Me ohritgs th ve eee) Mb hy baby be here ha ae DM eethy hie pa helt a ia ty 654 DxIg: oP SCIENTIFIC LIBRARY wy) AS MoMamMmMwmtamaAmmMAMawmAMBVMrMMamMmMMsK x va) & ES EIEILI III EDIE III EIS LSI ELI EIEN LYS N Netoad tu a — is i Bole CS betes is ( J ee 601 5 2 517 |. ee 420 — 103-50 > 2 ee 329 : . 240 = =e pa a Fo, 196 10 current on ...... 152 250°4 b—18:2,4/=164 "22 ee 1961 29°6 Lk eee 18°70 PAST 2 ee Eee V9 30-7 a eee 16°95 30°2 _o-eeeeee 16:08 30°4 ' 2) ee 15°25 30°3 13m 10s end of eur.! i ee 14:58 103:0 t=18 0, ¢t’=18-4 “a ee eee 14-523 Nose nawocane 522, ee os) coscce ee 520 —103°50 Lok eee 510 Se 494 _s, 4:05 Ee 476 2 ek Sa eee 460 2) 440 2. 2 419 Ls {= ee 400 fe 379 2 360 1 2 ee ee 341 With the aid of the numbers recorded in the Ist and 2nd columns of the above table a curve is drawn, representing the variations of temperature of the calorimeter. It is composed of three nearly straight parts (the regular course of which serves as a proof that the readings are free from mistakes) ; the inclination of the first and third branches enables us to determine the influence of external heating or cooling on the temperature of the calorimeter. We find easily in the present example :— 16 _ A. W. Witkowski on the Initial cooling ......... 0:0894 degree per minute. Pal oS ee 0°0195- - 3 . Mean ga Pie Sees oe 00544 _—,, = This mean value I accept as determining the external cooling influence during the principal period of the experiment, when the gas current is flowing. I have found that this simple mode of reckoning gives nearly identical results with the more elaborate method of calculating the corresponding cor- rection which has been proposed by Reznault. It seems, moreover, that a more laborious determination of the external heating or cooling effect would be useless, on account of the following anomaly, which presented itself in a more or less marked degree in every experiment :—The transition from the rapid fall of temperature, caused by the cold gas-stream, to the less marked cooling observable during the final period, is always preceded by a slight depression of temperature (as in the preceding example) ; in experiments at high tempera- tures the phenomenon is exactly reversed. Undoubtedly these anomalous variations of temperature are caused by the fact that the direct conduction of heat (or cold) from the heater to the calorimeter is slightly modified by the gas- current itself. This disturbing cause did not escape the attention of Regnault (/. c. pp. 83, 214), but he did not sue- ceed either in getting rid of it, or in taking it into account. Some uncertainty thus remains in every determination of the specific heat. In the foregoing example I considered the movement of heat as finished at the end of the 14th minute. The initial and final temperatures of the calorimeter are thus :—20-152 and 14°523 ; when corrected with regard to the temperatures of the stem (¢ and ¢’) they are :—20°162 and 14°514, whence the total fall of temperature =5°648. From this there is to be subtracted the fall of temperature caused by external influences (0°0544 per minute), the amount of which is :— 4x 0:0544=0°218. Thus we obtain the corrected fall of temperature =5°430. As regards the initial temperature of the air, it is equal to — 103°50 + 2°01=—101°:49, because the mean deflexion 30°15 millims. on the galvanometer-scale corresponds to a gain of 2°01 degrees. The final temperature of the gas is to be calculated by taking the arithmetic mean of the tempera- tures of the calorimeter at the beginning (20°16) and at the end of the current ; the latter we find on the temperature- Thermodynamic Properties of Air. Ly. curve, it is 14°94. Therefore final temp. =17%55, total rise of temperature of the gas =101°49 + 17°55 =119° 04. According to Bartoli and Stracciati the specific heat of water at the temperature of the experiment is 0°9996, the sp. heat at +15° being taken as unity. Therefore we have finally : 253°829 x 0°9996 x 5°430=c, x 48°8842 x 119-04, whence it follows: c,=0°2368 as the mean value of the specific heat of air between the limits —17° and +100°. § 10. In the annexed table I have collected all the data serving to characterize the different determinations of the specific heat of air at constant atmospheric pressure. The columns headed I—XI. contain the following quantities :— I. Mass of air passed through the calorimeter in grs. II. Equivalent mass of calorimeter in grs. of water. Ill. Velocity of current: grs. per min. IV. External heating of calorimeter, before and after the | current, in a0 degr. per min. Y. Time of influx of heat into the calorimeter in minutes. VI. Initial and final temperatures of calorimeter (corr.). VII. Total rise of temperature (corrected). VIII. Ditference of temperatures of heater and gas, as indi- cated by the galvanometer (degrees). IX. Initial and final temperature of the gas (degrees). X. Specific heat of air, under a pressure exceeding slightly the atmospheric, between temperatures indicated in LX, XI. Mean values of the foregoing. The whole of these results may be summed up as follows:— isenween -— 20° and +98? ..........5..%. Gr O2an 2 mA Srathibe ad. kre Onin ey con chs ¢, =0°2374 ‘5 <= JU) Ree 2 U7 aan net alr =072502 5: pale eter eee PO oe. eeu soe 4: ¢;=0°2427 On the ground of these results we may assert with certainty that the specific heat c, does not vary in a sensible manner down to a temperature of about —100°. At the lowest temperatures, however, there is apparently a small increase in the quantity c, of about 2 per cent. But I think there is sufficient reason to conclude that even this small increase is only apparent, namely, that it ought to be ascribed to the influence of pressure rather than to that of the temperature. Phil. Mag. 8. 5. Vol, 42. No. 254. July 1896. C A. W. Witkowski on the 18 PLES-0< ‘IX ( | | | oe | G126-0| GLLT+ F8ES-0) FL-GT + 1186-0| PL-GT+ 9983-0] FS-GT + | LLE3-0| Go-FI+ 186-0) 61-61 6966:0] GS-8T 6486-0) €L- LT 0866-0! 96-LT 9966-0} 19-61 C9&G-0) S6-6T 9966-0} 99-06 6966-0) 60-61 PLEG-0| €E-06 T286:0| FFL €L166-0| $8-6T 18&6-0| 66-61 | 6L€%-0] £¢-8T ox OTO-ST |866-81 'G6-€ 668-EL |666-LT | 9-€ 669-E1 |66F-9L | SG GG8-ET |1P8-9L | 9G P8G-GL \GEE-ST | 0 969-06 |666-LT 610-06 |L16-L1 LGE-GT |1S6-91 VVS-6L jOSG-9T L1V-1G |SET-8T F08-16 |06€-81 669-16 |S86-61 869-6L |E8P-81 VL8-16 |0S6-81 LOT-6L |G16-G1 OLT-1G |€68-81 069-06 |G61-8T 606-61 PrP LT ‘TA 6E6—|F89 — 966—-|E69 — G66 — |999 — F6G — |SS9 — LEL—|var— 0-6) SIT j6Lé G-E| SEL |¢cP GS) 991 |vrV Ce OLL 126 G-€| 89L |88P 0-€| 98L |8sP Coy eau VOLE G-G| OTE |88€ GG| 9LT |96P O-F| OPT |SEP G-G| GEL |V9s G-G| 6ZL |S6E G-G| SLL -\9&6P “A ‘AI TGP-7VG 006-VPG 8L9-FPS SOL-SVG G86:SVG ee V98-GVG 866-TVG GLG-VVG I1E-976 LS9-SVG | 790-GFG 19-46 G19-FFS GE0-SFG PE9-EFS FZE-GES EEE-EFG GO9-1FG eee | ee “IL TF68E- [PV PP96-9E COT8-0& OFTe-1e 0S0G-6& 0068-7& TG2Z6-9& OFTE-LE GhG8-LE 0960-6P 6689-87 LETE-GG 8696-E1 1¥66-LE LL99-6& 9919-86 6S00-66 9966-06 ‘T 19 wr. 2es of A . Thermodynanue Propert LG¥G-0 ie LEV6-0| 18-81 +/ S6-0L1—| S¢-IL— 16¥G-0) 6L-L1+| 92-FLZ1—| FL: — 69V6-0| 6G-2T +} G99T— 9866-0) I6-L1 +] 2-691— 69EG-0| FR-LT + 8982-0] 6¢-L1 + F98G-0| €8-21 + F98Z-0| F-GT + F9&Z-0| 90-91 + LGES-0| Z6-L1 + €886-0| 6¢-91 + 8686-0] 60-11 + FLES-0| 9G¢-CT + 8883-0] 96-FL + \| 198-0] s¢-eT+ IEE LOE (C1772 | (0) Ce Sali) ss 10-601 — L6-GOL— C9-GOL — ¢0-60T — SOLO Te FL-TOT— 68-LOL— ¢9-cOI— 9683-0] G9-GI +] SL-4L— 088-0] 92-9 +] 08-92 — 8ZES-0| BS-EL+| GF-LL— | 88&3-0 88-91 +] 02-91 — a) |e to [le 60-6— 10-6 — eo = 910-4 — O&F:S — 6E6-9 — T&6-7 — VLG-G— 668-9 — POL: O1E-F— OLE S 86S-E — 698-6 — 1&6-6— 888-6 — 669-6 — SVS- — 88&-ST FrO-F1 69L-E1 0°6-SI 999-1 VIG-V1 088-€T 999-61 GL0-ST LLP-PL 0&6-FL 062-71 0S6-E1 666-G6T 988-LT CEP 1G 88E-06 LLE-0G 086-61 L68-06 691-06 C9E-0G 68L-L1 GL9-81 CV9-06 G8¢-sI 986-61 68¢-L1 689-91 668-71 PLO-PT LITT GEL-FL |€8I-8T GOL-LT |LTS-FI GL8-FI |OES-8T 619 — |6E0E — OST + |98II— Gls a Go Oils VI6—|l6el— 68 + 1/968 S6I— |768 VEL—|Es6 S9L— |L08 GOS — |6FOL— EVL—|616 66L— |208 LE —|¢6o) SSL — |F69 6ST — 1809 696 —|F64 SOLS OCoe= 606—|00L— SéE—|81l— 62209 618-076 SES-0FG L8S-0FG L0G-SVG 869-GVG 668-696 O&6-1VG LVS-666 618-976 96¢-076 PV 1-666 1¥6-1VG 657-096 69G-6VE SEER —— ee | LLE-FFC LOE-GVG 188-1&6 869-PFG GI6BF-0E GLOL-1E L6GL-¥& GIGI-SE LG60-19 GV88-8P 696-EG 8069-67 CGIS-97 6698-67 60LL-FE 067S-9E L88¢9-LE 899S-1E LLPI-SS 890L-6E 666G-6F SL6P-86 GELL-8E 2 \ 3 C 20 AGW Watkowsla Guahe Indeed, we shall see later on that the influence of pressure on the specific heat at very low temperatures is very considerable; for instance, at a temperature of —144° a doubling of the atmospheric pressure brings about an increase of specific heat _ by 0:03. Now the air on entering the heater is clearly under a pressure exceeding the atmospheric by an amount indicated by the mercury manometer. Jn the liquid-oxygen series of . my experiments this was about 70 centims. of mercury. Part of this pressure-head is absorbed by the resistance of the heater ; but on entering the cooler there remained still an additional pressure of about 48 centims. This is amply sufficient to account for the observed small increase of the specific heat. In what follows I shall therefore consider the specific heat of air under atmospheric pressure asa constant (0°2372) from +100° down to —170°. § 11. We are now prepared to take up the more general problem proposed in § 2, to determine the dependence of the — specific heat ¢ on pressure, at different temperatures. That a dependence of this kind does really exist may be inferred from the fact that the values of the second differential 2 coefficient a (§ 2, equation 1) are in general different from 9 zero. The values of or can be obtained from the results - Ot? : recorded in the first part of the present memoir. Denoting by v the volume, under the pressure p, at 6 degrees, of a mass - of air which occupies the volume 1 at 0°, under atmospheric pressure, we have v=o (T+e0)5 ... .. 2 a denotes here the mean coefficient of expansion under the pressure p, between 0° and 6°, y the coefficient of com- pressibility at 0°, depending on p only. The values of a — have been given in a table in § 15, those of 4, will be found in the table of compressibility ‘§ 17, vol. xli. p. 809) in the column headed “0.” {n what follows I shall assume t=273 +0. 2 In order to obtain oe I chose the graphical method of eal- culation, which seemed more direct and reliable than the use of empirical formulas such as those of Clausius, van der Thermodynamic Properties of Air. 21 Waals, &. It is most advantageous to perform the differen- tiations upon that quantity which has been directly measured, and the variations of which are most marked, 7.e. upon the coefficient a, Differentiating twice equation ( (6) we obtain Orr _ O°Y _ 2m 02 | Mop O°% 02 08 poo p oF or OF 07a To obtain 56 and AYE of values of « arranged in curves of equal pressure, abscisse representing temperatures ; it is in fact the diagram alluded to in § 14 (Part I.). These curves were divided in short pieces, approaching to straight lines; the differences of (7) I constructed on a large scale a diagram ordinates of their ends gave oF the values so obtained were considered as corresponding to the middle point of each piece. Another diagram was then constructed with ee as ordinates. 0 The curves were carefully smoothed, care being taken to keep. the whole of them in sight in doing so. ‘The process of differentiation repeated furnished the values of O°» OG? Using th Pa ep b , ealeulated by equ: sing ese values 3 ean ve NOW Calculatec Vv equa- tion (7). It would be superfluous to reproduce here the vast number of values thus obtained ; some of them will be given later on. An idea of the curious shape of the curves ov Ya On 92 * It might be objected that this method of calculation is not capable of yielding results of any high accuracy. Indeed, it cannot be denied that in drawing long curves along a comparatively small number of observed points, the success depends in a large measure on the firmness of eye and steadiness of the drawer’s hand. Yet on the other hand it is to be remarked that the curves control one another, gross errors are thus easily avoided. Although graphical differentiation, if accurately done, is a very tedious process, it is unfortunately not possible to perform it by mechanical means, since, as far as I know, mechanical differentiators (working in a similar manner to the numerous integrators) do not exist. If Tam right they are even impossible on dynamical grounds, 69655 can be obtained by inspection of PI. I., where the values of have been collected on isothermals, from —100° to —144°.. 22 A. W. Witkowski on the The shape of these curves leads forcibly to the conclusion 2 that for small pressures (p=1 atm.) g cannot be zero throughout the whole range of temperatures. It is very small indeed for temperatures above —100°; but near the critical temperature its values cannot be neglected. This is, of course, an inference obtained by extrapolation (dotted parts of the curves on Pl. I.), since no experiments are available on expansion of air at low temperatures under atmospheric. pressure. Although this extrapolation does not seem to be doubéfal, and, moreover, any errors in it do not influence the final pnr2 result, namely the integral a dp,inamarked degree, yet 1 it seemed desirable to test its probability in an indirect way. For that purpose I integrated twice the extrapolated values of 0’v : Oe nical quadratures, adding to the result 1+ 973 in lieu of (for p=1 atm.), with respect to temperature, by mecha- constant of integration. It appears from this calculation that at a temperature 0= — 140° (hydrogen scale), a constant pressure (1 atm.) air-thermometer would indicate —140°76. I know of no experiments to corroborate this result. From Olszewski’s experiments on constant volume gas-thermo- meters*) there may be quoted the following results: at a temperature of —143°-7 (hydrogen scale) a constant volume nitrogen thermometer indicated —144°-4, a similar oxygen thermometer —145°:5. This is not inconsistent with the above extrapolation. § 12. In order to obtain the values of the specific heat ¢, according to equation (4) it remains to calculate the integrals "0 ap, along the isothermals 2”, » and dp bei 38 py Gg ine Senden tally sp art dp being ex- pressed in atmospheres. These integrals multiplied by the respective absolute temperatures ¢ and by the constant factor 18:714 represent the difference between the specific heat ¢, and the specific heat ¢,, under atmospheric pressure, which is very nearly a constant, =0°2372. The integrations have been performed by Simpson’s formula, 2 with the help of a large diagram of o, a reduced reproduction of which will be found on Pl. J. The results are embodied in the following tables :— * “ Rozprawy ” of Cracow Acad. vol. xiv. (Math. Class). Thermodynamic Properties of Air. 23 =—144, ¢=129. = — 125, 7=148. : .07u G2 D. 08 co Cy: P | = 10° aE e as oz 10 1360 0-504: 10 211 0-283 a ’ 20 300 0°352 20 1740 0°866 25 2390 1101 30 456 0°452 | 40 825 0°620 50 1406 0-931 56°9 0 1:106 @=—140, t=188. 60 316 1-087 | 70 — 76 1:040 5 — 5 1:031 p- — 108 Ow Cp. t u On 10 850 0°408 20 1070 0-640 30 2395 0°993 40 9064 2°607 6=—135, 1= 138. Pp 108 Ov op 2 ot? P 1039? | % ‘oe BL ols 10 151 0-272 ————=_ >>| i al |e aia 3) 29%) | @ |e | | B | & | oe 20 648 0-484 40 382 0-479 30 1110 0-689 0 50 610 0-614 45 8699 2-602 eae 5 Gene od a 70 —56 0-777 50 —1501 3-004 be ae oe 5D 0 2-848 60 — 295 2°785 65 = Ge 2-758 =—130, t=143. p 1080” Cp d=—115, t=158 rola 10 311 0-302 Pp —19°9” Cp 20 418 0-397 RYE 30 685 0-536 ee eee = 40 9993 0-873 10 121 0-267 50 2880 1:826 20 135 0-305 53: 0 1-963 30 159 0-348 55 — 303 1-957 40 207 0-400 60 — 357 1-905 50 335 0-476 65 — 168 1:872 60 45] 0-604 | 70 —108 1 855 70 41 0°657 75 —~100 1842 75 29 0-662 24 A. W. Witkowski on the é=—110, t=163. d= —95, t=178. 30° Cy P 10 5 10 108 0-264 20 115 0°298 30 119 0:333 40 136 0°370 50 204 0-419 60 444 0-509 70 152 0-607 75 75 0-623 6=—105, t=168. 0=—50, t=223. Pp. 1020” Co Dp. 1080” Cp rola Yo Yan 10 89 0-261 10 19 (0-244 20 90 0-288 20 22 0-252 30 93 0-317 30 26 0-262 40 100 0-346 40 30 0-274 50 145 0-382 50 32 0-286 60 279 0:445 60 32 0-300 70 293 0°539 70 30 0312 75 115 0:564 80 29 0-324 90 28 0:336 100 | or 0:347 G=—100, t=1738. 6=0, t=273. : 108 Q7v Co. Ds ca sv Cy. P 10 5B P 10 Se P 10 77 0-258 10 9 O20 ss 20 79 0-283 20 9 0-245 30 80 (Q-309 30 9 0-250 40 81 0-834 40 9 0:254 50 107 0-363 50 9 0-259 60 180 0:408 60 9 0 264 70 174 0-469 70 9 0268 80 97 0-512 80 = 0:273 90 32 0-532 90 9 0-277 100 13 0:538 160 9 0-282 Thermodynamic Properties of Azr. 25 The variations of the specific heat cp), as revealed by these tables, have been represented in « graphical form on PI. II. It will be remarked that with increasing pressure the specific heat increases, the more considerably the lower the tempe- rature of the corresponding isothermal. In the vicinity of the critical temperature these increments are largest, and in the critical state itself the specific heat tends to infinity. This might have been anticipated, on the ground of equation (2), § 2, because oP =() in the critical state, whilst ¢. and OP vemain et Ov PLO finite. The most interesting feature of the diagram (Plate II.) is that at temperatures above the critical the specific heat rises with increasing pressure only to a maximum value, corre- sponding to a certain limiting pressure (which isa function of the temperature). Under pressures exceeding this limiting value the specific heat remains nearly constant, with bat a slight tendency to decrease. The lower the temperature, the smaller is this limiting pressure, and the more marked the transition from increase to approximate constancy of the specific heat. It would seem as if these pressures marked a limit between truly gaseous states and a gaso-fluid condition of matter, in which the intrinsic pressures attain a prepon- derance against which the external pressure has but little influence. It is interesting to note that the curves of the coefficient of expansion a, under constant pressure (Part I., plate i.), show similar bends for pressures which are not much different from the limiting pressures of the specific-heat eurves. We shall see that neither the curves of the specific heat at constant volume, nor those of the coefficient of expan- sion at constant volume, show any trace of bends of this sort. 13. Itisa more difficult matter to calculate the variations of the specific heat at constant volume. At first sight it would seem easiest to apply the equation (3), § 2:— 0% t OD ov) Jim OC But we shall see that the variations of pressure at constant volume are so nearly proportional to those of the temperature, that the calculation of the second differential coefticient 2 or is practically impossible. In order to find the variations of pressure of air of any density kept ata constant volume, I shall refer once more to 26 A. W. Witkowski on the the results obtained in Part I. Through the origin of the diagram of compressibility (Part I., plate ii.) draw any straight line. The intersections of it with the isothermals pv=const. mark evidently a series of pressures corresponding to the respective temperatures, and satisfying the condition v=const.; it is supposed that v=1 when @=0°, and the pressure is atmospheric. Using the original diagram of pv, { determined in this manner the constant volume relation of Se if 1 p and @ for several densities of air, from v= io to P= 900° The results are given in the following table. ss Z a a Das = X a 10 20 25 30 40 50 6. Pressure in atmospheres. +100 | 13-680 27°41 34°28 41°17 55:08 | 69:09 + 16 | 10542 21-01 26°20 31:38 41-70 0 9-949 19:80 24-68 29°54 39°20 48 74 — 30d 8640 17-12 21°30 25°44 33°67 41-70 — 785} 7-005 13°76 17°05 20°30 26°64 02°75 —103°5| 6°065 11-82 14:60 17-28 22°48 27°40 —130 5°055 9°71 11-90 14:90 17-99 21°65 —135 4°850 9°26 11:32 13°29 16°98 20°35 —140 4-668 8:87 10°82 12°65 16°14 19°29 —145 4°466 8°43 10°25 11°95 15°10 17:97 iG abet te. ee pie) mie 60 80 100. |) 120° | 150 |" 200; 0. Pressure in atmospheres. +100 83°28 | 112°14 + 16 62°34 83:04 | 10392 | 125-41 0 58°53 77°52 96°80 | 116°40 — 3d 49°70 65 50 81:00 96-40 | 120-00 — 785) 38°65 50°06 60°80 71-02 85°83 | 110-80 —103°5} 32°10 40°88 48°75 56°U9 66:13 81°50 —1380 25:08 31-03 39°90 39°95 44-80 50°32 —135 23°40 28°74 32°90 | 36:18 39°60 43°44 — 140 22 08 26-74 30°35 32°84 35°39 37°80 —145 20°40 24°50 27 35 29-12 30°30 |. Thermodynamic Properties of Air. 27 In fig. 4 we find a graphical representation of these results by means of curves of equal density. Ke ave On ops SAIC ACNE = PETER {Sees ENR es HAY ye Some time ago Ramsay and Young announced an important generalization of the law of Charles, according to which the constant-volume relation of pressure and temper ature (in the 28 - A, W. Witkowski on the gaseous and liquid condition of matter alike) would be a linear one, at any density. It is now known that a law of that kind is not generally true, or that it holds good only approximately. Yet it is remarkable how nearly it is fulfilled in the case of atmospheric air at widely different temperatures and densities. The curves of fig. 4 depart only insignificantly from straight lines. But none of them cuts the axis of abscissee at the point —273°—so often spoken of (by a curious confusion of ideas) as absolute zero —except, perhaps, those corresponding to very low densities ; the pressure of dense gas decreases far more rapidly than that. The constant-volume relation p= F (6) willbe perhaps more clearly expressed by introducing the pressure-coefficient B of expansion defined by the equation | p=poll + Be), po being the pressure exerted at 0° by the gas, when compressed to a density p=— (unit of p= density at 0° under atmospheric pressure). The values of $6 are as follows :— | p= 20. 40. | 60. | 80. 100. | 120. 0. 100,000 x B. +100 386 | 406 426 447 — 785) 387 409 431 452 474 496 —103°5| 389 412 435 457 480 501 — 130 392 416 439 462 484 505 — 140 394 420 444 467 490 513. —145 396 424 449 472 495 517 The pressure coefficient does not vary much through a range of 245°, provided the density be kept constant. An increase of density causes it to augment rapidly. In con- trast with the tortuous curves representing the coefficient a, those of @ form a narrow nearly straight bundle, con- verging approximately to one point, namely, @=0°00367 for p— 14, From what has been just said, it follows that equation (3) is not suitable for calculating ¢,. I preferred to Thermodynamic Properties of Air. 29 use for that purpose the relation (st) C= Cp + 18'714 LOFF Op Ov z. e. to obtain the values of the specific heat at constant volume by means of those of cp already calculated. To simplify the calculation, put pu=7; then it follows that >) CDE ae ov on a (30) = 35), Op : The values of ry; will be found easily by the preceding therefore G@—G—18- 714 section ; those of oa can be obtained by graphical differen- tiation on the diagram of compressibility (Part I., pl. 1i.). The necessary data and the results of this calculation are collected in the following tables :— O=—140, t=1383. v. D. Cp- oF. or. Cy. 2. a nee 4-668 | 0-305 | 0:0392 |—0-:0055] 0-219 | 1:39 = ee 8:87 | 0-385 | 0-083 |—0-0055] 0:278 | 1:38 = les | 1265 | 0-464 | 01363 |—0:0055] 0322 | 144 ao 19:29 | 0624 | 0:239 |—0:0059] 0-483 | 1:44 2: Gtk 22:08 | 0703 | 0306 |—0:0066| 0-457 | 1°54 ples 26-74 | 0-859 | 0-435 |—0-0078| 0-501 | 1:70 ...| 80°35 | 1:021 | 0539 |—0-0104] 0535 | 1-91 30 A. W. Witkowski on the 6@=—135, t=138. v. p- Cp. a of. Cv. 2. ae 495 | 0-281 | 0038 |—0-0051! 0200 | 1-41 a bt se 926 | 0330 | 0-082 |—0-0051| 0227 | 1-45 = ae 13:29 | 0382 | 0131 |—0-0051| 0-254 | 1:50 = ras 20:35 | 0-490 | 0-234 |—0-0055| 0313 | 1:56 = ie 23-40 | 0546 | 0-295 |—0:0054| 0:334 | 164 = ace 28-74 | 0657 | 0-415 |—0-0086| 0361 | 1°82 1 || 3290 | 0-785 | 0530 |—0:0080] 0388 | 202 100 @= 130, Fe v. Dp. Cp. or on. Cv. = a - 5-055 | 0-265 | 00385 |—0:0043] 0-183 | 1-45 = pact: 9-71 | 0299 | 0-081 |—0-0043] 0201 | 1-49 = or 1400 | 0337 | 0-1276 |—0-:0043| 0-220 | 1-53 = Ree 21°65 | 0-416 | 02275 |—0:0045| 0-259 | 1-61 5 ae 25-08 | 0-458 | 0-287 |—00047) 0-270 | 1-70 = ns 31:03 | 0556 | 0-400 |—0-0056) 0306 | 1:82 0366 | 1:89 1...) 35:90 | 0694 | 0521 |—0-0062 100 Thermodynamic Properties of Air. 31 6=—103°5, t=169°5. OP 07 op Us : Cpe ——. es Go: on P Pp 30 Op 4 Cy 1 Patiget “aye De rue io" 6:065 0:249 0:0376 |—0:0027 1173 1:44 1 2 ae 11°82 0-264 0-077 |—0:0027| 0-180 1:47 ae 17-28 0:278 0-121 |—0:0027| 0-181 1-54 30 - shee 27-40 | 0:305 | 0-213 |—0-:0027| 0-186 | 1:64 = yer 3210 | 0320 | 0265 |—0-0028] 0185 | 1-73 = ee 40°88. | 0345 | 0-364 |—0-0027| 0-189 | 1:83 = ...| 4875 | 0871 | 0-491 |—0:0027| 0-172 | 2-16 @= —78'°5, #=194°5 v p Cp. or ae Cy - = “eo 7-005 | 0-246 | 0037 |—0-0019| 0-174 | 1:42 = ie 13-76 | 0-256 | 0-076 |—0-0019| 0-177 | 1-45 = 20:30 | 0-266 | 0-118 |—0-0018) 0-178 | 1:50 = a 3275 | 0-286 | 0-208 |-00018| O-181 | 1:58 = ee 38°65 | 0-295 | 0257 |-0:0017) 0-180 | 1-64 = et 5006 | 0316 | 0354 |—0-0016| 0-187 | 1-69 = __| 60°80 | 0:389 | 0:473 |—0-0016) 0-184 | 1:84 32 A. W. Witkowski on the d= —35, 1=238. | 1 | OP o7 | Cp Uv. E Cy. an —— - =e : rely OP | 2 ——}——— 5 ESN | oo 8-640 | 0-242 | 0-037 |—0-0010! 0-171 | 1-42 1 oo 1712 | 0-248 | 0-075 |—0-0009) 0-174 | 1:43 =~ 25-44 | 0:255 | 0-116 |—0-0009| o-174 | 1-46 = coe 41-74 | 0-270 | 0-204 |—0-:0008! 0-178 | 1:52 Oo = as 49°70 | 0-278 | 0-250 |—0:0007! o-181 | 1:54 Seta 65°50 | 0294 | 0-342 eee 0-190 | 1:55 30 ae 81:00 | 0-310 | 0-455 |—0-0005! 0-190 | 1:63 100 | 6=0, t=273 v. Dp. Cp. oP | Oo”. | Cy. oe rely OP Cy een eee ae Teena 9°949 0-241 0:037 —0-00051 | 0-°170 | 1-42 1 Tee 19:80 | 0-245 | 0-075 |- 000051! 0-172 | 1:43 a wee 29°54 | 0250 | 0115 |-0:00050 0-178 | 144 ee 48-78 | 0-259 | 0-203 |—0:00036) 0-171 | 1-52 50 | = 58°33 | 0-264 | 0-244 |—0:00025| 0-175 | 151 oe: 1 77-52 | 0272 | 0-342 |—0-00010! 0-175 | 1:56 ao | ni 96-80 | 0-282 | 0-446 lo 0177 | 1-60 100 ° | § 15. These results prove conclusively that the specitic heat at constant volume is a variable quantity. For increasing pressure the quantity ¢, increases at all temperatures, the more so the lower the temperature. corresponding isothermals converge approximately to the value 0°169, which is the specific heat of air of ordinary density. For small pressures the Thermodynanuc Properties of Air. 33 To obtain a graphical representation of the variations of c, I constructed isothermals of that quantity, considering it at first as a function of the density 2 . These lines are curves, turning their concave sides to the axis of abscisse. After- wards I made the remark that a far simpler law results when ¢, is considered as a function of the pressure p. As shown in fig. 5 the isothermals of c drawn on that supposition are Fig. 5, very nearly straight lines. This means that the increments of the specific heat at constant volume are proportional to the increments of pressure caused by increased density, tempera- ture being kept constant. This empirical relation holds at all temperatures between 0° and — 140°, and for all densities up to the hundredfold of the ordinary density. According to this diagram it is possible to express the values of c» between the just mentioned limits by the following linear equations :— Phil. Mag. 8. 5. Vol. 42. No. 254. July 1896. D 34. A. W. Witkowski on the 6=—140°, ¢,=0°1694+0:0135 (p—1), = —135°, ¢,=0°169+0-00722 (p—1), 0=—130°, ¢,=0:169 +0:00432 (p—1), 6= —10375,¢ =0°169+0-00056 (p—1), 6=— 78°'°5,¢c,=0°169 +0:00038 (p—1), 0=— 35°, ¢ =0°169 +0°00024 (p—T), d= 08; ce, =0°169 + 000008 (p—1). As regards the fact of the specific heat at constant volume increasing with increasing pressure, these results are in perfect accord with the direct determinations of Proi. Joly. A numerical comparison cannot be made properly, because these experiments have been performed at higher temperatures (+50° in the mean). Yet the following result of Prof. Joly may be quoted (J. c. page 99). The specific heat at constant volume of compressed air, of absolute density =0 0205 (which corresponds to a pressure of about 19:51 atmospheres), has been found =0°1721 ; from the same experiments it is con- cluded, that the value of c, under atmospheric pressure would be 0°17154. From these numbers there results an increase of cp, per atmosphere = (0°1721—0°17154) : 18°51=0-00008. Considering the difference of temperatures, this agrees well with my own results. Prof. Joly has also investigated the influence of the tempera- ture on the specific heat ¢, of compressed gases. For carbonic acid of absolute density 0°124 he finds c,=0°1971 at +50°, and ¢c,=0°1894 at + 90°; this means an increase of specific heat at low temperatures. He remarks also, that under small pressures the intluence of the temperature is quite insensible. All these conclusions are in perfect agreement with what has been said above with regard to the specific heat of air. § 16. By means of the results arrived at in § 14 we may now calculate the ratio k= ~ of the two specific heats; the values of & are given in the tables of § 14 in the last column. The general features of the variations of & will be best under- stood if we consider & as a function of the temperature, at constant volume, or at constant density. The corresponding curves are shown in fig. 6. With regard to the variability of k our knowledge is ex- ceedingly scanty. ‘The only fact known till now in this respect Thermodynamic Properties of Air. 39 is the experimental result of Wiillner, that the ratio k increases slightly with decreasing temperature (from 1:40289 at + 100° to 1°40526 at 0°, for air of ordinary density). An increase of z eee nes see Aes So Le bee lel IC % \-F aed 7 Be 1 ee a ene ie ee Se | f this kind is also shown by the curves of fig. 6. But, more- over, it follows, that with decreasing temperature & reaches a maximum value, which is followed by an abrupt fall. At all densities for which & has been calculated the maximum of D2 36 Thermodynamic Properties of Air. k corresponds to a temperature of about —120°. At ordinary temperatures the temperature-variations of k are exceedingly minute, for all degrees of condensation of the gas. At temperatures approaching the critical the increments of the ratio are the more marked the greater the density ; in the critical state & is infinite. With the aid of the diagram (fig. 6) the following table of values of cp : c, has been prepared :— a= 10 20. 30 50. 60. 80. 100. | 0. Values of cp: Cy. @ | 142 | 148 | 1-44) 451 153 | 155 160 = 99 | 1-42 |. 1-43 | 145 1 P51 153 | 1:55 161 249 | 1:42 | 1-43) 1-46 BS Pe aeons 1-65 S60 42 — 144 AG) clases 158 | 161 1-72 | — g0 | 142 | 145 | 1:50 | 158 | 1:64 <) deouamneee 00 W464 47 sae aes 1-71 1:30 | 2-10 —120 | 1°45 149° | 156 | 1:67") ae79: |e —140 | 1:38 1-41 1-46 150 | 1:54 | 1-70 | 1-80 Although the general course of the curves of & is very clearly marked, yet some irregularities manifest themselves in the diagram of fig. 6, chiefly at the highest and lowest tempera- tures, where the graphical calculation has been also less certain. I have not attempted to correct them arbitrarily, but I drew the curves as near as possible along the calculated points (marked on the diagram by dots). § 17. In concluding I wish to state expressly that the absolute numerical values of the several thermodynamic quantities given in §§ 12, 14, and 16, being obtained by a graphical method of calculation, cannot claim a degree of exactness comparable with that of direct experimental results: Notwithstanding this I considered it useful to spare neither time nor trouble to obtain them, in order to throw some light on these important and wholly unexplored relations. : During the preparation of the manuscript of the present paper I became acquainted with a memoir of Ser. Silvio Lussano (Nuovo Cimento, 1894, ser. iii. tom. xxxvi. pp. 1, 70, 130 ; 1895, ser. 11. tom. i1., p. 8327; “ Sul calore specifico dei gas”) on the influence of pressure and temperature on the specific heat of gases at constant pressure. The results of Sgr. Lussano, being obtained at higher temperatures, are not Melting-points of Aluminium, Silver, Gold, Copper, §c. 37 directly comparable with mine. As regards the influence of pressure Ser. Lussano finds, in the limits of pressures em- ployed, an increase of ¢, with increasing pressure ; but the influence of the temperature is just contrary to that which I have found at low temperatures. It cannot be doubted that at sufficiently low temperatures the specific heat c, increases with decreasing temperature, since in the critical state its value is positive infinity. This point must therefore be reserved for further researches, the more so, as the increase of c, with increasing temperature, at higher temperatures, has been proved long ago in some gases (carbon dioxide &c.) without any doubt. Physical Laboratory of the Yaghellonian University, Cracow, November, 1895. Il. Afelting-points of Aluminium, Silver, Gold, Copper, and Platinum. ByS.W. Hotman, with R. R. Lawrence and L. Barr*. HE following melting-points are offered as provisional only, but with the belief that they are more reliable than previous data. The absolute values depend in part upon the assumption of 1072° C. as the melting-point of pure gold, the recent determination of Holborn and Wien at the Reichs- anstalt. Should that datum, however, be shown to require revision, the validity of the present measurements would not be impaired, but new values of the melting-points could be readily computed from them which would be consistent with the better value for gold. Al. Ag. Au. Cu. Pt: 60° SOs tee (LO G2—-C. | 1095° 1760° Assumed. The Pure Metals used were of a high degree of fineness, except unfortunately the platinum. The gold contained less than 0-01 per cent. total impurities, these being, if any, probably minute traces of silver and pla- tinum. It was obtained as part of a specially prepared lot from the United States Assay Office in New York through the courtesy of Professor H. G. Torrey, upon whose authority the above statement is made. The purity was at least as great as the best “proof” metal used at the United States or London mints. * From an advance proof of the Proceedings of the American Academy vol. xxxi. (n. s. xxiii.) p. 218, communicated by Prof. Holman, 38 . Messrs. Hohnan, Lawrence, and Barr on the The silver was from the same source and equally pure. The aluminium was manufactured and given by the Pitts- burg Reduction Company, of Pittsburg, Penn., and was stated by Mr. Alfred E. Hunt, President of the Company, to con- tain but 0°07 per cent. of impurity, consisting entirely of silicon. The platinum was the ordinary platinum wire supplied by Carpentier, of Paris, with his Le Chatelier thermo-electric pyrometers. It presumably contained 0°5 per cent. or more of impurity. The copper was electrolytically produced, and was from the Lake Superior region. It was kindly given by Mr. Maurice B. Patch, of the Buffalo Smelting Company, Buffalo, N.Y., who stated that it showed by analysis 99°99 + per cent. _of Cu, and contained no Ag, As, or 8, and only 0°0002 per cent. of Fe. The Less Pure Metals —Partly for the purpose of testing the effect of impurities, other samples of gold and copper were employed with the results stated later. These were :-— Dentists’ Gold.—This was a gold-foil employed by dentists, purchased as being of good quality. Ingot Copper.—This was also from Mr. Patch, of the Buffalo Smelting Company, who gave its analysis as :— Cte 4) th ye oe SE ee AD Song onat ae eee mn ees Ass irs Yi iicesteeeme ay. mane dale ae eer ee ct Be: a Sie Rae eens Oe is tm eee ae es ali 100-001 This was the company’s “ regular run” of copper. Commercial Electrolytic Copper.—A sample of commercial electrolytic rolled sheet copper, furnished by a friend, and not assumed to be of unusual purity. It was probably Montana copper. Commercial Hard-drawn Copper Wire-—This was from a lot purchased for electrical testing purposes, which showed a — specific resistance of 0°1440 international ohm per metre- gram, or an electrical conductivity of about 98-3 per cent. referred to Matthiessen’s copper. Methods and Apparatus.—The method consists in measuring _the thermal electromotive force of a couple ‘composed of one wire of platinum and the other of a-10-per-cent. rhodo- platinum alloy. One junction is immersed in the melting or Melting-points of Aluminium, Silver, Gold, Copper, Sc. 39 solidifying metal, and the other surrounded by ice. The wire was that furnished by Carpentier, of Paris (through Queen & Co., of Philadelphia), with the Le Chatelier pyrometer. The E.M.F. was measured in microvolts (international) by the Poggendorff null method modified for rapid and con- venient “working. The disposition of apparatus is shown in fig. 1. Bisa battery of sufficiently steady E.M.F. (A single Fie. 1. Samson-Leclanché cell was entirely satisfactory.) In direct circuit with this were two water rheostats, W, in series; an ammeter, A, which was a Weston voltmeter (No. 395) with the calibrating coil only in use ; and a manganine wire resist- ance, a,b, c,d, divided into sections, each of accurately known resistance. T is the thermo-couple connected through a sen- sitive galvanometer, G, and key to any desired sections of the coil a, b, c,d. The water rheostats were of about 100 okms and 8 ohms respectively, and the vertical motion of their plungers thus served to give a coarse and fine adjustment to the resistance in the circuit. The current could thus be promptly and closely adjusted. The voltmeter was one of the type having a “calibrating coil;”” that is, one having a connexion by means of which the nsual high resistance series eoil could be cut out, leaving its resistance about 117 ohms. Any of the Weston voltmeters with a special connexion made to effect that res: lt would answer equally well. The volt- meter was preferred to a mil-ammeter as probably more reliable. The instrament was carefully and repeatedly cali- brated throughout its scale by an application of the Poggen- dorff method, measuring by the Clark cell the drop of potential ina known resistance through which a current was passing in 40 Messrs. Holman, Lawrence, and Barr on the series with the ammeter, and at the same instant reading the ammeter. The calibrations at different times were checked at the same point, with an average deviation of only a few hundredths of one per cent. A test for temperature error showed a change of but O°1 per cent. for a change of 15° C.; so that, as the temperature during the work was constant within a few degrees, no correction was needed. The manganine coil, fig. 2, consisted of about 16 feet of No. 20 wire, had a total resistance Fie. 2. of about 8°8 ohms, and was divided into nine sections by copper po- tential wires leading into different points along the coil. These sec- tions were so designed that, by suitably shiftmg the connexions along a, b, ce, &c., any thermal E.M.F. which was to be measured could be balanced by a current which would deflect the ammeter to a point between 90 and 140 di- visions (readable to tenths)—cor- responding to currents from 0-006 to 0:009 ampere roughly. The coil was immersed directly in kero- sene, and as its temperature-coefficient was but 0:001 per 1°C., the correction became very small. The relation and actual resistance (international ohms) of the whole coil and its several sections were repeatedly determined against a standard ohm by the differential galvanometer, and checked by a modified Wheatstone-bridge arrangement. These data were reliable probably well within 0 05 per cent. throughout. In the thermo-couple circuit, the sensitiveness necessary in the galvanometer to give the smallest E.M.F. to 0-1 per cent. was easily computed to be only about 7°7.10° (mm. defi. at 1 m. per ampere ord/c). The instrument as actually used exceeded this requirement, averaging about5.10". Its resist- ance, all in series, was 14°3 ohms. The cold junction ¢ of the thermo-couple was fused together in an oxyhydrogen flame. The wires, insulated from each other by having one strung through a very fine glass tube, were run down another tube of about 4 inch inside diameter and 8 or 10 inches long. This tube was fused together at the bottom and top, as well as at some intermediate points, and when in use was always packed in a double vessel of cracked ice, as shown in fig. 3. The intermediate junctions from which the copper leads ei i Melting-points of Aluminium, Silver, Gold, Copper, we 41 went off to galvanometer and key were soldered. They were kept at an equal temperature by the device of enclosing them in a stoppered glass tube, which was packed with hair-felt into a one-inch hole in a five-inch cube of cast iron. ‘This arrangement was entirely satisfactory, but seems to possess no mnaterial advantage over making the junction of the copper leads with the Pt and Pt-Rh serve as the cold junction, and immersing this in ice as in fig. 3, except that the latter makes a rather more bulky mass to insert in the ice. The wires were also fused together at the hot junction except when this was unnecessary on account of their being immersed in metal. It may be noted here that, as a null method was employed, the total resistance of the thermal circuit, or any variation in it, was without effect other than a corresponding change in sensitiveness. As the hot junction was to be immersed in vapour of sulphur as one of the known temperatures, the following apparatus was designed for this purpose. It is substantially the sulphur boiling-point apparatus of Griffiths, and is shown in fig. 4. Pia 3. Fie. 4. A glass tube, A, similar to the Victor Meyer vapour-density tube, 16 inches long and with a two-inch bulb, was provided with an asbestos jacket and hood, B, B, The upper few inches of the tube were wound with a spiral wire spring, 8, which rendered this part efficient as a condenser. The top was closed with a layer of asbestos, Two overlapping diaphragms of asbestos were inserted in the tube at Dand E. ‘The couple passed downward through a glass tube to the asbestos tubular 42. Messrs. Holman, Lawrence, and Barr on the hood, ©, which served as an umbrella to shed the dripping cooler sulphur, and as a radiation-screen. The hood, how- ever, had openings top and bottom for the free circulation of the vapour. An asbestos diaphragm, H, upon which the bulb rested, reduced the chances of superheating. For the melting metals, after trial of several devices, the one shown in fig. 5 (of exactly half size) was settled upon as Fig. 5. oe proving very satisfactory. The crucible, C (usually of fire- clay), is supported by clay blocks in the double-walled fire- clay furnace, F. A carbon block, H, channelled to fit the crucible, forms its cover, and a carbon diaphragm, D, inside the crucible serves to support some powdered carbon shown by the dotted mass. The object of these carbon parts was to prevent oxidation of molten metals, and they proved very effective in the case of aluminium, silver, and copper. GG was an asbestos diaphragm supporting a non-conducting layer of fibrous asbestos, AA. The temperature was controlled by the blast-lamp B. The clay crucible was one inch in diameter outside, and the amount of metal employed ranged from 11 grams (gold) to 385 grams (copper). Larger amounts might be advantageous, but with 30 to 385 grams it was easily possible to obtain a constant indication for five minutes during the melting or solidifying of copper. No difficulty whatever Melting-points of Aluminium, Silver, Gold, Copper, §c. 43 was experienced with this arrangement with silver, gold, or copper. Withaluminium, however, a peculiar action ‘occurred, the cause of which in the time available for investigation could not be determined beyond doubt. The phenomenon was that after a few minutes of constant temperature at the melting-point, the indication of the thermo-couple fell off with increasing rapidity, On w ithdrawing the couple, cleaning it, or clipping it off and restoring it to place, the melting metal meanwhile being untouched, the indications returned fo their original high value. The apparent explanation was the for- mation of a 1 slag between the wires; but this was not entirely satisfactory. ‘The use of a plumbago crucible in place of the clay and an entirely fresh lot of aluminium did not remove the phenomenon, and gave the same initial readings, which, it could not be doubted, were the ones corresponding to the melting-point. The fusion of the aluminium was, however, the least sharply defined of all the metals used. The fusion of platinum was, of course, differently effected. For this the two wires of the couple were laid close together on a piece of lime. An oxyhydrogen flame was then directed upon their ends and the platinum fused into a globule which with care could be made to travel slowly up the wire. There was no difficulty in obtaining steady temperatures for a sufh- cient period to make the necessary readings, and check results to 0-1 per cent. were obtained on different days. The galvanometer, keys, coils, and all junctions of dis- similar metals, were, so far as possible, covered with boxes of wood, pasteboard, or asbestos to maintain uniformity of temperature, and thus miniinize local thermo-electric disturb- ances. With this precaution, no sensible trouble from that source was experienced. The procedure is as follows :—To take the observation for vapour of sulphur, for instance, the hot and cold junctions are exposed as described. After a sufficient time the main circuit is closed, the thermal circuit is connected to a suitable part of a, b, c, d, and the rheostats W are adjusted until on pressing the key no deflexion occurs in the galvanometer G. At this instant A is read, which gives the current ¢ in the main circuit. The adjustment is disturbed and remade a number of times, and the resulting readings should check to the nearest tenth of a division of A, provided the metal has reached a steady state of temperature. By this adjustment the drop of potential er due to the current ¢ amperes in the part 7 ohms of the resistance a, 0, ¢, d, spanned by the thermal circuit is made equal to the total re- sultant .M.F. in the thermal circuit. The latter, which will be 44 Messrs. Holman, Lawrence, and Barr on the denoted by =*e or XGe, is the algebraic sum of the thermal H}.M.F. proper of the junctions, te the Thomson E.M.F. in the wires, and of any “stray” or local thermal E.M.F. in the circuit. The last was found to be negligible throughout the work. To observe the melting-point, the furnace containing the metal is heated more or less rapidly until the melting-point is approached. The blast-lamp is then adjusted to give a slowly rising temperature. The thermal circuit, w ith the couple previously fused into the metal, is connected to a suitable section of a, b, c, d. The rheostats are continually adjusted for zero deflexions of the galvanometer G, and the corre- sponding readings of A are taken. These will show gradually increasing values; but the rise will presently be interrupted by a series of constant readings, after which the readings will again steadily increase. This period of constant, or nearly constant, readings of A is that in which the latent heat of fusion is being absorbed, and its duration is frequently several minutes. The temper ature at that time is, of course, that of the melting-point. The reverse process, starting w ith the metal ina molten state and cooling it oradually, shows a similar period of selidification. No difference was discovered between the ascending and descending readings when a sufficient amount of the ‘metal and a slow rate of ‘heating and cooliig were employed. With small amounts the steady reading was more or less masked by phenomena which were clearly due to inequality in distri- bution of temperature throughout the mass of mixed liquid and solid metal. In the case of aluminium, however, some- thing more than this irregularity was observed, as elsewhere stated, but the time at command did not permit a study beyond the point of satisfying ourselves that the point observed was unquestionably the true melting-point. This work was done chiefly as the thesis work of Messrs. Lawrence and Barr. The efficient assistance of Mr. C. L. Norton contributed materially to its progress and success The computation of temper atures t trom the observed electro- motive forces } ¢ involves a knowledge of the function con- necting the two, 7. e. of the function se=ft), or. t= (Se) This problem has been elsewhere discussed by one of the authors of this paper *. In that article two interpolation formulz were developed. They were respectively of the following forms, applying to the %* Phil. Mag. xli. p. 465, Melting-points of Aluminium, Silver, Gold, Copper, §c. 45 case where one junction of the couple is kept at 0° C., and the other is at any other temperature ¢ C., or Tr=¢+ 273° absolute; m and n are constants, different for the two expressions; >i e denotes the resultant thermal E.M.F. of the circuit, viz. that which is the object of direct measurement. The first, called the exponential equation, is yye=mr—B (where B=mr, =m x 273"). The second expression, called the logarithmic equation, is t n t yea, of low >,e=—n log t + log mz. Both formule have been applied to the data of the present investigation given in Table 1., with results shown below. The Avenarius formula has also been applied for purposes of comparison. a To evaluate the constants m and n of the exponential equation (for method, consult the paper referred to) it is necessary to have values of je at three known temperatures. Of these, however, one may be 3,¢=0, at T= 278°, 2, e. with both junctions in ice. It therefore remains to fix upon two other temperatures between which to interpolate, or, in other words, two other temperatures which shall be assumed as known. In looking over the ground, it seemed that the boiling-point of sulphur, being so high and so accurately determined by Callendar and Griffiths*, 444-53 + 0°082(H —760), was preeminently one of these points. The other must be much higher, and the melting-point of pure gold seemed to be almost, if not quite, the only one upon which reliance could be placed. Apart from freedom from oxidation and its conveniently high point of fusion, gold seemed the more suitable because its melting-point had recently been so carefully measured by Holborn and Wien, and because the metal could be obtained of the necessary purity. Add to these considerations the fact that its melting-point in a state of at least fairly high purity has been measured by more experimenters than that of any other high melting metal, so that it serves as an excellent connecting link between their work, and we have claims which no other substances can at present offer. The fusion-point of gold was therefore chosen as the second reference or calibration temperature. As to the figure to be assumed as the melting- * Phil. Trans, clxxxii. pp. 119, 157 (1891). 46 Messrs. Holman, Lawrence, and Barr on the point of gold, there is room for differences of opinion. The claims of the work of Holborn and Wien, supported to some extent by considerations advanced by Barus*, lend much weight to the conclusion that Violle’s value of 1035° is con- siderably too low. Granting this, and in the absence of sufficient basis for the assignment of weights to the work of divers other investigators, the simplest and best step seemed to be to adopt provisionally, without modification, Holborn and Wien’s value, 1072°. These two points settled upon, the constants m and n could be computed as elsewhere described, and the equation trans- posed to deduce other values of ¢ from observed values of S(e. Representing mtj by 8, a constant, the equation for the tem- perature as a function of S}e takes the form ef SFT a) (ss af 228 _oi30, m which is, of course, easily solved by logarithms. The data given in Table I. yield the values m = 0°3901, n = 1:488, 8 = 1645, in international microvolts and degrees Centigrade, so that Ste=0-3901 71645, or t= 14884 / 20° t 1645 _ 03901 From these the temperatures of column 6 have been com- puted. The constants of the logarithmic formula have been com- puted from the same data for sulphur and gold, the method being sufficiently obvious. The equation becomes Lie= 249650 1, The corresponding melting- and boiling-points are given in Table I. column 7. Substitution of the same data in the Avenarius equation yields dhe=(th—le) {9°7335 + 00048449 (t, + t,)}. The corresponding melting- and boiling-points are given in column 5. Provisional Values of Melting-points. In the paper referred to it was shown, Ist, that the loga- rithmic expression fitted the Barus comparisons of the irido- platinum couple with the air thermometer within the limits 400° to 1200° C. with no sensible systematic error; 2nd, that * Am, Jour. Sci. xlviii. p. 336, Melting-points of Aluminium, Silver, Gold, Copper, Se. 47 the exponential equation similarly fitted the Holborn and Wien comparison of the rhodo-platinum couple with the air thermo- meter within the same limits; 3rd, that the exponential equation diverged systematically, although slightly, from the Barus data, and the logarithmic from the Holborn and Wien data, by about equal and opposite amounts both inside and outside these limits, but much more markedly between 0° and 400° than at higher points. TABLE I. Melting-points. [ | | Temperatures. De Date. | Subst. icru- ; 7 ae chy Assumed| From From | From tet, | Provis- as Cor- | Aven. | Expon. |Log Eq.| — 5 ional Beck. NetideGac \- gute. ti. Values. 3-2 |H,O | 8853 | 99-64 4-10 |H,O | 890-4 | 10057 888-1 |{100-10}} 874] 9t7 | 1073 | 995 ©,,H,| 2213 | 2183 3-23 |C,,H,| 2224 | 218-9 C,,H.| 2216 | 218-2 9218 |[218°5] | 2066 | 211-4 | 2224 | 2169 3-? |S 5287 | 444°7 3-22 |S 5289 | 445:2 3-29 |S 5287 | 4445 5288 | [444-8] 4-24|Cu | 16463 1095- 1095:0 | 1096-5 | 1095-5 1095 4-99 |Au | 16002 | [lo72]| — se = = | (1072) 4-299 | Ae | 14093 - 975: 972 | 969: | 9705 | 970 5-2/3) Pt | 30313 — | 1695 | 1735: | 1783 | 1759 | 1760 ae et |) e638" 665°5 | 6625 | 656-2 | 6594 | 660 Aven. B(¢=(t,—t,) {9°7335 +0:0048449(¢,+¢,)}. Exp. 2fe=0-3901 7/185 — 1645. Log. )e=249655 726. Inspection of columns 6 and 7, Table I., will show that the computed boiling-points of water and napthalin by the ex- ponential and logarithmic equations depart widely from the known temperatures in opposite directions, by about equal amounts, and in the directions according with the departures from the Barus and Holborn and Wien data. Also, that the differences between the computed melting-points intermediate 48 Messrs. Holman, Lawrence, and Barr on the between sulphur and gold differ but slightly by the two formule, thus confirming the former conclusions. It is obvious, therefore, that although either of the two formule would yield fairly good interpolations for Al, Ag, and Cu, yet that a mean between the two would probably quite nearly offset against each other the systematic errors of the respective equations. This is also true in the dangerous process of extrapolation for the platinum melting-point, where the chances of error in the result seem to be probably very much reduced by averaging. The means of the melting- points computed by the exponential and logarithmic equations are, therefore, regarded as the nearest available approxima- tions, and the round numbers of column 9 are adopted as provisional values to represent the results of the work. Comparison of the results of the Avenarius formula, column 5, will show that they depart widely from the others in the direction which would have been anticipated from the conclusions of the previous paper, thus further strengthening those inferences. In addition to the foregoing, the melting-points of three other samples of copper and one other of gold were measured. The gold was dentists’ gold “ foil,’ purchased in Boston. This is usuaily classed as “‘ very nearly pure,” but its analysis was not known. No special interest, therefore, attaches to it beyond the indication that it gives of the sign and order of magnitude of the error (about —4°) which would be introduced by the ase of such gold in the calibration of the Le Chatelier pyrometer, or in similar ways*. ‘The melting-point was found to be 1068°. The four coppers yielded the appended results :— TABLE II. Be Melting- | Purity of microvolts.| poits, C.| Metal, Description. 0 IK 16463 1095-0 99°99+ | Electrolytic. Probably Lake Superior copper, Buffalo Smelting Co. 16448 10943 99:83 Ordinary ingot. Same source. 16456 10947 Unknown. | Electrolytic. Probably from Montana. 16446 10942 | Unknown.| Commercial hard drawn wire from Washburn and Moen Co. Sp. Elect. Conductivity (referred to Matthiessen value) 98°3 per cent. * Holman, Calibration of the Le Chatelier Thermo-electric Pyrometer. See Proceedings of the American Academy, xxxl. (.s, xxiil.), p. 234. Meliing-points of Aluminium, Silver, Gold, Copper, &c. 49 The concordance of these results on various coppers, together with the completely satisfactory behaviour of the metal in fusion, and the ease and cheapness of obtaining the metal of a very high grade of fineness, suggest the decided availability of copper in a direct study of high temperatures or melting- points by the gas-thermometer. A large mass of the metal could be employed, and a constant and uniform temperature for a protracted period thus secured for the bulb of the gas-thermometer, or for other apparatus immersed in the molten or solidifying material. There are unfortunately too few substances which fulfil even these requirements. An added merit lies in the nearness to the gold melting-point, enabling the two to be satisfactorily connected by some means of relative measurement. It also appears that the use of good commercial copper would introduce sensibly less error (3° less) into the calibra- tion of the Le Chatelier pyrometer than the use of the ‘“‘dentists’ gold”’ above tested, which is as good metal as would readily be obtained in the market by most observers. Reliability of the Results —The points involved are :— Instrumental errors. Purity of the metal. Was the observed point the real melting-point ? Validity of the interpolation equation. Error in the assumed melting-point of gold and boiling- point of sulphur. The investigation was planned and the apparatus arranged with the intention of reducing the combined instrumental errors below one-tenth of one per cent. in the measurement of Le above 200° C. ‘Tests, check measurements, and a dis- cussion of the sources of error, unnecessary to detail here, have given satisfactory demonstration that an even higher accuracy than this was attained. So far, therefore, as constant or variable instrumental errors are concerned, it is believed that no error beyond 0°5 to 1° C. exists in the results, while probably this estimate is large. The error from impurities must have been exceptionally small, as the analysis of the metals indicates. Some impurities from alloying with the platinum and rhodium of the thermo- couple must have entered during the experimenting, but as results at different stages of the work checked those obtained upon the first use of the metal, and as renewals of the metal made no difference in readings beyond the limits of other variations (about 5 parts in 10,000), the error from this source must have been negligible. In the case of platinum the metal at command was un- Phil. Mag. 8. 5. Vol. 42. No. 254. July 1896. 50 Messrs. Holman, Lawrence, and Barr on the fortunately not of known composition, nor was it possible at the time to obtain any whose purity was known. An analysis of the wire used may perhaps be obtained later, and it is hoped to carry out further measurements with the better platinum now obtainable through the recent advances made in its manufacture in Germany and England. | The aluminium was of a very high grade, but it is thought that still better may be obtained, and the peculiar occurrence attending its melting-point measurements should be further investigated. , The actual effect of the small impurities cannot be numeric- ally estimated, but must have been inconsiderable except for platinum, where the error probably has the positive sign. As to the third point, there was no reasonable doubt left in the minds of the observers that the observed temperatures were sensibly the melting-points. Except as noted for aluminium, the readings with rising and falling temperatures did not exceed about one partin one thousand. Also entirely independent observations on separate days, and with renewals of the metals in some cases, were equally concordant. The average difference was much less than the error of reading the ammeter. As an example of the concordance, and at the same time as showing the homogeneity of the thermo wire, three calibrations in sulphur are quoted in Table ILI. Tas eE ITI. Computed : Date. Le, microvolts. | Temperature of 4 none edie Sulphur. : March ?.....c00+ 5287 444-73 5290 March 22 ......... 5289 44518 5287 March 29 ......... 5287 444-53 5293 Between these observations a considerable length of the wires was necessarily clipped off. Reduced to a common temperature of 445°, the maximum difference is but six micro- volts in 5290, or 0-11 per cent., while the average deviation of a single observation is but 0°02 microvolt, or 0:04 per cent., and of the mean but 0°02/ 73 =0°012 microvolt, or 0024 per cent. At higher temperatures the discrepancy was even smaller. The validity of the interpolation formule has been already Melting-points of Aluminium, Silver, Gold, Copper, &c. 51 discussed. A statement of the extreme error which may have been introduced into the results by this source should, how- ever, be added. ‘This is believed to be for aluminium less than +29, for silver less than +2°, for copper less than +0°5°, and for platinum less than + 10°. Comparison with the temperatures computed by the Ave- narius equation shows errors by the latter to be about 1°5 times as great for water and naphthalin, and of the same signs. It is therefore much less reliable, especially for the platinum temperature, and no weight is attached to its results. Melting-points by various Authorities—A collection of these is given in Table IV. Hxcept in the case of the Barus data, the results are set down directly as given by their authors. A further discussion of these with reference to the purity of the metals used, and the characteristic errors of the methods employed, would doubtless prove instructive, and might partly remove or account for some of the apparent discrepancies,— a task which will perhaps be undertaken later. TABLE IV. Metals. Authority. Date. | Method. Ale) Agee Ae | Cue | (e) fe) le} Q [Els ges i bee 1895 | Th.-el. 660 | 970 | [1072]| 1095 MBM Sire snt0 2 ct cna wime'sc TOPO 1 Sp. EUG. ah. 4c 954 | 1035 | 1054 WiedeWUr: 22.5 s......000- 1884 | Sp. Ht. | ... 960} ... | 1100 Le Chatelier ............ ra Dineel. |) G3on\e 7 035) MaMlendar (26.4 50se00. 0 ine ee Sieh [945]| L037 | Erhard and Schertel...| ... ae ue 954 | 1075 Barus, by Log. Eq. *...| 1894 | Th.-el. | 641 | 985 | 1090 | 1095 by Kg 3 oc... re ae Sep 986 | 1091 | 1096 Holborn and Wien ...| 1892 | Th.-el. Bic 968 | 1072 | 1082 Tfean of independent absolute measure- ments, i.e. excluding H., L. & B.,| 641 | 964 | 1068 | 1083 Le C., and C. N.B.—Values in brackets [ |] are those assumed by the observers, and upon them their other values depend to a greater or less extent. Rogers Laboratory of Physics, Massachusetts Institute of Technology, Boston, October 1895. * See discussion by Holman, Phil. Mag. xli. p. 465. Hh 2 [ 52 ] Ill. A Further Examination of the Edison Effect in Glow Lamps. By J. A. ¥uemine, M.A., D.Sc., FERS. 2 fo fessor of Electrical Engineering in University Coliege, London*. §1. jae experiments described in this paper had for their object the further examination of an effect which can be produced in certain forms of electric incandescence lamps and to which attention was first drawn by Mr. Edison in 1884. This effect may be generally described as follows :—A carbon filament incandescence lamp having the ordinary horse-shoe loop carbon has a metallic plate placed in the exhausted bulb, the plate being carried on a platinum wire sealed through the globe, and fixed so as to stand up between the legs of the horse-shoe (see fig. 1). If the lamp is set in action at the Fig. 1. Fig. 2. usual incandescence by a continuous current of the proper strength, and a suitable sensitive galvanometer is connected between the insulated metal plate and the posztive terminal of the lamp, it will in general be found to indicate a current of some milliamperes flowing through it. The direction of this current is from the positive electrode of the lamp through the galvanometer to the insulated metal plate, or wire. When the same galvanometer is connected between the negative pole of the lamp and the middle plate, unless it is very sensitive, it indicates no current. This effect was very carefully examined * Communicated by the Physical Society: read March 27th, 1896. On the Edison Effect in Glow Lamps. 53 by Mr. W. H. Preece in 1885, and he subjected it to a systematic examination by the aid of a number of lamps having such metal plates placed in various positions*. By this observer a number of very interesting facts were col- lected, the result of which was to point out the general nature of the phenomenon. A sufficient number of new questions were, however, suggested by the information so acquired to invite further inquiry. Whilst confirming and re-examining the experimental results obtained by Mr. Preece, some facts that had previously escaped notice presented themselves, which it is the object of this paper to describe. § 2. The first experiments were made with a lamp of the form shown in fig. 2, similar to some used by Mr. Preece in his experiments. A metal plate, generally of aluminium, is supported on a platinum wire sealed through the bulb or glass receiver, the plate being so fixed that its plane is at right angles to the plane of the loop of the carbon, and as nearly as possible midway between the legs. The plate there- fore projects between the legs of the horse-shoe carbon, and the carbon conductur arches over it without touching it. The plate is entirely insulated from the carbon. The preliminary experiments with this normal type of middle-plate lamp consisted in determining the effective potential-difference between the third terminal and one or other of the two electrodes of the carbon filament when the lamp was subjected to varying steady electromotive forces sufficient to raise the temperature of the carbon from dull red to vivid incandescence, and in determining the magnitude of the current flowing in a circuit connecting the middle plate with one or other of the electrodes of the lamp. § 3. Haperiment 1.--An ordinary carbun filament electric lamp, having the horse-shoe shaped conductor, hada platinum plate (see fig. 3) about 25 centimetres long by 1°5 centi- metres wide welded to a platinum wire, sealed through the side of the bulb. The plate was so placed as to project between the legs of the carbon conductor, having its plane at right angles to the plane of the horse-shoe, and initially fixed about halfway between the two legs. ‘This lamp will be de- scribed in the subsequent paragraphs as Lamp No. 4. Under a steady electromotive force of 40 volts, this lamp took 3°7 amperes when working at the normal temperature corre- * “Qn a Peculiar Behaviour of Glow-Lamps when raised to High Incandescence,” by W. H. Preece, F.R.S. Proceedings of the Royal Society, 1885, p. 219. 5A Prof. J. A. Fleming on the sponding to about 3°5 watts per candle-power. When a milamperemeter having a resistance of 6372 ohms was joined bet ween the base P of the positive leg of the carbon (see fig. 4) and the middle plate M, a current was found passing through - the galvanometer from the terminal P to the plate M. This : Fig. 3. LOE, LAMP NO 4 AK ; TO BATTERY Fig. 4. current had a magnitude of about 3 milliamperes when the carbon was in the normal state of incandescence. If the milamperemeter was connected between the negative electrode of the lamp and the middle plate, no current per- ceptible by this galvanometer was found. On replacing the Edison Effect in Glow Lamps. 55 milamperemeter by a more sensitive Hlliott mirror galvano- meter (resistance 7142 ohms), it was found that a small current passed through it, when joined in between the negative electrode of the lamp and the middle plate, but that this current had a magnitude hardly exceeding ‘0001 of a milli- ampere when the lamp was at its normal incandescence. In order to avoid repetition, it may be here said that, unless otherwise stated, the terminal of the lamp in connexion with the positive pole of the working battery will be spoken of as the positive electrode of the lamp; that in connexion with the negative pole of the battery as the negative electrode. For brevity’s sake, the half of the carbon filament between the centre of the filament and the positive electrode will be called the positive leg, and the other half the negative leg. § 4. A preliminary series of experiments was made with lamp No. 4 by placing the lamp in a photometer and determining the watts per candle-power and the current taken by the lamp corresponding to various working electromotive forces, taken over the whole range of electromotive force from that necessary just to render the filament incandescent to the highest the lamp could with safety endure. In any subse- quent experiments, the simple measurement of the potential- difference between the electrodes of the lamp enabled the rate of dissipation of energy in the filament and the watts per candle-power to be deduced. It may here be remarked that in the preliminary experiments some difficulties arose from the occlusion of residual gas by the middle metal plate, but finally this was overcome, and the vacuum in these experi- mental bulbs made and preserved as perfect as in good ordinary commercial lamps. The following results were then obtained with this lamp No.4. The lamp was raised to various degrees of incandescence by varying the working volts by the aid of a rheostat in series with the lamp. The milamperemeter was employed to measure the effective potential-difference between the positive electrode of the lamp and the middle plate and then, tabulating against the working volts of the lamp the current in milliamperes flowing through the galvanometer, the potential-difference between the middle plate and the positive electrode of the lamp was calculated from these figures. The results are given in the table below (Table No. 1). 56 Prof. J. A. Fleming on the TasLeE No.1. Lame No. 4. Milamperemeter. Table showing the volts between the middle plate and the positive electrode, and the current flowing through a galvanometer of 6372 ohms resistance connecting them, taken for various working voltages of the lamp. Volts be- | Current in Voltoiee Current in Working | tween plate milli- Working evesn alee milli- voltsof and positive| amperes volts of |od eee amperes lamp. lamp elec- |through gal-|| lamp. Ae Bal! through gal- trode. vanometer. vanometer. 30 "54 "085 36 LOT 1°69 32 12 "190 37 127 2°01 32 5 1°6 20 38 149 2°36 30 2°8 “44 39 17-0 2°71 BSD. aged “74 40) 18°9 2°99 a4 5:3 “84 41 21-4 3°37 34°5 GL i 4? 23°4 Ee fi! 30 78 1°23 43 25:2 ode 44 26°8 4-25 The results given in table No. 1 are plotted in curve No. 1, in which horizontal abscissee represent to scale the working volts of the lamp and vertical ordinates the milliampere currents through the galvanometer. It will be seen that the curve representing the current from lamp electrode to plate takes a rather sharp turn upwards at a point corresponding to 33 working volts, and this occurs when the lamp is working at about 7°8 watts per candle-power. Beyond this point the curve is very approximately a straight line. Accordingly, at and beyond the volts at which the carbon filament becomes. fairly well incandescent, the effective potential-difference between the middle plate and the positive lamp electrode is very nearly a linear function of the lamp voltage ; and at the normal working volts, viz. 40 volts, this potential-difference between the middle plate and the positive electrode so deter-— mined is apparently about half that between the lamp terminals, the plate being nearly midway between the carbon legs. The results given in Table 1 are the mean of several obser- vations, but it was noticed that when the lamp was maintained at a steady voltage, the potential-difference between the middle plate and the positive electrode would often jump Edison Effect in Glow Lamps. 57 suddenly from one value to another. This effect renders it difficult to obtain the stable values of the plate and positive electrode potential-difference. Corresponding to any definite steady voltage on this lamp, the current may have one or other of two values, but not always permanently preserving TABLE No. 1.—CuRvE No. 1. nee Tee ee HEE ans Current through Galvanometer in Milliamperes. 2B So Skee BS) 400 c4oe 44 G48 Working Volts of Lamp. VERE ; a galvanometer deflexion indicating say 10 volts between the plate and positive electrode of the lamp will often slowly increase until after a few minutes it is 12 or 14 volts, yet all the time the working volts on the lamp are 58 Prof. J. A. Fleming on the remaining perfectly constant. It will then often suddenly jump perhaps to 22 volts, and then slowly decrease to 19 volts, or so. This tendency of the potential-difference between the middle plate and positive lamp electrode to jump from a low to a high value, or vice versdé, is most marked in lamps in which the plate is about half-way, and symmetrically placed, between the legs of the carbon. We shall speak of these two values as the high and low value of the current through the galvanometer, and defer until later a discussion of some other causes tending to make the current pass from a high to a low value or the reverse, as well as its possible explanation. In Table No. 2 are tabulated a set of observations on the same lamp No. 4, showing these double values which the potential- difference and current may have, and it may be here noted that in the previous Table No. 1, the higher values have been taken in those cases in which double values exist. Taste No. 2. Lamp No. 4. Milamperemeter. Table showing the multiple values of the potential-difference between the middle plate and positive electrode of the lamp corresponding to various given working voltages. Volts be- Current Volts be- Current, : tween the |through the tween the | through the Working |niddle plate] graded gal-|| Working |middle plate} graded gal- voltsiot Grad positive] vanometer || volts of the |and positive | vanometer the lamp. | electrode of| in milli- lamp. | electrode of} in milli- the lamp. | amperes. the lamp. | amperes. 30 6 095 39 4-3 “761 32 1-1 174 : 140 | 2-22 34 2°0 317 40 D1 809 35 2-6 412 e 18:1 | 2:87 36 3°2 D07 41 a3 841 37 3:9 618 184 | 2-91 38 43 682 42 6:4 10m s Ad 714 5 20°0 3°17 < 1HCOF 4] alee 43 6-2 -983 22°0 3°49 . These observations are plotted in Curve No. 2,in which the abscisse represent the working volts of the lamp and the Edison Effect in Glow Lamps. 59 ordinates the current in milliamperes flowing through the galvanometer connecting the positive electrode and the middle plate. It is seen that corresponding to any working pressure above 38 volts for this lamp, which is equivalent to 4:2 watts per candle-power, there are two possible values of the effective TaBLeE No. 2.—Curve No. 2. : oe Qe ee _ bow ial ac i rome ilk * att tt : i Pee eee i Current Pees Galvanometer in Pee Working Volts of Lamp. potential-difference between the middle plate and the positive electrode. As the working voltage of the lamp is gradually raised, the reading of the galvanometer inserted between the middle plate and positive electrode is also increased, but there is a great tendency to jump from a certain low value to a 60 Prof. J. A. Fleming on the higher one, and this occurs when the working pressure of the lamp is preserved steady. There is also an effect produced by the presence of a magnet near the lamp bulb. When the current is at the low value corresponding to any working voltage, the galvanometer reading does not seem to be per- ceptibly altered by bringing a magnet near the lamp, but when it is at its high value, the reading is sometimes increased for a little, showing a steady deflexion, and then immediately falls to its low value. §5. Experiment 2.—The difference of potential between the middle plate and the positive electrode of the lamp depends to a considerable extent upon the position of the middle plate. Supposing the plate to be placed with its plane perpendicular to the plane of the carbon horse-shoe and then moved to various positions between the two legs of the carbon, it is found that the difference of potential between the plate and the positive electrode will have difterent values according to the position of the plate. This fact was elucidated by means of the same lamp No. 4.as used above. By carefully tapping the lamp, the supporting platinum wire carrying the platinum middle plate could be bent so as to displace the plate from its symmetrical position as regards the two carbon legs, and bring it nearer to one or other of the legs. In several different positions the current flowing through the milampere- meter, when connected between the middle plate and positive electrode, was measured, the lamp being kept meanwhile at the same working electromotive force. Iistimating as nearly as possible the fractional distances, the plate was placed at distances from the negative leg equal to 7,4, 4, 2, and ,% of the whole distance between the positive and negative legs, and the lamp being taken through a definite cycle of volts, the potential-difference between the middle plate and the positive electrode was measured with the milamperemeter. The results are collected in the follow- ing tables. The diagrams in fig. 6 represent the horse-shoe carbon loop and the middle plate M in various positions, the galvanometer G being inserted between the plate M and the positive electrode P. By the phrase “whole distance” in the following tables is meant the whole distance or width of the space between the positive and negative carbon leg :-— Edison Effect in Glow Lamps. 61 TasLe No. 3. Lampe No. 4. Milamperemeter. Table showing the potential-difference between the middle plate and positive electrode of the lamp at various posi- tions of the plate and at various working voltages. Volts be- | Current Volts be- Current Working | tween the [through the) Working | tween the |through the volts of the|middle plate] galvano- || volts of the middle plate) galvano- lamp. and positive|meterinmil-|| lamp. and positive/meterin mil- electrode. | liamperes. electrode. | liamperes. Middle plate at =, of whole || Middle plate at ? of whole distance from negative leg. || distance from negative leg. ol oc "142 dl “) 142 34 2°2 “317 3d4 1°4 "222 37 6:0 "952 37 2°2 "D349 39 10°2 1°61 a9 2°5 "396 4} 14°2 2°24 41 2°9 460 43 16°8 3°0 ‘476 2-66 | 43 Middle plate at + of whole|| Middle plate at ;% of whole distance from negative leg. || distance from negative leg. 31 9 "142 dl 9 "142 d4 1°8 "285 34 15 "238 a7 D1 809 a7 a4 "539 a9 70 Ill 3g 4°8 “761 4} 8°7 1°38 Al OT 904 43 9°5 1°50 43 6°8 1:07 Middle plate 4 of whole distance from negative leg. 31 “9 "142 d4 1:7 269 37 3°5 "D00 39 4-3 682 41 5°6 888 43 6:2 "983 62 Prof. J. A. Fleming on the The results of this Table No. 3 are plotted in the curves No. 3. These curves are to be interpreted as follows :—The two vertical lines P and N represent the two legs of the TABLE No. 3.—CuRvE No. 3. The middle plate was moved along into different positions between the two carbon legs indicated by the ‘horizontal distances, and at each position the current between the middle plate and positive electrode of the lamp is represented by the vertical ordinate of a curve. The several curves correspond to different working volts on the lamp. “UT \ l | | { nz Goat leg of Ghnad Ourrent through Galvanometer in Milliamperes. on eps I = : +Leg 1/10 1/4 1/2 3 3/4 9/10 —Leg Position of Plate between legs. carbon horse-shoe. At various distances on the way from P to N the milliampere current through a galvanometer con- nected between the middle plate, placed at that point, and the Edison Effect in Glow Lamps. 63 positive electrode of the lamp is represented by the magnitude of the vertical ordinate of each curve. For every one of the different voltages at which the lamp is worked, there is there- fore a curve representing by its ordinates this current strength through a galvanometer inserted between the middle plate, placed at these positions, and the positive electrode of the lamp, and it is seen that there isa minimum value for this current at a position equal to ? of the whole distance between the legs reckoned from the negative leg. Imagine the middle plate therefore connected through a galvanometer with the positive electrode of the lamp, and let the middle plate be first placed close to the positive leg and then moved continuously nearer towards the negative leg. The current through the galvanometer would first fall off as the plate receded from the positive leg, and after reaching a minimum at a point about } of the whole distance between the legs reckoned from the positive leg, would rise up to a maximum when the middle plate was as nearly in contact with the negative leg as possible without actually touching it. § 6. Haperitment 3.—In order to explore more thoroughly the action of the different portions of the incandescence carbon conductor in producing this effect, a lamp was taken having a horse-shoe shaped carbon, and a pair of small platinum cylin- Fig. 5. LAMP NO 3 ders, held on platinum wires sealed through the glass, so placed as to embrace without touching the carbon conductor. One of these cylinders, X, was placed so as to embrace the carbon near the bottom of the leg, and the other, Y, near the spring of the arch (see fig. 5). These small cylinders had a 64 Prof. J. A. Fleming on the length of about 12 millims. and a diameter of about 8 millims. so that the distance from the carbon filament to the inner surface of the cylinder was about 3 or 4 millims. The lamp had a rather thick carbon, and at an electromotive force of 48 volts took a current of 1°32 amperes to raise it to its normal incandescence of 18°8 candles, corresponding to 3°3 watts per candle-power. This lamp will be alluded to as Lamp No. 3. It is obvious that there are four possible arrangements in which a current can be obtained between an embracing cylinder and a positive electrode of the lamp. ‘These are illustrated in fig. 6, in which the horse-shoe shaped line stands Fig. 6. Position Position Position Position (1). - (Q): (3). (4). LAMP NO 3 les for the carbon filament, X and Y are the platinum cylinders, P and N are the positive and negative electrodes of the lamp, and G is the galvanometer. We will call these arrangements (1), (2), (3), (4), as figured. It will be seen that if we imagine the carbon filament straight- ened out, these four arrangements are equivalent to being able to slide a cylinder along the filament into four positions, and in each position measuring the potential-difference be- tween the cylinder and the positive end of the carbon. We are thus able to place an embracing collecting-plate at four different places along the carbon conductor, and determine the potential-difference between this embracing cylinder and the positive electrode of the lamp. A series of experiments was made with lamp No. 3, in which the working volis of the lamp were raised to various values, and in each case the potential-difference between one of the cylinders X or Y and Edison Effect in Glow Lamps. 65 the positive electrode of the lamp was observed as before by means of the milamperemeter. The results are given in Table 4. TaBLE No. 4. Lamp No. 38. JMlanperemeter. Table showing the potential-difference between a platinum cylinder embracing the carbon and the positive electrode of the lamp, and the current flowing thr ‘ough the galvano- meter in milliamperes ; for the four positions shown in fig. 6. Volts be- Cay is Volts be- es te Working | tween cylin- amperes Working | tween cylin- amperes volts of the| der and through the volts of the; der and through the lamp. positive galvano- lamp. positive galvano- electrode. eto electrode. TSG. Position (1). Position (2). 43 16 "29 43 1-2 18) 45 2°4. 38 45 2-0 roe 46 2°9 “46 46 2°9 “36 Aq a7 58 47 37 08 48 4-2 67 48 42 67 49 A°7 “TA 49 4°9 78 50 D°2 "82 50 a1 Zool ol a9 “93 aL D3 "84 Position (3). Position (4). 43 2°1 "33 43 Pati "39 45 ay) 62 45 4:0 63 46 49 "78 46 a9 “94 47 6°8 1:08 47 8:0 1°26 48 8:2 1°30 48 Se 5d 49 10°4 1°65 49 12°6 ee) 50 12°3 1°95 50 sa! 2°38 a1 14°9 2°36 ol 13°0 2°85 These observations are plotted in Curve No. 4. Phil. Mag. 8. 5. Vol. 42. No. 254. July 1896. F 66 Prof. J. A. Fleming on the This table of observations shows us that taking the lamp at any definite voltage, the potential-difference between the positive electrode and a cylinder embracing the carbon filaments is greatest when that cylinder is as low down near TaBLE No. 4.—CurvE No. 4. \ ’ E | | | ay, | r Th 4) —— | E ve y Fe PosiTijon (1), positilon(4) | | | rata ee = us Dn Current through Galvanometer in Milliamperes. Working Volts of Lamp. the foot of the negative leg of the carbon as possible. If the cylinder is placed near the top of the negative leg that potential-difference becomes less. If the cylinder is taken near the top of the positive leg or near the base of the positive leg itis least, and it seems to be a minimum when the cylinder Edison Effect in Glow Lamps. 67 surrounds the top of the positive leg, and is as far as possible away from the foot of the negative leg. We have here a confirmation of the fact observed with respect to lamp No. 4, viz.: that the potential-difference between the positive lamp electrode and the metal plate held somewhere near the incan- descent carbon conductor is greatest when the plate is as near as possible to the foot of the negative leg or negative elec- trode. In this lamp No. 3, in which in all positions the cylinder employed is placed very near some point on the incandescing conductor, the current through the galvanometer joining the positive electrode and the cylinder has never been observed to jump or to take double values as in the case of lamp No. 4. If a sensitive galvanometer is connected to the two insu- lated cylinders X and Y, and if in addition there js a battery in series with this galvanometer, then no current can be de- tected in such an arrangement even when the battery has an electromotive force of 120 volts, whether the lamp carbon is incandescent or not. Just as in the case of lamp No. 4, the current obtained by connecting either cylinder with the nega- tive electrode of the lamp is excessively small. In order to obtain curves showing the mode of variation of the effective difference of potential between one or other of the metal cylinders X and Y and the positive electrode of the lamp, a set of observations was made on the lamp when sub- mitted to various working voltages, and at the same time the milamperemeter was connected first between the positive electrode and cylinder X and then between the positive electrode and cylinder Y, with the following tabulated results (p. 68). These results, when plotted out in curves in which hori- zontal ordinates represent the working volts of the lamp and the vertical ones the milliampere currents going through the galvanometer, in both cases have the same general form as curve No. 1 plotted for the case of lamp No. 4. F 2 68 Prof. J. A. Fleming on the TaBLE No. 5. Lamp No. 3. Milamperemeter. Table showing the potential-differences between the positive | electrode of the lamp and the two cylinders X and Y respectively, and the corresponding currents through the galvanometer. l | Volts between =o Volts between | Milliampere cylinder X and Milliampere cylinder Y and current flowing vee the positive |currentthrough) “the positive | through the volts of the electrode P of the galvano- | electrode P of galvanometer lamp. the lamp. | ™eter connect-| the lamp. | connecting Position (1). ing X and P. | Position (3). Y and P. | 84 ‘1 015 ‘1 O15 | 85 als 023 a a 5. 086 20 031 ‘3 git 37 pide ese: “4 060 | 38 “6 095 7 aera 39 8 126 9 145 oy 40 1-05. 166 11 apd Al 13 206 16 25 a 42 1:8 285 2-0 31 43 2-1 333 2°8 44 44 2°6 412 3:5 55 45. 3-0 476 45 17 46 3°6 571 5°8 92 Aq 4-2 659 72 1-12 | 48 4-9 ‘791 8-8 1:39 AO fd Abs 889 10-9 1-72 50 6-2 984 13°6 2°15 Percviel & ydocarten | ecupee 15-1 2°39 a ee eae 18-6 295 | § 7. Experiment 4.—The magnitude of the current found on connecting any galvanometer between one of the cylinders and the positive electrode of the lamp was found to be de- pendent to some degree on the perfection of the vacuum. Lamp No. 3 when first made had not a very perfect vacuum. A series of measurements was, however, made with it, and the same repeated after re-exhaustion. The results are tabulated together below. Edison Liffect in Glow Lamps. 69 TABLE No. 6. Lamp No. 3. Elliott Galvanometer. Table showing the relative values of the potential-difference between cylinder Y and the positive electrode for good and imperfect vacua in the case of lamp No. 3. Serr high vacuum in the lamp.’ Imperfect vacuum in the lamp. Working oa | ee ere atene Vole taba P. taken up in and positive taken up in | and positive carbon. electrode. carbon. electrode. 40 6°75 2°02 eth 4°17 Al eo 2°89 | Ss) 7:25 42 5°30 362 | 65 8°39 43 4-90) 454 | 5 9-80 44 450 608 | 4:3 11:96 | 45 415 7-50 4-0 13-76 — | 46 3°84 es) one TOSOSh 2 47 3:55 10°33 Be | 16 Ot 48 3°30 Pee a2 | 28:28 AQ and 16°3 30 22205) AQ) 290 138°4 2°8 22599 >I. 2°74 21°8 PA) 23°93 | Sy 2°58 24°4 2°4. 28°26 The imperfection of the vacuum is indicated by the higher watts per candle-power absorbed at low voltages, and we see that at any given working pressure the potential-ditference between the positive electrode and the cylinder Y embracing the top of the negative leg is greater when the vacuum is imperfect than whenitis very good. The presence of residual air tends to bring down the potential of the embracing cylinder more nearly to that of the carbon at the point adja- cent to it. § 8. Hxperiment 5.—A series of observations was next made in which the potential-difference between the middle plate and the positive electrode was determined by the aid of a condenser. If a condenser of capacity U in microfarads is charged to a potential of V volts and discharged through a ballistic galvanometer, we can determine the ballistic constant of the galvanometer. A second observation of a like nature 70 Prof. J. A. Fleming on the in which the “throw” of the same galvanometer is observed when the same condenser is charged by contact with two points concerning which we require to know the potential- difference, gives us the means of calculating the electrostatic potential-difference in volts. A condenser of ‘987 microfarad capacity carefully determined was charged to a potential of 54 volts and discharged through a certain ballistic galvano- meter having a needle whose periodic time of vibration was about three seconds. The resulting “ throw” of the galvano- meter was 5° 30!. Hence a discharge of 54 x°987=53°3 microcoulombs through the galvanometer produces a “ throw” of 5° 30’. Neglecting a very small correction for the loga- rithmic decrement, in this case not of importance, we have for the ballistic constant R the value 53°3=R sin 4(5° 30’) =R x :04798 ; hence R=1110. The same condenser was then connected between the middle plate and positive electrode of lamp No. 4 and then discharged through the same ballistic galvanometer. The lamp was subjected to a working pressure of 39 volts as de- termined by a corrected voltmeter attached to the electrodes of the lamp. ‘The charge of the condenser was sent through the ballistic galvanometer, and a “throw” of 4° obtained. If vis the potential-difference between the middle plate and positive electrode of the lamp, we have the following equation for v in terms of the ballistic constant and angle of “ throw”: °987 v=1110 sin 2° =1110 x 0349 4) ee v= ES = 39 nearly. The potential-difference between the middle plate and the positive electrode as determined by this method is therefore exactly the same as the potential-difference between the positive and negative electrodes of the lamp.- In other words, when the filament is brought to full incandescence, the middle metal plate is brought to the same potential as the negative elec- trode of the lamp. This observation was repeated with several other Jamps having middle plates in various positions and of various forms, and always with the same result, viz., that the potential of the middle plate when insulated is brought down nearly to that of the negative electrode. Edison Effect in Glow Lamps. 71 § 9. Lxperiment 6.—In order to confirm the results ob- tained by the condenser method and to eliminate all the conditions which necessarily exist when we attempt to measure potential-difference galvanometrically, an electro- static method of measuring the potential-difference at any instant between the metal plate and the positive electrode of the lamp was next used. For this purpose a Kelvin multi- cellular electrostatic voltmeter was employed to determine the potential-difference between the positive and negative electrodes of the lamp and between the positive electrode of the lamp and the middle plate, with the following results :— A lamp (No. 4) having the plate fixed between the carbon legs was raised to various working voltages and the potential- differences above mentioned taken. TaBLE No. 7. Lamp No. 4. Kelvin Electrostatic Voltmeter. Static potential-difference in volts between middle plate Working volts of the lamp. and positive electrode of the lamp. Al Al ord 98°7 61:0 61°95 These observations confirm conclusively the previous re- sults. The insulated metal middle plate is in this case brought to the same potential as the base of the negative -leg of the carbon; and hence, on measuring electrostatically the poten- tial-difference between that metal plate and the positive electrode of the lamp, we find it to be the same as the poten- tial-difference between the two electrodes of the lamp. § 10. Haperiment 7.—In order to see if this was the case when the metal collecting-plate had a very small surface placed at some distance from the negative electrode of the lamp, the lamp called No. 1 was employed. In this lamp a platinum wire threaded through the turns of a double spiral 100 volt carbon lamp (see § 11). The lamp was raised to various working voltages, and the electrostatic voltmeter employed to measure at the same time the static potential- difference between the positive electrode of the lamp and the platinum wire, with the following results :— A2 Prof. J. A. Fleming on the TaBLE No. 8. Lamp No.1. Electrostatic Voltmeter. Static potential-difference in volts between platinum wire Working volts of the lamp. and positive electrode of the lamp. 62 D3 79 (ids) 97 | 85 118 | 107 The figures in the above Table No. 8 show that when the surface of the collecting-plate is very small and is placed some distance from the base of the negative leg of the carbon itis brought down only to the potential of some point (probably the nearest point) on the carbon conductor, and that there- fore the potential-difference between the plate and positive electrode of the lamp is somewhat less than the potential- difference between the working terminals of the lamp. At the same time, however, the electrostatic voltmeter shows no measurable potential-difference between the negative terminal of the lamp and the platinum wire, and the most sensitive galvanometer between these points gives no indication of any current. By means of the electrostatic voltmeter it was, however, ascertained that in those cases in which the metallic plate presented considerable surface (several square centimetres) and was placed so that some portion of it was not removed by more than’a centimetre or two from the base of the negative leg of the carbon, it was brought down almost immediately to the potential of the negative terminal of the lamp. If the middle plate is placed at a little distance from the carbon loop then, on testing by the condenser method, it is found that the plate is not instantly brought down to the potential of the negative terminal, but that some few seconds haye to elapse before this is the case. . § 11. A series of experiments was then undertaken in order to determine the effect of varying (1) the surface, and (2) the position of the metal plate in the bulb, and in these experi- ments tke plate was sometimes of platinum and sometimes of aluminium. In all cases the vacuum was a very perfect one, any occluded gases in the plates being got rid of by special means. = Edison Effect in Glow Lamps. (fe Experiment 8.