of 14 centim., is represented in fig. 80. The main figure is thus a narrow line of light, corresponding to the central line of the rectangle, which forks at each end, and is surrounded by a broad band. The lower ground is an oblong, rounded at the small ends. A plane circular disk, as mentioned in the introduction, gives no special figure on the illuminated ground obtained in all the figures, unless we regard the bright central point of the image as such a figure. The rays produce a circular disk, which is not sharply defined, with the feebly illuminated ground, and Shape of the Kathode in Geissler’s Tubes. 469 brighter zone at the edge ; the centre point is, of course, bright. An ellipse whose axes measure 10 mm. and 20 mm., on the other hand, gives a comparatively complicated figure (fig. 31) at a distance of wall of 1 cm. in a vessel of 94 cm. diameter. Tn allthese figures the ground expands the more the density of the gas is reduced. If we use kathodes made up of several of these simpler forms joined together, we of course obtain much more com- plicated images. The images obtained with the comparatively simple form of kathode fig. 32a may serve as example. A square out of whose edges smaller squares have been cut (fig. 326) shows the central portion of the phosphorescent image completely; but, to save space, the figure gives only two of the streams of light which project from the four sides. To enter at present further into detail in describing a large number of these phenomena, which are often characterized by surprising beauty, would be without scientific interest, since the simpler cases already described sufiiciently represent whatever is new and characteristic amongst phenomena of the kind, viz. :— (1) The fact that such figures are produced. (2) The circumstance that the magnitude of the images varies with the density of the gas, and exceeds the magnitude of the kathode itself at high exhaustions. This latter phenomenon, to which I have devoted a separate series of experiments, may be supposed to occur in either of two ways: either the direction of the rays varies with the change of density, the pencil emitted by a plane becoming more divergent the smaller the density of the gas becomes ; or the direction of the rays remains constant, and as the den- sity of the gas decreases the previously unobserved rays of those elements of the surface which are situated obliquely to the outward-directed rays become strengthened. Hixperimental trial gives as result that the first-named reason (variation in direction of rays with variation of den- sity) is to be preferred. Of the different methods of proof employed I will mention only one here. If we cut slits in a plane disk, the spaces in the disk show themselves in the phosphorescent image, for which the disk acts as a kathode, as narrow dark lines. A number of con- centric and equidistant semicircular cuts were made in a disk, so that the outside one lay near the edge of the disk (fig. 33), In the phosphorescent image there appear, even at the highest density at which it is visible, the same number of dark semi- circular lines, showing that even at the highest density the phosphorescence produced by the elements on the edge of the 470 Dr. HE. Goldstein on the Influence of the disk is manifest. If the exhaustion be carried further, the dark semicircular lines move further apart ; and at a constant density the distance between any two of the dark semicircles is greater the further the pair in question lies from the centre. This last behaviour manifests itself also if the phosphorescent image is received on a plane surface parallel to the kathode instead of upon a spherical wall. The phenomena described for plane disks lead to the follow- ing conclusions :— (1) The different points of a plane kathode-surface are not of equal value in the emission of kathode-rays, but the inten- sity of the rays depends on the position of the elements by which they are radiated with respect to the contour-line of the kathode. , (2) The rays of a plane kathode-plate do not in general form a parallel pencil* ; but the inclination of the rays varies from element to element, in accordance with the distance from the contour-line of the plate. (3) The direction of the radiation from each separate ele- ment varies moreover with the density of the gas. Thesmaller the density becomes, the more does the direction of radiation differ from the normal to the element; and the direction of deviation is always outwards. Whether any density exists at which there would be devia- tion from the normal in the opposite direction (7. e. inwards), at which therefore the rays would be convergent, is a question to which an answer must for the present be deferred. The deviations which make their appearance as the density dimi- nishes are the more considerable the nearer the element in question lies to the edge of the surface. 