—A normal 100-volt carbon-filament lamp, having a carbon filament coiled in a spiral of two turns (see fig. 7) had a short stout platinum wire (‘024 inch diam.) Fie. 7: LAMP NO} sealed across the bulb so as to thread through, without touching, the spirals of the carbon. The lamp at 100 volts took 1°54 amperes and gave an illumination of 40 candles, equivalent to a power absorption of 3°9 watts per candle-power. The vacuum was very good. This lamp will hereafter be called Lamp No. 1. As before, no current could be detected by a galvanometer when joined up between the platinum wire and the negative electrode, but when the galvanometer was connected between the platinum wire and the positive elec- trode of the lamp a current of some milliamperes was found passing through it. As in the case of lamp No. 4, this lamp was characterized by a great tendency to change suddenly the value of the current flowing through the galvanometer when the working volts on the lamp were kept perfectly con- stant. In the first series of observations the milamperemeter was employed to measure the current flowing between the positive electrode of the lamp and the platinum wire when it was connected between these points, and at and beyond a working-pressure of 90 volts or so the galvanometer would often jump suddenly from one reading to another, when the lamp working volts were kept perfectly constant. In the following table, No. 9, are collected the results when the working pressure of the lamp was gradually raised from 80 to 100 volts :— 74 Prof. J. A. Fleming on the TasLe No. 9.. Lamp No. 1. Milamperemeter. Table showing the potential-difference between the positive electrode and the platinum wire, and the current flowing through the galvanometer connecting them, for various voltages of the lamp. | | are ee as Milliampere cae wae orking platinum current Working _ platinum current volts of the| yi. ang [through the! voltsofthe) [:1. ang | through the lamp. | positive eaten? lamp. positive ca electrode. en electrode. ris 80 4 | p16 99 | 47 270 a 2 | +032 ‘ 2-4 381 | 82 3 | 048 93 Lg 302 83 2 | +0382 “ 2:6 ‘413 84 “4 ‘064 94 3°2 "509 86 “4 064 9-4 1:49 5 7 “114 95 4-9 ‘78 87 9) 080 1. 296 5°8 “92 88 ‘8 127 || 97 71 .| aa , “9 142 || 98 83 | 1:32 90 1:0 159 | 99 8:9: li tee 1:3 206 || 100 8°6 1:37 91 1-4 229 : 10°3 1-64 These figures show that at any definite working electro- motive force of the lamp the current between the positive electrode and the middle plate has very variable values, and that it suddenly changes from one value to another without any apparent reason, the working volts of the lamp remaining constant all the time. If the surface of the collecting-plate is large, say several square centimetres, the potential-difference existing between it and the positive electrode is not found to be so much reduced by attempting to measure it with a galvanometer of about 6000 ohms resistance as it is when the collecting wire presents, as in this lamp No. 1, only a small total surface of about one square centimetre. § 12. Experiment 9.—A horse-shoe carbon filament, taking 1:3 ampere of current at a working-pressure of 42°5 volts, had a middle plate made of a long piece of platinum wire bent up in a zigzag shape so as to form a rectangular-shaped grating (see fig. 8). The object of this was to ascertain Edison Effect in Glow Lamps. 19 whether a middle plate offering a surface pierced with many apertures was as effective in producing the current as a solid Fig. 8. plate of about the same general outline. Practically it was found that this was the case. The magnitude of the currents obtained at various working voltages are of the same magnitude approximately as in the case of a lamp like No. 4, that is to say some 3—4 milliamperes at full incandescence. - § 13. A set of experiments was then undertaken with the object of examining the special effect of varying the position of the middle plate, and a series of lamps was used in which latinum or aluminium plates held on platinum wires were placed in the lamp bulb, or in tubes opening into it, in various positions. These lamps are generally 50-volt lamps of usual type, and had single horse-shoe shaped filaments. Experiment 10.—A lamp-bulb had a side tube blown on it (see fig. 9) and a plate about 6 centims. long and 1°5 centims. wide welded to a platinum wire was sealed into it. The platinum plate was placed vertically and edgeways in the side tube and the side tube was in such a position that the plane of the platinum plate coincided with the plane of the horse- shoe filament. This lamp, called henceforth No. 2, when worked at 48 volts took 1°3 amperes of current and gave a light of 17°5 candles, equivalent to a power-consumption of 3°55 watts per candle-power. The vacuum was very good. In the case of this lamp the current between the positive electrode of the lamp and the platinum plate was found to be numerically very much smaller at the usual working pressure of the lamp than was found to be the case in those lamps in 76 Prof. J. A. Fleming on the which the middle plate was placed between the carbon legs or in the form of a cylinder embracing the carbon. The current obtained at any definite working voltage was considerably greater when the leg of the carbon nearest the plate was the positive leg than when it was the negative leg. Fig. 9. LAMP NOe A series of observations were taken using the lamp at dif- ferent voltages and measuring with the Elliott galvanometer the potential-difference between the platinum plate and positive electrode of the lamp, and these results were as tabulated below in Table No. 10. TasLE No. 10. Lamp No. 2. Elliott Galvanometer. . Table showing the potential-difference between the platinum plate and the positive electrode of the lamp at various working voltages. Positive leg of carbon nearest the platinum plate. | Volts | Volts | between : | between Working Watts per ee Working | Watts per ' volts of ae | adie. ae eee te of the| candle- ieee lamp. | power. positive sea ace’ positive | electrode. electrode. 43 O20 45085 43. 3°59 199 ak 5°80 al es LY) 3°32 "236 45 4°42 "144 50 3°12 "239 AOU > 4 10 OG Pl apd 2°94 "302 | | ! AT 880 4 172 Edison Effect in Glow Lamps. nd If we compare together the results obtained with this lamp No. 2, in which a plate is placed edgeways on and outside the carbon loop, with the results obtained in the case of lamp No. 3, in which the plates embraced the carbon in the form of cylinders, we see the difference produced by the change of position of the plate. Both these lamps, No. 2 and No.3,are48-volt lamps when working at normal incandescence. Referring to Table No. 7 in § 7, we see that for lamp No. 3 at 48 volts the voltage difference of the positive electrode and the platinum cylinders was respectively 13°2 and 18°3 volts as measured with the Elliott galvanometer, and this indicated a current of about 1°3 and 1°8 milliamperes flowing through the resistances from the positive lamp electrode to the metal plate ; but in the case of lamp No. 2, at 48 volts the potential- difference between the platinum plate and the positive lamp electrode was only *2 volt, and this corresponded to a current of 03 milliampere nearly. Accordingly the current is greatly diminished when the collecting-plate is placed edgeways to and someway outside the loop of the carbon. At normal incandescence the current between the positive lamp electrode and the middle plate when joined by the galvanometer is about 03 or *04 milliampere when the positive leg of the carbon is nearest the middle plate, but only about °02 or ‘03 milliampere when the negative leg is nearest the plate. § 14. Haperiment 11.—In order to compare the previous results just given with those obtained when the collecting- plate was placed broadside to and yet outside the carbon loop, Fig. 10. f LAMP NO 6 a lamp was made as in fig. 10 in which an aluminium plate was held on a platinum wire just outside one leg of the 78 Prof. J. A. Fleming on the carbon and with its plane perpendicular to the plane of the horse-shoe. The aluminium plate was 5 centims. long and 1 centim. wide, and distant from the nearest leg of the carbon about *5 centim. This lamp therefore differed from lamp no. 4 in having the plate outside the carbon loop rather than between the legs. It may be noticed that in this lamp the current here obtained by joining the positive lamp electrode to the plate through a galvanometer was slightly greater when the leg nearest the plate was negative than when it was the positive leg, whereas in the case of lamp No. 2 it is just the reverse. This lamp exhibited also the same effect as lamp No. 4, in that the current flowing between electrode and plate is very liable to “jump” from one value to another even when the lamp is kept at constant volts. The following tabular result of the observations shows this. This lamp is called Lamp No. 6 and was a 50-volt horse-shoe carbon lamp, taking 1°33 amperes of current at a working electromotive force of 50 volts. TaBLE No. 11. Lame No. 6. Milamperemeter. Table showing the potential-difference between the positive electrode of the lamp and the aluminium plate, and the current in milliamperes flowing through a galvanometer connecting them. Vacuum good. | r Potential- |,,.,,. Potential- |,,.,,. difference of |Milliampere difference of |Milliampere Working the positive |, current Working | the positive | _ Current volts of the. Hactrods through the | volts of the electrode through the damp." 7) and plate galvano- || lamp. and plate galvano- | in volts. er in volts. eee 32 ai 016 ~~ AG 3°8 ‘601 34 3 ‘O47 Oise eRe “555 36 6 ‘095 bln 1aeae oleae 37 8 BBA || Fens 7 a Daeg "602 38 1-0 “Laoe a iH 16°2 2°97 39 1-2 19) #1 | 48 4+] “650 40) Ry Dod Jn Boe 17-7 2°80 41 2-0 Oh fee 42 "666 42 2-3 O64 <1 awe 183 | 2-90 43 2°8 “444 50 19°5 3°03 hea! 371 491 < 20-0 3°17 | ae 4-0 634 4 4" 650 | | Edison Effect in Glow Lamps. 79 The results in Table No. 11 are plotted in curve No. 5. This table shows that when the lamp is kept at a constant voltage the current through the galvanometer jumps from one value to another. The fluctuation of the current takes place when the negative leg of the carbon is the one farthest TABLE No. 11.—Curve No. 5. 40 3°0 bo Oo Current through Galvanometer in Milliamperes. Hedpe eRReeee= Pop ts Walee eyso] ee a ete 30 32 34. 36. 38 40: 42) 44 46 48 50 Working Volts of Lamp. 0 from the plate. When the leg adjacent to the aluminium plate is the negative one then the current is steady at any definite voltage of the lamp. § 15. From the above experiments it is clear that the current obtained when a galvanometer is connected between a metallic plate and the positive electrode of the lamp is greater 80 Prof. J. A. Fleming on the in proportion as the collecting-plate is larger and in propor- tion as it is brought into close proximity to the base of the negative leg of the carbon. Also that a plate so placed 1s brought down to the potential of the negative electrode. It seemed desirable to see how far the removal of the collecting- plate to a great distance from the negative leg would influence these results, and experiments were accordingly tried with a tube of the form shown in fig. 11. Fig. 11. LAMP NO ————— SI NGHES Experiment 12.—‘n this case a glass tube about eighteen inches long and three-quarters of an inch in diameter was attached to a lamp bulb. The end of the glass tube furthest from the bulb was closed and an aluminium plate welded to a platinum wire was sealed in near this closed end. The plate had a length of about 3 centimetres and a width of about 1 centimetre. The tube formed an extension of the bulb- space, and accordingly this arrangement formed a device by which a metal plate could be removed to a distance of some eighteen inches from the incandescent conductor contained in the bulb. On placing this lamp on a circuit and bringing the carbon to normal incandescence and connecting the ter- minals of the Hlliott galvanometer respectively to the aluminium plate and the positive electrode of the lamp, a very small current was found to be passing through it, not, however, exceeding one ten-thousandth of a milliampere. When the galvanometer was joined in between the aluminium plate and the negative leg of the carbon no current whatever could be detected with this galvanometer, which was sufficiently sensitive to show one hundred-thousandth of a milliampere. We thus find that the removal of the plate to a distance of some © Edison Effect in Glow Lamps. 81 eighteen inches from the incandescent conductors practically extinguishes the phenomenon. Experiment 13.—Another similar bulb was provided haying a side tube blown on it of half the length, viz. about 9 inches long. At the end of this tube was placed a small aluminium plate as before, and the tube was bent up about the middle at right angles (see fig. 12). When the carbon conductor in Fig. 12, the bulb, which was that of an ordinary 50-volt 16 candle- power lamp, was rendered incandescent by being connected to a circuit of appropriate electromotive force, and the Elliott galvanometer connected in between the aluminium plate and the positive electrode of the lamp, a current of not more than about one twenty-thousandth of a milliampere was detected. The fact that the ‘“‘ Edison effect ” was extinguished when the collecting-plate was placed at the extremity of an elbow-tube was first observed and recorded by Mr. Preece. § 16. The effect of position and size of the plate having been examined, the next step which naturally suggested itself was to determine the effect of the different portions of the Incandescent conductor in the production of it. Haperiment 14.—A lamp like No. 4 was provided, but in which one leg of the carbon was enclosed in a glass tube of the size of a quill. The glass tube was sealed on to the platinum wire and extended nearly up to the bend of the carbon (see fig. 13). This lamp, called No. 9, was placed on the circuit in such a manner that the shielded leg was the Phil. Mag. 8. 5. Vol. 42. No. 254. July 1896. G 82 Prof. J. A. Fleming on the positive leg, and a series of observations taken as usual of the current flowing through the milamperemeter when connected between the middle plate, placed between the carbon legs, Fig. 13, LAMP NO 9 NO CURRENT FLOWING LAMP NO 9 CURRENT FLOWING and the positive electrode of the lamp. The results are as tabulated below in Table No. 12. The lamp took 1:25 ampere of current at a working electromotive force of 42 volts. TABLE No. 12. Lampe No. 9. MMilamperemeter. Table showing the potential-difference between the middle plate and positive electrode of the lamp, and the current flowing through a galvanometer connecting them, when the positive leg of the carbon is shielded in a glass tube. volts of the lamp. 36 a8 40 Al 42 43 Potential- Bt AN Ors difference of| Milliampere Working [middle plate| current and positive |through gal- electrode | vanometer. in volts. 2 Wz “2 "048 "95 a ie Mie 74 19 1°8 "29 oil "49 4°2 "66 44 Working volts of the lamp. — Ad 46 AT 48 49 50 ol Potential- difference of |Milliampere middle plate] current and positive |through gal- electrode | vanometer. in volts. 6°9 "936 (ar) 109 SET 1°53 12°4 1°96 15-1 2°39 19- 3°03 23°1 3°66 | Edison Effect in Glow Lamps. 83 So far the results are quite normal, and if the results in the above Table No. 12 are compared with those in Table 2 for a similarly constructed lamp with no tubular shield we find that the magnitude of the current flowing from the positive elec- trode to the middle plate is in the two cases very much the same. The lamp No. 9 was then placed on the circuit in such a manner that the leg shielded by the glass tube was the negative leg, and a similar series of observations of the current between the positive leg (now the uncovered leg) and the middle plate was made. The results were as follows in Table No. 13 :-— TABLE No. 13. Lamp No. 9. Milamperemeter. Table showing the potential-difference between the middle plate and positive electrode, and the current flowing through a galvanometer connecting them, when the negative leg of the carbon is shielded in a glass tube. Potential-differen 77° Working volts of | of middle nae me ee ee the lamp. ne in galyanometer. AD “10 "016 AT 15 "024 AQ 25 "039 ol 30 044 On comparing the results in Table No. 13 and the previous one No. 12 we see what an immense reduction in the current flowing between the positive electrode and the middle plate is produced by shielding the negative leg. Hence the action in virtue of which the current is produced is greatly interfered with by enclosing or covering up the negative leg of the carbon. In this particular case at 51 volts, the current between the positive electrode of the lamp and the middle plate when the negative leg is covered up is only ;5 of that which it is when the posztive leg is covered up. The results in Tables Nos. 12 and 13 are plotted together in Curve No. 6. G 2 84 Prof. J. A. Fleming on the § 17. The question remained to be settled whether the nature of the tubular screen in any way affected the results, and the glass tube was accordingly replaced by a metal (aluminium) tube and a lamp (No. 10) taken in which one of TasiEs No. 12 anp 13.—CurvE Neo. 6. Current through Galvanometer in Milliamperes. Boe pee, ee aie ed SA REA 34 36 38 40 42 44 46 48 50 52 o4 Working Volts of Lamp. the carbon legs (see fig. 14) was surrounded by an aluminium cylinder extending nearly the whole length of the leg, and also a middle plate of aluminium was placed between the legs. Both the plate and the cylinder were held on platinum wires sealed through the glass. The lamp took 1-25 amperes of current at 41°5 volts. Edison Effect in Glow Lamps. 85 Experiment 15.—The lamp was placed on a cireuit so that the leg shielded by the aluminium cylinder was the positive leg. ‘The milamperemeter was then connected between the positive electrode of the lamp and the middle plate, and the usual measurements made. It was found that the current “jumped ”’ a good deal, and that high and low values of the Fig. 14, LAMP NO 10 galvanometer current occurred, even when the terminal voltage of the lamp was kept perfectly constant. The lamp was then reversed on the circuit so that the shielded leg was the negative one, all other arrangements: remaining the same. The current now between the positive electrode and the middle plate was practically zero, at any rate too small to be measured with this galvanometer. Hence we see that shielding the negative leg, whether by glass or a metallic cylinder, entirely cuts off the production of a current between the positive lamp electrode and the middle plate. § 18. Leperiment 16.—Another series of experiments was made with the lamp No. 10 in which the galvanometer was connected between the positive electrode of the lamp and the aluminium cylinder (see fig. 15), the leg inside the cylinder being either the positive or the negative leg. In this case the middle plate remained unused and insulated and acted as a shield between the cylinder and the carbon leg which was not contained in the cylinder. It was found that when the cylinder surrounds the negative leg and its surface is, therefore, as much exposed to it as possible the current is a maximum, but that when it includes 86 Prof. J. A. Fleming on the the positive leg the current is greatly diminished, both by reason of the fact that it opposes less surface to the negative Fig. 15. LAMP NO (0 LAMP NO10 leg, and also because the middle plate acts as a shield between ‘it and the negative leg of the carbon. § 19. Hxperiment 17.—In order finally to demonstrate that the negative leg of the carbon loop was the chief active agent in this production of a current between the middle plate and the positive electrode, a lamp like No. 4 was taken having a metal middle plate between the legs, and this middle plate had attached to it a mica screen (see fig. 16) a little Fig. 16. \ Oy SWS WN S| A&V7 SSSSSIAAQHQy \S \: SSN SSS \. Ww = MIDDLE PLATE SHIELDED MIDDLE PLATE EXPOSED larger than the plate, and so fixed by a loose rivet that it could be shaken in front of the plate so as to shield one side of it, or shaken on one side so as to fully expose the plate.. This device was in fact a removable shield attached to one Edison Effect in Glow Lamps. 87 surface of the metal middle plate, and when placed up against it it shielded one surface from, and when jerked on one side it exposed that surface to, the carbon leg opposite to that surface. This lamp (called No. 5) was set on the circuit in the first place so that the leg of the carbon horse-shoe opposite to the mica-shielded side of the middle plate was the positive leg. If the carbon was brought up to an incan- descence corresponding to about 3°5 or 4 watts per candle- power and the galvanometer connected between the positive electrode and the middle plate, then it was found that the effect on the galvanometer current which was produced by the interposition or withdrawal of the screen of mica between the positive leg and the plate was not very great. It reduced the current through the galvanemeter from about -44 mil- liampere to °38 milliampere. If, however, the current flowing through the lamp carbon is reversed in direction so that the mica screen is interposed on that side of the middle metal plate which faces the negative leg, the result is very different. When the screen is down, the current flowing through the galvanometer from the positive electrode to the middle plate being as before °44 milliampere, the interposition of the mica screen on the side of the plate facing the negative leg reduced the current at once to zero. We find therefore, that the interposition of a mica screen between the middle plate and the negative leg reduces to zero the current flowing between the positive lamp electrode and the middle plate. As in all other lamps with a middle plate set exactly between the legs, the current through the galvanometer joining the middle plate and positive electrode is very liable to “jump ” from a low to a higher value or vce versd. When the current has its higher value corresponding to any given voltage on the lamp terminals, the effect of screening is less marked, and although the interposition of the mica screen on the side facing the negative leg has an effect of reducing the current flowing through the galvanometer connected between the middle plate and positive electrode it is not by any means reduced to zero. § 20. The foregoing experiments afford proof that the production of the current through a galvanometer joined between the positive electrode of the lamp and a metal plate placed somewhere in the vacuous bulb, is an effect due chiefly ~to the negative leg of the carbon, and that shielding the negative leg by enclosing it in a glass or metal tube, or covering with a mica screen that surface of the plate which is exposed to the negative leg, either quite prevents or greatly reduces the production of this current. The experiments 88 Prof. J. A. Fleming on the also have shown that the magnitude of the current flowing through the galvanometer is increased by bringing the plate near to the base of the negative leg, or, better still, making the metal plate in the form of a cylinder and making this cylinder surround the negative leg near its base ; and cor- respondingly it is diminished by removing it from the negative leg to a considerable distance, or by shielding this collecting-plate from the radiation from the negative leg of the carbon. The experiments with the condenser have also given evidence that when an insulated metal plate is sealed into a lamp this plate is brought down either instantly or in a very short period of time to the potential of the negative leg near its base or to that of the negative electrode of the lamp. In looking for an explanation of these facts we are assisted by our previous knowledge that in carbon incan- descence lamps, when working at an efficiency equivalent to ‘3 to 4 watts per candle-power, there is a gradual loss of carbon from all parts of the conductor. We know also that the carbon molecules which are projected from the conductor are thrown off into a space so highly vacuous that their mean free path is of a length comparable with, or greater than that of the dimensions of the glass bulb. The existence of ‘molecular shadows in incandescence lamps * affords evidence that from intensely heated portions of the carbon conductor carbon molecules are projected in straight lines and move freely forward until they impinge against the glass. Com- mercial experience informs us that at and above a tem- perature corresponding to 3 watts per candle-power this loss -of carbon becomes very rapid and thins away the filament in one place, or generally reduces the diameter of the carbon .conductor. Hence we have every reason to believe that when in a normal state of incandescence the carbon conductor in a lamp is throwing off im all directions carbon molecules, and that in the vacuum usually obtained the mean free path of — ‘these projected molecules is comparable with the dimensions of the vessel containing the conductor. The whole of the experiments which are detailed here seem to be capable of consistent interpretation if we may justifiably make the hypothesis that these carbon molecules or atoms so projected from the conductor when intensely heated by the current flowing through it are all negatively charged. Some of the observed facts seem to point to the conclusion that the molecules projected from the incandescent conductor, whether they are portions of the conductor itself or molecules of the residual gases, respectively carry away negative charges * See J. A. Fleming, ‘ Philosophical Magazine, August 1885, p. 141. Edison Effect in Glow Lamps. 89 proportional in magnitude to the potential of the conductor at the point from which they are thrown off. They may, therefore, be looked upon as condensers of small but definite electrostatic capacity charged to the potential (negative) of that part of the incandescent conductor at which they separate from it. We have then in addition to explain how it comes to pass that there are few or no projected molecules charged positively. Two suggestions may be made on this point: either the radiation of matter is wholly confined to that half of the conductor at a negative potential or the incandescent carbon molecule thrown off from the heated conductor cannot retain a positive charge. There is much to lead to the conclusion that from all parts of the incan- descent carbon conductor there is a constant radiation of matter carrying a negative electric charge. The nearer down to the negative electrode of the carbon we select our point of observation the greater is this molecular charge found to be. It will be convenient to denote this conveyance of electric charge by moving charged molecules by the term molecular electrovection. We can then state the hypothesis thus—from all portions of the negative leg of the carbon loop a process of molecular electrovection is going on when the conductor is incandescent, the molecular charge being negative, and equal in potential to that of the point on the conductor from which it is projected. § 21. On the assumption that a molecular shower of nega- tively charged atoms was being projected against the middle plate when the conductor of the lamp was incandescent. it was considered probable that a positively charged conductor connected to the middle plate would be discharged, and this was found to be the case. Experiment 18.—A lamp of the form of No. 4, having a middle metal plate placed between the carbon legs, had its middle plate connected to one terminal of the Hlliott gal- vanometer. The other terminal of the galvanometer was connected to one terminal of a condenser of 5 microfarads capacity. The other terminal of the condenser was connected by a wire to the gas pipes of the laboratory. The lamp was actuated by secondary batteries (see fig. 17) not very well insulated. If the condenser was charged to a potential of 90 volts so that the plate next the galvanometer was pos?- tively charged, then this positive charge was instantly dis- charged when the carbon was rendered incandescent. If, however, the plate of the condenser in connexion with the middle plate through the galvanometer was charged negatively the condenser was not discharged when the lamp was illumi- 90 Prof. J. A. Fleming on the nated by rendering its carbon incandescent. It is a very striking experiment to see a condenser charged with this amount (250 microcoulombs) of electricity instantly discharged when its positive coating is brought into connexion with the middle plate of sucha lamp. The discharge may be brought 70’SecY BATTERY To EARTH about either by joining up the positive side of the condenser to the middle plate first, and then rendering the carbon of the lamp incandescent by switching on the lamp, or the lamp may be first of all illuminated and then the junction of the condenser effected. In both cases the middle plate when positively electrified is instantly discharged. It was found that if the lamp carbon is rendered incandescent bya highly insulated secondary battery then in order to produce the discharge, the plate of the condenser not in connexion with the middle plate, and which is negatevely charged, must be somewhere connected with the battery circuit. It does not matter, however, whether the wire from the negative side of the condenser is in connexion with the positive or the negative pole of the secondary battery actuating the lamp ; all that is necessary is that the negative side of the condenser should be in conducting connexion with the circuit of the incandescent carbon. ‘The experiment may be interpreted by considering that this negative charge of the condenser can escape out of the incandescent conductor and discharge across the highly vacuous space to the positively electrified cool middle metal plate; but that a positive charge cannot be discharged out of the hot conductor, or, which amounts to the same thing, a negative charge cannot discharge across from the cool metal plate to the incandescent carbon which is positively charged. We have then a unilateral conductivity exhibited by this highly vacuous space bounded by two Edison Effect in Glow Lamps. 91 electrodes one of which is incandescent and the other of which is cold. Negative electricity is discharged at once out of the hot surface but not out of the cold, and a negative discharge can take place from hot to cold but not vice versd. When the discharge of a charged condenser is effected by connecting the positive plate, through a galvano- meter, with a metal plate sealed into the lamp and the negative plate with the lamp circuit, and then switching on the lamp, there is a curious instant of delay betore the discharge begins. When the metal plate is placed very near the negative leg of the carbon the discharge of the condenser is complete in one instant. This the case when a lamp of the type No. 4 (fig. 18) is used. If, however, we employ a lamp of the type No. 2 (fig. 10), in which the metal plate is at some distance from the negative leg of the carbon, the discharge of the condenser is long drawn out and the electric charge in it is as it were tapped off slowly and notin one short sharp discharge. Moreover this effect of discharging a condenser takes place only when the carbon is above a fair red heat. At brilliant incandescence and when the carbon is above a temperature corresponding to 3 watts per candle-power, the discharging power of a lamp of the type of No. 4 is very great. A con- denser of 10 or 20 microfarads capacity charged to 50 volts is discharged instantly if its positive plate is connected to the metal plate placed not far from the negative end of the incandescent carbon conductor. The foregoing results were confirmed with lamps of other types. Using, for instance, a lamp like No. 6 with the aluminium plate placed outside the carbon horse-shoe and near the leg, the same discharging power for positive elec- tricity was found. It was not dependent on the direction of the current through the lamp carbon, although it seemed a little more vigorous when the leg nearest the plate was the negative leg. As above observed, the rate of discharge was much reduced when employing a lamp having the metal plate placed edgeways on to the carbon and some way from it, as, for instance, when employing a lamp of the form of No. 2. § 22. Hwperiment 19.—A series of experiments was in this case also tried to determine the effect of shielding the negative leg of the carbon. The lamp no. 9 was employed, in which one leg of the carbon was enclosed in a glass tube connecting the positive plate of a charged condenser through a galvano- meter with the middle plate of the lamp, and the negative plate of the condenser somewhere to the battery circuit ; it -was found that when the shielded leg of the carbon was the positive leg the condenser was discharged as before. UH, 92 Prof. J. A. Fleming on the however, the shielded leg or leg enclosed in the glass tube was made the negative leg, which could be done by reversing the current through the carbon conductor, then the condenser was not discharged when its positive plate was connected with the middle plate. The same fact was less perfectly exhibited by employing the lamp with the middle plate having a removable mica shield on one side. Weare thus able to assure ourselves that the active agent in producing this discharging effect upon a positively charged body connected to the middle plate is the negative leg of the carbon conductor. The experiments were varied in many ways, but all pointed to the conclusion that if a charged condenser is connected to two terminals, one of which is a metal plate and the other a carbon conductor, both enclosed in a high vacuum but yet separated from each other by an inch or so of distance, the condenser is discharged instantly when the carbon terminal is rendered highly incandescent, provided that the negative plate of the con- denser is in connexion with it. § 23. If the condenser is left in contact with the middle plate under some circumstances, not only is it discharged if previously charged but is charged again in an opposite direction. Heperiment 20.—A condenser of 5 microfarads capacity perfectly discharged has its poles or terminals connected for one instant, one with the middle plate of No. 4 lamp and the other with the positive electrode of the lamp (see fig. 18). Fig. 18. plu s uISNIGNOD N P On removing it and testing it with the galvanometer G it is found that the condenser plate in connexion with the middle plate of the lamp has received a negative charge and the other plate of the condenser a positive charge. | Edison Effect in Glow Lamps. 93 If, however, the condenser is connected between the negative electrode of the lamp and the metal middle plate of the lamp, on insulating and testing it we find it has not the slightest charge. It is very astonishing to see how instantly a condenser of very large capacity is charged when one pole of the con- denser is connected to the middle plate and the other to the positive elecirede of the lamp. § 24. In considering the behaviour of the heated carbon electrode and the cool metal plate in their respective powers of discharging the positive or negative charge of the con- denser, it seemed that the fundamental fact was the power of the heated surface to discharge negative electricity out of itself. Hence arose the question, how far the observed facts would be modified if the middle metal plate itself could be also heated. One way by which this might have been done would have been to have rendered this plate incandescent by heating it by radiant heat concentrated by means of a powerful mirror or Jens. Some experiments tried in this way were not satisfactory, and consequently a method was adopted in which a middle plate of carbon could be rendered incandescent electrically. Experiment 21.—A vacuum tube was provided with two carbon conductors (see fig. 19), one the ordinary carbon Fig. 19. twa INSULATED SECONDARY BATTERY filament L of a 50 volt lamp, and the other the small carbon S of a4 volt lamp. The smaller carbon was sealed in the usual way through the glass and placed so as to stand symmetrically between the legs of the Jar ger carbon loop. The smaller carbon could be rendered incandescent by an insulated battery of fifteen secondary cells, appropriate 94 Prof. J. A. Fleming on the resistance being introduced. The larger carbon also could be rendered incandescent by the proper electromotive force. If the smaller carbon was kept cold and employed simply as a third electrode or middle plate, all the phenomena previously described as happening with metal middle plates of aluminium or platinum teok place. If the small (cold) carbon loop is connected through a galvanometer with the positive electrode of the larger carbon loop when this last is rendered incan- descent by a current, we find as usual a current of a few milliamperes passing through the galvanometer from the positive electrode of the peer carbon to the small carbon. If the small carbon (still cold) is connected through the galvanometer to the negative electrode of the larger carbon we get no current. This is the normal effect, and it is the same for a cold carbon conductor used as a middle plate as for a metal middle plate. Leperiment 22.—The next experiment consisted in making this small carbon incandescent by an insulated secondary battery, appropriate resistance being inserted so that the carbon was brought to the normal condition of temperature as indicated by its incandescence. When this was done the galvanometer was inserted between the positive electrode of the large carbon loop and one of the electrodes of the small carbon loop. A current was obtained as before. On con- necting the galvanometer between the negative electrode of the large carbon loop and one of the electrodes of the small carbon loop a current of nearly equal value was now obtained. In this last experiment it was found to be immaterial whetner the terminal of the galvanometer was joined to the positive or to the negative electrode of the small carbon loop. Hence we find that when the small carbon Joop is not incandescent and is used as a middle plate or electrode, it is brought down together with the insulated battery attached to it to the same potential as the negative end of the large incandescent carbon, and we get as usual a current through a galvanometer con- nected between the positive electrode of the large incandescent carbon and any point on the small cold carbon, vand no current between the negative electrode of the large hot carbon and the small cold one. On rendering the smaller carbon loop incandescent this is all changed. The smaller carbon, now hot, is not brought down to the potential of the negative ends of the larger carbon, and we get a current through : a galvano- meter connected between either positive or negative electrode of the large hot carbon and any point on the circuit of the smaller equally hot carbon. § 25. Haperiment 23.— With this same vacuum tube having Edison Effect in Glow Lamps. 95 double carbons, further experiments were performed on the discharging power of the hot and cold electrodes for positive and negative electricity. The two carbons could be rendered incandescent either simultaneously or singly by two sets of insulated secondary batteries attached to each respectively. For the sake of distinction we shall speak of the large carbon loop in this bulb as the L loop and the smaller one as the S loop. A condenser of 5 microfarads capacity (see fig. 20) Fig. 20. S l m ite” : ‘ BATTERY g + oe CONDENSER / | N was employed, which was charged to a potential of about 50 volts. When the positive plate of this charged condenser was attached to the carbon L and the negative side to the earbon 8, then on making L incandescent by its own insulated battery and keeping 8S cold, the condenser was found not to be discharged when insulated and tested by a galvanometer. If, however, the same charged condenser was connected in the same way to the two carbons and the carbon 8, to which the negative side of the condenser was attached, was made incandescent, the condenser was instantly discharged. If the direction of the charging of the condenser was reversed the same rule was found to hold good. The condenser was discharged if the negatively charged plate of the condenser was connected to the zneandescent carbon loop, but not if it was connected to the cold carbon loop. Beginning with the condenser charged and connecting it in between the two carbon loops, neither of them being incandescent, then the condenser was discharged instantly if that loop to which the negatively charged side of the condenser was attached was rendered incandescent, but not discharged if the loop to which the positive side of the condenser was connected was rendered incandescent. If both loops were rendered incan- 96 Prof. J. A. Fleming on the descent simultaneously the condenser in any case was dis- charged, but apparently at an accelerated rate. These experiments show again that if two carbon electrodes are sealed into a high vacuum, negative electricity escapes very freely out of either electrode if it is rendered incandescent, but that the escape or discharge of positive electricity is not in the same way facilitated by heating the positive electrode. Accordingly a highly vacuous space bounded by two carbon electrodes separated by a distance less than the mean free path of the gaseous molecule at that pressure, presents a unilateral conductivity when one of these electrodes is cold and the other highly incandescent. For if the hot electrode is connected to a negatively charged body and the cold electrode to a positively charged body, discharge takes place across the vacuous space, but if the charges are reversed then no discharge takes place. The negative charge can escape from the heated electrode but not from the cold one. § 26. Hapertment 24.—The question of the apparent uni- lateral conductivity of the vacuous space bounded by a hot and a cold electrode was then further examined by the aid of the lamp No. 6 formerly used. In this lamp an aluminium plate is sealed into the vacuum and placed just outside the carbon horse-shoe. If a sensitive galvanometer (the high resistance Hlliott galvanometer) is joined up between the metal plate and the negative electrode of the lamp, then, asin other cases when the Jamp is !n action, Fig. 21. N No CURRENT no current of a magnitude much greater than ‘0001 ofa milliampere is detected. If a single Clark standard cell is inserted in the galvanometer circuit (see fig. 21) with its negative pole attached to the middle plate and its positive Edison Effect in Glow Lamps. 97. pole te the galvanometer terminal, the current is barely if at allincreased. In this case the negative pole of the Clark cell is in connexion with a cold metal electrode and the positive pole is in connexion through the galvanometer with the incandescent carbon electrode, and under these circumstances the galvanometer detects no current flowing. The position of the Clark cell is now reversed, and it is joined up so that its positive pole is in connexion with the middle plate and its. negative pole in connexion, through the galvanometer, with the incandescent carbon electrode. It is then found that a considerable current of some few milliamperes in magnitude is flowing through the galvanometer. The direction of this current in the ordinary way of speaking is from the negative electrode of the lamp through the galvanometer to the metal plate sealed into the bulb. We thus find that a negative current of electricity can be made to flow across the vacuous space between the incandescent carbon and the metal plate from the hot carbon to the cooler metal plate, but not in the reverse direction. The space presents an apparently uni- lateral conductivity. § 27. Experiment 25.—The same experiment was repeated, only using instead of a Clark cell an insulated secondary battery of 25 small cells.) When the secondary battery (see fig. 21) was connected with its negative pole to the metal plate and its positive pole through the galvanometer to the negative electrode of the carbon, no current greater than that found with the Clark cell similarly arranged was found ; but if the secondary battery was reversed and joined up with its positive pole to the middle plate and its negative pole through the galvanometer to the negative electrode of the incandescent carbon, then so strong a current flowed through the galvanometer that it could not be measured without shunting-down the galvanometer considerably. The same experiments were repeated with the lamps having the zigzag wire as a metal plate, No. 7, and the same general results obtained. ‘These experiments therefore show that in a circuit which consists partly of a galvanometer-wire and partly of a highly vacuous space bounded by two electrodes—one a metal plate and the other an incandescent carbon surface,—the insertion of an electromotive force in one direction can produce a very sensible current, but that if the electromotive force is reversed then no current flows. The direction of the electro- motive force must be such as to urge negative electricity from the hot surface to the cold across the vacuum space. | § 28. Laperiment 26.—In order to make use of different parts of the incandescent conductor as the electrode opposed Phil. Mag. 8. 5. Vol. 42. No. 254. July 1896. H 98 “Prof. J. A. Fleming on the- to the metal plate, recourse was had to the lamp No. 3, with metal (aluminium) cylinders embracing without touching the carbon at two different places. These “cylinders, as before, we will call X and Y (see fig. 22). Cylinder X was the one near the base of the positive leo of the carbon, and cylinder Y was the one near the top of the negative leg. W hen the galvanometer was ‘connected between the negative electrode of te lamp and the cylinder X surrounding the lower part of the positive leg, no perceptible current was found to be passing when the carbon was rendered incandescent. On inserting a single Clark cell in series with the galvanometer so that the - negative pole of the cell was in connexion with the cylinder X and the positive pole of the cell through the galvano- meter in connexion with the negative electr ode of the lamp, hardly any perceptible current was found to be passing (see fig. 22). a Clark cell was then reversed, connecting Ve 2 22. “LAMP NO3 positive pole of the cell to the cylinder X and the negative pole througn the galvanometer to the negative electrode of the lamp. On bringing the lamp into. ‘action, a considerable current of several milliamperes was found to be passing in such a direction that a current of positive electricity was flowing across the vacuous space from the metal cylinder to the hot carbon, or a negative current from the hot carbon to the cooler | metal aon On switchin g-off the lamp, there was a curious “kick ” or ‘throw ” of the galvanometer, indicating a sudden rush of “aan ers in the same direction as the steady current which the cell had been sending. _ These effects occurred also when the cylinder Y was employed, and the galvanometer with or without the cell in series joined in between the negative Edisin Effect in Glow Lamps. © 99 electrode of the lamp and the cylinder Y embracing the top part of the negative leg of the carbon (see fig. 22) ; but in the ‘last-case the steady current sent by the cell across the vacuous ‘space between the cylinder and the hot carbon was only about a quarter as great in magnitude as when the cylinder X was employed. There was the same kind of “kick”’ of the galvano- meter on breaking the lamp-circuit. These experiments evi- dently showed that the highly vacuous space between the hot carbon traversed by its own current, which rendered it incan- descent, and the insulated cylinder possessed a sort of unilateral conductivity, negative electricity from a separate source of small electromotive force being able to be forced through it from the hot carbon surface to the cooler metal surface, but not in an opposite direction. § 29. In the above-recorded experiments the carbon con- ‘ductor was rendered incandescent by a unidirectional or con- tinuous current in a highly perfect vacuum. In seeking for an hypothesis to connect them together, it became essential to ascertain how the effects would be modified if the vacuum was imperfect and if the current was alternating instead of continuous. Experiment 27.—The fundamental experiment was therefore repeated with the normal type of lamp (No. 4), having a middle metal plate placed symmetrically between the legs of the carbon. A lamp of this type was set in action by an alternating current of suitable strength and of which the frequency was some 80 to 100 per second. On connecting the milampere- meter between either of the electrodes of the lamp and the middle plate, a continuous electric current was found flowing through the galvanometer. The direction of this current was such that positive electricity was found to flow from either lamp terminal to the middle plate of the lamp. In other words, a continuous current of negative electricity flowed out of the middle plate to one or other of the two terminals of the lamp, viz. to that terminal to which the other extremity of the gal- vanometer was joined. Hence, since in this case each leg of the carbon becomes in rapid succession positive and negative -when the lamp is. operated with an alternating current, the ‘unilateral effect observed of a current flowing between the ‘middle plate and the positive leg, when the current through ‘the carbon is a continuous current, is here found to exist equally between the middle plate and both terminals of the lamp. This is only what might have been expected. The potential of the middle plate 1s then not the same as that of the base of either leg of the carbon, but something between the two depending upon the. ee the plate. 100 Prof. J. A. Fleming on the » §30. Ezperiment 28.—The effect of lowering the vacuum was also the subject of experiment. Ina lamp with a highly perfect vacuum no current greater than about ‘0001 milli- ampere is observed when a very sensitive high-resistance -galvanometer is joined up between the negative electrode of the carbon and the insulated middle plate, and, as we have seen, the experiments with the electrostatic voltmeter showed that the plate was brought down under these circumstances to the potential of the base of the negative leg of the carbon. If, instead of employing a very perfect vacuum, a bad one is pro- duced by imperfectly exhausting the lamp, then it is found that under these conditions the Elliott galvanometer indicates a not inconsiderable current of something approaching to a milliampere when joined in between the negative electrode of © -the lamp and the middle plate. Hence, when the vacuum is imperfect the equality in potential between the middle plate and the negative electrode is not maintained. The direction of the current in this last case is such as to show that negative electricity is flowing through the galvano- meter from the negative electrode of the lamp to the middle plate. In other words, negative charge is carried over from the plate to the positive leg of the carbon across the imperfectly vacuous space ; and the means by which this is effected is the residual air. This seems to afford proof that the normal effect of the molecular electrovection of negative electricity from the negative leg is due to carbon molecules, and that the presence of residual air exhibits itself, when present beyond a certain amount, in producing an effect which the carbon molecular electrovection cannot produce. § 31. Laperiment 29.—It seemed very desirable to ascertain if the effect of molecular electrovection exists in the case of an incandescent platinum wire rendered vividly incandescent in a highly perfect vacuum. A bulb was accordingly con- structed similar in every way to lamp No. 4, but having a platinum-wire horse-shoe conductor and a platinum middle plate. When this wire was rendered highly incandescent by a continuous current, a sensitive galvanometer (the high- resistance LHlliott) showed a current of about one five- thousandth of a milliampere when connected between the positive electrode of the incandescent wire and the middle plate, but little or no current when connected between the negative electrode and the middle plate. This molecular electrovection current was thus very much less in magnitude than that observed in the case of the carbon filament lamps, but it is in the same direction. We are, however, enabled to state that at a condition of vivid incandescence just short of Edison Effect in Glow Lamps. = ——‘101 fusion a platinum wire zn vacuo exhibits the same effects as a earbon filament, and that it can disturb the electrical condition of an insulated metal plate near it sealed into the same vacuum and tends to bring it down towards the potential of the negative end of that platinum wire. On the hypothesis that all these effects are due to a scattering of negatively charged molecules from the incandescent con- ductor, we must affirm that the same process goes on in a platinum wire rendered incandescent in a vacuum, only that the radiation of matter is far greater in the case of the incandescent carbon than it is in the case of the incandescent platinum. § 33. Ifa lamp is selected having an insulated plate fixed between the legs of the carbon filament, it is found that under certain conditions the electric conductivity of the vacuous space between the plate and the negative leg is much affected by the presence of a magnetic field. Ifa galvanometer, preferably a movable coil galvanometer, having a resistance of about 500 or 600 ohms, is connected between the middle plate and the negative leg it will show but little current passing when the lamp is incandescent at normal temperature. If the volts on the lamp terminal are raised so that the filament is brought into a state of incandescence corresponding to about 2°5 or 3 watts per candle, then the galvanometer will show a small current passing through it. If then a horse-shoe magnet is held so as to create a magnetic field the direction of which is across the space between the plate and the negative leg, the current indicated by the galvanometer immediately decreases considerably. This happens irrespective of the direction of the field so long as it is across the direction of the line joining the negative leg and the middle plate. This indicates that the presence of this transverse field increases the resistance of the rarefied gas. The galvanometer current responds to the presence of the magnet in a manner which shows that the resistance to the flow of the current through the gas is increased by creating a magnetic field at right angles to the line of the current. The general fact that gaseous resistance is increased by such a transverse magnetic field has been already noted and described by Professor J.J.Thomson. The behaviour of bismuth as regards electrical resistance in a magnetic field is strikingly similar. The “jumping ” of the current from one value to a higher, which has been already mentioned, appears to be due to some- thing equivalent to a sudden change in the resistance of the space between the negative leg and the middle plate when the lamp is in action and at high incandescence. The fact of “CC? 102 On the Degree of Dissociation of Electrolytes at 0°. sending a small current through this space seems to effect-a change in the qualities of the rarefied gas as a conductor which makes it conduct better. There are certain aiter-effects in some cases which are strongly similar to the polarization of electrodes observed in the case of liquid electrolysis, and which seem to point to the validity of the view that gaseous con- duction is effected by a similar process. - The experiments also confirm the opinion of Professor J. J. Thomson that gases, or at least certain gases ina rarefied con- dition, are very good conductors, and they show that the greatest part of the obstacle to conduction through a vacuum- tube is at the electrodes and may be largely ‘removed by heating the kathode to incandescence. IV. Note on the Deyree of Dissociation of Electrolytes at 0°. By Meyer WivpErmasn, PA.D.* N the Philosophical Magazine, February 1896, Mr. Wood I published a paper, “The Degree of Dissociation of some Electrolytes at 0°,” in which he, by a curve, illustrates certain molecular freezing-point depressions, by some misapprehen- sion attributing them to me. The reader will see from the paper which he cites (Phil. Mag. July 1895) that, contrary to his statement, Arrhenius’s generalization finds an excellent confirmation. In the interest of the matter I wish to add a few words on the following point. The good agreement between the degree of dissociation as obtained from the freezing-point depressions (at 0°) and from electric conductivity (18° and 25°) has sien shown that there can only be a little difference between the degrees of dissociation as obtained from electric conductivity at 0° and at 25°. Mr. Walden’s inv estigations (Zeitschr. 7. phys. Chem.) on the electric conductivity of acids at different temperatures lead to the same conclusion. What I suggested in my paper was that, as we find some differ- ences between the degrees of dissociitien of acetic acid at 18° (Kohlrausch) and at 25° (Ostwald), the electric conduc- tivity of salts and acids, &c. should be investigated near to the freezing temperature in order to ascertain the small differences possibly existing. This is of interest because of the importance of Arrhenius’s generalization ; but it re- quires accurate work, and must only be carried out on a broad basis, as has been done by Kohlrausch and Ostwald at other temperatures. Mr. Wood does not investigate the * C ommunicated by the Author, Dr. 8. P. Thompson on Hyperphosphorescence. 103 L., directly but makes inter polations, using the temperature- coefficients which have been determined a good distance from 0°, and so runs into the danger of introducing errors into the calculated degrees of dissociation greater than the differences he has to determine. His results (at 0°) de- viate from Prof. Ostwald’s (at 25°) in some cases irregularly by several per cent., and his investigations are limited to three acids and two salts. For this reason the investigation of the matter remains as desirable as it was before. Christ Church, Oxford, May 1896. V5 On Hyperphosphorescence. By Strvanus P. Toomeson, D.Sc, FAR.S.* Hf recent researches of H. Becquerelt on the emission by compounds of uranium and by metallic uranium of invisible radiations which very closely resemble those dis- covered by Wiedemannt{ and by Réntgen§, and which yet unquestionably consist of transverse vibrations, are of so great importance that any experiments upon the same line, however incomplete, are of interest to physicists. In January last the writer and his assistant Mr. Miles Walker were repeating Réntgen’s now familiar experiments on the production of photographic shadows by the emanations from Crookes’s tubes, and were casting about for means. to shorten the long exposures then necessary, when the idea occurred to them which has independently suggested itself to many other experimenters, namely that of employing fluo- rescent substances in contact with the photographic film to hasten the photographic action by the emission of rays of a visible sort when stimulated by the x-rays. Accordingly, having prepared skeets of paper or of aluminium covered with fluorescent material, they tried the effect of inserting them in some cases below the glass plate, in other cases above the glass plate with the fluorescent surface next the film, and-in yet other cases above the plate but with the fluorescent sur- face outside. The materials so tried were sulphide of calcium, finely powdered fluor-spar, sulphide of zine (natural blende), sulphate of zinc (artificial), fluoride of uranium and ammo- nium, and sundry platino-cyanides. - * Communicated by the Author. + Co umptes Rendus, cxxil. pp. 559, 790, &e. ft Zeitschrift fiir Elektrochemie, i il Ds 159 (Aug. 1895). ‘Ss peengeecr sent der Wi ee Pha iysit-medic. Gesellschaft, 1 1895, - 104 -Dr. 8. P. Thompson on Hyperphosphor escence. __ When sheets of paper or aluminium covered with these were placed face down upon the sensitive film, so that the 2-rays were compelled to pass first through them, some results were obtained tending to show that the method might have some advantages: but the resulting negatives were always patchy and irregular. The most striking effect, however, was quite unexpected. Care had been taken to keep these prepared sheets of fluorescent material in the dark for a sufficiently long time for all visible phosphorescence or persistent fluo- rescence to disappear. This, in the case of the sulphide of calcium, required many hours. The powdered fluor was also heated beforehand. Nevertheless, though no visible phos- phorescence was present, the sensitive films were fogged by rays emitted from these materials. Fluor-spar and the pla- tino-cyanides did not produce any noticeable fogging, however. Even after being kept six weeks in darkness the sulphide of ealcium is very active in the emission of rays that will affect a photographic plate. While these experiments were in progress other experi- ments were begun to ascertain if from any other sources, such as sunlight or the light of the arc lamp, any rays could be obtained having, like the x-rays, the power of penetrating opague bodies. From the are lamp, with an exposure of about two hours, shadows of pieces of metal were obtained on a photographic plate through a piece of pine-wood several millimetres thick ; but aluminium was found to be totally opaque to everything radiated from the are and to sunlight. While the experiments on fogging were still in hand there was published the observation of M. Henry on the effect of sulphide of zinc in apparently augmenting the transparency of aluminium to a-rays ; an observation which had an obvious bearing on that which was under investigation. A number of small portions of the fluorescent substances with which we were experimenting were then placed upon the front of a sheet of aluminium about 0°5 millimetre thick, behind which was a gelatino-bromide plate (a Cadett’s “lightning ”’ plate) ; and these were left for several days upon the sill of a window facing south to receive so much sunlight (several hours as it happened) as penetrates in February into a back street in the heart of London. On developing the plate it was found that behind those spots where portions of uranium nitrate and uranium ammonium fluoride had been placed, photographic action had taken place through the aluminium sheet. No very distinct effect had been been produced by the other substances. On communicating these observations to Sir G. G. Stokes he drew the writer’s attention to the similar obser- ‘Dr. 8. P. Thompson on Hyperphosphorescence. 105 vations of M. Becquerel with respect to uranium salts, ob- servations which have since been so remarkably extended. ‘While agreeing with the Réntgen rays in the property of penetrating aluminium, zinc, and other opaque materials, and in exercising photographic actions, the Becquerel rays differ in the circumstance that they can be refracted and polarized. Whatever the Rontgen rays may eventually prove to be, the Becquerel rays consist of transverse waves of an exceedingly high ultra-violet order. The circumstance that the strongest fluorescent effects are found in the compounds of two metals having such heavy atomic weights as platinum and uranium, when correlated with the other circumstance that the absorbing power towards ‘x-rays is greatest in elements of the greatest atomic weights, naturally suggests a new application of the law of reciprocity between emission and absorption. If that law can hold good in the phenomena of the Roéntgen rays, or of the closely- related Becquerel rays, one would argue that the best sub- stances to employ as emitters of such radiations would be those substances which absorb them most freely. Now the property of emitting Rontgen rays has been observed in many substances, but always under the stimulation of the kathodic discharge. In Rontgen’s original research glass was the radiator. Porter and Jackson independently found platinum- foil to be superior. Roiti has found porcelain and mica also to serve. The writer has observed Rontgen rays to be emitted from the following substances exposed to kathode discharges :—cale-spar, apatite, rubies, sapphires, diamonds, uranium glass, scheelite, tourmaline, a phosphorescent enamel containing 6U per cent. of sulphide of calcium, sulphide of zine (hexagonal blende), zinc, aluminium, copper, iron, mag- nesium, and platinum. Of the metals in the above list, iron and platinum appeared to work better than copper, aluminium, or magnesium. The low melting-points of the last two render them unsuitable. Metallic uranium would have been tried had it been possible* to obtain a specimen; but all inquiries in London proved fruitless. Of the other substances named, the phosphorescent materials seemed to have some advantages over ordinary glass, but they are not so convenient to manage as the metals. Apatite was tried because, consist- ing as it does chiefly of phosphate of lime, it was thought that the w-rays emitted from its surface could be more certainly * [While these lines have been going through the press, a specimen of metallic uranium has been given me by Mr. C. Vautin. It emits x-rays freely under the kathode discharge,—S. P. T.] 106 = Dr. 8. P. Thompson. on Hyper ‘phosphorescence. absorbed by Wee len ace he a-rays emitted from denser materials such as platinum. . At an early stage of these investigations the use of a fluo- rescent screen revealed the fact that the relative transparency of flesh and bone differed with different materials used as emitters, and depended also upon the degree of exhaustion. The necessary inference that the x-rays are not all of one kind, but are heterogeneous, was announced by the writer ee the same time* that the same conclusion was drawn by MM. Benoitt and Hurmuzescu from other causes. To the rays emitted from apatite, bone was indeed found to be more opaque than to those emitted from platinum. But apatite, when subjected to the kathode discharge, continues to give out gases which after a very few seconds spoil the vacuum ; and the tube containing apatite as an anti-kathode could not, con- sequently, be used except attached to the pump. Glass was found to be more transparent to «-rays emitted from platinum than to x-rays emitted in the same tube from glass. The extraordinary property exhibited by the uranium com- pounds of emitting a persistent invisible radiation that will pass through aluminium and produce photographic action would suggest that these rays are identical with Roéntgen’s were it not that Becquerel’s success in reflecting, refracting, and polarizing them proves that they are more akin to ultra- violet light. The latter does not indeed penetrate aluminium: but it has long been known that ultra-violet rays penetrate films of silver which though thin are thick enough to reflect all visible kinds of light. It would seem to be proved, thea, that Becquerel’s rays differ from the known ultra-violet in degree rather than in kind, being rays of higher frequency and shorter wave- length. That their properties are inter- ‘mediate between those of ultra-violet and of the Rontgen rays furnishes a strong presumption that the latter also differ only in degree, and are an extreme species of ultra-violet light. It should not be forgotten that so far back as 1857 M. Niépce de Saint Victor observed many cases in which an object, an engraving on paper or a figured piece of percelain or marble, immediately after exposure to sunlight, was found capable of giving a photographic impression to a sheet of paper prepared with chloride of silver, with which it was placed in contact. He even used, after exposure to light, cardboard imbibed with salts of uranium or with tartaric acid, and found such to be capable of emitting rays that were Pe, active. There was no ey made, how- Comptes Reus @ exxil. p- 807. | ST lid eax, ?. 779... Magnetic Field due to an Elliptical Curr ent. 107 ever, to: investigate the possibility -of transmitting these invisible radiations through opaque bodies. - The phenomenon of persistent emission of these invisible rays by the uranium compounds long after any electrical or Juminous stimulus has ceased to be applied would seem, therefore, to bear the same relation to the transient emission of them in the. Crookes tube as the persistent emission of visible light by phosphorescent bodies does to the transient emission of light by fluorescent bodies. Hence the writer ventures to give to the new phenomenon thus independently observed by M. Becquerel and by himself the name of hyper- phosphorescence. A hyper-phosphorescent body is one which, after due stimulus, exhibits a persistent emission of invistble rays not included in the hitherto recognized spectrum. June 6, 1896. VI. On the Magnetic Freld due to an Elliptical Current at a point in tts plane within wt. By J. Virtamu Jonas, WIA B.Se., FoR. spelt oan and Professor of Physics in: the University ollege of S. Wales and Monmouthshire, Cardif®. § 1. : a communication presented to Section A of the British Associationt at Oxford in 1894, giving an account of measurements made to determine the value of the International Ohm in absolute measure by the method of Lorenz, I referred to a small error consequent on the fact that my standard coil is wound on a cylinder, the section of which at right angles to the generating lines is not a circle but an ellipse of small excentricity. In considering the effect of this ellipticity on the value of the resistance calculated from the observations, it must be noted that the ordinary formula implies that the coil is circular. This formulais ~ R = Ma, where R=the resistance in absolute measure, M=the coefficient of mutual induction of the standard coil and disk circumference, n=the number of revolutions of the disk per second. But we are primarily concerned with the balance of the electromotive force between the ends of the resistance when * Communicated by the Phy sical Society : read May 22, 1896. + Report of Electric Standards ears arene If., Brit. Ass. Report, 1894. 108 Prof. J. V. Jones on the Magnetic Field the current is passing through it, and the electromotive force between the points of contact of the brushes on a radius of the rotating disk when the same current is passing through the standard coil; and this balance gives us, in the general ease, the formula R = 20n | r Har, oar Lah et we % where dp and a, are the distances from the centre of the disk of the points at which the internal and external brushes are applied, and H is the magnetic-field intensity at a point on the radius through these points of contact at a distance r from the centre when unit current is passing through the standard coil. [If the coil is circular and coaxial with the disk, this formula simplifies into the formula first mentioned. | § 2. In the case of the coil used in my observations, the dimensions of which are given below, the excentricity of the elliptical section is so small that the value of the integral (A) differs only by a small quantity from the value it would have for a coil otherwise similar but of circular section with radius equal to the arithmetic mean of the semiaxes of the elliptical section ; and to a first approximation we may assume that the percentage correction to be applied to the value of the integral for the circular coil to obtain its value for the elliptical coil is the same as the percentage correction to be applied to its value for the circle in which the mean plane cuts the cireular coil to obtain its value for the ellipse in which the mean plane cuts the elliptical coil. It will be sufficient for our purpose, therefore, to calculate the latter percentage correction. . § 8. Let H, be the value of the field intensity at a given point.in the disk due to unit current in the ellipse, and H, the value of the field intensity at the same point due to unit current in the circle coplanar and concentric with the ellipse and of radius c equal to the arithmetic mean of its major and minor semiaxes. Then we have, in this case, A=2a a H, dr QB = 2a nf ‘ H,dr+2a a| ‘ (H,—H,) dr ° a ay =u M,+2en| rede a =n (Me+ B), due to an Elliptical Current. 109 where M. =the coefficient of mutual induction of the circle and disk circumference, | and eo —H.,. $4. To obtain the value of B, we must first find. an ee for the intensity of magnetic field (H.) due to an elliptical current at a point in its plane within it in terms of the semiaxes of the ellipse and the coordinates of the pomt. Let the equation to oe ellipse be ; 2+5=1, and let £, be the coordinates of the point in question. 3 The intensity of the magnetic field at the point (&, 7) may be expressed by the formula le. 2m mee, o -P where p, 8 are the polar coordinates of a point on the ellipse referred to the point (&, 7) as origin. Forming the polar equation to the ellipse with the point (€, 7) as origin, solving for ~, and substituting in the above equation, we have E ep oo H = BPE ae |, dO »/f” cos? 6 4+ 2h? cos O sin O +9? sin’ 0, where f? =P —7’, f= af, hi? = En, Let $*, x’ be determined by the equations gp? oe x =)" +9 eS ee yeni} and we have Jel ab (27 Fey ee dO / fp? cos 0+ x? sin? 8 tab = gon Bs x where 2 Bihan) = { 7 40 VG cos OF x sin’ 6, 0 an elliptic integral of the second kind. The value of K(¢, 7 110 Magnetié Field due to an Elliptical Current. for any values‘of 6 and y may be readily calculated by finding their arithmetico-geometrical mean (v. alae : See pte rals, chap. xili.). a ‘5. In alte ease of my standard coil ; | 8 a=10°5419 inches, 6=10°5340 inches, an the angle made by the radius of brush contact ithe iis major axis is approximately 55°. I have calculated the values of H- and H, for points on this radius distant 1 inch, 2 inches, 3 inches, &ie., from the centre, with the following results : — | ie He--22. om ro+2e. r H.+2a 0 094896 094896 — ‘000000 ‘000000 ] "095542 "095542 “000000 ‘000000 De 097551 _ 097552 “000001 ‘000002 .... 3 ~*301142 "101144 000002 ‘000006 + 106764 "106768 “000004 - - 000017 5 *115252 *115260 ~ 000008 “000040 6 "128235 "128250 "000015 ‘000089 on - *149170 "149198. ‘000028 "000199 o=He—He. ~ § 6. We are now in a position to calculate ae value of B. In the apparatus I used : ao= "0585, a= 6°4949. By numerical integration between tase oe we — LS eee pe 000163, and re rodr = 00643. Also we have a= 64949, and c=10°5377,4 = - = and hence M,=94:014, and therefore _ sce a); B+M,=:0000684, or the required correction is ‘00684 per cent. And by the argument contained in § 2 this may ‘be taken High Tensions in Moving Liquids. 111 to be to a first approximation the correction to be applied in the case of the coil. Now the coefficient of mutual induction of the coil and disk calculated on the assumption that the section of the coil at right angles to the generating lines is a circle of radius ¢c is equal to 16613°75. Adding the calcu- Jated percentage correction to this value we have finally for the apparatus used by me R=n (16613°75 + 1:14) =16614°89 n. ‘The value of the International Ohm in absolute measure previously given by me in the paper to which I have referred was -99976 x 10° absolute units. _ The value corrected for the coil ellipticity is -99983 x 10° absolute units. VIL. High Tensions in Moving Liquids. X | To the Editors of the Philosophical Magazine. GENTLEMEN, OME years ago, after some holiday enjoyment of making “ducks and drakes”’ on a calm sea with flat smooth pebbles, it occurred to me as strange that I had never seen any theory given of “ducks and drakes”’ ; but convinced that a phenomenon, so beautiful as these light rebounds of solid from liquid, and so defiant of those rules of propriety so concisely laid down in our treatises on hydrodynamics for’ liquids aspiring to be perfect, must have been handled by some master of fluid motion, I thought it would be a good exercise to work out a sketch explanation of the phenomenon and see how far it coincided with the authoritative theory when found. But without an exhaustive search I have yet come to the conclusion that there is really no theory of the phenomenon published, for 1 have not encountered even an allusion to-an explanation of these most elegant “ducks and drakes.”” Under these circumstances, and at a time when hydrodynamicians are making vigorous efforts to break away from the academic allurements of the perfect liquid and to do ‘some service (hard service it seems to be) in the cause of the plain liquids of nature with their lamentable imperfection of an inveterate viscosity, it seems to me that there may be some justification for the brief publication of my rough sketch of a theory, because it brings out the possibility of the existence of high tension in liquids-in motion, so that ina general theory 112 > Mr. W. Sutherland on - of the motion of natural liquids both viscosity and capacity for exerting tension have to be taken into account. Of course one gathers either directly or indirectly that most of. the great writers on hydrodynamics, beginning with, say, Poisson and Stokes, saw the philosophical necessity for recognizing tension in liquids in motion ; and Maxwell, when introducing his idea of the ‘‘ time of relaxation ”’ of an impul- sively generated tensile strain, intended it to apply even to natural gases as well as to liquids. The merit of the “ ducks and drakes ” phenomenon is that it brings liquid tension from the region of scientific imagination to that of actual fact, and demonstrates in a brilliant manner that tension in moving liquids is no mere subordinate matter only slightly altering the properties of the liquid from those of the ideal perfect one, but produces a fundamental change. Of course static tension, of which Worthington appears to be the latest inves- tigator, has already received a certain amount of practical attention. 5 The broad facts of “ducks and drakes” are, that a solid body having a flat face and made to impinge with this face on a liquid surface parallel to it tends to rebound from the surface if the component velocity parallel to the surface exceeds a certain value; the tendency depending on the rela- tion between the area of the face and the mass of the body, and also on the angle the direction of its velocity makes with - the normal to the liquid surface: the larger the mass of the body per unit area of flat face the smaller is the ratio of the normal velocity before impact to that after ; the smaller the angle that the velocity makes with the normal the smaller is the ratio of the normal velocity before impact to that after, until a limiting angle is reached at which the ratio appears to be zero, so that for smaller angles the rebound ceases entirely. Of the existence of this limiting angle with ordi- nary stone, glass, and oyster-shells, and sea or river water, I have satisfied myself by many trials, and I have thought of making a quantitative study of the laws of the rebound of solid from liquid, but see no immediate prospect of the neces- sary time. But for present purposes the existence of the limiting angle is an important fact, because it implies also what has been already stated, namely, that with a given normal velocity there must be associated a velocity parallel to the surface not less than a certain value if there is to be rebound ; and the increasing efficiency of the rebound with increasing angle implies that the velocity parallel to the surface is the most important element in the conditions of rebound. Evidently there is an entire difference between High Tensions in Moving Liquids. 113 the laws of rebound of a solid from a flat liquid and from a flat solid surface. Let us suppose the flat face of the solid to be a square of side a, and also that it does not pass discontinuously into the rest of the surface, but by means ofa thin strip of curved surface passing tangentially into it all round, the sections of the strip by planes normal to the side of the square being arcs of radius r. Suppose the solid to move with the flat face horizontal, and with horizontal velocity u and vertical ve- locity v at the instant when it encounters a horizontal liquid surface. To trace the effects of the encounter we had better for a moment imagine wu to be zero, so that we have first the simple case of normal impact with velocity v. The first effect of the impact is to establish both motion and compression in the water near the solid, and also to compress the solid and diminish its motion. This goes on till the instant when the face of the solid and the liquid in contact with it are moving with the same velocity. But by this time part of the energy imparted to the liquid by the compression has changed itself into motion within the mass of the liquid ; and apparently in all ordinary cases this part of the ener is usually a large fraction, so that the liquid has only a little compressional energy left with which to attempt to thrust the solid body away from it; and thus the rebound fails, the dis- tinction between the encounter of two solids and that of a solid and a liquid being that in the latter case a large fraction of the available energy is soon changed into energy of motion within the liquid. Under these circumstances it comes to pass that, in consequence of the motion in the liquid, its sur- face near the solid takes the form of a curved depression tangential to the curved edges of the face. When the vertical velocity v is zero, the effect of impact with only horizontal velocity can be studied separately. The first effect is the establishment of intense tensile strain in both solid and liquid. With viscous communication of motion to the liquid and from the solid the tensile strain in the liquid tends to relieve itself rapidly by generating motion within the mass; but the solid for some little time must tend to restore the strain as fast as the liquid relaxes it, so that we have a short period of constant tension in the liquid near the solid. When both velocities u and v are in existence, a combina- tion of the states of affairs just described occurs ; by the end of some short time ¢ the vertical velocity v is destroyed, and the surface of the liquid contains a curved depression which is tangential to the curved edge of the flat face of the solid; the depression moves with a velocity comparable but not Phil. Mag. 8. 5. Vol. 42. No. 254. July 1896. I 114 Mr. W. Sutherland on equal to that of the solid, for the surface of the liquid near the solid has been set in motion by it. Let two sides of the square flat face be parallel to the direction of wu, then we may liken the surface of the depression in the liquid to a stretched membrane, and the front and back edges to portions of cylindrical surfaces of radius 7, over which the stretched membrane passes with the tension perpendicular to the axes of the cylinders, and therefore exerting pressure on the cylinders ; at the side edges the tension is parallel to the axis and is therefore devoid of pressure effect. Let 6 be the width of the strip of curved edge in contact with stretched liquid, and let the tension near the surface of the liquid be T per unit width, then the lifting pressure on each area ab is abl'/r, making an angle 6/2r with the vertical ; the total lifting force due to tension is therefore 2 cos (b/2r)abT/r. This result can obviously be extended to the case where the face of the solid is not flat with rounded edges but is any eurved surface ; let A be the area of contact between solid and liquid, T the mean tension, and 1/7 the mean curvature of the face in the direction of the tension, then each unit of A is subject to a normal pressure T/r, and the total vertical lifting pressure is the sum of the vertical components of all the normal pressures. Thus, then, we can include all cases in the one general expression sufficient for our purposes if we say that the lifting force is equal to cAT/r where ¢ is a con- stant, A is that part of the face of the solid in contact with the liquid and having finite curvature, the average value of which is 1/r in the direction of T; c, A, T, and r being also average values for the duration of the impact. Now suppose for a moment that the solid has only the vertical velocity v at the moment of impact, and let h be the distance below the free surface of the liquid to which its face penetrates before it is brought to rest, then we may assume the energy given to the liquid to be proportional to A?, and then h?=kmv?/2 where m is the mass of the solid and & is a constant. Then when w is not zero we have to take account of the fact that the force cAT/r opposes the descent of the solid, doing work AcAT/r against it, and therefore 1? =k(mv?/2—hcAT/?). Then the uplifting force cAT/r will in most cases act on the solid through distance h, and discharge it from the surface of the liquid with a vertical velocity v’ upwards given by the equation mv?/2=heAT/r, vy”? 1 ee hal thr/keAT fligh Tensions in Moving Liquids. 115 If T is proportional to the excess of the velocity u above a lower limit U, so that T=K(u—U) where K is a constant, then v?/=1/{1+hr/KkeA(u—U)}, and this expression corresponds to the general laws of ‘ ducks and drakes,’”’ for since it holds only for values of u greater than U there is a certain minimum horizontal velocity required by a solid which is to rebound from a liquid ; for horizontal velocities greater than this there is rebound, but the energy of the vertical motion after impact is always less than that before impact, although it becomes more and more nearly equal to it the greater « becomes ; also it appears from the last equation that with finite velocities the angle of incidence for which rebound is possible has a limiting value, because tan z=u/v ; and u having the lower limit U, and v the upper limit V of experimental possibility, tan 2 and therefore a has a lower limit. Again, as h increases with m, and A generally increases with the size of the face of the solid, it follows from the equation that the smaller the mass of the body and the larger the face the more nearly does v’” equal v’, whence the advantage of thin flakes of stone and shell for getting “ducks and drakes.” It is to be remembered that in the case of a flat face the area over which there is finite curvature is only the small strip of transition from the flat surface to the rest of the surface, and thus A becomes very small, but so also does 7 become small, and the effect of the shape of the face is best expressed by making A the product of an average width a and an average length 6 in the direction of motion, so that A/r becomes ab/r, which depends on a and the angle b/r. It should be noticed that the velocities are not great which are required to produce the phenomena of ducks and drakes, for at the last rebound of a series of ten or twelve the motions are very gentle, but the tension called forth must be remarkably high seeing that the impact lasts so short a time. We all know the wonderful manner in which Kelvin has helped us to grasp the coexistence in the ether of apparently irreconcilable properties by his homely instances of jelly and pitch, and it seems to me that “ ducks and drakes ” carry in themselves a suggestiveness only communicated to jelly and pitch by the sagacity and imagination of a master mind. WILLIAM SUTHERLAND. Melbourne, March 1, 1896. Ranke | VILL. Notices respecting New Books. Azimuth Tables for the Higher Declinations. By H. B. Goopwin. London: Longmans, Green, & Co. 1896. (THESE tables, extending from 24° to 30° Declination, may be considered supplementary to those of Burdwood and Davis. The limits embrace the moon, larger planets, and a belt of bright stars. The latter are more particularly useful in the Southern Hemisphere, which contains no practical pole-star. Unlike the tables of Burdwood and Davis, these have for one argument the star’s altitude, excepting in the supplementary por- tion termed Table B, which follows the ordinary usage of having as argument the star’s Hour-angle. — The tables are very legibly printed in old-face type, which lends itself peculiarly to figure work. The omission, however, of the lead- ing figures excepting at the change of the degree is a very doubtful advantage, and it is very probable that a table giving degrees and tenths only with all the figures printed would be a more useful one in the hands of the navigator. The subdivision of the degree into minutes possesses no advantages whatever, and only adds to the labour of differencing and interpolation. We observe a few figure errors, but on the whole the tables appear to be fairly accu- rately printed and read, and they should be a valuable addition to the chart-room of the skilful navigator, and an incentive to the more general use of star observations in practical seamanship. In the introduction the author states that Burdwood mentions only three bright stars between the equator and 23° §. (the limits of his tables). If we take, however, the stars in the Nautical Almanac within the author’s limit of brightness (Mag. 2°4), we find ten stars against four comprised in Goodwin’s tables. Again, the author states ‘‘for the moon, the tables will be brought into requisition for approximately one third of the month,” overlooking the fact that when the moon’s node is between 270° and 90° the declination of the moon never exceeds the obliquity of the ecliptic. This will be for a period of over nine years successively, or one-half the revolution of the node. IX. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from vol. xli. p. 524.] March 11th, 1896.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read :— 1. ‘On an Alpine Nickel-bearing Serpentine with Fulgurites.’ By Miss E. Aston, B.Sc. With Petrographical Notes by Prof. T. G; Bonney, De, LL.D., F-R.8., V.P:G:8. The specimens described were collected on the summit of the The Pliocene Glaciation of Subalpine Switzerland. 117 Riffelhorn (near Zermatt) by Prof. W. Ramsay, F.R.S., and J. Eccles, Esq., F.G.S. As they showed some very well marked ‘lightning- tubes,’ the former thought that possibly analyses might prove interesting. These were undertaken by Miss Aston at University College, London. ‘The rock is a serpentine, somewhat schistose from pressure, which has been formed by the alteration of a rock chiefly composed of olivine and augite. One of the analyses gives 4:92 per cent. of nickel oxide and hardly any lime. Prof. Bonney detected some awaruite under the microscope, but not nearly enough to account for the analysis. Reasons are given to show that the nickel oxide probably replaced lime in the pyroxenic constituent of the rock. The tubes, about 54; inch in diameter, are round in section, cleanly drilled, and lined with a very thin film of dark brown or black glass. The microscopic structure of this is described, as well as that of glass made by melting the rock with a blow- pipe (using oxygen). Some fulgurite-glass from the Hornli has also been examined (much resembling that described by Mr. Rutley from Monte Viso), and an analysis of this rock is given. 2. ‘The Pliocene Glaciation, Pre-Glacial Valleys, and Lake-Basins of Subalpine Switzerland: with a Note on the Microscopic Struc- ture of Tavayanaz Diabasic Tufa.’ By C.S. Du Riche Preller, M.A., PED EGS. F:C.8.; A.L-MCLE., M.1EE. I. The main object of this paper, which is the sequel to one read last session, was to solve the problem whether the Pliocene glacio- fluviatile conglomerates of the Swiss lowlands were deposited on a plateau or in already existing valleys. or the purpose of this enquiry, the author examined last summer a large additional number of glacial high- and low-level deposits throughout the Zurich Valley over an area more than 40 miles in length; and his investi- gations further led him to important conclusions with respect to the combination of causes which determined the formation of the lake- basins lying in the same zone at the foot of the Alps. II. The author established the true characteristics of the Pliocene nagelfluh as distinguished from Miocene, purely fluviatile conglome- rate on the one hand, and from glacio-fluviatile Pleistocene gravels on the other. With respect to the origin of the Pliocene conglome- rate, he contended that the material composing the same was not transported from a great distance, but was, in the main, derived from the enormous accumulations of Miocene nagelfluh at the foot of the Alps. Specimens of Miocene nagelfluh-pebbles were exhibited, in- cluding the so-called ‘ Tavayanaz Sandstone,’ which the author, in an Appendix to the paper, showed to be diabasic tufa. III. The author described in detail a variety of glacial exposures, and showed that Pliocene nagelfluh in situ, of which he exhibited numerous specimens, occurred not only on the ridges of the hills, but, at a gradually ascending level, also at and near the floor of the Ziirich Valley. 118 Geological Society :— Hence he contended that at the advent of the first glaciation the Ziirich Valley was already eroded, and that, consequently, the term ‘ Deckenschotter,’ or plateau-gravel, was not strictly applicable to the Pliocene glacio-fluviatile deposits of the Swiss lowlands. In his view, the isolated high-level deposits were formed during the inter- mittent shrinkage of the Upper Pliocene ice-sheet, while the low- level deposits were formed during the subsequent recession of individual glaciers left in the several valleys. IV. The author reconstructed the pre-Glacial floor of the Ztirich Valley upon the evidence of the solid rock and of the low-level Phocene nageltiuh deposits, with the result that the depth of the lower part of the Valley was approximately that of the present day, while the floor of the upper part was at a higher level (maximum, 300 feet above present lake-level), and was subsequently lowered by earth-movements. He further adduced evidence that the Sub- alpine valleys of the Reuss, Aare, and Rhine were likewise excavated before the first glaciation. By calculation, he arrived at an estimate of the time required for the excavation of the Ziirich Valley, and contrasted the erosive energy of the river with the impotence, on mechanical grounds, of a glacier 7000 times larger in volume. V. The author showed that the Lake of Ziirich owes its origin, in the first instance, to a zonal subsidence (probably between the first and second glaciation) of about 1000 feet, as evidenced by the reversed dip of the disturbed molasse-strata between the lakes of Ziirich and Zug. During the second and third Ice-periods, the original Jake-basin was gradually filled with glacial and fluviatile deposits at both ends, and was finally restricted to its present dimensions by a post-Glacial bar deposited at its lower end by a tributary river. In the author’s view, the other Subalpine lakes, extending from the Lake of Constance to Lac Bourget in Savoy, owe their origin and present limits, in the main, to the operation of similar causes. VI. With regard to the main question, the author averred that the Lower and Middle Pliocene period was, in Switzerland, entirely one of erosion and denudation on a prodigious scale. Irrespective of the evidence he had adduced, he was therefore driven to the conclusion that at the advent of the first Ice-period in Upper Pliocene times, the principal Subalpine valleys must have been already excavated approximately to their present depth, and that ever since then the action of the great Alpine and Subalpine rivers has been, as it is still in our own day, mainly directed to regaining the old valley- floors by removing those enormous accumulations of glacial and glacio-fluviatile material, which are respectively the direct and indirect products of three successive and general glaciations. 3. ‘Notes concerning certain Linear Marks in a Sedimentary Rock.’ By Prof. J. KE. Talmage, D.Sc., F.G.S. The marks described in the paper occur in a fine-grained argil- On Submerged Land-surfaces at Barry. 119 laceous sandstone referred by the U.S. Geological Survey to the Triassic or Jura-Trias period, which is found on a low tableland within 2 miles of the bluffs overlooking Glen Canyon. The marks commonly appear as straight lines intersecting at right angles, but some have a pinnate distribution, suggesting engravings of frost- flowers. A description of the markings is given, and various experiments made in the Jaboratory to illustrate the effects of formation of crystals formed over sediment are described. March 25th.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read :— 1. ‘On Submerged Land-surfaces at Barry, Glamorganshire.’ By A. Strahan, Esq., M.A., F.G.S. With Notes on the Fauna and Flora by Clement Reid, Esq., F.L.S., F.G.S., and an Appendix on the Microzoa by Prof. T. Rupert Jones, F.R.S., F.G.S., and F, Chapman, Esq., F.R.M.S. Excavations for a new dock at Barry have disclosed a series of freshwater or slightly estuarine silts with intercalated peats, below sea-level on the north-eastern side of the island. The site of the excavation was overflowed by the tide until the year 1884, when the docks were commenced. The newest deposits seen are therefore Blown Sand, Scrobicularia-clay, and sand or shingle with recent marine shells. These rest on an eroded surface of blue silt, with sedges in position of growth. Four peat-beds occur in this silt, at 4, 11, 20, and 35 feet below Ordnance datum respectively. The upper- most peat contains a seam of shell-marl, partly composed of the shells of ostracoda and partly of Bythinia, Limnea, &c. The second is a mass of matted sedges. ‘The third is aland-surface, and in places consists almost wholly of timber with the stools and roots in situ. The fourth is also an old land-surface, as is proved not only by the presence of roots in place beneath it, but by numerous Jand-shells. A fragment of a polished flint-celt was found by Mr. Storrie embedded in the lower part of the uppermost peat. By a comparison with the existing maritime marshes of the neighbourhood, it is shown that the fourth peat indicates a sub- sidence of not less than 565 feet. The sea encroached upon the area in consequence of this sub- sidence. It entered by the lowest of three low cols in the southern water-parting of the Cadoxton river, thus isolating the portion of land now known as Barry Island. A slight further movement would have converted the water-parting into a chain of islands. 2. ‘On a Phosphatic Chalk with Holaster planus at Lewes.’ By A. Strahan, Esq., M.A., F.G.S. With an Appendix on the Ostracoda and Foraminifera by F. Chapman, Hsq., F.R.M.S. This rock, which occurs at the base of the Upper Chalk, at the 120 Geological Society :— horizon of the Chalk Rock, does not exceed 13 foot in thickness and persists for a few yards only. In composition and microscopic cha- racter it presents a close analogy to the Taplow phosphatic deposit, which, however, occurs at the top of the Upper Chalk. Like it, it consists of brown phosphatic grains embedded in a white chalky matrix. The grains include a large number of pellets, attributable to small fish, phosphatized foraminifera, chips of bone, &c. Fish- teeth also occur in abundance. To complete the resemblance, the Lewes deposit rests on a floor of hard nodular chalk, beneath which is a white chalk traversed by irregular branching pipes filled with the brown variety. Such ‘floors’ are attributed to concretionary action ensuing upon a pause in the sedimentation. The piped chalk is compared with the structure known as Spongia paradowica. It is concluded that phosphatized deposits may occur at any horizon in the Chalk ; that the phosphatization is due to small fishes, attracted by an unusual abundance of food; that they are shallow- water deposits, and associated with a pause or change in the sedi- mentation. Mr. Chapman furnishes a list of 42 species and varieties of foraminifera and 6 species of ostracoda. The former indicate a deeper water origin than do those of the Taplow Chalk. He notes the occurrence for the first time in this country of Gypsina Coete, Marrson. 3. ‘On the Classification of the Strata between the Kimeridgian and the Aptian.’ By Dr. A. P. Pavlow, Professor of Geology in the University of Moscow, For.Corr.G.8. In this paper the author discusses the new evidence respecting the paleontology of the Lower Cretaceous and Upper Jurassic deposits of Russia which has come to light since the publication by himself and Mr. Lamplugh of ‘ Les Argiles de Speeton et leurs Equivalents’ (Moscow, 1892). He is now enabled to fix with certainty the zones of Hoplites riasensis and Olcostephanus hoplitoides of the provinces of Riasan and Simbirsk, and is thus in a position to correct and complete his former classification of the Upper Jurassic and Lower Cretaceous rocks of Russia, and to define more strictly their relationship equivalent to the strata of other countries. The whole of the Petchorian Series—that is, the zones of Ammonites stenomphalus and Amm. Keyserlingi—is now regarded as Lower Neocomian of a hitherto unknown boreal type, notwith- standing the affinity of its fauna with that of the underlying Jurassic (Aquilonian) strata. The author is thus led to carry up into the Cretaceous the corresponding stages in Western Europe, including the upper part of the zone of Belemnites lateralis of Speeton and Lincolnshire, the Upper Berriasian of South-eastern France, and probably the Hils Beds of Germany, instead of classing these with the Jurassic as he had previously done. A table is given in which the detailed correlation of the rocks Upper Lias and Inferior Oolite in Northamptonshire. 121 between the Kimeridgian and the Aptian of the various regions is attempted. The comparison of the beds of England and Germany with those of Russia is supported by some new evidence based on the Aucelle, four species of which are described as occurring in the Claxby Ironstone and Spilsby Sandstone of Lincolnshire. In conclusion, the author shows that in the period under con- sideration the shore-lines of Europe have been shifted by slow progressive movements passing latitudinally through the region, and that these movements did not affect the whole area simultaneously. Hence many complicated interchanges of fauna were brought about, which can only be unravelled by studying the whole course of events over wide areas. April 15th.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read :— 1. ‘The Junction-Beds of the Upper Lias and Inferior Oolite in Northamptonshire.—Part I. Physical and Chemical,’ By Beeby Thompson, Esq., F.G.S., F.C.S. The author, while combating the view that a considerable unconformity exists between the Upper Lias and the Inferior Oolite of Northamptonshire, brings together much evidence to illustrate the effects of slipping, and to show that these effects may be mistaken for those of unconformity. He also applies the evidence which he has collected to illustrate certain points in the physics of valley- formation. After giving details as to the horizon of the springs of the district, the distribution of water in the Inferior Oolite, and the development of the springs, be argues that every valley of the district has been elongated in the direction which it now has by a stream originating in a spring always at its head, and that the development of channels towards particular points of discharge has been the chief agent in initiating the formation and guiding the direction of all the minor valleys of the river-system within the influence of the same set of beds. A description of the characters of the slopes follows, and their significance is discussed, The structure of the hills and valleys of the district occupies the next portion of the paper, and the author considers that corresponding to the deepening of a valley by denudation there is uplifting of the beds below it, and at the same time an outward and upward thrust along the hillside which lifts beds there; also, that hills are reduced in height by sinking as well as by denudation of their upper parts. In discussing the question of unconformity between the Inferior Oolite and Upper Lias, the rarity of exposures of true junctions is noted, the junctions which have been chiefly examined by other observers being obscured by slipping ; and reasons are given for inferring an absence of unconformity at the horizon, both on account of the character of the true junctions, and from other considerations. The author, however, gives reasons Phil. Mag. 8. 5. Vol. 42. No, 254. July 1896. K 122 Geological Society. for believing that a slight unconformity occurs in the Upper Lias, so that the lower part of the juwrenszs-zone is absent, and not its upper part as has been elsewhere inferred. 2. ‘Contributions to the Stratigraphy and Paleontology of the Globigerina-limestones of the Maltese Islands.’ By J. H. Cooke, Ksq., F.L.S., F.G.S. A bibliography of the Globigerina-limestones is followed by some remarks on the physical features and general distribution of the strata. The limestones are divided into nine subdivisions, lettered A to I, the former being uppermost. Four seams of phosphatic nodules form the subdivisions B, D, G, and I, and local nodule-bands also occur in EK. The subdivision G serves as a line of demarcation between the Langhian Series (Miocene) and the Aquitanian (Oligocene). Details of the lithological and paleontological cha- racters of the various subdivisions are given, and the author concludes that I and the lower part of H were laid down on a sinking sea-floor, in about 300 fathoms of water; that the upper part of H and G, F, E, D, composed to a large extent of Globigerina and other pelagic organisms, were probably deposited in about 1000 fathoms; while C, B, and A were probably laid down, like I and the lower part of H, in about 300 fathoms of water. 3. ‘On the Geology of the Neighbourhood of Carmarthen.’ By Miss Margaret C. Crosfield and Miss Ethel G. Skeat. The area described lies approximately within a 4-mile radius of Carmarthen. The beds of the district have been subjected to com- plicated foldings, amongst which an earlier set, giving rise to a number of small anticlines with north-and-south axes, and a later more extensive set, due to the series of earth-movements which pro- duced the great Condrusian ridge, producing anticlines and synclines having a general east-and-west trend, can be made out. The rocks forming the subject of the present paper occur in one limb of a complex anticline produced during the latter set of movements. in this limb beds of the following ages occur:—Tremadoc Slates, Lower and Upper Arenig, Llanvirn, Llandeilo, and Bala. These beds are described in detail. A regular succession of strata from Tremadoc Slates to Decranograptus-shales is found, while the Bala beds of Mount Pleasant abut on Arenig strata, aud the reason for this irregularity has not yet been decided by the authors. The beds are compared with those of other areas. The Tremadoec Slates are equivalents of Stage 3.a of the Christiania district ; the Lower Arenig Beds with Phyllograptus angustifolius, and the Upper Arevig with Didymograptus nitidus, &c. resemble those of other British areas ; the Llanvirn Beds contain Didymograptus bifidus and other fossils ; the Didymograptus Murchisoni-beds are well known elsewhere. The Llandeilo Limestone is probably represented by sandy beds with Asaphus tyrannus; and the Dicranograptus-shales are like those of the Haverfordwest region. The Bala Beds of Mount Pleasant. Intelligence and Miscellaneous Articles. 123 contain Stygina Murchisone and other fossils found elsewhere in Bala rocks. A description of new fossils forms the concluding portion of the paper. X. Intelligence and Miscellaneous Articles. ON A ROTATIONAL MOTION OF THE KATHODE DISK IN THE CROOKES TUBE. BY FRANCIS E. NIPHER. T is well known that the equations which represent the pro- perties of the magnetic field external to a conductor are incon- sistent when applied to points within the body of the conductor. Assuming the total magnetic force within to be tangent to a circle whose centre is at the wire centre, and that the surfaces of equal potential are radial planes. Assuming the force due to an element 3 2 : 2d , of the conductor of infinite length and of section ds to be — it follows that the force at any point without the conductor varies inversely, and at an internal point directly, as the distance from the centre. Jf now within the wire we assume any radial plane as a datum equipotential plane, and determine the locus of any other equipotential surface, such that the difference of potential, measured along the lines of force, is constant, this surface turns out to be one having as a cross-section a spiral known as the lituus having the radius as an external asymptote, and reaching the centre after an infinite number of turns. It is evident that these internal surfaces of equal potential cannot be both radial planes and spiral cylinders. Maxwell disposes of this absurdity to which the equations lead in the single sentence which closes section 606 of his ‘ Electricity and Magnetism.’ He says: “ Within the substance of the con- ductor, there is no such thing as magnetic potential.” It has long seemed to me that this failure of the equations must be the result of leaving some elements of the problem out of the discussion. I have spent a great amount of time in seeking for some rotational phenomenon hitherto unrepresented in the equations. Until recently the results were wholly negative. While recently experimenting with a Crookes tube I observed that the circular aluminium disk of the kathode became slightly loose on the aluminium wire, and that it was constantly rocking in rotary motion on the wire. After several days of use, during which it had been decided to construct a tube with disks capable of rotation, the kathode disk suddenly became loosened, and began to rotate slowly on the wire as an axis. The bearings were somewhat rough, and the disk was not per- fectly balanced. It often stopped, but then began to rock against the obstacle until it again freed itself. The direction of rotation was contrary to the hands of a clock, when the disk was viewed 124 Intelligence and Miscellaneous Articles. from the point where the kathode wire pierces the wall of the tube. All attempts to accelerate or retard the motion by means of strong bar magnets, as in Barlow’s wheel, were without effect. Placing the tube at various distances from the induction-coil and giving the disk all possible positions in the earth’s field produced no change in the rotation. A more decided rotation was produced by using the brush-discharge of a 24-inch Holtz machine. No rotation has been produced as yet when the leading wires were in metallic contact with the conductors of the Holtz machine, but when the leads consisted of rods having spherical terminals, separated by short spark intervals, the rotation was always seen. When the loose disk was made the anode, no tendency to rotation was observed. Thus far all attempts to produce the effect in air of ordinary pressure have failed, but the work in this direction is not yet concluded. In the tube used, the tendency to rotation was not observed until by long use the vacuum had become very high, and it has now nearly reached the limit where the sparks pass around the tube, rather than through it. The leading-in wires are at right angles to each other in the tube used. Tubes are now in preparation which will have rotary disks facing each other as well as at right angles to each other, and various other features, by which it is hoped that many questions which at onee suggest themselves may be answered. There is much reason to suspect that the gas particles do not shoot off normally from the surface of the disk, but in a vortex the axis of which is in the two dark spots opposite the kathode faces. The fact that the anode does not respond, and that similar experiments in open air have thus far failed, seems to point to the kathode dis- charge as the direct active agent. This view is not easily reconciled with the result of the experiment made by Crookes with the hemi- cylindrical kathode (‘ Nature,’ July 3, 1879, p. 229, fig. 3), but the figure shown does not seem to quite agree with the description of it. Experiments are now in preparation which will decide this question. It is possible that the rotation observed is a direct action and reaction between the current in the disk and the ex- ternal field due to the current. In this case the rotation apparently ought to be producible in open air, and on the anode terminal of the Crookes tube. Whatever may be the direct agency producing this rotation, it seems apparent that we now have an experimental basis for impos- ing a term representing a rotation into the equations representing the conditions within a conductor.—Transactions of the Academy of Science of St. Louis, vol. vi. no. 7 (May 8, 1896). Pinl Mag 5. 7 Volwaiim lam Be I] a |e EHH asl | in L_| fl i | a =o age. 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Mag.S.5.Vol.42.PLIL. aC | ras) |_| | imei ait Ec maa EEE / Bee lala aiate al PEE es eh ee AEP el eh Detbe eal Se IS ial epee THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND [FIFTH SERIES] 4,77 AS paren LAS a EE SSE ~~ <=. gu ALERG UFS EL VSa6: ) XI. Onthe Convergency of Fourier’s Series. By W. WILLIAMS, B.Sc., Royal College of Science, London™. Me r4\HE convergency of Fourier’s series is a subject which . has been so fully investigated by eminent mathemati- cians that it is necessary to offer some apology for venturing to discuss it afresh. Itis, however, a subject of such singular difficulty,—a difficulty which has only been partially over- come,—and the investigations connected with it are so laborious and abstruse in character, that any simplification that may be effected in the method of attack is of value quite apart from any fresh light that may be thrown upon the con- vergency itself. The chief difficulty connected with the investigation is that of assigning the necessary conditions to be fulfilled by the function which determines the coefficients of the series, and this difficulty arises from the highly general manner in which the term “ function ”’ is defined and employed in modern analysis. Of course, if we confine ourselves to the comparatively simple functions which occur in the prac- tical applications of the series, functions, for example, which are continuous and obey the laws of the differential calculus, much of this difficulty disappears. But it is necessary that we should, in such a case, state clearly the limitation which we make, as otherwise our investigation partakes of a too general character, and proves too much. For, as we shall * Communicated by the Author. Phil. Mag. 8. 5. Vol. 42. No. 255. Aug. 1896. L ©9655 126 Mr. W. Williams on the afterwards see, even when we limit ourselves to functions which are finite and continuous, the limitation is too general, and we cannot determine whether Fourier’s series is con- -vergent or not until we know something of the nature of the continuity of the function. 2. The object of the present paper is to simplify the investigation of the subject, to bring it within the reach of the student acquainted only with the elements of the Infini- tesimal Calculus, and to exhibit in an elementary manner the nature of the difficulties that have to be surmounted and the principal results obtained. At the same time, in addition to simplifying the discussion, and rendering it perhaps more interesting and instructive, it is hoped that some additional light will have been thrown upon the question of the con- vergency, and that the limits within which the convergency holds will be found to be to some extent widened and more clearly discussed. a 3. The literature of Fourier’s series is very extensive, few mathematical subjects having, perhaps, been so widely dis- cussed. A very valuable account, both critical and historical, of the chief investigations into the subject has been given by Arnold Sachse (“ Versuch einer Geschichte der Darstellung _ willkiihrlicher Functionen einer Variabeln durch trigonome- trischen Reihen,” Gottingen, 1879) in an essay which has been translated and published in the Bulletin des Sciences Mathé- matiques, vol. iv. (1880). It is not proposed to enter here into the history of the subject, or. to discuss the elementary properties of Fourier’s series, such properties being treated and illustrated in ordinary text-books. We have here to take Fourier’s series in its most general form, as it stands, and determine the conditions under which it is convergent. 4. Fourier showed that if an arbitrary function of 2 can be expanded into a series of the form | glee E(v)=tay+ Sa, cos na + Sp, sin na, 1 1 LSEOE the coefficients will be determined by the definite integrals — = =|" F'(v) cos nvdv, a F'(v) sin nvdv, ca) a TT} ae v being written for x under the sign of integration. To investigate the posszbility of the expansion, it is, therefore, necessary to determine the most general conditions which the function must satisfy in order that the series thus defined may be convergent and tend to the limit F(z). 5. Of the different methods that have been employed in Convergency of Fourier’s Series. 127 this investigation, there are two of particular importance on ‘account of the results to which they have led, and the fact that they are still the methods most generally employed in mathematical text-books. These are the methods of Poisson and Dirichlet. 6. Poisson proceeds * by forming, from the given Fourier series, another derived from it by multiplying each term of the latter in succession by ascending powers of a quantity g less than unity, and then finding to what limit this derived series tends when g tends to the value 1. This method has given rise to numerous and interesting investigations. In particular, the method in the hands of Stokes in England led to the discevery of the infinitely slow convergence of a periodic series in the neighbourhood of a discontinuity. Stokes showed that when a periodic series represents a dis- continuous function, the rate of convergence of the series increases indefinitely at the point of discontinuity, or that, if a certain number of terms is required to represent the continuous portion of the function to a given degree of approximation, the number required to represent the function to the same degree of approximation becomes greater and greater as we approach a discontinuity. This important discovery was published, in Dec. 1847, in a paper “On the critical values of the Sums of Periodic Series”? (Cambridge Philosophical Society). ‘The subject was independently in- vestigated, and the same result discovered by Seidel, and pub- lished in 1848 (Journal of the Bavarian Academy, 1847-49), another remarkable instance of two investigators proceeding independently along the same line of inquiry. 7. Dirichlet’s method of proceeding is to form an expres- sion for the sum of the first n terms of the series taken in order, and to find the limit to which this tends when n is in- creased indefinitely. ‘This method was. given by Dirichlet in 1829 (Journal de Crelle, vol. iv. p. 157), in a paper which contains the first rigorous investigation into the convergency of Fourier’s series. The method is more direct than Poisson’s, it enables us to investigate the limitations more simply and effectively, and it has formed the basis for most of the researches that have been subsequently made into the subject. 8. Dirichlet starts with the finite series mF (v) Ov+ = S cos na F'(v) cos nrav T 1 MS e ~ e + ~> sin nw F(v) sin rvdv, 1 aa * Mémoires de Académie des Sciences, 1828, p. 574. L 2 128 _ Mr. W. Williams on the ‘which becomes Fourier’s series when n=. Grouping to- gether corresponding terms in nz, and summing the series so formed, he gets ae F(v)dvt+ Ls j F(v) (cos nx cos nv +sin nz sin nv) 2, 277 —7 5 ae ld —t =| ine ipetes |. (2) cosmiosaaen 277, —T aa 1 ? =7 = a) F(v) ($+ Sen n(v—z) |dv, —T 1 sordrle sin (2n+1)4(v—2) Qa Naa sin 4(v—2) Oo sin (2n+1)4(v—2) where : , sin $(v—2) is the value of [$+ cos n(v—z)], : | by a well-known summation in ordinary trigonometry. This final expression may be called the integral sum of the series. It involves two variables, or rather it involves the same variable twice over, namely, once in determining the coefficients of the series, and then in assigning to the series its different values. This double use of the same variable is denoted by the different svmbols employed in the two cases, namely, vin the one case, and 2 in the other. We may, therefore, call v the variable of integration, and x the variable of summation. Denoting the expression by 8,, Dirichlet’s problem is to determine the limiting value of 8, when n=x for all values of « between +7. This limiting value we may conveniently denote by Sa. : 9. Asa result of his investigation, Dirichlet proved that if the function F is finite, and single-valued between +7, and has only a finite number of discontinuities and maxima and minima between those limits, then Fourier’s series is con- vergent, and tends to the value F(z) for all values of « “except those which correspond to the discontinuities and the limits +7 ; the value of the series at a point of discontinuity being the mean of the values of the parent function on either side of the discontinuity and infinitely close to it, and its value at either limit the mean of the values of the parent function at the two limits. This result has been made the subject of further inquiry by later mathematicians, notably Riemann, Heine, Cantor, and P. Du Bois-Reymond, the inquiry relating to the necessity for the conditions laid down by Dirichiet. For an account of these investigations, and of Convergency of Fourier’s Series. 129 the results obtained, reference must be made to Sachse’s paper already mentioned. 10. The method employed by Dirichlet to determine the value of 8S, when n=©o is to break up the integral into the sum of elements which are alternately positive and negative, that is, into an alternating series with terms of finite magni- tude. The manipulation of this series is, however, very laborious, and the method of evaluating 8, by means of it is long, and highly involved and indirect, and consequently is not suited to the needs of the average mathematical student. The investigation given in the following paper is a simplified form of Dirichlet’s in the sense that it depends upon the evaluation of the same integral Sp. But the difficulties at- tending Dirichlet’s evaluation are avoided by breaking up the integral into three portions, two of which are of finite range, the limits being —7 to —h, and h to 7 respectively, while the third portion is taken between +h, A being infi- nitely small. It is then easy to show in a simple and straightforward manner that the two first portions vanish when n=, and that, therefore, the value of the integral depends only upon the infinitely thin strip taken between +h. By this means we’are enabled not only to evaluate S, more easily and directly, but to investigate the limitations to which the function F(x) must be subjected in a simpler manner. For, as we shall see, the conditions that have to be fulfilled by the function F(x) in order that the terms of the series may be finite and determinate, and that the nth term may be infinitely small when n=, which are conditions that have to be fulfilled in the case of every series, are sufficient to ensure that the two portions of 8, which lie outside the limits +/ vanish when n=. The difficulties attending the determination of the remaining conditions to be fulfilled by the function are thus removed to the infinitely small portion of it which lies between +A. ‘The investigation is given, first, for the case of functions which obey the laws of the differential calculus, this being the only case which occurs in ordinary analysis. Afterwards, the case of functions in which this condition is not fulfilled is taken up. II. 11. Let F(x) be a finite, single-valued, and continuous periodic function; and where continuous, let it be differen- tiable. Then, since Fis periodic, and of period 277, the limits of integration may be shifted through any distance at pleasure, provided the interval between them remains unaltered and equal to 27. Hence, whatever may be the value of the sum- 130 Mr. W. Williams on the mation variable x, we get, by putting ies and inte- grating between +7, | Sine nae F(O+e) . sin Aye 30 = =|" F(@+2)00+ oe cos n008; 5 ee Lis gee) a so that the function under the sign of integration becomes infinite only when @=0, 12. In the particular case when F(@+<) has a constant value ¢ all the terms on the right in Qa) vanish eneeEs the first, the value of which isc. Hence in this case S. At. in addition, the limits of integration are from —7 = 0, or from 0 to z, instead of from —z to am, we get S.=4e. These results will be required later. 13. Since the function under the sign of integration becomes infinite when 0=0, we have to break up the integral into three portions A, B, C, taken respectively between the limits —7 to —h, —h t0 i and h to 7* We shall now show that A and C yanish when n=<0 for values of # as small as we please, and therefore that the value of S. depends only upon the infinitely thin strip B within which the function integrated becomes infinite. 14, Consider first the portion C. Let (2n+1)40=4, and F(@+z4 put +4) ry = (40). Then oe 1 (Qn+1)37 ~ a(2n+1) (2n+1)3 es x(a mri) aOR Whatever x may be, we can always choose ht so that (2n+1)3 1h, isa multiple of 7. The integral can therefore be broken up into a number m of elements in each of which the range is 27, and one element at the upper limit in which the range is > or — This latter element will have a finite value a. For a given value of n let p be the value of the numerically greatest of the remaining m elements. Then the sum of the (m+1) elements ae between +mp-+a; and therefore C lies Beivcen taper ; since is <1. But when z m ae +1) 2n+1 * The reasoning ie precisely the same if the limits are —z to he —h to g, and g to a, h and g being independent small quantities. T Or, if (2n+1)3/ is not a multiple of mw, each element of range 27 can be broken up into four portions in each of which sin ¢ preserves the same ‘sign, so ) that the reasoning of (14) is still applicable. Convergency of Fourier’s Series. 131 increases without limit, p diminishes without limit. For each of the above m elements can be broken up into two parts of equal range 7, in one of which sin ¢ is positive, in the other nega- tive. The value of each element will therefore be of the form 2 (p1—p2) where p; is some value of x (554) taken between the limits of the first portion of the element, and p, between those : : oh of the second. But as n increases, the change in Oil oan i) when ¢ changes by 27 diminishes; and since y is everywhere finite and continuous, p, and p, tend to the same value. Hence by increasing n sufficiently, we can make p,;—p, as small as we please; and therefore in the limit when n= © it vanishes. In other words, since as 7 increases x(=55) tends to remain constant during the integration of any element while sin ¢ passes through all the values included between +1, each element tends to the value zero, the value it would really have if x( mri) remained absolutely constant during the inte- gration. | 15. This holds for all finite values of 4 however small. When A is very small, p, and p, will have their greatest values in the neighbourhood of 6=(2n+1)$h, in which case (putting «=0 for convenience, the reasoning being applicable for any value of «) ey: pew 5, an Oy ul a pny El +) as 1D) é ‘ 27 ee where ¢ is some value lying between 0 and Fp te and is in- finitely small compared with h. (p,—p,) can therefore be made as small as we please for values of h as small as we please provided f is so chosen that and ee are both infinitely small. But since F is everywhere conti- nuous, and n is to be increased without limit, this condition can always be satisfied. Hence the limit of p, and therefore of C, is zero for values of h as small as we please; and in the same manner we may show that the limit of A is zero. The value of 8. therefore depends only upon the value of the infinitely thin strip B of breadth 2A within which the function integrated becomes infinite, and is independent of the values of F(0+.x) outside this strip. Consequently, we 132 Mr. W. Williams on the may, outside the strip B, assign to F(@+.) any continuous finite values at pleasure. 16. Since within the strip B the range of integration is infinitely small, we may replace F(@+.x) by F(«)+ 6F'(2). We then get, putting 36 for sin 40, tees — sin —— 1)39 4 5 = © ("sin (an-+ 1)1698, ee , 2a a - my which reduces to the first term on the right because the integral of the term involving F’(x) is zero. The value of S, when n= is therefore the same as the value it would have if F(84+ 2) remained constant throughout and equal to F(z). Hence 8,,=F(z) by (12). 17. If we change the limits of integration in 8, from —7 and a to —7 and 0, or 0 and 7 respectively, we can evaluate the integral exactly as before. For since the portion taken between —a and —h, or between h and 7, vanishes when n=, the value of the integral depends only upon the inf- nitely thin strip taken between —/ and 0, or 0 and A. Hence, replacing F(@+ 2) in this strip by F(2) + @F’(), it follows, as before, that the value of the integral is the same as the value it would have if F(@+.2) remained constant throughout and equal to F(z). Hence in this case 8, =3F (x) by the latter portion of (12). From this it follows that in the original integral taken between +7, F(@+.2) may change abruptly in value or experience a discontinuity when 9=0; for we can break up the integral into two portions at the point @=0, and evaluate re AV each portion by the above as if the other were absent. If F(@+ 2) is discontinuous when @=0, it will have different values at that point according to whether @ attains the value zero from the negative or from the positive side. Thus, let @ have a small numerical value 6, and lei O0A= —6, OB=6,AA’/=F(«—6), BB’=F(2#+6). Then when 6 vanishes, F(xz—6) becomes F(2—0) or OA”, and F(a#+6) becomes F(#+0) or OB”. If, then, we evaluate each of the above portions asif the other were absent we get OA” or $F (4—0) for the first portion, and }OB” or 3F(2+0) for the second. Convergency of Fourter’s Series. 133 Hence in such a case 8, =3[F(a—0)+F(2+0)]*. F(04+2) may have such discontinuities for other values of ae as well, provided their number is finite. For if we break up the integrals A and C between neighbouring discontinuities into separate portions, we may show, as in (14) and (15), that each of these portions vanishes whenn=«. Hence, since there is only a finite number of them, their sum vanishes, and there- fore A and C vanish when n=; so that, as before, the value of S,, depends only upon the value of the infinitely thin strip which lies between +f. Consequently F(@+.#) may have any jinite number of discontinuities between +1, the value of S,, at any discontinuity being the mean of the values to which F(6+2) tends as the discontinuity is approached from either side. 18. If F(@+2) is not periodic, we may regard the portion of it included between +7 as a wave of an arbitrary periodic function with, in general, finite discontinuities at +7, +37, &c.; so that when w= +7, S.=3[F(—7) + F(a)] by (1a)t. * Or thus, f 2 16 = [| F642 yee ae He+( F(e+2) Oe n+1)36 20] ea j , sin (2n+1)36 - Ly. [Fe—6)+F (e+e) ntti 9, Hence, applying to this the method of (16), we get 3[F(#—0)+F(«+9)]. t Or thus :—If F(6+-.2) is not periodic, ta que sin (2n+1)40 Sn=o- | F(6+2) i ae 38. —nm—Z If x lies between 0 and z, Sn= Bm F(6+2 ye aE oe oak F(6--e— ee (nt 1)a a sin 40 sin 30 and if x lies between O and — zr, 2 i =T—L 7 . 9 i = B| Fetetae ) ee oo+9 = F@+2) 39. In both cases the function under the sign of integration becomes infinite only when 6=0, and the integration can therefore be effected by the methods given above. ae x=r in the former, or x= —z in the latter, we get ¥ sin sin (2n+ 1)30 2" * % sin (2n+ 1); 1)30 6, LS ae +9) sin 36 ar Qn |, (—wre) sin 36 — ° the limit of eoeeg when 2=00 , is 8. =4(F(—m)+F(n)]. 134 Mr. W. Williams on the 19. Hence, finally, if F is finite, single-valued, and con- tinuous between +7, or, if not continuous, has only a finite number of finite. discontinuities, and where continuous is differentiable, then Fourier’s series is convergent, and tends to the limit F(x) for all values of w except those corresponding to. the discontinuities and the values +7, +37, &c. The value of: the series at a point of discontinuity is 4[F («¢—0) + F(#+0)], the mean of the values to: which the function tends when ap- proaching the discontinuity from either side ; and its value at +7, &e., is $[ F(7) + F(—7) ], the mean of the values of the function at the two limits. . IIl. 20. The simplification in the above method of evaluating the integral 8, consists in having first proved that the two portions A and C taken respectively between the limits —7 to —h, and h tog vanish when n=x however near to the value zero we take the ordinates +h, so that the value of the integral depends only upon the value of the infinitely thin strip B taken between +h. S,, is therefore independent of the values of F(@+.x) outside the strip B, and consequently is the same as if F(@+.) remained constant throughout and equal to its mean value F(x) within B. That is, 8, = F(z). 21. The vanishing of A and C when n= depends upon the fact that the function integrated, namely y(3@) sin (2n+1)46- has an énjinite number of finite oscillations (that is, oscillations of finite amplitude) between —7 and —A, and between h and 7. Hence, since the number is infinite and the ampli- tudes finite, neighbouring oscillations differ, infinitely little from each other, and therefore the area included between the ordinates —7 and —h, or h and 7, and the portions of the. function and the axis of @ intercepted by them is infinitely small. In other words, the mean value of the function from —7 to —h, and from h to 7 is.zero, and therefore the integral of the function between the same limits is also zero. But the function itself is not zero: it is merely indeterminate,—the oscillations being, as it were, too fine-grained to be traced individually. The transformation (2n+1)40=¢, however, resolves these oscillations, however fine-grained they may be, into oscillations of finite period cutting the axis of @ at equal intervals a7. We are therefore enabled to deal with each. individual oscillation instead of with the oscillations as-a whole, and so to determine the precise effect of each upon the value of §,,. : : 22. If we break up the portions A and C of the integral S,, Convergency of Fourier’s Series. 135 into (m+1) elements as above, without transforming the yariable we can show as before that each element vanishes when n=. But the sum of the m elements taken in this form is not determinate when n=x. For as n increases without limit, m also increases without limit, and therefore the sum tends to the indeterminate yalue © x0, as in the case of any definite integral. We have thus no means of determining whether A and C vanish when n=. But by means of the transformation (2n+1)40=¢, we see that each element is Sone of the form. am (2n+ Seam) oll (5 ae )sin fog. Here the integral, independently of the facto ! a m(2n-1)’ or infinitely small when n=, and this multiplied by oo gives us an infinitesimal of the second order. Hence the sum of the m elements is ag really (00 x0), but (co x0"), or @ x 0), eee the form — — when looked sae is found to be derived from = Daa ee real limit is <1. It is this that determines the convergence of 8, to its limiting value. 23. It is necessary to remark that in general an element of | Aqr Qn+1 vanishes when n= only when @ is, numerically, not less than h, and h is not less than the value necessary to ensure that f F(h+t)—F(h) 2 and a me are both infinitely small, ¢ being the integral S, in which the range of integration is s—— = or <5 =i (see 15). Ofcourse, since ¢ can be diminished without ei by increasing n without limit, and F(@+z2) is continuous, this condition can be satisfied for values of h less than any assignable finite limit, however small. But as n increases without limit, the two infinitesimals ¢ and A must. diminish at different rates ; for whereas ¢ tends to the value zero at a constant rate, h ate be so at a coustonity dime- h may be oon , &c. The nishing rate, Thus, ¢ being on = it consequence of this is that in the integral (Fete oaks ee 38, 136 ~ Mr. W. Williams on the although f/ is infinitely small and F(@+~) is corti between 0 and h, we cannot without a special examination treat F(@+ 2) as constant in the integral, and write F( {” sin aE 0. —h For, since must be infinitely small compared with 2?, 1 2n+1 . aT however small A may be, pbuen tha has an infinite num- 2 é ber of oscillations between 0 and A. In such a case we must write the integral in the form F(a le sin aa Cry 208+ | [F@+8)— Fla) Os 1)365 5 7 and determine oe what conditions, if any, the second term vanishes. 24. Now although the function F (@+.) is continuous between 0 and A, and therefore F(72+6)—F(2) is infinitely small between the same limits, it by no means follows that the second term in the above vanishes when n=. Its vanishing depends upon the nature of the continuity of the function F, and we have only proved that it vanishes when the continuity i is such as to admit of the existence of a derived function F’. In modern analysis, a function F(z) is said to be continuous at the point 2 if, 6 and e being positive quan- tities as small as we please, and @* any positive quantity at pleasure between 0 and 1, we have for all values of @ F(2+68)—F(z) less in absolute magnitude than e (Cayley, art. ‘‘ Function,” Lncyc. Britt.). In other words, F(z) is continuous at a point 2 if a region (a—6) to (+6) can be found such that the values of the function for all points within this region (that is, F(2+0@6) for all values of ¢ between 0 and 1) differ from its value at # by a quantity = ~~ 3 , ~ =a ~ Soy = - ~ ~ =. = >. ~ ~ ~ ~ ~ > -~<, =, ~s . > w danger of applying to them, without a special examination, processes which have been derived only from the study of functions possessing ordinary continuity. It is precisely in the case of functions of this kind that the integral sin a +1)36 TE(0-+2)—F(a)] 00 becomes indeterminate in value whenn=c. If the function possesses ordinary continuity we know that the integral va- nishes ; otherwise the integral may be quite indeterminate. For the infinite number of oscillations of eed when n= may conspire with the oscillations of Fle 0) —F (zx) to produce any value whatever, finite or infinite. In cases of this kind we can determine nothing as to the value of the integral until we know something as to the nature of the continuity of the function; for the ordinary definition of a continuous function is £00 general, and does not confer upon the function enough properties to enable us by means of known processes of integration to evaluate the integral. 27. The conditions under which Fourier’s series has been, up to the present, proved to be convergent are :— i. That the function F(z) must not become infinite. ii. It must be continuous and determinate except at a finite number of points, where it may change abruptly in value or experience a discontinuity. iil. It must, wherever it is continuous, possess ordinary continuity. . These conditions are sufficient for all the cases that occur in ordinary analysis. The third condition, moreover, is necessary in all such cases, since processes involving differ- entiation constitute an essential part of the Infinitesimal Calculus. From the point of view of the general theory of Convergency of Fourier’s Series. 139 functions, however, it is necessary to consider the cases in which this condition does not hold. 28. The investigation of Dirichlet involves the first and second of these conditions, but not the third. The third is replaced by the more general one that F(z) must not have an infinite number of maxima and minima between +7. In Dirichlet’s investigation this condition is applied to the function throughout the whole extent of the integral §,, that is for all the values of the variable of integration 6. This, howeyer, is not necessary. For it has already been shown that the portions A and C of the integral vanish when n= if only the function is finite and continuous—the nature of the continuity being immaterial. The third condition should therefore apply only to the infinitely small range of values of F(@+.2) which lie on either side of 2=0. We shall now show that this condition is sufficient to ensure that the integral h l [feet Fe] SE 6 —h 2 vanishes when n=, and that therefore 8, =F («). This integral can be put into the form {90 a Lane h being infinitely small, while m is infinitely great and 6(6) infinitely small between 0 and A. Since $(0) has not an infinite number of maxima and minima, it will ultimately preserve the same sign, and either constantly increase or constantly diminish between 0 and h. Let it constantly de- crease. ‘Then, dividing the variable by m, we get 6G) "an8e This integral can now be broken up into the sum of a series of elements which are alternately positive and negative and ] diminish numerically). Hence the integral becomes an alter- nating series with constantly diminishing terms, and its value is therefore less than the first term, which is itself infinitely small. That is, the integral vanishes. Again, let 6(@) con- stantly increase between 0 and h. Then its greatest value will be $(h), and [d(h)—¢(@)] will therefore constantly constantly diminishing numerically (since cla and (7) 140 Mr. W. Williams on the diminish. Hence the integral { t4e)-69] 800 vanishes by the above when n=. But this integral is equal to sca eae | 80 ae 56: and therefore, since the first term and the difference of the two are both infinitely small, the second term must also be infinitely small. Thus in both cases the integral vanishes, so that S,=I(z). It is interesting to note that the alter- nating series which appears in Dirichlet’s investigation appears also here, but in a different manner. For whereas in the former case it appears with terms of finite magnitude, here its terms are infinitely small, because the two portions of the integral 8, which lie outside the infinitely thin strip bounded by +A have already been disposed of. There is therefore no trouble in manipulating the series ; for all that we have todo is to show that the terms decrease numerically, since the series can then be neglected, the first term being infinitely small. 29. Functions having an infinite number of maxima and minima are of two kinds, according as to whether the ampli- tudes of the oscillations are finite or infinitely small. In the former case the functions are discontinuous, for they violate the definition in (24) ; in the latter case they are determinate and continuous. Dirichlet maintained that all functions which have only a finite number of indeterminate values, and are elsewhere continuous, give rise to convergent Fourier series *; but Du Bois-Reymond and Schwarz have given examples of functions which are determinate and continuous, but for which Fourier’s series is divergentt. These functions are of the class mentioned in (26) for which the integral {, e+ —F@) Soe is infinite or indeterminate. 30. The condition that F(@+ 2) must not have an infinite number of maxima and minima is not a necessary condition in order that Fourier’s series may tend to the value F(a). For Lipschitz | has shown that the series may be still con- * Sachse’s Essay, p. 19. + Ibid. p. 49. t Ibid. p. 21. Convergency of Fourier’s Series. 141 vergent, and tend to the limit F(x), even when F(@+2z) has an infinite number of maxima and minima, provided that at all the points where the function oscillates, the numerical value of F(vx+0@+6) —F(v@+6@) is always less than Bo*, when 6 tends towards the value zero, B being a finite constant, and a@a positive exponent: Here again it is really necessary to apply the condition only to the infinitely small range of values of the variable of integration which lie on either side of 6=0; for if the condition is satisfied for these values, the integral h oy 1 [F(e+6)—F(a)] Be See vanishes, and therefore, as before, S,=F(«#). This integral vanishes under the given conditions because its value cannot be greater than the value it would have if sin (2n+1)30 were replaced by unity, and all the negative values of F(2+0)—F (x) made positive. Hence, since for all values of @ between 0 and h, h being infinitely small, the numerical value of F(x+0)— F (z) is < BO", the integral cannot be greater than 2Bh* h 2B) GaaOU, or b) 0 which is infinitely small, since # is a finite exponent. Thus, the function may have an infinite number of maxima and minima of this type, and still give rise to a convergent Fourier series, whose converging limit is F(x). 31. It is not necessary that F(@+#) should be finite throughout between +7. It may become infinite at a finite number of points a, a,... provided that lim (4te¢ al F(0+ 2)o@ a—U,6 vanishes, 4, and p, being any independent positive fractions. For if this vanishes, then lim a tee si C=O Pa evra, also vanishes, unless @ passes through the value zero, for it tends to the value utp lim: (i es sea[zeo|, 0+ 2)d2 |, —pe Phil. Mag. S. 5. Vol. 42. No. 255. Aug. 1896. M 142 Mr. W. Williams on the Hence, any element of the form ee. Es #) sin md 7 es ih oee) must vanish when e=0, provided F has not an infinite number of oscillations at the point a, for it cannot exceed the value it would have if sin m@ were put equal to I all through. The sum of the finite number of elements of this form which occur in the integral 8, at the points a,a,... is therefore zero. Again, since (8+) is continuous up to (a—py,e) and beyond (a+ p.€), we can always choose for ¢ a value such that F(a+pe+t) —F(a+pe) isas small as we please, however small : 20 pe may be, ¢ being = or < Brey? and n=«. Hence, by (14), the elements p which occur in the neighbourhood of the infinite values of F(@+ 2) are infinitely small when n=o , and therefore, as before, A and C vanish when n=o. HI, then, (6+) is not infinite when 6=0, 8, =F (a), provided the conditions relating to the portion B are fulfilled; but if F(6 +.) is infinite when 0=0, the value of B is «, and therefore S,=«, or the series is divergent, as we should expect. Hence, if the function contains a finite number of infinite values of the above kind, Fourier’s series 1s, ceteris paribus, convergent for all values of 2 except those corre- sponding to the infinite values, and for these values of # the series is divergent. 32. If the function F(@+.) is indeterminate over a finite range of values of x-—for example, if it has an infinite number of discontinuities, or maxima and minima of finite amplitude, over that range—the coefficients of the series and therefore S, cannot be determinate. But the function may have an infinite number of discontinuities, or maxima and minima of finite amplitude, or singularities in the neighbourhood of a finite number of poznts ; for, since the range within which these singularities occur in the neighbourhood of one of these points is infinitely small, and the function is never in- finite, the elements of the integrals which determine the coefficients and 8, corresponding to this range must be infinitely small. Hence, since there is only a finite number of such points, the sum of the elements corresponding to them vanishes, so that the values of the integrals are determined only by the continuous portions of the function. Hence, the coefficients of the series are finite and determinate, and 8, tends to a definite limit for all values of 2 except those corre- sponding to the indeterminate points in the function; and Convergency of Fourter’s Series. 143 for these points the integrals ('e (a jayne ee 20 0 2 are indeterminate in value. 33. We may therefore summarize the conditions under which Fourier’s series is convergent as follows, taking first the case where the function F has no infinite yalues—the ease of a function having infinite values being discussed later. In order that the series me | FO v)dv+ = 00 nel F'(v) cos nv Qu ] e oe © i E > sin nae F(v) sin nvdv I ot may be convergent when n= for any value of « i.) The coefficients must be finite and determinate ; (ii.) The nth coefficient must vanish when n= x These are conditions that hold in the case of every series, independently of its particular character. They are therefore necessary conditions, but they are not sufficient. 34. The first condition is satisfied if the function which determines the coefficients is not indeterminate or discon- tinuous over a finite range of values of the variable, but is continuous and determinate except, possibly, in the neigh- bourhood of a finite number of points where it may have any number whatever of discontinuous, indeterminate, or singular values. The second of the above conditions is also fulfilled under the same circumstances. For, if we take the coeffi- cients + {Fe COS RV Ov, =| Ga) sin NV OU, TUS Ns T ) —a and divide the variable all through by n, we get So ve (“) COS VAL, a Tey sin vdv. n n NT} —nz NT |) —nr Then breaking up each integral into n elements of range 27 and applying ‘the method of - (14) we can show that the inte- grals vanish when n is infinitely great. 35. The condition given above to ensure that the coefficients of the series are finite and determinate (namely, that F(x) must be determinate and continuous, except in the neighbour- hood of a finite number of points) is a special case of Riemann’s general condition as to the integrability of a M 2 144 Mr. W. Williams on the function *. Riemann’s condition is as follows :—Consider a function F(2) between a and 6. Divide (6—a) into intervals 6; 6)... &,, so that (6—a) = (6,4+6,+...4+5,). Let D denote the numerical value of the difference between the greatest and least values of F(a) within the interval 5,; similarly D, for the interval 6,, &. Then D, is called the oscllation of the b function within the interval 6,. In order that F(x) 02% may have a determinate value, 5 (6,D,+6,D,+6;D3+...+6,Dz2) must tend to the value zero when 6, 6,...6, are diminished without limit, the necessary and sufficient condition for which is that the sum of the intervals within which the oscillations D are greater than a given finite quantity o, however small, must be infinitely small when the intervals are infinitely small. If the oscillation within an interval 6 taken on either side of a given point is always >o when 6 is diminished without limit, the function is said to be discontinuous at that point, and the point is spoken of asa point of discontinuity ; and, on the other hand, if the oscillation is 198°5 J 156 Mr. R. Appleyard on Dielectrics. — Resistance during Melting. If the temperature of paraffin-wax is raised much higher than is indicated in Table I., the change of state, as melting is approached, is characterized by a corresponding decrease in resistance. In order to examine this effect, a special con- denser consisting of two horizontal circular plates, 11 in. diameter, was used. The lower plate was provided with a projecting rim to retain the wax, and was rather larger than the top plate. Three small wafers of thin ebonite sheet (16 mils) were used as distance-pieces. Melted wax was then poured in, filling the space between the plates. There are so many disturbing influences affecting the resist- ance during the change of state, connected with the latent heat of solidification, the unequal melting, the absence or not of ‘electrification,’ and the contractions and expansions of the wax, that only qualitative results can be given. Heating.—Starting at about 20° C. below the melting- point, the resistance rapidly diminishes until actual meltiny begins; there is then a definite fall to something like one third of what the resistance was just before melting. If heat is still applied to the condenser, the resistance keeps steady until the melting is complete ; after which the resistance again diminishes steadily. So far as I am able to discover there is no ‘ electrification” while the wax is in the melted condition. The spark-resisting power of the melted wax is at least one third that of the solid. The melted wax in this particular condenser broke down under 1200 steady volts; the insulation heals, as in the case of oil, to break down again in a few seconds. Cooling.—A converse process occurs during cooling ; and as the cooling is more uniform than the heating the effects can be more easily noted. The resistance of the melted wax gradually increases until the first crystals appear, at which stage it remains more or less constant until the process is nearly complete, when it very rapidly increases to about three times the value it had during the partial crystallization; it then behaves as solid wax. APPENDIX I. When an extra wire (fig. 1) is added from the +testing- battery to some point near the middle of the cleaned end of the lead, intercepting the path of leakage (a) at that end, the circuits can be represented by fig. 2. The (a) leakage is Mr. R. Appleyard on Dielectrics. 157 here m+n, and the ‘“suard”? wire is supposed to come between mand n. Let 6, 9, and r denote the resistances of ae Io a. the battery, galvanometer, and the dielectric resistance of the condenser, respectively ; let EH be the E.M.F. of the testing battery, and G the current through the galvanometer when the “ ouard”’ wire is applied. It is clear that m shunts the galvanometer, and n shunts the battery ; and we have to find the error which this introduces into the results. From fig. 2, by Kirchhoff’s laws, we have G= no a gk @1B) (6+g+r)+ past (nrg + brm + brg + bmg + nbg) Let k= (nrg + brm-+brg-+bmg +nbg), eC) then « may be regarded as equivalent to a resistance added to the simple circuit b+ 9+r. To evaluate x, we will put m=n=r; which means that the whole leakage, m+n, is assumed to be only twice the resistance of the dielectric of the condenser, and corresponds to a worse lead than any I have employed throughout these tests. In this case, (2) reduces to 3 bg Be which has now to be compared with (b+g+7) in (1). Taking the very lowest observed value of 7, which was 2x 10° ohms, and putting g=8000, and 6=200 ohms, we have p 1 b+g+r 50,000? so that « is quite negligible in equation (1), and the error introduced by the “ guard” wire is practically nl. Phil. Mag. 8. 5. Vol. 42. No. 255, Aug. 1896. N K=9tbt 158 Mr. R. Appleyard on Dielectrics. Apprnpix II... Change of Dielectric-resistance with Temperature. Let the resistance at some fixed temperature be R; and let Ry, Ry, Rs, &c. be the resistances at 1°, 2°, 3°. . abo R. The assumption is that the resistance diminishes Le, of itself for every 1° rise of temperature. In this case, ~ tap = R — Lg nr R r= R—R? = ° 5 » . ° ; . (1) and | | R= R,— a Or, putting in the value of n, Rae ho = a Hence R RY z =R( 2), R=R(R) 5 hee and, generally, 3 R R R, : ‘ = a. a If r and @ are any two values of ¢, we have F R, wg R= RR) ee Ry log R, —log R, ye bata )=— eg By putting observed values of R,, R,, 7, and @ in this last expression, the value of = may be found, and substituted C: in (8), which then becomes the working formula. In the paper, (ie) is represented by a. Comparison of « for Centigrade and Fahrenheit Scales.—Let R, be the resistance 1° C. above that at which R is measured. Then, by the preceding, aa = Measurement of Alternating Electric Currents. 159 and (2) becomes R,= Ret, But 1° F. may be expressed as (3) C., so that . Rs) = Ra, uremia eis Serie. ih() and Ru ) will be the resistance at 1° sh Hence Rs) =Ra,. ee | enn) Thus, from (4) and (5), 5 ap a3), or, log “=(2) log a. XIU. On New Instruments for the Direct Measurement of the Frequency of Alternating or Pulsating Electric Currents. By ALBERT CAMPBELL, B.A.* Be many experiments with alternating currents it is a very great convenience to be able to draw the supply from an ordinary lighting circuit, but the value of such a source of current is often lessened by the fact that the frequency of alternation is usually variable, the limits of variation being in some cases very wide indeed. It was for the purpose of getting rid of this uncertainty that, about a year ago, I devised the two instruments described below. Most methods of measuring frequency depend either on Impedance measurements or on the production of Resonance (or Synchronism). The former I avoided, for unfortunately the wave-form as well as the frequency affects impedance, and I aimed at an instrument which would give trustworthy readings for any kind of pulsating current whatever. Of the Resonance (or Synchronism) methods two are familiar. The first consists in running a small synchronous motor and measuring its speed by a speed-counter or indicator. This is a rather laborious way, and not very accurate if only a tachometer is used. In the second method+ a stretched wire carrying the alternating current is placed in a constant magnetic field; by varying the stretchin g-weight the wire is * Communicated by the Physical Society: read May 22, 1896. + Due to Professors Ayrton and Perry. N 2 160 Mr. A. Campbell on the Measwrement of the tuned until it is set into strong vibration, and then the frequency is calculated from the tension, length, and mass of the wire. The original arrangement has been simplified, I believe, by Mr. Alexander Russell, of Faraday House, who uses a steel wire thrown into vibration by an iron-cored choking-coil placed near it. In both arrangements some uncertainty is introduced by the wire pussing over a bridge or pulley. In my first type of instrument I developed the last- mentioned arrangement. The working parts of the instru- ment are shown in fig. 1:— Fig. 1. A steel wire, W, is fastened at one end to a spring, S, and at the other to a rack, R, sliding in guides. Near the wire is fixed an electromagnet M with a laminated core; this magnet is excited by the given alternating current. By turning the pinion P the wire can be tightened until it is thrown into vigorous vibration by the magnet. The pointer Q attached to the pinion then shows directly the frequency ona suitably graduated scale. Many varieties of this arrangement may be used ; for example, the pointer may be fastened to 8, or other kinds of magnifying-gear may replace the rack-and- inion. ‘ With careful use I believe that this type is accurate to within less than 0°2 per cent., but it is not so convenient as ~ the second type, which I now proceed to describe. This more practical instrument is shown diagrammatically in fig. 2. Here M is a choking-coil fixed near a steel strip A*, which can be moved back and forward through the clamp B by a rack-and-pinion, not shown. A’s change of length is * J find, since writing the above, that in 1889 Professors Ayrton and Perry suggested the use of a variable magnetic toneue near an alternatin y suge o 5 g electromagnet. Their idea, however, was never embodied in a direct- 1ead.ng practical instrument. Frequency of Alternating Electric Currents. 161 magnified by the rack-and-pinion D and E and the pointer F. The protruded length of A is altered until the alternating Fig, 2. field due to M causes the maximum resonance, and the fre- quency is read off on the scale G. By proper choice of the dimensions of the vibrator and the rack-and-pinion a very extended scale may be obtained. I have constructed one instrument in which the pointer goes more than twice round the circumference from 40 periods per sec. to 150 periods per sec., and at the middle part of the scale the accuracy of reading is within 0:3 per cent. The electromagnet M is usually of fine wire, and has a non-inductive resistance in circuit with it, so that the current taken is very small. The reading is usually taken at the point of maximum resonance. ‘This is observed by means of the sound given out or by watching the variation in amplitude either directly or by mirror, light-spot, and scale. Sometimes I fix near the vibrator an adjustable piece, against which it rattles or jars when the resonance is sufficient. This jarring piece may be made part of an electric circuit, including a lamp or an indi- eating instrument, in such a way that the circuit becomes broken when the greatest resonance occurs. The instrument can be used as a speed-indicator for machinery by attaching to the rotating shaft a suitable com- mutator to make and break an electric circuit carried to the instrument, which may thus be at any distance. If we keep to simple English we might call such an instrument a ‘ Wave-teller,” but to make the meaning clearer I propose to name it a ‘‘ Frequency-teller.”’ In conclusion [ may mention that since there is very little inertia in the moving parts the readings can be taken rapidly, and thus the instrument can be made to follow fairly quick changes in frequency. 162 Dr. Silvanus P. Thompson on { XIV. Some Experiments with Rintgen’s Rays. P g ) By Stivanus P. THompson, D.Se., FRS* HE following isa brief narration of points observed by me during the past three months, and which are now brought before the Physical Society. 1. Many experiments have been made to observe rola tion of ‘v-rays, but no trace has been found. Tourmalines of several colours, and thicknesses varying from 0°1 millim. to 6 millim., have been used. Andalusite, mica, cale-spar cut in slices parallel to the axis, epidote, and ripidolite have been tried without result. The method pursued has chiefly been to cut the slice of crystal into three parts, laying two of them upon the third, one of the upper parts having its axis parallel to the axis of the under part, while the other had its axis laid at right angles. In this way equal thicknesses of crystal were compared side by side. Thinking that results might be obtained from dichroic crystals containing a metal of consi- derable atomic weight, slices were tried of crystals of sulphate of nickel, sulphate of nickel and potassium, sulphate ef cobalt and potassium, sulphate of cobalt and ammonium, fluosilicate of cobalt, and fluosilicate of nickel, but no trace of polarization was seen. Another method consisted in comparing the opacity of tourmaline in a direction parallel to the axis with that of an equal thickness in a direction at right angles to the axis. Not the slightest difference was observed either in the photo- graphic shadows or with the use of a luminescent screen of barium platinocyanide. 2. For several weeks in the months of February and March experiments were made with many different forms of bulb to determine the source of the x-rays and the form of tube most favourable to their production. In common with the con- clusions ef so many other observers, it was found that the effective source was in every case a surface against which the kathodic discharge was directed. A form of tube which gave Fig. 1. results superior to those of any Crookes tube at the time in the market is shown in fig. 1, in which the kathode consisted * Communicated by the Physical Society : read June 12, 1896, some Experiments. with Rontgen’s Rays. 163 of a number of iron wires spread out from a centre, and the antikathode, which also served as anode, was a spade-shaped piece of iron or platinum. Another form of which many bulbs were tried was provided with an external kathode of foil, and an internal anode projecting to about the centre, terminating in a small spade of platinum-foil as antikathode (fig.2). This also gave good results, but was liable to be pierced Fig, 2. at high stages of exhaustion. With this form various experi- ments were tried as to the influence of the material of the antikathodic surface. Glass was found to work quite well, but to be more troublesome than metal. A phosphorescent enamel made by fusing together two parts of a soft lead-glass with one part of Balmain’s luminous paint was also tried. The result of these experiments was to show that, contrary to the opinion then current that the presence of much phospho- ‘rescence or fluorescence was promotive of the production of the x-rays, the 2-rays were most freely emitted when the conditions were such as to waste as little as possible of their energy in internal fluorescent effects: that in fact a metal surface was preferable to a surface of glass, enamel, or por- celain for receiving the impact of the kathodic discharge. At about this time Mr. Jackson’s perfected form of focus- tube was brought out, a tube which for photographic purposes was found superior to any other form, and has not yet been ‘surpassed. 3. Observing in some of these experiments that the metal spade used as antikathode became red-hot, a special tube was constructed for me by Mr. Gardiner to test the question ~whether the high temperature of the antikathode was, or was “not, prejudicial to the emission of w-rays. This special tube (fig. 3) was furnished with an antikathode of platinum-foil mounted so that while serving both as antikathode and as anode it could be heated by passing a current through it ‘from an auxiliary battery. Observing the activity of the “tube by means of a luminescent screen of platinocyanide of “potassium, it was found that the heating of the antikathode, “so far from being disadvantageous, decidedly promoted the 164 Dr. Silvanus P. Thompson on emission of x-rays, and increased the continuity and brilliancy of the luminescence. Various amounts of current were sent through the platinum, the most effective result being obtained by currents which heated the surface to visible redness. Whether the effect is a direct one or an indirect owing to the driving out of occluded gases is not yet determined. 4, When watching with the luminescent screen the emis- sion of #-rays within bulbs connected with the pump, some observations were made of direct importance with regard to the state of exhaustion that is best. The degree of vacuum which suffices for the production of kathodic shadows is known not to be sufficient for the production of w-rays. It is also known that when evacuation is pushed very far the internal resistance of the bulbs rises very high, so that they become almost non-conductive. If a bulb is exhausted, and heated during exhaustion, and the vacuum pushed almost to non-conductivity, and if a little air is again admitted and the tube again exhausted, the high degree of vacuum is again very soon reached, probably because during the first ex- haustion the gases absorbed upon the walls of the bulb were mostly removed. After three or four repetitions of this process the transition from the low state of vacuum to the high state is exceedingly rapid. Ifa bulb in such a condition is examined by the luminescent screen while the pump is at work, scarcely any trace of x-rays can be noticed so long as the vacuum is such that the resistance is low. A pair of discharging-points arranged as a shunt to the tube serves as an approximate gauge. Kathodic shadows can be seen when the resistance is so low that the discharge- points do not spark even when placed 3 millimetres apart. When the resistance rises so that the spark-points must be put 20 or 30 millimetres apart x-rays begin to be given off ; and are given off both trom the back and from the front of the antikathode. The bulb, as seen upon the adjacent screen, shows two pale lumis some Experiments with Roéntgen’s Rays. 165 nous regions divided by a fine oblique black line which is in the plane of the antikathode (fig. 4). If the pump goes on Fig. 4. (ett PLLITELE Yip Yy pe Mba sexrrc2ao UP yyy rarer sare rrape rane iy yy LLY YG) YY LY Yy Y thy ep Z LORETO TIE TITLED ILOTEL TT LLLY UY LLTLELELLE LY G working, in two or three seconds, or while only a few cubic centimetres of mercury pass through the pump, the pheno- menon changes. The luminosity behind the antikathode dies out, and that in front of the antikathode increases; so that there is seen simply a bright anterior region ending at the oblique plane of the antikathode, beyend which all is dark (fig. 5). This oblique delimitation can also be seen in the yellow phosphorescence upon the walls of the bulb. This sudden transition occurs after the resistance of the bulb has passed its minimum. The brightest luminescence occurs when the spark-length exceeds 40-50 millimetres. The lumi- nosity does not fall off much even at very small angles to the plane of the antikathode, proving that the emission of w- rays does not follow Lambert’s law of the cosine by any means, Hxperiments on this point are still in progress, 166 Some Euperiments with Rontgen’s Rays. 5. The phenomenon of diselectrification by x-rays is very readily demonstrated. For this purpose I have found a very convenient instrument to be an electroscope consisting of two strips of aluminium leaf (which is lighter than gold leaf) suspended in a thin-glass jar entirely covered with a fine metal gauze. It is charged with a dry pile, and a metal cap is then placed over the charging knob, so that it is entirely electrostatically screened from external electrical influences. Positive and negative electrifications are both readily discharged, even at the distance of several feet from the bulb. 6. On the first announcement of the diselectrifying pro- perties of x-rays, I attempted to obtain electric dust-figures as shadows of metallic objects by applying the 2-rays to dis- charge electrified surfaces of glass or ebonite upon which mixed powders of red lead and sulphur were then dusted. These were obtained almost at the first trial; but to produce them satisfactorily requires a little care. The object whose shadow is to be obtained—a pair of scissors, for example—is laid upon a thin sheet of aluminium placed to stand on four feet at the height of about 20 millim. over the sheet of ebonite or varnished glass upon which the shadow is tobe thrown. This sheet of ebonite is first carefully diselectrified by passing it over an alcohol flame, and then laid upon an earthed sheet of foil upon the table. The aluminium tray with the scissors upon it is placed over the ebonite. A guard-box of lead with a rectangular hole in its top is placed over all. Then the aluminium tray is charged electrically by a small influence-machine which has one pole put to earth and the other connected to the aluminium tray. In this state of things the ebonite plate hes in an electro- static field, but is not electrified upon its upper surface. The x-rays are now caused to fall upon the aluminium tray, through which they pass save when obstructed by the metallic object, and, discharging the tray, virtually carry down the electrification upon the surface of the ebonite in straight lines, leaving the shadowed portions unelectrified. The influence-machine is disconnected, the aluminium tray re- moved, the sheet of ebonite lifted off the table, and the mixed powders are forthwith dusted over its surface, revealing the shadow. Both positive and negative shadows can be obtained. Several alternate dispositions are possible. These observations were made early in February before the announcement by M. Righi of some similar cases of production of shadows by 2-rays. 7. I have also made some observations upon the reflexion On the Theory of Optical Images. 167 of x-rays. The production of diffuse reflexion by solid bodies is very easily observed; but hitherto I have no clear evidence of specular reflexion. Air unfortunately itself sets up dif- fusion, behaving as a semi-opaque fluid. If ordinary expe- riments on the reflexion of light had to be carried on in dense smoke or in miiky water,.a similar diffusion would interfere with specular reflexion. In one set of experiments a V-tube made of lead pipes set at right angles, and open at the bottom, was used, the z-ray source ‘being made to shine down one limb, while a shielded photographic plate was placed at the upper end of the other. The surfaces to reflect «-rays were placed at the open lower ends at 45° to the lines of incidence and of presumed reflexion. Reflexion of a sort was indeed ‘obtained when surfaces of metal and of glass were placed across the bottom of the tubes. But an effect was also obtained even when nothing was placed across the open bottom. Itseems exceedingly doubtful whether true specular reflexion has been observed in any case. XV. Onthe Theory of Optical Images, with Special Reference to the Microscope. By Lord RayueicH, Sec. Rh. S.* HE special subject of this paper has been treated from two distinct points of view. In the work of Helmholtz + the method followed is analogous to that which had long been used in the theory of the telescope. It consists in tracing the image representative of a mathematical point in the object, the point being regarded as self-luminous. The limit to definition depends upon the fact that owing to diffraction the image thrown even by a perfect lens is not confined to a point, but distends itself over a patch or disk of light of finite dia- ‘meter. Two points in the object can appear fully separated only when the representative disks are nearly clear of one another. The application to the microscope was traced by means of a somewhat extended form of Lagrange’s general optical theorem, and the conclusion was reached that the smallest resolvable distance ¢ is given by e=)/sin a, X being the wave-length in the medium where the object is situated, and a the divergence-angle of the extreme ray (the semi-angular aperture) in the same medium. If Ay be the wave-length in vacuum, Sy een Oy SehiD. Cire. tnnes vo owrink Sh) * Communicated by the Author. + Pogg. Ann, Jubelband, 1874. 168 Lord Rayleigh on the Theory of Optical Images, » being the refractive index of the medium ; and thus €= SA, /mesinae. +. » -. cen The denominator wsina is the quantity now well known (after Abbe) as the “ numerical aperture.” The extreme value possible for « is a right angle, so that for the microscopic limit we have C= ay/f- .« s + «| oer The limit can be depressed only by a diminution in A», such as photography makes possible, or by an increase in p, the refractive index of the medium in which the object is situated. | This method, in which the object is considered point by point, seems the most straight-forward, and to a great extent it solves the problem without more ado. When the repre- sentative disks are thoroughly clear of one another, the two points in which they originate are resolved, and on the other hand, when the disks overlap the points are not distinctly separated. Open questions can relate only to intermediate cases of partial overlapping and various degrees of resolution. In these cases (as has been insisted upon by Dr. Stoney) we have to consider the relative phases of the overlapping lights before we can arrive at a complete conclusion. If the various points of the object are self-luminous, there is no permanent phase-relation between the lights of the overlapping disks, and the resultant illumination is arrived at by simple addition of separate intensities. ‘This is the situation of affairs in the ordinary use of a telescope, whether the object be a double star, the disk of the sun, the disk of the moon, or a terrestrial body. The distribution of light in the image of a double point, or of a double line, was especially considered in a former paper *, and we shall return to the subject later. When, as sometimes happens in the use of the telescope, and more frequently in the use of the microscope, the over- lapping lights have permanent phase-relations, these inter- mediate cases require a further treatment; and this is a matter of some importance as involving the behaviour of the instrument in respect to the finest detail which it is capable of rendering. We shall see that the image of a double point under various conditions can be delineated without difficulty. In the earliest paper by Prof. Abbe t, which somewhat * “ Investigations in Optics, with special reference to the Spectroscope.’’ Phil. Mag. vol. vili. p. 266 (1879). t+ Archiv. f. Mikr, Anat. vol. ix. p. 418 (1873). with Special Reference to the Microscope. 169 preceded that of Helmholtz, similar conclusions were reached; bat the demonstrations were deferred, and, indeed, they do not appear ever to have been set forth in a systematic manner. Although some of the positions then taken up, as for example that the larger features and the finer structure of a micro- scopic object are delineated by different processes, have since had to be abandoned*, the publication of this paper marks a great advance, and has contributed powerfully to the modern development of the microscope f. In Prof. Abbe’s method of treating the matter the typical object is not a luminous point, but a grating illuminated by plane waves. Thence arise the well-known diffraction spectra, which are focussed near the back of the object-glass in its principal focal plane. If the light be homogeneous, the spectra are reduced to points, and the final image may be regarded as due to the simultaneous action of these points acting as secondary centres of light. It is argued that the complete representation of the object requires the co-operation of all the spectra. When only a few are present, the representation is imperfect ; and when there is only one—for this purpose the central image counts as a spectrum—the representation wholly fails. That this point of view offers great advantages, at least when the object under consideration is really a grating, is at once evident. More especially is this the case in respect of the question of the limit of resolution. It is certain that if one spectrum only be operative, the image must consist of a uniform field of light, and that no sign can appear of the real periodic structure of the object. From this considera- tion the resolving-power is readily deduced, and it may be convenient to recapitulate the argument for the case of perpendicular incidence. In fig. 1 AB represents the axis, A being in the plane of the object (grating) and B in the plane of the image. The various diffraction spectra are focussed by the lens LL! in the principal focal plane, So repre- senting the central image due to rays which issue normally from the grating. After passing So the rays diverge in a * Dallenger’s edition of Carpenter's ‘ Microscope,’ p. 64, 1891. + It would seem that the present subject, like many others, has suffered from over specialization, much that is familiar to the micro- scopist being almost unknown to physicists, and vice versd. For myself I must confess that it is only recently, in consequence of a discussion between Mr. L. Wright and Dr. G. J. Stoney in the ‘ English Mechanic’ (Sept., Oct., Nov., 1894; Nov. 8, Dec. 13, 1895; Jan. 17, 1896), that I have become acquainted with the distinguishing features of Prof. Abbe’s work, and have learned that it was conducted upon different lines to that of Helmholtz. Iam also indebted to Dr. Stoney for a demonstration of some of Abbe’s experiments. 170 Lord Rayleigh on the Theory of Optical Images, cone corresponding to the aperture of the lens and illuminate a circle CD in the plane of the image, whose centre is B. The first lateral spectrum 8, is formed by rays diffracted from Fig. 1. the grating at a certain angle ; and in the critical case the region of the image illuminated by the rays diverging from S, just includes B. The extreme ray §,B evidently proceeds from A, which is the image of B. The condition for the co-operation at B of the first lateral spectrum is thus that the angle of diffraction do not exceed the semi-angular aperture a. By elementary theory we know that the sine of the angle of diffraction is /e, so that the action of the lateral spectrum requires that e exceed A/sina. If we allow the. incidence upon the grating to be oblique, the limit becomes 3A/sin a, as in (1). We have seen that if one spectrum only illuminate B, the field shows no structure. If two spectra illuminate it with equal intensities, the field is occupied by ordinary interference bands, exactly as in the well known experiments of Fresnel. And it is important to remark that the character of these bands is always the same, both as respects the graduation of light and shade, and in the fact that they have no focus. When more than two spectra co-operate, the resulting inter- ference phenomena are more complicated, and there is opportunity for a completer representation of the special features of the original grating *. * These effects were strikingly illustrated in some observations upon gratings with 6000 lines to the inch, set up vertically in a dark room and illuminated by sunlight from a distant vertical slit. The object-glass of the microscrope was a quarter inch. When the original grating, divided, upon glass (by Nobert), was examined in this way, the lines were well seen if the instrument was in focus, but, as usual, a compara- tively slight disturbance of focus caused all structure to disappear. When, however, a photographic copy of the same glass original, made with Special Reference to the Microscope. ial While it is certain that the image ultimately formed may be considered to be due to the spectra focussed at So, S,..., the degree of conformity of the image to the original object is another question. From some of the expositions that have been given it might be inferred that if all the spectra emitted from the grating were utilized, the image would be a complete representation of the original. By considering the case of a very fine grating, which might afford no lateral spectra at all, it is easy to see that this conclusion is incorrect, but the matter stands in need of further elucidation. Again, it is not quite clear at what point the utilization of a spectrum really begins. All the spectra which the grating is competent to furnish are focussed in the plane 8) 8,; and some of them might be supposed to operate partially even although the part of the image under examination is outside the geometrical cone defined by the aperture of the object-glass. For these and other reasons it will be seen that the spectrum theory * valuable as it is, needs a good deal of supplementing, even when the representation of a grating under parallel ugh is in question. ~ When the object under examination is not a grating or a structure in which the pattern is repeated an indefinite number of times, but for example a double point, or when the incident light is not parallel, the spectrum theory, as hitherto developed, is inapplicable. As an extreme example of tbe latter case we may imagine the grating to be self-luminous. It is obvious that the problem thus presented must be within the scope of any complete theory, and equally so that here there are no spectra formed, as these require the radiations from the different with bitumen, was substituted for it, very different effects ensued. The structure could be seen even although the object-glass were drawn back through 14 inch from its focussed position; and the visible lines were twice as close, as if at the rate of 12,000 to the inch. The difference between the two cases is easily explained upon Abbe’s theory. A soda flame viewed through the original showed a_ strong central image (spectrum of zero order) and comparatively faint spectra of the first and higher orders. A similar examination of the copy revealed very brilliant spectra of- the first order on both sides, and a relatively feeble central image. The case is thus approximately the same as when in Abbe’s experiment all spectra except the first (on the two sides) are blocked out. * The special theory initiated by Prof. Abbe is usually called the “diffraction theory,” a nomenclature against which it is necessary to protest. Whatever may be the view taken, any theory of resolving power of optical instruments must be a diffraction theory in a certain sense, so that the name is not distinctive. Diffraction is more naturally regarded as the obstacle to fine definition, and not, as with some expo- nents of Prof. Abbe’s theory, the machinery by which good definition is brought about. 172 Lord Rayleigh on the Theory of Optical Images, elements of the grating to possess permanent phase-relations. It appears, therefore, to be a desideratum that the matter should be reconsidered from the older point of view, according to which the typical object is a point and nota grating. Such a treatment illustrates the important principle that the theory of resolving-power is essentially the same for all instruments. The peculiarities of the microscope arise from the fact that the divergence-angles are not limited to be small, and from the different character of the illumination usually employed ; but, theoretically considered, these are differences of detail. The investigation can, without much difficulty, be extended to gratings, and the results so obtained confirm for the most part the conclusions of the spectrum theory. It will be convenient to commence our discussion by a simple investigation of the resolving-power of an optical instrument for a self-luminous double point, such as will be applicable equally to the telescope and to the microscope. In fig 2 AB represents the axis, A being a point of the object and B a point of the image. By the operation of the object- glass LL’ all the rays issuing from A arrive in the same phase at B. Thus if A be self-luminous, the illumination is a maximum at B, where all the secondary waves agree in phase. Fig, 2. B is in fact the centre of the diffraction disk which constitutes the image of A. At neighbouring points the illumination is less, in consequence of the discrepancies of phase which there enter. In like manner, if we take a neighbouring point Pin the plane of the object, the waves which issue from it will arrive at B with phases no longer absolutely accordant, and the discrepancy of phase will increase as the interval AP increases. When the interval is very small, the discrepancy of phase, though mathematically existent, produces no prac- tical effect, and the illumination at B due to P is as important as that due to A, the intensities of the two luminous centres being supposed equal. Under these conditions it is clear that A and P are not separated in the image. The question is, to what amount must the distance AP be increased in order that the difference of situation may make itself felt in the image. This is necessarily a question of degree ; but it does not require detailed calculations in order to show that weth Special Reference to the Microscope. 1723 the discrepancy first becomes conspicuous when the phases corresponding to the various secondary waves which travel from P to B range over about a complete period. The illumi- nation at B due to P then becomes comparatively small, in- deed for some forms of aperture evanescent. The extreme discrepancy is that between the waves which travel through the outermost parts of the object-glass at L and L’; so that, if we adopt the above standard of resolution, the question is, where must P be situated in order that the relative retarda- tion of the rays PLand PL’ may on their arrival at B amount to a wave-length (A). In virtue of the general law that the reduced optical path is stationary in value, this retardation may be calculated without allowance for the different paths, pursued on the further side of L, L’, so that its value is simply PL—PL'. Now since AP is very small, AL’— PL’ is equal to AP.sina, where @ is the semi-angular aperture L/AB. In like manner PL—AL has the same value, so that PL—PL/=2AP.sina. According to the standard adopted, the condition of resolution is therefore that AP, or e, should exceed $)/sin a, as in (1). If e be less than this, the images overlap too much; while if ¢ greatly exceed the above value the images become unneces- sarily separated. In the above argument the whole space between the object and the lens is supposed to be occupied by matter of one refractive index, and » represents the wave-length zn this medium of the kind of light employed. If the restriction as to uniformity be violated, what we have ultimately to do with is the wave-length in the medium immediately surrounding the object. The statement of the law of resolving-power has been made in a form appropriate to the microscope, but it admits also of immediate application to the telescope. If 2R be the diameter of the object-glass, and D the distance of the object, the angle subtended by AP is e/D, and the angular resolving-power is given by DDisinucen piety ei peewee) op ( the well-known formula. This method of derivation makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in difterené forms. In the case of the telescope we have to do with a Phil. Mag. 8. 5. Vol. 42. No. 255. Aug. 1896. () 174 ~=Lord Rayleigh on the Theory of Optical Images, linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear and it is expressed in terms of angular aperture. In the above discussion it has been supposed for the sake of simplicity that the points to be discriminated are self-lumi- nous, or at least behave asif they were such. It is of interest to inquire how far this condition can be satisfied when the object is seen by borrowed light. We may imagine that the object takes the form of an opaque screen, perforated at two points, and illuminated by distant sources situated behind. - Tf the source of light be reduced to a point, so that a single train of plane waves falls upon the screen, there is a perma- nent phase-relation between the waves incident at the two points, and therefore also between the waves scattered from them. In this case the two points are as far as possible from behaving as if they were self-luminous. If the incidence be perpendicular, the secondary waves issue in the same phase ; but in the case of obliquity there is a permanent phase- difference. This difference, measured in wave-lengths, in- creases tp to e, the distance between the points, the limit being attained as the incidence becomes grazing. - When the light originates in distant independent sources, not limited to a point, there is no longer an absolutely definite phase-relationship between the secondary radiations from the. two apertures ; but this condition of things may be practically maintained, if the angular magnitude of the source be not too: large. Jor example, if the source be limited to an angle 0 round the normal to the screen, the maximum phase-difference measured in wave-lengths is esin @, so that if sin @ be a small fraction of X/e, the finiteness of @ has but little effect. When, however, sin @ is so great that e sin @ becomes a considerable multiple of X, the secondary radiations become approximately independent, and the apertures behave like self-luminous points. It is evident that even with a complete hemi-. spherical illumination this condition can scarcely be attained when e¢ is less than 2. | The use of a condenser allows the widely-extended source to be dispensed with. By this means an image of a distant source composed of independently radiating parts, such as a lamp-flame, may be thrown upon the object, and it might at first sight be supposed that the problem under consideration was thus completely solved in all cases, inasmuch as the two apertures correspond to different parts of the flame. But we have to remember here and everywhere that optical images are not perfect, and that to a point of the fame corresponds with Special Reference to the Microscope. 175 in the image, not a point, but a disk of finite magnitude. When this consideration is taken into account, the same limitation as before is encountered. — For what is the smallest disk into which the condenser is capable of concentrating the light received from a distant point? Fig. 2 and the former argument apply almost without modification, and they show that the radius A P of the disk has the value 4)/sina, where @ is the semi-angular aperture of the condenser. Accordingly the diameter of the disk cannot be reduced below 2X; and if ¢ be less than » the radiations from the two apertures are only partially inde- pendent of one another. It seems fair to conclude that the function of the condenser in microscopic practice is to cause the object to behave, at any rate in some degree, as if it were self-luminous, and thus to obviate the sharply-marked interference-bands which arise when permanent and definite phase-relations are permitted to exist between the radiations which issue from various points of the object. As we shall have occasion later to employ Lagrange’s theorem, it may be well to point out how an instantaneous proof of it may be given upon the principles already applied. As before, A B (fig. 3) represents the axis of the instrument, Fig. 3. A and B being conjugate points. P is a point near A in the plane through A perpendicular to the axis, and Q is its image in the perpendicular plane through B. Since A and B are conjugate, the optical distance between them is the same for all paths, e.g. for ARS Band AL MB. And, since AP, BQ are perpendicular to the axis, the optical distance from P to Q is the same (to the first order of small quantities) as from A to B. Consequently the optical distance PRS Q is the same as ARS B. Thus, if pw, »’ be the refractive indices in the neighbourhood of A and B respectively, a and 8 the divergence-angles R A L, 8S BM for a given ray, we have ie Ae esima— nw BON sim By a" < =” (0) O02 176 Lord Rayleigh on the Theory of Optical Images, where AP, BQ denote the corresponding linear magnitudes of the two images. This is the theorem of Lagrange, extended by Helmholtz so as to apply to finite divergence-angles*. We now pass on to the actual calculation of the images to be expected upon Fresnel’s principles in the various cases that may arise. The origin of coordinates (E=0, 7=0) in the focal plane is the geometrical image of the radiant point. If the vibration incident upon the lens be represented by cos (27Vt/A), where V is the velocity of light, the vibration at any point &, 7 in the focal plane ist = splot 4 ifs | aed, - ne in which f denotes the focal length, and the integration with respect to « and y is to be extended over the aperture of the lens. If for brevity we write 2né)\f=p, 2ry/rAf=q, - -. sees (7) may be put into the form oT S 2 sin (Vt —f)— xf 8 (Vif). se) S={j sin (pa+qy)dzdy, . ... C=\j cos (pa + qy) da dy. Me It will suffice for our present purpose to limit ourselves to the case where the aperture is symmetrical with respect to x and y. We have then S=0, and C=\| cos px cos qydedy, . =). es the phase of the vibration being the same at all points of the diffraction pattern. When the aperture is rectangular, of width a parallel to x, and of width 6 parallel to y, the limits of integration are from —3a to +44 for x, and from —}% to+4b for y. Thus ___, sin (w7Ea/Af) sin (arnb/Af) s C=ab mec Se (13) and by (9) the amplitude of vibration (irrespective of sign) is C/Af. This expression gives the dittraction pattern due toa single point of the object whose geometrical image is at $=0, Te rf where * T learn from Czapski’s excellent Theorie der Optischen Instrumente that a similar derivation of Lagrange’s theorem from the principle of minimum path had already been given many years ago by Hockin (Micros. Soc. Journ. vol. iv. p. 337, 1884). t See for example Enc. Brit., “ Wave Theory,” p. 430 (1878). with Special Reference to the Microscope. 