11. Convex kathodes of regular outline also produce regular phosphorescent images. Convex spherical forms, so far as I have observed, give the same figures as plane kathodes of the same outline—only of larger dimensions at an equal distance of wall, in consequence of the stronger divergence of the rays. With cylindrical convex surfaces the figures obtained with plane surfaces of similar outline are deformed, as might have been expected ; the image is, ceteris paribus, more expanded at right angles to the axis of the cylinder than parallel to the * If we assume that each point of a kathode emits, not simply one ray, but a small conical pencil of rays, then in the above proposition, ins of “ray” we must read “ axis of conical pencil of rays.” I am still oceu- pied with experiments to determine the limit of aperture which we can ascribe to the pencil of rays from a point of a surface. Shape of the Kathode in Geissler’s Tubes. 471 axis, and that in greater degree the greater the curvature of the surface. 12. Still another class of simple forms of kathodes which produce figures are such as may be termed “ interrupted;’’ to which belong, amongst others, prismatic tubes open at the ends and cut off at right angles, then (plane) figures formed by bending wire (¢. g. polygons of wire), and so on. The images given by such wire kathodes are amongst the most beautiful which can be obtained. In order to render intelligible at least the general mode of their formation, the fol- lowing may be mentioned:— If a cylindrical or prismatic tube cut off at right angles to its axis and open at both ends be employed as a kathode, then as the exhaustion proceeds a conical pencil of rays issues from each of the open ends of the tube, the axis of which is coin- cident with the axis of the tube, and which expands more and more into the gas-space the further the exhaustion is carried. Assuming rectilinear rays, the pencil is then so directed as if it issued from a metal plate closing the actual opening of the tube. When the exhaustion is sufficiently great, this pencil reaches to the wall of the vessel and excites phosphorescence there. The phosphorescent image of this pencil forms the phos- phorescent figure produced by a tube-shaped kathode. In general, there are two images produced corresponding to the two pencils which issue from the two openings of the tube, and which are congruent if, for example, the discharge- vessel be spherical and the middle point of axis of the tube coincide with the centre of the sphere. We have a similar result to that obtained with a cylindrical kathode, when the wall of the tube kathode is saddle-shaped, such for example as is formed by the revolution of an are of a circle about an axis lying on its convex side. If we imagine such a tube of very small height, we obtain a ease which can also be realized by surrounding a space with a wire of the corresponding form. Just as pencils of rays issued at right angles to the opening of the tube, so they issue from the wire kathode at right angles to its plane, to all appearance as if the empty space surrounded by the wire acted as a kathode. The luminous figures obiained from wire kathodes are larger than the space enclosed by the wire, even at small dis- tances of the wall from the kathode. The images may show great changes with change of pressure. I content myself with 472 Notices respecting New Books. giving as example the image represented in fig. 34 6, given at high exhaustion on the wall of a spherical vessel by a regular pentagon of 12 millim. in the side bent out of wire about 1 millim. thick (fig. 34). The normal to the polygon at its centre point was placed radially. The waving contour-line which passes through the ends of the five-rayed star forms a perfectly sharply defined contour- line. If we employ a regular wire polygon of some other number of sides (3-8), we obtain a similar luminous star with the corresponding number of rays. With polygons with an odd number of sides, the rays of the star correspond in direction to the longer radii of the kathode-poly gon. With polygons of an even number of sides, on the other hand, the axes of the rays correspond to the shorter radii of the polygon, and thus appear to intersect the sides of the polygon at right angles. With the phenomena which are given by interrupted kathodes may be connected an observation made with plates perforated with holes, which is at first sight surprising. If we make use of a square plate perforated with a number of holes (fig. 35), we might perhaps expect that the places from which