177 7=0. Sometimes, as in the application to a grating, we wish to consider the image due to a uniformly luminous line, parallel to 7, and this can always be derived by integration trom the expression applicable to a point. But there is a distinction to be observed according as the radiations from the various parts of the line are independent or are subject to a fixed phase-relation. In the former case we have to deal only with the intensity, represented by I? or C?/A?f?; and we get ee a*b sin? (7Ea/Af) 2 ey | are 2: by means of the known integral St coyene S a ee i tae= | ee ipa ct (15) LZ i —o —e@ This gives, as a function of &, the intensity due to a self-lumi- nous line whose geometrical image coincides with & =0. Under the second head of a fixed phase-relation we need only consider the case where the radiations from the various parts of the line start in the same phase. We get, almost as before, Lee __ sin (7Ea/Af) yw) __ Cdn=a San ee Ch Pee (16) for the expression of the resultant amplitude corresponding to &. In order to make use of these results we require a table of the values of sin u/u, and of sin? u/u’. The following will suffice for our purposes :— | TABLE I, 4u sin wu sin? w du sin & sin? % T o yr 7 ue ue 0 + 1:0000 1-0000 9 +:1000 0100 1 -9003 *8105 10 a DAS ‘0162 2 6366 4053 ll 0818 “0067 3 °3001 “0901 12 “0000 “0000 4 0000 “0000 13 — 0692 "0048 | 5 — ‘1801 0324 14 — ‘0909 "0083 6 — ‘2122 -0450 15 — 0600 0036 | 7 ~ +1286 0165 16 0000 0000 8 | | | 0000 ‘0000 When we have to deal with a single point or a single line 178 only, this table gives directly the distribution of light in the image, u being equated to wa/Af. The illumination first vanishes when w=7, or &/f=X/a. On a former occasion* it has been shown that a self- luminous point or line at u= —7ris barely separated from one at w=(. It will be of interest to consider this case under three different conditions as to phase-relationship : (i.) when the phases are the same, as will happen when the illumina- tion is by plane waves incident perpendicularly ; (i1.) when the phases are opposite ; and (il1.) when the phase-difference is a quarter period, which gives the same result for the in- Lord Rayleigh on the- Theory of Optical Images, Tass Il. | ; sin u sin wu sin 2% 4u uU u a u ‘ie sin (u+7) __ sin (w+7) sin?(w+7)) ut@r Uta (w+ 7 )? | —4... +1-0000 —1-:0000 +1:000 —3... +1°2004 — 6002 + ‘949 —2... 4+. 1°2732 ‘0000 + -900 ieee +1:2004 + :6002 — + 949 Ozs + 1:0000 +1:0000 +1-000 ha + 7202 +1:0804 + ‘918 Die: + 4244. + °8488 + ‘671 ee + ‘1715 + 4287 + °326 As “0000 ‘0000 “000 Bess — ‘0800 — ‘2801 — ‘206 GO: — 0849 — ‘3395 — ‘247 lees — ‘0468 — ‘2105 — 152 Ore “0000 “0000 “000 9... + -0308 + -1693 + ‘122 LOZ + :0364 + -2183 + -156 1th Peer + :0218 + ‘1419 + -101 ieee “0000 ‘0000 “OGO tensity as if the apertures were self-luminous. The annexed table gives the numerical values required. -In cases (i.) and (iii.) the resultant amplitude is symmetrical with respect to the point u=—%37 midway between the two geometrical images ; in case (i1.) the sign is reversed, but this of course has no effect upon the intensity. Graphs of the three functions are given in fig. 4, the geometrical images being at the points marked —7z and 0. It will be seen that while in case lii., relating to self-luminous points or lines, there is an approach to separation, nothing but an accurate comparison with the curve due to a single source would reveal the duplicity in case i. On the other hand, in case ii., where * Phil. Mag. vol. viii. p. 266, 1879. with Special Reference to the Microscope. 179 there is a phase-difference of half a period between the radiations, the separation may be regarded as complete. | Fig. 4, en ys Cre Ss PEC ANCEE EEE Eee SUE ARCRaE ES gas BUECANECEE Ea SiMe erein& he Hee OCecercanced (EEE EEENEED EER Bar ceeene ce gate 917]: | ~ In a certain sense the last conclusion remains undisturbed even when the double point is still closer, and also when the aperture is of any other symmetrical form, e. g. circular. For at the point of symmetry in the image, midway between the two geometrical images of the radiant points, the com- ponent amplitudes are necessarily equal in numerical value and opposite in sign, so that the resultant amplitude or illu- mination vanishes. For example, suppose that the aperture is rectangular and that the points or lines are twice as close as before, the geometrical images being situated at w= —}7, u=0. The resultant amplitude is represented by /(~), where sinw sin (wu+47) — — ° ° e e ie I (~) U U +4 LD ( ) The values of f(u) are given in Table III. They show that the resultant vanishes at the place of symmetry w= —}7, 180 Lord Rayleigh on the Theory of Optical Images, and rises to a maximum at a point near w=47, considerably beyond the geometrical image at w=0. Moreover, the value of the maximum itself is much less than before, a feature which would become more and more pronounced as the points were taken closer. At this stage the image becomes only a TasueE III. Au 4u — Ft (u). a F (uw). ose +:00 Ly eRe 2 sie. -— "05 Oe +°36 6.2: eee | | RCE ye +60 (Pete 23 7 SE AB +:-64 ese eaee —13 Seek 1 +°48 Gr eee +°02 OL tte +21 | | very incomplete representation of the object ; but if the forma- tion of a black line in the centre of the pattern be supposed to constitute resolution, then resolution occurs at all degrees of closeness*. We shall see later, from calculations conducted by the same method, that a grating of an equal degree of closeness would show no structure at all but would present a uniformly illuminated field. * These results are easily illustrated experimentally. JI have used two parallel slits, formed in films of tin-foil or of chemically deposited silver, of which one is conveniently made longer than the other. These slits are held vertically and are viewed through a small telescope, pro- vided with a high-power eye-piece, whose horizontal aperture is re- stricted to a small width. The distance may first be so chosen that when backed by a neighbouring flame the double part of the slit just manifests its character by a faint shadow along the centre. If the flame is replaced by sunlight shining through a distant vertical slit, the effect depends upon the precise adjustment. When everything is in line the image is at its brightest, but there is now no sign of resclution of the double part of the slit. A very slight sideways displacement, in my case effected most conveniently by moving the telescope, brings in the half-period retardation, showing itself by a black bar down the centre. An increased displacement, leading to a relative retardation of three halves of a period, gives much the same result, complicated, however, by chromatic effects. In conformity with theory the black bar down the image of the double slit may still be observed when the distance is increased much beyond that at which duplicity disappears under flame illumination. For these experiments I chose the telescope, not only on account of the greater facility of manipulation which it allows, but also in order to make it clear that the theory is general, and that such effects are not limited, as is sometimes supposed, to the case of the microscope. with Special Reference to the Microscope. 181 But before proceeding to such calculations we may deduce by Lagrange’s theorem the interval ¢ in the original object corresponding to that between u=0 and w=7 in the image, and thence effect a comparison with a grating by means of Abbe’s theory. The linear dimension (&) of the image cor- responding to u=7 is given by €=Af/a; and from Lagrange’s theorem | eam Gy-sin a, 1 een (Lika in which @ is the “semi-angular aperture,’ and B=a/2/. Thus, corresponding to u=7, 66 e=3$)/ sin @. The case of a double point or line represented in fig. 4 lies therefore at the extreme limit of resolution for a grating in which the period is the interval between the double points. And if the incidence of the light upon the grating were limited to be perpendicular, the period would have to be doubled before the grating could show any structure. When the aperture is circular, of radius R, the diffraction pattern is symmetrical about the geometrical image (p=0, q=0), and it suffices to consider points situated upon the axis of € for which 7 (and g) vanish. Thus from (12) +R — Jeospe COUT 2) cos pa (R?— 2?) daz . (18) 7 | i ‘This integral is the Bessel function of order unity, de- finable by JEG) = a (z cos d) sin’ d dd. ome (19) Thus, if c=Rcos ¢, st 251(pR) ¢ ett eanrae ei heipvae py e(20) or, if we write wu=7& .2R/Af, (21)* This notation agrees with that employed for the rectungular aperture if we consider that 2R corresponds with a. The illumination at various parts of the image of a double point may be investigated as before, especially if we limit ourselves to points which lie upon the line joining the two * Enc. Brit., “ Wave Theory,” p. 482. 182 Lord Rayleigh on the Theory of Optical Images, geometrical images. The only difference in the calculations is that represented by the substitution of 2J, for sine. We shall not, however, occupy space by tables and drawings such as have been given for a rectangular aperture. It may suffice to consider the three principal points in the image due to a double source whose geometrical images are situated at u=0 and w= —z7, these being the points just mentioned and that midway between them at w=—4m. The values of the functions required are 3 2J,(0)/0 =1:0000 = ¥ {1:0000}. 23 (a) /a4 "1812 = ./{-03283}. 23, (4m) /4or = “7217 = /{°5209%. - In the case (corresponding to i. fig. 4) where there is simi- larity of phase, we have at the geometrical images amplitudes 11812 as against 1°4434 at the point midway between. When there is opposition of phase the first becomes +°8188, and the last zero*. When the phases differ by a quarter period, or when the sources are self-]uminous (iii. fig. 4), the amplitudes at the geometrical images are ./{1°0328} or 10163, and at the middle point ./{1°0418} or 1:0207. The partial separation, indicated by the central depression in curve iii. fig. 4, is thus lost when the rectangular aperture is exchanged for a circular one of equal width. It should be borne in mind that these results do not apply to a double lzne, which in the case of a circular aperture behaves differently from a double poznt. There is one respect in which the theory is deficient, and the deficiency is the more important the larger the angular aperture. The formula (7) from which we start assumes that a radiant point radiates equally in all directions, or at least that the radiation from it after leaving the object- glass is equally dense over the whole area of the section. In the case of telescopes, and microscopes of moderate angular aperture, this assumption can lead to no appreciable error ; but it may be otherwise when the angular aperture is very large. The radiation from an ideal centre of transverse vibrations is certainly not uniform in various directions, and indeed vanishes in that of primary vibration. If we suppose such an ideal source to be situated upon the axis of a wide-angled object-glass, we might expect the dif- fraction pattern to be less closely limited in that axial plane * The zero illumination extends to all points upon the line of sym- metry. . with Special Reference to the Microscope. 183 which includes the direction of primary vibration than in that which is perpendicular to it. The result for a double point illuminated by borrowed light would be a better degree of separation when the primary vibrations are perpendicular to to the line of junction than when they are parallel to it. Although it is trae that complications and uncertainties under this head are not without influence upon the theory of the microscopic limit, it is not to be supposed that any con- siderable variation from that laid down by Abbe and Helm- holtz is admissible. Indeed, in the case of a grating the theory of Abbe is still adequate. so far as the limit of resolution is concerned ; for, as Dr. Stoney has remarked, the irregularity of radiation in different directions tells only upon the relative brightness and not upon the angular position of the spectra. And it will remain true that there ean be no resolution without the cooperation of two spectra at least. 3 a, In Table II. and fig. 4 we have considered the image of a double point or line as formed by a lens of rectangular aperture. It is now proposed to extend the calculation to the case where the series of points or lines is infinite, con- stituting a row of points or a grating. The intervals are supposed to be strictly equal, and also the luminous intensities. When the aperture is rectangular, the calculation is the same whether we are dealing with a row of points or witha grating, but we have to distinguish according as the various centres radiate independently, viz., as if they were self-luminous, or are connected by phase-relations. We will commence with the former case. at he If the geometrical images of the various luminous points are situated at w=0, w= tv, u= +22, K&e., the expressions for the intensity at any point u of the field may be written as an infinite series, Gd) = sin’u sin?(w+v) , sin?(w—v) ue (Ce) (i—0)* sin?(u+2v) , sin?(uw—2v) (w+ 2v)? (uw—2v)? ? - Being an even function of « and periodic in period v, (22) may be expanded by Fourier’s theorem in a series of cosines. Thus 2arru x K(u) =I, + Tcos m+... +1 cos Baek IG (23) ee peer (2) and the character of the field of light will be determined when 184 Lord Rayleigh on the Theory of Optical Images, the values of the constants Ip, I,, &c., are known. For these we have as usual ae AROLe ee ‘f “T(u) 008 a U 1D) and it only remains to effect the integrations. To this end we may observe that each term in the series (22) must in reality make an equal contribution to I. It will come to the same thing whether, as indicated in (24), we integrate the sum of the series from 0 to v, or integrate a single term of it, e.g. the first, from —o to +0. We may therefore take 1 (+2 sin?x T Ih = =| A du= s : 5 5 e = (25) VU )—a dU... = an LS SO pe am 2 (+ sin?u whe Qrru v To evaluate (26) we have Osim COSISH 9 A a|, i, Vke ae ie carer ea du =|" du Sie u cos su) du, and ae 3 oo dy SD u COS SU) = — =SiN su u 2 Boe = so that by (15) (s being positive) +2 gin? = sin MOOS Myo} — 3 4S 4 }. u 2 + sin (2+s)u + Tn (2—s)u; 4 —- 4 the minus sign being taken when 2—s is negative. Hence —@ 2 TP lees) or 0). . en according as v exceeds or falls short of rz. We may now trace the effect of altering the value of v. When v is large, a considerable number of terms in the Fourier expansion (23) are of importance, and the discon- tinuous character of the luminous grating or row of points is fairly well represented in the image. As v diminishes, the higher terms drop out in succession, until when v falls below %4 only Ij and 1, remain. From this point onwards 1, con- with Special Reference to the Microscope. 185 tinues to diminish until it also finally disappears when wv drops below zw. The field is then uniformly illuminated, showing no trace of the original structure. The case v=7 is that of fig. 4, and curve ili. shows that at a stage when an infinite series shows no structure, a pazr of luminous points or lines of the same closeness are still in some degree separated. It will be remembered that v= corresponds to e=+4)/sina, e being the linear period of the original object and a the semi-angular aperture. We will now pass on to consider the case of a grating or row of points perforated in an opaque screen and illuminated by plane waves of light. If the incidence be oblique, the phase of the radiation emitted varies by equal steps as we pass from one element to the next. But for the sake of simplicity we will commence with the case of perpendicular incidence, where the radiations from the various elements all start in the same phase. We have now to superpose ampii- tudes, and not as before intensities. If A be the resultant amplitude, we may write _sinw sin(u+v) , sin(u—v) A(u) = er, ga aL 2aru Qrru =A,+Aicos —— +...+A, cos 5 SE ee a - (28) When v is very small, the infinite series identifies itself more and more nearly with the integral 1 (+? sin u , Se — du, viz. —. u v Uv J—@ In general we have, as in the last problem, oon: +0 a do=5| ne. A=2| secs dus (29) so that Ay=z/v. As regards A,, writing s for 2rr/v, we have fos am SE eas ei +), —a U Vv ae =— the lower sign applying when (1—s) is negative. Accord- ingly, A(u)= 24 142 c08=™ +2c08 ==" 4, ie } . (30) the series being continued so long as 27r=1, a=7s, where s is real. Thus y Ji) eee ee 0 a If s?>1, we must write z /(s?—1) for /(1—s?). Hence, if s< i, J [SE dex V(l-#), . - 62) ib: Jee | re while, if s>1, | ene 0 X * J1(x) sin sx . i da — 4/(s°—1) se We are here concerned only with (52), (54), and we con- elude that Ajp=2/v, and that A,=—-—_———., or0, . -. © {a8} according as s is less or greater than 1, viz. according as 2r7 is less or greater than v. If we compare this result with the corresponding one (80) for a rectangular aperture of equal width (2R=a), we see that the various terms representing the several spectra enter or disappear at the same time; but there is one important difference to be noted. In the case of the rectangular aper- ture the spectra enter suddenly and with their fu!l effect, whereas in the present case there is no such discontinuity, the effect of a spectrum which has just entered being infi- nitely small. As will appear more clearly by another method of investigation, the discontinuity has its origin in the sudden rise of the ordinate of the rectangular aperture from zero to its full value. with Special Reference to the Microscope. 191 In the method referred to the form of the aperture is sup- posed to remain symmetrical with respect to both axes, but otherwise is kept open, the integration with respect to x being postponed. Starting from (12) and considering only those points of the image for which 7 and gq in equation (8) vanish, we have as applicable to the image of a single lumi- nous source C= \y cos pa da dy=2\ycospade . deere (50) in which 2y denotes the whole height of the aperture at the point x. This gives the amplitude asa function of p. If there be a row of luminous points, from which start radiations in the same phase,-we have an infinite series of terms, similar to (57) and derived from it by the addition to p of positive and negative integral multiples of a constant (p,) repre- senting the period. Thesum of the series A(p) is necessarily periodic, so that we may write A(p)=Ao+ .--+A,cos 2rap/p,)+...; . (58) and, as in previous investigations, we may take +20 A= C cos Sp dp, ° e ° ° ° (59) — co s (not quite the same as before) standing for 2rm/p,, and a constant factor being omitted. To ensure convergency we will treat this as the limit of +0 | on Ceosspd porta’ 24 Gi G0) the sign of the exponent being taken negative, and A being ultimately made to vanish. Taking first the integration with respect to p, we have e+"? cos xp cos s api= ee + ; iy P nS P h? (< S)° h? (x s)? F) and thus i hy dz hy dx ES let (+s)? y le (a—s)2’ in which h is to be made to vanish. In the limit the inte- grals receive sensible contributions only from the neigh- bourhoods of z= +s; and since +o dy { fae. P F : F alt (61) iy Pe 192 Lord Rayleigh on the Theory of Optical Images, we get A = o(y ey, )= 27 2 ° | oa (62) From (62) we see that the occurrence of the term in A,, 2. ¢. the appearance of the spectrum of the rth order, is asso- elated with the value of a particular ordinate of the object- glass. If the ordinate be zero, z.e. if the abscissa exceed numerically the half-width of the object-glass, the term in question vanishes. ‘The first appearance of it corresponds to $a=2ra/p,=rrf/éi, in which a is the entire width of the object-glass and &, the linear period in the image. By (17a), 1 in the equation | ae 8p Lay kp+1_ 2" Hence they must contain a self-conjugate subgroup of this order when p>3 and p#7. We shall first consider all the possible groups that contain such a self-conjugate subgroup. * M. Levavasseur gives an enumeration of these groups, without ex- plaining how they were obtained, in Comptes Rendus, March 2, 1896. His enumeration is not quite correct. He states that there are three groups which exist only when p—1 is a multiple of 4 without being also a multiple of 8. We shall prove that there are only two such groups. {+ Communicated by the Author. 196 Dr. G. A. Miller on the Operation Groups The few groups which do not contain such a subgroup will be considered afterwards. The eight systems of intransitivity* of the given self- conjugate subgroup are systems of nonprimitivity of the required groups. Hence each one of these groups must have a p,1 isomorphism to some group of order 8. As all of the latter contain subgroups of order 4, all of the former must contain subgroups of order 4p. Since the average number of elements in all the substitu- tions of a group is n—af, n being the degree and a the num- ber of systems of intransitivity of the group, every subgroup of a regular group must be intransitive ; and an intransitive subgroup of half the order of a transitive group must contain two and only two systems of intransitivity, which are also systems of nonprimitivity of the transitive group. Hach one of the groups under consideration must therefore contain a subgroup of order 4p, which may be formed by making some regular group of this order simply isomorphic to itselft. Since the groups of order 4p are known§, our problem is reduced to the construction of the nonprimitive groups containing as heads one of the five regular groups of order 4p in 1, 1 correspondence to itself. In what follows we shall consider p>2, as the groups of order 16 are well known ||. We shall first construct all the groups which contain as heads one of the two commutative groups of order 4p in 1,1 correspondence to itself. The cyclical head will be denoted by H cyc., and the non-cyclical by H. Groups containing H cye. Since there are 2( p—1) positive integers which are less than 4p and prime to 4p, H cye. contains 2(p—1) substitutions of order 4p. The largest group which transforms H cye. into itself without interchanging its systems transforms these substitutions according to a regular commutative group (L) * Every operation group of a given order may be represented by a regular substitution group of the same order. Cf. Cayley, ‘ American Journal of Mathematics,’ vol. i. p. 52; also Dyck, Mathematische Annalen, vol, xxii. p. 84. + Cf. Frobenius, Crelle, ci. p. 287. t Cf. Netto’s ‘ Theory of Substitutions’ (Cole’s translation), § 98. § Cf. Holder, Mathematische Annalen, vol. xliii. p. 411; also Cole and Glover, ‘ American Journal of Mathematics,’ vol. xv. pp. 202-214. || Young, ‘ American Journal of Mathematics, vol. xv. p. 160; Hélder, Mathematische Annalen, vol. xliii. p. 409; Miller, Comptes Rendus, Feb. 17, 1896. of order 8p, p being any prime number. 197 of order 2(p—1), containing 3 and only 3 substitutions of order 2. These correspond to the substitutions which trans- form those of order 4p in H cye. into their Frade A 2ptl, . 4p—t powers. We have therefore to examine four types of tails that may be added to H cye., viz. those which are commuta- tive to the substitutions of H cyc., and those which transform these substitutions into one of the three given powers. Since half of the substitutions of H cyc. are the squares of its substitutions there can be only two commutative groups ; viz. the cyclical group (G,), and the group (G,) obtained by adding to H cye. a substitution (¢) which simply interchanges its systems. The squares of the substitutions in the tail of G, are also the squares of the substitutions of H cye. We represent the three substitutions* of the second order which are commutative to ¢ and transform the substitutions of H cyc. into the three given powers by s1, so, 83. Sit, Sot, Sst may be used to construct three distinct tails. The first of these contains 2p substitutions of order 2 and 2p of order 4, the second contains 4 of order 2 and 4(p—1) of order 2p, the third contains only substitutions of order 2. We represent the groups containing these tails respectively by G3, Gy, G;. Since s; is commutative only with the subgroup of order 4 in H cyc., and half of the substitutions of this subgroup are squares of its substitutions, there is only one more tail of this type. This contains only substitutions of order 8. Similarly we see that there is only one additional tail of each of the other two types; and that the former of these contains 4 substitutions of order 4 and 4(p—1) of order 4p, while the latter contains only substitutions of order 4. We represent the three groups containing these tails respectively by Ge, G:, Gs. Hence, when p>2, there are always 8 groups and only 8 that contain a cyclical subgroup of order 4p. In what follows we need not consider the groups in which such a subgroup occurs. When p=2, 2p—1 and 2p+1 are not congruent to 1 and 3 respectively with respect to mod 4, as is the case * That such substitutions can always be found follows from the fact that we may transform a generating substitution of a transitive cyclical group into any other generating substitution by a substitution whose degree is at least one less than the degree of the group. Since the first power of this substitution which is commutative to the group must be contained in the group, its order must be equal to the exponent to which the power into which it transforms the substitutions belongs with respect to mod «, « being the order of the given cycle. 198 Dr. G. A. Miller on the Operation Groups for the other values of p. Hence some of our remarks do not apply to this case. In fact there are only 6 groups of order 16 which contain a cyclical subgroup of order 8. Groups containing TH. By adding ¢ to this head we obtain the third and last commutative group (Gp) of order 8p. There are, therefore, three and only three commutative groups of this order for every value of p>2. When p=2 there are five such groups. The tail of G, contains 4 substitutions of order 2 and 4{p—1) of order 2p. The squares of these substitutions are clearly the same as the squares of those of H. It remains to find the non-commutative groups that contain H. The isomorphic group of order 8 contains at least three substitutions of the second order. If this group is commuta- tive the corresponding tail must transform the substitutions of H into their —1 powers, as 2p has primitive roots*. We can easily find a substitution (s’) of the second order which trans- forms one of the 4 cycles of a substitution of order 2p in H into its —1 power. By making s’ symmetrical in the ele- ments of the other cycles of the same substitution we obtain a substitution (s) which evidently transforms H into itself. The tail of the group (Gyo) generated by st and H contains only substitutions of the second order. Since s is commuta- tive to the substitutions of the second order in H, we may construct a group (G,) whose tail contains only substitutions of the fourth order by using, in place of s, the product of a substitution of the second order in one of the systems of H into s. The other two groups which may be constructed in the same way as Gj, are conjugate to it with respect to (s9), the pth power of two cycles commutative to ¢, these cycles being contained in some substitution of H whose order is 2p. It remains to examine the case when the isomorphic group of order 8 is not commutative. Since this group of order 8 contains at least 3 substitutions of the second order and is non-commutative, it is fully deter- mined. The corresponding tail must interchange two of the divisions of the head and transform the substitutions of the other two divisions into their —1 powers. The group (Gy) generated by H and sszé clearly satisfies these conditions. Its tail contains 2p substitutions of order 2 and 2p of order 4. The other possible group is conjugate to Gy. with respect to a substitution of the second order in one of the systems of H. #* Of. Serret’s Cours d’ Algébre Supérieure, vol. ii. p. 82. of order 8p, p being any prime number. 199 We have now found 12 groups of order 8p which exist for every value of p>2. As the remaining groups cannot con- tain a commutative group of order 4p, they must transform the substitutions of the self-conjugate subgroup of order p accord- ing to a cyclic group of order 4 or 8. Such groups can exist only when p—1 isa multiple of 4 or 8. We shall examine these two cases separately. Groups which exist only when p—1 1s a multiple of 4. We shall first consider the case when p—1 is not also a multiple of 8. The substitutions which are commutative to those of the self-conjugate subgroup of order p form a com- mutative group of order 2p. This cyclical group is therefore also a self-conjugate subgroup of the required groups, and its four systems of intransitivity are four systems of nonprimi- tivity of the required groups. Hence we may regard it as the head (H,) of the required groups. The tail to these groups contains 4p substitutions which transform the substitutions of the head into a power e which belongs to the exponent 4, mod 2p. We can easily find a substitution s which transforms the substitutions of the head into their a power, and is of order 4 and commutative to ¢, t representing a substitution of the 4th order which simply interchanges the 4 systems of the head cyclically. H, and st generate a group (G;3) whose tail contains 2p substitutions of the second order and 4p of the fourth order. As s is commutative only with the subgroup of order 2 contained in H, there can be only one more group of this type. This (G4) may be obtained by using the product of a substitution of the second order in one of the systems of H, into s in place of s. The tail of G,, contains 2p substitutions of order 4, and 4p of order 8. It remains to consider the case when p—1 is a multiple of 8. The preceding 14 groups are all present in this case. If there is an additional group it must transform the substitu- tions of the self-conjugate subgroup of order p according to a cyclical group of order 8. We can easily find a substitution (s;) which is symmetrical in the systems of the given selt- conjugate subgroup and transforms its substitutions into their B powers, 8 belonging to the exponent 8, mod p. Hy, and st (¢ being a substitution of order 8 which merely interchanges the given systems cyclically) generate a group (Gy5) whose tail contains p substitutions of order 2, 2p of order 4, and 4p of order 8. As the tail of G,; is not commu- tative to any substitution in the subgroup of order p, with 200 Operation Groups of order 8p, p being any prime number. the exception of identity, there can be only one group of this type. Hence there are always 12 groups of order 8p (p>2) which contain a self-conjugate subgroup of order p; when p—1L zs a multiple of 4 or 8 there are respectively 14 or 15 such groups. It remains to consider the Groups of order 8p which do not contain a self-conjugate subgroup of order p. When p=7, the equation Sp Pee re is satisfied by k=b=1 as well as by k=0, b=8. If the sub- group of order p is not self-conjugate there must be 8 such subgroups. These contain 8 x 6 = 48 substitutions besides identity. The subgroup of order 8 must therefore be self- conjugate, and its 7 systems of iniransitivity must be systems of nonprimitivity of the required groups. Since the substitutions of the group (H,) of order 8 cannot be commutative to the entire group, they must be trans- formed according to a group of order 7. Hence all these substitutions are of the second order, and H, is fully deter- mined. If we add to H,a substitution (¢) of order 7 which simply permutes its 7 systems cyclically, we obtain a group (Gy.) whose tail contains only substitutions of order 7. As no substitution of H., besides identity, is commutative to ¢, there can be no other group of this type. Hence there are 13 groups of order 56; 12 of these con- tain a self-conjugate subgroup: of order 7. The remaining one contains 8 conjugate subgroups of order 7 and a self- conjugate subgroup of order 8. The last group occurs for the first time as a group of degree 8*. The only other value of p> 2 for which there can be groups which do not contain a self-conjugate subgroup of order p is 8. In this case it is known that there are three such groupsf. Hence all the groups of order 8p are completely determined. Paris, June 1896. * oh Cole, ‘ Bulletin of the New York Mathematical Society,’ vol. ii 189 p- + of Leyavasseur, Comptes Rendus, March 2, 1896. [ 201 J _¥ ) \ XVII. On the Theory of Moving Electrons and Electric Charges. By J. Larmor*, 1 aS an interesting paper by Mr. W. B. Morton, communi- cated by the Physical Society to the Philosophical Magazine for June, there is a criticism of a portion of my paper on “A Dynamical Theory of the Electric and Luminiferous Medium’, which if valid would affect its whole tenor. As, however, the formule of that paper were to a considerable extent obtained by two independent trains of reasoning, it would have to be shown that both were wrong before an error could be fully substantiated. Asa matter of fact, Mr. Morton’s criticism arises from his reading into the analysis assumptions which are not there, but which had been used, with the proper limitations to secure accuracy, in another place in the previous part of the paper. As the point is really fundamental, and as the analytical statement in the memoir is no doubt too brief to convey at once a grasp of the procedure employed, without somewhat detailed consideration on the reader’s part, I beg leave to offer the following general explanation. The facts of chemical physics point to electrification being distributed in an atomic manner, so that an atom of electricity, say an electron, has the same claims to separate and permanent existence as an atom of matter. The fundamental question then is, how far the conception of separate isolated electrons, pervading the ether of free space, can provide an explanation of electrodynamic and optical phenomena. In the paper re- ferred to I have gone further back, and have considered the question how far such a simple underlying scheme is able by itself to provide an explanation of physical phenomena in general ; for it will obviously not be permissible to import into our dynamical notion of an atom of matter more than simple electric properties, unless these latter prove to be in- sufficient to include all actual knowledge of its relations. The conclusion arrived at in the memoir is that there is nothing in the ascertained laws of general physics which points to insufficiency in that scheme ; while there are some experimental results which somewhat militate against the existence of interatomic forces of any kind other than those included in it. The main feature of the theory referred to is that the ether * Communicated by the Physical Society. + Phil. Trans, 1894 (A) , pp. 719-822, and 1895! (A), pp. 695-743. 202 Mr. J. Larmor on the Theory of is not matter, as ordinarily assumed, nor in any way like matter ; it is the uniform substratum (analytical basis, if one is disposed to use that term, for it can never be the direct object of perception) in which the atoms of matter consist as permanent configurations of strain and motion. As was to be expected, the relations of inertia and elasticity of this uniform medium are simpler than those of matter, which is merely a molecular aggregate involved in its constitution. In fact, the only way to arrive at a scheme of the relations between ether and matter which shall be a complete dynamical theory and not merely descriptive, is to abolish the apparent duality in the phenomena, either by taking as here the mole- cules of matter to constitute singularities (in the mathe- matical sense of the theory of functions) in the uniform eether, or else by trying to make out the ether to be ordinary matter, and so giving up any atiempt to explain why matter is molecularly constituted. This molecular constitution of matter is essential to the former theory, just as it is to all other theories or illustrations, like the vortex theories, which hypothecate a uniform underlying medium; it is quite unintelligible—or rather quite unexplained—on the latter type of theory. But however these things may be, the point criticised by Mr. Morton does not involve any considerations so refined, or—as possibly may be said—so ambiguous. The sections to which he objects claim to be a reconstruction of ordinary electrodynamic theory on the basis of permanent electrons associated with the atoms of matter. Whatever view one may entertain as to the presence of qualities other than electric in the atom, all are I think now-a-days agreed that the electron is there. And whatever view one may have as to the validity and sufficiency of an ether with simple rotational elasticity, the formal equations to which that theory leads for free space are just those equations of Maxwell which Hertz’s experi- mental work has fully verified. The problem of electrodynamics is then that of the free zether, whose properties are represented analytically by these acknowledged equations, disturbed by the action of the electrons of material atoms moving abcut in it. The original Amperean electrodynamics, proceeding by consideration of elements of current, has not proved valid or sufficient in matters involving electric radiation, or even ordinary electrodynaimic force. A most successful modification of it was that proposed by Weber, in which elements of current were replaced, as the fundamental object of consideration, by moving electric particles which acted on each other at a dis- tance according to a law of force involving their velocities. Moving Electrons and Electric Charges. 203 This theory was, however, shown long ago by Lord Kelvin and Professor von Helmholtz to be untenable, on account of its violating the principles of the modern theory of energy ;: now, of course, direct action at a distance is altogether out of court. The present question is whether a theory of electrons: which act on each other, not directly according to a law of force, but mediately by propagation of the effect across the intervening ether, suffices to avoid the discrepancies of earlier theories and give a consistent account of electrical and optical phenomena ; and it is maintained that the answer is altogether in the affirmative. This question is, presumably, sufficiently important and fundamental to justify the present detailed explanation. At the end of the first of the two papers referred to, building chiefly on the analytical results of previous theorists, the steady ethereal disturbance carried along by a moving electron had been investigated, and also the law of the force exerted on each other by two moving electrons through the intervention of the ether between them. This was on the hypothesis that each electron carried along with it a steady trail of ethereal disturbance, but that no sensible derange- ment of this steady motion ever occurred such as would lead to loss of the energy of the system by the starting of waves. If the velocities of the electrons remain always small compared with that of radiation, then, however their mutual influences alter their motions, this steady trail will instantaneously adjust itself to the new conditions without sensible excitation of radiation, and the theory will apply. But if any of the elec- trons are moving with velocities comparable with that of radiation, a change in velocity will involve derangement of this steady trail of ethereal strain and motion, giving rise to wave-motion which will carry off some of the energy by radiation. Accordingly in such a case it is altogether nuga- tory to speak of laws of action between electrons: the complete theory must then take account not only of the positions and velocities of each of the electrons at each instant, but also of the state of each volume-element of the surrounding eether. And the theory of mutual actions of electrons as expressed in the memoir was in fact thus restricted to cases in which their velocities were small compared with that of radiation : unless that condition is satisfied there is no such theory at all. In the second paper (§ 15, segg.) the general problem is attacked : it is now nota question of a set of electrons by themselves, each with a definite steady trail, but of the ethereal medium in general, including such electrons as exist in it. The analysis there given determines from foundations 204 Theory of Moving Electrons and Electric Charges. which all who adopt Maxwell’s electrical scheme for free ether must allow, expressions for the force (P’, Q’, R’) which acts on an element of volume of the free ether, and for the force e (P, Q, R), ordinarily called electric force, which acts on an electron e; and it uses these forces for further develop- ment of the theory. What Mr. Morton’s computation virtually does is to assume that the trail of each electron is steady, and then to transfer to the electron itself the forcive due to (P’, Q’, R’) acting on this ethereal trail. In the special case of no radiation, and of velocities small compared with that of radiation, this forcive can, as above explained, be transmitted through the ether to the electron itself, and be supposed there applied. But to so transmit it in general is to miss the point of the theory, and, as Mr. Morton himself remarks, to reach the absurdity that the force on a moving charge depends not only on the state of the surrounding ether but on the state of the sether at a distance. As regards the main subject of Mr. Morton’s paper, it may be of interest to state the following general theorem. Suppose a system of charged conductors is in steady translatory motion through the quiescent zther with velocity u, and let v repre- sent the velocity of radiation in free ether: consider a cor- relative system of conductors obtained by uniform geometrical elongation of the actual system along the direction of motion in the ratio of (1—w?/v’)— to unity, and find the electrostatic distribution of the same charges on this system supposed at rest: then the actual distribution of the charges on the moving system wil] be exactly correlative, viz., equal charges will exist on all corresponding elements of the two systems. This proposition is, however, limited to the case in which none of the bodies of the moving system are dielectrics, but all are conductors. Finally, I take advantage of the present opportunity to draw attention to some special points in which the analysis of the second part of my memoir is incomplete. In §§ 28, 29, on the mechanical pressure of radiation, a statical forcive has been overlooked ; when this is included the result practically agrees with that given by Maxwell. In §§ 34-6, on the material forcives in polarized media, the tractions on inter- faces of transition remain to be developed, and the theory may be otherwise improved. I hope presently to treat this subject at length. Cambridge, June 4, 1896. er 20), "| XVIIL. Notices respecting New Books. — Jumes Clerk Maxwell and Modern Physics. By R.'T. GLAZEBROOK, FRS. (Century Science Series.) London: Cassell & Co., 1896., — fourteen years have now elapsed since Prof. Campbell and Mr. Garnett published their biography and letters of Maxwell ; the shock occasioned by his death had then scarcely passed away. At that time, although all regarded him as one of the founders of modern physics, few even among physicists realized the magnitude of his discoveries and research, and probably none imagined that his ideas concerning the ether would so soon receive the remark- able development which they have derived from the life-work of Hertz. For, so far as regards the problem of the ether, Hertz has been the chief exponent of Maxwell, just as Maxwell had previously explained and extended the views of Faraday. But Maxwell contributed by his laboursto many other physical questions, everywhere not only adding to the stock of knowledge but furnishing suggestions for future work. Mr. Glazebrook gives, in a form suited to the general reader, a brief account of Maxwell’s work in three of these departments of knowledge—the properties of Cartesian ovals, the theory of compound colours, and the dynamical theory of gases. He reserves a longer chapter for the electrical theories, of which a very concise account is given, as clear as the mathematical nature of the subject will allow in a non-mathematical volume. It should not be forgotten, however, that Maxwell was not only a great thinker and experimenter, but also an organizer. The present school of physics at Cambridge owes its existence and much of its efficiency to him, and has served as a model for the newer provincial colleges. It is fitting that the story of Maxwell’s work should be told by one so intimately acquainted with his Cambridge life as Mr. Glazebrook, and more especially by one who has had the good fortune to call him master and friend. > alo dele An Elementary Treatise on the Integral Calculus, containing Applications to Plane Curves and Surfaces, and also a Chapter on the Calculus of Variations, with numerous Examples. By BrysaMIn WinLIAMson, /.R.S. (Longmans: pp. xvili+512.) Tuts is the seventh edition of a work which first saw the light in 1875, in the humble guise of pp. vi+267. It has thus attained its majority and enormously increased in importance. On the appearance of the sixth edition in 1891 we noted the great advances that had been made on former editions, so that in the case of so well-known a work it is only necessary to point out the new features. The Calculus of Variations, which in the last edition formed chapter xv. with some 34 pages only, is now chapter xvi. and, in two sections—“ Single Integrals and Multiple Integrals,’—now occupies double the space. Another novelty is chapter xv. (12 pp.), “on the Sign of Substitution,” inserted principally ‘with a view to its employment in the Calculus of Variations.” This symbol Dr. Williamson states was _ first Phil. Mag. 8. 5. Vol. 42. No. 255. Aug. 1896. Q 206 Geological Society. introduced into analysis by Sarrus in his prize memoir,‘ Recherches sur le Caleul des Variations” (1846). Solution and Electrolysis. By W.C. Dampizr Wueruam, M.A. Cambridge, University Press, 1895. In choosing the title of this volume Mr. Whetham has very aptly indicated the connexion of his subject with both physics and chemistry ; for while solution is essentially a chemical process electrolysis is quite as closely allied to purely physical phenomena. Such borderland subjects, apart from the fact that they interest two sections of scientific workers, derive additional importance as beg the meeting-point of two theories, which, although originally framed to explain phenomena totally different in nature, must now be made to harmonize. The process of adjustment is not usually an easy one, and many are the discussions which it provokes, even when the experimental data have been carefully ascertained. The subject of solution is passing through this stage at the present time, but the accumulation of experimental evidence has received a great stimulus by the adoption of a provisional theory. According to this theory the molecules of a dissolved substance move through the solvent independeutly of the latter, in a manner comparable with the motion of gas molecules through the space containing them; in the case of electrolytes it is further assumed that the molecules are dissociated into their constituent ions to a greater or less degree according to the concentration of the solution. The reconciliation of this so-called physical theory with other doctrines of chemistry and physics is, however, not yet complete. The author proposes to accept the hydrate theory of solution, according to which solvent and dissolved substance form a large complex molecule, making the assumption that the chemical forces acting within the molecule do not interfere with the physical independence of its constituents. Mr. Whetham has followed Ostwald in giving an account of the general properties of solutions, but bis materials for the portion of the treatise dealing with electrolytes were much more scattered, the only previous attempts to collect them having been made by Wiedemann (1883), and by the Electrolysis Committee of the British Association. The author has selected the more important parts of these reports and presents them, together with other and more recent matter, in a form suited to the needs of students. The book is issued as a volume of the Cambridge Natural Science Manuals. James L. Howarp. XIX. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 123.] April 29th, 1896.—Dr. Henry Hicks, F.R.S., President, in the Chair, The following communications were read :— 1. ‘ Descriptions of New Fossils from the Carboniferous Lime- stone.—I. On Pemmatites constipatus, sp. nov., a Lithistid Sponge. Intelligence and Miscellaneous Articles. 207 Il. On Paleacis humilis, sp. nov., a new Perforate Coral; with Remarks on the Genus. III. On the Jaw-apparatus of an Annelid, Eunicites Reidiit, sp. nov.’ By George Jennings Hinde, Ph.D., F.G.S, 2. ‘The Eocene Deposits of Dorset.’ By Clement Reid, Esy., PiS.; F.G.S. The new survey of the western end of the Hampshire Basin shows that the Reading Beds become fluviatile and gravelly in Dorset (as was already known), and contain, in addition to Chalk flints, many fragments of Greensand chert. The London Clay thins greatly and becomes more sandy, but is apparently still marine. The Bagshot Sands become coarser and more fluviatile, changing rapidly west.of Moreton Station, till they consist mainly of coarse subangular gravel. These gravels, formerly referred to the Reading Series, are now shown to be continuous with the Bagshot Sands, which as they become coarser cut through the London Clay and Reading Beds to rest directly on. the Chalk. The Bagshot gravels contain, besides Chalk flints and Greensand chert, fragments of Purbeck marble and numerous Paleozoic grits and other stones probably derived from the Permian breccias of Devon. Thus there is evidence of disturbance and overlap in Cretaceous or early Eocene times, causing Reading Beds to rest on Upper Greensand. Later disturbances allowed the Bagshot river to cut into Greeusand, Wealden, Purbeck, Permian breccia, Culm Mea- sures, and granite. Foiding of the strata seems to have taken ~ place during at least four different periods in the district. between Dorchester and Weymouth, which appears to have been a region of special weakness. The Eocene gravels contain all the foreign rocks known to occur in the Plateau-gravels between Brighton and Dorchester. The fragments of Greensand chert, so abundant in the Plateau-gravels, have not been derived, as supposed, from the central axis of the Weald. They come, as already-formed pebbles, from the Eocene of Dorset, and originally from the Greensand of Devon. 2. ‘ Discovery of Mammalian Remains in the Old River-gravels of the Derwent near Derby.’—Part I. By H. H. Arnold-Bemrose; Esq. M.A. F.G.S. ~ XX. Intelligence and Miscellaneous Articles. ON THE REFRACTIVE INDICES OF SOME SUBSTANCES FOR VERY SHORT ELECTRICAL WAVES. BY DR, A, LAMPA. HE wave-length of the rays of electrical force used was 8 millim. This number follows from the dimensions of the exciter, but was also ascertained by means of an interference experiment. In reference to the arrangement of the experiments, it may be ob- served that a coherer was used for demonstrating the electrical rays. Experiments showed that in the experiment on refraction it is possible to get a pretty sharp adjustment for the maximum 208 Intelligence and Miscellaneous Articles. action on the coherer; and hence the arrangement was used for some quantitative deter minations. The refractive indices of a series of solid and liquid substances were determined. The following values were obtained for the wave- length in question corresponding to a value of N=37-500 x 10°. Para fine 2225 n=1'524 7? =2°32 Ebonite | o- oee 1:739 ra 4 Crown-glass .......... 2°381 5°16 Plinteolisse see os 2°849 8-41 Sulphiary pees. keer: 1:802 3°24 Benzolep eae... TOW ules Giivieenittemer sr sci: 1843 3:4 Oil of turpentine ...... 1°782 3°17 Vaseline eee ss... : 1°626 2°65 Oil of aimondsee.:, «i... 1°734 3°01 Absolute alcohol ...... 2:568 6°60 Distilled -water-...... . 8:972 80°45 — Wiener Berichte, July 1896. A LECTURE EXPERIMENT ON DIATHERMANCITY. BY DR. SILVIO LUSSANO. A very simple and elegant method of showing toa large audience the transparency or opacity of bodies for calorific radiations is the following, which is based on the change of colour some substances experience by variations of temperature. Double iodide of silver and mercury is prepared ina fine powder. At the ordinary temperature it has a beautiful canary-yellow colour, changing to a purple-red at the temperature of about 49°, and resuming its original colour when cold. This double iodide is prepared by mixing in molecular proportions the two substances Hel, and 2Ag¢I, then adding to the mixture alcohol which partly dissolves the mercuric iodide; the magma is then well stirred together in a mortar, alcohol being added from time to time. The mixture, which at first is red, then changes to orange, and, after some time, becomes of a canary-yellow colour; the alcohol is allowed to evaporate, the magma being stirred all the time. The double iodide thus pr epared i is spread on cardboard, forming a screen of a canary-yellow colour sensitive to calorific radiations. If, then, this is placed below a metal ball strongly heated, the colour of the screen changes, showing the heating due to the radiations. The same thing takes place if a plate of ebonite is interposed between the ball and the screen; but if a plate of a substance opaque to thermal radiations is placed on the ebonite, the shadow of this plate is projected on the screen, showing a yellow colour on a red ground. In this way it can be understood that it is easy to obtain the projections of athermanous substances enclosed between two ebonite plates.—Communicated by the Author from ‘Il Nuovo Cimento, May 1896. THE LONDON, EDINBURGH, ayn DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE.” [FIFTH SERIES. | SEPTEMBER 1896. XXI. On the Use of Bare Wire for Resistance-coils. By F. W. Bursratt, 1A., formerly Scholar of St. John’s College, Cambridge*. I. Introduction. a is perhaps somewhat surprising that the form of resistance-coils as used in the ordinary box has, during the last twenty years, changed less than any other kind of electrical instrument. The most serious defects of the pre- sent form of resistance-box are, firstly, the difficulty of ascer- taining the temperature of the wire forming the resistance, and, secondly, that the method of short-circuiting any required number of coils by means of divided brass blocks and taper plugs leads to contact-resistances which are often of very variable amount. A resistance-coil, the wire of which is covered with silk wound very closely and then covered with paraffin, of necessity conducts heat very badly, and therefore the temperature, as shown by a thermometer placed in the box, gives but little information as to the temperature of the resistance-wire. Ihave endeavoured to overcome the temperature difficulty by using manganin wire, but the uncertain nature of this material has forced me to abandon its use. The suggestion for the employment of a bare wire immersed in oil is due to Mr. H. H. Griffiths, and it is with the developments of this suggestion that the * Communicated by the Physical Society : read June 26, 1896, Phil. Mag. 8. 5. Vol, 42. No. 256. Sept. 1896. R 210 Mr. F. W. Burstall on the Use of present paper deals. There can be no doubt that with a bare wire immersed in oil the heating by the testing current is much less than with covered wire, and further, the tempe- rature of the wire can be accurately measured ; but perhaps one of the most important advantages in the use of a bare wire lies in the fact that the wire can be annealed in a most perfect manner by the passage of a sufficiently large current to heat it to a red-heat for a few seconds. It has long been known that well-annealed coils are much less liable to change than coils which have not been so treated. Dr. Lindeck, of the Reichsanstalt, has, in his various papers, laid great stress upon the necessity for annealing standard coils, which is effected by heating the coil in an air-bath to about 140°, the highest temperature a silk-covered coil can bear without material injury. The heating of the wire to a red-heat is, of course, much more efficient than the method adopted by Dr. Lindeck for freeing the wire from undue stress. | The wire which I have employed for the whole of the resistance-box was drawn from one cast of platinum-silver, a material which experience has shown to be the most perfect for resistance-measurement. The two forms of resistance-box usually employed are the series form and the dial form. In the former a number of coils are placed in series, and any required number can be short-circuited. This form, though it requires comparatively few coils, has the disadvantage that any fluctuation in one plug causes an error in the final measurement, and if any considerable number be used, it is almost impossible to pre- vent variation in the sum of the contact-resistances. For these reasons it seemed advisable to adopt the second form of box, the dial pattern, in which the number of plugs employed is a minimum, and remains the same whatever resistance is being measured. It is not essential to make standard resistances in order to calibrate a resistance-box, as each dial can be measured in terms of the preceding dial. This method, however, perpe- tuates any errors that may have been made in the measure- ment of any of the smaller coils, and it is not possible to measure the coils in the box with the same accuracy that can be attained in the determination of the standard coils. If have therefore constructed standard coils for every dial, and their values have been obtained from a 1 ohm coil inde- pendently of the resistance-box. Bare Wire for Resistance-corls. 211 I]. Construction of the Resistance-box and Standards. The resistance-box has five dials, each consisting of nine coils, ranging from 5 of an ohm to 1000 ohms, and four pairs of proportional arms ranging from 1 to 1000 ohms. The ;1, ohm coils have a length of 96 millim., the wire having a diameter of ‘63 millim. JBeing so short, there is no difficulty in supporting the coils. The wire of the 1 ohm coils has the same diameter and a length of 960 millim. These coils were at first wound into short spirals, and were allowed to hang freely from their terminals. It soon, however, became apparent that the con- volutions of the spiral required to be fixed rigidly to the ebonite top. The method that has been finally adopted is to screw the spiral into holes pierced in a mica plate ; this plate being screwed top and bottom to a brass bar which is attached to the ebonite top. In the coils of from 10 to 1000 ohms it is not easy to find a form of bobbin on which to wind the great lengths of bare wire required in such a manner as to avoid short circuits, and to bring the wire in contact as little as possible with the in- sulator. The form I have ultimately adopted is as follows (fig. 1):—To a central brass rod are attached, for the 10 ohm and 100 ohm coils, two small brass crosses at a distance of about 150 millim. apart; to the ends of the arms of these crosses are screwed serrated strips of mica, the pitch of the serrations being about 1 millim. The resistance-wire is then bifilarly wound into these serrations. The 1000 ohm coils are of the same form, but from their greater length, 250 ~ millim., it is necessary to employ a third cross in order to strengthen the mica, and even then difficulty has been expe- rienced owing to the mica bending under the coil-tension, culminating in several cases in the breakage of the wire. For the 10 ohm coils wire having a diameter of *30 millim- and a length of 2400 millim. has been used. For the 100 ohm coils, a diameter of *15 millim. and a length of 6200 millim. For the 1000 ohm coils, a diameter of ‘075 millim. and a length of 14500 millim. The top is of ebonite, 86 centimetres long, 28 centim. wide, and 19 millim. thick. Instead of using divided blocks for the dials, conical plugs, having a maximum diameter of 9 millim., and a taper of 1 in 12, fitting into conical sockets have been employed*. The * This method of constructing the plugs is due to Mr. R. W. Paul, Proceedings of the Physical Society, 1892. R 2 ®D © SS Vg, re it ‘~e= i 212 fa i we ueuunguarteverrrers Tm ire Fn oe iT On the Use of Bare Wire for Resistance-coils. 213 plugs are connected with the zero socket of the previous dial by means of heavy flexible leads, having a copper core, 5 millim. in diameter, composed of copper wires of diameter *2 of a millim. It was found necessary to use comparatively large wire, as the first set of connecting leads, built up of wire ‘07 millim. in diameter, parted with the constant turning and gave rise to a variable plug-resistance. The use of the conical plug in a solid conical socket is completely free from errors caused by the change of shape of the insu- lating material ; further, such forms can be easily and accu- rately machined, a matter of no small importance to those who make their own apparatus. The terminals are of large diameter (25 millim.), and are arranged with the screw in the moveable part, so that the top of the fixed part can be readily cleaned. The proportional arms are fitted with the usual divided blocks. The whole of the metallic part is made of phosphor-bronze, a material which is harder and less liable to oxidation than ordinary brass. The containing box is lined with copper for the reception of the oil. The form of bobbin and the wire for the standard resistance- coils are the same in the 1 and 10 ohm standards ; but in the 100 and 1000 ohm standards the mica is stiffened by being slipped into a brass back, like the back of an ordinary tenon saw, which quite prevents any tendency to bend. The temperature is measured by means of a thermometer placed in a pierced tube which lies inside the coil. The coils are inclosed in an outer brass case and fitted with the usual copper terminals for use with mercury-cup connexions. The 5 ohm standard is of manganin, of the usual British- Association pattern. The oil employed is a pure heavy hydrocarbon oil, obtained from Messrs. Price’s Patent Candle Company ; it is free from any trace of alkali or acid, and experiments conducted by Messrs. Price prove that it has no action on the wire. Ill. Construction of Bridge and Galvanometer. The bridge employed was of the usual equal-armed pattern, having a straight wire of platino-iridium 1°5 millim. in dia- meter and 500 millim. long. The wire is stretched imme- diately over the scale by means of two brass split chucks, these chucks terminating in circular brass rods, having a diameter of 6 millim. The rods slide in heavy brass blocks, 214 Mr. F. W. Burstall on the Use of and the wire can be tightened by nuts on the ends of the rods. Thus the wire is not soldered to the terminals, and can be removed for repair. The scale is divided into 1000 parts, and the divisions are then divided into 10 by estimation ; this is easily done with the aid of a good magnifier. The slider moves on the scale itself, and is provided with a fine adjustment. The connexion to the galvanometer is made by a platinum-tipped spring, resting on a platinum wire which is laid parallel to the main wire. The equal coils are made of manganin, and have a resistance of about 10 ohms. They have several times been adjusted to exact equality, but have never preserved that equality for a long period. This in- equality, however, is unimportant, since it is eliminated by double balancing, which has been done at least once during each set of determinations. The actual amount of inequality at the present time is shown by the facts that, with 1 ohm in each of the outer arms, the bridge centre (¢. e. the mean of the readings when the coils are interchanged) is 500-25, whilst with 1 ohm in each arm it is 500°4, and with 10 ohms in each arm it is 500°5. The wire is mounted on a stout marble base. To protect the wire as much as possible from heat radiated from the observer’s body two blocks of wood have been hollowed in such a manner that they can be slid over the wire ; the slider itself being wrapped in cotton-wool. These precautions re- duce the effect of the thermo-currents to a few scale-divisions on the galvanometer. The effect of thermo-currents on the galvanometer was eliminated by the galvanometer-circuit being kept closed, the battery-circuit being made and broken as required. In order to connect the box-coils and the standards to the bridge, three pairs of heavy flexible copper leads have been constructed ; one pair has mercury-cups, intended for the reception of the standard coils, at one extremity; a second pair has conical plugs, so that any particular coil in the box can be measured alone ; the third pair and the other six extremities of the leads are provided with heavy copper spades, by means of which connexion can be made with the terminals of the box and the bridge. The three pairs of leads are adjusted to exact equality one with another, and each has a resistance of ‘00966 ohms at a temperature of 11°°8. The values of these resistances do not enter into any determination as the leads were always in pairs, one in each arm of the bridge. The galvanometer is a four-coil astatic instrument, the resistance of each coil being 60 ohms. The magnet system is supported by a fine quartz fibre 260 millim. long. In Bare Wire for Resistance-cotls. 215 order to diminish as far as possible the effects of the vibration caused by London traffic, thick rubber blocks are placed on the pier supporting the galvanometer ; this precaution has made it possible to work at any time except when large masses of iron are being moved in the neighbouring goods station. The scale is placed 3 metres from the mirror. The motion of the mirror is observed by means of a small electric lamp which projects the image of a fine wire on to the mirror, thence it is reflected on to a ground-glass scale. The observer ~ is at a considerable distance from the galvanometer, a matter of some convenience since the zero is thus not so liable to be changed. The galvanometer gives a distinct movement for an alteration of ‘00001 of an ohm, with 10 ohms in every arm, the battery being one Hellesen cell, together with an added resistance in series with it of 10 ohms. The galva- nometer is connected to the bridge by 20 gauge rubber- covered high insulation wires ; the rubber covering is neces- sary as | have found serious errors introduced unless the insulation of the galvanometer connexion is extremely good, IV. Determination of Standards. The temperature difficulties which are most liable to cause inaccuracy in resistance measurements have been greatly simplified by the remarkable uniformity of temperature of the room in which the measurements have been made. The room is almost entirely underground, and is protected on all sides by other portions of the building from the heat of the sun. It is lighted by one small electric lamp, which gives rise to no appreciable change of temperature. The presence of one experimenter causes the temperature of the air to rise about *2 of a degree during the first half hour, and then it becomes constant ; but the temperature of the resistance-box and standards, the latter being placed in earthenware vessels and surrounded by sawdust, takes several hours to rise as much as *03 of a degree. The bridge-wire was calibrated by a method due, I believe, to Mr. Griffiths. In one of the outer arms is placed, by means of mercury-cups, a coil of low resistance, called the gauge- coil; on the other hand, the gap can be short-circuited by means of a thick copper bar. In the opposite outer arms are placed three resistance-boxes in parallel. The object of this arrangement is to secure the necessary fine adjustment. Commencing with the slider at one end of the wire, the gauge-coil being in place, a balance is obtained by adjusting the resistance in the boxes, the slider remaining fixed. The 216 Mr. F. W. Burstall on the Use of gauge-coil is then removed and the copper bar substituted ; the slider is then moved until a new balance is obtained. Pre- ceeding thus, the whole wire is divided into a number of parts the resistances of which are equal. From these observations a chart can be prepared showing the deviation in resistance of the wire from a wire of uniform resistance per unit of length. One of the great advantages of this method is that, when an abnormal value has been obtained, it is a simple matter to come back to that particular portion of the wire for a check measurement. The gauge-coil was equal to the resistance of 22°293 mean scale-divisions (each 0°5 millim.), and the greatest error at any point of the wire amounted to ‘4 of a scale-division. Throughout the whole of the com- parison of the coils this calibration of the wire has been employed, and several apparently discrepant observations have been thus brought into line. The temperature-coefficient of the bridge-wire has been found by raising the temperature of the room from 10° 4 te 18°1, the bridge having in one arm a coil of known tem- perature-coefficient, and was found to be ‘071 per cent. per degree. | The thermometer employed, which is of hard Jena glass, is divided into tenths of a degree, each tenth being approxi- mately *5 millim. in length. By means of a small reading telescope it can with ease be read to ‘O01 of a degree. It was tested at the Reichsanstalt and, over the range employed, was accurate to at least ‘05 of a degree. The temperature-coefficient of the platinum-silver wire, over a range from 10° to 25°, was determined by immersing a coil of about 1 ohm in paraftin-oil at 25°, and allowing it to cool very slowly. It was found to be ‘000274 per ohm per degree. . The 1 ohm coil from which the standards have been built up is of manganin, and when tested in June 1894 by Mr. Glazebrook had a resistance of 1°00026 ohms at 13°4, I was, however, so doubtful of the constancy of this standard that in December 1895 I constructed a bare platinum-silver 1 ohm coil. This was compared with the manganin standard, and the mean of eleven determinations gave its value as 1:00000-+:000274 (t—14-96). No doubt the manganin coil had changed its value in the eighteen months that had elapsed since it was tested, so that the above figures were not true ohms. The 10 ohm standard was obtained by the use of three Bare Wire for Resistance-coils. 217 approximate 3 ohm coils*, first placed in parallel and balanced against a 1 ohm coil, and then in series with the 1 ohm coil and balanced against the 10 ohm coil. Instead of connecting the legs of the coils by mercury-cups, as is usually done, “the fasible metal made by Mr. F. Thomas, of Cambridge, was used. This metal, which melts at 60°, gives very constant contact resistances, and does not seem to i injure in any way the amalgamated terminals of the coils. I first determined the value of a manganin 10 ohm coil, which had been made for nearly a year. ‘The value obtained on December 20, 1895, was 9°9987 at 9°°3. This coil was used as a standard to which to adjust the platinum-silver 10 ohm coil. The value thus obtained for the latter was 9°9895 at 10°-3. On stepping up to the platinum-silver 10 ohm coil, the value found on December 30 was 9:9905 at 10° 6. Taking into account the known temperature-coefficient, the latter at 10°°3 would be 9°9897, which differs by only two parts in 100,000 from its comme value. To obtain the value of the ;/5 ohm coil, which was of man- ganin, a oe was form d 1D two 1 ohm coils, a 10 ohm coil, and the qo ohm coil, and a balance obtained by shunting one oF the 1 ohm coils f. On January 12th, a value of (99934 at 11° 2 was obtained. bb) bk) 13th, 9° 99 "099932 99 10°°2 The. temperature-coefficient of the wire was known to be ‘000004 per degree. Between these two determinations the bridge had been dismounted. This coil was again tested on April 8th, and had then a value of :099944 at 12°1, whereas, if it had remained unaltered, its value at that temperature should have been -099938. This change is, however, too small to cause any error in the box-coils. For testing coils which are very nearly in the proportion of 1 to any power of 10 this method is extremely sensitive, and certainly more accurate than making the comparison by means of the wire bridge, provided that the resistances of three out of the four coils for ming the bridge are accurately known. In obtaining the values of the 1 ohm and 10 ohm standard coils, not more than 50 scale-divisions of the wire had been employed, hence a small error in the total resistance of the bridge-wire would not cause any inaccuracy in the values so obtained. The resistance of the bridge-wire was determined 99 >) _* This method is described in the B. A. Reports, 1888. - + This method is described by Mr. Glazebrook, B, A. Reports, 1894, 218 Mr. F. W. Burstall on the Use of in the first instance by placing the standard 1 ohm coil in parallel with a coil of slightly smaller resistance than the bridge-wire. This gave the resistance per scale-division of the wire as ‘00087 at 10°1. After the value of the ~, ohm coil had been found, the resistance of the bridge-wire was determined by balancing the 4, ohm coil against a coil of slightly smaller resistance than the bridge-wire ; the 7/, ohm coil was then removed, and the gap short-circuited The actual figures are of interest as showing the value of a cali- brated wire. ‘lohmin A. Gaugein D. Temperature 10°8. Reading 394:0. Correction for calibration —°3. Short circuit in A. Gauge in D. Reading 967°9. Correction for calibration, —°2. Hence, if p be the resistance per scale-division, "1 ohm coil=2 x 574 p=1148 p. On interchanging the coils,— ‘l1ohm in D. Gauge in A. Reading 32:9. Correction for calibration, 0. Short circuit in D. Gauge in A. Reading 607°0. Correction for calibration, —°1. This also gives ‘1 ohm coil=1148 p. Whence p='00008705 at 10°-8. A and D being the two outer gaps of the bridge. The 100 and 1000 ohm standard coils were determined on similar bridges. The 100 ohm coil,— On April 14, had a value 99-913, at 10°°8. in le eigen 3 oe 004, Leos Whereas it should have been 99:960, according to the observation on the earlier date. This discrepancy is, I believe, due to the fact that the shunt required on one of the 10 ohm coils forming the bridge was greater than 12,000 ohms, which was the largest resistance at my disposal : in order to obtain a balance one of the 10 ohm coils had to be warmed, by means of a water-bath, about 2° above the tempe- Bare Wire for Resistance-coils. 219 rature of the room, which led to some uncertainty as to the actual temperature. The 1000 ohm standard coil was obtained by forming a bridge with the 1, 10, 100, and 1000 ohm coils, and had a value, on April 28, of 1000-24 ohms at 12°38. No other determination has, as yet, been made. The coils were adjusted so as to be right at 15°. V. Calibration of the Resistance-bow. For the first three of the dials the coils were balanced against standard coils (fig. 2), and the differences obtained Fig. 2. ee ye Oe BO FO): © 5) Ce) oo ° °© oO © oO oo .o) to} fo) ra) Le) (2) ©5°0 @50 oa) 260 O 5 © 0-1 GHm STANDARD WIRE BRIDGE. by means of the wire bridge. In order to connect the conical plugs to the arms of the wire bridge, the flexible leads with conical ends were used; the standard in the opposite arm being connected by means of the leads with mercury- cup ends. For the 1 and 100 ohms in the proportional arms spade- ended leads were used, and attached to the terminals at the ends of the proportional arms (see diagram). For the sake of convenience of comparison, I have reduced the resistances to their values at 11°C. The values of the 7/5 ohm dial are as follows :— No. of Coil. Omori HS oar OD 220. Mr. F. W. Burstall on the Use of Jan.12. Jan.20. Jan. 22. Jan.24. Jan 25. Jan.26. Mar.11. Mar.i4. Mean. A0007 “LOOTL: : ann .3.0 gee 10065 10065 ‘10073 -10073 10012. 10012 +=-10009 -10008 -10008 wewcss. 7AOOUZ eee 10067 +=:10069 +=-10063 °10061 °10063 _—..... "10050 eae “‘VOO008 “TOOT4 ci cas- erg apense acess ‘10011 “100103 ae 09976 “09974 --099fo" 2a 09973 09972 -099(S. eee 09982" -O99S(-” -. 22a eee “09985 “~-09985 - 22S eeeeee “10046. 10046". > ee 10042. -..225. See “10003, 1LOO002iy Gaara eeaes BP 8s 10003. - .....2. eee “TOO055 ~~ TOO), Sao cae, 0 bc anes: “10066, =. ...2.4 See It will be noticed that, in coils 1 and 3, I have rejected certain values determined on dates before March 11; the reason being that, when the new flexible leads were attached in February, these two coils were touched and slightly bent, and had in consequence to be re-annealed. The values of the 1 ohm coils are— No. of Coil. Jan. 8. Jan. 11. Jan.26. Feb. 12. Feb. 16. Mean. Wain AS 99929 aS (ad ee a "99931 "99930 Pee anncson 99956 QUOD Oak teat eRe iice ae cathe "99956 Dinas cseaee “99569 GOOD OS Se ere on mt aaa ngy ee waetent 99568 eee “99964 0969) “GOST? =. ea ee a, Pe ‘99968 Dip ssustes ‘99776 Lie Pees. ae Roser namen ees 99975 G cacres Dee cied 100007, 1:00007-—_ +s... 1:00008 1:00007 DRS St Mee ae ‘99976 ‘99979 ‘99978 -99980 “99978 Oieesecenn cela "99878 99875 -99875 -99878 ‘99877 eRe eam! Baca 1:00053 "> 100051... .55-.- 1:00053 100054 Values of the proportional arms are— April 3. Mar. 8. Mar. 16. Mean. 1 sineXs eee 99863 99860 ‘99860 99861 ieines eee 99645 99641 99642 ‘99643 Considerable trouble was experienced in the determination of the 1 ohm coils in the proportional arms, owing mainly to variations in the resistance of the plugs, which were fitted into the usual divided blocks. The amount of this error is of little moment when compared with the 10 ohm coil. The 1 ohm coils have not been employed in the determination of the larger resistances. The values of the 10 ohm coils are :— 10073 10010 “10050 ‘10011 09974 09985 10045 “10003 ‘10061 Bare Wire for Resistance-coils. 221 No. of Ooil. March 8. April 3. April 4. Mean. 1. eessGseseesc 9:9765 DO(G4 ye escecaaee 99764 i ian ce weaneee 9-9926 99925. 7. 8 |e) scaeeeaee 9:9925 Siceccaeeace UT Lhe ceeece 10:0033 10-0033 10:0033 es ee SOOO mo) Scavkeca 9:9973 9:9974 Secs anceses 9:9999 10-0000 10-0001 10-0000 Gieearscces 9:9574 DDT focmececes 9:9573 igen 9:9558 D955 0 9 sans. oee 9°9556 Bi sowbcwscaes 9:9863 9:9858 9-9864 9:9862 ee 9°9748 9:9753 9:9758 9°9753 The values of the proportional arms are :— Mar. 8. Mar. 16. Mar.17. April3. April4. Mean. Rn eX «....., 99513 9°9506 99513 99507 99509 9:9509 ia V2... 100106 100099 10:0103 10:0098 100101 10-0101 Desiring to obtain a check measurement, I balanced the nine ‘1 ohm coils against the 1 and 10 ohm standards in parallel, and obtained the value ‘90224 at 13°, while the first five coils of the dial, when balanced against the two 1 ohin coils in parallel, gave °50125 at 138°°2. The actual values for the sums of the nine and five respectively, as found by the separate determinations, were ‘90259 and 50147. Of course any contact-error due to the plugs would appear when the values of the coils are added up. When the separate values of the nine coils are added up, the contact-error will have entered 18 times into the result, and for five coils 10 times ; on the other hand, when the coils are measured in series, the contact-error will only enter twice in each case, and the differences between the two sets of values in both cases are explained by the ascertained result that the contact-resistance of each plug is ‘00002. It is somewhat bold to assert that an error of -00004 ohms has not entered into the determination of each of the 7, ohm coils. The standard itself is certainly correct, as will be seen by reference to its values on the various dates ; the only possible explanation would be that the connecting leads of the two arms had not equal resistances. A subsequent test, however, proved that they were equal. I was, therefore, driven to the conclusion that the contact-resistance as above found was real, and not due to an experimental error. The resistance of the box from terminal to terminal with each plug in zero was obtained in three ways. Firstly, by short-circuiting the mercury-cups in one of the arms of the bridge, and measuring the resistance of the leads and plugs 222 Mr. F. W. Burstall on the Use of on the bridge-wire. This gave a value of ‘00967 ohm at 12°°8. Secondly, the first coil of the 31, ohm dial, together with the leads, was- balanced against the 745 ohm standard ; subtracting from this resistance the known resistance. of the box-coil, we get a value of :00964 ohm for the resistance of the leads, at 12°-4. Thirdly, a similar method was employed to measure the first coil in the 1 ohm dial, and this determi- nation gave the resistance of the leads as -00954 chm at 10°°3. In order that these three observations may agree it is necessary to assume that the temperature-coefiicient of the copper leads is about ‘00005 ohm per degree. This is rather high, but the temperature range is too small for an accurate determination. The values of the coils in the 100 dial were obtained on the box itself. Inthe gap A (fig. 3) the 1 ohm standard coil Fig. 3. 1 OHM STANDARD eo 8 & FO was placed; this, together with the first three dials, gave a resistance of about 100°9 ohms; and constituted one arm of a Wheatstone bridge, the two 10 ohm coils in the proportional arms formed two other arms, the fourth arm was any one of the 100 ohm coils, which was connected to the gap C by means of the two flexible leads with conical ends. The plug from the centre of the 100 dial was in the zero of the 1000 dial so as to complete the circuit from the gap A to the gap C. The smallest resistance in the box was 7), of an ohm, so that the last two figures of the resistance had to be obtained by interpolation from the swings of the galvanometer. The battery employed was one storage-cell, and the current was commuted for each observation. With the coils of the gal- vanometer placed in series an alteration of ;4, of an ohm in the box caused a total galvanometer swing of about 116 scale- divisions. Bare Wire for Resistance-coils. 223 The values of the 100 ohm coils are: — No. of Coil. April 5. April 6. 1 ayer 100°511 100°510 Be eee 100°967 COR Man Deen) Were... 100°266 2 a ae 100-300 100°305 Dogon sts 100°362 100°365 ue 100°671 100°676 Gee 100°603 100°607 Ones occ 100°434 100°435 ars 100°845 100°850 The 100 ohm proportional arms were determined by the same method as was used for the 100 ohm standard coils. Their values are :— April17. April 20, April 21. Mean: ioetex’ §. 100224 HOO 219 100:220 100°221 roi «100°312 100°314 100°309 100°312 The 1000 ohm coils were also measured on the box itself. In the gap A (fig. 4) was placed the 100 ohm standard coil ; Fig. 4. 100 OHM STANDARD this, together with the first four dials, formed one arm of a Wheatstone bridge ; the two other arms were the 100 ohm coils in the proportional arms. A single flexible lead connected the last coil of the 100 dial with any required coil on the 1000 dial. Another lead connected the other terminal of the coil to be measured to the terminal of the proportional arm Y. The current was provided by two storage-cells. The values of the 1000 ohm coils are :— 224 Prof. A. McAulay on the Wave-Surface and Rotation ra April 25. 1 Bee 1023°35 2 Be 1027°30. Binge neee 942°05. re ake 102204. Db aeenent LOTT 2T os eae Noa 1032-04 TS se 1007-44. Biabsorce.2 1003°45 _ so Ae 1026-42 The values of the proportional arms are :— April 27 ILC ine, 7. Ca ee 947-92 NOOO mM Fo. 2.2 e. 994°21 My object in giving the whole of the figures relating to the resistance-coils is to show to what an extent bare wire coils are to be trusted. Whether the coils retain their values as well as the resistance standards of the British Association, time alone can decide. There is no reason to suppose that, if the coils are kept continuously in an oil-bath, and the oil kept free from water, any considerable alteration can take place. XXII. On the Wave-Surface and Rotation of Polarization Plane in an Aeolotropie Electromagnetic Medium. By Prof. A. McAutay, University of Tasmania *. N the ‘ Philosophical Magazine’ for June 1885, p. 397 (also ‘ Electrical Papers,’ vol. ii. p. 1), Mr. Heaviside has in- vestigated in a very instructive manner the properties of the’ electromagnetic wave-surface and index-surface, and the relations in a plane wave of the electric and magnetic forces and the displacement and induction. In noticing that in one respect his investigation can be simplified, | have been led to some simple connexions between the electromagnetic surface and Fresnel’s surface. The most important result is that the former can in two ways by a real pure strain be converted into a Fresnel surface ; the axes of the strain being in the two cases those of permittivity and inductivity. , Thus all the peculiarities—such as double sheet, singular * Communicated by the Author. of Polarization Plane in an Aeolotropic Medium. 225 point, &c.—of the Fresnel surface, and no more, are repeated in the electromagnetic surface. I am not familiar with the details of experimental work in Physical Optics, and therefore cannot say whether there is conclusive evidence that the Fresnel surface is accurately the form of the true optical wave-surface. We see by the above statement that the mere qualitées of double refraction, conical refraction, &c. will not. serve to distinguish between the Fresnel and general electromagnetic wave-surfaces. The notation and language of Quaternions will be used below, and Mr. Heaviside’s valuable practice of denoting (whenever desirable) vectors by Clarendon type will be followed. Prof. Hathaway’s (‘Primer of Quaternions,’ Macmillan, N.Y., 1896) term “ nonion ” for “linear vector function of a vector’ will be used. [But I should like, in passing, to say that I think the term a bad one. Some single term is almost indispensable, and I had suggested “ Hamiltonian.”’ Prof. Hathaway rightly objected that Hamilton’s name shouid not thus be appropriated to a minor function occurring in Quaternions. I therefore prefer “nonion.” But there is this serious objection to thus indiscriminately extending the principle which underlies the formation of the word ‘“‘quaternion”’—that there will be many kends of qua- ternions, many kinds of nonions, &c. Tor instance, a unit rotor would be a quaternion, and what I have in Octonions ealled a self-conjugate pencil function would be a nonion.] If y be a nonion, and y’ its conjugate, the strain corre- sponding to y’—! may be called the reciprocal conjugate of the strain corresponding to y. It is physically described as follows :—If a given strain be effected by first making a pure strain and: then a rotation, the pure strain may be called the pure part of, and the rotation the rotation of, the given strain. The reciprocal of a given pure strain is naturally defined as the pure strain whose axes are those of the given strain and whose elongations are the reciprocals of those of the given strain. The reciprocal conjugate of a given strain is then one whose pure part is the reciprocal of the pure part of the given strain and whose rotation is the same as that of the given strain. We require the following Lemma.—If RB be a given surface, and 8 tts polar reciprocal with regard to a given origin; and if by a homogeneous strain which leaves the origin unmoved R become W, and by the reciprocal conjugate strain S become 8’, then S' is the polar reciprocal of R! with regard to the same origin. Phil. Mag. 8. 5. Vol. 42. No. 256. Sept. 1896. S 226 Prof. A. McAulay on the Wave-Surface and Rotation Fix the attention on a tangent plane of R and the corre- sponding point of S, and on the plane (tangential to R’) and point (of 8’) into which these are strained. Let p be the coordinate vector (the origin being the given one) of any point of the tangent plane of R, p’ the corre- sponding strained value of p, o the vector of the point on 8, and o! the strained value of co. Let y be the given strain, so that y'—! is the reciprocal conjugate. Thus we have P=; @=7 '¢, .. = er Spo =—l . . 4. eee for all values of p (in travelling over the tangent plane). It at once follows that and Spo’ = —1 for all values of p’. This proves the proposition. The equations that Mr. Heaviside uses in considering the wave-surface are : : VVH=cE=D,.'.. 7 ee —VVE=ywH=B, .... . (4) where c and w are self-conjugate nonions, viz. permittivity and inductivity respectively, and where H, E, B, D are as usual. The medium is immovable, and ¢ and wu have constant values at all points. In order to bring these into harmony with the notation of my paper “On the Mathematical Theory of Hlectro- magnetism ”” (Phil. Trans. vol. elxxxiii. 1892, A, p. 685: this paper will be referred to below as “ M.T. E.”’), I prefer to write them } \ VV'H = cH =D!) . > ee Wolfe, J aoe p' being the coordinate vector of an actual point of the medium. Suppose now, in accordance with “ M.T. H.,” we write p = XP). 6 Ae 2 ee where y is an arbitrary nonion, which, however, has a constant value. If then we put H’ == Xie ist Fp’ = a | E, Baie yb We Do nig aD: | po =m xu’, of = myo’, m having the usual meaning with regard to y, (5) and (6) (3) of Polarization Plane in an Aeolotropic Medium. 227 become (3) and (4) respectively. This statement can easily be verified independently of “ M.T. H.” In the language of “ M.T. H.” this is equivalent to taking for the standard position not the actual fixed position of matter, but a homogeneously strained (7!) state of that. By suitably choosing y we can make either ¢ or wa constant scalar. I[t will be sufficient to consider only one of these cases. Let m/= py! py’ M3’, where py’, Mo’, w3’ are the actual prin- cipal inductivities (?. ¢., m’ stands towards pw’ as m towards x). Put atin Fe gt oy) ee) Thus He ee OG OPE aGlO) and equation (8) becomes He 5 BY 2H, Bo =m?y?B, Di =m? p'?D, . ecg Cal) w=], c= wie pls, H = Since now in eq. (4) w=1, we see at once that in the ideal space denoted by p,H, D, &c. the wave-surface of propagation of H and E or Band D will be a Fresnel surface, and the corresponding index-surface will be its polar reciprocal. The equation of this ideal wave-surface being expressed in terms of p, the true wave-surface will be obtained by straining by the function y or m’—?u because p’=yxp. The ideal index-surface is the polar reciprocal of the ideal wave-surface, and similarly for the actual surfaves. Hence, by the lemma above, the actual index-surface is obtained from the ideal by straining by y’—! or m? p'-3, This change of variables from p to p’ thus enables us to reduce the finding of the wave-surface from the index-surface to the ordinary Fresnel case, and thus saves us from the only part of Mr. Heaviside’s investigation which is very complex. If we notice that in equation (1) above the relation between o’ and a is the ordinary intensity relation, and remember that p’ and o” are naturally taken as the coordinate vectors of points on the wave- and index-surfaces respectively ; and if we bear in mind the fundamental properties of intensities and fluxes, we shall find that all Mr. Heaviside’s results for the actual case can be written down from the corresponding ones for the simplified ideal case. For instance, if we show in the simplified case that o = VBD/3S8(BH + DB), 228 Prof. A. McAulay on the Wave-Surface and Rotation it will follow that o! = VB'D'/4S9(B'H! +D’E), because the expression on the right is an intensity. It can easily be verified directly that Mr. Heaviside’s wave- surface strains by means of the function «—? into a Fresnel surface and similarly for the index-surface. In writing the above it has occurred to me that it is easy by the methods of “M.T. H.”’ to construct any number of mediums which shall, according to equations (5) and (6), rotate the plane of polarization of an electromagnetic plane polarized wave. Itshould be carefully noticed that the special electrical theory of “M.T.H.” is not here involved. We deal with Maxwell’s theory pure and simple, as exemplified by equations (5) and (6) above. It is only the mathematical methods of “M. T. EH.” that are about to be used. In the mediums in question pw’ and ¢’ vary in space but not in time. I will first describe such a medium, and then indicate how it is constructed. | pe’ and c! vary spirally, according to a certain law to be mentioned directly, about a certain axis fixed in the medium. For the sake of conciseness, suppose this axis is vertical. Describe a circular cylinder of any radius R, having this axis for its axis. Qn this cylinder describe a spiral making an angle @ (between O° and +45°) with the horizon given by the equation tan 20 = 2h/R,-. «ee ee where / is a given constant length (positive, say, to fix the ideas, though it must also be possibly negative). This spiral will be referred to as the first spiral. A spiral on the same cylinder cutting the first perpendicularly will be referred to as the second spiral. Thus, through every point of the medium we have a first spiral and a second spiral. The principal axes of permittivity and inductivity are the tangents to these two spirals and the line at right angles to both (i. e., the perpendicular from the point on the axis). The first axis will mean that along the tangent to the first spiral, and the first permittivity will mean the corresponding principal permittivity, and similarly for the first inductivity ; similarly also for the second axis, permittivity, and inductivity. The third axis is of course the remaining one, and similarly for permittivity and conductivity. The third permittivity and third inductivity have constant values cy and fo throughout the medium. The first permittivity and inductivity are cy cot? 8 and py cot? 0 respectively, and the second are Cy tan® 0 and py tan” @ respectively. In this medium a plane polarized wave with normal along of Polarization Plane in an Aeolotropic Medium. 229 the axis is possible, and will suffer rotation in the direction in which the first spiral goes round the axis. The rotation is one radian for every distance h travelled by the wave. It will thus be seen that for a point infinitely near the axis the first and second spirals (and therefore the corresponding axes) are infinitely nearly inclined at an angle of 45° to the horizon. As we recede to an infinite distance from the axis, the inclination of the first axis continuously diminishes to zero, the second axis being, of course, always at right angles to the first. Also, infinitely near the axis the permittivity and inductivity are infinitely nearly isotropic, and as we recede to infinity the first permittivity and inductivity continuously increase to infinity, while the second continuously decrease to zero. The geometrical mean of the first and second permit- tivities is always the constant third, and similarly for the inductivities. We thus see that strictly within the four corners of Max- well’s theory we find room for the explanation of the rotation of the plane of polarized light in crystals. We may instruc- tively picture (however far from the real truth the picture may be) such a substance as quartz to be made up of a bundle of parallel ropes (as they may be called), each rope being such a medium as just described. To make the theory strictly applicable the average diameter of a rope should be large compared with the wave-length of light. There seems little doubt, however, that even if the average diameter were com- parable or even small compared with the wave-length there would be a rotation of the plane of polarization. To construct the above medium, first note that for an immovable medium equations (3) and (4) are precisely equi- valent to equations (5) and (6). Suppose the permittivity and inductivity referred to the standard position (¢ and p) are constant scalars cy and wy. Then many solutions of equations (3) and (4) are known. But p’ may be taken as any given function of p. Hence we have corresponding solutions—which are fully known—for the actual position. Remembering the connexions of intensities and fluxes with the position of matter, we see, among other things, that the line-integrals of EK’ and H’ referred to the actual position are the line-integrals of H and H referred to the standard position. In any particular case this fact enables us to see at once how H’ and H’ are distributed in the actual space when the solution for EK and H is known. For instance, the above statements about the rotation of the plane of polarization in the medium described are seen at once to follow from the following con- struction of that medium :— 230 Wave-Surface and Rotation of Polarization Plane. Let the actual position be obtained from the standard position by the simplest kind of torsion round the axis (St.-Venant’s torsion-problem for a circular cylinder). Use columnar coordinates R, ¢, z for the actual position of matter, the axis being the axis of torsion. Let i, 7, & (¢ and 7 being functions of the position of a point) be unit vectors in the directions of dR, dd, and dz respectively. Thus we put per pe 7 | oe so that the torsion is a radian per length h along the axis. For brevity put al ial and note that rkr-1=k, Thus dp’=rdpr-1+2V.Vdrr-', p! =r{dp+h—'dzVkp}r-}. Fiionibediag that dz= —Skdp we see that ( being an arbi- trary vector), YO=TYOr),. . . se where V¥j,O=o—h Vipsok. . >. 2 anne Now assuming that C=O) #P=Py. + - 6 =e where Co and py are constant scalars, we see by eq. (9) § 9 of “MDE. 2 that = OoXX', MW =MoNX’, + « - + (18) since by physical considerations it is obvious that m=1. Now XX O=TNOX Tor 7! q =r{r—or—h"VkpSkr wr —hkSkpr—ar—h-2V kpSkpr- onl os =o—h"Vkp'Sko— hkSkp’w—h-*V kp/Skp’a, or putting Vkp’= Ry, XX O=o—h R(JSlho+kSjo) —h-?RYySjo. . (19) This gives XNI=t eS ee and if tan*@+h-'Rtan@d—1=0,. . . 2 (2) or tan 20=2) R71). cen ey Xx'o= cot?d where w=jcosO+ksin@. . (28) On the Continuity of Isothermal Transformation. 231 It will be found that these results together with equation (18) give the actual medium described above. It is possible that a torsion other than the simplest (from a strain point of view) would give simpler electromagnetic results. The above torsion is the only one I have examined. Tnstructive results are obtained by considering the wave- surface and the ray in the p space and their associated wave- surface and ray in the actual p! space. If a disturbance emanate from a point on the axis of the medium, its wave- surface is a sphere both in the standard and actual positions of matter, but the ray, while straight in the standard position, is a diverging spiral in the actual position that circulates round the axis, one complete revolution taking place while the ray moves a distance 2zcrh in the direction of the axis. University of Tasmania, Hobart, May 380, 1896. XXIII. On the Continuity of Isothermal Transformation from the Liquid to the Gaseous State. By THomas Preston, rs a Oe ANE EN any substance passes from the liquid to the gaseous state by isothermal transformation, the relation between pressure and volume is represented diagram- matically by a curve such as that shown in fig. 1. In this Bigs oO Vv curve, the part AB refers to the condition of the substance in which it is altogether liquid, and along this part the volume * From the Trans. Roy. Dub, Soc. n.s. vol, vi. partiv, Communi- cated by the Author, . 232 Mr. T. Preston on the Continuity of Isothermal alters only slightly as the pressure is varied. When the bee is gradually reduced, however (the temperature eing maintained constant), a point B is reached at which the liquid begins to boil, and the whole mass may be transformed into the gaseous state under constant pressure, if heat be supplied to keep the temperature constant while the volume is allowed to increase from B to D. The part BD of the isothermal is consequently a right line parallel to the axis of volume, and at D the whole mass is in the condition of saturated vapour. Beyond D the curve DE is approximately a rectangular hyperbola as it represents the isothermal of a gaseous substance which approximately obeys Boyle’s law. Very shortly after Andrews’ celebrated experiments on the isothermals of carbon dioxide, and on the continuous trans- formation of matter from the gaseous to the liquid state, Professor James Thomson, in an ingenious speculation (sug- gested by the shape of the isothermals immediately above the critical temperature), proposed an isothermal curve of the form represented in fig. 2, which embraces the idea of conti- Fig. 2. O Vv nuity of transformation, so much insisted on by Andrews. Here, in passing from B to D, the substance is supposed to be homogeneous throughout, and not to be partly liquid and partly vapour as in the corresponding part BD of the iso- thermal of fig. 1. The word homogeneous must here, how- ever, be taken with some reservation, for although the mass, asa whole, may be apparently homogeneous—that is, one cubic centimetre may be on the whole the same as another,— yet when considered in very small portions the mass may be intensely heterogeneous. For example, small portions may Transformation from the Liquid to the Gaseous State. 233 approach the gaseous state more nearly than the liquid, while others may be more decidedly in the liquid condition *. Since the time of Andrews and Thomson, various attempts have been made to deduce from dynamical principles a general relation connecting the volume, pressure, and temperature of a substance which will apply to the liquid as well as the gaseous condition of matter, and which will also hold through- out the transformation from one state to the other. Of these the most notable examples are those of Van der Waals and Clausius, both of whom obtained equations (founded on cer- tain assumptions) for the isothermal curves which, when traced, presented the characteristics of the curve suggested by James Thomson, as shown in fig. 2. A difficulty which presents itself at once to the acceptance of such a curve as representing a realizable series of trans- formations, is that the part MN represents conditions of the substance in which the volume and the pressure increase together. As a consequence, this part of the curve has been generally regarded as unrealizable, and experimental evidence of it has been nowhere found in nature ; yet, the interesting phenomena of superheating and supersaturation are so well represented by the portions BM and DN that the whole curve has been admitted as a possible, if not a necessary, generalization. It is to this unrealizable part of the curve that I now wish to attract attention, and I shall endeavour to show that there is a conceivable condition of the substance which satisfies the extraordinary demands of the portion MN, viz., that the pressure and volume shall increase together, and that through- out the transformation the substance shall be in equilibrium, although necessarily unstable. For this purpose, let us consider the condition of the sub- stance at any point of the isothermal between B and D, What really happens in practice is, that bubbles of vapour are formed in the interior of the liquid mass, and by reason of the action of gravity these rise vertically upwards, and the result is that the mass becomes separated into two portions, the upper part of the containing vessel being filled with vapour, and the lower part by the remaining liquid. The action of gravity is thus to separate the vapour bubbles from the liquid, and it is on this account, as we shall see, that the part BD of the isothermal is, in practice, a right line as shown in fig. 1. If, however, we imagine the action of gravity to be removed, then a bubble of vapour when formed would * This view has been put forward more than once in the Author's ‘Theory of Heat,’ e. g., p. 896, 234 Mr. T. Preston on the Continuity of Isothermal remain 2n situ, except in so far as it might drift with currents in the mass. The formation of bubbles, under these con- ditions, would cause the mass to swell into a spongy condition —a heterogeneous mixture of liquid and vapour,—in which, if the equilibrium could be maintained, the volume and pres- sure would vary according to laws very different from the simple law of constant pressure which governs the transforma- tion of ordinary boiling under the action of gravity (fig. 1). In order to determine, under these conditions, how the pressure varies with the volume, at constant temperature, let us consider the case of a mass of liquid in which a spherical bubble of the vapour of the liquid has been formed, as shown in fig. 8. For the sake of clearness, let the mass be enclosed Fig. 3.—Bubble surrounded by liquid. aa Y in a cylinder by means of a piston, so that the volume and external pressure can be varied at pleasure, then, if p be the pressure, applied through the piston (which we may term the external pressure of the mass, in the ordinary sense), the pressure at any point in the interior of the liquid will be p+e, where c is a quantity depending on the surface film, and, as it arises from the mutual attraction of molecules well within each other’s sphere of action, may be very large. But, if a be the vapour-pressure within the bubble, the relation connecting p and @ is le amemet e e e e ~ ° (1) where 7 is the radius of the bubble, and T the surface-tension Transformation from the Liquid to the Gaseous State. 235 of the surface film separating the liquid and vapour. It is clear, therefore, that if @ remains sensibly constant, p must increase as 7 increases, or in other words, the external pressure and the volume must increase simultaneously, if equilibrium is to be maintained. The saturated vapour-pressure @, however, is not quite constant, but varies at constant temperature with the curva- ture of the film with which it is in contact, and if a) be taken to represent the normal saturated vapour-pressure, that is the pressure of a saturated vapour in contact with a plane surface of its own liquid, then the saturated vapour-pressure in contact with a concave spherical surface, of radius 7, is easily shown to be where p is the density of the liquid, and p, the density of the saturated vapour. Hence the relation (1) connecting p and 7 becomes j 9 p1 2) 5 =. sa By=pt pe bea ps (2) In this equation all the quantities other than p and r may be taken as remaining constant during an isothermal trans- formation, and consequently, within certain limits, the volume and external pressure of the mass should increase together. This equation, however, cannot be expected to hold in the extreme case in which the bubble is so small that the mass within it ceases to possess distinctly the properties of a vapour, or in the other extreme case, in which the bubbles become so large and numerous that the remaining liquid, by reason of being drawn out into thin films, or otherwise, ceases to behave as a liquid in regard to the transmission of hydro- static pressure &c. Within certain limits, however, equation (2) gives the relation between the external pressure and the volume of the mass. Thus, in the case of a single bubble, if the whole mass be taken as unity, and the mass of vapour within the bubble he m, then the mass of the liquid portion will be 1—m, and the whole volume will be i, Le pa P1 But, if the radius of the bubble be 7, we have Vv — Tp ° e e e e ° 2 (4) 236 Mr. T. Preston on the Continuity of Isothermal consequently, equation (3) becomes 4 : ( i gag | ) i! =—T i ===} + — e ° ° 9) eee 2 Pi ©) or, denoting the specific volumes of the liquid and vapour by v, and va, we have, frem equation (5), at: ae vy CU Th SS} . a) Now equation (2) gives ae Vo r= : . 2 2 ae By—P y—Vy Therefore (6) becomes (ea \a—p)'= Fem). 8) Vg—U Consequently, since the right-hand member of this equation remains constant, the equation of the isothermal curve assumes the hyperbolic form (v—v;) (@o—p)?=constant. . . . . ) This equation holds for a spherical bubble of vapour sur- rounded by its own liquid, and in this case it is to be noted that p must always be less than a, or the external pressure of the mass must be less than the normal saturated vapour- pressure, and this is what is indicated by the portion MC of the isothermal lying below the right line BD in fig. 2. So far we have considered the case of a single bubble, surrounded by its own liquid, but the foregoing reasoning will apply when a number of equal bubbles are formed. If the bubbles are of different sizes, however, the capillary pressures arising from the curvatures of their surface filnis will be different, and equilibrium will be impossible—the larger bubbles tending to expand, and the smaller to collapse. lt would appear, therefore, that the mass might be gradually transformed from the liquid to the gaseous condition, by allowing a system of equal bubbles to gradually increase in size while the volume increased to v, and the external pressure to @, and this value would be reached if the bubbles could be supposed to increase gradually till the whole mass reached the state of vapour. Long before this final condition could be reached, however, the liquid portions of the mass, which interlace the bubbles and fill the spaces between them, would be drawn out into thin films, and the conditions would be such that the foregoing reasoning could not be applied.. The action of the distended surface film, in fact, will be such as to draw the liquid parts which fill the spaces between the bubbles Transformation from the Liquid to the Gaseous State. 237 into spherical drops, so that a stage is ultimately reached in which the mass consists of a system of spherical drops sur- rounded by their own vapour (fig. 4). The state of affairs is now reversed, for instead of having vapour in contact with a concave liquid surface, and therefore Fig. 4.—Liquid drops surrounded by vapour. O O OO OO O OO O O Oo exe) 09900 290 H(oyl@) (DVO) O O 90.0000 OO oO @.er@ C0000 O9 CO OOO O O O0000 ODO) O O50 O 000 O {e {fe 10 10 10 iO O 1 O O O O ie O O at a pressure less than @,, the normal saturated vapour-pressure, we have saturated vapour in contact with convex liquid sur- faces, and therefore at a pressure aw, greater than wp. Hence, in this limit, we may take the pressure on the enclosing piston to be that of the saturated vapour, namely a, the mass will be subject to an external pressure greater than @), namely p=a, and this brings us into the region CN (fig. 2) of the isothermal which lies above the normal pressure line BD. In this it is assumed that the mass is largely in the condition of saturated vapour, and that the liquid exists as a system of equal spherical droplets, swimming in their own vapour. If the drops were of different radii equilibrium would be impossible, as evaporation would take place at the surfaces of the smaller drops, and condensation at the surfaces of the larger. This instability is made evident by the equation which shows how the vapour-pressure increases as the radii of the liquid drops diminish, and when the drops are small, # may exceed wy by a considerable quantity. There is a limit, however, beyond which, if the radii of 238 Mr. T. Preston on the Continuity of Isothermal the drops be diminished, the foregoing equation will cease to apply, and the pressure a, after reaching a maximum, will gradually diminish, and finally recede to the value a, when the drops of liquid vanish. This is the process which takes place along the falling part ND (fig. 2) of the isothermal. Similarly, in the initial phases of the transformation here imagined, namely, when small bubbles are beginning to be formed within the mass, it is clear that equation (2) ceases to apply when the bubbles are so small that they cease to possess the distinctive properties of vapour, and it consequently follows, that although @a may be very much less than a, at some part of the branch BMC, yet a condition is attained with bubbles of a certain diameter in which a is a minimum, and from which it increases in both directions to the normal vapour-pressure @p. Thus, the part BM (fig. 2) of the isothermal is accounted for, and therefore the whole succession of conditions repre- sented by an isothermal, such as that imagined by James Thomson, is rendered conceivable. Such a succession, of course, cannot be regarded as realizable, for although the con- dition represented by every point of the curve is shown to be possible, and one of equilibrium, when the bubbles (or drops) are all of the same size, yet the equilibrium is essentially unstable, for when there is any departure from uniformity, all differences tend to become exaggerated, and the mass may depart from the condition of equilibrium with explosive violence. It is interesting to note that the mass may be transformed from the condition B to the condition D by two distinct routes of transformation—one along the right line BD, in which the condition is stable, and the other along the curved path BMOND, in which the condition is unstable,—yet the principle of conservation of energy forces us to conclude that the work done against external pressure, while the mass expands from B to D, must be the same in the two cases, and for this reason it has been concluded that whatever the shape of the curve AMND may be, the area of the loop BMC must be equal to the area of the loop CND. At first sight we might apply the same reasoning to the transformation from B to C, or from D to C, and rush to the conclusion that the area of each loop must be zero, or else that we are here presented with a violation of the principle of conservation of energy. But it must be remarked that although at the point C of the diagram the mass, in both cases, has the same tempera- ture, pressure, and volume, yet in one case all the vapour is Transformation from the Liquid to the Gaseous State. 239 collected into one portion of the chamber, and all the liquid into the other, whereas iu the other case the vapour and liquid are not distinctly separated from each other, but inter- mixed in some way so as to occupy the whole space as an apparently homogeneous mass. Hence the point C represents two distinct conditions of the mass in which the pressure, volume, and temperature are the same, but in which the internal energies may differ very considerably. Thus, although less external work is done in passing from B to C along the curve BMC than in passing along the right line BOC, yet in virtue of the arrangement-of the mass, the internal energy at C in the former case may be considerably greater than in the latter. This, indeed, must be the case if the arrangement of the mass be of the bubble and drop nature here suggested. For if a-given mass, existing partly as liquid and partly as vapour, be arranged in such a way that the liquid is collected together in one part of the containing vessel, while the vapour is all collected in the remainder (as ordinarily occurs), and if we desire to change it from this arrangement into one like that described above, in which the vapour is disseminated through the liquid in bubbles, or in which the whole vessel is filled with vapour and drops, a certain amount of work must be done in order to effect the transformation—namely, the equivalent of the surface energy possessed by the enormously increased surface area of the bubbles and drops in the new condition. Thus, although less external work is done in passing along the isothermal BMC than along the rectilinear path BC, yet the mass in the former case possesses more surface energy than in the latter, and the excess of external work in the latter transformation is represented in the former by an excess of internal work spent in generating the excess of surface film. Similar remarks apply to the portion CND, for in passing along this curve the external work done is greater than that performed in passing along CD, but this is compensated by the destruction of the surface film. Thus, along BMC there is on the whole a creation of surface film with less external work, and along CND there is destruction of surface film accompanied by increased external work—the excess in the former being equal to the defect in the latter. In conclusion, it may be remarked that the views here put forward seem to have an important bearing on many interest- ing questions connected with the boiling-points of liquids, and the manner in which they are affected by the presence of dissolved salts. It is sufficient to merely point out, at present, 240 Prof. J. G. MacGregor on Abstract Dynamies and that obviously any operation which increases the surface-ten= sion of the film separating a figuid from its own vapour will also raise the boiling-point, for when T is increased, a greater vapour-pressure @ within a buljble will be required in order to enable it to expand against a given external pressure. This prediction of the theory appears to be in accordance with the observed facts. Aes ee —__ ee ~~ XXIV. Whe Hypotheses of Abstract Dynamics and the ques- tion of the number of the Elastic Constants. By Prof. J. G. MacGregor, D.Sc., Dalhousie College, Halifax, N.S,* ie a fol'mer paper + an attempt was made to formulate the hypotheses employed in Abstract Dynamics, when bodies are considered as consisting of particles exerting forces upon one another at a distance. As these may be expressed in varlous Ways, Newton’s Second Law of Motion, owing to its very genelal employment, was selected as one of them, and it was sought to determine what others are required in order to establish both the equations of motion and the law of the conservation of energy. It was shown that the following indepenglent assumptions are both necessary and sufficient for this jyarpose, viz., (a) the Third Law in its wide sense, 2. e., as ass@rting that action and reaction are not only equal and Opposite but also in the same straight line, and () the law “of the conservation of natural forces, 2. e., that natural forces are such that the work done during any change of the con- figuration of a system depends only upon the initial and final configurations, or that 2(Xd«+Ydy+Zdz) is a complete differential. Both (a) and (d) are assertions about natural forces, (a) referring to magnitude, direction, and action-line, and (b) to magnitude. They may be combined in one by noting that when (a) holds, 2(Xdx+Ydy+Zdz) becomes =Sds, where 8 is the stress between any pair of particles and s their distance from one another, and that the condition - that }Sds shall be a complete differential is that each S shall be a function of all the s’s, or in more precise terms, that the stresses between the various pairs of particles shall be propor- tional to the rates of change, with respect to the corresponding distances respectively, of a function of the distances of all the pairs of particles of the system. Thus the requisite hypotheses reduce to two, viz., (1) the * An abstract (with some additions) of a paper read before the Royal Society of Canada. Communicated by the Author. + Trans. Roy. Soc. Canada, vol. x. sec. iii. (1892) p. 3. the question of the number of the Elastic Constants. 241 Law of Force—Newton’s Second Law, and (2) the Law of Stress, just enunciated. To these, however, must be added a third, viz., (3) the Law of the constitution of bodies, that bodies may be regarded as consisting of particles acting on one another at a distance. In the paper* of which this is an abstract, a similar attempt is made to formulate the hypotheses employed when, as in the study of fluids and elastic solids, bodies are considered as. consisting of elements which exert forces on contiguous elements only, across surfaces of contact. In obtaining the equations of motion, in this case, the Third Law is applied, when, the traction at #, y, zon one end of a parallelopiped with dz, dy, dz as edges being called P, the traction on the other end is put equal to — (P =° oe dx ). The Second Law is partially applied when the quotient of the force on an element by its acceleration is put equal to pdx dy dz, p being the density. It is only partially applied, however ; for as p varies with the time, there is nothing in the resulting equation to show that the quotient of force by acceleration is constant, as the Second Law states. Accordingly the equa- tions of motion thus obtained are insufficient completely to determine the motion. An additional equation is necessary, viz., one which completes the application of the Second Law by expressing in some form or other, that the pdadydz of the equations of motion is constant. This is the so-called equation of continuity, which is thus only a partial application of the Second Law. It was regarded by Rankine as re- quiring an independent axiom {, and is derived by other writers by asserting, in a vague kind of way, the impossibility of the annihilation and the creation of matter, the constancy of mass, or the continuity of the motion considered. In order to obtain the law of the conservation of energy, it is necessary to assume, in addition, that the work done f by the stress components during a strain, viz., the integral, between the initial and final states of strain, of §\\ (Bde+ Qdf+ Rdg + Sda+ Tdb + Ude) dex dy de, * Trans. Roy. Soc. Canada [2], vol. i. sec. iii. p. 85 (1895). t+ ‘ Applied Mechanics,’ 9th ed. p. 411. t I use the term—work done by a force—in its ordinary sense, as being the product of the force into the component, in the direction of the force, of the displacement (relative, of course, to a dynamical refer- ence system) of its point or place of application. The definition of this term which Newcomb (Phil. Mag. [5] xxvii. (1889) p. 115) proposed to substitute for the ordinary one would not be suited to the contact-action conception, See note in the Proc. and Trans. of the Nova Scotian Institute of Science, vol. viii. (1890-94) p. 460. Phil. Mag. 8. 5. Vol. 42. No. 256. Sept. 1896. fh 242 Prof. J. G. MacGregor on Abstract Dynamics and results in the production of an equivalent amount of potential energy. This is equivalent to the assumption that the above expression is a complete differential, which is again equiva- lent to the assumption that the stress components, P, Q, R, S, T, U, at a point, are proportional to the rates of change, with respect to the corresponding strain components, e, /, g, a, b, ¢ respectively, of a function of all these strain com- ponents. The Third Law and the hypothesis just enunciated are both statements partially specifying natural stresses. We may combine them in one by assuming that natural forces may be regarded as stresses between contiguous elements of a body (or medium), the components of the stress at a point having the relations as to magnitude just specified. Thus in cases of contact-action also, the purely dynamical hypotheses reduce to two,—(1) The Law of Force— Newton’s Second Law, and (2) the Law of Stress, as just enunciated. In such cases also there is, however, a third hypothesis, viz., (3) the Law of the constitution- of bodies, that bodies may be regarded as consisting of elements exerting forces upon contiguous elements only, across their surfaces of contact. The above results have a bearing on the controversy with regard to the rari-constant and the multi-constant theories of elasticity. For in order to form an estimate of the relative probability of deductions from the two theories, accuracy in deduction being assumed, we must compare the hypotheses employed. The multi-constant theorists, in applying the contact-action conception of bodies, have usually employed as dynamical hypotheses the Second and Third Laws of Motion and the Law of the conservation of energy, which together are equi- valent in hypothetical content to the above Laws of Force and of Stress, or to the Laws of the conservation and the trans- ference of energy. The rari-constant theorists have used the molecular, or rather the point-atom, conception of bodies, and have em- ployed as dynamical hypotheses the Second Law and the assumption that the stress between any pair of particles is a function of their distance, not of the distances of all the pairs of particles of the system. Their dynamical hypotheses have thus a greater hypothetical content than the Laws of Force and Stress, and therefore also than the Laws of Energy. It would appear, however, that the discrepancy between the results deduced from the two theories with regard to the number of the elastic constants is not due to the additional the question of the number of the Elastic Constants. 243 assumption which the rari-constant theorists have employed over and above those equivalent to the laws of energy. If we take Mr. Love’s account of Cauchy’s deduction of the stress-strain relations * as being fairly representative of de- ductions of the kind (I have not access to the literature of the subject), this seems obvious. For if, in this deduction, the stresses between particles be regarded as functions of the distances of all the pairs of particles of the system, not of the distances between the attracting particles themselves only, while the expressions for the elastic constants will be changed, they will still reduce to fifteen. Hence, so far as the number of independent constants is concerned, the rari-constant theorists may be said to have employed dynamical assump- tions equivalent to the laws of energy. This being so, the apparent discrepancy between the results of the two theories must be due to the difference in the assumptions made as to the constitution of bodies. Now the distance-action conception of the constitution of bodies involves a larger assumption than the contact-action concep- tion. This is obvious from the fact that if we assume the molecular hypothesis, or rather the point-atom hypothesis, it can then be proved that bodies may be regarded as consisting of elements exerting forces on contiguous elements only, across surfaces of contact, while the molecular hypothesis cannot be thus deduced from that of contact-action. Thus the point-atom hypothesis may be regarded as consisting of two parts, (a) that bodies may be regarded as consisting of elements exhibiting contact-action; and (b) that this is due to their consisting of point-atoms acting on one another at a distance. Moreover, in the deduction of the rari-constant result, the second part of the hypothesis has been employed. For it is obvious from Mr. Love’s sketch of Cauchy’s reason- ing, that the possibility of reducing the constants to fifteen is due to the simplicity, one is tempted to say artificiality, of the point-atom conception. It follows at once that unverified deductions from the molecular hypothesis must have a lower degree of probability than similar deductions from the rival hypothesis. While the multi-constant result is thus the more probable of the two, it cannot be said to be certain. Mr. Love repre- sents the opponents of the molecular theory as urging against it, “that the known laws of energy lead to results which are certainly true whether the molecular hypothesis be correct or no” t+. Hven, however, if we regard the laws of * «Treatise on the Mathematical Theory of Elasticity,’ p. 110} 1. Loe: cit, p. 16. fo 244 The Hypotheses of Abstract Dynamics. energy themselves as certainly true, the results of their application to the study of elasticity cannot have the same certainty, because of the additional hypothesis (3) which, as seen above, is made in applying them. As the point-atom hypothesis may be expressed in the two parts given above, it follows, if the conclusion reached above is correct, viz., that the dynamical hypotheses practically employed in the two theories are of the same hypothetical content, that the rari-constant theorist must accept the multi- constant result. He must hold that with the assumption (a) only the number of independent constants cannot be reduced to less than 21, but that with the additional assumption (6) they are reducible to 15. It is thus obvious that there is no real discrepancy between the results of the two theories. According to the one, all bodies which may be regarded as exhibiting contact-action will be capable of having their elastic qualities completely characterized by 21 constants, and unless we have further data with regard to these bodies, 21 constants will be requisite for this purpose. According to the other, in the case of bodies which may be regarded as exhibiting contact-action because of their consisting of point- atoms, the number of the constants may be reduced to 15. It would seem to be a simple matter, not indeed to devise and execute conclusive experiments to settle the question of the existence of relations among the 21 constants, but to interpret such experiments when made. For if the elastic constants were found to be reducible to 15, the multi-constant theory would obviously be proved to be inadequate. If other relations were found to hold than those deduced from the point-atom hypothesis, the point-atom conception would be shown to be erroneous and the contact-action conception to be inadequate. If it were found that there were no relations among the 21 constants, the point-atom hypothesis would be disproved and the contact-action conception would be shown, so tar as the number of the elastic constants is concerned, to be adequate. Simple logical considerations of this kind are sometimes overlooked by writers in the enthusiasm produced by successful application of the contact-action conception. Thus Mr. Love says * :—“ Even if the experimental evidence were all fairly interpretable in favour of the other side, if there were a general consensus that Cauchy’s relations hold good, and that Poisson’s ratio is 4, for materials carefully examined, that would not amount to a proof of the molecular hypothesis. It would still be open to us to reject that hypo- thesis as not axiomatic, and in the present state of science we * Loe. cit. p. 19. The Electric Discharge in a Magnetic Field. 245 must so reject it. . . . Unless the hypothesis were axiomatic, there could be no reason to adopt it to-day. Modern Physics is perfectly capable of deducing a theory of elasticity from the known laws of energy, without the aid of a subsidiary hypothesis about intermolecular force, and being in that position, it is bound to discard the hypothesis. Such a device is merely a phase in the development of scientific thought, and, having served its turn as a means of introducing gener- ality into the subject, it must give place again to a still more general method.” It is of course quite obvious that the experimental verification of Cauchy’s relations would not prove the molecular hypothesis; but it would show the contact-action conception to be inadequate. It would still be open to any one with a preconceived idea as to what is axiomatic to discard the former, but in doing so he would find himself unable to account for known facts which had been predicted by the aid of the discarded hypothesis. That modern physics is capable of deducing a theory of elasticity from the known laws of energy without the aid of a molecular hypothesis is surely a mere assertion, if as doubtless is the case, a satisfactory theory is meant. The experimental deter- mination of any general relations among the 21 constants would prove the theory in its present state to be inadequate and unsatisfactory, and the verification of Cauchy’s relations would show that, while the molecular hypothesis must of course be regarded as merely a phase in the development of scientific thought, it has not yet quite completely served its turn as an instrument of generalisation. XXV. The Electric Discharge in a Magnetic F reld. By Sir Davip Savomons*. HE study of the electric discharge im vacuo does not appear to have been followed with the same energy as has been applied to other branches of electrical science, until quite recent times. I would venture to divide the historic period of the subject into four, as follows :— (1) The time when Messrs. Warren De La Rue, Gassiot, Spottiswoode, and Moulton were working upon the subject. (2) When Professor Crookes made his discoveries. (3) The still more recent investigations of Professor J. J. Thomson. (4) The application to photography by employing the so- called x-rays which are abundantly produced by special forms of tubes. * Communicated by the Author, 246 Sir David Salomons on the Electric I do not intend to deal with the last three periods ; but in regard to the first, although many interesting facts were hrought to light, the subject does not appear to have been systematized, nor am I able to find a great deal published on the subject before the period of Professor Crookes, perhaps for the reason that no one has taken the pains to collect all the information and publish it together. . Many important discoveries were no duvubt made and the facts published in some obscure quarter, where they probably remain to this day. The general interest which now exists in science and the large technical Press were non-existent but a very few years ago. | I now propose to describe briefly a number of points of interest in connexion with vacuum-tubes and some classes of work which may be performed by their use, the outcome of work extending over twenty-five years. It appeared to me that two points required settling in regard to these tubes, which, however, are not completely exhausted as the name would suggest; viz. :— (1) “That the number of bands produced in a given tube should be brought under control, that is to say, that the conditions under which they are formed should be solved.” (2) “That the reason for their existence should also be found out.” In regard to the first point, I believe that this question is solved and the results given in a paper by me published in the ‘ Proceedings of the Royal Society,’ in volume lvi. The origin of the bands has been surmised by many of the early workers, in fact they have asswmed that they are pro- duced in consequence of self-inductive effects; but I have not been able to discover any proof that such is the case. I shall be able to show by experiments to be described that this view is correct ; and from the methods adopted, which are probably the only means available for the purpose, give the clue why the first investigators did not advance beyond a state of conjecture. | The tubes I employed contained rarefied air and various other gases; but I found for the particular class of experi- ments that rarefied air sufficed in all cases, and that it was not necessary to proceed to very high exhaustion. The great efforts made by earlier investigators in trying to obtain enormous electromotive force appeared to me wrong for the class of experiment they were entering upon. I therefore tried the opposite course—one which has proved so successful in mathematics, viz. the reduction of the leadin factor to the smallest quantity possible,—and observed what . Discharge in a Magnetic Freld. 247 took place. I soon found that a vast number of the pheno- mena described as fundamental were superposed phenomena ; and that when exceedingly small E.M.F. was employed the various phenomena were seen in their purity, and on raising the E.M.F. the various changes could be seen, up to the complex appearance described in some of the early papers. The E.M.F. employed in the following experiments was sometimes as low as 700 volts and rarely over 2000. It has been known for a long time that the discharge through the vacuum-tube is affected by the magnetic field, but beyond this circumstance I cannot find anything that has been published upon the subject classifying results. Having worked to that point when I could control what took place within the tube, it became a comparatively easy matter to investigate the discharge in the magnetic field provided a sufficiently powerful magnet could be obtained. All the electromagnets in existence were built on the Faraday-magnet type, and this pattern was found incon- venient. I therefore had a special magnet constructed weighing 13 cwt., with a field probably far more powerful than any which had been made before, with the polepieces capable of being approached and distanced by means of screws, and a variety of other details introduced which made the apparatus a piece of engineering work as well as one suitable for scientific investigation. This magnet is shown in, fie... 1, Fail not repeat what I have already published on the subject beyond referring to two points :— Firstly, that the glass of the tube has a considerable influ- ence in creating the bands; and 7 Secondly, that the bands as generally seen are spurious, and can only be viewed in their purity at the moment when the current is so reduced that they disappear from view. There may be other stages beyond this point which the eye cannot see, and that such is probable is shown from the fact that when the tube is made of fluorescent glass the current may be still further reduced and the bands be visible. For producing the current I employed Apps’s coils of various sizes, the contact-breakers being special mechanical forms devised by myself, and worked by an electro-motor. I also employed the alternate current from an alternator, raised to a suitable pressure by means of a transformer. The induction-coils had primary coils so wound that a 100- volt current could be put on direct, without the insertion of a resistance. The number of turns of wire in the primaries is so great that the self-induction reduces the length of the 248 Sir David Salomons on the Electric spark from the secondary, because no large amount of current can traverse the primary coil. But there is a point in favour of using an induction-coil such as described which does not appear to have been taken ad- vantage of. The spark at the vibrator is far more pronounced than if a lower electromotive force were employed for the primary current. Indeed, so much energy can be developed at the vibrator on the “ break ” that it is possible to obtain the equivalent to a direct intermittent current in the tube, or at any rate, so far as the eye is concerned this only exists, the effects due to the current in the opposite direction not being visible. Consequently two types of current can be produce: by means of the induction-coil. Discharge in a Magnetic Field. 249 The phenomena were the same whether the alternate current from an induction-coil, or the alternate current pro- duced by the alternator, was used, so far as the visible effects were concerned. When a tube, as shown in fig. 2, 300 millims. long and 25 Fig. 2. ( } - —-— = ee ew ee ee ew eee em em we eew ec ec encore seo Me DoSSprlOTTC OTS COT SST BAT @aTeteUeessesere——=> --l 1 2 i 1 ! ae y . nN al millims. in diameter, containing brush electrodes at each end, is placed between the poles of the unexcited large magnet (see fig. 8) and has a very small alternate current traversing it, Fig. 3. the bands are produced in the usual way. Now excite the magnet, the switches having been so adjusted that one pole is N. and one 8.,a great change is now observed within the tube, If the E.M.F. of the current is very small, the bands 250 Sir David Salomons on the Electric will disappear altogether and no current will pass. This stage will be referred to later. In such an event raise the E.M.F. until the bands are plainly seen. It will then be noticed that the bands which at first extended across the tube have now divided into two columns, and are very much smaller than before, their position being equatorial. It will further be noticed that the convex sides are all one way in one column of bands and in the opposite direction in the other column of bands, indicating that the two currents have been completely separated and travel through the tube at opposite sides, meeting only at the electrodes. Moreover, the bands are smaller where the field is strongest. Also they will here be placed closer together and be more numerous. In fact, the condition of things can be made such, that where the field is most powerful the bands disappear and a line of light only is visible. But a low-power microscope will resolve this line of light into bands, that is to say, they are so close together that the eye alone does not appreciate their existence. Probably the best way to make the experiment is to place the tube between the poles of the magnet when excited. Then cut off the exciting current, and watch the tube during the time that the magnetism is falling. The various stages can be seen better this way, as they take place slowly. Fig. 4 Fig. 4. ee a me oe enn + oo +s woe ++ 2 ee se es oe eee eee mot nn = = a rw + one + - oe rns eens ee eee + 22 oe oe ee ee + eer” shows the tube with the divided current appearing as two lines of light. Fig. 5 illustrates one line of bands when the Fig. 5. GGGe teu ee magnetism is less strong. Fig. 6 shows two lines of bands Fig. 6. in the tube, when looked at from another point of view. Fig. 7 shows the bands fillmg the tube, the magnetism Discharge in a Magnetic Field. 251 having fallen still further. Fig. 8 the next stage. Fig. 9 Fig. 8. the appearance of the tube when the magnetism ceases to have influence. Before proceeding to describe other experiments it is well to analyse what takes place. My own view is that we have here shown in a very pretty way Ampéere’s well-known experiment of the influence of a current flowing in one con- ductor upon a current flowing in an adjacent conductor. This experiment is usually shown by wires, one arranged as a moving conductor. In the instance of the vacuum-tube the current is passing through a conductor perfectly free to move or, perhaps, it would be better to say that the current is fr ee to place itself, without any appreciable opposing resistance, in the position it tends to take up under the influence of the magnetic field, which latter may be regarded as a current travelling in a circular conductor, which may be resolved into straight line currents parallel to the tube currents. The experiment described, therefore, shows that the two currents try, not to move out of the field, as it might be ex- pressed, but tend to take up definite positions, which naturally must be in opposite directions, when influenced by certain powerful currents in their proximity, z.e., the magnetic field. lt might appear that the resistance of the gas in the centre of the field, where no bands appear, has been increased, and therefore the current chooses a path of least resistance, viz., at the sides of the tube, farthest from the strongest portion of the field. This may, or may not, be an accessory in the case. I venture to believe, for the reason that the alternate current has been separated into its two constituents on opposite sides, that the true explanation is that of Am- pere’s theory. When the resistance of the tube is actually measured it is found to be higher when the magnet is excited, and this, of course, would be expected, since e the current is then travel ling through a much smaller sectional area. Consequently the test of resistance has no value to prove that the gas contained within the tube has a higher resistance, because under no circumstances can the resistance of the gas in the Strongest part of the field be measured, as the curr ent 252 Sir David Salomons on the Electric refuses to travel that road, though possibly some indirect method might be devised. Another conclusion may also be deduced from this experi- ment. It is that since the bands become more numerous in the strongest part of the field, they are produced by self-inductive effects. To put this in unscientific language, the discharge is comparable to that of a lightning-discharge through a good conductor, the peculiarities of which were first pointed out by Professor Hughes; that is to say, the discharge of the current through the gas is checked, and then proceeds again, checked again, and so on; and it is fairly evident that at the points of these various checks heat is developed, and the residual matter in the tube raised to a high temperature, producing what are termed bright bands. That the bright bands consist of heated matter is most probable for the reason that they may be seen from all points of view. If instead of employing the alternate current the induction- coil is so adjusted as to produce an intermittent direct one, only one line of bands appears, equatorially placed, on one side or the other, according as the current is in one direction or the opposite one. The analysis of the column of bands is the same as that of one of the columns when the alternate current is employed. Reversing the current through the tube has no effect upon the appearance of the tube, since the currents change sides. But if the poles of the magnet are reversed, then the convexity of the column of bands becomes reversed ; and this, of course, would be expected. It has already been stated that when the current flowing through the tube is exceedingly small, the tube remains dark and no current would appear to pass. It seems to me that the probable explanation for this is that the current is, so to speak, driven into the glass, which has se high a resistance that no appreciable amount passes. In fact, the whole of the experiments show that the larger the amount of the current which flows through the tube, the more nearly do the bands approach to the centre, or, in other words, the smaller is the space at the centre of the tube which appears dark. If the tube, with the current flowing through it, is placed in an unsymmetrical field, then the lines of bands become distorted, more or less spiral in form. This is because the Fig. 10. VA ee ae eel lee Vad) oR) lo add hdc dat ha aa field being unsymmetrical the currents tend to take up dif- ferent positions in various portions of the tube (see fig. 10). Discharge in a Magnetic Field. 253 If both poles are made N., or S., and the tube placed between them, the bands in the tube will cross at the centre and appear as in fig. 11, the dotted lines representing bands to avoid confusion. Fig. 11. Let us now consider what takes place when the same tube is placed between the poles N. and S. with an increased current. The bands now stretch nearly across the tube. In the strongest portion of the field there stand out very bright and well defined the magnetic lines of force filling the tube in a three-dimensional form. The effect is very striking and ee Besides, the whole tube is filled with a faint ight. Hig, 12 is a general diagram showing what takes place ; and fig. 13 illustrates the tube in greater detail. The pheno- menon is beautifully shown in the globular tube, fig. 14. Fig. 12. Fie. 13. Of course, what appear to be the lines of force are not really the lines made visible but the effects due to the form of the field; since if an effect is due to the field at any given point and varies with the strength of the field, the result will take upon itself the form of the lines of force. It is known that the re- sistance to the passage of the current is less with the lines of force than across them, which effect may have some influence in producing the phenomenon. The bright lines are nothing more than bright bands very closely packed; and the form is due to self-induction. 254 Sir David Salomons on the Electrie In fact, all points on similar lines of force in a magneti¢ field lying between the N. and S. poles make up a figure somewhat like the shell! of an egg ; and the appearance of what I term the visible field appears to be like a vast num- Fig. 14, ber of transparent coloured egg-shells placed symmetrically one within the other, although, of course, each shell is not symmetrical with any other, the inner ones being more elon- gated and the outer ones more spherical, the centre one of all being a straight line. | By holding the tube which has been experimented with in various positions in regard to the poles of the magnet, whether they be N. and 8., or both N. or bothS8., a variety of appear- ances are seen in the tube according to the position in which it is held. All the effects can be traced to what I term the Ampérian explanation. i From the experiments which have been described it is evident that a very important opening suggests itself as to the practical use of vacuum-tubes, viz. that of exploring the magnetic field. [have used such tubes for this purpose for many years past, and have been able to plot out in a few minutes mentally that which takesa long time by the methods generally employed. J am ready to admit that the usual process is more accurate when absolute determinations are required ; but usually all that is wished for is to ascertain the general character of a field and the extent of the leakage, and this can be done at once by employing vacuum-tubes. Discharge in a Magnetic Feld. ia The question naturally arises whether in the case of solid conductors the current becomes displaced when such con- ductors are placed in the magnetic field. It is well known that metals, bismuth in particular, offer considerably more resistance to the passage of the current in the magnetic field, everything else being equal. It occurred to me that this increased resistance is possibly spurious, and due simply to the displacement of the current, the displacement being easier to effect in some metals than in others. I made a large number of experiments in regard to this question, and found that this displacement does take place, although in a very small degree when compared with that which results in the case of a conductor consisting of rarefied gas. A few years ago the displacement was noticed by Mr. Hall, and is gene- rally known under the name of the “ Hall effect ;”” but the phenomenon had been observed by myself many years pre- viously, although I did not publish it, believing it to be a known fact. I made a large number of experiments with galvanometers built on the D’Arsonval-Deprez type, and obtained very vary- ing results by modifying the magnetic field. By increasing the field a maximum sensibility was reached, which decreased on further increasing the field. The various experiments described no doubt indicate the cause of this, viz. that the field being made too powerful, less current passes through the coil, and the sensibility begins to fall. I had a special galvanometer-apparatus made to fit my large magnet, converting it probably into the largest galvano- meter of the type extant; but the sensibility is exceedingly small when the magnet is fully excited, and increases rapidly when the excitation is somewhat diminished. A pretty way to illustrate the sensibility is the following. A small current is passed through the galvanometer-coil when the magnet is excited, and the coil-current increased until a small deflexion is produced. The exciting current is then turned off to permit the magnetism to fall gradually. The deflexion will then become greater and greater, until the dot of light passes the end of the scale, after which the sensibility again decreases as the magnetism falls. From all that has been said up to this point, I think it is worth while for a course of experiments to be made on the varying resistances of different metals in the magnetic field with varying currents. It is probable that it will be found that there is no constant for any given metal ; and if this should be shown to be the case, my view that the increased resistance of the metal in the magnetic field is spurious will be proved. 256 Sir David Salomons on the Electric Returning once more to the vacuum-tube, we observed the separation of the alternate current within it into two distinet paths. It occurred to me that it might be possible to com- pletely separate the two currents. I therefore constructed tubes as shown in figs. 15, 16, and 17, in order to observe Fig. 15. whether the currents would be separated into the tubes, which on experiment I found to be. the case. It was not neces- Discharge in a Magnetic Fieid. 257 sary to place the whole tube between the poles. If one of the electrodes was placed between the poles it was generally sufficient, provided that the plane of the tube was placed equatorially. When such a tube was placed axially, as in fig. 17, the two columns of bands appeared in each section of the tube. A tube constructed as in fig. 18 was then employed, the Fig. 18. (on end electrodes being joined together, the currents separated from the centre to the end electrodes. But in this case the path traversed by each current was practically equal in resistance. Another tube therefore was employed where the distances were unequal, as in fig. 19, the result being the same, and Fig. 19. : = conclusively showing that the alternate current can be divided into its two constituents. A tube as shown in fig. 20 was now taken. The centre Fig. 20. bulb being placed between the poles of the magnet, and the other two electrodes joined together, the alternate current was divided into two currents, one in each arm of the tube. A second similar tube was now connected with this one and Phil, Mag. 8. 5. Vol. 42. No. 256. Sepé. 1896. U 258 Sir David Salomons on the Electric joined up as shown in fig. 21, the connecting-wires being of considerable length. ‘The current traversing the second Fig. 21. tube was again analysed by another large electromagnet ; and it was found that only one type of current existed in each arm of this analysing-tube. Consequently, the current tra- versing the connecting-wires must of necessity have been an intermittent direct current. Another double tube was now taken ; but instead of being a vacuum-tube it contained water, the analysing-tube still being a vacuum-tube. The results were the same, although less marked. It would therefore appear that we have a magnetic means of converting the alternate current into two currents of a direct intermittent type, which two currents can be coupled up so as to form cne intermittent direct current in one direction. So far, 1 have only succeeded in producing this result with very small currents. When the ordinary electric spark in air (fig. 22) is placed Fig. 22. in a powerful magnetic field and the magnet excited, two additional semicircular displaced discharges appear, as in fig. 23, the colour of these supplementary discharges being of a different tint. Fig. 23. When the current is reversed, the displacement is reversed, as in fig. 24. Discharge in a Magnetic Field. Zou When the coil is arranged to give an intermittent direct dis- charge in the secondary only, one seinicircle of light appears, as shown in fig. 23; and when the current is reversed, it is as in fig. 26. : Fig, 25, These experiments led me to try another, which may have some bearing on the reason for the zigzag form of the dis- charge in air. ‘Taking once more the vacuum-tube and placing it in the magnetic field, 1 permitted a very consider- able alternate current to traverse the tuhe. First, the two columns of bands appear; then the lines of force ; and finally these phenomena remain, with an additional one, namely, a series of zigzag dischar ges throughout the tube, permanent in character, but varying their form continually. It is quite possible that these zigzag discharges consist of de- formed bands which meet and form zigzag or sinuous lines. That they should vary in form may possibly be in consequence of the ever-changing temperature of the gases within the tube, due to so large a current passing. Hence it is not impossible that the zigzag discharge in air is due to the magnetic pro- perties of the current itself. Of course further experiment is needed to demonstrate the truth of what I have suggested as a probability. D2 [ 260 } XXVI. On the Longitudinal Component in Light. By Prof. GzorcE Francois FirzGrraup, .A., ScD., F.RS., JHE AIS Od ge | most investigations on the propagation of light attention has been concentrated on the transverse nature of the vibration. Longitudinal motions have been relegated to the case of pressural waves, and investigators have devoted them- selves to separating the two as much as possible. In Sir George Stokes’s classical paper on Diffraction, and in Lord Kelvin’s Baltimore Lectures, the existence of a longitudinal component is mentioned ; but it is mentioned only to show that it is very small and that the motion is mostly transverse. Now the longitudinal component is no doubt generally smali except in the immediate neighbourhood of a source ; but it by no means follows that, as a consequence, the actual direction of motion is transverse at all points ina wave. In every complicated wave there are points and often lines along which the trans- verse component vanishes, and at all these places the smali longitudinal component may be, and often is, of great relative importance, so that the actual motion is largely in the direc- tion of wave propagation at these places. I. The simplest case is that of a simple oscillator whose theory has been completely worked out by Hertz. There are two kinds of oscillator, an electric and a magnetic one. They are exactly complementary, the magnetic forces in one cor- responding exactly with the electric forces in the other. If the oscillator be taken as an electric one parallel to z, we have for the components of the vector potential PIG o, H=H, Pf; and the components of the electric force, which are in general poa¥—-&, Q=aG- 7 R=aHn-S, where fie dk | dG@ | di 7 da say, aden become in this case : @H ; CH 2 sdk aoe LEIS Oe aoa ~ Oe dy It is particularly to be observed that P and Q arise entirely from J, which was dismissed by Maxwell as not coming into consideration in cases of wave propagation on account of there being no varying electrification. This is true as regards -* Communicated by the Author. On the Longitudinal Component in Light. 261 propagation, but not at all as regards origination. In all eases of origination we have to do with conduction, or its equivalent convection, and in most such cases we have changing electrification which brings in the J term. The longitudinal component at each point is eee, e Y ° 2 e T= 7b +o. Q+-.R 22 Wee af a SRC SE ps (27 sin pt— gr + 7, COS pt—qr). This is no doubt very small at a distance from the oscillator ae 1 compared with the transverse component which involves - and in consequence the motion is transverse at most places. On the axis of z, however, the transverse component, which is proportional to p the distance from the axis, vanishes entirely. Hence along the axis there is a beam of purely longitudinal vibration, of no doubt small amplitude, but nevertheless existing necessarily in order that there may be no compressions. This all appears on the face of Hertz’s investigation. He carefully studied the forces as represented by the above equations, and has plotted them and shown that they represent a series of whirl rings thrown off from the oscillator and growing gradually thinner and thinner until at a distance the rings become nearly plane waves, and the opposite sides being always a wave-length apart are the two opposite phases of the wave. The accompanying diagram roughly represents this state of affairs. It is evident on the most cursory consideration that these waves must have a longitudinal region. The lines of force in any one wave are up to the axis @ p)) along any one spherical surface ail round; and if there is not to be concentration anywhere, 2. e. if there is no electrification of the medium, they must turn round and be continuous with the return phase of the wave. The reason why they are so feebly concen- trated in this return region is because it is soenormously extended. If the wave-length be small compared with the distance from the origin, the flows 262 Prof. G. F. FitzGerald on the — up and down along the equator are very close to one another and consequently the force is concentrated ; while this same force which is concentrated within a wave-length has the whole hemisphere to return in, and so the longitudinal concentration is quite small, and that is what is represented by the small value of the longitudinal component at any point. The total quantity of longitudinal component must be, on the whole, equal to the transverse component at the equator. lI. In the ease of several simple oscillators oriented in dif- ferent directions the resultant vector potential can be repre- sented by A=US (pt —qr) 4 ysin Pie r r where U and V are vectors at right angles to one another. The effect is the same as if two opposite electrons were moving on opposite sides in an elliptic orbit whose plane was that of U and V and whose axes were these two lines. It is interesting to observe that this case, coupled with a slow rotation of the ellipse which would be produced by almost any small disturbing force in its plane, has been shown by Dr. Stoney to be a sufficient cause for the double lines in spectra which are so common and which are familiar to everyone in the double sodium line. If the directions of U and V be taken as those of « and y, and z be taken perpendicular to the plane of this ellipse, we may take F=F, cos Sota ace Ee, H20: and we get a sort of corkscrew wave with a longitudinal component which can be represented by SI ae {Leos (pt—qr+)}; 7 where ¢ is the angle between 7 and z, and L and / are func- tions of Fy, Go, 7, @, and g. This component vanishes along the axis perpendicular to the plane of the ellipse, and ig a maximum in this plane. If ’,= Gp, this simplifies to sin z q CG = {2q sin (pt—gr— é)+- cos (pt—qr—O)}. This case is rather interesting, as being the form of magnetic Longitudinal Component in Light. 263 wave that is thrown off into space by the rotation of each of the earth’s magnetic poles. The more complex wave thrown out by the earth with its two magnetic poles comes under the next head ; but it is wayes of this type which must be thrown off by the planets rotating round the sun, if they are electrified, and by their gravitating property if gravitation be propagated in the same way as electromagnetic disturbances. Ill. We can produce any desired combination of complex doublets by operating on a simple doublet with a function _ S oA =). The typical term of such a function may (i) -(@):(ae)=* ne £23 (ptr) r be taken as If we write we get as a typical case, hou, (C= lal (0 Also, remembering that A?u+?.u=0, we have for the electric force corresponding to this typical case of a vector potential, : Cpr: du ° du ere om we Be pe Ns it Se ha Q . da dy’ K dx dz da’ Now this operation will introduce all sorts of powers of Z r and of g, and I only want to calculate the principal term in the longitudinal component. In making this approximation we may simplify the calculation by observing that the largest terms are always due to differentiations with respect to the circular part of u, and that differentiation with respect to 2, y, 2, or r lowers a term by one. We may then leave out all differentiation with respect to coordinates outside the circular part in terms of the second order, and it is well to reduce the differentiations represented by 6 so as to produce : Li aN : ae terms of the form pe and 6 ee Of course it very much simplifies calculation to use the typical form e—” for the circular functions. We thus get for the values of the components of electric force to the second order :— 264 Prof. G. F. FitzGerald on the pe =652 ; 3008 pt— qr Ue t— —14 19/8 +9)— 4 (at B+y— |} O=, 9 3 5 es Bs be sine 2h ee JS Bae Tey a yg 2% cos pt—gr R=(.- ee — 2 [8 4 BF fant + y+ (B—P)are} [SSOP Ee Uf av a In this form it is Bart at once that the highest terms vanish in the longitudinal component o=P=+Q=+R- = [ety + 2) {221-8 9) tay? +2) — 20h early + 2) +7? (a+ 8 +2y— $a + By) +24 2BFY—Jaty2) | PM In order to get this we have to observe that when applied to the circular part only (2) OFC ip r is Any particular typical term of this order vanishes over the sin pt—qr 1h quartic cone the coefficient of 6 This is the cone of intersections of the systems of spheres ee ye 42° 20 with the cubics 04 x*(1L—B—y) +a(y?+ 2°) $= aa? (y +2) +y?) (at B+ 2y—3)a+Byt +2*4(a+2B+y—3)y +42}, In the particular case of a series of end-on vibrators for which 8=y=0, this cubic breaks up into the plane r=0 and the quadric cone y+e= Ae a(y+z). Longitudinal Component in Light. 265 In every case the quartic cone intersects every plane per- pendicular to the axis of w in a bicircular quartic. In the case of a complex oscillator whose components are not all parallel to the axis of 2, as in the case just studied, the longitudinal component will vanish to this order over a quartic cone so long as we confine ourselves to a typical term 6. ‘This cone is of the form Uz (x? +y? + 2?) (aya? + diy? + 12”) — faa? (y +2) +by? (e+ a) +c27(a+y) + ly22? + m22a? + nx?y? + ayz(pet+qy+rz)}. In general it is quite evident that the motion along the radius does not vanish. On considering the general case, we may observe that if the differentiations involved in 6 are such that for every term a+ 8++y¥ is either even or odd, then there will be a complex surface all over which the normal component will vanish to the second order of small quantities; but that if 2+ 8++y¥ be even in some terms and odd in others, we shall have o of the form o=U cos pi—qr+t V sin pt—gqr, and this will only vanish over the curve of intersection of We Vand V=0. 3 IV. If we now consider the case of diffraction through a narrow aperture, it is simpler to take the case of the electric displacement of the incident wave as parallel to the edges. In this case the electric force is everywhere parallel to the edge, and consequently its longitudinal component every- where vanishes. On the other hand the magnetic force is perpendicular to the slit and has a longitudinal component everywhere except in the plane through the slit perpendicular to the wave-face. In considering the more complicated case of the electric displacement being perpendicular to the slit, it is necessary to take account of the nature of the edges, whether they are non-conductors or conductors, whether they are erystalline, and so forth, because their electrification Kc. must come into consideration. Similarly, in the case of the electric displacement being parallel to the slit the magnetic properties of the edges inay be important. In this case, too, their conductivity influences the effective width of the slit, as is evidently the case when we are dealing with wire gratings in the path of the Hertzian radiations. ‘These questions are involved in a complicated way in the whole discussion of the effect of a grating on the plane of polarization of the incident 266 Prof. G. F. FitzGerald on the light. I will take the simple case of a slit bounded by obstacles which completely stop all action. Although such do not exist, very close approximations to them do exist. If we take the slit as parallel to z, and make this axis the centre of the slit, and assume the phase the same all over the slit, we have for the vector potential at a point 2, y, 0, due to any line of the slit at a distance y from its centre, -* cos pl yr gy 0 r where Integrating this for the width of the slit, ¢.e. from +6 to —b, we get for the complete value of the vector potential H=2H,| * ‘is C08 pl—=9P dy, =p) sO If When we are dealing with the case of 6b being a small quantity we may take jute dy=f (yo—y), : and we have ee ee i SE y=Kyr+0) fob) a ae ap 2b? fax =20(7 ue mee 0 (7) = cos (pt—gr) _ dy/o r and when y=0 is put in P= ay tye +P=p +27, Ss 6? d?u a = aes oa y=2(ut os. dip ) If we now integrate with respect to z we get Haat | | vaya: REL folemnes a: 0 Riner ae (bf £4 og hl nes Now \" udz is a function of p only, and is a Bessel func- / A But Longttudinal Component in Light. 267 tion subject to the equation ot red J 5 dp? == p dp sr) JO, so that we can write 3 9 H=40h,(J+ aes ) ee ge i? dd) oe ed) 1 dJ =ub louie, ae ery cae ses By means of the differential equation we may of course express : ‘ ] all the differentials of J in terms of J and - “ . We may, how- : p ever, simplify matters very much in the ordinary case of light by observing that q is generally a very large number, so that terms involving its powers are large. Keeping to these we 2 nN see that ae =—q'J, and that the highest term in si is dp de (@Y'5 . Using these terms only we get ; H=4HJ(t— ues (2) +...) zo) \O = OGY ut von sin € =—4H J - qy — AH Jd 4 € ao bay. p p Without going into the question as to the best series to ex- press J by it is evident from its integral form and from the dynamics from which it is derived that it must represent a wave propagation. In fact by integrating by parts it could be expanded in the form J =J, cos (pt—gp) +z sin (pt —gqp). In any case we can see that for any constant value of p H passes through a series of values giving the alternate lights and darks on a screen illuminated by a narrow slit. Considering now the magnetic force we have 268 Prof. G. &. FitzGerald on the and hence the longitudinal magnetic component From this it is evident that in every such case m=O so far as H is a function of p only. Thus we get a) =. = prey isn g @e COS = sin a Coes This shows that m2 does not in general vanish but has alterna- tions of value like H. The tangential component has for its most important term It is evident that this longitudinal displacement is necessary at the edge of the beam in order to prevent any concentration of the magnetic force. So far as our a priori knowledge of pure ether is concerned there seems no sufficient reason for not supposing a concentration of magnetic force just as probable as one of electric force. It would certainly com- plicate our equations very much to suppose both. If both existed we might have two kinds of pressural waves, one a wave of electric condensation and rarefaction, and the other a wave of magnetic condensation and rarefaction. It is quite evident from all these cases and from general considerations that the edge of every beam of light is bordered by a region where there are longitudinal vibrations taking lace. : V. Asa final example I take the case of a series of slits forming an optical grating. In this case the simplest supposition is to assume that the opacity of the grating varies in a simply periodic manner. This leads to the same sort of equation for H as in the last case except that the intensity in each line is proportional to (1+ cos ly), where /= au and s is the interval between the lines. $ This leads to the integral H=2H{ ( Ses Mi) 7 OO here Sua * r=xy tyo—y +2’. Now from general considerations it is evident that it must be possible to expand this in terms of cos ly by Fourier’s Longitudinal Component tn Light. 269 theorem, so that H=h, +h, cos ly+h, cos 2ly+h3cos 3ly+... Observing then that H being a function of a) and yo only satisfies the equation ae 2 Gi. =e 2 De aie Ny we get that in general aN, dy? + (g?—rl)hn=0, so that hn rb-cos Ve—nWl? —n'l? . x, so long as nl is q hi — ees Vn2—g?e as the value cannot increase to infinity. We thus get the general form for H, H=H) cos (pt —ga) + H, cos ly cos (pt— Vg?—Pa) +... +H, cos nly cos (pt— fg?—nl?. 2) +... +H, cos mlye—VwP—¢ cos pt +... It would appear from this that at the surface of the grating, where e=0 when ¢=0, H=H)+H,cosly+...+H, cosnly+... It would consequently seem that this must-in general represent the distribution of opacity at the grating, and that in the case of a simply periodic distribution the general form of H would be H=H, cos (pt—qa) + H, cos ly cos (pt— Vq?—/?. x). We thus get an interesting form for the double integral for H. The magnetic force to be calculated from this is dH dH oe dy’ esa, y=0, and consequently a= —1H, sin ly cos (pt— Vg?—F?. 2), B= qHosin (pt—ge)+ Vy?—PH, cos ly sin (pt— Vq?—P2). In this a is the longitudinal component of the magnetic force. This represents a series of waves being propagated away from the grating, together with a series of elliptic 270 On the Longitudinal Component in Light. Ts whirls whose length is = and breadth fae The length Gir is the same as the width of the lines of the grating, and the 2 breadth somewhat greater than the length of a wave= ee is especially obvious in this case that some longitudinal com- ponent exists. The existence of the terms depending on e—¥#?—¢x shows that there may be something analogous to total re- flexion with its extinction wave in the case of a grating in respect of the spectra that are of a higher order than can be transmitted by the grating. It would seem, then, that the whole energy of the wave might not be distributed over the spectra unless the variation of opacity in each line be judiciously made. This may also be connected with the high absorbing and radiating powers of rough surfaces and with the action of coherers. “It is a matter for consideration whether it would not be worth while manufacturing photographic gratings by causing the two first spectra on each side of the central image, together with this central image, or without it, to interfere on the surface of a sensitive film. We might thereby produce a grating which had such a distribution of opacity as to repro- duce only these first order spectra and have all the light that passed through concentrated in them. Similarly we might manufacture a grating which would have the light concen- trated in any desired pair of spectra, though this would practically come to the same thing as the first proposal, with the lines closer together. This comes to the same thing as producing gratings by means of the interference of two beams of parallel rays of monochromatic light in the manner that Wiener has shown to be possible. In all these cuses it is quite evident that a longitudinal component of either electric or magnetic force is essential to the existence of waves whose intensity is not constant all over their surface, and that it 1s a practically universal con- comitant of all waves of noncondensational type. That in the case of short waves which vary slowly from point to point, the intensity of the longitudinal component at any place will be in general very smal!, because the area is very large over which the motion along the surface at one place has at its dis- posal in which to turn and be continuous with the motion back along the face of the next wave. This does not make it unimportant, however. Ina great many cases the total flow along the face of a wave must somewhere flow longitudinally Measurement of large and small Alternating Currents. 271 so as to be continuous with the flow back along the other face of the wave. Unless these longitudinal flows are taken into consideration the whole energy of the wave is not accounted for. If the rate of variation of intensity over the surface be comparable with a wave-length, as in the case of fine gratings, the longitudinal component is a large part of the phenomenon, and, in fact, represents a large part of the energy in this case transmitted to the secondary image. This is all quite obvious in the case of gratings from the ordinary theory, for the equations given as a solution of this case represent a series of waves being transmitted in different directions from the grating corresponding to the directions of the secondary spectra. XXVIII. On the Measurement of very large and very small Alternating Currents. By ALBERT CAMPBELL, B.A.* a IR-core transformers, although quite inefficient for ordinary lighting circuits, are yet much more valuable for testing purposes than most people are aware of. By the help of such transformers it is possible to extend almost indefinitely the ranges of many ordinary measuring instru- ments. If the secondary of an ironless transformer be kept in open circuit the secondary volts are accurately proportional to the primary P.D. if the frequency is constant, and hence by using an electrostatic voltmeter on the secondary we can transform either up or down, and thus measure voltages above or below the range of the electrostatic instrument. Of course the arrangement would have to be calibrated; this might sometimes be done by taking a reading for which both the primary and secondary voltages lay within the range of the voltmeter used. — The above way of using an air-core transformer was sug- gested to me some time ago by Mr. Hugh EHrat Harrison, of Faraday House. I hear since from Mr. Mather that it has been also used at the Central Technical College f. If we attempt to measure current (in the primary) by observing the voltage on an open-circuit secondary, we find that for a given primary current the readings depend also on the frequency. It therefore occurred to me that the secondary. * Communicated by the Physical Society: real June 12, 1896. + Since writing the above I have listened with interest to the paper on the “ True Resistance of the Electric Arc,” by Messrs. Frith and Rodgers. Their beautiful application of an air-core transformer to measure a small alternating current superimposed on a large direct current might, I think, be also employed to separate a darge alternating current from a much smaller direct current. 272 Mr. A. Campbell on the Measurement of very circuit should be closed and should besides be highly znductive. In practice this was found to work with perfect success, the primary current being proportional to the secondary current, which latter was measured by an ammeter. To find the most favourable conditions, let ],, 1, be the primary and secondary currents respectively ; R, the resistance of the pec circuit ; N its inductance ; M the mutual inductance between primary and secondary. Let p=27n, where n is the frequency of alternation. Here M and N are constant, while R, may be variable with temperature. At first let us assume that the P.D. follows a ss sine curve. Then I, _ VR2+ pW 41) | a ( Now let the inductance of the secondary circuit quite swamp its resistance, so that we may neglect the term R,” in com- parison with p’N*. In this case we obtain Ape Nl ie = WM? Eee ee Se ee Se (2) i.e. the ratio of the primary current to the secondary current is independent of the frequency of alternation and the resistances of the coils. We shall see below to what extent this valuable result can be realized in practice. It is clear that in the > e N e e above case, since E =o , the secondary current I, is in exactly opposite phase to I. Now suppose the primary P.D. to be no longer a pure sine function of the time but to follow any periodic curve. ‘The curve of primary current can then be decomposed into a number of sine curves of various frequencies ; each of these will produce a secondary of opposite phase, and the ratio of : N each primary component to its secondary will = i Accordingly the total secondary current curve will be of the same wave-form as the primary and in opposite phase to it, while the rato of current transformation will be the same as for a pure sine-curve alternating current*. * In this I have assumed that the Fourier series for the wave-form contains no constant term, z. e., that there is no constant component in the current. If there is such a component, nothing corresponding to it will appear in the secondary circuit, and the ratio of current transformation will be by no means the same as if the current were purely alternating. In fact an air-core transformer affords a good means of separating out the purely alternating part of any periodic current. large and very small Alternating Currents. 273 Unfortunately, in practice we cannot quite attain to the e . N condition Re =, but we can get near enough to make the 2 error quite small. In the following table are given (approxi- mately), for different values of 2 , the values of the-ratio 7" 2 for frequencies of n=80 ~ per sec., and n=40 ~ per sec., if the ratio =1 when n=~. TABLE I.—Transformation Ratios. = eee 4 280: poet 166 1-00 1-02 1:08 50 1000 «=| ~—s«1:005 1-02 oF on) Se eto A 00S 10 ~ 1000 1-0002 1-0008 By this it will be seen that “if x2 =0, the error in the transformation ratio from »=80 to n=c becomes Insignifi- cant ; and that if = = 25 the ratio is approximately constant down to n=40. R R In practice it is easy to make y= 9 but to get N = 25 would require a rather lavish expenditure of copper wire. Instead of finding the ratio of a particular transformer (with ammeter) once for all, a simple way is to find it each time for the frequency to be used, the strength of the primary current being chosen so as to lie within: “the range of the instruments available. The following instance will make the method clearer. Suppose we want to measure currents up to 1000 amperes with an electrodynamometer and a Kelvin balance, each up to 100 amperes. Let the transformer have a “ current ratio ” of about 10 when the balance is the only load on the secondary. The electrodynamameter is inserted in the primary circuit, and a primary current of (say) 98°2 amperes is found to produce (say) 10 amperes in the secondary. If the electrodynamometer be now taken out of circuit, any\ primar y current up to LOQU amperes can be measured ° by reading the balance in the ness y-and multiplying by 9°82. ‘Phil.-Mag. 8. 5. Vol. 42. No. 256. Sept. 1896. — 274 Mr. A. Campbell on the Measurement of very In an exactly similar way very small alternating currents may be measured. In order to avoid errors due to stray magnetic fields the transformer may be wound with double coils placed side by side with their axes parallel and reversed in the well-known manner. It might also be well to have the position of one or more turns of the primary or secondary adjustable with a scale to show the proper position for each particular frequency. For the purposes of calibrating at any frequency a second primary of a different number of turns from the first may be wound on the transformer, and the relationship of the two primaries may be determined once for all. For example, if the first primary is for 1000 amperes the second may have 100 times the number of turns and be suit- able for 10 amperes. The correction for any particular frequency or wave-form may then be found experimentally by using the second primary only. I may mention that with very simple instruments I have used an air-core transformer to measure currents between 1000 and 2000 amperes. | Added June 12th, 1896. | In order to get a larger increase of secondary voltage a Fig. 1. well-known method is to connect up a transformer with the primary and secondary in series as in fig. 1. By a somewhat large and very small Alternating Currents. 275 similar method the ratio of current transformation may some- times be increased. The connexions in this case are shown in fig. 2. : AMPERES Transformers with Iron Cores. I have recently investigated the case of transformers with tron cores whose secondary circuits’were made highly induc- tive. This was done by short-circuiting the secondary in each case through a Kelvin 100-ampere balance. Two transformers were thus tested—an iron-ring trans- former with very small magnetic leakage, and a small trans- former with open iron circuit. - The first of these had a primary of 764 turns of No. 16 8.W.G. wire, and over this a secondary of 48 turns of 7/16 wire. The core of the second was a short bundle of iron wires, over which were wound the primary of 38 turns of No. 16 8.W.G. wire, and over it a secondary of about 3000 turns of No. 26 8.W.G. The ring transformer was first tested -with a Kelvin 10- ampere balance as secondary load, the frequency being 84 ~ per second. ‘The balance had a resistance of about 0°55 ohm and an inductance of about 0-0016 henry. The results given in Table IL. show that. with this amount of- resistance in the Io: Las ead) secondary the L is by no means constant. 1 X 2 276 Measurement of large and small Alternating Currents. TABLE II. Iron-ring Transformer. Secondary Load 10-ampere Balance. poe ere Ratio : eae ee eee ey _ 00764 9:28 mer’ Seo Aci ae eae: = Rees Ch aaee ae TaBLeE LII. Iron-ring Transformer. Secondary Load 100-ampere Balance. pumas current. Repo He Tea Spd) meee oo pee one OP Sea ieee ibaa en | Similar measurements were then made with a 100-ampere balance as secondary load. From Table ILI., which gives some of the actually observed ratios, it will be seen that the ratio of current transformation is practically constant. With almost the same arrangement of secondary circuit experiments were made to find to what extent the ratio 1, iF was affected by change of frequency. Table IV. gives tlic results of these and shows that the ratio 7s almost BA): of frequency through the range tried. Representation of the Periodic System of the Elements. 277% TasB.e LV. Ring Transformer. Frequency, ~ per sec. I, Error from 84 Te ~ per second. 40 | 15-48 0-7 per cent. 57 ch 1552 0:45 per cent. eS ee eee ee eee 84 15:59 | The results in Table V. of a similar experiment with the transformer of open magnetic circuit described above show how different its behaviour is. TABLE V. Transformer with open Iron Circuit. ~~ per second. I, | Error from 84 ae | ~ per second. 44 28:1 | 24-3 per ceut. 84 871 | It seems clear, therefore, that iron-ring transformers may in many cases be used in a similar way to that described above for air-core transformers; but care must be taken to have the resistance of the secondary circuit sufficiently small. In conclusion I beg to thank Messrs. Lovell, Macalister, Sankey, and Norman for their kind help in some of the experiments. XXVIII. Remarks upon the Analytical Representation of the Periodic System of the Elements. By Dr. A. GOLDHAMMER*. eo attempts have been made in recent times to represent analytically the periodic dependence of the general chemical behaviour of the elements upon their atomic weights; these two researches, entirely independent of each other, and published at an interval of about eight years, have led to the same result in a remarkable way. IF’. Flawitzky in Kasan in 1887 f, and J. Thomsen in Copenhagen in 1895 tf, represent the chemical character of an element e as a function of its * Translated from a separate impression from the Zedtschr. f. anorg. Chemie, vol. xii. (1896), communicated by the Author. + F. Flawitzky, Verh. d. Naturf.-Ges. Univ. Kasan (1887). t J. Thomsen, Zeitschr, f. anorg. Chemie (1895), ix. pp. 283-280, 278 Dr, A. Goldhammer on the Analytical Representation atomic weight p in the form e=acot wh”, | mer where a is an unknown constant, and b and ¢ are constants easily determined for each period. The-views-of the two authors differ somewhat; whilst F. Flawitzky, in agreement with L. Meyer *, considers V, Cr, Mn, Nb, Mo as electronegative or acid-forming, and Cu, Zn, Ga, Ag, Cd; In as positive, according to Thomsen V, Cr, Mn, Nb, Mo are electropositive, and Cu, Zn, Ga, Ag, Cd, In negative; from this it followsat once that Mendeleeff’s eighth group of positive metals, Fe, Co, Ni, Ru, Rh, Pd, Os, Ir, Pt, must be left out of consideration by F. Flawitzky, whilst J. Thomsen takes these metals into consideration. F. Flawitzky remarks further that in his method of repre- sentation N, O, F appear just as well as analogues of P, 5S, Cl, As, Se, Br, Sb, Te, I, as of V, Cr, Mn, Nb, Mo, —, Di, —, —, Ta, W, which latter analogy is true in fact only in a remote sense ; according to Thomsen, on the other hand, this is not the case, since the elements analogous to V, Cr, Mn, &e., ought to fall into the period Li—F between B and QC, and in that from Na—Cl between Al and Si. If we might take these views of J. Thomsen as valid be- yond dispute, then the question of the analytical representation of the periodic system of the elements would be nearly solved. But if we hold with the views of L. Meyer the matter is somewhat different ; the cotangents can then serve only as a rough approximation to the truth. Since I, as a physicist, cannot venture to enter upon details of chemical views, I permit myself here to show only by way of experiment how the general character of the chemical elements as given by L. Meyer may be represented geometri- | cally or analytically. | In the system of Mendeleeff we have, as is well known, six periods : Li—Cl ; K—Br; Rb—I; Cs—?; ? Bi?; ?—?. After the electropositive alkaline metals Li, Be we have in the first period a gradual passage through B, C to the electro- negative acid-forming N, O, F ; from EF a rapid passage to the positive Na, Mg, and then again after Al, which has some claim to possess negative properties, a series of more and more decidedly negative elements Si, P, 8, Cl. From Cl to the positive K, Ca, Se we have obviously a leap in-the properties of the elements ; then follow negative V, the partly negative partly positive Cr, Mn, positive Fe, Co, Ni, * L. Meyer, Die modernen Theorien der Chemie (4th ed. 1880), i, p. 167-169, . of the Periodic System of the Elements. 279 Cu, Zn, Ga, the “ positivity ”’ first increasing then decreasing (a maximum occurring somewhere between Cu and Zn), then follow elements becoming more and more negative, As, Se, Br. Ti and Ge ease the passage through the zero-point. In the remaining periods we have a complete analogy with the second ; it will be sufficient, therefore, to consider this period a little more closely. eRe Meee Let us express the general connexion between e and p by e=T'(p), and let us regard e and p as rectangular coordinates of a point in the plane e, p ; then e=F'( p) is the equation of a periodic curve. As we do not know any numerical values of e, it is only possible to form some opinion as to the shape of the curve by our knowledge of the properties of the elements. If we assume that e=+o between Cl and K, Br and Rb, T and Cs, &¢., as F. Flawitzky and J. Thomsen assume, then we conclude that our curve must consist of as many separate parts as there are periods of elements. But, as we know, the periods are unequal ; thus, for the elements of the second, third, and fifth periods the number 48 (atomic-weight units) fits, whilst for the ceesium-period this number seems to be 1:5 times too great. Hence we see that the separate portions of the curve cannot be identical ; only in form do they re- semble each other. The curve (fig. 1) drawn with two asymptotes, agrees with the properties of the elements of the second period ; for the following periods we have exactly similar curves, each con- sisting of six portions, AB, BC, CD, DH, HF, and FG. We remark next that the analogous elements are represented by the points of the corresponding portions of the curve ; thus upon the portion AB we have the positive elements Ke Ca, Se: Rb; siSr,0 Y, Cs, Ba, La, Ce, ee the transition elements Ti, Zr, Di (?), —, Th (?) corresponding to the point B. From the properties of V, Cr, Mn we may further conclude that these elements are represented by the points of the portion of the curve CD ; thus upon the portion CD we have the negative elements Ver Mn Nb, Mo, —, Di 2, Riedy ae Ta, W, —, b] P] P 280 Dr. A. Goldhammer on the Analytical Representation — In the same way it is easy to see that the portions of the curve DE, EF, FG correspond to :— DE +: Fe; "Co, Ni, Cu; EF+: Zn, Ga, Ru, Rheds A ©, Gd; cine Os, Ir, Pe, Au; He, Ti, RG 2.7 Se Be : “Sb. Te; iy Pa are: Bi, Tr La ’] , y] ; whilst the transition elements Ge, Sn, —, Pb fall at the point F. In all these periods the portion of the curve BC remains free from known elements ; but if we compare the portions of the curve AC, EG, which correspond pretty well amongst themselves, and if we observe that the elements corresponding to the portion EF find their analogues (if imperfect) in the elements corresponding to the portion AB (Ca—Zn, Sr—Cd, Sc—Ga, Y—In, &c.) itis easy to draw the following con- clusion:—the elements which may possibly exist between Ti and V, or Zr and Nb, or Ce and Di ought to appear as imperfect analogues of the elements As, Se, Br, Sb, Te, I As to the period Li—Cl, which is much smaller than the rest (only 30-32) it is easy to surmise that here also the curve possesses the form ABCDEFG. In fact, Li, Be, evidently correspond to the portion of the curve AB, the transition ele- ments B, C, correspond to the point B, but the next following negative elements N, O, F’, possess exactly the character they ought to have if N, O, F, are to be represented by the points of the portion BC of the curve ; N, O, F are imperfect ana- logues of As, Se, Br, &c. Further, we find in the period Li—Cl a sufficient place between F and Na for a series of elements which would fall upon the portion CDE of the curve ; these would be analogues of V, Cr, Mn, Fe, Co, Ni; the newly discovered element argon would perhaps correspond to the point D. ie eee It is well known that sodium is not a good analogue of Cu, Ag, Au; this indicates that sodium falls somewhere about the point E, and is thus much nearer to Li, Rb, Cs. We have also, exactly as before, the positive metals Mg, Al for the portion of the curve EF ; for the point F the transition element Si, and finally the negative elements P, §, Cl, corre- sponding to the portion of the curve FG. For the atomic weights smaller than that of lithium we have only hydrogen and helium; but since H stands nearer of the Periodic System of the Elements. 281 to Na than to K, and helium appears to be a sufficiently in- active element, we may infer that in the period ?—Li we have only the portion of the curve EFG ; then H would fal about the point E, and helium at the point F. HHS EERE EEE Ee SRGRCRUS ARES CRERES pena SESEESSEE sHlse seaftes iN seriesiitusiteses Geimrestins Sersscerserasesr /arsieni pT sanayinestiesiteer’ si anit Seuunnem eases UTEETETT STTEET HH PEE eee Ht BEE H POSH ageees s BoSaeES touneaoaes Fig. 1. So far we have left the valency of the elements out of sight. But, as we know, there exist for each chemical value two series of elements analogous amongst themselves ; according to the usual manner of writing we have, for example, the bivalent and trivalent elements arranged according to in- creasing atomic weight : Bey Carenisndin Bay iit on) C3. Mey 2 Ymi)Cd, =. He and 282 Representation of the Periodic System of the Elements. where the elements of the lower series in each set appear to be more metallic in melting-point and other properties than the elements of the upper series ; the same holds good also for nega- tive elements ; thus we have, for example, for the valency 6 O, Gr, Mo, er) i; Gi 5. ste although here the relations are of a somewhat complicated character. At all events it is clear that for each determined value a of the valency the properties of the elements alter periodically with increasing atomic weight, so that e=/(a, p) represents for each a a wave-shaped or zigzag curve. The question now arises whether we really have two different relationships between e and p in the form e=F(p) and e=f(a,p); the true answer can, of course, only be furnished by the theory of the elements to be developed. But if we recall certain problems of theoretical physics, for example, in heat-conduction, sound, and light, we perceive at once that we have there also at least two relations of a similar kind; the one relationship appears as the integral of a differential equation, the other as a so-called limiting condition inde- pendent of the first ; the two contain an undetermined para- meter, which often appears as a whole positive number (e. g., in the theory of the vibration of strings). Hence it appears not improbable that the chemical theory of the future will also lead to two relationships, e=f(a,p), and e=(a,p),. . . . (2) where a—the valency—a whole positive number plays the part of an undetermined parameter. It is to be remarked that so far we always find a<8; but in any case it is not impossible that certain special conditions of the problem might exclude certain values of a. If we now eliminate a from both equations we obtain the relationship of the form e=F(p), that is our curve of fig. 1. Now we are in position to take another step. If the rela- tionships (2) are really independent, then e may be eliminated from them ; this leads to the relationship of the form Alp (G: Pp) 0s Beet ogee ee em which will give for each a a completely determinate series of values p, the values of p thus obtained represent, then, the atomic weights of the actually existing elements. It may well happen that the number of the real and positive roots of equation (3) will be finite for each a, hence also the number Geological Society. 