the metal has been removed would appear dark in the phosphorescent images, or at least would correspond te mimima of light. We find, however, that these points are really maxima of light; thus with the kathode fig. 35 we obtain 16 very bright points of light. The reason is to be found in the fact that the walls of each perforation form a short open tube ; and, according to what we have seen, a bright pencil of light issues from such a tube, which at suitable exhaustion extends to the wall and excites phosphorescence there. ‘Berlin, Physical Institute of the University. LII. Notices respecting New Books. Graphical Determination of Forces in Engineering Structures. By James B. Coatmers, C.L. London: Macmillan. 1881. 405+ xxvi pages, 6 plates, 267 cuts. (pais is a large and important work, aiming at being a complete treatise on use of graphic methods in engineering-designs. It is a high-class work, requiring a fair knowledge of modern geo- metry for its comprehension. To facilitate this (to the Engineer) a special Chapter on ‘* Projective Geometry” (66 pages) is given ; within this compass a wide range is compressed, e. g. projections, homology, Carnot’s, Pascal’s, Desargues’s theorems, &e. Notices respecting New Books. 473 In application to Engineering great superiority is claimed for graphic methods over computation. The practical applications are skilfully and neatly worked out; and the study of them is an intellec- tual treat (not easy reading). The scope of the work is very wide: Resultants of Forces, Moments, Centre of Gravity, Moments of Inertia, and Stresses in Structures, ¢.g.in Frames, Beams (supported, fixed, and continuous), Arches (rigid and elastic), Suspension- Bridges, Retaining Walls, and Tunnels are all treated by graphic methods. ‘These processes are only meant to supersede computa- tion: analysis is often used for their actual elucidation; thus the explanation of the graphic methods for the Elastic Arch covers 20 pages of a somewhat difficult analysis. In some cases the graphic methods have decided advantage, chiefly when the work is simply a repeated application of the theorem of the “polygon of forces ;” the diagrams of these are simple and can be quickly drawn. But in cases where sums of pro- ducts are required (e. g. m moments of forces, moments of inertia, &c.), the advantage is not so clear: the process increases greatly in complexity as the number of variable factors in each product in- creases, the diagrams become intricate, and are finally a network. of lines (see fig. 65-1, fig. 143 pl. 1, pl. va), requiring great skill in their original preparation, and-not to be unravelled in after-ex- amination without careful study. The risk of mistake in construc- tion, not so much from inaccurate drawing as from mistaking one point or line for another, in such a network must be considerable, and quite analogous to that of numerical slips in computing. Even in the simple case of the sum of the products of two factors, the result would probably be got more quickly with a slide-rule or Crelle’s mutiplication-table than by the very neat graphic process given; but in the more complex cases of several factors computation would surely be quicker. The processes given are by no means always the shortest. Thus the determination of the pressures on the supports due to a single load placed on a beam requires only the division of the line repre- sentative of the load into segments inversely proportional to the segments of the beam on either side of the load. This requires only three lines for its complete graphic solution; but the process given (the same as for the general case of many loads) requires seven lines. When several processes are available for the same purpose, it would surely suffice to give the best, unless each has peculiar ad- vantages in special cases, which should then be stated. Now, for finding stresses in frameworks three processes are given, covering 66 pages. No. i., by “‘ Method of Sections,” requiring at every section a preliminary reduction of the frame on one side thereof to an ideal triangle and evaluation of the Resultant force thereon: this is a difficult and troublesome process. This troublesome pre- - liminary is avoided in No. ii., the Method of Sections proper: this is nearly the same in its application as No. iii., but gives rise to Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 21 474 Notices respecting New Books. stress-diagrams sometimes imperfectly “reciprocal” to the original —a slight disadvantage. No. iii. is Clerk-Maxwell’s beautiful pro- cess: this is the simplest and easiest of the three; its simplicity seems to depend on the complete reciprocity of the stress-diagram with the original figure. Methods i. and ii. might have been omitted with advantage, and more space given to the last. This Chapter is illustrated by numerous* well-chosen examples. The three pro- cesses therein are really a graphic solution of the “conditions of equilibrium ” among the forces at each section or joint; as there are thus only two equations for each section or jomt, the magni- tudes of two stresses can be found for each section or joint. Thus the problem is indeterminate for a frame at any of whose joints so many bars meet as to require the determination of more than two stresses thereat. This is actually the case with two of the frames (figs. 49 and 51) for which finished stress-diagrams are given with- out comment. Some explanation is surely wanted in the text as to how this indeterminateness (which is inherent in both) is to be met. One of these (No. 51) is solved in Rankine’s ‘ Civil Engineering,’ art. 576, by a method of dissecting the complex Truss into partial Trusses, which bridges the difficulty by (tacitly) assuming the inter- action of the partial Trusses. In Clerk-Maxwell’s process for Frames under dead load the graphic methods probably appear at their best; but with moving load the greatest stress in each bar occurs with a different state of load, thus involving a tolerably complete special diagram for each bar, greatly increasing the work and the intricacy of the finished drawing. ; In investigating the stability of Retaining Walls and Masonry Arches, again, the graphic methods have decided advantage over computation: this arises partly from the fact of the cross-sections being solid, so that the limit within which the centre of pressure at each joint should fall is easily known to be the middle third. The tracing of lines of pressure and resistance therein is well ex- plained and illustrated. In the case of the Arch, however, one difficulty (indeterminate- ness) has not been adequately met. In general many lines of pressure and resistance could perhaps be traced within the “ core” or admissible limits (the middle third); and the question is, which is the true line? The author says, “the true line of pressures is that which is nearest the axial line” (art. 181); this seems doubtful. Moseley’s Principle of Least Resistance gives a means of locating it so that the passive resistance required at the spring- ing shall be the least: this seems sound for rigid material; but its applicability to non-rigid material is not so clear. Of all the processes given, the applications to Continuous Beams and the Elastic Arch are naturally the most intricate. These are masterly specimens of the power of graphic work in the hands of * There are several lines wrong in lower part of fig. 57 b. Notices respecting New Books. 475 one skilled in its use. The amount of drawing required for the complete investigation of any one arch seems very great. PI. v.a, the finished (?) result for an arch, is so complex a whole (although several preliminary drawings are omitted from it) as to require great care for its comprehension; and even it seems (arts. 214, 219) to be only a part of what is required. Among practical details, it is laid down (art. 121) that “an arch ought to be wholly in compression.” Now this principle is ob- viously right for masonry ; but there can be no occasion for applying it to iron or steel arches (as in art. 183): this would surely be a waste of power. The theory of earth-pressure given, depending on the “angle of repose” and frictional stability, is complex and difficult (covering 23 pages before application to retaining walls). The “angle of repose” is an item which in many cases can hardly be said to be known at all, so that mathematical refinements are of little use. Rankine’s theory (which is much simpler) seems good enough for such imperfect data. There are numerous references to foreign works on geometry and graphic statics ; the influence of these is obvious in the diction. The author is thoroughly at home in the practical application of graphic methods ; but for a didactic work the mathematical render- ing might be improved. Thus there is occasional obscurity in the explanations, e. g. props. xxxix., xlii.,and arts. 80, 161, 223: results to be derived as the fourth term of a proportion are commonly pre- sented as(a:b::c: Us mere identity; the insertion of the a name or symbol for the required fourth term would be more useful (e. g. in aiding its discovery in the diagrams). There is also a cer- tain looseness of exp7ession, e. g. moments termed forces (pp. 113, 139), the use of the term “ centre of gravity” of forces (pp. 268, 274): also of notation, ¢. g. in use of symbols A and d, & and J (passim), and of — in geometry (pp. 363, 364); also of analysis, €é. g. omission, removal, or