283 of the actually existing elements will be finite and perfectly determinate. The question is otten‘asked, ‘“‘ Why do there exist only elements of a few definite atomic weights?” From our point of view the question is similar to the one, “ Why can a string give only definite notes ?”’ From the above considerations it appears to result clearly that an analytical expression for e=F(p) is more complicated than is the case for the simple cotangent: an expression of the form e=a Cos nh t"(A +cotan 7/ ) 7 might suit better. But since the periods of the elements turn out to be unequal (0 to ?, ? to 86, 36 to 84, 84 to 132, 132 to 168 ?, 168 to 216, 216 to 264 ?) the constants 4, ¢, d,/, A would be themselves independent of p. In such cases trigonometrical functions offer no special advantage. It might perhaps be simpler to take Aineaee alana é= — aoe Papi (Paap? Pa 3 - spl PoP Mee p—p) ++ (p—Dp;)( P —P2) (P—P3)--- where 1, P2, P3-.- denote the roots of the equation ==, p, p’, p'”, ... the roots of the equation e=0, and Ay, Ag, A;,... and B denote constants. XXIX. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p, 207.] May 13th, 1896.—Dr. Henry Hicks, F.R.S., President, in the Chair. HE following communications were read :— 1. ‘An Account of a Head or Gateway driven into the Eastern Boundary-fault of the South Staffordshire Coal Field.’ By William Farnworth, Esq., F.G.S. The author describes certain peculiarities observed during the driving of a head towards the fault separating the Coal Measures and Permian rocks, from a pit situated 4 miles east of Walsall, at the southern extremity of the Cannock Chase Coal Field. 2. ‘On the Geographical Evolution of Jamaica. By J. W. Spencer, M.A., Ph.D., F.G.S. The object of the paper is to set forth the physical and geological 284 7 Geological Society :— characteristics of Jamaica which bear upon the problem of its late high elevation and former connexion with the continent, and to trace across the neighbouring seas and islands to the mainland the evidences of the former linking of Jamaica to North and South America, The first part of the paper treats of the growth of the island, and the following events are described. After the formation of the mechanical sediments, limestones, and igneous rocks which constitute the basement of the ‘ White Limestones,’ the latter group was accumulated in later Eocene and early Miocene times to a thickness of 2000 feet, and they indicate a subsidence of 3000 feet below sea-level. Their formation was followed by a Pliocene or Mio-Pliocene elevation in an epoch of long duration ; the uplift was inferior to a later (post-Layton) one, but sufficient for the removal of Miocene limestone below sea-level. The period was one of general elevation, general dislocation of strata, and great erosion. The formation of the Layton marly beds with loams and gravels which succeeded this period is referred to the end of Pliocene times. In early Pleistocene times the ‘ post-Layton’ elevation occurred, causing an uplift of from 7000 to 11,000 feet above sea-level. The strata were not greatly deformed, but the epoch was one of enormous erosion. A subsidence somewhat resembling that of the Layton formation followed this erosion in late Pleistocene times, and caused the accumulation of the loams and gravels of the Liguanea forma- tion. In modern times minor changes have occurred, causing the formation of terraces, of channels over banks, of coralline limestone, and of the modern coral terraces. The second part of the paper treats of the continental connexions of Jamaica. The author gives details of the submerged plateaux and drowned valleys which are analogous to those still existing above sea-level. They indicate that the former altitude of the West Indian plateau, and some portions of the adjoining continent, reached 25 miles: ~ but the floors of the Mexican Gulf and Honduras aud the Caribbean Sea formed low plains draining into the Pacific Ocean, for at that time the eastern region was high, while the Mexican area was generally low. There was a generally high elevation of the Antillean region during the great Mio-Pliocene period, with probable continental connexion ; at the close of the Pliocene period a general subsidence flooded the coastal plains of the continent, and reduced the West Indies to fewer and much smaller islands than those which now exist. But the earlier portion of the Pleistocene period was that of the great continental elevation, when the lately formed Pliocene topography was deeply dissected by rain and rivers, yet there were apparently several pauses of terrestrial movements at different altitudes, as indicated by the various base-levels of erosion. At this time Jamaica and other islands formed a mountainous tableland bordering the Mexican and Caribbean plains. Afterwards the later Pliocene continent was depressed, so as to flood most of the coastal plains of the continent and reduce the islands to small proportions, and Dundry Hill: its Upper Portion. 285 since then the minor oscillations have brought the old continent to the present conditions. While the east was going down, the Mexican region and western lands were being raised to form high tablelands. 3. ‘Dundry Hill: its Upper Portion, or the Beds marked as Inferior Oolite (G5) in the Maps of the Geological Survey.’. By S. S. Buckman, Esq., F.G.S., and E. Wilson, Esq., F.G.S. The authors give an account of previous geological work relating to Dundry Hill, especially that which refers to the correlation of its strata. Then they describe the different exposures on the Hill, together with the results of various excavations carried out by quarrymen under their superintendence for the purpose of the present communication. Besides demonstrating the sequence of the strata of Dundry Hill, the authors are able to show as special results :— The rapid easterly attenuation of the Freestone. That there is a non-sequence in the Dundry deposits. That the chief fossiliferous bed—the [ronshot Oolite—extends over a very small area. That the absence of this bed is due to removal by almost contem- poraneous denudation. That in the easternmost portion of the Hill this bed and all other subjacent beds of what is called ‘Inferior Oolite’ have been removed by this denudation, so that only a thin cap of what would be called ‘ upper beds of Inferior Oolite’ rests on a thick clay-bed of the age of the Midford Sands. That deposits contemporaneous with what are called ‘ Upper lias’ and ‘ Midford Sands’ in other places are found in some thickness at Dundry Hill, attaining as much as 65 feet. That the Lias Marlstone-rock is present at Dundry Hill and crops out in many places on its flanks, but that this rock-bed is also wanting from many parts of the Hill. That the Geological Survey have presumably mistaken this Marlstone-rock (which is an Ironshot stone) for the Ironshot Oolite—the chief fossiliferous bed of the Dundry Inferior Qolite, and formerly called Humphriescanum - zone — beds nearly 100 feet apart. That, as a consequence, the map of the Geological Survey shows round the greater portion of the Hill the boundary- line of the base of the Inferior Oolite drawn as much below the Marlstone as would have been correct if this rock had actually been the well-known Ironshot Oolite. That, as a further consequence of this, the map of the Geological Survey shows coloured as Inferior Oolite strata which are mapped as Lower lias, Middle Lias, Upper Lias, and Midford Sands in other localities; and that in places the limit for Inferior Oolite, according to the Survey, is as much as 600 yards beyond that of the authors. 286 Geological Society :-— The authors append a map of the strata of Dundry Hill, coloured on a paleontological basis; and they show how it may be compared with the map of the Geological Survey, and with a map by Sanders. May 27th.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read :— 1. ‘On the Pliocene Deposits of Holland, and their Relation to the English and Belgian Crags ; with a Suggestion for the Establish- ment of a new Zone “ Amstelien,’ and some Remarks on the Geographical Conditions of the Pliocene Epoch in Northern Europe.’ By F. W. Harmer, Esq., F.G.S. The author draws attention to some papers by Dr. J. Lorié, of Utrecht, describing the strata met with in some deep borings in Holland, which show that the Newer Pliocene is in that country nearly 500 feet thick, and that it has been depressed more than 1000 feet below its original position. He enquires whether this subsidence can be connected with the elevation of the Older Pliocene in Belgium and Kent, and how far these earth-movements can be traced in East Anglia and influenced the deposition of the English Crag. He gives particulars of the alterations in level which have taken place during and since the Crag period in England and on the Continent, showing that the two movements of upheaval and subsidence have much in common, and especially that they re- gularly increase in degree to the north and south respectively. He gives a map showing the extension of the Diestien deposits of Belgium, and their probable connexion with the Lenham Beds, and opposes the view of M. Dollfus that the Diestien sea was closed to the south, though the connexion with it was probably cut off by the elevation of the southern part of the area at the close of the Diestien epoch, which also caused the Scaldisien sea to retreat to the north. At the close of the Scaldisien period the sea retired from Belgium altogether, no beds equivalent to the Upper Crag of England being known in that country. A similar alteration of the margin of the Crag sea can be traced in East Anglia. He analyses the fauna of the Scaldisien and Poederlien, and shows its close correspondence with that of the Walton bed and the difference between it and the Upper Crag, which contains Arctic shells. He describes the beds met with in the Dutch borings, regarded by Dr. Lorié as Diestien and Scaldisien, and their fauna, at some length. He concludes that a large part of them are altogether newer than the latter formation, and are equivalent to the Butley Crag, and he proposes for them the term ‘ Amstelien.’ He doubts whether any deposits of similar age to the Norwich Crag or Chillesford Beds have been met with in the sous-sol of Holland, which he considers became at that time a land-area; and The Pliocene Deposits of Holland. 287 he gives a section to show wherein his classification of the Dutch strata differs from that of Dr. Lorie. The distinction between the divisions adopted by the author comes out more clearly from the consideration of the abundant and characteristic species only, of each of which he gives lists. Although the Amstelien beds are more than 400 feet in thickness, they contain a shallow-water fauna, and were deposited in a basin which subsided pari passu with their accumulation. In the map an attempt is made to show the limits of the sea of the Anglo-Dutch basin during the various stages of the Pliocene epoch. "Tt is suggested that the Chillesford Clay was deposited in an estuary through which the Rhine discharged into the North Sea, its presence in the western portion of the Pliocene basin being caused by the elevation of Holland after the deposition of the Amsteline and a subsidence in Suffolk, which carried the Chillesford Beds over an area which was not covered by the Norwich Crag sea. No equivalents of the Weybourn Crag or of the Cromer beds (Forest Bed series) have been found in the Dutch borings. These are to be referred to the Pliocene, as pointed out by Mr. Reid, but possibly some of the unfossiliferous pebbly gravels of Norfolk and Suffolk may be Pleistocene. The Weybourn Crag marks a re-invasion of East Anglia by the sea; but previously to the deposition of the Cromer beds the southern margin of the Pliocene gulf had again retreated to the north, and an estuary, similar to that of the Chillesford Clay but situated farther east, received the waters of the Rhine, which brought down the drifted remains ot mammalia and some southern mollusca. © The newest portion of the Cromer deposits is of an Arctic character, and seems to show that no great interval separated the Pliocene and the Pleistocene periods. A second subsidence of the Dutch area took place in Pleistocene times; the Glacial and post-Glacial beds being 600 feet thick under Amsterdam. No Till or Contorted Drift similar to the deposits occurring in Kast Anglia and in the district north-east of the Luyder Zee has been met with in these borings. The glaciation of Holland proceeded from the Baltic and not from Norway, and the Baltic ice does not seem to have reached the Dutch coast; still less could it have travelled thence in the direction of East Anglia. The two prominent physical features of the Pliocene period were the Rhine and the basin of the North Sea. The hypothesis of a permanent basin with shifting shore-lines, in contiguity to which the shallow-water deposits of the Upper Crag were deposited, seems to agree with all the facts of the case, and to throw light on the geographical conditions of the Pliocene epoch. [ 288 |] XXX. Intelligence and Miscellaneous Articles. ON A DAMPING ACTION OF THE MAGNETIC FIELD ON ROTATING INSULATORS. BY WILLIAM DUANE. ig results from the experiments described by the author, that if an insulator is made to rotate in a magnetic field about an axis at right angles to the lines of force, a damping action is exerted in opposition and nearly proportional to the angular velocity. If the insulator is paramagnetic, such an action might be ex- plained on the assumption that the magnetic axis of the insulator does not coincide with the magnetizing force of the field, but is displaced in the direction of the rotation. A somewhat more general assumption sufficing for the explanation is, that for an insulator at rest the induced magnetism does not vanish at once, but after an appreciable time. If it vanishes ver y rapidly we get the proportionality observed between the damping force and the velocity. For a diamagnetic insulator with true diamagnetic polarity the corresponding assumption would give a force accelerating the rota- tion. Nevertheless, according to several theories of diamagnetism, even a diamagnetic body has paramagnetic polarity. According to such theories the explanation given applies also to diamagnetic bodies.—Wiedemann’s Annalen, No. 7, 1896. THE ACTION OF MAGNETISM ON ELECTROMOTIVE FORCE. BY ALFRED H. BUCHERER. The results of this investigation may be stated thus :— 1. In neutral ferrous salts, if one of the two equal iron elec- trodes is magnetized, there is no electromotive force produced which amounts to 0:00001 volt. The currents observed by Gross and others could not be referred to a change of the electrochemical potential of the magnetized iron. 2. The forces produced by magnetizing a circuit which contains magnetic substances as electrodes are to be ascribed to variations of concentration which the magnetized electrode produces when dissolved. _ 8. In the case of ferric salts, the direction of the currents pro- duced by magnetization depends almost exclusively on their degree of concentration at the two electrodes. 4. If only ferrous salts are present, the direction of the currents produced by magnetization depends on the total concentration of the iron salts. 5. The currents designated by Rowland as primary ones are agitation-currents.— Wiedemann’s Annalen, No. 7, 1896. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF ee aren [FIFTH SERIES.] OCTOBER 1896. XXXI1. Osmotic Pressure. By J. H. Poyntine, Se.D., FP LRS., Professor of Physics, Mason College, Birmingham*. INCE the osmotic pressure of a solution is of the same KD order as the “gas pressure”’ of the dissolved substance at the same density, we are naturally tempted to think of it as an extra pressure produced by the motion of the dissolved molecules. But if we start from this supposition we soon find . eurselves surrounded by the difficulties of the dissociation hypothesis. These are so great that it appears worth while to examine our ideas of liquid structure in the hope that they will suggest to us some hypothesis which will free us froin the necessity of assuming dissociation. I shall try to show in this paper that osmotic pressure may be accounted for as an indirect result arising, not from disso- ciation but from its very opposite, the greater complexity of the molecules in the solution, due to some kind of combination between salt and solvent. The facts of liquid viscosity, diffusion, and surface conver- sion to vapour may apparently be represented by imagining a liquid to be, in the main, a solid structure, inasmuch as the molecules cohere and resist strain of any kind. But the molecules have so much energy, potential or kinetic or both, that they are not very far from instability. In a mass of connected molecules irregularly distributed and irregularly vibrating, concentrations of energy must occur, and “at the * Communicated by the Author. Phil. Mag. 8. 5. Vol. 42. No. 257. Oct. 1896. ¥ 290 Prof. J. H. Poynting on Osmotic Pressure. points of concentration individual molecules may receive so much energy that they are able to do the work needed to free them from their immediate surroundings. Such molecules will travel off, and as they lose their energy will form new connexions with new surroundings. ‘Thus the solid structure is continually breaking down and renewing itself. If we impose a shear strain on the structure, the strain will of course disappear with the structure in which it is produced. But the breaking down will always lag slightly behind the imposition of the shear, and the still surviving shear strain will be accompanied by a resistance the same in kind as the resistance to shear in a solid, though in a liquid it is only recognized as viscosity. This is the view first set forth by Poisson and developed by Maxwell, and it is to be noted that it gives an explanation of liquid viscosity entirely different from the diffusion explanation which so satisfactorily accounts for gaseous viscosity. We may obtain an expression for the coefficient of viscosity by the following method, which is perhaps rather simpler than that of Maxwell. We must assume that a certain frac- tion, say A, of the molecules of the liquid get free per second, and that this fraction remains practically the same when the liquid is sheared. Hence if s is the strain still existing at any instant, it is breaking down at the rate As per second. If the liquid is moving steadily in parallel planes perpendicular to an axis along which w is measured, and if the velocity is v at a distance xz from the reference plane, = is the rate at which shear is being imposed on the liquid. But since the steady state is reached the rate of imposition equals the rate of decay, or dv Fr se rt fee eee ey (1) If n is the coefticient of rigidity of the structure, the stress due to s is ns, and by our supposition this is the viscous stress, or — =n, ee Se. oer where 7 is the coefficient of viscosity. Dividing (2) by (1) we obtain fe a) ne We may compare the liquid breakdown here imagined with Prof. J. H. Poynting on Osmotic Pressure. 20% that which must occur in an electrolytic conductor. If D is the “ displacement” or “induction” in an electrolyte, and if w is the factor of decay per second, wD is the quantity dis- appearing per second and dissipating its energy as heat. This may be equated in the steady state to the new “ displace- ment” or “induction” introduced per second per square centimetre, or to the current-density C. Hence KE ee (1) where E is the slope of potential, and K is the specific induc- tive capacity. But Ohm’s law gives us 4 C= ie ° ° . ° ° ° ° ° (5) where p is the specific resistance ; whence At } Creer ee oh tikog i ( 0) Returning to equation (3), we see that if n is constant, 7 varies inversely as’. For instance, when the temperature rises the molecules have more energy, the breaking down of structure is more frequent, and X is greater. Probably 7 is not very much altered, though it doubtless tends to decrease. Hence 7 should decrease, and this is in accordance with observation. On the other hand, when a salt is dissolved in a liquid, if, as we are going to suppose, it makes the mole- cules on the average less energetic by partially combining the more energetic solvent molecules with the less energetic salt molecules, they are on the average rather further from instability, X is less and 7 is greater. This again agrees with observation. At the same time the specific electric resistance p is dimi- nished. This would require that in (6) either w or K, or both, should be increased, probably both ; and this brings out a point which must be noted, that the factor of decay X in (3) is not likely to be the same as yw in (6); for while one relates rather to the molecules and their relative positions, the other most probably relates to the atoms and their positions in the molecules. Maxwell (Proc. Roy. Soc. exlvili. 1873) gave an account of some experiments which he made to test this view of liquid viscosity by shearing a liquid and looking out for double refraction. He could only observe it in the case of Canada balsam, in which it had already been found by Mach, and here the “rate of relaxation”? was so great that he could not Y 2 C=~D= 292 Prof. J. H. Poynting on Osmotic Pressure. observe any double refraction after the shearing motion ceased. Kundt (Ann. Phys. Chem. xiii. 1881) made a series of expe- riments and found double refraction in many sheared liquids, notably in olive-oil, but never in a pure liquid with a definite chemical constitution. The more complex the molecules apparently the less is A, and the greater is the shear strain still remaining at any instant of the motion. But in liquids such as water or glycerine, the decay is so rapid that no optically appreciable amount remains. Still it is very possible that olive-oil is only an extreme case, and that water and other apparently inactive liquids would show the effect if we could sufficiently increase the shear, and I think Kundt’s results may be claimed as sup- porting the hypothesis. Possibly, too, the observation of Quincke, that double refraction is observed in a liquid close to a very hot wire, gives further support. The unequal heating may perhaps be regarded as producing shear strains in the solid structure which are renewed by the supply of heat as fast as they break down. In the case of breaking down of structure near the surface of a liquid the moving molecules may succeed in escaping altogether, and may fly off as gas molecules if they are directed upwards and have enough energy. Of course there may be many molecules able to move about and yet not able to evaporate ; for though they may be able to travel when in the body of the liquid, they may not have energy enough to get clear away from their neighbours when these are all on one side and all pull in one direction as they do at the surface. In the case of practically non-evaporating liquids, such as mercury at ordinary temperatures, we must suppose that only a very minute fraction are thus able to do the work needed to overcome the large cohesion of their neighbours. It will be convenient to use the term ‘ mobility’ to de- scribe the number of “free” or ‘‘ mobilised’? molecules crossing a square centimetre per second in a liquid, where by “ free” or ‘mobilised’ we mean those which are changing their surroundings and forming new connexions. Hvidently we may extend the term to a gas, remembering that then all the molecules are mobilised, and that the mobility is propor- tional to the pressure. When a square centimetre is taken on the surface of a liquid, the mobility upwards is the rate of evaporation, and the mobility of the vapour downwards is the rate of conden- sation. When the two mobilities are equal the pressure of the vapour is the vapour-tension. The mobility in the body of the liquid is probably far Prof. J. H. Poynting on Osmotic Pressure. 293 greater than that at the surface for the reason already given; viz. that in the one case the neighbouring molecules entirely surround one which tends to get free, while at the surface they are all on one side and so tend to pull back and retain a mo- lecule which may be inclined to move away. If, however, the internal mobility at a given temperature is altered, say by the pressure, or by the presence of some substance in solution, the surface mobility will be altered too. We shall assume that it is altered in the same ratio as the internal mobility, an assumption which appears to be justified by the account which it will enable us to give of the effect of pres- sure and of solution. Let us now apply this idea to the familiar case of rise in a capillary tube standing in a liquid having only its own vapour above it. Or let us take the more general case of a liquid in a vessel with tubes which are wet rising above the flat sur- face, and with tubes which are not wet coming out of the side Fig. 1. and turning upwards, and of such diameters that the liquid does not rise to the top of the tube, as in fig. 1. Thomson’s 294 Prof. J. H. Poynting on Osmotic Pressure. theorem shows that there is ultimately a balance between evaporation and condensation at each surface, or that the vapour-tension is less at the surfaces a and b than the normal amount existing at c, while at d, e, and f it is greater. In other words, the surface mobility gradually increases as we o downwards. This is usually connected with the curvature of the liquid surface, but, as I have tried to show in a former paper (Proc. Phys. Soc. vol. iv. p. 271, Phil. Mag. July 1881), it should rather be connected with the increased pressure of the liquid just under the surface as we descend ; the curva- ture of the surface is a non-essential accompaniment. Taking the pressure of the vapour at the flat surface ¢ in fig. 1 as w, and the densities of liquid and vapour as p and a respectively, then at a level h below or above ¢ the hydro- static pressure is greater or less than at ¢ by gph, =P say, while the vapour-pressure is greater or less than at ¢ by oO e e goh=— ; or the increase in vapour-pressure at a surface as we descend is proportional to the increase in hydrostatic pres- sure just under that surface. This is accounted for if we suppose that the increased hydrostatic pressure results in increased mobility, and therefore increased evaporation from the surface. The vapour-pressure increases from @ to ow + —2 = a(1+ =) : or the coefficient of increase of its mobility is — per unit of hydrostatic pressure, and this is the coefficient we must assume for the increase of internal liquid mobility to account for the facts on this theory. We have no direct evidence that increase of pressure does thus increase liquid mobility. The justification is to be sought in such explanations of known facts as that just given*. It is perhaps worth noting that we obtain the true state of affairs externally if we picture the liquid in fig. 1 as a kind * Liquid viscosity should decrease if mobility increases, and should therefore, in our view, decrease with increase of pressure were mobility alone concerned. But rigidity also comes in, and we must ascribe to this complication the result that, in water, pressure lessens the viscosity while in turpentine it increases it (Cohen, Wied. Ann. No. 4, 1892). But it would appear fair to seek support for the supposition of increased mobility in the “flowing” of solids under great stresses, as in the stamp- ing and wiredrawing of metal, when the molecules undoubtedly change their positions with very greatly increased rapidity when under great strain. on Prof. J. H. Poynting on Osmotic Pressure. 295 of open framework, or as a spongy structure through which the molecules of vapour pass freely so that they are at the same pressure within and without the liquid at the same level. But this conception must be used only to give us the net result, and not as representing the actual condition. If, in addition to the vapour, any soluble gas is present in the vessel, it too will exist both inside and out in quantities increasing as we descend, and it must be in equilibrium at all levels. So that if near the flat surface the density of the gas in solution is x times the density at the same level outside, the same ratio will hold at all depths. Again the net external result is the same as if we picture to ourselves a spongy structure through which the gas passes freely. As a further illustration of the change of mobility with pressure, we may take the alteration of the melting-point which I have discussed in the paper mentioned above. Thus, in the case of water, water and ice are in equilibrium under 1 atmo. at 0°, and therefore have equal vapour-tensions and equal surface mobilities. If, however, we put on pressure, the coefficients of increase of mobility are, as we have just Oo Oo Oyo seen, — and ——, where p and p’ are the densities of water @ @® and ice, and o and @ the density and pressure of the vapour respectively. Since p is greater than p’ the water mobility is increased less than the ice mobility, and so at the surface of contact the ice sends more molecules to the water than it receives in return, that is to say, it melts. Below 0° the vapour-pressures and mobilities at atmospheric pressure are different, the mobility of water being greater than that of ice. But if we put on sufficient pressure we may once more equa- lize the mobilities and so lower the melting-point to the new temperature. Thus if a and aw’ are the vapour-pressures of water and ice at —d@, and P is the pressure making the mobilities equal, or the pressure reducing the melting-point to —dé, o(1+ ~2)=0/(1 + =) ap ‘ Pp fare o—o'=Po(5—>) oe s AM ae on area 6 cea (7) a formula equivalent to that of Kirchhoff deduced by purely thermodynamic considerations. For using the ordinary for- mula for lowering of melting-point, 1}! ] dé ie ~—=)= a e . ° . ° a te p L @? (7a) 296 Prof. J. H. Poynting on Osmotic Pressure. we obtain Kirchhoff’s result, olucdd a era Now let us consider the case of a dilute solution of a non- evaporating salt. We know by direct observation that the vapour-tension is reduced by the presence of the salt, and we must suppose, on the hypothesis here advocated, that this reduction is due to a decrease in the mobility of the liquid. Let us follow out this idea by imagining that we have in the same chamber maintained at a constant temperature two deep vessels, one containing the pure solvent the other a dilute solution. In this chamber we shall suppose that above the liquids there is only the vapour of the solvent. To begin with, we may suppose that each vessel is half full and at the same level. Then the pure solvent will distill over into the solution, and will continue to do so until the difference in level in the two vessels is such that each surface is in equili- brium with the vapour at its level. The hydrostatic pressure in the solution at the level of the surface of the pure solvent will then be the osmotic pressure. If we imagine a number of non-wettable tubes inserted, as in fig. 1, in the sides of the two vessels at various depths and turned upwards, the diame- ters being so adjusted that the liquid does not flow out of any of them, then in any pair at the same level we realize Fitz- gerald’s semi-permeable membrane; and at each level the two liquids must have equal vapour-tensions, which implies that their mobilities are equal at each level. This also comes out from our equations. Let a, a’ be the flat surface vapour- tensions of solvent and solution, p the density of the liquid— practically the same for each—and H the final difference in level between the two surfaces, so that the osmotic pressure P=gpH. If M, M’ be the mobilities at the surface-levels, Mw WwW ao” Now as we descend in the solution the mobility increases, and the rate of increase is <- per unit pressure. For depth H this increase is gp a = a or the mobility P M’=M'(1+9%5 == M (149 =a C ~ roy Vice ee Bat a=o'+gqHo, Prof. J. H. Poynting on Osmotic Pressure. 297 whence M’=M, or at the level of the solvent surface the mobilities are equal. This equality will be maintained if we descend equal distances in the two liquids below that level. So that if we now connect the two vessels at any level by a horizontal tube with a semipermeable membrane in it, the solvent mobilities on the two sides of the membrane are equal, and therefore the solvent diffuses through at equal rates in the two directions. ' We may then explain in the following general terms the rise which occurs when we place a semipermeabie vessel con- taining a solution into a solvent. The solvent molecules are entering the membrane on both sides, but the mobility or number set free per second from the pure solvent is greater than the number set free from the solution. The membrane goes on absorbing the solvent from each side till it becomes saturated, 2. e¢. holds so much that it returns as many mole- cules as it receives. It is receiving more from the pure solvent side, and therefore when saturated for that side it is supersaturated for the other. Consequently more molecules are sent into the solution than are received from it, and the solution grows until the growing pressure so much increases the mobility that it is equal on both sides of the membrane. If the solution and solvent are in two vessels separated by an indefinitely produced vertical and semipermeable membrane, it is evident that ultimately the two will be in equilibrium at every level, whether in liquid or vapour. We may apply the same idea to the change of melting- point in a solution. In the soiution the solid mobility is unchanged, but that of the solution is lowered by the fraction sg — where P is the osmotic pressure ; and to find the new melting-point, we must find the temperature d@ below the normal melting-point at which this is equal to the difference between the liquid and solid mobilities. Taking pressures to represent mobilities, GD ore But pe. ad? (OQ) — (ny == 6 ) whence we obtain the ordinary result Pé Sat eat MAGE Ios (8) Comparing the above result with the lowering due to pressure 298 Prof. J. H. Poynting on Osmotic Pressure. (7 and 7a), we see that the lowering due to a given osmotic pressure in the solution is greater than that due to an equal pressure on the pure solvent in the ratio ie 1 Tah os ey ae. pp p. or v:v—v. In the case of ice and water the ratio is 1 : 1:092—1 aa fe SES 2 —— om ieee | It now remains to see if we can give any reasonable account of the decrease in mobility in a liquid when a salt is present in solution. If the molecules of salt were simply mixed with those of the solvent, or if they combined to form stable non-evaporating compounds with the solvent, which compounds were simply mixed, then the mixture should have the same vapour-tension as the pure solvent. For we might regard the salt or compound molecules at the surface as equally reducing the effective evaporating and the effective condensing area, somewhat as a perforated plate or gauze laid on the sur- face would do. But the salt probably combines with the solvent to form unstable molecules which continually inter- change constituents, so that when near the surface they may serve equally with those of the pure solvent to entangle the molecules of vapour coming downwards, these descending vapour molecules. taking the place of molecules attached to the salt. Probably, however, they are less energetic than the pure solvent molecules and "do not contribute so much to evaporation. We shall make the supposition that they do not contribute at all. Let then each of the salt molecules combine on the average with a of the solvent molecules, and in such a way that it prevents those a molecules from evaporating while the com- pound molecules formed will entangle returning molecules, each of the a being replaceable by a vapour molecule. Then we may regard the solution as solvent, having a number of molecules simply mixed up and inactive as regards evapora- tion but active in effecting condensation. If N is the number of gramme molecules of solvent per litre, and n the number of gramme molecules of salt added, the number of solvent molecules left is N—an. Were the n compound molecules quite active both as regards evaporation and condensation the mobilities outwards and inwards would Prof. J. H. Poynting on Osmotic Pressure. 299 be altered in the same ratio and the vapour-tension would be unaltered. But we are supposing that they are inactive for evaporation only and that their a molecules of combined solvent are still active for condensation. So that in the solution there are only N—an active for evaporation, while there are still N active for condensation. Hence the vapour- —an N the solvent and solution vapour-tensions, Or if wand wo’ are tension is reduced in the ratio N @oNS an ao . N and If each salt molecule takes one solvent molecule, so that a==1, we have Z—al on coweee INI which is the usual result deduced for dilute solutions from the van’t Hoff value of the osmotic pressure. We may, of course, work backwards from this result, and the work may be put in the following form :— If P is the pressure in the solution necessary to restore its mobility te that of the solvent, z.e. to increase it in the ratio ase, a(1 4+ <7 law, @p or aw — a’ op Mage Bo eer N and __ nap Ne If M is the molecular weight of the solvent Fa 7d +at) oO omy ee os ale (1+ at) 300 Mr. Frederick Bedell on where i is the value for hydrogen at 0°, and this is o 0/7 H 000896 Where A= i. atmo. Also NM=1000p. Substituting these values we obtain eal? 2 Ap(1+at) ~ N° M‘0-0000896 QnA 0-0896 = 22-3nA(1+ at). if a has any other value than 1 we must put P=22:3anA(1+ at), whence we see that if each salt molecule combines with two or with three solvent molecules the osmotic pressure is double or treble the normal value. The supposition here made is no doubt crude in its simplicity, but my attempts to introduce other considerations, such as change in density in the solution, have led to such complicated results that much more extravagant suppositions had to be made to reconcile these results with experiments. I therefore leave the hypothesis in this crude form, in which it will at least serve to show that it is not necessary to ascribe osmotic pressure to dissociation but rather to association or some kind of combination of salt and solvent. P 1+at) XXXII. Admittance and Impedance Lect. By FREDERICK BEDELL*. fe quantities chiefly considered in the discussion of alternating currents are electromotive forces and cur- rents, the values of these being determined for different con- ditions. Hlectromotive forces and currents are commonly represented by vector diagrams; and the change in these diagrams, as some one quantity is varied, is shown by the loci of the vectors which are altered thereby. What may be termed electromotive force and current loci are thus deter- mined. The numerical values for which these are constructed necessarily depend upon some condition involving an assumed _ * Communicated by the Physical Society: read June 26, 1896. Admittance and Impedance Loci. d01 value either of the current or of the electromotive force: thus we may assume a certain current to be constant (as the pri- mary current of a transformer), and construct an electromotive- force diagram with loci showing the changes in the various electromotive forces as some part of the circuit is changed ; or we may assume the impressed electromotive force constant, and ascertain current loci for the same variation. Let us limit ourselves to the transformer. In the first case above it will be found that the constant assumed primary current J, is a factor in the value of every line representing the compo- nents of the primary electromotive force H,. By factoring out I, we have an impedance diagram similar to the electro- molive-force diagram, and without any assumption as to the value of the current or electromotive force. Similarly each line in a current diagram, constructed for a constant impressed electromotive force H,, represents a current which is a mul- tiple of an admittance (the reciprocal of an impedance) and the factor H,. By factoring out EH, an admittance diagram is consequently obtained, similar to the current diagram but with no assumption as to the current or electromotive force. Admittance and impedance diagrams accordingly correspond to current and electromotive-force diagrams respectively, differing from them only by a factor. Impedance and admittance loci, or electromotive force and current loci, for the primary of a transformer will in general be ares of circles for changes in any one of the constants of the primary or the secondary circuit. Some interesting relations avise from the reciprocal nature of admitiance and impedance. Let us note the following relations between reciprocal vectors :— If any vector has an are of a circle for its locus, a vector proportional to its reciprocal will have an arc of a circle for a locus. In fig. 1 let p, be any vector from the origin O, having its locus as shown upon the are of a circle. The vector p2, drawn in the direction of py and proportional to its reciprocal, will have its locus upon an arc of a circle, which may be shown as follows. Let p; and p;/ represent the vector in any two positions, OA and OA’. ‘The intercepts Oa and Oa’ will represent the reciprocal vectors p, and p,’; for in the similar triangles OA’a and OAd’, Pics Px Pa. > Pos Hence Pt P2 =PiP2= 2 constant. The value of this constant product of p, and pz is OG". 302 Mr. Frederick Bedell on ~ Fig. 1.— Reciprocal Vectors, p, and py. A Fig. 2.—Reciprocal Vectors. By a suitable selection of scale, the loci of p, and its reci- procal pp may be represented as arcs of the same circle, as in Admittance and Impedance Loci. 303 1; or they may be represented by different circles, as in 2. In the latter case, Ses Eh Eh dg dS P1 P2=OG,. OG, = a constant. As the origin O approaches the circle which represents the locus of p,, the centre of the reciprocal circle becomes more distant and its radius becomes greater. When the origin O is a point in the circumference of the first circle, the centre of the reciprocal circle is at an infinite distance ; that is, the reciprocal locus is a straight line. Let us apply these principles to the transformer diagrams. The locus of the primary impedance, as some particular: quan- tity is varied, is a portion of a circle. For example, this may be shown to be the case when the secondary resistance is varied. Since the admittance of the primary is the reciprocal of its impedance, the admittance may be represented by the vector p in the above construction, if the impedance is repre- sented by p,. These loci may be drawn to scale for actual values. In a constant current transformer the primary elec- tromotive force varies directly as the primary impedance. In a constant potential transformer the primary current varies directly as the primary admittance. But the admittance is the reciprocal of the impedance ; hence if we have an arc of a circle for the locus of the primary electromotive force when the primary current is maintained constant, we may employ the above method to obtain the are of a circle which will be the locus for the primary current when the transformer is supplied with a constant electromotive force. The converse operation may likewise be performed. In fig. 3 let the circle C, represent the locus of the primary electromotive force Ii, during some particular change of con- dition, the primary curr ent. meanwhile being maintained constant and in the direction OA. The difference in phase between the current and electromotive force is the angle ¢. The locus of the primary current under the same change of conditions, if the primary electromotive force is maintained constant, is the dotted circle C,, which is reciprocal to C,. If the constant electromotive force is drawn in the direction OA, the locus of the primary current is the circle C,’, drawn so that the angles AOC, and AOC,’ are equal. An application of the method of reciprocal vectors is shown in fig. 4. Positive rotation is counter-clockwise. The semi- circle JKN represents the locus of the primary electromotive force of a transformer, when the primary current is constant 304 Mr. Frederick Bedell on Fig. 3. Fig. 4.—Method of obtaining Primary Current Locus by the Principle of Reciprocal Vectors. e — See pe Oo -_ afliz \ N H a oren\cinculT ty = \ XK _1 OPEN CIRCUIT -\ 3 if \ : / O 0 \ ye Ne y) XN 2 Ne ae Bisa ~~ — eal and is in the direction of OA, and the secondary resistance is varied. Admittance and Impedance Loct. 305 The eiectromotive force has the position OJ on open circuit and ON on short circuit. OH is the power electromotive force on open circuit, and includes the effects of primary resistance and the losses due to hysteresis and eddy currents ; HJ is the electromotive force to overcome the primary self- induction. These are in the direction of the primary current, and at right angles to it, respectively. A line from J to K, at right angles to the secondary current, would show the reaction of the secondary upon the primary. It is to be noted that the line NH represents the effects due to magnetic leakagé. It is desired to find the locus for the primary cur- rent when the primary electromotive force has a constant value, and is drawn in the direction OA. The angle of lag 4, between the primary electromotive force and cur rent on open circuit, is JOH. Accordingly, with a constant electromotive force in the direction OA, the open circuit current I) is laid off lagging behind the electr omotive force at an angle of AQO7’=0,=JOH. The open cireuit current I) miy be laid off to any convenient scale. To construct the locus for the primary current proceed as follows:—Lay off the line OC, so that the angles AOC, and AOC, are equal. The point C, is located so that OC, : OC, :: Oj’: O7. The primary current: locus is then drawn as the arc of a circle with C, as a centre, passing through 7’. The limits of the primary electromotive force locus are the points J and N. The corresponding limits of the primary current locus are the points’ and nn’. It will be noted that these points correspond to the points 7 and n on the circle Cj, which are reciprocal to the points J and N. In the absence of magnetic leakage the points N and H coincide. The point n’ would then lie in the line OA. The deviation of the primary current locus from the line OA is produced by magnetic leakage. An experimental curve showing the primary current locus for a constant potential transformer, as affected by magnetic leakage, is shown in fig. 5. The reciprocal relation between admittance and impedance vectors gives a simple method for determining the conditions for consonance and resonance in transformer circuits*, | Figure 6 is given as a par ticular instance in illustration of the statement given above that loci produced by the variation of any one constant are usually ares of circles. The primary loci are always ares of circies. The diagram shows the chauges due to a variation in the secondary self induction. * “ Resonance in Transformer Circuits,” by Bedell and Crehore, ‘The Physical Review,’ vol. ii. p. 442. Ponti. oO. Volo 42. No: 257. Oct. 1896. Z 306 Mr. Frederick Bedell on Fig. 5.—Primary Current Locus for Constant Potential Transformer ; Determined Experimentally. OPEN CIRCUIT O Fig. 6.—Effect of the Variation of the External Secondary Self-Induction in a Constant Current Transformer. Fig. 7 shows the effect of magnetic leakage. The curves shown are loci for primary electromotive force, when the primary current is 1,. The primary electromotive force is composed of the components OH, to overcome ohmic resist- ance and supply open-circuit losses, HJ to overcome self- induction, and (with absence of magnetic leakage) JK) to overcome the back electromotive force of mutual induction. Admittance und Impedance Loci. 307 The semicircle J KH is the locus for the primary electro- motive force in the absence of magnetic leakage. The semi- eircle JK’N is the locus for the primary electromotive force Fig. 7.—Effect of Magnetic Leakage. - OPEN CIRCUIT Q when the coefficient of magnetic leakage € is constant from open circuit to short circuit. In this case we have the relations Hes dN et iE Wi Se wie ee ea Ne NE Tie, NOE JK’ JN Srl re NP gait N/a In an actual transformer the magnetic leakage is not con- stant, but varies with the load. The locus represented by the dotted curve J K’’N is for such a case in which the magnetic leakage is zero on open circuit and increases to the maximum at short circuit. Where the magnetic leakage is variable, it is determined for any point as K” by the ratio of JK” to J Ko. TK” IR Thus let us suppose that the back electromotive force JK”, actually induced in the primary by the secondary current I,, is eighty-one volts ; and that JK, which would be the back electromotive force in the absence of magnetic leakage, is 100 volts. We then have the equation 81 9 1—t=/ Fa = ip 09 L2 ee) 308 MM. Oumoff and Samoiloff on Electric which indicates that the mutual induction is nine-tenths of the value it would have in the case of no magnetic leakage. The coefficient of magnetic leakage is accordingly found to be 10 per cent. ; thus :— 6¢=1-—0°9=0°10. Fig. 7 is drawn to represent the values of the various elec- tromotive forces in the primary circuit of a transformer, for a given value of the primary current and for different values of the secondary resistance. If the magnitude of each line is divided by the primary current I,, fig. 7 represents the values for the primary impedance (without any assumption as to constant current or electromotive force) for different values of the secondary resistance. The effect of magnetic leakage upon the primary impedance of any transformer is thus shown for different values of the secondary resistance. The above construction affords a simple method of studying the conditions for a decrease of the primary impedance of a transformer when the secondary circuit is closed. Curves corresponding to the dotted curve in fig. 7 have been experimentally determined t by the writer. Cornell University, May 1896. XXXIV. Electric Images in the Field of a Hittorf’s ( Crookes’) Tube. By N. Oumorsr and A. SaMoitorrt. HE influence exercised by a Hittorf’s tube on electrified bodies shows that the electric field created in the interior of the tube extends also to the exterior. Lvidently the objects brought into this field, whether to explore its elec- trical properties or, as in the experiments of Lenard and Rontgen, to produce or to receive shadows acquire a new electrical condition and by their presence modify the primi-_ tive field. It is impossible to estimate @ priori this modifi- cation and the part it plays in the production of the pheno- mena observed. In investigating these questions we finally adopted an experimental method intended to furnish us with the means of forming a general idea of the electrical pro- perties of the field of a Hittorf’s tube and the modifications which it undergoes. * Discussed at length before the Physical Society by Mr. E. C. Rimington in his paper “On Air-core Transformers,” Philosophical Magazine, vol. xxxvii. p. 394. t ‘Proceedings of the International Electrical Congress,’ Chicago. 1893, p. 234. { Communicated by Lord Kelvin, F.R.S. Images in the Field of a Mittorf’s (Crookes’) Tube. 309 With this end in view we replace the photographic plate or the fluorescent screen by a plate of ebonite. The electric field is maintained for two or three minutes, after which the action of the tube is arrested and the ebonite plate withdrawn from its position. By a quick movement the objects on the plate are thrown to the ground and we proceed to develop the images by sprinkling over the plate a mixture of sulphur and minium. As is well known, the sulphur adheres to those portions which are positively, the minium to those which are negatively electrified. Thus the colour of the spots shows the electric condition of the shadows, and the comparison of their configuration with that of the objects indicates the modifications introduced in the mode of action of the field. The tube used in our experiments had the shape of a pear with flattened base (fig. 1) ; & is the kathode, a the anode. Fig. 1. & WME, 3 In the central part of the base there was a fluorescent spot about a centimetre in diameter ; and at some distance there was a less intense fluorescent zone concentric with the spot. At a few centimetres below the tube is placed a plate or sereen of ebonite 6, which rests ordinarily on the rim of a glass vessel 13 cm. in diameter and 21 cm. in depth. The manner of supporting the plate is quite immaterial provided that the support is clear of the central portion of the plate. Thus the screen, or at any rate its central portion, is sur- rounded by air on both sides. The objects are placed either above or below the plate ; in the latter case they are held by projecting arms which are bent over the rim of the vessel. The-images were developed on both faces of the screen ; we have also employed two screens placed one on the other and developed the images on the four faces of the screens. 310 MM. Oumoft and Samuiloft on Electric We proceed to the description of the experiments :-— (1) No object being interposed between the tube and the screen we obtain on the two faces of the latter an intensely red spot corresponding to the fluorescent spot in the tube ; the remainder of the plate acquires a reddish tint. The same effect is obtained on the four faces of two ebonite plates placed one on the other and making good contact. Thus the fiuo- rescent spot of the Hittorf’s tube sets up a negative electrifi- cation on the faces of dielectrics in its neighbourhood, whether these faces are turned towards the tube or away from it. On the portions of juxtaposed plates which are not in intimate contact we find yellow spots and red ones opposite to each other. The spot formed on the front face of the plate is sharply defined ; for this reason we must conclude that the action of the tube is propagated by trajectories emanating from its surface. (2) On covering the ebonite plate by a sheet of zine the plate appears red on both sides. On putting the same sheet below the plate and in contact with it the face of the plate turned towards the zine acquires a yellow hue, the opposite face an indefinite tint. We may say in short, that every body introduced into the field, if in perfect contact with a dielec- tric, does not change the negative electrification of the latter produced by the field, provided the body is between the tube and the dielectric; when the dielectric is between the tube and the body, the negative action of the field is replaced by a positive action... This conclusion is confirmed by the following experiments :— (3) Figures cut out of metal (lead, zinc, aluminium), glass, and paper in perfect contact with the screen give, when they are placed above it, red images, and when they are beneath, yellow images. The images are bordered by a neutral band; the rest of the screen is red. On placing a glass plate beneath the plate of ebonite on which the cuttings are arranged the red ground which sur- rounds the images of the objects changes to an intense yellow field ; as to the images, their colour appears to tend to black. Occasionally yellow tufts are seen which come from points corresponding to projecting points of the objects. The rim of the glass vessel which supports the ebonite plate always gives a circle of an intense yellow except at the points which are not in contact with the ebonite ; to these points corre- spond red arcs. (4) A rectangle cut from a sheet of lead and having a rectangular opening in the middle was placed above the plate and in contact with it. The image of the metallic portion is Images in the Field of a Hittorf’s (Crookes’) Tube. 311 red, as usual, the image of the opening is black. On raising this object to a height of one centimetre above the screen by a inetal stalk cemented by wax toa glass disk (fig. 2), we obtain the image fig. 3. The white parts are the neutral Fig. 2. Fig. 3. i portions ; they are black in the image and correspond to the solid parts of the object which were not in contact with the screen. The image of the disk, which was in contact with the screen, is red, which is indicated in the figure by parallel lines. The image of the opening is markedly larger than the opening itself and of an intense yellow colour. The rest of the plate is also yellow; this colour is represented in the figure by a network of lines crossing one another at right angles. The rectilinear margins of the object show them- selves in the image as curved lines: in the image of the exterior rectangle these curves turn their convexity inwards ; while in the image of the interior rectangle the curves de- scribed have their convexity directed outwards. The fact that the image ot the opening is markedly larger than the opening itself shows that we could construct the image by imagining curvilinear rays which, on passing the aperture, converged towards certain points of the tube. (5) A rectangle cut from a sheet of lead with a rectangular opening in the middle was placed beneath the ebonite plate and in contact withit. The image of the solid parts is intense yellow ; the image of the opening is black; the rectilinear margins of the opening are replaced by curves which are convex inwards. The same object (fig. 4) was lowered one centimetre beneath the screen. The image is represented by fig. 5. The solid parts of the object (white in the figure) are black in the image. The image of the opening is red, smaller than the opening, and bounded by four curves which turn their convex sides to the centre of the figure. We 312 MM. Oumoff and Samoiloff on Electric should therefore obtain this by constructing curvilimear rays emerging from certain points of the tube in the direction of Fig. 4. Fig, 5. the opening. Thus we see generally that transporting the object from one side of the screen to the other results in the interversion of the phenomenon. We may mention that a metallic strip with parallel mar- gins, curved into a circular are and fixed by its summit on the screen (fig. 6), gives a black shadow (fig. 7) enlarged at its two ends and surrounded by a reddish field. Fic. 6. (6) Fig. 8 shows the image of a lead band, curved and fixed vertically on the screen by one of its margins. Fig. 9 shows the change which the image undergoes when a glass plate is placed beneath the ebonite screen. (7) Lead strips of equal length but different widths were bent into circular cylinders of the same diameter (about 2 cm.). On placing one of these cylinders vertically on the ebonite screen its base is represented by a red circle ; in the interior there is a thin black band (neutral) which surrounds a yellow spot. On placing a glass plate beneath the ebonite the central yellow spot diminishes markedly and the neutral bands in the interior, as well as at the exterior, increase in width. The | Images in the Field of a Hittorf’s (Crookes’) Tube. 313 dimensions of the central spot diminish when the height of the cylinder is increased. Comparing this phenomenon with that described in (4) we see that the yellow spot should be regarded as the image of an aperture. On covering the cylinder by a metal disk the central yellow spot disappears and we obtain red traces in the central part of the image. The diminution experienced by the spot when a glass plate is brought under the ebonite screen would apparently lead us io seek the aperture towards which the rays proceeding from certain points in the tube converge in the optical image of the circular section of the cylinder nearest to the tube and obtained by regarding the glass as a mirror. The central spot of the image of a cylinder placed beneath the ebonite plate is red ; its size remains the same whatever be the height of the cylinder provided that its diameter remains the same. The phenomena are not altered if the lead cylinders are replaced by glass ones. The following additional experiments correspond to those described-above :—on placing on the ebonite brass weights of 500 grams, 200 grams, and 5 decigr., it is only the last, which represents a thin piece of metal, that gives a red image; the first two do not give distinct images. In the image of a coin placed above the screen we find red portions correspond- ing to the points which were in contact with the screen, and black and yellowish portions corresponding to the depressions of the coin. If this last is placed beneath the ebonite, the red colour is replaced by yellow. We obtain in this manner the design on the faces of the coin. In all these experiments the duration of the action of the Hittorf’s tube has an influence on the clearness and intensity of the image ; prolonged action imparts a red or yellow colo- ration (according to the circumstances) to the neutral bands. By obtaining the images of objects by our method and by the photographic method we bave proved that the yellow colour corresponds to the parts of the figure directly attacked by the w-rays; the red colour to the images of the objects, and the neutral bands to the shadows which surround, for example, the images of the cylinders. Preliminary experiments have shown us that analogous phenomena are obtained on replacing the Hittorf’s tube by a metallic point connected to the conductor of an electric machine. Like phenomena, under slightly different con- ditions, have been obtained by means of electric discharges by M. Augusto Righi (Memorie della Accademia delle scienze dell’ Istituto di Bologna, (4) in. 1881, pp. 291 to 304, and pp. 461 to 496) ; there is in this memoir a sketch of a 314 B. Rosing on the Participation of Matter theory. We think that it is indispensable to complete the experiments above described in order to elucidate the various questions which present themselves, and we limit ourselves to a general conclusion that the phenomena observed should be attributed to electric fluxes proceeding from the Hittorf’s tube and the objects in its neighbourhood, together with a dielec- tric polarization ; in this sense the similarity of the electric fields of a Hittorf’s tube and of an electrified conductor must be admitted; we must therefore take it into account in the study of the electric properties of Réntgen’s rays. April 1896. XXXIV. On the Possibility of explaining the Phenomena of Magnetism by the Hypothests of Participation of Matter in the Motion of the Magnetic Field. By B. Rosine, Fellow of the Russian Physico-chemical Society®. a. theories of magnetism, whatever their physical foun- dations, are founded from the point of view of dynamics on the supposition of the existence of two principal types of physical coordinates ; the one fixing the intensity and the distribution ° of magnetic induction, the other defining the state of the magnetized matter. But the coordinates, as is known, can be in general either of positional or of kinosthenic character}; 2. e. they can occur in the expression for the energy of a system either explicitly or only through their differential coefficients. Therefore we may imagine three combinations of our magnetic coordinates, and consequently divide all possible hypotheses on magnetism into three cate- gories. The first category, when both types of cocrdinates are positional ; Weber’s hypothesis, for instance, of Molecular Magnets belongs to it. The other, when the one type is positional and the other kinosthenic ; such is Ampere’s hy- pothesis of Molecular Electric Currents in Maxwell’s version#: the latier takes the energy of the electric currents to be kinetic. A third combination is still possible—when both types of coordinates belong to the kinosthenic type, 2. e. when it is supposed that matter when magnetized is put into the same motion as the surrounding magnetic field. ’é shall take this third assumption—Have we the right to consider the magne- * Communicated by the Author. + See J. J. Thoinson’s ‘Applications of Dynamics to Physics and Chemistry,’ p. 10. t See Maxwell’s ‘Treatise on Electricity and Magnetism,’ 1892, Vola i. chap: xxi : in the Motion of the Magnetic Field. 315 tization of matter as a purely kinetic process, and to explain all magnetic phenomena—such as polarity of paramagnetic and diamagnetic bodies, magnecrystallic force, hysteresis—as simple mechanical consequences of the participation of matter in the motion of zther which takes place in magnetic induc- tion tubes? Of this we have no positive proof; but this hypothesis is attractive by reason of its simplicity, and at the same time does not contain anything improbable. To explain all phenomena by means of the properties of matter in motion and to deduce all laws from the laws of kinetic energy— has not this always been what natural philosophy has striven to achieve? The idea of connecting the motion of matter and ether dynamically is also not novel: in this way only was Helmholtz enabled to explain the phenomenon of anomalous dispersion. Magnetism also possesses its own anomalous dis- persion : it is paramagnetic polarity of some bodies in relation to diamagnetic polarity of others. And in reality, as we shall see further on, the paramagnetic refraction of lines of mag- netic foree—to use Faraday’s deep and expressive language— is just the same mechanical consequence of absorption of energy as is the anomalous dispersion of lines of the light- radiation. Diamagnetism of matter, as is known, is explained very easily by admitting the existence of molecular electric currents, excited by the surrounding magnetic field and cir- culating freely and without resistance on the surface of the particles of matter. Hlectromagnetism* shows that the energy of a system of spherical currents, referred to one of these currents, is equal to Bee) OO. eco et Olle a w=-3|)2? gas = sy Pd83- - - A) where the integrals are extended over the surface of the current in question, @ is the stream-function, and 0 and O« are the magnetic potentials due to the present current and the surrounding ones respectively. The sign & refers to all the surrounding currents. : Adapting this formula to the case of molecular spherical currents excited by the magnetic field H, and introducing the intensity of magnetization I instead of the magnetic moment of currents, after the transformation the formula for ae energy of molecular currents, referred to unit of volume, will be * See Burbury’s “ On the Induction of Electric Currents in Conducting Shells,” Phil. Trans, 1888, p. 302. 316 B. Rosing on the Participation of Matter W=S(2+1)P+1n, . |e where ¢ is the aggregate volume of the particles in unit of volume. At the same time, by applying Lagrange’s equation to the expression of the energy of molecular currents, we get the following relation between the magnetization I and the mag- netic force H :— An /2 =: +1)1+H=0. > ae It is evident that this equation can be got by applying Lagrange’s equation directly to formula (2) and by regarding I as a velocity. | Formula (3) represents a case of diamagnetism, ee = 5) ae a 3 = +1) From it we find the coefficient of magnetization « to be UE 2 eee ae k= H = EAT ae 5 «cle. Gero annns (4) ale te 1) 3 \e and, lastly, that of the magnetic permeability to be ae = p= af ts I+3 The formula (5) of magnetic permeability is found by assuming the hypothesis of molecular currents, excited by the magnetic field on the surface of particles which are themselves absolutely impermeable. It is remarkable that the same formula can be found by assuming another hypo- thesis, namely that which takes magnetic induction to be a flux, propagating through media of different conductivity. In reality, as is known, the problem of distribution of magnetic induction in space corresponds exactly with that of electric eurrents*. But we know from Electrokinematics that the conductivity of a medium consisting of spheres of conduc- tivity #2, disseminated through a medium of conductivity py, is * See Maxwell’s ‘ Treatise on Electricity and Magnetism,’ 1892, vol. ii. p. 04. + Ibidem, vol. i. p. 57. in the Motion of the Magnetic Field. 317 2 pb, + fy + 2€(2— w= —— Le (6) py + fg — € (My — fA) Applying this formula to our case of magnetic induction existing in a space amongst particles of matter absolutely impermeable, we must take u, to be equal to 1, and py equal to 0. The formula (6) will then take the following form : l—e LE paiea % hhaas Target) I+5 which is identical with formula (5). Itis easy to see trom this formula that the coefficient of magnetization « is equal to —I k= ea \ sies ot tes nope (8) 3s +1) and I is connected to H by the formula a7 (2 41)1+H=0. Le haa (a) The magnetic energy of unit of volume is, as we know from electromagnetism, expressed in terms ef the magnetic induction B and magnetic force H by the formula Wie opr or By transforming this formula and using the relation (9) we get mee a foo, t W= g,, BH = g (H+ 41) i = 3 4 31H sacl ° pet pel Dae / 2 =, H+1H—5 IH= 5 H’+ 1H + + (< +1) 2. Here = H’ is the energy of unit volume of magnetic field and 2a (2 the terms LH + = ( iF 1) IP represent the magnetic energy of the matter. These terms, also formule (7), (8), and (9), are, as we see, identical with those found before. Such a coinci- dence in the results of the hypothesis of Magnetic Flux with those of the hypothesis of Molecular Electric Currents permits of our concluding that a system of spherical currents excited without resistance on the surface of particles of matter is merely 318 B. Rosing on the Participation of Matter a mathematical fiction, representing the conditions of the propa- gation of lines of tnduction in the space occupied by the particles of matter, namely the conditions of their reflexion at the surface of these particles. Formula (3) or (8) shows that neither of the hypotheses, when excluding the participation of matter, can explain para- magnetic phenomena: the first, because the magnetic moment of induced currents always appears in a direction opposed to the magnetic field; the second, because the presence of abso- lutely impermeable matter always lessens the magnetic per- meability of space. Consequently we are obliged to introduce a supplementary hypothesis expressing this participation in some way or other. We introduce it here by supposing that the matter, when in a magnetic field, is itself put into some motion ; and con- sequently, besides the system of coordinates representing molecular electric currents, coordinates also exist which fix this magnetic motion for each particle. As these new coor- dinates, we suppose, are of kinosthenic character, the new terms, appearing in the magnetic energy of a substance, are of the form ALJ and 4yvJ?; where J is the vector defining in every point the velocity of magnetic motion of matter, and the coefficients ) and v depend on the nature of a substance, and denote—the first, r, the connexion between the motion of magnetic induction and the magnetic motion of matter, and the second, v, the inertia of this latter motion. Thus the magnetic energy of unit of volume wiil be repre- sented by the following expression :— W= z(- = 1) P+ IH +A1I + $y ee By applying to this expression the principle of Least Action, we obtain Lagrange’s equation in a new form : for coordinate I d (Ad 2 5 (a (E+ 1)E+.d +H) =0, .. a for coordinate J £ QL) =0: 3 oo eee Hence, after integrating and putting the initial conditions 1=J=H=0, we have in the Motion of the Magnetic Field. 319 ae +1 )[+23 +H =0 (13) AL+vJ =0 and therefore — H i 0 eae he ue gether or k= ress x : c 6 e (15) Formula (15) now contains both cases of magnetization: that of magnetic and that of paramagnetic bodies. In reality, when the coefficient X is sufficiently large and v sufficiently small, « assumes positive values and we enter the sphere of para- magnetism. From the equations (13) we obtain besides this 2 a I and oo Pee. y 2 2» whence it is evident that—given a comparatively large value to X and small value to y—the velocity of magnetic motion of matter and its energy under the same magnetization I are comparatively greater. We conclude from this, that the absorption of energy by motion of matter in paramagnetic bodies is comparatively greater than in diamagnetic ones, as has been already pointed out, and that in consequence thereof appears that anomalous propagation of the magnetic induction- tubes which is observed in paramagnetic bodies. Besides that, as we already decided to regard the phenomenon of diamagnetism as the reflexion of lines of induction at the sur- faces of particles of matter, we must now consider paramag- netism to be also the reflexion of the induction lines, but taking place without change of sign. Thus we find here the same phenomenon of double-signed reflexion with and with- out change of sign as we also see in other branches of physics, as for instance in the reflexion of waves of light and sound at the surfaces separating media of different nature. In the case of a crystalline substance the magnetic energy of unit of volume is expressed by a formula which is analogous to formula (10), but the vectors I, J, H are replaced here by their components (A, B, C), (L, M, N), and (a, 8, y) re- spectively. By applying to it Lagrange’s equations we get a system of equations : 320 B. Rosing on the Participation of Matcer Atr ath Ar 3 3 41)042e. L4 Aye M+ 0..N=—9, Nez A+ Avy B+Az2 C= — (ver L + vyz M42, N), Nyc A+ Ayy B+ Aye C= — (ty L+ vy M+, N), Nz At+AyB+A,C=—(,, L+yzM+vz2N); ¢ +1)A +n Dy M+reN=~a, 2 (2 +1)B+2ry L+ dy M+ N= — =. which on excluding L, M, N will be reduced to three equations : A= Kya + kK + K3y B=kyat K{B + ky ie = // // // C7 at Kk, B+ks ny where i fs fea / HO Coy RC Cg ly Ia These are, as we know, the fundamental equations for mag- netization fot a Cry Seliine substance. The coefficients «1, Ky, 3 - here may have both positive and negative values depending upon the values €), 2, €3) Azz, Avy, Nyy, - ©: Very Veg ee the different axes of the crystal. Lastly, by introducing into the formula of energy values of 1 LL, M, N from the above equations, and by adding ge M, we vet W= = BH cos BH. S77 Thus we see that the results found by means of the hypothesis of mechanical participation of matter in phenomena of mag- netic induction answer well enough to the fundamental requirements of the theory of magnetism. However, these suppositions are not sufficient to explain all phenomena of magnetism, for instance the phenomena which take place when iron and such metals are magnetized. The phenomenon of magnetic remanescence forces us, on the other hand, to suppose the existence of magnetic deformations that take place at the magnetic motion of matter, and therefore to accept a new type of coordinates which would define them. Actually, whatever the magnetic motion of matter, it is, of in the Motion of the Magnetic Freld. d21 course, a periodic motion round the axis of the vector J. Arising inside matter, it must produce there a kind of pressure, counterbalanced by the elastic forces of matter, and must therefore be accompanied by certain deformations. We suppose that this pressure is kinetic in character, ¢ e., it passes on bv collisions from particle to particle. Now it is easy to prove that such a kinetic pressure must be proportional to the square of the velocity J, and that at the moment of the change of this pressure forces of reaction appear which act backward on the vector J. Actually, the hypothesis of the existence of kinetic pressure produced by the magnetic motion of matter is dynamically equi- valent to supposing that a connexion exists between this motion of matter and the motion arising at its deformations. There- fore, if we denote the coordinates fixing magnetic deformations by the letters p,, Pero then the above hypothesis will mean that terms exist in the formula of Lagrange’s function of the tollowing kind :— PaPa t+ Pape + ce og 8 0 : ges (17) where p_, Pz +++ are coefficients defining the connexion be- tween the two motions. Therefore, in Lagrange’s equation tor the vector J, besides the forces contained already in formula (12), new forces appear and the equation is :— d d 4 : fo % ay ott vy) == Fe el ae gam 50 ee lata) + Pgpgd +t -..J=0, . (18) if we denote by © the coordinate the velocity of which is 1 Cae dO Seer AMES ee | a 5 oe eae 9 J ap (19) Besides this we shall get the fullowing equations relating to coordinates p_, Pgs e+ 3 ih a 2p - eran) (PP)aPat GPa = Bp Pe saan | wee | Op - ols P Fie ee a — — — s 20) (PP) 3Pa+ aPp Op, B Ps | \ Phil. Mag. 8. 5. Vol. 42. No. 257. Oct. 1896. 2A 322 B. Rosing on the Participation of Matter Here the terms (pp) p., (PP) aPp? ... represent forces of inertia for the coordinates p,, Parr: and the function ¥F represents the free energy of deformations according to Helmholtz’s theory. It must be observed, however, that we simplified the formule by taking the coordinates p_, p grit: to be independent of each other, and the functions p_, p grt to depend only on the coordinates © and p,, Parse respectively. On the supposition of indefinitely slow changes in the coordi- nates Pp, Pg+++ Wwe can neglect the forces of inertia ;. further, by giving to the equations the form dp. ; dJ oF 70? + Po dt = op, dp dJ oF B 2 So eS oS eS ke TPs a OP. dJ dJ | we can neglect the forces Pa? PB ae? °° 7 OB the same grounds. Lastly, putting dp qo Pa =a, (21) dO ” dO we get the equations in the case of indefinitely slow changes to be :— oJ" = o ) | ee ee «= Vee Pia pets or | B OPg yj which show the equilibrium bctween the components of pressure proportional to J* and the corresponding forces of elasticity. Let us now consider equation (18). After integrating from the initial moment, when [=J=H=0, this equation gives : Al+w+ppItppwt...— "OP a: Jdit — 03 34: ala BL 8 0 30 4 Jo 3028 Once more assuming the indefinite slowness of change, we shall have for static magnetization : in the Motion of the Magnetic Field. 323 Po. Jd AL+yvJ — ( Pa Jdp,—( , 0°83 Jdp,— He =O), v9 00 e 0 role) because we can negiect the terms containing Py Pg ++ and can accept p_, Pgr+++ as the independent variables under the signs of integration. Then, on introducing significations (21), we obtain M+5-+( ™ x Jdp,,+ o,Sdpgt...=0.. (23) Jo 0 Thus we have the following system of equations in case of static magnetization :—Lagrange’s equation (11) for the vector I, which remains unchanged under the new suppositions, equation (23), and the system of equations (22) : a [Ag 62 i LEG Hyrars]=o AL + yd +{ 0 5. ole or a=, Oa OP, 26 OPg Let us integrate the first of these equations and introduce the J from it into the second term of the second equation. Then, by making use of quantities o J, o,J,... from the oe eller | ogJdps +: ive 20, Jo oJ third equation, and by introducing all these quantities under the signs of integration in the second equation, after denoting the sum . oF oF Le Sek Pe Op, pat a by oF, or or 6k = ont ae l a f eee e e e 24 Op, /4 ae ap, hB* ) (24) the system of our equations will be transformed into the following system : Ar /2 2 I = 3 ie +1) Ae) co cl (0 ene ©) T=eH—0™| > Sette |S en GeO) ee A ee ro) J? ' Oh wits c | OP. ond es (27) 2A 2 324 B. Rosing on the Participation of Matter Here the coefficient «is expressed by the above formula (15), —e —— eee Aq er?” and oF is defined by equation (24). This system of equations represents the general conditions of static magnetization on the supposition of the existence of magnetic pressure and magnetic deformations. We will pro- ceed to examine these formule. Formula (oF I=xH—«- | — eH—#- | — shows that the process of magnetization is composed of two processes, one, expressed by term «H, is a process which can be completely reversible and which represents, as we have already had occasion to see, a simple reflexion of induction- lines from matter; the other process is expressed by the term _ h(E Palade: and arises in consequence of absorption of energy by the mag- netic deformations. The value of this term wholly depends on the free energy F of deformations. It is in the nature of these deformations that the explanation of all the complex and intricate phenomena which appear in the magnetization of iron must be sought. It is evident from equation (25), that in a paramagnetic substance—given I and H positive—the vector J has the oppo- site sign to the coefficient A, and « having a positive value, the product Ke - is greater than nzl. On the other hand, when I and H are increased, and consequently J too, the de- formations likewise increase, and with them F. Therefore the integral Ses vj Jd taken from the beginning of magnetization I=J=H=0 isa positive quantity. Thus, owing to the absorption of energy in a paramagnetic substance, magnetization increases. To show this still more clearly, we will put the equations in the Motion of the Magnetic Field. 325 into differential form. Let us suppose that the process of magnetization takes place at constant temperature. In this case the free energy IF is a function only of the coordinates Pay Pp»---+ But these coordinates can be expressed by the system of equations (27) as a function of J’. Therefore the energy F may also be considered as a function of the same quantity J’. In this way we have ara OF a A BR om If we now differentiate the equation (26), considering H as an independent variable and using the formula (28), we have aT _y_ 2D ad an ~ vy OJ? dH’ let us replace a by its expression from equation (25); dJ Lr4c 72 dl eas ee +0) a +1]; we have, lastly, 20F dl _ Te aie e A 2 ee (28) 3 \e OJ? This is the differential equation of static and isothermic eee, F magnetization. Here, as has been said above, = must be considered as a function of J’, where J, in its turn, is ex- pressed in terms of I and H by help of equation (25), 3 The form of this function of F is defined by the way in which F depends on p,, pg. -.. a8 shown in equations (27). Actually, by differentiating the equations (27) at a constant temperature, = (= =e) L+rJ +H=0. toe or G,dJ2 = Spe (Pe opdJ* = Opa Pe Mae and by introducing the quantities dp,, dpg,... from here in the expression (24) for dF, we shall haye 326 B. Rosing on the Participation of Matter oF oF fy, Oper gi Op \ 2, = | on Shh to Sep te dJ?; OP, OPS whence, by comparing this equation with (28), we have oF OF oF OP 0 oa=4 o. SR +0357 +. ye OP, OP : Semele oF or, more simply, taking Oh. =, aA: =e eee oF a3 Apa dpe QJ? \c, diog P, 2p dlog Pz Raa \ ae - (30) where @ is the absolute temperature, and Pe, Ps,....are supposed for simplicity to be only functions of this tempe- rature and of the coordinates p,, pg, ... . respectively. It is by this equation, in conjunction with equations (25), (27), and (29), that the process of maguetization is completely defined. >F First of all, it is to be seen from equation (30) that IE Ap abe Pid log : eee are, in general, is a positive quantity, as greater than nil. dl Therefore, as shown by equation (29), 7H is for a para- magnetic substance always larger than « if only OF sy 3 pst Pee pe ae 4n(= +1) dl EK } °. ¥s e fo) v 7H® infinitely great, and, lastly, 3 aS ni ee RS od a Aor (= +1 ) € >F if with increasing of H, and therefore of J*, iE becomes Vv ee ae tr(=+ 1 ) statical magnetization 1s impossible. [In the latter case, as is easily proved, the process of mag- netization represents a kind of free motion at a constant mag- netic force. Nevertheless, the equations of this process are When the equation cannot give real solutions, and in the Motion of the Magnetic Freld. 327 included in the general equations, and can be shown as follows :— EHi=const., (2 qd )I+.J+H=0, pe »Upeg y a 2 2 a peeai eee BIA aa Duden? ‘ mee (pp)eia + Gap, ta0P?'= 5 eee oF (PP spe + Gepet opel? = Opa The new terms introduced in the equations appertaining to the coordinates pa, Dg,.++-3 (PP)oPat Gaps (PP) ape +:Gigpg,--- represent the forces of inertia and viscosity respectively. It is clear that in the curve of magnetization showing the de- pendence of magnetization I on the magnetic force H, this process is shown by the straight-lined parts of it parallel to the axis of magnetization. | The same equation shows, further, that at the commence- ment of magnetization a must be equal to «, because in these conditions = P =(; and therefore oT =0, if only = is not ©, which can happen only in particular cases ; for instance, near the temperature of recalescence. This is the least value that Ge can have; it is not great, and ¢f the dH deformations were not existing, the magnetization of iron would not differ much from the magnetization of other paramagnetic bodies. But that in consequence of these deformations, increases very rapidly, and -—-— increases with it. The di quantity FAL exists as long as the deformations change ; when the deformations cease to change, the differential coefficient dl e e e —. again takes small values. This ceasing of change of dH deformations must be therefore supposed in order to explain so-called magnetic saturation. But if we take into considera- tion that magnetic deformations most likely do not represent 328 B. Rosing on the Participation of Matter changes of volume or form, but of the structure of matter— like that which takes place in recalescence, as is most pro- bable,—then there is nothing impossible in this hypothesis. The explanation of another very important phenomenon— magnetic hysteresis—is based on the same phenomenon of magnetic deformations; we must only suppose that the same hysteresis exists in the changing of magnetic defor- mations. It is also interesting to see to what our hypothesis could lead in the case of a deamagnetic substance. In this last case, when «<0, 2. e. the reflexion of magnetic induction from the particles of matter takes place with the changing of the sign, the absorption of energy by deformations gives rise to a quite opposite effect. Formula (29) shows that when «<0, the absolute value of - cannot be more than K, —1 SVE eee (241 )—* 3 \e y because, as it is very easy to see from this formula, the fol- lowing inequality always holds here, 3 =e (2 +1)>1. Further, the same formula shows that s is lessened always with increasing of oo and therefore in all such cases, when magnetic deformations increase the most the differential coefficient a falls to its least value. 7 Owing to this, when we assume the character of the change of deformations in a diamagnetic body to be the same as in a paramagnetic one, we shall have for a diamagnetic substance a curve of magnetization of quite a different form, namely, like the line O MN shown in the figure. Similarly, when the mag- netizing force is decreased, the deformations change more slowly, in consequence of hysteresis, than when it is in- creased, and the return curve NPQ descends below the curve OMN and intersects the axis of H before O in the point P. Again, with a further decrease vf H, magnetization becomes positive, and the body at H=0 has a paramagnetic residual. ‘This, as is known, was observed by Messrs. Quintus- Icilius, Tumlirtz, Lodge, and others. Besides the diiferential equation of magnetization, it is tn the Motion of the Magnetic Field. 329 important to examine the signification of the integral — \ldy, which represents, as is known, the area of a closed curve of magnetization. If we write the equation (11) in the form 7 (= ; )o+ al ded) dH 3 dt dade Jee ; the term — ee will represent the force by which the exterior € magnetic field acts on the coordinate, the velocity of which is I. In the time dé it is obvious that this force will per- form the work aw=- eae Therefore during the complete cycle of magnetization the magnetic field will perform the work W=— {lH, where the integral is extended along the curve of magneti- zation. On the other hand, if we differentiate equation (26) 25 multiply it by J, and substitute for J its expression from (2: »] ), then we 330 B. Rosing on the Participation of Matter shall have Jdl—JedH = —«8F; and therefore -F(- aa Hdl + Ar : 33 +1) «ldH +«HdH =—K — © oF. After integrating along the closed curve, we have, in consequence of equalities which hold in this case, {HdH=JIdI=0, {Hdl=—f dH, the equality — (14 F(E +1) e) | ua = o [aF, But formula (15) shows that 2 “Lek =( +1)e=0 3 3 consequently —\IdH= Jj 6F. Farther, aap OF df =6F — Yi] —~ do, where @ is the absolute temperature. But the theory of Free Energy tells us that d¥=dU—ds8, where U is the complete energy of the body and S@ its bound energy. Therefore be oF jéF= \dU—fase— 59 d0= JdU — jGdS=\dU—A JQ, because oe =8, 7. ¢. the entropy, and @dS=AdQ, where Q is the quantity of heat supplied to the body and A the mecha- nical equivalent of heat. In the case of an isothermice process, when the body on completing the cycle arrives at the initial conditions, we have jdU=0; and therefore in the Motion of the Magnetic Freld. ddl But in the case of deformations produced by exterior forces far is, in natural conditions, either nz or a positive quantity. Therefore \IdH is a negative quantity, and magnetization proceeds along the curve in a direction opposite to that in which clock-hands move ; and the work performed by the mag- netic field is positive, and leaves the body in the form of heat. Thus, in conclusion, we see that, from the point of view of the hypothesis which considers the magnetic induction as a kind of motion of ether communicated also to matter, we can explain the phenomenon of magnetization as a simple re- flexion of tubes of induction from matter, where this reflexion appears with or without a change of sign, with this or that intensity, depending on the forces of reaction of matter which exist at the moment of reflexion. These forces of reaction depend, in their turn, firstly, on the inertia of matter in relation to the magnetic motion and on the coeffi- ecient of connexion of ether and matter, which determine the sion of reflexion; secondly, also on the elastic forces in these substances in which magnetic motion is accompanied by magnetic deformations. In those bodies which have a comparatively large magnetic inertia, the reflexion takes place with change of sign and the intensity of reflected induction is greater, the less the inertia and other forces of resistance; this ts a normal magnetization, and these bodies are so-called dia- magnetic bodies. In others where the inertia is less than a certain quantity, the reflexion takes place without change of sign, and every increase of resistance of matter 1s accompanied by increase of reflexion. These are so-called paramagnetic bodies. | By following in this way the hypothesis treated of here, one can reduce to the same principles the phenomena observed at rapid and alternate magnetization and find an answer to the very important question of the existence of magnetic inertia and viscosity, and of their réle in the magnetic circuit. This question, however, necessitates very minute study, and we shall return to it in the future. At present we will only remark that the results to which this hypothesis brings us are directly opposed to those which are arrived at from the point of view of Weber-Ewing’s theory. In opposition to this theory, the magnetization of iron here rises with the increase of resistance offered by the forces of inertia or viscosity. In this way inertia, when the magnetizing current is closed rapidly, must involve a greater magnetization; the same is to be said concerning viscosity; on the other hand, when mag- netizing current is alternate, viscosity alone increases it; whereas inertia lessens it; and as in all probability, owing to 332 Dr. G. J. Stoney on Microscopic Vision. the rearrangement of particles, the viscosity steadily lessens, this entitles us to suppose that with an alternate magnetization the maximum of it does not reach that quantity attained by a static process. And certainly the most recent observations on the exhaustion of iron in transformers seem to corroborate this. From the point of view of the present hypothesis, the exhaus- tion of ircn is nothing but the rearrangement of its particles, in consequence of which the magnetization is performed with a smaller absorption of energy, and therefore calls for a less pronounced magnetic effect. Physico-chemical Society. The University, St. Petersburg, Russia, June 15, 1896. XXXV. Microscopic Vision. By G. JOHNSTONE STONEY, WEA TIS. 3 hee Part I.— FUNDAMENTAL PRINCIPLES f. 1. ISION, whether by the naked eye or with the as- sistance of optical instruments, may be studied in many ways; since a correct investigation may start from any one of the innumerable possible resolutions of the disturbance which exists throughout the ether in front of and close to the object. But two only of these will be here considered, viz.: that most obvious resolution in which the ether in front of the object is regarded as traversed by undulations of hemu- spherical waves emanating from each physical point of the surface of the object, and that other equally general but less obvious resolution of the disturbance in this portion of the eether into undulations of uniform plane waves transmitted forwards in all or some directions from the whole extent of the objective field. 2. The first of these modes of resolution---that into sphe- rical waves—is the foundation of Airy’s method of studying the images formed by telescopes, in which the image is re- garded as arising from the overlapping and interference of the spurious disks with attendant rings which in the image take the place of points on the object. This method has on this account been sometimes called the Spurious Disk Theory. The second mode of resolution—that into plane waves—is the foundation of Abbe’s method of studying the images formed * Communicated by the Author. rir : + Part II. deals with the application of these principles to the mierc- scope as at present made. Dr. G. J. Stoney on Microscopic Viseon. 333 by microscopes ; and has usually been called the Diffraction Theory, because it gives a special prominence to the fact that when we pass beyond the meagre hypotheses of geometrical optics, we find that diffracted light* is “the machinery by which good definition is brought about.” It was undoubtedly desirable to emphasise this tact, because an error prevailed and is not yet extinct that diffracted light intervenes only to impair the image ; and it can scarcely be made any objection to the name that it runs counter to this error. As, however, both processes are only methods of investigation, it would perhaps be desirable to avoid calling either of them a theory. On this account, and to avoid cavilling about mere names, the two methods of investigation are in the present memoir distinguished as the Airy and the Abbe modes of pro- cedure f. 3. Ina recent paper by Lord Rayleigh the generality of Abbe’s method seems not to have been appreciated (see Phil. Mag. for last August, p. 167); and the main object of the present communication is to offer a fuller account of this generality than the writer has elsewhere given (see. “On the Foundation of the Diffraction Theory ” ; ‘ English Mechanic ’ for December 13, 1895, p. 380), and to trace its consequences. 4. ‘Two terms have been used above in the first paragraph which need to be defined. (a) By a physical point is to be understood an element of the volume of the object (if the object be translucent), or of its superficial layer (if it be opaque), which element of volume is small enough to justify us in substituting for it in our investigation a mathematical point regarded as a centre of an undulation of hemispherical waves. The physical point is small enough for this use of it, if its linear dimensions are in any considerable degree less than 4/4, where » is the wave- length of the light employed. To give definite form to our conceptions we may suppose its dimensions to be comparable with 4/10. This is a convenient size; since if an opening of this size were made in a thin opaque screen, and if a pencil of light were incident from any direction upon it, the hole is small enough to ensure that the light which gets through shall spread on the other side of the sereen in the form of * Light which advances in other directions than those prescribed by geometrical optics is called diffracted light. + Lord Rayleigh suggests the name Spectrum Theory for the method of investigation which proceeds by resolving the light into plane waves ; but will perhaps not press this name on the acceptance of scientific men when he finds that the limitation which the name implies has no existence. 