change of variables under summatory symbol (pp. 162, 268; 150, 275, 277; 281); these latter mistakes generally correct themselves in the final results. There are also two mistakes in the geometric theorems. Thus, Poncelet’s condi- tion of projectivity (prop. xxxii.) is stated in too general terms without due limitations, and the example given is non-projective. Again, in the proof of Pascal’s theorem (prop. xlvi.), the conic and its inscribed hexagon are projected into a circle and inscribed hexagon with opposite sides parallel and one pair equal (which is not generally possible); and it is stated that ‘the points of the hexagon joined two and two concur in a point P” (and they actu- ally do in the figure in consequence of its being a regular hexagon), which is not generally true. Several minor points might be improved (in a new edition). Thus there is hardly enough lettering on some of the diagrams for their easy comprehension ; and in many cases the symbols given are DEAS ge . 77 476 Votices respecting New Books. too complex for use on a diagram—e. g. one length in fig. 100 is marked thus : . , 2 a om.(2+S ye Bie. a Z, a Now in all such cases a single symbol (with reference in the text) would be better. The numbering of the diagrams also should be made consecutive; there are at present three numberings inter- mixed, which renders reference difficult. The number of mis- prints also is very great, especially among the references. Even with these faults the work is a valuable one, and no one can read it without learning much. ALLAN CunnineHaM, Major R.E. Questions in Pure Mathematics proposed at the B.A. and B.Sc. Pass and Honours Examinations of the University of London, with complete Solutions by J. E. A. Straeatt, M.A. Van Voorst, 1882; pp. viii+245. Tue title sufficiently indicates the nature of the work. The solu- tions, we think, are in all cases neat, and in many instances they are elegant. Mr. Steggall does not confine himself to single solu- tions, but often gives two or more proofs of the same question. The work is very carefully printed, and there are, we believe, very few typographical errors. On p. 13 another mode of solution might have been indicated, depending on the fact that the sinister side vanishes when vw=y=z. We venture to suggest that on p. 25 reference might have been made to Euc. vi. 3 and A as also readily furnishing a solution; and the equation on p. 37 might be worked from the fact that the terms on one side are reciprocals of those on the other. But these and other instances we could bring for- ward only illustrate the well-known fact that there are more ways than one of attacking problems; and the exigencies of space have no doubt restricted the author in general to the single solution he adopts. On pp. 21, 45, occur, as we think, two slight maccuracies in expression. We note the following slips :—p. 120, “Solving for y” read “w,” and for “cosxv” read “cos*v”; p. 164, for “ —3y” read “+3y”; p. 224, for “ >1” read “<1.” * Slo w SS a ee SE = : SS gee Ee FS Daa ena a at ee a ~ ae eae a “ ey Sete, | f a 2 + +. = z Page 217, line 10, for af put £Y . g — 221, line 4, for cos (2a+28) put sin (20426). - — — 222, line 4, for cos* 6 put cos* 26, ta — 223, line 30, for n read 2, bis. pe Post 8vo, cloth, 6s. QUESTIONS IN PURE MATHEMATICS PROPOSED AT THE B.A. AND B.Sc. PASS AND HONOURS EXAMINATIONS OF THE UNIVERSITY OF LONDON. 4 WITH COMPLETE SOLUTIONS By J. E. A. STEGGALL, M.A.,, Late Scholar of Trinity College, Cambridge; Fielden Lecturer in Mathematics at the Owens College, Manchester. JoHn Van Voorst, 1 Paternoster Row. 8vo, cloth, 383 pages, with 88 Illustrations (drawn to scale), £1 1s. . A TREATISE ON THE DISTILLATION OF COAL-TAR AND AMMONIACAL. LIQUOR, AND THE SEPARATION FROM THEM OF VALUABLE PRODUCTS. By GEORGE LUNGE, Ph.D., F.CS., Professor of Technical Chemistry in the Federal Polytechnic School, Zurich. By the same Author. A THEORETICAL AND PRACTICAL TREATISE ON THE MANUFACTURE OF SULPHURIC ACID AND ALKALI. 3 vols., £4 16s, JoHN VAN Voerst, 1 Paternoster Row. Demy post 8yo, cloth, post free, 5s. A TREATISE ON THE TRANSIT INSTRUMENT, As applied to the Determination of Time, for the use of Country Gentlemen, By LATIMER CLARK, M.LC.E. A popular description of the. method of obtaining accurate Greenwich time the Transit Instrument. It also contains Tables of the Transit of the principal _ Stars for 1882, calculated in ordinary Greenwich time. ; A. J. Frost, 6 Westminster Chambers, London, 8S.W. THE LONDON, EDINBURGH, AND DUBLIN Philosophical Magazine and Journal of Science. A Journal devoted to Physics, Astronomy, Mechanics, Chemistry, Mineralogy, and the Allied Sciences. Monthly, price 2s. 6d. 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