334 Dr. G. J. Stoney on Microscopic Vision. hemispherical waves; and at the same time the opening is a large one when compared with the transversal* of the light waves, since molecular considerations indicate that this trans- versal (or rather these transversals, since there are two, an electric and a magnetic one at right angles to one another) must be regarded as of a length which is from the thousandth to the ten thousandth of a wave-length. Hence the directions of transversals will not be affected in passing through the opening. On this account, if the incident light be a beam ot plane waves, whether polarized or not, the intensity of the light will differ on the various parts of the hemispherical waves which spread beyond the screen, being a maximum in the direction of the prolongation of the normal to the in- cident waves. This must be taken into account in attempts to apply Airy’s method of investigation to microscopic vision, since until this is sufficiently done the investigation is too imperfect for us to be justified in relying on its results except so far as they can be confirmed by Abbe’s method or some other which does not involve the above consideration. A further and more serious imperfection is introduced when Airy’s method is applied only to the light between the objective and the image, and not also to the light between the object and the objective. An inquiry conducted in this way begins too late, after the more important of the events that affect the image have occurred. Nevertheless it seems to be the only one which has as yet been made by Airy’s method ; see, for example, the investigation on p. 176 of Lord Rayleigh’s paper. We shall learn in the second part of this memoir what it is that in this case is being ascertained. (>) The other term in paragraph 1 that requires definition is the objective field. By this term is to be understood the whole of the object and its surroundings of which an image is formed by the telescope or microscope, or in the eye of the observer. Accordingly the objective field at and surrounding the object corresponds to ‘ the field of view’ at and surround- ing the image of it which is formed in the eye, or at the focus of an optical instrament. , * The word transversal is here and elsewhere used for the transversal of the displacement under the dynamical wave theory of light. The dynamical wave theory is that used throughout this memoir, except where otherwise stated ; since, in the present state of our know- ledge, it is more easily handled than the electromagnetic wave theory, and since, except in special cases (as for example the distribution of intensity over a spherical wave), it furnishes the same results. Besides, the dynamical theory usually carries us as far as we can go, for, in the special cases where the electromagnetic theory may yield a different result, it seldom happens that we yet know that result. d Dr. G. J. Stoney on Microscopic Vision. 335 5. The following important optical theorem may now be enunciated, which in its generality compares with Fourier’s Theorem, of which it is, in fact, in ultimate analysis, an extension. PROPOSITION 1. However complex the contents of the objective field, and whether vt or parts of wt be self-luminous or illuminated in any way, however special, the light which emanates from it may be resolved into undulations each of which consists of unform plane waves; on the hypothesis that each point of the object emits continuously the same light: an hypothesis the suffi- ciency of which will appear in Part IL. of this memoir. By an undulation is meant a succession or train of waves, and by a uniform wave is meant one which is at each instant alike in every part of each wave surface. 6. To prove this theorem we proceed very much in the same way as in dealing with Fourier’s Theorem. We begin by positing repetitions of the objective field. For this pur- pose let a plane be drawn through some point of the objective field, and preferably perpendicular to the line of sight. This plane may be called the Objective Plane. Let a square be drawn in this plane which may be of any size, provided that it shall include within it the projection upon the plane, from the point of view of the observer, of the contents of the ob- jective field: in other words, the square is to be large enough for the whole of the objective field—the whole of what the observer can see—to fall within that square, and preferably well within it. Divide the whole plane up into squares of this size by two systems of equidistant parallel lines, and imagine an exact repetition of the contents of the objective field to occupy the position relatively to each of these except the first, which is the same as the position actually occupied by the contents of the real objective field in reference to the first square. Next suppose light to be emitted from every point of each of these replicas, which ts at each instant similar in every respect—t.e. the same in direction, intensity, phase, and position of transversal—as is the light from the cor- responding point of the original objective field at that instant. Under these circumstances a point p in the original objec- tive field, along with the corresponding points p! p" &e. in the replicas of the objective field, form a system of pvints equally spaced over a plane which is parallel to the objective plane. Now it is known, from the theory of diffraction gratings (see the figure on p. 340), that such a system of 336 Dr. G. J. Stoney on Microscopie Vision. points equally spaced in a plane, and all emitting light which at each instant is exactly similar, will produce a disturbed condition of the ether which is resolvable into plane waves advancing in certain definite* directions. The same is true of each other point of the original objective plane with its replicas. Hence, and since by the principle of the super- position of small motions the total disturbance in the sether caused by the whole contents of the objective field and of all its replicas is the resultant produced by a simple geometrical summation of the disturbances which would be produced by the several points of the original field and their replicas, it follows that in ultimate analysis the total disturbance is re- solvable into the undulations of plane waves into which its * The luminous effects produced in these definite directions are maxima, and they are accompanied by luminous effects produced in other directions _ also; but it is legitimate to leave these out of account. We are in fact investigating the disturbance within a jayer of limited thickness, the layer between the objective plane and the plane in which the front of the objective lies; and the luminous energy expended on any effects within that layer, other than those producing the plane wave dealt with in the text, can be made relatively as sinall as we please by increasing the spacing between the replicas. This will perhaps be inade clearer by considering the analogue in a Fourier’s expansion. If the first 2 terms of a Fourier’s expansion of any function be added together, they furnish an approximation to that function which is nearer the larger m is, and which can be made as close an approximation as we please by increasing ». Now the sources of similar light p, p’, p”, &c., furnish a number of fans of undulations of plane waves, each fan analogous to a limited number of terms of a Fourier’s expansion, this ihmited number being proporticnal for each fan to 6/A, where 6 is the spacing of p, p', p’, &c., and A is the wave-length. They are therefore susceptible of indefinite inciease by increasing 6, Moreover, the fans which have the smaller number of terms become rapidly the fainter: see the figure on p. 340, in which the closer the ruling the smaller will be the number of terms of the corresponding fan. The outcome of these considerations is that the ztherial disturbance in fiont of the objective plane may be such that to resolve the whole of it with absolute accuracy into undulations of plane waves would require that these undulations shall spread in all (corresponding to 6 being in- definitely large) instead of some (corresponding to 6 being finite) directions. But, practically, a very moderate value for 6 is sufficient ; ‘since the approximation is carried far enough when the outstanding luminous effects are too faint either to be seen by the eye or to affect a photographic plate sensibly. Even if the clusest of the replicas were much closer in than we have ‘supposed, they would not sensibly interfere with the vision of the original object. Two or more diatoms seen together within the same field of view do not sensibly interfere with the most satisfactory vision of each of them, nor would they if they all emitted ight from their correspoud- ing points which was strictly the same at each instant in phase, direction of transversal, and intensity. Each would still be as fully seen as our eyes ale capable of seeing, notwithstanding the presence of the others. Se 7 Ti Dr. G. J. Stoney on Microscopie Vision. 337 constituent disturbances are resolvable. The number of these undulations may be reduced wherever any of them travel in the same direction, since any number of undulations of plane waves of wave-length A travelling in the same direction may be combined into a single undulation of plane waves travelling in that direction. Hence the total disturbance is resolvable into undulations of uniform plane waves, only one of which for each value of X travels in each direction. ¢. This valuable optical theorem bears a remarkably close analogy to Fourier’s Theorem for the expansion of an immense class of functions. Thus by Fourier’s Theorem a portion of curve mn along with equidistant repetitions of the same to the left and right may be expanded in the form wv 21x y=Aot Ai cos” +A, cos 2-2 +... Dare ae + B, sin — +B, sin 2 ra +... a in which the values of the constants Ay, Ay, A», &e., B,, B,, &c., depend on what direction has been selecied for the line over which the repetitions are to be disposed, and on what interval has been chosen for a (a being mm’, the spacing of the curves from one another). So in our optical theorem, the plane waves into which the light emitted by a point p in the objective field is to be resolved will depend on what plane has been chosen for the objective plane, and on the intervals at which p, p’, p”, &c., are to occur in that plane, as well as on whether the lines joining them lie (as we have placed them above) at right angles to one another, or in other available positions. However, just as in a Fourier’s expansion the original curve is always correctly represented whatever assumption we may have made as regards the orientation of the axis of w and the length of the line a, and it is only the situation of its replicas which is affected by this choice ; so under our theorem the light in front of the objective field is always adequately resolved whatever selection we may have made as regards the optional matters (provided the conditions laid down in the footnote on p. 336 are observed), and it is only where its replicas are to be regarded as situated that is affected by that choice. Moreover, when once we have made Phil. Mag. 8. 5. Vol, 42. No. 257. Oct. 1896. 2B n” m n m’” Nn’ ™m 4 338 Dr. G. J. Stoney on Microscopie Vision. our choice as regards these optional matters, the plane waves emanating from the whole field into which the light emitted by the point p is to be resolved under our theorem, become as definite and unique as do the coefficients of a Fourier’s series when once we have decided on the direction of the line mm’ and have selected a value for a. This, however, still leaves a considerable latitude under our theorem, as to what the undulations of plane waves shall be, since the objective field may be variously chosen, and the only conditions which limit the positions to be selected for the replicas are that they and the original objective field be equally spaced relatively to the objective plane, and that the nearest of the replicas shall lie far enough outside the objective field to ensure that whether sources of light exist in them or not shall not sensibly interfere with what is seen by the observer. They are to him stars below his horizon, whose positions or even existence in no perceptible degree affect the distinctness with which he sees the stars that are above his horizon. 8. Principles of Reversal—-A further insight into what it is that occurs may be gained by a simple expedient. Picture a portion of the objective plane, of limited but large size—large enough to have the original objective field near its middle, and a great many of its replicas disposed round it. If all of these emit light that is exactly similarly circumstanced, then, as already explained, it appears that they, acting together, will produce undulations of very nearly uniform plane waves which will become more and more disentangled from one another the farther out they go. It is in fact when thus disentangled that their consisting of almost quite plane waves becomes most obvious. The approximation to accurately uniform plane waves can, of course, be carried as far as we please by increasing the number of replicas engaged in emitting the light. Let now all the zetherial motions be suddenly reversed, and let at the same time the objective field and its replicas be got out of the way. The distant undulations which were before advancing outwards will now travel inwards without ceasing to be uniform plane waves, and will by simple geometrical superposition, according as they overlap one another, repro- duce at each step of their inward journey exactly the same disturbed state of the ether as had prevailed at the same stations on the outward journey, except that the directions of all motions are reversed. Hence plane waves converging in- wards would by their superposition produce precisely the same disturbance in the ether, except only with reversed motions, as that which on the outward journey prevailed close in front Dr. G. J. Stoney on Microscopie Vision. 339 of the object in the objective field ; and, finally, if the travelling backwards is continued long enough for the undulations to reach the positions that had been occupied by the original object, they will there produce an image of it the most perfect which the light that had been emitted by the object is capable of producing. This image thus becomes a standard of per- fection which may be approached but cannot be exceeded by the images formed by any optical contrivance from the same light. “y rom the way in which the standard image is formed it is manifest that it is an image of the same size and general shape as the object or group of objects represented by it. The further excellence of this image depends upon the amount of detail upon the object which it is competent to reproduce ; and this varies, as we shall find presently, with the wave- length of the light employed, and with the way in which that light has been supplied to the object. The standard image may be regarded either as viewed from beyond, or as being transformed into a picture by being thrown on a screen able to scatter whatever light falls on it. The screen should not be flat, but with such prominences and depressions as will enable it to catch the light everywhere exactly where the image is formed. Such a picture is entitled to the name of the standard picture, since it has on it all that part of the detail on the real object which the light is capable of showing* 9. Theorem 2. The Standard Image.—Let us consider somewhat more closely how the standard image is formed. It is formed by the coalescence and mutual interference of uniform plane waves. Now when we consider how these same undulations originated when starting on their outward journey and remember that the condition of the ether is the same on their return, except as regards the direction of the motions; when we further remember that the point p * Another way of conceiving the standard image which is for some purposes more convenient, is fo imagine the retreat of the luminous undulations to be carried farther backwards (the condenser of the microscope and any other obstruction being of course removed); and then, at a given instant, to conceive the setherial motions to be again reversed. ‘Ihe undulations will thereupon travel forwards (2. e. in the direction in which the light originally moved), will re-form the standard image when they veach the position that had been occupied by the object, and will thence proceed to the objective of the microscope in precisely the same state as was the light that was transmitted to it by the real object. Jt thus appears that ‘the source of light, the condenser, and the object may be all removed, and that the standard image emitting its hight forward may be substituted at them. 2B2 340 Dr. G. J. Stoney on Microscopic Vision. and its replicas emitted portions of light which at the instant of starting were exactly alike, and that the undulations which result from this state of things may be thrown into groups of undulations, each of which is the same as would have been emitted by one or other of the uniform rulings of equidistant lines represented in the accompanying figure, as well as the 2 aN © a SM EIN SEX OC ww Zax S y S y Zz ee RE S we Se BR cK KL ps Sexe BN S WZ S V iS ZS IN VE MOSSVGSN a N SS eS vast number of others that would arise from sufficiently ex- tending the figure ; when we further bear in mind that every equal element of any one of the lines in each such ruling emits the same amount of light, which is in the same state as that emitted by p except as regards intensity : when all these things are taken into account we find that the entire of the standard image may be regarded as built up of such luminous rulings superposed upon and interfering with one another— | each of these rulings being due to the convergence and mutual interference of two or more undulations of the uniform plane waves which (since the reversal) have been travelling inwards, and each ruling accordingly being uniform and extending across and even beyond the whole range of the objective field. This is our second theorem. It may be enunciated as follows :— PROPOSITION 2. The standard image may be regarded as resulting from the superposition and mutual interference of uniform luminous rulings of equidistant parallel bright lines extending over the whole field of view; each ruling being produced by the Dr. G. J. Stoney on Microscopic Vision. 341 convergence upon it, after the reversal, of two or more of the undulations of uniform plane waves into which the light emitted by the object may be resolved. 10. Of course other resolutions than the two hitherto considered—that into spherical wayes thrown off from the several points of the surface of an object, and that into plane waves thrown off from the surface as a whole—are possible : and in fact, if a resolution of the disturbance in the eether between the object and the objective of a microscope is made into plane waves, these will become curved while passing through and after emerging from the objective ; and it is as curved waves that they reach and produce the microscopic image. They, in fact, become convex waves that are nearly spherical. The centres of these nearly spherical waves are obviously the points of the focal plane (or rather, focal sur- face, for it is slightly curved) of parallel light incident on the objective. This focal plane lies between the objective and the microscopic image, and in all the cases that need to be con- sidered it lies near the objective, and therefore sufficiently far from the microscopic image to render the curvature of the waves where they reach that image but slight. 11. Magnijfication—Let us now return to the standard image. It is of the same size as the object. If we could by any contrivance increase the wave-lengths of the light that forms it—if, for instance, we could make the wave-lengths a thousand times larger, making them the same fractions of a millimetre which actual light-waves are of a micron—we should in this way enlarge the image 1000 times, since the interference of the longer waves coming in the same directions as before would produce rulings all of which would be 1000 times coarser than before. This enlarged image would obviously contain precisely the same amount of detail as the standard zmage. This method of enlarging an image is only practicable on a small scale, since we can but slightly increase wave-lengths (as when we place the object in a highly refracting medium and its image in the air); but what is very much the same result may be brought about in another way, viz., by dimi- nishing the inclination of the beams of plane waves to one another, without altering the lengths of the waves ; since the ruling which results from the interference of two such beams may be made coarser either by lengthening the waves of which each beam consists, or by diminishing the inclination of the beams to one another. 12. Useful work done by the objecttve-—The useful part of what is accomplished by the objective of a microscope is that 342 Dr. G. J. Stoney on Microscopic Vision. it diminishes the inclination of these beams to one another. This brings about two desired results: it enlarges the image, and it makes it possible for its constituent beams, after they have passed the focal image, to be collected by the eyepiece and transmitted through so small an opening as the pupil of the eye, instead of diverging over the great extent to which they were spreading when they left the object. 13. Useless work done by the oljective—But the objective cannot accomplish this useful work without at the same time producing other effects which are undesirable. Thus, it transforms the beams of plane waves into convex beams, as explained in § 10. This somewhat distorts the image. The image is still more distorted in the direction of the line of sight, whereby any elevation on the object is shown as unduly prominent in the image™. Neither of these distortions, however, would cause the amount of detail in the microscopic image to fall short of that in the standard image. That which above all produces this defect, and produces it however well the spherical and chromatic aberrations of the objective may have been corrected, is that the angular aper- ture of the objective falls short of 180°. With the best immersion-lenses the angular aperture is about 120° or 180°, so that little more than half the ight would be caught by the objective, if the light were emitted equally in all direc- tions. One part of the light thus excluded is that which in the standard image brings out the finest part of the detail which that image can reach, since it is the light which pro- duces the finest of the rulings that form the standard image. There is another imperfection consequent upon this exclu- sion of part of the light emitted by the object, viz., the intrusion into the microscopic Image of intercostal markings, false resolutions, a general haze of light, and so on—additions to the image and other alterations of it which have nothing to correspond to them either in the object under examination orinits standard image. ‘The following is perhaps the easiest way of understanding how they arise. 14. The Visual Substitute.—In order to study microscopic vision, or vision of any kind, with full effect, it is well to begin with the consideration that what we seem to see with the naked eye is never the natural object itself, nor is it an enlargement of it when we examine it through a microscope or telescope. What we see is, in fact, only a visual substitute for the real object in the first case, and for an enlargement of the same when we use an instrument; and the study of * This distortion may be traced by an elementary investigation in geometrical optics. _ Dr. G. J. Stoney on Microscopic Vision. 343 vision, whether microscopic, telescopic, or with the naked eye, is in fact the study of what this visual substitute is and how it stands related to the real object, 2. e., what alteration the real object would have to undergo to be transformed into its visual substitute, which is what seems to us to be the object presented to us. The real object, O, sends forward the light which enters the eye, and, in addition, other light which does not enter the eye, whereas its visual substitute, S, is to be defined as that other object from which would emanate the light which enters the eye and it only. It is evident that objects O and 8 will seem to us exactly alike, but that whereas we receive the whole of the light which 8 is competent to dispense, we receive only a part of that emitted by O. Similarly, when we use a micro- scope or telescope, what we seem to see is a visual object, C, which would emit exactly the light which the eye takes in, and it only ; and this is in all cases less than the light which an enlargement of the object would emit, and may differ from it in other respects also. It is, accordingly, to the study of what these visual substitutes are that we should apply our- selves. But as this is a branch of optics which is as yet almost wholly unexplored *, we must, for the present, be content with the inferences we can draw from such general considera- tions as the following :— 15. Proposition 3.—The objective of a microscope has an angular aperture which is necessarily less than 180°. Hence the image formed by it is formed by a part only of the light emitted by the object. Imagine a hemisphere in front of the object, of so large a size that the whole object may be treated as though it were * In one simple case investigated by the writer the visual substitute fora thin line of light proved to be a double line with a narrow interval and with very thin appendage-lines on either side. Here we have some of the phenomena presented by microscopes—a spurious resolution into a double line, and appendage-lines which are of the same nature as inter- costal markings. See abstract of communication to British Association, at p. 583 of the ‘ Report’ for 1894, 344 Dr. G. J. Stoney on Microscopie Vision. at its centre. The luminous beams* of plane waves, each emanating from the whole front of the surface of the object, spread over this hemisphere, and the only case we need at present consider is where the pupil of the eye (in naked-eye observations) or the front lens of the objective (when we use a microscope) takes in only the beams A, viz., those beams of parallel waves thrown off from the surface of the object which are directed towards the middle sector of the hemisphere, and fails to admit the beams B, which are directed towards the mar- ginal parts of the hemisphere. The excluded beams are partly Ba, those which, if reversed, form the finer of the rulings that go to build up the standard image. The rest of these beams, viz. Bb, are the more oblique members of those fans of beams which produce the coarser rulings—the whole of the standard image being made up of these finer and coarser rulings (see § 9), whereas the image seen by the observer is made up by the beams A alone—by those which the front lens of the objective can catch. : Let us now define —B to be the same light as + B, except that all the phases in —B are at each instant the reverse of what they arein +B. In other words we get the light —B by adding a to all phases in the light B; hence if the light +B and the light — B are both present, they exactly cancel one another. Now the whole light emitted by the object is A+B; and it is this light which forms the standard image. Hence, if we add the light —B to the standard image, and can find what modification of that image is thereby effected, we thus arrive at the best image which the light A can form: an image which the image actually formed on a large scale by the objective may approach in perfection, but cannotexceed. We may appropriately name it Standard Image No. 2. In order to arrive at standard image No. 2, we may add the portions of light —Ba and —Bd in succession to standard image No. 1, as these together make up the whole of the light | —B. The addition of —Ba simply obliterates the finer of the rulings out of which the standard image is constructed. * It is convenient to use the word undulation where the waves extend to an infinite or to an indefinite distance in their plane, and to employ the terms beam and pencil where we intend the lateral extent of the waves to be regarded as limited. Practically luminous beams of plane waves emanating from the objective field, which is, of course, of limited extent, may be used instead of the undulations of the theory, which emanate from the entire objective plane; since the waves of a beam, unless very narrow, do not differ sensibly from the waves of the undulation, except close up to its bounding eylinder. Dr. G. J. Stoney on Microscopic Vision. 345 ‘The chief (though not quite the only) effect of this is simply to render the image incapable of exhibiting some very fine detail upon the object which before it was able to reach. But the addition of — Bd has a worse effect. J+ udds to the image an entirely new set of fine rulings which do not represent any of the features which exist upon the object, and by this ight such false effects as intercostal markings, spurious resolutions, a general haze of light, &., are apt to be, and often are, pro- duced. Hence we may enunciate Proposition 3 as follows:— -Propostrion 8. When, of the light emitted by the olyject, only part is employed to form the microscopic image, then features may. intrude them- selves into the microscopic image which are not present in the standard image, and which do not represent anything upon the object. | | | 16. Proposition 4. False Colouwration—Another deceptive effect which is to be referred to the limited apertures of objectives is the appearance given to uncoloured objects of being coloured. Only the general principle to be kept in view will be stated here, as a fuller treatment of this phe- nomenon can be more conveniently made in connexion with individual instances which will be dealt with in Part II. of this memoir. . The whole light of wave-length X which is sent forward by the object may be divided into A, which is admitted to the objective, and B, which is excluded. A similar partition into these two portions is to be made of the whole light of each wave-length, but the proportion in which the whole light is divided between them in general varies from one wave-length to another. Hence, if the illumination is by white light and the object uncoloured, there may be a pre- ponderance of Leht of some colours in A as compared with others, and an equal deficiency of these same colours in B. In such cases the image seen in the microscope, since it is exclusively formed by the light A, has not got the colours mixed in the same proportions as they are in white light, and accordingly appears coloured. Hence PROPOSITION 4. Under the same circumstances as in Proposition 3, the par- tition of the light between the portions rececved by and excluded from the oljective, will in general be different for different wave- lengths ; and-when the difference is marked a colourless object will appear to be coloured in the mreroscope. 346 Dr. G. J. Stoney on Microscopic Vision. 17. Proposition 5. The Condenser.—The standard image admits of being either better or worse. It manifestly admits of being improved by forming it out of light of shorter wave- length ; and this may be accomplished either by exchanging the colour of the illumination employed for a colour of higher refrangibility, or by mounting the object ina highly refracting medium. 3 But the degree in which the standard image correctly represents the object. usually depends even more upon the condenser. In fact, the disturbance of the ether in front of the object is determined partly by the features of the object and partly by the condition of the light which illuminates it. This is evident because if the reversal spoken of in § 8 were to take place without removing the object, the light in re- tracing its steps would first reproduce the disturbed state that had existed in front of the object ; would next form the standard image upon the surface of the object ; and would then pass through the object and form beyond it whatever disturbed state of the ether had existed between the con- denser and the object. Hence, that the standard image may represent the features of the object unmixed with other appearances not belonging to the object, it is essential that the light provided by the condenser shall be as nearly uniform and featureless as possible where it reaches the part of the object which is being scrutinised. Hence the importance of thin sections, and of a very well-corrected condenser. The management of stops, and their function, can be better treated of in Part II. of this memoir, when we can enter into details. For the present we content ourselves with a very general proposition, viz. :— PROPOSITION 5. The standard image is the outcome, partly of the features upon the object, and partly of the state of the light by which the object 7s illuminated. It may be improved by increasing the degree in which the first of these factors, and by decreasing the degree in which the second, contributes to produce, to modify, or to efface detail in the image. 18. Proposition 6.—When an object is mounted in a more refractive medium than that in front of the objective, standard image No. 1, which depends on the wave-length of the light as it quits the object, is thereby improved ; but standard image No. 2 is not enabled to grasp any finer detail upon the object than it would have grasped if the object had been in a medium - of the same refractive index as that in front of the objective. Dr. G. J. Stoney on Meroscopic Vision. 347 That is, none of the luminous rulings which form the useful part of standard image No. 2—none of those that represent any feature of the “object, excluding those which produce false effects like intercostal markings—are made any finer by mounting the object in a medium of extra high refractive index. But nevertheless an important effect is pr sroduced, Viz. that the finer of the rulings are made relatively brighter than they were before, so that, ceteris paribus, the detail which they portray becomes more conspicuous. This is evident from the accompanying diagram, in which ab is the front of the objective and o the object. Both figures a 6 (a a ee T 4) represent the course of one of the more oblique beams of parallel waves from the whole surface of the object, the first figure representing what occurs when the object is mounted in a medium of the same refractive index as the cover-glass and immersion oil, and the second figure representing what occurs when the object i is mounted in an optically denser medium. Ceteris paribus, the ratio of the brightness of the beam that reaches the objective in the two cases is as cosi/cos 7, which son ); where n and n’ are the refractive indices in the two media. 348 Dr. G. J. Stoney on Microscopie Vision. This is a fraction which the more deviates from unity the greater 7 is, 1.¢. the more oblique the beam. Hence, the more oblique beams, which bring out the finer detail, are more increased in brightness than the less inclined, which deal with the larger features of the object. Hence PROPOSITION 6, Mounting the olject in a medium of eatra high refractive index will, ceteris paribus, increase the conspicuousness of the jiner detail to be seen upon tt. Of course other factors, some of which may be even more potent, have to be taken into consideration, such as the ratio of the index of refraction of the object to that of the medium in which it is mounted ; for the farther this ratio is from unity, the more conspicuous do all the features of the object become. 19. Proposition 7. Optical Contact—Another proposition which is of use in interpreting the phenomena presented by the microscope is a consequence of the condition of the ether in the rare medium when light is totally reflected from a surface separating a dense and a rare medium. What then occurs has been investigated by Sir George Stokes, in his masterly paper “On the Formation of the Central Spot of Newton’s Rings beyond the Critical Angle”’ (vol. ii. of Stokes’s Collected Papers, p. 56). It is therefore only necessary here to enunciate the result of that investigation in the form in which it explains optical events which the micro- scopist has occasion to make use of. Normally, when a microscopic object is ‘‘mounted dry,” 2.é€. is situated in an air-space between the slip and the cover-glass, no rays from it can, while traversing the cover- glass, be more inclined to the vertical than the “ critical angle.” Now immersion objectives are specially designed to admit rays that have passed upwards through the cover-glass in more inclined directions. Accordingly, when an object that is mounted dry is examined by an immersion objective, what normally happens is that only a part of the aperture of the objective is made use of. The event is, however, different if the microscopic object is excessively close to the cover- glass, owing to the phenomenon investigated by Sir George Stokes. | It follows from Sir George Stokes’s investigation that when a plane separates an optically dense from a rare medium, then there is a very thin layer of the rare medium of which the optical properties are peculiar. In cases of total reflexion, the 15 Dr. G. J. Stoney on Microscopic Vision. 349 ether within this layer is brought into a disturbed condition. The disturbance in reality penetrates further down, but fades out by a law so rapid that it is only sensible within a very short distance (which depends on the wave-length) of the plane separating the media. ‘The layer of this small thickness, within which the disturbance is sensible, may be called the Stokes’s Layer. It further follows from the investigation, that if light emanates from a point within the Stokes’s layer, it will be able to pass up through the dense medium at angles that exceed the critical angle. It is easy to verify this experimentally. Take a glass prism—one of the pendants of a glass chandelier is sufficient. Hold it at the distance of distinct vision from the eye, and turn it till the light of the sky is seen like a silvery sheen, totally reflected from the inside of one of its faces. Then, without moving the prism or the eye, press a piece of chalk against the outside of that face. A small portion of the chalk can thereby be brought so close to the glass that the intervening chink is less than the thickness of the Stokes’s layer. This small portion of the chalk will then be seen through the face of the prism, while the rest of the chalk and the hand that holds it, which are beyond the Stokes’s layer, are quite unseen. The light from the chalk, by which it is seen, has obviously passed through the glass at an angle which is beyond the critical angle. Similarly : PROPOSITION 7. Tf a microscopic olject, mounted dry, is so close to the cover- glass that the chink of air between it and the cover-glass is less than the thickness of the Stokes’s layer, then light from it can pass up through the cover-ylass and the owl above it, at angles both within and beyond the critical angle, and may accordingly reach any part of the front of an objective whose NA is more than 1. 20. With the help of these seven propositions, supple- menting the more familiar Jaws of optics, nearly everything in microscopic vision may be explained, and useful rules can be deduced for the manipulation of the instrument. The next part of this memoir will deal with applications of this kind. [To be continued. | frs50 4 XXXVI. The Genesis of Dalton’s Atomic Theory. By Henry Drsus, PA.D., FRS* IR H. E. ROSCOE and Mr. A. Harden have lately published a book f entitled ‘A New View of the Origin of Dalton’s Atomic Theory,’ with the following introductory remarks :— 7 ‘“‘Jt may seem remarkable that, after the lapse of nearly a century, since John Dalton first applied the atomic theory of matter to chemical phenomena, it should be possible to find anything new respecting the genesis of his ideas. The ex- planation is to be found in the unlooked for discovery, in the rooms of the Literary and Philosophical Society of Manchester, where the whole of Dalton’s experimental work was carried out, of his Laboratory and Lecture Note-Books contained in a number of manuscript volumes. A careful study of these has led us to conclusions concerning the origin of the atomic theory of Chemistry which differ widely from those which have been generally accepted. It has hitherto been supposed that it was the experimental discovery of the law of combina- tion in multiple proportions which led Dalton, seeking for an explanation of this most remarkable fact, to the idea that chemical combination consists in the approximation of atoms of definite and characteristic weight, the atomic theory being thus adopted to explain the facts discovered by chemical analysis. ... The actual relations are, therefore, precisely the inverse of those which are usually accepted. Itwas the theory of the existence of atoms of different weights which led Dalton to the discovery of the facts of combination in multiple pro- portions.” This view of Roscoe and Harden is not new! Two years ago 1 published a pamphlett, wherein it is clearly stated that the atomic theory led Dalton to the discovery of the law of multiple proportions. It is gratifying to me that Dalton’s Note-books confirm the view expressed by me in May 1894. In the same essay (p. 58), I have shown that several years before Avogadro Dalton had formed the hypothesis that equal volumes of different gases contain under normal conditions of temperature and pressure an equal number of molecules. * Communicated by the Author. t ‘A New View of the Origin of Dalton’s Atomic Theory, a Contri- bution to Chemical History,’ by Henry EK. Roscoe and Arthur Harden. London: Macmillan & Co. 1896. t ‘Ueber einige Fundamentalsatze der Chemie, insbesondere das Dalton-Avogadro’sche Gesetz. Hine historische Untersuchung von Dr. Heinrich Debus.’ Cassel: Gustay Klaunig, 1894, pp. 44-45. The Genesis of Dalton’s Atomic Theory. ao1 According to Roscoe and Harden this latter statement of mine is not correct. My argument rests, they assert, on a confusion between the relative density of the atoms and the relative density of the gases made up of these atoms. I cannot allow Dalton’s merits to be set aside in this manner, and I feel at the same time obliged to show that I am not guilty of the mistake attributed to me. The atomic theory and the law of equal volumes (law of Avogadro) constitute the basis of scientific chemistry. As it is a matter of importance for everyone to know how the foundation of his house has been laid, I believe the following discussion will not be. unacceptable to scientific chemists, especially on account of some new matter considered in it. As Dalton’s nomenclature and views differ in several points from those now in vogue, a few explanations will be necessary. The elementary gases consist, according to Dalton, of very small, indivisible particles, called atoms. Hach atom is sur- rounded by an atmosphere of heat of from one to two thousand times its own size. Whatever, therefore, may be the shape or figure of the solid atom abstractedly, when sur- rounded by such an atmosphere it must be globular ; but as all the globules in any small given volume are subject to the same pressure, they must be equal in bulk, and will, there- fore, be arranged in horizontal strata, like a pile of shot (N.S, 145). The volume of the molecule of a gas is equal to the volume of the solid nucleus plus the volume of the atmosphere of heat. Compound molecules result from the juxtaposition of two or more different atoms. A molecule of oxygen is composed of only one atom of oxygen, a molecule of carbonic oxide of an atom of carbon and one of oxygen. Dalton usually employs the word atom ; he calls a molecule of water an ‘‘ atom of water ;”’? a molecule of ammonia an “ atom of ammonia.” I shall express Dalton’s ideas in modern phrase- ology. Abbreviations. N.S. stands for: ‘New System of Chemical Philosophy,’ by John Dalton. Manchester, 1808-1810. R. i » ‘A New View of the Origin of Dalton’s Atomic Theory,’ by H. H. Roscoe and A. Harden. London: Macmillan & Co., 1896. O. i; 5 Ostwald’s Klasstker, No. 8. Leipzig: W. Hngelmann. * » Alembic Club Reprints, No. 2. Edinburgh: W. F. Clay. 352 Dr. H. Dabus on the Genesis of D. stands for ‘ Ueber einige Fundamentalsitze der Che- mie, insbesondere das Dalton-Avoga- dro’sche Oe von Dr. Heinrich Debus. Cassel: Gustav Klaunig, 1894. M ‘3 » Molecular Weight. : S . » Specific oravity. M/S = 5, Molecular volume. Division of numbers is expressed thus, M/S: M Zz = IS3 (Oz kn) page ... in this paper. The empirical law that equal volumes of different gases contain, at normal temperatures and pressure, an equal num- ber of molecules will be represented by the symbols M/S=C. I, DALTON’s Atomic THEORY. The opinion used to be common amongst chemists * that Dalton had originated the idea of indivisible particles (atoms) for the explanation of the law of multiple proportions. This, however, is not the case. The idea that the objects of ob- servation are aggregates of exceedingly small indivisible par- ticles is older than science itself; it is attributed to a Phe- nician philosopher, Moschus, living at Sidon at about 1100 B.c. (D. 35). His views, developed by the Greeks, were forgotten after the destruction of the Roman empire, but resuscitated by Gassendi about the middle of the 17th century. Boyle, who called the atomic hypothesis the Phenician philosophy 7, applied it to the explanation of chemical phenomena, and Newton to the explanation of Boyle’s law. Also the chemists of the last century employed the atomic doctrine for the illustration of chemical change (D. 38-40). Dalton, who — seems to have obtained the idea of atoms from Newton (R. 13, 123), applied it, almost from the beginning of his scientific career, to the explanation of physical phenomena, such as diffusion, absorption, and expansion. In 1803 he discovered a method how to determine the relative w eight of atoms, and added to the atomic philosophy a series of principles. The group of principles so added by Dalton I propose to eail Dalton’s ‘atomic theory.” The Sale (putas are :— * Liebig, Handbuch der Cheme, Heidelberg, 1843, P: 65. + ©The Pwo of the Right Hon. Robert Boyle.’ London, 1744, vol. i. p. 228. Dalton’?s Atomic Theory. Soa (1) When only one combination of two bodies, A and B, can be obtained, it must be supposed to be a binary one, a compound of one atom of A with one atom of B, unless some cause appear to the contrary. (2) When two combinations are known, they must be pre- sumed to be a binary (A+B) and a ternary (A,+ B) or (A+B,). (3) When three combinations are obtained, we may expect one to be a binary and the other two ternary. (4) When four combinations are observed, we should ex- pect one binary, two ternary, and one quaternary (A,+ B) or (A+ Bs). . (5) A binary compound should always be specifically heavier than the mere mixture of its two ingredients. (6) A ternary compound should be specifically heavier than the mixture of a binary and a simple which would, if combined, constitute it; &e. (7) The above rules and observations equally apply when two bodies, such as (C+D) and (D+E) are com- bined (N.S. 214). : The question is: How did Dalton arrive at these principles ? Roseoe and Harden think that the answer to this question is contained in some notes which Dalton had written down for a lecture delivered in London on Jan. 27th, 1810 (R. 138). The pertinent passages of the notes are as follows :— “ As the ensuing lectures on the subject of chemical ele- ments and their combinations will perhaps be thought by many to possess a good deal of novelty as well as importance, it may be proper to give a brief historical sketch of the train of thonght and experience which led me to the conclusions about to be detailed. “Having been long accustomed to make meteorological observations, and to speculate upon the nature and constitu- tion of the atmosphere, it often struck me with wonder how a compound atmosphere, or a mixture of two or more elastic fluids, should constitute apparently a homogeneous mass, or one in all mechanical relations agreeing with a simple atmo- sphere.” In explanation of the foregoing remarks it may be men- tioned that the molecules of all gases, therefore the atoms of the constituents of the atmosphere, oxygen and nitrogen, were at the time assumed by Dalton to be of equal volume: in other words, equal volumes of oxygen and nitrogen gas would, under normal conditions, contain an equal number of mole- cules (N.S. 188). Hence the specific gravity of an atom of Phil. Mag. 8. 5. Vol. 42. No. 257. Oct. 1896. 2 BD4 Dr.-H. Debus on the Genesis of oxygen must be greater than the specific gravity of an atom of nitrogen. This view, in connexion with the general theory of gases then in vogue, led to the conclusion that, in a mixture of oxygen and nitrogen, the heavier atoms of oxygen ought to form a layer at the bottom of the vessel and the lighter nitrogen atoms a separate layer at the top. - Experiments, on the other hand, proved that air, taken from different heights, was of uniform composition. Dalton also found that a lighter gas, placed above a heavier gas, will gradually diffuse downwards (N.S. 151). To explain these observations a weak chemical affinity was assumed between the molecules of different gases. The globular molecules Dalton considered to be arranged like a pile of shot (N.S. 145, 147), and as all the molecules are subject to the same pressure and exert the same counter-pressure, they must be all, independent of their nature, of the same size (N.S. 188), M/S == M’/S’= M”/S”= Ve Se The air is composed of 77°88 vols. of nitrogen, 21:2 vols. of oxygen, and 0°066 vol. of carbonic acid. Hence, according to the above law, for every molecule of carbonic acid there are 31°8 mols. of oxygen and 118 mols. of nitrogen present in eur atmosphere. Now, if a weak chemical affinity is the cause of diffusion, then compounds of a very complicated nature must result. This appeared to Dalton very improbable, and accordingly he rejected the chemical explanation of the diffusion of gases. Dalton goes on with his notes as follows :— “In the year 1801 I hit upon an hypothesis (N.S. 153) which completely obviated these difficulties. According to this, we were to suppose that the atoms of one kind did not repel the atoms of another kind, but only those of their own kind. This hypothesis most effectually provided for the dif- fusion of any one gas through another, whatever might be their specific gravities, and perfectly reconciled any mixture of gases to the Newtonian theorem (R. 15). Every atom of both or all the gases in the mixture was the centre of repul- ‘sion to the proximate particles of its own kind, disregarding those of the other kind. All the gases united their effort in counteracting the pressure of the atmosphere, or any other pressure that might be opposed to them. This hypothesis, however beautiful might be its application, had some impro- ‘bable features. We were to suppose as many distinct kinds -of repulsive power as of gases ; and, moreover, to suppose Dalton’s Atomic Theory. - 355 that heat was not the repulsive power in any one case ; positions certainly not very probable. ‘““ Upon reconsidering this subject, it occurred to me that I had never contemplated the effect of difference of size in the particles of elastic fluids, or when the expression M/S=C is of different value for different gases. And if the sizes be different, then on the supposition that the repulsive power is heat, no equilibrium can be established by particles of unequal sizes pressing against each other. . “This idea occurred to me in 1805. I soon found that the sizes of the particles of elastic fluids must be different. For a measure of azotic gas and one of oxygen, if chemically united, would make nearly two measures of nitric oxide, and those two could not have more molecules of nitric oxide than one measure had of oxygen or nitrogen. “Hence the suggestion that all gases of different kinds have a difference in the size of their molecules ; and thus we arrive at the reason for that diffusion of every gas through every other gas, without calling in any other repulsive power than the well-known one of heat. “This then is the present view which I have of the consti- tution of a mixture of elastic fluids (year 1810). The different sizes of the particles of elastic fluids under like circumstances of temperature and pressure being once established, it became an object to determine the relative sizes and weights, together with the relative number of atoms in a given volume. ‘This led the way to the combinations of gases, and the number of atoms entering into such combinations, the particulars of which will be detailed more at large in the sequel..... es (R. 13-17). From these statements of Dalton, Roscoe and Harden deduce the following genesis of the atomic theory :— ‘The balance of evidence is, therefore, strongly in favour of the statement made in London by Dalton himself in 1810, that he was led to the atomic theory of chemistry in the first instance by purely physical considerations in opposition to the view hitherto held by chemists, that the discovery by Dalton of the fact of combination in multiple proportions led him to devise the atomic theory as an explanation. It, there- fore, becomes necessary for us to modify our view as to the foundation of the atomic theory. There seems to be no doubt that the idea of atomic structure arose in Dalton’s mind as a purely physical conception, forced upon him by his study of the physical properties of the atmosphere and other gases. Confronted, in the course of his study, with the problem of ascertaining the relative diameters of the par- 2C2 356 Dr. H. Debus on the Genesis of ticles, of which, he was firmly convinced, all gases were made up, he had recourse to the results of chemical analysis. Assisted by the assumption that combination always takes place, in the simplest possible way, he thus arrived at the idea that combination takes place between particles of different weights, and this it was which differentiated his theory from the historic speculations of the Greeks. The extension of this idea to substances in general necessarily led him to the law of combination in multiple proportions, and the. com- parison with experiment brilliantly confirmed the truth of his deduction ” (R. 49-51). The problem of ascertaining the relative diameters, or rather the relative volumes, of the molecules of different gases, led Dalton, according to Roscoe and Harden, to the invention of the atomic theory. Inthe pamphlet mentioned before (p. 350), I have stated that Dalton wished to verify the hypothesis M/S=C, viz. to ascertain whether the molecular volumes of different gases are of equal or of different magnitudes. For this purpose he required to know the respective molecular and atomic weights. This necessity led him to the formation of the atomic theory (D. 58). I am much pleased to observe that, with regard to the problem which originated the atomic theory, Roscoe and Harden, after a careful study of Dalton’s note-books, arrive at the same view which I published two years ago, but I regret very much that I cannot approve the reasons which have guided their judgment. The first assertion of Roscoe and Harden, “the balance of evidence is, therefore, strongly in favour of the statement made in London by Dalton himself in 1810, that he was led to the atomic theory of chemistry, in the first instance, by purely physical considerations,’ I have not met, nor do I remember to have seen in any of Dalton’s writings, nor am I able to deduce such an assertion from Dalton’s notes, quoted before. These notes treat of two distinct subjects, the theories of gaseous diffusion and the problems of the atomic theory. The description passes abruptly from the one to the other without any connecting link. How did Dalton get over the chasm which separates the two? We want to know the genesis of Dalton’s methods of determining atomic weights. This, the essence of the matter, Messrs. Roscoe and Harden pass over in silence ! Dalton explained the diffusion of gases on the assumption that the molecules of different gases are not of the same size. The question, therefore, was, Are the molecules of different gases really of unequal volume? “J soon found,” says Dalton’s Atomic Theory. 3957 Dalton,” that the sizes of the particles of gases must be dif- ferent. Fora measure of azotic gas and one of oxygen, if chemically united, would make nearly two measures of nitric oxide, and those two could not have more atoms (molecules) of nitric oxide than one measure had of azote or oxygen. Hence the suggestion that all gases of ditferent kinds have a difference in the size of their molecules ; and thus we arrive at the reason for that diffusion of every gas through every other gas....” (R. 16-17). The old view of Dalton, that in gases the force of cohesion is quite overcome by the force of repulsion, and that, in consequence, the particles of the elementary gases consist of single atoms, would lead to the conclusion which he drew from the volumetric proportions of nitrogen and oxygen in nitric oxide, without requiring the atomic theory as described on p. 353. Passing on to the atomic theory we have the remarks :— “The ditterent sizes of the particles of gases, under like circumstances of temperature and pressure, being once estab- lished, it became an object to determine the relative sizes and weights together with the relative number of atoms in a given volume.” If we remember that these quotations are not from a running narrative, but from notes intended for a lecture, where the lecturer could at any moment make verbal explanations and additions, then we may ask whether, between the notes on the diffusion of gases and those on the atomic theory, there is, or there is not, a connexion similar to the one between cause and effect, as Roscoe and Harden assume? On this point Dalton is absolutely silent. We wish to know the origin of the methods by means of which Dalton determined the size, weight, and numbers of the atoms ; and we cannot discern how he arrived at these methods from his theory of gaseous diffusion. Messrs. Roscoe and Harden do not say one word on this subject. May not Dalton have been engaged in the calculation of molecular and atomic weights and molecular volumes before he recog- nized that the size of the molecules of different gases Must be different? A few facts show that he was so engaged. The idea of considering the influence of the size of the mole- cules on diffusion occurred to Dalton, according to his own statement, in 1805. The result of his consideration was the abandonment of the theory of diffusion formed in 1801 (de- scribed on pp. 354, 355), and the formation of a new view, which ascribed diffusion to difference of size of the molecules of the diffusing gases. | This new view is, according to Roscoe and Harden, the source of Dalton’s atomic theory. If so, then the atomic 358 Dr. H. Debus on the Genesis of theory cannot have been formed before the year 1805. But Roscoe and Harden found in Dalton’s note-book a table of atomic weights dated the 6th of September, 1803. This date shows that the theory is at least two years older than it ought to be according to Roscoe and Harden’s view (R. 29). In order to get over this difficulty, they assume (R. 25) that Dalton committed a clerical error by writing 1805 instead of 1803 in his description of the formation of the theory of diffusion based on an unequal size of the particles. Daltcn does not say that the theory of diffusion led him to the con- ception of the atomic theory. The statement that it did do so is only an inference of Messrs. Roscoe and Harden. Therefore they are not justified in attributing a clerical error to him, and transferring the conception of the theory of diffusion from 1805 to 1803. Dalton’s paper, “ Experimental Enquiry into the Pro- portions of the several Gases or Hlastic Fluids constituting the Atmosphere,’ was printed in the ‘ Memoirs of the Literary and Philosophical Society of Manchester,’ second series, vol. 1. 1805, under Dalton’s supervision as Secretary of the Society (R. 31). We have in this paper the following remarks on the principle that the elastic or repulsive power of each molecule is confined to its own kind :—“ This principle accords with all experience, and, I have no doubt, will soon be perceived and acknowledged by Chemists and Philosophers in general” (Al. 5). Now this principle is the principle of the theory of diffusion formed in 1801 (pp. 354, 355); consequently he must have still held this theory in 1805, at the time when the paper was printed, and the theory of diffusion which superseded it must have been formed at a later period in the year 1805. Therefore this later theory of the diffusion of gases cannot have been the origin of the atomic theory of 1803. The conclusion we arrive at is: “ The opinion of Roscoe and Harden that the theory of the diffusion of gases of 1805 led Dalton to the con- ception of his atomic theory is not in accordance with facts.” II. The Genesis of Dalton’s Atomic Theory. The notes published by Roscoe and Harden enable me to render my view of the genesis of this theory, described on p- 356 (D. 58), more accurate and complete. In order to explain equilibrium in a mixture of gases, Dalton had adopted, in the year 1801, the hypothesis M/S=C. But he was not able for several years to test his conception by experiments, as no method was known for the determination of M, the molecular weight. The desire to discover such a method made him, probably, very observant of all circum- stances which could promote his wish (N.S. 187-188). Dalton’s Atomic Theory. ~ 309 Two factors determine every great advance in science—a fact, and a mind prepared for the full and complete appre- ciation of the fact. Moreover, the fact must be at hand when it is wanted by the mind. These conditions were satisfied when Galileo observed the oscillating lamp in the Cathedral of Pisa; when Newton saw the falling apple ; when Malus observed the ray reflected from the window of the Luxem- bourg ; when Lavoisier was informed of the discovery of oxygen by Scheele and Priestley (D. 20-21). The discovery of oxygen is the great fact with which the history of scientific chemistry commences ; but neither of the discoverers—neither Priestley nor Scheele—recognized the significance of the discovery. Lavoisier’s mind was the good soil wherein the seed bore fruit, because it was well prepared by a careful repetition of the experiments of Black and Mever. These experiments prove that carbonates are combinations of a gas which can be transferred from one base to another. Quicklime absorbs carbonic acid from the atmosphere and turns into carbonate of lime. These facts raised in Lavoisier’s mind the question : Do metals absorb a gas from the atmo- sphere during calcination? The answer from his own expe- riments was a decided “ Yes.”? But as he could not prepare the gas absorbed, the investigation could not proceed. Then, just at the right moment, Scheele and Priestley informed Lavoisier of the discovery of oxygen, and the antiphlogistic chemistry was born (D. 21). Dalton, the meteorologist, wished to determine the compo- sition of the atmosphere. Tor this purpose he tried the absorption of oxygen with nitric oxide. In his note-book occurs the following memorandum, dated August 4th, 1803:— ‘It appears, too, that a very rapid mixture of equal parts of common air and nitric oxide give 112 or 120 residuum. Consequently, that oxygen joins to nitric oxide sometimes 1:7: 1 or at other times 3°4:1” (R. 38, Al. 8). _ In the Essay on the Composition of the Atmosphere occurs the remark, ‘‘ These facts clearly point to the theory of the process ; the elements of oxygen may combine with a certain portion of nitric oxide, or with twice that portion, but with no intermediate quantity’ (R.33, Al. 9). A month after the date of the above note, on September 6th, 1803, the note-book contains a list of atonsic weights (R. 29), and on the 19th of the same month the diameters of the molecules of a certain number of gases were written down R. 41). . May we venture to conclude, on the strength of these facts, that the observations of the proportions in which nitric oxide and oxygen combine over water originated in Dalton’s mind 360 Dr. H. Debus on the Genesis of the idea that the atoms combine chemically only according to very small numbers—one atom of A with one, two, or three atoms of B? ‘There are strong reasons in support of this conclusion. Dalton, who for some years had held the hypothesis M/S=C (N.S. 188), who was accustomed to explain expansion, diffu- sion, solution, &c., in a mechanical way by means of the old atomic theory, as Boyle did 120 years before Dalton’s time, was naturally led by the observation of the combining pro- portions of oxygen and nitric oxide to the view that in simple compounds one atom of A is united to one or two atoms of B. His previous speculations and observations (p. 354) had prepared him for this conception, and once the idea was formed the transition to the tenets described on p. 353 was easy. Proust and others had made observations like Dalton, but to none had this explanation occurred. My present view of the origin of Dalton’s atomic theory 1s :— Dalton wished to verify the hypothesis M/S=C;; for this purpose he endeavoured to find methods for the determination of the atomic and molecular weights. The observations of the combining proportions of nitric oxide and oxygen suggested to him a principle which enabled him to form such methods. In judging this view, one has to remember that the obser- vations on the combining proportions of oxygen and nitric oxide noted on August 4th, 1803, were followed within a month by calculations of atomic weights and the diameters of atoms and molecules. (R.38 and 41.) III. Roscoe and Harden’s Critique. The first part of my view of the genesis of Dalton’s atomic theory, described above, is, according to Roscoe and Harden, not correct. They say :— ““The view expressed by Debus, that the use of the term specific gravities by Thomson in his account of the atomic theory implied the acceptance of the law M/S=C by Dalton in 1804, is also seen to be incorrect. Dalton expressly states in 1803 (R. 27) that the specific gravities of different gases and the specific gravities of their particles are not the same thing. He never appears to have believed in the law M/S=C, and this only occurred to him as a possible alternative, at once shown to be inconsistent with fact, to the statement which he recognized as the true one, viz. that no two gases agree in the size of their particles” (R. 47). In order to forma correct opinion of the assertions contained in this quotation, we must go back and consider the statements of Dalton on which these assertions are founded. _Dalton’s Atomic Theory. 361 Dalton, in his Note-book, i. p. 246 (R. 27), has the following memorandum :— “ Though it is probable that the specific gravities of different elastic fluids (gases) has some relation to that of their ultimate particles, yet it is certain that they are not the same thing ; for the ulterior particles of water or steam are certainly of greater specific gravity than those of oxygen, yet the last is heavier than steam.” Instead of building on the dictum contained in this quotation weighty conclusions, as Messrs. Roscoe and Harden do, I confess that I do not understand it. What is the difference between the specific gravity of a gas and that of one of its ulterior particles or molecules? According to Dalton, the molecular volume is =M/S (N.S. 226, note). The specific gravity of a molecule, s, is expressed by the quotient of the molecular weight and molecular volume : Molecular weight M _ at Molecular volume M/S~ °~ * Hence, 8, the specific gravity of the gas, =s, the specific gravity of one of its molecules ; or, in other words, both are the same thing. This result follows from Dalton’s definition of the molecular volume, and is opposed to his assertion that the specific gravities of gases and the specific gravities of their molecules are not the same thing, and also to the conclusions of Roscoe and Harden, based on this erroneous assertion. Therefore it does not follow that Dalton did never believe in the hypothesis M/S =C, or that the first part of my view stated on p- 360 is incorrect. Messrs. Roscoe and Harden assert that he (Dalton) “ never appears to have believed in the law of equal volumes (hypo- thesis M/S=C), and this only occurred to him as a possible alternative, at once shown to be inconsistent with fact, to the statement which he recognized as the true one, viz. that no two gases agree in the size of their particles ” (R. 47). What does Dalton himself say on this subject ?—“ At the time I formed the theory of mixed gases (year 1801) I had a confused idea, as many have, I suppose, at this time, that the particles of gases are all of the same size, that a given volume of oxygen contains just as many particles as the same volume of hydrogen” (N.S. 188). And with regard to the statement “that no two gases agree in the size of their particles,’ he says, ““This idea occurred to me in 1805.” Therefore the idea that a given volume of oxygen contains just as many particles as the same volume of hydrogen occurred to Dalton at least four years before the time at which he recognized 362. Dr. H. Debus on the Genesis of “that no two gases agree in the size of their particlés.” ~Con- sequently, the first idea (M/S=C) did not “ oceur to him only. as a possible alternative, at once shown to be inconsistent with fact, to the statement which he recognized as the true one, viz. that no two elastic fluids agree in the size of their particles,” but was held by Dalton, more or less, from 1801 to 1805, and only abandoned when he could not bring it into agreement with his later atomistic views. It has been shown on p. 361 that the memorandum in Dalton’s Note-book, i. p. 246, is not correct, and that the specific gravity of a gas and the specific gravity of one of its molecules are the same thing. But how, we may ask, could Dalton contradict his own definition? On p. 260 of his Note-book, i. (R. 42), occurs a table with the following heading :—“ The molecules of gases arranged according to their specific gravities ;” and then follow in arithmetical order the molecular weights of eleven gases. The specific gravity of the molecules and the molecular weights are therefore expressed by the same number. : If M represents the molecular weight, s the specific gravity, and v the volume of a molecule, we have WV == As M is put =s, v must be =1; and as this relation is assumed to be general, all gases have the same molecular volume, or M/S=C. Hence the molecular weight and the specific gravity of a molecule are then, according to the table, ‘“‘ the same thing.” If we now substitute in Dalton’s memorandum quoted on p- 361, which is not intelligible by itself, for the words “ spe- cific gravities of molecules” the words ‘‘ molecular weights,” we obtain :—“ Though itis probable that the specific gravities of different elastic fluids (gases) has some relation to their molecular weights, yet it is certain that they are not the same thing ” (R. 27)—a perfectly intelligible statement. | Therefore, on p. 246 of Note-book, i., the hypothesis M/S=C is rejected, and on p. 260 accepted. ~ How are these contradictory statements to be explained ? On p. 188 of his celebrated work, ‘ New System of Che- mical Philosophy,’ Dalton says :—“ At the time I formed the theory of mixed gases, I had a confused idea, as many have, I suppose, at this time, that the particles of gases are all of the same size.” Consequently there was a time when Dalton believed in the hypothesis M/S=C, and his endeavour was to verify the same by experiment. Accordingly, he lost no time in calculating M for oxygen and steam, as soon as he had Dalton’s Atonie Theory. 363 formed his atomic theory. According to this theory, the mole- cular weight of steam ought to be greater than the molecular weight of oxygen, and this result in connexion with the hypo- thesis M/S=C would require the specific gravity of steam to be greater than the specific gravity of oxygen. Hxperiments gave opposite resuits; they made the specific gravity of oxygen greater than the specific gravity of steam. Hence, one of the two—the new atomic theory or the hypothesis M/S=C—must be wrong. Dalton rejected the latter (Note- book, 1. p. 246). The extension of the investigation to other gases, however, furnished several examples which gave nearly the same value for M/S=C. Note-book, i. p. 258 (R. 41), contains a table of 12 gases with their specific gravities and Dalton’s molecular weights. I have recalculated the specific gravities on the unit of hydrogen, and in place of the diameters of molecules calculated by Dalton i have deemed it sufficient to give the molecular volume, M/S. Taste of the 19th Sept. 1803 (R. 41). Molecular Specific Name of the gas. Weight. Gravity. M/S. REMORSE My or cri aaieiecrelnalsers aeons 1 1:00 1:00 PPG BOM rere gn ainccat onidcupavaeaacioes 5°66 14°60 0°38 J. 1G REL ss hguse ga Sade Sbeacnic suena 4:00 12°5 0:32 Matrous oxide’ i500) 5. esas tects 13°66 20°9 0°65 INIEPIC: OXTAE 5.520450. 0cscenneetee 9°66 14:3 0:67 Carbonic Oxide 2.2, .wecsacce sox 10:10 13:0 0-77 Carbonic acid ........ Bee ee 15-70 19°5 0-80 Pivdrocarbon 2,52 :2.832..)1 eos 540 8°6 0:63 2 TN STO) 1 cee 5:00 7d _ 066 Sulphurous acid s,2,.:.c.d.0sh++-: 20:00 29:0 0:69 Sulphuretted hydrogen ......... 15°40 14:0 11 SIZE TTL ss ee ee nee ee 6°66 9:0 0-74 The values of M/S are not equal for the different gases, but may be arranged in three groups :-— Ee IT. III. M/S. M/S. M/S, Nitrogen ... 0°32 Hydrocarbon ......... 0-63 Hydrogen ... 1:0 Oxygen...... 0-38 Nitrous oxide ......... . 0°65 Sulphuretted | Ve ATMIMONIAs si vc5s>5- oie 0°66 hydrogen j Nitric oxide............ 0-67 Sulphurous acid ...... 0:69 (SO,) SHAM ot. arpecued chieces O74 Carbonic oxide ...... O77 Carbonic acid ......... 0°80 (CO,) 364 Dr. H. Debus on the Genesis of | The values of M/S=C are dependent on the specific gravities, the chemical composition, and the theories about the constitution of gases. ‘The composition of water is, according to Lavoisier, 85 pts. of oxygen and 15 pts. of hydrogen, according to Gay-Lussac and Humboldt 87-4 pts. of oxygen and 12°6 pts. of hydrogen. Lavoisier’s numbers make the atomic weight of oxygen =5°66, Gay-Lussac’s and Hum- boldt’s =7. The errors of observation in Dalton’s time were so considerable that he might have assumed for from 50 to 66 per cent. of the gases in the above list the same molecular volume. The numbers obtained for M/S=C, therefore, le!t it undecided whether the hypothesis, that equal volumes of different gases contain the same number of molecules, is true or not true. The probabilities are, perhaps, slightly in favour of the hypothesis. This seems to have caused Dalton to return to his old view, that the particles of gases are all of the same size, or M/S=C. ‘This is my explanation of the contradictory statements on two pages, 246 and 260, of his Note-book, i. (R. 27, 42) (pp. 861, 362). The near agreement of several of the numbers of M/S in the last table caused a series of new experimental investigations. Dalton, who up to this time had done very little practical work in chemistry, now began with great zeal to determine the composition of important substances, such as ammonia, marsh-gas, and ole- fiant-gas. The results of these investigations, as far as they concern gases, are collected in a table at the end of the second part of the New System. Five out of 16 gases, or 31 per cent., and if errors of ob- servation of 2 per cent. are allowed three more, or, together, 50 per cent. of the gases examined, possess the same molecular volume. JDalton’s experiments have not explained why 50 per cent. of the gases examined do not conform to the hypothesis M/S=C, and they could not do so, the chemical knowledge of the day not being sufficiently advanced. Asa matter of fact, it has required the practical work of half a century to convert the hypothesis M/S=C into an empirical law. . Thomas Thomson, the author of the celebrated work “ Sys- tem of Chemistry,’ himself a chemist of eminence, paid a visit to his friend Dalton in August 1804. On this occasion the latter communicated to him the principles of the new atomic theory and the results obtained by their application. In 1807 a new edition of the ‘System of Chemistry’ came out, in which Thomson, with Dalton’s permission, published a sketch of the new theory (vol. mi. p. 424). Thomson’s de- scription is extremely clear and accurate, and Dalton has, as Dalton’s Atomic Theory. 365 far as I know, never taken exception to any of its statements. Now Thomson always calls the relative weight of atoms the ‘density of atoms.”” His table of molecular weights is called table of the density of atoms (molecules) (vol. i. p. 429). Elementary physics teaches that the weights and densities of substances are proportional when the substances under con- sideration are of the same volume. If we say for density specific gravity, then Thomson’s report of Daiton’s atomic views, and Dalton’s statement in Note-book, i. p. 260 (R. 42) are in perfect agreement. Accordingly, Dalton had not, in August 1804, thrown the hypothesis M/S=C overboard. He did so in the following year, 1805, when he could not bring it. into agreement with his atomistic views (p. 851) ; and when he found it refractory in this respect, he called it “a confused idea’”’ (N.S. 188). Messrs. Roscoe and Harden charge me on pp. 10-11 of their book with a “confusion of ideas.” They say :—“ Debus further argues that when Dalton communicated his theory to Thomson, he must have held the opinion that these two relations, the relative density and the relative weight of the atoms, were identical, or what Debus appears to consider to be the same thing, that the relative densities of the gases were identical with the relative weight of their atoms. .. . On the strength of this argument, which appears to rest on a confusion between the relative density of the atoms and the relative density of the gases made up of those atoms... .” 1 have not asserted that the relative weight and the relative density of the atoms were IDENTICAL. I have expressed my- self in the following manner :—“ We must conclude that Dalton, at the time when he communicated his ideas to Thomson, considered that the molecular weights of the gases stand to each other in the same ratio as the densities of their molecules” (D.51). As for the confusion between the relative density of the atoms or molecules and the relative density of the gases made up of those atoms or molecules, I must refer to p. 361, where it has been shown, if we write for density specific gravity, that according to Dalton’s own definition, the specific gravity of a gas is equal to the specific gravity of one of its molecules. Therefore, the confusion is not on my side ! The Italian physicist Amadeo Avogadro became acquainted with Dalton’s atomic theory through Thomson’s report (0. no. 8, p. 7, note). He puts on Thomson’s statements the same interpretation as Ido. Dalton’s object is to find the atomic weights of the elements, and the molecular weights of 366 Dr. H. Debus on the Genesis of the compounds formed of these elements. The sum of the weights of the atoms in a molecule is his molecular weight. Avogadro determines the molecular weights directly from the specific gravities of the gases. The molecular weight is, if Imay say so, the end of Dalton’s and the beginning of Avo- gadro’s work. About the constituents of the molecules, the atoms, Avogadro is absolutely silent. He knows only mole- cules and parts of molecules. Whether there is or is not a limit to the division of a molecule he does not say. Avogadro treats the subject like a theoretic mechanician, who considers his particles divisible or not, according to the nature of his problem. The unit of Dalton is the indivisible atom, the unit of Avogadro the divisible molecule (D. 70). It is worthy of notice that Avogadro is not conscious of these differences between Dalton and himself. He criticises Dalton’s work as if he and Dalton were engaged with the solution of the same problems, and calling attention to the agreement of some of his results with those of Dalton, he says :—‘ This agreement is in favour of our hypothesis, which is essentially nothing else but the system of Dalton improved by a sure expedient* to which we have been led by the facts discovered by Gay-Lussac” (O. no. 8, p. 22). - Avogadro could only identify his system with Dalton’s on the assumption that both systems rested on the same principle. This principle is the hypothesis M/S=C. As Avogadro received his information about Dalton’s work from Thomson, it follows that he put the same interpretation on Thomson’s words as I have done, and as the latter published his book in the year 1807, and Avogadro his essay in 1811, it appears highly probable that Avogadro received the first intimation of the hypothesis M/S=C from Dalton. The great merit of Avogadro is founded on his proposal to consider the mole- cules of the elementary gases divisible into two or more parts, because thereby the hypothesis M/S=C became of practical importance. But are the hypothetical molecular weights of Avogadro the real molecular weights? ‘This question could only be answered by the synthesis of the molecules from the con- stituent atoms. The sum of their weights is the molecular weight. Therefore, logically considered, the atomic weights’ must precede the molecular weights. The determination of the atomic weights was, accordingly, the task of Dalton and his generation. This is the real reason why the hypothesis M/S=C received no attention in Dalton’s and Avogadro’s time and was soon forgotten. Fifty years later, after * The division of molecules. Dalton’s Atomic Theory. 367 thousands of vapour densities had been taken, it reappeared in the form of an empirical law. Chemists have often wondered why Dalton did not acknow- ledge as correct the observations of Gay-Lussac that gases always combine in simple volumetric proportions. Various improbable or absurd reasons* have been assigned for his reluctance to adopt the results of the distinguished French chemist. The real reason is near at hand. Dalton could not accept Gay-Lussac’s law of the combination of gases in simple volumetric proportions, because, if he had done so, he would have abandoned the chief principle of his atomic theory. I will illustrate this assertion by an example. The first principle of Dalton is, that when two elements form only one compound, the compound is a binary one unless some cause appears to the contrary. Only one compound of hydrogen and oxygen and only one compound of hydrogen and nitrogen were known, hence’ the formula of the first would be HO and of the second HN. Nitric oxide, on account of its low specific gravity, was like- wise considered to be a binary compound of the formula NO. (N.S. 317.) Water, according to Gay-Lussac, is a compound of one voluine of oxygen and two volumes of hydrogen. If we assume one volume of hydrogen to contain 1000 atoms (molecules), then, if Dalton’s formula HO is right, one volume of oxygen must contain 2000 atoms. eas Nitric oxide is formed, according to Gay-Lussac, of one volume of nitrogen and one volume of oxygen. Therefore, if Dalton’s formula NO is correct, one volume of nitrogen, like one volume of oxygen, must contain 2000 atoms. Hence we have :— one volume of hydrogen 1000 atoms, one volume of oxygen 2000 _ ,, one volume of nitrogen 2000 _,, Now Gay-Lussac asserts that ammonia is a compound of one volume of nitrogen and three volumes of hydrogen— one volume of nitrogen 2000 atoms, three volumes of hydrogen 3000 __,, and its formula would be N.H, if Gay-Lussac’s observations are correct. Dalton’s principle requires the formula NH. Hence the alternative presented itself to Dalton either to reject his first principle or Gay-Lussac’s observation. As the atomic theory hy 47. Grundztige der theoretischen Chemie von Lothar Meyer, 1890, p- ° 368 Notices respecting New Books. was strongly supported by experience he rejected Gay- Lussac’s law, and considered his own inaccurate observations to be correct and the more exact results of the French chemist to be faulty. Some of the results of this investigation are :— (1) Dalton was investigating the state of equilibrium in mixed gases in the year 1801. This investigation caused him to adopt the hypothesis M/S=C. (2) Itis highly probable that the hypothesis M/S=C and the observations of the proportions in which nitric oxide and oxygen combine led Dalton to the invention of his atomic theory. (3 Atomistic views caused Dalton to abandon the hypothesis M/S=C in the year 1805. : (4) If we remember that all theories in chemistry are of a provisional character, and that they are subject to changes in course of time, then we cannot deny our admiration to the great work of Dalton. It was he who first attempted to weigh molecules and atoms and measure their volumes. XXXVI. Notices respecting New Books. The Intellectual Rise in Electricity; a History. By Park BrEn- JAMIN, Ph.D., LL.B. London: Longmans, 1895. eke electrical properties of rubbed amber and the phenomena exhibited by the lodestone have been known since the very earliest historic times; their discovery was probably coeval with those of amber and lodestone. While the electrical fact remained for many centuries isolated and apparently useless, the orientation of suspended lodestone or of magnets derived from it soon sug- gested the mariner’s compass and led to important advances in magnetic science, followed later by theories of attraction and repul- sion. In the work before us Dr. Benjamin traces in a very inter- esting manner the development of these facts and theories up till the time of Franklin, when the recognition of electricity as a natural force led to its being more universally studied. The author has searched among the manuscripts and books of many- lands and all ages in order to find material for his history, and he has even been assisted by the labours of those who have investi- gated the ruins and records of ancient civilization in Pheenicia, Egypt, and Scandinavia. Such a search necessarily occupies many years, and we owe its satisfactory termination to the author’s patience and enthusiasm for his subject. A very plausible theory is put forward to account for the intro- duction of the lodestone into Europe. It is supposed that the inhabitants of Central Asia first became acquainted with its pro- perties ; migrating eastwards as Mongols they carried the know- ledge into China, and travelling north-westward as Finns and Notices respecting New Books. 369 Lapps they introduced navigation by compass into Scandinavia. The subsequent dissemination of the knowledge to various Euro- pean ports took place through the medium of traders to the Baltic. “Vixere fortes ante Gilbertum,” if we may be pardoned for altering Horace; the author has discovered at least two such philosophers, Neckam and Peregrinus. We cannot agree with Dr. Benjamin in his criticism of a statement by Peregrinus (p. 174), which he considers erroneous. Concerning the rubbing of iron against lode- stone or a magnet Peregrinus writes: “ You will infer what part of the iron is attracted to each part of the heavens from knowing that the part of the iron which has touched the southern part of the magnet is turned to the northern part of the sky. The con- trary will happen with respect to that end of the iron which has touched the north part of the stone, namely, it will direct itself towards the south.” For the thirteenth century this is surely a very concise and straightforward description, contrasting greatly with the author’s confusion of true north polarity and north-seeking magnetism. The volume contains several reproductions of interesting old prints and good portraits of Gilbert, von Guericke, and Franklin. Jie Lig El. An Introductory Treatise on the Lunar Theory. By E. W. Brown, M.A., Professor of Applied Mathematics in Haverford College, Pa. (Cambridge University Press.) Iv may be said, and indeed it has been remarked by foreign and English writers alike, that the English student of mathematics is exceedingly fortunate in the excellence and abundance of the mathematical text-books at his disposal. It is therefore not a little curious that the only elementary exposition of either the Lunar or the Planetary Theory has existed in the form of a single and, it must be admitted, very inadequate introductory treatise. At the same time, the field for original research offered by these particular cases of the general problem of Three Bodies has been, with notable exceptions, singularly neglected by English mathematicians; and it is at least doubtful if the contributions of Lubbock, Airy, Cayley, and Adams are sufficient to relieve English mathematics of the serious charge of having neglected an im- portant branch of the science. For this state of things the want of a good elementary and, at the same time, comprehensive treatise was doubtless largely responsible, for there was apparently little to attract the student to take up a subject in which it would be necessary for him at an early stage to master the contents of a great number of scattered and exceptionally obscure original memoirs. {t is therefore with reason that we extend a special welcome to Prof. Brown’s treatise. The author, who, although holding an appointment abroad, was formerly Fellow of Christ’s College, Cambridge, is already favourably known both on account of his own contributions to the most modern form of the Lunar Theory and also for his elucidation of the work of the older theorists. The work divides itself practically into two distinct parts. the ial. Mages: 0. Vol, 42. Nov 25¢. Oel. 1896. 2D 370 Notices respecting New Books. first part forming an introduction to the second, which contains accounts of the various theories in detail, although it must be understood that the author adheres strictly to his intention of giving an explanation of the methods, and not the actual results obtained from them. After the necessary force functions have been found, the ordinary simplifications introduced by neglect- ing the Moon’s mass, and assuming the Sun to describe an elliptic orbit round the earth according to Kepler’s laws, together with the consequent corrections, are examined, and a numerical estimate of the resulting error is given. The equations of motion are next found as they are required for the methods of de Ponté- eoulant, Laplace, and Hill, and in addition the ten first integrals arising from the equations in the problem of Three Bodies. The third chapter is devoted to a discussion of undisturbed elliptic motion, the expansions being made with the aid of Bessel’s fune- tions, and the question of convergence being taken into considera- tion. The two principal methods of obtaining a solution, namely, by continued approximation, and the Variation of the Arbitrary Constants occurring in any orbit which may be taken as “ inter- mediate,” can now be considered, and the equations for the variations of the elements in disturbed motion are obtained in an elementary way and also by Jacobi’s more elegant method. In this connexion some description is given of Lagrange’s canonical system with Hansen’s extension, and some theorems of Jacobi, Hamilton, and Cayley are alsoincluded. The development of the forms and properties of the disturbing function brings the reader to the point at which it becomes necessary to study the principal methods separately. De Pontécoulant’s method is very properly selected by Prof. Brown as a basis for the elucidation of properties common to all, and consequently receives the fullest treatment, the inequalities being grouped according to their origin, and the consideration of the arbitrary constants, to which a whole chapter is devoted, being particularly lucid. Delaunay’s method, which is, next described, is important mainly on account of the high order of approximation to which the literal developments are carried, but also because it possesses very wide applications and possibilities for development which, according to Dr. Hill, have not yet been fully realized. It should be mentioned that Prof. Brown has suc- ceeded in simplifying many of the explanations as they appear in the Théorie du Mouvement de la Lune, as he has also done in his account of Hansen’s method. The latter has peculiar difficulties and obscurities, and these the author has taken pains to remove, by no means without success. Last of all the theories considered in detail is the one initiated by Dr. Hill and based on the use of rectangular coordinates referred to moving axes. It is interesting to note that these were first applied to the Lunar Theory by Euler, although he had originally used cylindrical coordinates for the purpose, and it is also remarkable that their power in the analysis of geometrical as well as dynamical problems is only now becoming generally recognized. It is in this most modern method of treatment of the lunar inequalities that Prof. Brown’s own investigations have been made. An Geological Society. 371 historical account of the work of other theorists is appended; and the last chapter is devoted to the inequalities in the moon’s motion, arising from the action of the planets, the figure of the earth, and the motion of the ecliptic. Comparative tables of notation, which will certainly be found useful, together with an index complete the volume. The peculiar difficulties of the Lunar Theory arise mainly from the fact that the original investigators have generally confined themselves strictly to their own methods, and this independence of thought among the classical theorists may be fairly said to warrant Prof. Brown in his peculiar treatment of the subject. Neverthe- less, while in our present state of knowledge he does well in recognizing the importance of some acquaintance with the older methods and the necessity for a separate treatment fer each in order to show the relations which exist between them, the subject cannot be considered to be in a perfectly satisfactory state until a single uniform mode of treatment becomes possible without loss of rigour or completeness. There can be no doubt that the time for this will be hastened by Prof. Brown’s work. A highly commend- able feature of the book consists in the ample references, which will enable the reader to continue his study of the more recent theoretical investigations. It was of course impossible to include all of these developments, and the author has shown excellent judgment in his selection. If the work of Professor Gyldén is passed over almost without remark, this course is probably justified by practical considerations of expediency, although it is to be reoretted that his work is not better known in this country. The question of convergence being as it is of the utmost importance for the legitimate use of infinite series, has scarcely sufficient stress laid on it, although the absence of certain knowledge is a plausible excuse. The remarkable contributions of Cauchy to this subject might, however, with great advantage have been considered. But with this single exception, we have nothing but praise for the manner in which Prof. Brown has carried out his task, and we recognize his book as a most important and valuable contribution to a highly interesting branch of mathematics. It should. be mentioned that the volume in the matter of type and general arrangement is quite up to the high standard we have learnt to expect in books published under university auspices, and this fact serves no small part in the lucidity of the explanations. W. E. PLuMMER. XXXVI. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 287.] May 27th (con.).—Dr. Henry Hicks, F.R.S., President, in the Chair. 2. ‘The Linyula-Flags and Igneous Rocks of the Neighbourhood 372 Geological Society. of Dolgelly.’ By Philip Lake, Esq., M.A., F.G.S., and 8S. H. Rey- nolds, Esq., M.A., F.G.S. The area dealt with in this paper lies south and west of Dolgelly, between the Arthog road and the hill called Mynydd Gader, which lies in front of the precipices of Cader Idris. ‘The stratified rocks belong to the Middle and Upper Lingula-Flags and Tremadoc Slates. The Middle Lingula-Flags (Ffestiniog Series) consist of bluish slates with grit-bands containing the usual Lingu- lella, passing into Upper Lingula-Flags (Dolgelly Series) consisting of dark slates with Orthis lenticularts, Parabolina spinulosa, ete., and containing two andesitic lavas. These pass into the basal Tremadoc Slates with Dictyograptus flabelliformis, surmounted by an upper volcanic series with rhyolitic lava. Subsequent intrusions of diabase occurred, of a laccolitic character, but of such a nature as to lead the authors to suggest the possible intrusion of the diabase along a line of unconformity in one case; there is, however, no newer rock above the diabase to indicate of what date the overlying beds would be if such unconformity occurred. It is further shown that the important faults in the area were produced both before and after the diabase-intrusions, and in one case the movement appears to have been in one direction before the intrusions, and in the opposite direction afterwards. 3. ‘The Kildare Inlier.’ By 8. H. Reynolds, Esq., M.A., F.G.S., and C. I. Gardiner, Ksq., M.A., F.G.S. The area described in this paper is occupied by four prominent hills composed of Lower Paleozoic rocks rising as an inher from beneath Carboniferous beds. The authors give the foliowing suc- cession of rocks in descending order :— . Green and grey micaceous grits and shales of Dunmurry. . Red and black shales. Gap: no exposure seen. . Limestones of the Chair of Kildare. . Contemporaneous igneous rocks. . Fossiliferous ash of Grange Hill House. . Green gritty shales (unfossiliferous). Nos. 5 and 6 are referred with some doubt to the Llandovery Series, and perhaps also to higher series. The gap may conceal the uppermost beds of the Bala succession. The limestones of the Chair of Kildare are separated by the authors into four subdivisions of the same general age, and Agnostus trinodus, [Menus Bowmanna, Remopleurides longicostatus, and Cyphoniscus servalis range through- out. The contemporaneous igneous rocks of Grange Hill and of the Hill of Allen are shown by the fossils found in the pyroclastic rocks to be of Middle Bala age. The lavas consist of basalts and andesites which the authors separate into four groups distinguished by their . lithological characters. Petrographical details of these various rocks are given in the second part of the paper. The age of the lowest beds which have not yielded any fossils is doubtful. mre Oo THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE, fr =. : 2 1296 [FIFTH SERIES.] ¢ WOV13* « NOVEMBER 1896. XXXIX. Thermal Transpiration and Radiometer Motion. By WILLIAM SUTHERLAND*. Part 1.— Thermal Transpiration. | ae comparative neglect into which the radiometer has fallen is probably the natural compensation for the exalted interest of its two or three years’ reign over the scientific imagination twenty years ago. In reading amongst the papers about it published at that time, one gets an im- pression of the laboratory of Crookes as of an arsenal where night and day the equipment of a great expedition into the unknown was being pushed on under the sleepless eye of a patriot leader ; but in the answering bustle outside, Stokes, Schuster, Stoney, Fitzgerald, Pringsheim, Reynolds, and others soon showed that the new conquest was simply an outlying part of the Kinetic Theory of Gases. Or, to vary the figure, Crookes appears as a friendly counsel subjecting Nature to a passionate and eloquent cross-examination with his fellow physicists as judge and jury bringing in a verdict for Kinetic Theory. And then the interest died away rapidly, perhaps mostly on account of Reynolds’s great paper ‘ On cer- tain Dimensional Properties of Matter in the Gaseous State ” (Phil. Trans. clxx.), which was probably held to settle the essential points of general interest in radiometer motion as consequences of the kinetic theory of gases, especially as the same train of reasoning had led him to his discovery of * Communicated by the Author. Phil. Mag. 8. 5. Vol. 42. No. 258. Nov. 1896. 2K Eee, ak: \j4 a Me S. PAT ENN pee Se 374 Mr. W. Sutherland on Thermal Thermal Transpiration with the beautiful experimental estab- lishment of its simple quantitative laws, simple in the illumi- nation of his theory, but complex enough without it. Unfor- tunately the mathematical form of Reynolds’s theory is wearily cumbersome; one gathers that Maxwell found it distasteful, and Fitzgerald (Phil. Mag. [5] xi.) describes it as inelegant and unnecessarily elaborate. A great objection to Reynolds’s mathematics is that it does not join on naturally with that developed for the general pur- poses of the kinetic theory of gases ; it has a certain interest of individuality about it, but. this fails to compensate for the waste of mental energy to the reader who has to adapt himself to it. But what appears to me to be the fatal objection to Reynolds’s mathematical method, is that it takes the mind away from definite physical concepts of the actual operation of the causes of thermal transpiration and radiometer motion ; and the object of the present paper is to construct a theory of these that will fall into line with the current kinetic theory of gases and keep the physics of the phenomena to the fore. The most convenient starting-point is the laws discovered by Clausius (Pogg. Ann. exv. 1862) for the conduction of heat in gases. In a vertical cylinder of gas, bounded by a solid wall impermeable to heat and two conducting plane ends, the lower at temperature @, and the upper at a higher temperature 8, when the flow of heat has become steady, the pressure throughout the cylinder is constant, and the tempe- rature @ at distance w from the lower end of the cylinder whose whole length is / is given by the equation 03 = 0,2 + (02!—0,')/l, and the distribution of density is determined in accordance with these two results. Now in the establishment of the law of the temperature, it was shown by Clausius that in a mass of gas which is not uniform in temperature there is motion of the gas in the direction of variability ; but it is assumed (as it can easily be proved) that under ordinary circumstances this motion can never produce an appreciable departure from uniformity of pressure, because the rate at which a variation of pressure throughout a mass of gas is effaced is so rapid in comparison with the motion which might produce a variation of pressure, that such a variation can never get itself estab- lished to an appreciable extent. But when in place of an ordinary cylinder we consider a very fine tube, we must take account of the effect of viscosity in reducing the velocity with which an inequality of pressure along the tube can get itself effaced ; and if the tube becomes fine enough, this velocity Transpiration and Radiometer Motion. 375 may be reduced till it is merely comparable with, or even much smaller than, the velocity with which motion caused by varying temperature may be tending to establish inequality of pressure. Thus, then,.in discussing the conductivity of gas in a nonconducting tube of capillary dimensions, we could no longer enjoy the convenient simplification which comes into the problem of Clausius when he writes the pres- sure constant as one of his fundamental equations, but from purely kinetic considerations we should have to determine the laws both of the variation of pressure and of temperature associated with the steady flow of heat. But in the actual problem of thermal transpiration if we lose one simplification we gain another, because we have to do, not with noncon- ducting walls, but with walls conducting so well and with so large a thermal capacity compared to that of the gas, that the law of variation of temperature is fixed entirely by the pro- perties of the solid; so that the gas, if subject to varying pressure, is also subject to a fixed law of temperature which . we are freed from having to find. In the kinetic theory the molecules which are considered characteristic of an element are those that have experienced a collision in it; those passing through without collision are taken account of in the elements where they do collide. If the element is a short length of our tube, we do not consider the molecules rebounding from the solid wall as characteristic unless they also encounter other molecules in the element, and thus we might appear to be neglecting the most charac- teristic molecules of the element. But this is not really so, because those reflected from the side of the tube and moving to a cooler element, as a rule collide with those coming from a still cooler element and including an equal number that have come from its walls, so that the colliding pairs on the average possess the qualities that are to characterize the ele- ment in which they collide. Thus, then, if we do not have to take account of reflexion from the walls of the tube, we can consider the gas in it as part of an indefinite mass such that the temperature throughout a plane perpendicular to the axis is the same as that in the section of the tube made by the plane. We wish to find the number of molecules crossing any section of the tube. This is done by Clausius in his theory of conduction in gases, and with greater refinements of accuracy by Tait (Trans. Roy. Soc. Edinb. xxxiii.) ; but for the sake of clearness we will make the calculation here to a degree of accuracy suitable for present requirements. If there are n molecules per unit of volume in a small element dB, and each has v encounters per second, then the 2H2 376 Mr. W. Sutherland on Thermal number of molecules colliding in a second in dB is nvdB. It is not worth while to take account of Maxwell’s law of velo- cities ; and all molecules will be supposed to have the average velocity v and travel the mean free path 2% between two encounters, so that v=v/A. But we must take account of the variation of % with direction ; for a molecule travelling from a particular point bas a longer path in the direction of dimi- nishing density and a shorter path in that of increasing density, with a maximum parallel to the axis in one direction and a minimum in the other; while the path at right angles to the axis is the mean of the maximum and minimum, and is indeed the mean path 2 of all molecules leaving that point. Let 2,, be the maximum value there ; then it is equal to the minimum at distance 2,, along the axis of the tube, and must therefore be equal to the mean value at distance X,,/2 ; thus, then, Am=A+AmdA/de2, or Ap»=A+AAdA/de2=AUI +2X7/2). On the same principle, the free path of a molecule that leaves the point in any direction so that the projection of its path on the axis of the tube is x, has a value X+ rd//2. Of the num- ber nvdB/A of molecules that in unit time have a collision in dB, the fraction that cross a plane at any distance is found by drawing from the centre of dB as origin the surface whose polar equation is p=A+2A‘/2, and estimating the solid angle subtended at the origin by the segment of this surface cut off by the plane, supposed to be at distance w, as a fraction of 477. This is the required fraction, namely {1—#/(A + «d//2) }/2, or (L—wx/A+ a°r’/ 2X?) /2 nearly. Thus the number of molecules colliding in dB and crossing the plane before colliding again is in unit time nvdB(1—a/A—2°r//2X) /2X, in which we have changed the sign of 0’ so as to transfer the origin from dB to the plane. Now dB may be taken as Adz where A is the area of section of the tube ; the total number crossing the plane from the tube on one side of it in unit time is the integral from 0 to A, of Anv(1—w/A—a°n//2d?)da/2n, where A, is the maximum free path at such a distance from the plane that a molecule after colliding there and travelling perpendicular to the plane collides again just at the plane. Now A=c/n, where c is a parameter depending only on the size of the molecules ; thus the number is h | { ‘An2o( 1—naz/e—n?wr’ /2c?)daj2e. . . (1) 0 Now if mg and v are the values of x and wv at the plane Transpiration and Radiometer Motion. ae we can write n=n,+adn/de=n,+n'e and v=vyt+v'e and Ay=A,+MA,/2; substituting these values, integrating, neg- lecting products and squares of n’v’ and 0, and dropping the suffix 0 as of no more use we get Anv{l/4+A(v'/u—A//A)/12} ww. 2) The number crossing in unit time from the negative side of the tube is obtained from this by changing the sign of n’ and v’ so that the total gain in unit time from the positive to the negative side of the plane is (since \’/A= —n’/n) ie Oo Anwn(™ += )/6 ee ee which amounts to the same thing as if the gas had a velocity mo 6 v=o +> )/ sii rarer yee ai(4) along the tube ; but the result holds not only for a tube, but for any space filled with gas and for any direction in it in which n’ and v’ are the rates of variation of n and v. The law connecting n and v with position in the general case must be complicated, but for a gas in contact with a solid the thermal capacity of the latter is so great as to make v’ and v for the gas at the surface the same as for the solid there, so that the problem simplifies to that of getting the law of n. At a distance z from the solid surface the conditions of n and v are still such as to tend to produce a velocity like u,so that in the general case we have to consider the effect of viscosity in causing these velocities to influence one another. The friction per unit area parallel to the surface at zis ndu/dz, and the state of the gas cannot be steady till this is constant. Returning to the case of a tube, we see that the steady state will be reached when the velocity v and n are constant throughout a section, and the velocity wu is therefore also constant throughout the section. Now under ordinary circumstances there would be friction between the gas and the tube over the whole surface, and therefore in this case there must be an action between the solid and the gas equal and opposite to the friction, that is to say, that the solid wall of a tube along which heat is being conducted in constraining the gas to take its temperature and share in the conduction of heat exercises a traction on it. The total friction does not exactly neutralize the total traction, but leaves a small resultant part of it which we can determine thus: suppose the tube connects two infinite spaces at the same temperature 378 Mr. W. Sutherland on Thermal as the ends of the tube, the gas enters at one end with velocity 0 and leaves at the other with velocity w; in unit time the mass nmAu passes out with momentum nmAvw?’, and this therefore is the force exerted by the tube on the gas in it; this force acts only near the entrance in the part where the velocity is rising from 0 to u, so that in this part the total traction exceeds the total friction by nmAu?. In the velocity wu we have the cause of thermal transpiration, while that of radiometer motion is implied in the equation total unequilibrated traction=nmAu%. . . (5) If the spaces at the ends of the tube instead of being infinite are finite, the gas will flow till a fall of pressure is established to arrest it, but we cannot secure that u=0 all over any section of the tube by an application of pressure, because the flow established hy excess of pressure at one end of a capillary tube is not of uniform velocity throughout each section, but has a maximum velocity at the axis and a minimum at the surface ; hence to secure that there shall be no total flow in such a tube we have to establish a difference of pressure which acting alone would discharge a volume Aw per unit time in the opposite direction to that of u. Thus, then, our solution for the motion in a conducting tube when there is no total flow of gas along it consists of the super- position of a uniform velocity wand opposite velocities varying in conformity with the laws of flow in a capillary tube of uniform temperature, the result being to give a surface of zero velocity somewhere between the axis and the wall, with a circulation going up between this surface and the wall, and backward between this surface and the axis. According to the theory of the flow of gas in a capillary tube, if dp/dz or p’ is the rate of fall of pressure along the tube, where the pressure is p and 7 is the viscosity, then B, the volume measured at p delivered in unit time from a circular tube of radius R (O. HE. Meyer, Pogg. Ann. exxvii.), is B=qp' R/8y re when the slipping of the gas on the walls can be neglected ; but if shpping is to be taken account of let its coefficient be €; then B=ap'R*(1+46/R)/87. . 2 2 2 As the importance of § depends entirely on its ratio to R, and as we wish to discuss tubes of any minuteness whatever, a discussion of slipping becomes of first-rate importance to the subject in hand. T ranspiration and Radiometer Motion. 379 Kundt and Warburg (Pogg. Ann. clvi.) showed experi- mentally the existence of slipping by its effect on the apparent coefficient of viscosity at low enough densities of the gas in an oscillating disk apparatus for measuring viscosity, and they adduced theoretical reasons for the necessity of its existence and for some of its properties; they also measured its amount and verified some of its laws, and a little later Warburg demonstrated the slipping of gas on the walls of capillary tubes (Pogg. Ann. clix.) That siipping is a necessary consequence of the kinetic theory can easily be shown. Consider gas between two solid parallel planes, one fixed and the other moving parallel to itself with velocity w; then in the steady state there is a constant rate of diminution of velocity dw/dx in the gas between the plates. Suppose the molecules of the solid, like those of the gas, to be smooth spheres oscillating, but their centres at the surface having a mean position forming a plane. Consider a molecule of gas in collision with a molecule of solid; if its velocity of rebound makes an angle less than 7/2 with the normal to the plane, the molecule has little chance of colliding with another surface molecule of the solid ana is directly reflected; the majority of these directly reflected molecules of gas must strike the molecules of solid near their most prominent points, and therefore acquire from them very little of their velocity parallel to the plane ; thas a certain fraction 7 of the molecules of gas that encounter the surface leave it with practically the same velocity parallel to it as that with which they approached ; the remaining fraction 1—f, or those which at the instant of rebounding from a surface molecule have directions making an angle greater than 7/2 with the normal to the surface, must each penetrate into the hollow between two neighbouring solid molecules and suffer a second encounter with one of them under conditions which necessitate its taking up on the average any motion that the surface has parallel to itself. Now suppose that on the average the molecules of gas which collide with the solid come a distance /2 since their last collision with molecules of gas; then their average distance normally from the surface at the instant of last collision with their fellows will be the average distance of a hemisphere of radius \/2 from its base, which is A/4, and thus the molecules of gas which collide with the solid, which is fixed, reach it with a relative molar velocity Adw/dzt; but after the collision only the fraction / retain this, so that the gas in contact with the solid surface may be said to retain as a whole the velocity fAdw/dv4, which constitutes a velocity of 380 Mr. W. Sutherland on Thermal slipping, and shows how slipping arises, but does not give its amount correctly ; this, however, can soon be obtained. Let w, be the sudden change of velocity on passing from solid to gas; then the Adw/dx4 just given must be increased by w,, and then the average loss of momentum experienced by a molecule encountering the fixed surface is m(fAdw/dx4 + w,) ; but the number encountering unit surface in unit time is (2) nv/4, and therefore the frictional force exerted by unit surface of solid on the gas is nmv( fAdw/dw4+ w,)/4, which is equal to ndw/dz, the friction on parallel unit surface in the gas when the motion is steady : thus LO CAE PNG = dane 4)? ore (8) but 7=°'365 nmva or, working with the same methods of approximation as we have been using, 7=nmvA/4, and then w= x17), er f is a fraction which from its nature is unlikely to exceed 1/2, so that we can write w,=addw/dx with the knowledge that a isnot much different from unity. At both the moving and the fixed surfaces there is this discontinuity of amount w,, so that in the theory of viscosity, instead of writing dw/dz=w/D for the steady state, we must write dw w—2uwy, pi yerden w D? ".de DG an Dye an or & is called the coefficient of slipping ; under ordinary circumstances it may be neglected, but when D is comparable with 2, as it mostly is in connexion with thermal transpiration and radiometer motion, slipping becomes of fundamental importance. When D is only a fraction of » viscosity practically ceases, because the molecules traffic backwards and forwards between the solids with so few encounters amongst themselves that they hardly affect one another’s motion, but they still exercise friction on the solids whose amount is easily calculated. Suppose that the gas between two parallel solid planes at rest is also at rest, except of course for the velocities of agitation, and then let one of the planes be set moving parallel to itself with velocity w; then, as we have seen, the molecules colliding with it leave on the average with velocity fw, and when they reach the fixed plane a fraction f will have this velocity reduced to zero, while 1— f will retain it unaltered, so that on the average the molecules Q 8 Transpiration and Radiometer Motion. 381 leaving the fixed surface after their first encounters with the moving and with the fixed have velocity (1—/)/w; but without following up this process any farther we see that it implies that when the steady state has been reached the molecules leave the moving plane with velocity w, and the fixed plane with an average velocity w,, and these must be connected by the relations (1—f)w,+fw=w,, and (1—/)w,=w, ; whence y=w(l—/)/(2—-f), w=u/(2—/), which give (w,+w,)/2=w/2, as of course they ought. Hach molecule that encounters the moving plane gains momentum m(we—w,) or mwf/(2—f7), and nv/4 molecules encounter unit surface in unit time, so that the friction between solid and gas is Be reman fl (mae ire oe ra oe aC) if f=1/2 this becomes nmvw/12, it is a limiting value of nw/D(1+28/D) when D is negligible in comparison with ¢, and it is independent of the distance between the moving and fixed planes. We see therefore that we can carry the ex- pression 7/(D + 2¢) into the consideration of cases either where D is made very small or € very large. The expression (11) shows that in capillary tubes whose diameters are only a fraction of the mean free path—that is with very fine tubes such as the passages of porous plates and gas at ordinary pressures, or with ordinary capillary tubes and gas at low pressures, or in any tubes at low enough pressures—the flow of gas under pressure will not obey Poiseuille’s laws ; indeed in a line or two we can show that (11) leads at once to Graham’s laws of transpiration of gases through porous plates verified and extended by Reynolds. For if the gas is passing through a fine tube of radius R with velocity w at distance x from one end, then when the flow is steady a Ramvwf/2(2—f) =7Rdp/da, and taking account of the conditions at the two ends of a tube of length / by suffixes 1 and 2, TYwnam=TR’wynym=TRwengm = 2(2—f)\rR(p.—p,)/lv ; thus the time of transpiration of unit volume measured at the pressure p, being 1/7 R?w, is $ngnwl/(2—f)7R (p,—p,). Now Reynolds made some experiments in which p,—p, was kept a constant fraction of pa, and therefore proportional to nz, under which conditions the time of transpiration should 382 Mr. W. Sutherland on Thermal by our last expression be constant for a given gas and all values of p,, which was the experimental result obtained by Reynolds ; moreover if we wish to compare different gases, as at a given temperature v is proportional to 1/m? we see that the constant time of transpiration for each gas ought to to be as the square root of its molecular mass, which is Graham’s well-known experimental discovery verified by Reynolds. This digression into the properties of a gas in spaces where the linear dimensions are small compared to the free path has been made as an appendix to our consideration of slipping in order to clear up the limiting conditions towards which we tend in treating of high vacua. We can now return to thermal transpiration as we left it at (4). To secure no total flow on account of w along a tube of radius R we are to have B=ap’R4(14 40/R)/8n = Ru = —7Rvr(n'/n + v'/v)/6; (12) | but p=nmv’/3, so that p’/p=n'/n + 20'/v, and then p’R?(1 +46/R) /8n = —vA(p'/p—v'/v)/6. . (13) Now with the methods of approximation here employed n=nmvv/4 and p=nmv’/3, so that 7 =3Ap/4v, and then ‘( R2 / Fi d+4yp) +1} = . ee As €=aX the coefticient of p’/p is a function of only R/A, and therefore the controlling influence of the whole phenomenon of thermal transpiration is this ratio of R to X. If the molecules are smooth, perfectly restitutional forceless spheres n=79v/v), Where mn) and vp) are the values of 7 and v at 0°C.; but with the molecules of the natural gases, on account of molecular force, the function which expresses 7 in terms of v is more complicated (see “ Viscosity of Gases and Molecular Force,” Phil. Mag. [5] xxxvi.). But for present purposes it will suffice to use the simple relation just given by which we can express the last differential equation in terms of p and v as the only variables thus dp (Gate 3A Rr ld iL sh 15 dv \ 16)70* Nov" ) padv tn o> Ona (15) which can be written as dp y Cp Dp a hp ie vt ge) tee 0. D , 1 Up, 4 Let a and 8 stand for — XG + 56 (D =a Transpiration and Radiometer Motion. 383 then the integral of this is 2 ~ log g(p/v? —a) — ia! 2 (p/v? = 8) log g p/v=constant, or ati suffixes 1 and 2 to indicate the — of the tube, : yi ior —8 je EG 5) © nove? —2 28 p,/v,? abate 7c) 18 pan, oe But this is a very awkward form of result for comparison with the experimental data, and we shall be better served if content with an approximate solution of the differential equa- tion obtained by putting p’=dp/de=(pe—pi)/l and v= (%—v)/l, 2p=p2+ pi, 20=%) +), thus Pepi IR*v,” (ps a pi)? 6aRv (po +7) Opie i ag ee Pot Pr Any (v2 + v1) N( vet v,) ar Or This solution brings out at once the important point that with v and v, fixed, that is to say, the temperatures of the two ok constant, ‘there is a certain mean pressure (2+ ,)/2 for which p,—p, has a maximum value; applying the usual con- dition for a maximum, we find that Po—p, 1S a Maximum when po+p,=2(v2+21)7/3Rv. Before proceeding to test (17) by Reynolds’s experiments, we may remark that if the mean pressure (7, + ,)/2 is made so small that R/) is negligible in comparison with unity, then in (14) p’/p=v'/v, that is Po/P1 = 02/0, a result in accordance with the following common- sense argument that when the mean path of a molecule is a large multiple of the radius of the tube, the molecules of the tube have practically no influence on one another; and the number that wander in at one end during unit time being nyv,/4 and at the other n,v,/4, therinal transpiration will con- tinue till these are equal, fhape is till nyv,=ngv_ or p;/V, = fro/Vo- So far, our theoretical treatment has related to cylindrical tubes, while in Reynolds’s experiment the passages through which the gases transpire are the irregular chains of cav ities in a porous “plate ; now toa first appr oximation these irr egular cavities may be replaced by uniform tubes whose sectional area is equal to the average section of the cavities, but it is obvious that a better approximation to the natural cavities would be a succession of frustra of cones of length L and radii R; and R, at the end sections. The thermal transpiration through such a frustrum can be readily established from (15), for taking the origin of coordinates in one end and in the axis, then the radius at distance « along the frustrum is R=R,+ ca, where c¢ isa constant: thus for the fall of pressure Qa 384 Mr. W. Sutherland on Thermal from one end of the frustrum to the other iz daz, we have x from (15) Re p dv dR Rp, v dv c(AR?+2BR+1)’ where . Leo ye es Lae Soe a Nov A y) which, if we regard dv/dz, p, and v as having constant average values throughout the short length L, may be written : 3 : (OAS 1 ie R,A+B—(B?—A)? R,A+B+ (B?—A)? » dec 2B?—A) °° R,AA+B+(B’—A)! R,A+B—(B’—A) or | epee loess SM log f i me oe Dude oe 223? —A)s AR,R, + BCR, + R,) + (B?—A)?(R,—R,) + 1 | The form of this expression suggests that we should expand 3 the log by the approximate relation log (1+z)=z, which yields p dv (R,— R,)/e For a frustrum pointing in the opposite direction we should have to interchange R, and R, and change the sign of ec, which would give us our last expression with only the sign of R,—R, changed in the denominator; thus for a pair of frustra oppositely directed, we get ;. P 7 a . 9 P dp ef y On Ok MG 1 eB) ARR, + BR +R)+1— (BARR) ARR, +B +R) +1) or confining our attention to cases where (R,— R,)* may be neglected, and remembering that (R,—R,)=Le and that 2lidv/dx is equal to the difference of velocities at the two ends of the double frustrum, we see that an approximate integral solution of the differential equation of thermal trans- piration through a series of oppositely directed frustra in which R, and R, are not very different (R, not to exceed Transpiration and Radiometer Motion. 385 2R, say) is oe eg Spel as a) bess apelin CLS) Potpy e+, A'(p.+pi)?/4+ Bp, +pi)/2+ 1? where A’=9R,Ryv9 /Ny (v2 +21)"; B/=6a(R, + Ry) v9/No(ve+ 11)’, while for a uniform tube we have seen that the solution (17) is what this becomes when R,=R,=R. The simplicity of the case of frustra breaks down when R, becomes only a small fraction of R,, for then we cannot neglect (R,—R,)* as we did above. To make clear the comparison between (17) and (19) and experiment a brief description of Reynolds’s arrange- ments is necessary: imagine a cylinder divided into five compartments by planes perpendicular to its axis, the middle one filled by a plate of porous material, those on each side of it made into small gas-holders connectable with gas supply and manometers and separated from the end chambers by metal plates, the end chambers being intended to act as a sort of jacket to each of the gas-holders, the one having a stream of steam carried through it and the other a stream of cold water. When a stationary state of temperature is established along the cylinder, the two faces of the porous plate come to fixed temperatures @, and @,, corresponding to the molecular veloci- ties v, and v,, and the gas transpires from the cooler face of the plate to the hotter, till the pressures become p, and p; as given by the equation. The internal diameter of the cylinder was 38 mm. and the thickness of the porous plates varied from 1°5 to 14°2 mm., the materials being meerschaum and stucco. Reynolds gives the temperatures of the two jacket-chambers, but not those of the faces of the porous plate, which are the ones we require ; we will show afterwards how to obtain these approximately, but for the present it suffices to know that in any one series of experiments v, and v, remained constant, while the mean pressure (p,+ )/2 in the passages of the porous plate varied from about 760 mm. of mercury down to about 4. From any three sets of values of Po—Pp, and (po+p )/2 for any gas, it is possible by equation (19) to calculate (vg+%,)/(ve—v,) and A’ and B’, or from the whole series of measurements mean values of these can be calculated, and then at all mean pressures p.—p, can be calculated for comparison with the experimental values. For Reynolds’s meerschaum plate LI., having a thickness of 6°3 mm. and with the temperature of the steam-jacket at 100° C, and that of the water-jacket at 8°, the values of the 386 Mr. W. Sutherland on Thermal parameters in (19) are, with the mm. of mercury as unit of pressure, A (v2+2,)/2(v2—2,) B' xt al apne 16 0094 0-0 He kee 12 "0022 0-0 COS cere 16 012 0°0;5 2. e. 000005 5 These give the following comparison :— (potp,)/2 ... 764 328 217 940 508 231 127 Air4 p,—p,cal. ... 59 50 4-4 31 2-2 1:2 i PoP, exp... GL: ba 48> 30 oe eaten 9 (p+-p,/2 ... 767 330 199 108 508 254 127 H,1 p,—p cal 1. 238° 160. 112° 738- 38 "ee p—p exp. s.. 204 “In? - 112 (e 38 2:0 ‘9 (Po+Pp,)/2 ... 764 495 362 267 203 114 508 254 127 CO,4 Ps—Pr al... 37, 38-38 37 35° 29 | 205 ome fi po—p exp. «. 33 41 41 38 33 28 20 13 10 With the meerschaum plate III., having a thickness of 11-2 mm. and with the jackets at 100° and 17°6°, the para- meters are :— (vetv,)/2(v.—2,) B' A! 7a \ aes aC SS 18 “0094 0-0 j 5 Eau beae sn SwAee: 16°6 "00181 0-0 whence the comparison (pp 2... 77 698 508 317 . 209 - 198) —avaee Air} Po—p, cal. ... 52 5-1 4:8 4-] 39 38 27 Dap Otp-s DO. DA. 4 pede gee 2:3 (p,+p, 2s. 508 356 (211 102 71L 2S2e ieee Ried ep tal joy A De Ve ig TD 59 oil Sipe aoe 20 eee exputis.g p16 13 1-0 63 “49 37 ‘39 (potp,)/2 ... 864 762 470 290 193 121 76:2 H,4 PoP cal. ... Py. 812 lies 11-5 8:6 6-0 4-0 p.—p exp... 21 195 159 17 8-0 56 4-0 (act pai2 5. AB 2L (279) 2b GS) las. Sele H,lp,—pyeal. 3 2A VB «146 59796790) a8 Do—P1 EXP- ++ 27 16 1:68 "82 ‘96 58 With the stucco plate I., having a thickness of 6°3 mm. and with the temperatures of the jackets at 100° and 18°°4 (17° for H,), the parameters are :— Transpiration and Radiometer Motion. 387 (%+2,)/2(%,-%,) —-B A’ PCT gah Meee 20 045 "0,9 EI OU sara a 18 00917 0;61 which furnish the comparison (Po+D,)/2 ... 757 594 564 288 131 88-9 Air} P.—P, cal. ... °59 66 67 “79 "85 "82 Po—P, exp.... °56 63 67 "88 "92 ‘83 (pPo+p,)/2... 59°7 Seg 152 6°35 3°84 Air 4 p,—p, cal.... “77 64 “45 “94 “17 Po—P exp... “T4 58 38 20 17 (Po+p,)/2 ... 858 686 508 406 339 249 H,4 2p, al.... 356 375 S91 394 392 378 | Po—Pp, exp... 340 365 389 389 390 3:82 (p,+p,)/2 .. 203 152 825 508 178 762 Ep peal! 362 S55 255 191 “85°” -40 p,—p, exp... B73 385 264 193 84 40 These comparisons show that the equation (19) represents the facts of thermal transpiration, for the discrepancies between calculation and experiment are mostly of the same order as the experimental uncertainty, as can be seen from a careful comparison of the experimental data amongst them- selves. We have now to consider the relation between the experi- mental values of the parameters (v2 + )/2(¥2.—v,), B’, and A’ and their theoretical natures, First, as to (vp+ 1)/2(v.—1), which is equal to (0,2? +6,°)/2(0,;—6,°) where 6, and 6, are the temperatures of the two faces of the porous plate ; now the walls between the jackets and the air-chambers are of thin metal, and the chambers are of the same shape and size, so that the mean of the temperatures 6, and @, must be nearly equal to that of the two jacket temperatures 2, and 4,3; thus @.+0,;=%+%, which, with the values given for (vp + v;)/2(v2—v,), suffices to determine @, and 0,. ae) He) COs Gs—21a (48 74 Gi—2is 34 ~ 27 34 @,—273 77 79 Meerschaum III.. . 6,-2738 40:5 39 6,—278 16 77 Siueeoel Uy Re. G = 2g any eA oeain 40 Meerscbaum [I. 388 _ Mr. W. Sutherland on Thermal The temperatures @, and 6, are determined by the flow of heat from the thin metal wall of the hot jacket to that of the cold one, by conduction along the rubber walls of the cylinder, by radiation across the two gas-chambers, by con- vection-currents in the gas-chambers, and also by conduction through the gas of the chambers, but the conductivity of gases is so small compared to that of even badly-conducting solids, that the direct effect of gaseous conduction may be neglected, although the indirect effect of the conductivity of the gas in determining the amount of heat carried by con- vection may be appreciable, as would appear to be the case with hydrogen and meerschaum plate II. It would be possible to make a rough calculation as to what 0, and 0; ought to be according to the theory of conduction, but Rey- nolds states that the condition of the radiating surfaces and the sizes of the chambers were altered during the experi- ments, so that it is not worth while to do more than notice that the values obtained for the temperatures of the faces of the porous plates are consistent in a general way with what we should expect from the temperatures of the jackets, the thickness of the gas in the two chambers which was about 5 mm., and the given thicknesses of the plates. As to the values of B’, which stands for 6 avp(Re+ Ry)/no(v2 +0)" since mv? is proportional to 0, and (6,?+0,%)? is nearly the same in all the experiments, we should expect B’n9/m? to be constant for different gases with the same plate, and propor- tional to the mean radius of the passages in the plate; thus, | using the viscosities as obtainable from Graham’s experi- ments in terms of that for oxygen as unity, and the molecular masses in terms of that of hydrogen as 2, we have :— H,. Air, CO. WET oD 28°8 44 CT eae take mae “cas ‘90 SLs which give the following values of 10° B/no/m? :-— | H.. ° JAiry > acom Meerschaum Tie 2.2) en68 158 137 Meerschaum III. ... 56 158 Stucco . f 285 TDS This shows that the values yielded by hydrogen, instead of being equal to those given by air, are between 4 and } of them, a discrepancy whose cause will be found immediately; but it is to be noted that while the results for hydrogen Transpiration and Radiometer Motion. 389 make the mean radius of the passages in stucco 4:2 and 5:1 times those in meerschaum II. and III., those for air make it 4-8 and 4°8 times, and the agreement of the means 4°65 and 4-8 is close enough to show that our expression 6avy(R, + R,)/no(vs =f v1) is right enough as regards the occurrence of the mean radius ot the passages in it ; and moreover our equation (14) showed that R entered in the form R/A, so that the discrepancy just found must be due to some considerations being ignored in connexion with 2X. Now it is a well known fact established by experiment that gases are condensed in the passages of porous bodies. The condensing action exerted by a solid surface on a gas is easily expressed quantitatively, for near the end of section (8) of my paper on the Laws of Molecular Force (Phil. Mag. [5] xxxv.) the attraction of a cylinder of radius ¢, length h, and density p on a particle of mass m at distance z along the axis from the nearest end, the law of force being 3Amm'/r*, is 2Ammp[1/z—1/(e+h) -1/(2 +22)? 4+ 1/fe + (e+h)*}"], whence the attraction on a particle at small distance z from the surface of a solid may be written 2Ammp/z, and if the particle is one of the molecules of a gas, the condition of equilibrium in the gas is —dp/dz=2Ampnm/z or —dp/p=6Anp dz/zv’; and if p, is the pressure in the layer nearest to the surface which is at distance z, from the surface, and p, is the pressure at a distance z, where the effects of the solid are negligible, then 6A7rp vy log p,/p,.= LOZ a he en (20) a formula which makes the density of the gas in contact with the solid nearly proportional to the density where the gas is free, because with gases 6A7p/v? is a small fraction. This formula will be investigated a little further in my next paper, on ‘‘ Boyle’s Law at very Low Pressures.” A rigorous investigation for condensation in a tube would be simple enough, but it suffices for our present purposes to see that in most cases the density at the surface of the tube will be connected with the density at the axis by the relation Phil. Mag. 8. 5. Vol. 42. No. 258. Nov. 1896. 2F 390 - Mr. W. Sutherland on Thermal obtained by putting surface-density and axial density in place of p, and p, in the last formula. - It is easy also to obtain an expression for the average density, but as it is evident that for a given tube at a given tempera- ture the average density remains proportional to the density at the axis, which is the same as if there was no attraction between gas and solid, we see at once that the effect of sur-. face condensation on our investigation of thermal transpiration is to multiply the density by a factor which remains nearly. constant for a given tube or to divide X by the same factor,. and the effect of ignoring this factor as we have done is to- produce values of 10°B//m? which ought to be divided by the factor before they should be expected to be constant for’ any one plate. Now experiment has shown that hydrogen is much less condensed on solid surfaces than other gases, so_ that with hydrogen the factor will be nearly unity (probably), and therefore, from the last little table, that for air between 2: and 3; the factor for CO, ought to be larger still, as this gas” is much more liable to surface condensation than air, while: the last table would make the factor to be 137/68 or 2; but too much reliance must not be placed on the value of B’ for CQ;, as Reynolds found the trouble caused by the condensa-. tion of the CO, to be so great as to discourage him from making any further experiments with it. Thus the apparent discrepancy in the last table has furnished some new evidence. in connexion with condensation of gases in the passages of porous solids. As to the values of A’, which stands for DRoRyv9?/No” (v2+ v1)* . we see that as a is nearly 1 the value of B’?/16A! ought to ba. nearly equal to (R, + R,)?/4R.R,, and of course the value of the. ratio B”/16A’ is not affected by our ignoring condensation in the establishment.of the fundamental equations. In the case of hydrogen, the values of B’ and A’ for stucco I. lead to an unreal value of R,/Rj, and thus we see that the formula (19) for conical. passages is too much of a refinement for present purposes ; and therefore abiding by the formula (17) for cylindrical passages we may say that B”/16A’ ought to be not much different from unity. For stucco I. the values of B’/16A! are ‘86 for hydrogen and 2:5 for air, while for meerschaum II. and CO, the value is 1°8; these “dies are near enough to 1:0 to give satisfactory evidence of the general soundness of. the details in the theory. Reynolds, g guided by his theory, formulated his experimental Transpiration and Radiometer Motion. 391 results in a number of laws, but there is no occasion for us to follow these seriatim as they are all contained in the sym- bolical statements of equations (17) and (14), which we have already tested by the experimental results. An interesting result of thermal transpiration experiments is that they enable us to calculate the mean radius of the passages in porous materials, for in the case of hydrogen the measurements must be but little complicated by molecular force ; thus the values given for B’ in the case of hydrogen, if multiplied by 760 to pass from the mm. of mercury to the atmo as unit of pressure, and then divided by 1033°3 x 981 to pass to the dyne per sq. cm. as absolute unit of pressure, give us the values of 12av)R/no(v,+ ,)?; now as vet+v, may be taken as relating to a mean temperature of 57° C., (v2 + v;)?=40,? 330/273, and %=184400 cm. per see. and 4='00009, while a is nearly unity ; thus for the mean radius of the passages in Reynolds’s meerschaum II. we get ‘0000112 cm., in meer- schaum II]. -0000092, or say 1/10° em. for meerschaum, while for stucco I.the value is 000047 cm. ‘Thermal transpiration gives no information as to the number of passages, but this could be found from a measurement of the volume of air transpired by a plate in unit time under a measured excess of pressure on one side, or by other measurements relating to transpiration under pressure such as those made by Graham and Reynolds; for the delivery of gas could be calculated as that due to N tubes of radius R, the discharge of each being calculated according to O. E. Meyer’ s equation given in (7). In this way Pherpial and pressural transpiration measure- ments can be made to yield a measure of the average porosity of any solid through which hydrogen can pass. By artifi- cially altering the porosity in a series of preparations, as for instance by hardening stucco under different pressures and similar means, so that specific gravity would give a measure of relative porosity, it might be possible to find a porosity at which hydrogen just failed to pass, which would furnish an independent measure of the diameter of the hydrogen molecule. [To be continued. | 2F 2 [ 392 ] XL. On the Passage of Electricity through Gases exposed to Réntgen Rays. By J. J. Thomson, V.A., FBS, Cavendish Professor of Experimental Physics, Cambridge, and H. RutuerrorD, M.A., Trinity College, Cambridge, 1851 Exhibition Scholar, New Zealand University". fe facility with which a gas, by the application and removal of Réntgen rays, can be changed from a con- ductor to an insulator makes the use of these rays a valuable means of studying the conduction of electricity through gases, and the study of the properties of gases when in the state into which they are thrown by the rays promises to lead to results © of value in connexion with this subject. We have during the past few months made a series of experiments on the passage of electricity through gases exposed to the rays, the results of these experiments are contained in the following aper. s A gas retains its conducting property for a short time after the rays have ceased to pass through it. This can readily be shown by having a charged electrode shielded from the direct influence of these rays, which pass from the vacuum-tube through an aluminium window in a box covered with sheet lead; then, though there is no leak when the air in the neigh- bourhood of the electrode is still, yet on blowing across the space over the aluminium window on to the electrode the latter immediately begins to leak. To make a more detailed examination of this point we used the following apparatus. A closed aluminium vessel is placed in front of the window through which the rays pass. A tube through which air can be blown by a pair of bellows leads into this vessel: the rate at which the air passed through this tube was measured by a gas-meter placed in series with the tube ; a plug of glass wool. was placed in the tube leading to the vessel to keep out the dust. The air left the aluminium vessel through another tube, at the end of which was placed the arrangement for measuring the rate of leakage of electricity (usually a wire charged to a high potential placed in the axis of an earth- connected metal tube through which the stream of gas passed, the wire being connected with one pair of quadrants of an electrometer). This arrangement was carefully shielded from the direct effect of the rays, and there was no leak unless a current of air was passing through the apparatus; when, * Communicated by the Authors, having been read before Sectiun A of the British Association, 1896, On the Passage of Electricity through Gases. 393 however, the current of air was flowing there was a consider- able leak, showing that the air after exposure to the rays retained its conducting properties for the time (about $ second) it took to pass from the aluminium vessel to the charged electrode. We tried whether the conductivity of the gas would be destroyed by heating the gas during its passage from the place where it was exposed to the rays to the place where its conductivity was tested. To do this we inserted a piece of por- celain tubing which was raised to a white heat ; the gas after coming through this tube was so hot that it could hardly be borne by the hand ; the conductivity, however, did not seem to be at all impaired. If, however, the gas is made to bubble through water every trace of conductivity seems to disappear. The gas also lost its conductivity when forced through a plug of glass wool, though the rate of flow was kept the same as in an experiment which gave a rapid leak; if the same plug was inserted in the system of tubes before the gas reached the vessel where it was exposed to the Rontgen rays, in this case the conductivity was not diminished. This experiment seems to show that the structure in virtue of which the gas conducts is of such a coarse character that it is not able to survive the passage through the fine pores in a plug of glass wool. A diaphragm of fine wire gauze or muslin does not seem to affect the conductivity. A very suggestive result is the effect of passing a current of electricity through the gas on its way from the aluminium vessel where it is exposed to the Rontgen rays to the place where its conductivity isexamined. We tested this by inserting a metal tube in the circuit, along the axis of which an insu- lated wire was fixed connected with one terminal of a battery of small storage-cells, the other terminal of this battery was connected with the metal tube ; thus as the gas passed through the tube a current of electricity was sent through it. The passage of a current from a few cells was sufficient to greatly diminish the conductivity of the gas passing through the tube, and by increasing the number of cells the conductivity of the gas could be entirely destroyed. Thus the peculiar state into which a gas is thrown by the Rontgen rays is destroyed when a current of electricity passes through it. It is the current which destroys this state, not the electric field ; for if the central wire is enclosed in a glass tube so as to stop the current but maintain the electric field, the gas passes threugh with its conductivity unimpaired. The current pro- duces the same effect on the gas as it would produce on a very weak solution of an electrolyte. For imagine such a solution 394 Prof. J.J.Thomson and Mr. Rutherford on the Passage to pass through the tubes instead of the gas; then if enough electricity passed through the solution to decompose all the electrolyte the solution when it emerged would be a noncon- ductor ; and this is precisely what happens in the case of the gas. We shall find that the analogy between a dilute solution of an electrolyte and gas exposed to the Réntgen rays holds through a wide range of phenomena, and we have found it of great use in explaining many of the characteristic properties of conduction through gases. Thus Rontgen rays supply a means of communicating a charge of electricity to a gas. To do this, take an insulated wire charged up to a high potential and surrounded by a tube made of a non-conducting substance: let this tube lead into a large insulated metallic vessel connected with an electro- meter. If now air which has been exposed to Réntgen rays is blown through the tube into this vessel the electrometer will be deflected. This proves that the gas inside the vessel is charged with electricity. Ifthe Rontgen rays are stopped and the gas blown out of the vessel the charge disappears. In these experiments we took precautions against dust. The fact that the passage of a current of electricity through a gas destroys its conductivity explains a very characteristic property of the leakage of electricity through gases exposed to Rontgen rays; that is, for a given intensity of radiation the current through the gas does not exceed a certain maxi- mum value whatever the electromotive force may be, the current gets, as it were, “saturated.’’ The relation between the electromotive force and the current is shown in the fol- lowing curve, where the ordinates represent the current and Fig. 1. the abscissee the electromotive force. It is evident that this saturation must occur if the current destroys the conducting power of the gas, and that the maximum current will be the current which destroys the conductivity at the same rate as of Electricity through Guses exposed to Réntgen Rays. 395 this property is produced by the Roéntgen rays. Ifwe regard the gas as an electrolyte, then the passage of a quantity e of electricity will destroy e/e of the conducting particles, where e is the charge carried by one of these particles. Let n be the number of conducting particles in unit volume of the gas, q the rate at which these are produced by the rays, an? the rate at which these disappear independently of the passage of the current, ¢ the current through unit area of the gas, / the distance between the electrodes. Then we have dn ns : a = q—an = ie 3 ° e ° ° ° e 3) so that when the state of the gas is steady, 0=g—an?—-, eerie or ere. ence) le When the current is small this equation gives 1 Ole ; and as the number of conducting particles is independent of the current, the current will be proportional to the E.M.F. This corresponds to the straight part of the curve. In the general case the current is proportional to the pro- duct of n, the number of conducting molecules, and the potential gradient. If E is the difference of potential between the plates, U the sum of the velocities of the positively and negatively electrified particles when the potential gradient is unity, we have le t=neU/I or 2= OB Substituting this value of n in equation (2), we get 0=q- 2h? ar, ie otesie rs eS eee (3) We see from this that ¢ approaches the limit gel. Thus the limiting current is proportional to the distance between the electrodes ; so that when we approach saturation the current will increase as the distance between the electrodes increases, and we get what is at first sight the paradoxical result that a thin layer of air offers a greater resistance to the passage of a current than a thicker one. This is, however, easily accounted for if we remember that the current destroys the conducting- power, and that as in a thicker layer there are more con- ducting particles than in a thinner one the current required -to destroy them all will be greater. 396 Prof. J.J. Thomson and Mr. Rutherford on the Passage The experiments show that the effect of the distance between the electrodes (two parallel plates) on the current is very marked. The following tables show the result of some expe- riments on this point. Potential-Difference between Electrodes 60 volts. Distance between electrodes, Current (arbitrary in millimetres. scale.) gi iM «tA Mi ih 5 4 oF Ae” ah Mme tae 8 Nts tout ee eee Gr Bi ems co teh, Sie 1 it SBOE SE se ep a ee ee eee 3 ES are Sie OM 8 Pe Selah With this large potential-difference the current was satu- rated in all the experiments. The next table contains measurements with a small potential- difference. Potential-Difference between Electrodes 1:3 volt. Distance between electrodes, Current (arbitrary in millimetres. scale). 715 adel Mpeg ar 1) gH aera ee Ee ance 9357 2 SS ie eee 3 Oe isis as ke ee 8 LOIN tai OSes OOS 18 Pp me ere reat: |) In this case the effect of distance is not so well marked as in the previous one, where the H.M.F. was sufficient to satu- rate the current at all distances. The measurement of the rate of leak when the current is saturated enables us to form an estimate of the number of conducting particles present in the gas ; as in this case the number of conducting particles produced in unit time by the rays is equal to the quantity of the electrolyte destroyed by the current in the same time. Let us take the case of hydro- gen; when the current was saturated, the rate of leak between two plates each about 10 sq. cm. in area and 1 cm. apart was about 1 volt per second when a capacity of about 30 em. was in connexion with the electrometer. Thus the quantity of electricity passing between the plates in 1 second was of Electricity through Gases exposed to Réntgen Rays. 397 about 10-! electrostatic units, or 1/3 x10" electromagnetic units, and this quantity is sufficient to electrolyse all the electrolytic gas produced by the Roéntgen rays. Now 1 elec- tromagnetic unit of electricity sets free 10~* grammes of hydrogen, or about 1 c.c.at atmospheric temperature and pressure. Hence 1/3 x 10'! electromagnetic units correspond to about the same number of cub. centim. of hydrogen ; the volume of the space between the electrodes was about 10 c.c., so in this experiment the fraction of the gas electrolysed was only 1/3 x 10”, z.e., one three billionth of the whole amount of the gas. It is not surprising that some experiments we made to see if any alteration in pressure was produced when a gas was transinitting Rontgen rays should have given negative results. The preceding estimate gives the average number of conducting particles ; if the conducting state is intermittent there may at certain times be a much larger number of these molecules present. Itis probable that at all events, when the current is saturated the conducting power is intermittent. The action of the coil used to send the discharge through the vacuum tube is intermittent ; thus, if between the passage of two sparks the conductivity has time to vanish (and when any current is passing through the gas the rate at which it vanishes is very rapid) the gas will be alternately an insulator and then a conductor. | | ¢ The following experiment is explained by the intermittent character of the discharge. The gas exposed to the Réntgen rays was in a piece of lead tubing open at both ends; this was connected with one terminal of a battery, the other terminal of which was connected with a wire running down the axis of the tube. A blast of air was blown through this tube, and it was found that when the current between the wire and the tube was small, the blast diminished the current to a large extent, though a current approaching saturation was hardly affected by the blast. When the current was affected the gas blown out of the tube was conducting; when the current was not affected the gas did not conduct. If the gas were exposed to steady radiation it would not be affected by blowing unless the time taken by the gas to acquire the conducting state under the influence of the rays was com- parable with the time taken by the gas to pass through the tube ; this is inconsistent with what we know from other experiments as to the rapidity of action of the rays. If, how- ever, the state of the gas is intermittent, then, since the blast continues when the rays are not acting, it blows out conduct- ing gas, and so diminishes its average conductivity. To return to equation (3), if Lis the value of « when E 398 Prof. J.J. Thomson and Mr. Rutherford on the Passaye is infinite, we may write the equation in the form 2 fa Oe , oa. a where Lae ie cal is independent of both E and v. We have observed the relation between the current aa the electromotive force for several gases, and for different intensities of the Rontgen rays. The comparison of the re- sults of these experiments with equation (4) is given in the following tables :— Leakage through Chlorine Gas. Electromotive Current Current calculated Force. observed. by equation 4. eo 65 18 124 116 30 200 180 wi) 245 140 270 279 The observations marked with the asterisk were used to calculate the constants. Leakage through Air. - *9 22 18 ag 38 30 67 67 *70 83 140 90 86 The observations marked with the asterisk were used to calculate the value of the constants in equation 4. Leakage through Hydrogen. 5 18 19 9 31 18 53 48 oD 63 58 *70 65 The observations marked with the asterisks were used to calculate the constants in equation 4. --of Electricity through Gases exposed to Réntgen Rays. 399 Leakage through Chlorine. (Strong radiation.) Electromotive Current Current calculated Force. observed. by equation 4. 5 53 53°4 *1(0) 100 ; 21 189 183 oD 275 255 10 309 , 140 = aou 405 Leakage through Chlorine. (Weak radiation.) =5 10 85 16 15 Mecle(, 26 23 - ao aoe, 105 d4 37 Coal Gas (1). 14 10 9°8 2°8 17-3 4:2 22 23 84 32°3 33 16°38 38°3 40 30 43 110 45 44 Coal Gas (2). Weak radiation. 1-4 3°6 4-2 2°8 8 4°2 el 11°2 2°6 14°7 15-2 8-4 Zale Zee 12°6 32 30°4 16°8 38 Hydrogen. 3°4 5 5:1 75 6:9 a) 10 10°1 6 15 13°4 400 Prof. J.J. Thomson and Mr. Rutherford on the Passage Sulphuretted Hydrogen. (Strong radiation.) Electromotive Current Current calculated Force. observed. by equation 4. 15°6 8°7 34 18 iNet 68 30°8 28°5 126 40 Sulphuretted Hydrogen. (Weak radiation.) 15°6 3°8 34 6:3 6°2 68 8 8 136 8°7 Mercury Vapour. Ses 14:2 14°6 85 23 15°6 35 36°9 o4 55 59 68 75 136 (i) 8:2 As these measurements require the intensity of the radia- tion to be maintained constant during each series of observa- tions, a conditicn which it is very difficult to fulfil, we think the agreement between theory and observation is as close as could be expected. We have seen how from the measurement of the limiting current we could form an estimate of the proportion which the conducting particles bear to the rest of the molecules of the gas. We can, in addition, get from the curve represent- ing the relation between the current and the electromotive force an estimate of the velocity with which these particles move. ‘Taking equation (3) we shall endeavour to express the coefficients in terms of quantities which our experiments enable us to estimate. Let I be the limiting current when the electromctive force is infinite, then I=dgle. Let T be the time which elapses after the rays have been stopped for the number of conducting particles to fall to one half the number just before the rays ceased, no current passing through the gas. Then, just before the rays cease to fall on of Electricity through Gases exposed to Réntgen Rays, 401 the gas, we have from equation (2), x= {2} where N represents the number of conducting particles at this stage ; after the rays have ceased, we have dn A Cali or 1 ] we if t is the time which has elapsed after the rays have stopped, when t=T, n=4N, hence = —- 8 |e substituting for N its value, we get 1 T= —, ag or 1 le PG Ph Substituting for g and a the values just found, equation (4) becomes J De cre fen a ee or Ee I(1—.) — Th? Ue? . e ° ° ° ° (3) Thus in the straight part of the curve, where ¢ is small com- pared with I, we have approximately yo HUE oes ec (8) Now HU/I is the sum of the velocities of the positively and negatively charged particles in the electric field. Hence, equation (6) shows that the current bears to the maximum current the same ratio as the space described by the charged particles in time T bears to the distance between the elec- trodes. In an experiment where / was about 1 cm., the rate of leak through air for a potential-difference of 1 volt was about #5 of the maximum rate of leak, hence the charged 402 Prof. J.J. Thomson and Mr. Rutherford on the Passage particles must in the time T have moved through about 3 of a centimetre. The time T will depend upon the intensity of the radiation ; it could be determined by measuring the rate of leak at different points on the tube through which the conducting gas was blown in the experiment mentioned at the beginning of this paper. We hope to make such experi- ments and obtain exact values for T; in the meantime, from the rough experiments already made, we think we may con- clude that with the intensity of radiation we generally employed, T was cf the order of 3), of a second. This would make the velocities of the charged particles in the air about *33 cm./sec. for a gradient of one volt per cm. This velocity is very large compared with the velocity of ions through an electrolyte ; it is, however, small compared with the velocity with which an atom carrying an atomic charge would move throngh a gas at atmospheric pressure; if we calculate by the kinetic theory of gases this velocity, we find that for air it is of the order 50 em./sec.; this result seems to imply that the charged particles in the gas exposed-to the Rontgen rays are the centres of anaggregation of a considerable number of molecules. The relation between the current and electromotive force given by equation (4) corresponds to that obtained by experi- ment for a number of gases; it does not, however, exhibit a peculiarity which we have sometimes observed, especially when the radiation was strong, i. e., the existence of a part of the curve where the current increases faster than would be the case if Ohm’s law were true ; this is shown by the portion EF of the curve in fig. 2, which represents the relation be- ~ ~ A ~ ~ ~~ tween the current and electromotive force through sul- phuretted hydrogen. When the intensity of the Rontgen rays is altered, the alteration in the current is not the same of Electricity through Gases exposed to Réntgen Rays. 403: at different points in the curve. When the intensity of these rays is diminished, the saturation current is diminished in a larger proportion than the current for small electromotive forces. This is shown by the following diagram, which represents the » and E curves through chlorine gas for dif- ferent intensities of the Rontgen rays; the weak radiation was got by interposing a thick aluminium plate. In this diagram the ordinates for the weak radiation have been increased so as to make the ordinate for the saturation current of the weak radiation the same as that of the strong. When this is done the rest of the ‘‘ weak” curve is above the strong, showing that the diminution in the radiation has affected the saturation current to a greater extent than the weaker cur- rents. The saturation current depends only on the number of conducting particles produced by the rays ; for the smaller eurrents the diminution in the number of molecules is to some extent compensated for by the increase in the time taken for these to recombine ; thus T is increased when the intensity of the rays is diminished, so that, as we see from equation (6), the proportion between a small current and the saturation current is increased when the intensity of the rays is diminished. Whatever is the magnitude of the electromotive force, a diminution in the intensity of the rays is accompanied by a diminution in the current, so that the | and B curves for two intensities of radiation would not intersect if both were drawn on the same scale. If, however, instead of keeping the gas the same and altering the intensity of the radiation, we alter the gas and 404 Prof. J.J.Thomson and Mr. Rutherford on the Passage keep the intensity of the rays constant, then the I and HE curves for two different gases may intersect. This effect is shown in the following diagram, which represents the I and EK curves for hydrogen and air. We see that for small electromotive forces the current is greater in hydrogen than in air, while the saturation current is much greater in air than in hydrogen. ‘The saturation current depends merely Fig. 4. | | on the number of conducting particles produced by the rays, while the current in the earlier part of the curve depends on the space described by the conducting particles in the time T (see equation 6), and we infer that more conducting particles are produced by the rays in air than in hydrogen, but that the product of U, the velocity of these particles, and T, a time which is proportional to the time these particles linger after the rays are cut off, is greater for hydrogen than it is for air. In fig. 5 we give the curves for air, chlorine, sulphuretted hydrogen, and mercury vapour, the curves being drawn on such scales that the ordinate representing the saturation current is the same in all these cases. It will be noticed that the curves for air, for sulphuretted hydrogen, and for chlorine coincide, mercury vapour falls below, while the hydrogen- curve would be above. This shows that, using the notation of equation (6), UT is the same for air, chlorine, and sul- phuretted hydrogen, and that its value for these gases is smaller than for hydrogen and greater than for mercury vapour. It is remarkable that the shapes of the curves for air, sulphuretted hydrogen, and chlorine should agree so closely, of Electricity through Gases exposed to Réntgen Rays. 405 for the absolute values of the current in these gases is very different, the saturation current in sulphuretted hydrogen Fig. 5. be) ROS % NS ~ ™. XR. S BMF being in some cases three or four times that of air, while that of chlorine is in some cases as much as ten times that of air. The value of the saturation current varies greatly in different gases; of the gases we have tried it is least in hydrogen, greatest in mercury vapour, the saturation current in mercury vapour being about 20 times that for air. It does not seem to depend entirely on the density of the gas, as in sulphuretted hydrogen it is three or four times what it is in air, though the densities are nearly equal, while, though the density of the vapour of CH,I, is greater than that of mercury vapour, the saturation current in the former gas is only a small fraction of its value for the latter. The gases which have large saturation currents are those which contain the elements which have an abnormally large specific inductive capacity in comparison with their valency. We have made a large number of experiments with the view to seeing whether there is any polarization when a current of electricity passes through the gas; we have not, however, been able to satisfy ourselves of the existence of this effect. The absence of polarization implies, however, that the ions are able to give up their charges to the metal electrodes. Experiments on electritied gases show, however, that it is very difficult to get a charge of electricity from a gas to a metal unless the metal is exposed to radiation, either by the metal being sufficiently hot to be luminous, or when it is exposed to ultra-violet light. But in the case of the passage of electricity through a gas which has been exposed to Réntgen rays the Phil. Mag. 8. 5. Vol. 42. No. 258. Nov. 1896. 2G 406 On the Passage of Hiectricity through Gases. conduction takes place even when the system is not exposed to the direct radiation fron the exhausted tube; we think it probable therefore that the gas itself radiates after being ex- posed to the Rontgen rays. To test this we tried the following experiment. AB, CD Fig. 6. A CG D B are two concentric cylinders made of thick lead tubing, the base of the inner one was cardboard, so as to allow Réntgen rays to pass through the gas in the inner cylinder. A metal ring was placed between the two cylinders and connected — with one pair of quadrants of an electrometer so as to allow the leak from it when raised to a high potential to be mea- sured. A slit was cut in the inner cylinder in such a place and of such a size that no rays could pass through it directly from the bulb. The apparatus was filled with chlorine, as this gas is one which gives a very rapid rate of leak. When the slit was left open there was a rapid leak due to the diffu- sion from the inner cylinder of gas which had been exposed to Réntgen rays. When, however, the slit was covered up with a strip of paper the leak wholly disappeared, though the ring connected with the electrometer was placed at the same level as the slit and therefore exposed to any radiation that might come from the gas. ‘This radiation, if it exists, must therefore either be of very feeble intensity or else it must differ from the Réntgen rays in not making a gas through which it passes a conductor of electricity. We are inclined to think that when Rontgen rays are incident on a metallic surface the “ diffusely reflected” rays are not of the same character as the incident ones, and have not nearly the same power of rendering a gas through which they pass a conductor of electricity. We base this opinion on the experiments we have made to detect the existence of electrical effects due to the “reflected ” rays ; though we have made many attempts we have never been able to detect the existence of any electrical On the Resistance of the Electric Are. 407 effects from the reflected rays. Thus we introduced in the apparatus in fig. 6 a lead plate inclined at an angle of 45° to the axis of the cylinder, and so placed as to reflect the rays through the slit, which was covered with a strip of paper ; the arrangement was so sensitive that if the plate had reflected -anything like one per cent. of the rays incident upon it, the leak from the metal ring would have been easily detected ; there was, however, no trace of a leak. ‘The results of ex- periments on the photographic effects produced by rays diffusely reflected from metallic plates seem to show that these rays are fairly abundant. Taking this result in connexion with the absence of any noticeable electrical effect produced by these diffusely reflected rays, we think that the latter differ in character from the incident rays. We have not been able to detect any effect produced by a magnetic field on the rate of leak ; we tried with the lines of magnetic force parallel and also at right angles to the current, -and with both small and saturated currents. The rate of leak through air that had been dried by standing for three days in the presence of phosphorus pentoxide did not differ appreciably from the damp air of the room. In conclusion, we desire to thank Mr. KE. Everett for the _assistance he has given us in these experiments. The period during which a bulb gives out Rontgen rays at a uniform rate is not a long one, and as most of our experiments re- quired the rate of emission to be constant, they have entailed the use of a very large number of bulbs, all of which have been made by Mr. Everett. XLI. On the Resistance of the Electric Arc. By Jvuuius Fritu, 1851 FEehibition Scholar, the Owens College, Man- chester, and CHARLES Ropgers, B.Se., 1851 Le Scholar, Firth College, Sheffield. [Plates III. to V.] HERE seems to be some uncertainty as to what is meant by the resistance of the are. Any given arc is a phe- nomenon which exists at a detinite P.D. and current, and any attempt to measure its resistance must alter the state of the arc as little as possible or else we are no longer dealing with the same phenomenon. Hence it seems to us that the only way in which the resistance of the are can be measured is by the ratio of a very small increment of P.D. applied, to * Communicated by the Physical Society: read May 8, 1896. 2G 2 408 Messrs. J. Frith and C. Rodgers on the the small increment of current produced. It must also be borne in mind that the change in the current must be of so short a duration that the form of the carbons is not in any way altered. Apparently the only method which fulfils these conditions is one in which a small alternating current is used, super- imposed on the main continuous current. This has the effect -of rapidly increasing and decreasing by a small amount the current passing through the are. It seems probable that the effect on the are of each small increase of current is annulled by the decrease of current immediately following. In fact a comparatively large alternating current may be superimposed -on the main continuous current without producing any visible effect on the are. 3 We are thus led to define the resistance of the arc as the ratio of a small increment of P.D. applied, to the small incre- V dA It is most important to distinguish this quantity, which we ment of current produced. This may be briefly written call the “ instantaneous ”’ from the tangent of the incli- Vv TA’ nation of the tangent line of the curve representing the steady values of V and A, which we will call, for the sake of clear- (44 = 2) d s ness, the “ steady DE We have performed some experiments to exemplify the difference that exists between these two quantities; and also to show that in cases analogous with the arc, where, however, the result can be verified, the instantaneous = found by superimposing an alternating current, gives correct values _ for the resistance. In one of these experiments a glow-lamp, taking 10 am- peres at about 8 volts, was placed in series with three I.E.S. 50 ampere accumulators, and a current sent through against the E.M.F’. of the cells. This arrangement is just what is _ wanted to test the method, namely a resistance in series with a back E.M.F., both of which are functions of the current ; and, further, the resistance can be separated from the back K.M.F. and measured, and the result compared with the value dV ebtained for the resistance by the instantaneous re The result of this experiment is represented on PI, III. Here are plotted the curves connecting the current and P.D. between the outside terminals of the arrangement and also Resistance of the Electric Are: 409 between the terminals'of the lamp and of the battery. This last gives the back H.M.F., since the resistance of the cells was small enough to be neglected. The P.D. at the lamp divided by the current gives the resistance ; this is plotted on the same diagram ; to make it clearer, however, the scale of ohms is multiplied by 10. We have measured* the instantaneous = at various current strengths, and the values of this are plotted in a dotted line. It is seen that there is a very close agreement between these two measure- ments of resistance. On the same sheet are plotted values for the steady ue This differs considerably from both the resistance-curves. This leads us to see that the rapid excursions caused by the alternating current are not along the curve joining the steady values of V and A, but along a line which is everywhere more vertical than the tangent to the curve. This line is formed by joining the point on the curve to the instantaneous origin, which is distant from the origin of the diagram by an amount equal to the back H.M.F. at that particular current. Were the electrical excursions to travel along any intermediate path, the value obtained for the instantaneous a would be dependent on the frequency. As will be seen later, this is not the case between the experimental limits of 250 and 7 complete alter- nations per second. If, therefore, the arc, as has been affirmed by various authorities, consists of a back H.M.F. and a re- sistance, we feel justified in applying this method for the measurement of its resistance, which has been found correct in closely analogous cases. Now at very low frequencies indeed the electrical oscilla- tions would travel along the curve connecting the steady values of V and A ; and this is clearly the meaning of the critical frequency which we have observed with cored carbons (see p. 421), namely, that under the critical frequency the superimposed alternations travel on the steady value curve and become identical with the “ steady” gy : Several experimenters have obtained values for the resist- ance of the arc which agree fairly well amongst themselves, and which seem to show that the arc has a positive resistance f. * By method I. below. : + An abstract of papers bearing on this subject was given by Mrs Ayrton in the ‘ Electrician,’ Sept, 18, 1895. 410 Messrs. J. Frith and C. Rodgers on the It was pointed out, however, by Prof. Ayrton at the Ipswich meeting of the British Association, that although there was a marked agreement between the values obtained by these experimenters, they were not at all in accordance with the conclusions drawn by himself from consideration of the curves obtained by Mrs. Ayrton. These curves con- nect the P.D. between the carbons with the current passing through the are, for various fixed lengths of arc, and from them it is seen that for a given are-length an increase of P.D. is always accompanied by a decrease of current. From this fact Prof. Ayrton concluded that.if an attempt were made to measure the resistance of the arc by altering the P.D. between the carbons and finding the corresponding alteration of cur- rent produced, the resistance found by taking this ratio must be negative. This conclusion was strengthened by some experiments made by Mr. Mather at Prof. ” Ayrton’? s suggestion. In one of these experiments two points of equal potential were found in a circuit consisting of an arc, a battery, and a resistance. Another battery, consisting of a few ceils, of known H.M.F. and resistance was applied between these two equipotential points and the current flowing through the battery was noted. The resistances of the two parallel halves of the circuit, exclu- ding the arc, were known, so that the current which, taking the are resistance as zero, should flow through this battery ~ could be calculated. Now the value of this calculated cur- _ rent was found to be less than the observed value, no matter in which direction the P.D. was applied, and this result was also obtained when an alternating P.D. was used. Hence the resistance of the arc was apparently less than zero. The other experiment consisted in running the are ata steady P.D. and current, suddenly altering the resistance in circuit by a small amount, and noting the changes in the ammeter and voltmeter-readings so produced. The new con- ditions were maintained only long enough to allow of these readings being taken. The are was then brought back to its former condition before taking another reading. It was found that a change of P.D. in one direction was always accompanied bya change of current in the opposite direction. The results of both experiments were, however, only qualitative. All these experiments, together with the consideration of the curves found by Mrs. Ayrton, lead to the conclusion that the arc has a negative resistance, while former experimenters had all obtained a positive resistance. It was in order to throw some light on this discrepancy that we undertook a series of experiments to determine with Resistance of the Electric Arc. “= SEE som? degree of accuracy the resistance of the arc under various conditions. Methods. A number of methods were tried using alternating currents, of which the following were most successful :— Method I. is represented diagrammatically in fig. 1. D is Jaytes, Ne fll B Ul the armature of an alternator, the current from which passes round two circuits in parallel, one of which contains the are X, and the other an adjustable resistance R. By adjusting R the alternating currents in the two halves can be made equal. When this is the case the impedances of the two halves to -alternating currents must be equal. In the diagram the continuous-current circuit is shown to the left. It consists of a battery of accumulators B, the hand-adjusted arc-lamp X, the resistance K, the ammeter A, and (with the commutator C as shown) the resistance S and the alternator D. It will be noticed that the alternator D carries the continuous current, but this of course does not prevent its acting as an alternator. In order to measure the small alternating current indepen- dently of the continuous current flowing we used the air- transformer T, the thick wire coil of which was in series with the alternator D, the thin wire coil being connected with an 412 Messrs. J. Frith and C. Rodgers on the electrostatic voltmeter E. The reading of the electrostatic voltmeter is thus unaffected by the continuous current, while itis, ata given frequency, a measure of the alternating current flowing. By means of the commutator OC, the air-transformer T can be thrown into either circuit, the resistance S being by the same operation thrown into the other circuit. The resistance S is equal to that of the thick wire coil of T, so that when 8 replaces T the continuous current is unaffected by the change. Method of Experimenting. The are was run at the required current and P.D. by alter- ing the number of cells in B, K being always kept the same. The current was kept constant by adjusting the are by hand. Under normal conditions the current could be kept constant to within 1 per cent. R was now adjusted till the deflexion of E was the same when T was in either circuit. When balanced, a change of 0°01 ohm in R caused an appreciable difference in the deflexions of KE. It was found to be useless to adjust more accurately than this, since the small variations in quality always found in carbons produced differences of this order in the resistance of the arc. Let the value of R when a balance is obtained be R;. This is equal to the resistance, to alternating currents, of the bat- tery (b;), the resistance (k), the arc lamp and connexions (/), and the are (2). R,=k+6,+ 2. .- 7). =e The carbons are now firmly screwed together and the number of cells in B reduced till the continuous current is the same as before. R is again adjusted till the deflexions of E are equal ; and if R, is the new value thus obtained, Re=k+betd;... >.< b, being the resistance of the portion of the battery now used. The cells are next cut out, the mains leading to them short- circuited, and a third value R; obtained, RwSh4 1 2 oy From (ii.) and (ili.) we obtain the resistance of bj, and by proportion of any number of cells. Putting these values in (i.) we obtain the value of 2 in ohms. The advantages of this method are that no calibration of the electrometer is required, the speed of the alternator need not be constant for long periods together, various alternators giving different frequencies and wave-forms can be used without materially altering the circuit, and especially that Resistance of the Electric Are. 413 the resistance of the arc can be obtained directly in ohms as the difference of two readings of the box R. Method II. is shown diagrammatically in fig. 2; the arc Fig. 2. ES B Ha circuit in this case being shown to the right. X is the are, B the battery of accumulators, K the resistance, A the am- meter, and V the voltmeter across the arc. B and K were made large, K being about 1l ohms. The circuit shown on the left consists of the alternator D, the transformer T, which together with E is now used simply as a delicate alternate- current ammeter, a condenser F’, and a commutator C. By means of C we can put in circuit either the resistance R, or the arc-lamp X in series with the resistance 8S. The alter- nating current flowing through K is negligible compared with that flowing through X on account of the high resist- ance of K. The condenser F prevents any continuous current due to the P.D. at the arc from passing through the alter- nator. Method of Experimenting. If L is the self-induction of the circuit and F its capacity, the impedance I of the circuit is given by Ms R?+ ( = — Lo) ; where #=27 x frequency. Thisisa minimum when LF'o’=1. A414 Messrs. J. Frith and C. Rodgers on the’ The alternator was run at a speed corresponding to this fre- quency, at which the arrangement is most sensitive to changes of R. An experiment consists in adjusting R till the deflexions of E are the same whether R or S+ nn N? = 6? + 6 + 260’ cos(8—f'), . ~. see _ bsinB+0' sin 8’ tan Drip cone Se Gcose? 5 (10) Hquations (5) and (6) represent an undulation of uniform plane waves travelling in the same direction as U and V. We may call this resultant undulation W. Hquations (7), (8), (9), (10) enable us to determine the constants of any one of these three undulations, if we know those of the other two. It appears accordingly that any two of the three undulations U, V, W being given, the third can be found. It is an easy inference from this that any number of undu- lations of uniform plane waves of wave-length A, that travel in the same direction, may be combined into a single undula- tion of the same kind travelling in that direction: a proposition of which use was made above in the latter part of § 6, of Part [., p. 337. 29. Of elementary sheafs of beams, and of the single beams which may be substituted for them.—Beams of uniform plane waves may be emitted in any or all directions from the front Dr. G. J. Stoney on Microscopic Vision. 437 of the objective field, or from either of its “ standard images.” Draw what we have called the axial rays of these. They are lines radiating from the middle of the objective field, and each perpendicular to the waves of its own beam. Take a group of these axial rays which lie within a definite cone, then the corresponding beams may be called a sheaf of beams; and where the cone within which the axial rays are confined is a very acute one, the corresponding beams may be called an elementary sheaf of beams. The whole of the beams emitted by the objective field, or from either of its standard images, may obviously be conceived of as divided up into elementary sheafs of any required degree of minuteness. If we only have to deal with an image of limited extent like standard image No. 1, or standard image No. 2 (which are the same size as the objective field), then we are justified in substituting a single beam travelling along the axis of the cone for each elementary sheaf of beams. This may be proved as follows :— Let U be one of the beams whose axial ray lies within the elementary vone, and let @ be the angle between that axial ray and the axis of the cone. The cone, of course, has its vertex at the centre of the objective field. Let now V be an equivalent beam whose axial ray lies along the axis of the cone, and let the phase of V be such that U and V are in the same phase at the centre of the objective field. Then, as in § 15, let —V mean the same beam as + V, only with wadded to all its phases. Accordingly, if + V and —V are simulta- neously present they cancel one another absolutely. We may therefore add both of these to the elementary sheaf of beams without altering it. Now —V and U would produce a ruling which will be the coarser, z.e. with its luminous bands more widely spaced, the smaller the angle @ is. Moreover, since +V and U are in the same phase at the vertex of the cone, which is also the centre of the objective field, it follows that one of the minima of illumination of the ruling produced by —V and U will occupy that position. Now by making @ sufficiently small, the spacing of this ruling may be made so many times larger than the objective field that there is no appreciable illumination anywhere within the limits of the objective field. If this be so, we may suppress the beams —V and U without producing appreciable change within the limits of the objective field. When this is done, the elemen- tary sheaf of beams differs from what it was at first by having --V now in the place of U. By a similar process we may substitute V', V", &c. travelling along the axis of the elemen- tary cone for the other beams whose axial rays lie within the Phil. Mag. 8. 5. Vol. 42. No. 258. Nov. 1896. 21 438 Dr. G. J. Stoney on Microscopic Vision. cone. And, finally, all these V’s, since they travel'in pre- cisely the same direction, will, as is proved in the last section, coalesce into a single resultant beam W travelling along the axis of the cone, which single resultant may accordingly be substituted for the elementary sheaf of beams. The general conclusion is :—The whole of the light emitted from the objective field may, by Theorem 1, be resolved into beams of uniform plane waves ; these beams may be divided into small groups, each an elementary sheaf of beams; and each elementary sheaf of beams may have a single beam substituted for it.—In every subsequent step of our investigation we need only deal with these resultants—these secondary beams as they may be called—which, though many, are limited in number. 30. Another proof of Theorem 2.—Theorem 2 may be proved in many ways, and a proof which carries the analysis of an image down to its simplest elements will be found instructive. Describe a hemisphere in front of the objective field and round its centre. Call the point where the optic Fig, 2. axis of the microscope pierces this hemisphere, its pole. Planes passing through the optic axis may be called the meridional planes ; and the objective plane, being perpendicular to the axis of the microscope, will be its equatorial plane. Divide the equator of our hemisphere into seconds of are, z. e., into 1,296,000 parts, which will afford sufficiently minute divisions upon which the bases of elementary cones may abut. Draw parallels of latitude also at intervals of a second ; and draw meridians as in the figure, marking out in conjunctiou with the parallels of latitude the bases of the elementary cones, or rather pyramids. These become narrower the higher the latitude, and as soon as they have shrunk to half a second horizontally every alternate meridian may be omitted, until they have shrunk again till other meridians may be omitted without any of the little sectors Dr. G. J. Stoney on Microscopic Vision. 439 being more than a second in width. By this process the whole hemisphere may be mapped out into these patches placed in vertical series, each series with a corresponding series on the opposite side of the polar axis, and the whole ending up in one patch or in one pair of patches at the pole. From the middle of each patch draw a radius of the sphere, omitted from the diagram to avoid confusion, but easily con- ceived. These are the axial rays of the secondary beams W, which we are at liberty to substitute for the elementary sheafs of beams that really exist. 3 In this as in all similar problems it is convenient to begin by resolving each beam of light into two plane-polarized beams, one polarized in and the other perpendicular to the meridional plane in which its axial ray lies) We may then confine our attentivn first to the light polarized in one of these ways. Let us then call the secondary beams which are polarized in one of these ways a, 6, &., and the corresponding beams opposite to them and polarized in the same way, a’, U, &c., as in the figure. In general, beam a and beam a’ will not be alike. How- ever, heam a’ may by the proposition in § 23, p. 435, be sub- divided into a’; and a’, of which a’, shall be exactly similar to a. Accordingly a and a’, produce a definite ruling of equal and equidistant lines extending over the whole standard image ; and a’, has still to be disposed of. Resolve 6 into two beams of which 6, is similar to a’,, and 0b, is the other component, Then a’, and 5; produce another ruling, and b, has next to be disposed of. ‘lo do this, resolve 0! into 6’, and b',, of which 6’; is similar to 62. ‘Then b, and 6’; produce a ruling and 0b’, is what remains over. By continuing this process the whole of the vertical columns over a and a’ may be dispose: of ; and in a similar way the other columns can be treated. All the rulings extend over the whole of the standard image, and between them use up the whole of the light polarized one way, except that residium which is left over in the last patch at the pole. This residium can be made as small as we please by diminishing the size of our elementary cones; and of whatever amount it is, it only represents the limiting case of a ruling produced by two beams advancing at a vanishing angle to one another, and of which accordingly the spacing is infinite. A similar treatment applies to the light polarized the other way, which also produces its body of rulings; so that finally the whole of the light emitted by the objective field, however varied its contents, can be laid down on the standard image in the form of a number of luminous rulings of uniform parallel lines, each of them of that optically most simple character 212 ad 440 -Dr. G. J. Stoney on Microscopic Vision. which ts produced by a single pair of beams that are alike and polarized, either both in the plane of incidence or both perpendicu- larly to tt. A similar treatment applies to standard image No. 2, the only difference being that to analyse it we are to employ a sector of the hemisphere in the figure on p. 438 instead of the whole hemisphere. Hence Theorem 2 is fully proved. 31. The resolution not unique.—in order to follow the most simple process when combining the secondary beams in pairs, we have taken both the members of each pair from the same meridian. We might of course have combined them lateraily or obliquely, and we shall find it necessary to bear this in mind when dealing with some kinds of illumination that are found useful, e.g. annular illumination. It is obvious that it is legitimate to combine the secondary beams in any way which when completed has used up all the light : and our object should be to combine them in each case in whatever order is most convenient for the problem in hand. In the practical use of the microscope it is usually quite easy to see into what groups it is most advantageous to throw them. Jn whatever order they are taken the final result is the same; but one order differs from another in the degree in which it gives us information that is of use to us. It is sometimes convenient to think of an optical image as a kind of picture, and that the rulings are, as it were, suc- cessively painted in upon the field of view to form it. But if we conceive matters in this way we must remember that this luminous paint behaves after a very peculiar fashion. Where one ruling crosses another or overlies it, they may obliterate one another in some parts as well as strengthen one another in others, effects which will depend on the lengths and positions of the transversals in the two rulings and upon the relation in which their phases stand to one another. In this connexion it is very necessary to bear in mind that two rulings may be seemingly identical—~z. ¢., identical in position, spacing, intensity, &c., in such matters as the eye can perceive—and yet these rulings may behave quite differently towards the other rulings with which they are associated, owing to differences affecting the transversals and phases which our eyes are not fitted to take note of. Thus, what are apparently identical rulings might result from the interference of two beams little inclined to the optic axis, and from two others much inclined : or from two beams in the same meridian and two others in other positions: but these seemingly identical rulings would all behave differently towards the rest of the light with which they have to act. Dr. G. J. Stoney on Microscopie Vision. 44] 32. Criticism of the Abbe and the Airy methods.—The proof which we have just gone through is instructive in many ways. In the first place, it carries the analysis of the image down to rulings of the simplest kind that are known. In the second place, it makes the flexibility and Protean character of the whole process conspicuous ; for although we followed one particular order in combining the secondary beams in pairs to form rulings, it is manifest that this order was in no degree necessary, and that the secondary beams might have been grouped in an infinite number of different ways, the only condition being that whatever order we adopt we must take care to use up all the light. This means that the set of rulings which form an image is not unique: that there are an infinite number of such sets, any one of which will suffice to form the image. But, above all, the proof given in the last section brings well into view the source of the advantage which is found in employing Abbe’s mode of procedure as our instrument for searching out the causes of the phenomena presented by microscopic vision. By the process we have followed the light sent forward from the objective field has been analysed into beams of plane waves. Now this is only one of number- less possible ways of analysing that light. It is an analysis which may be made, not which must be made. But it has the advantage over every other analysis, that the resulting waves are uniform waves, exactly alike in every respect over the whole extent of each wave surface and each wave retaining its form and intensity unchanged during its advance. This sets us free from a sea of difficulties that embarass our progress when we attempt to employ any other resolution. If the analysis be made into curved waves of any kind—into those of Airy’s method or any others—the resulting waves are not uniform over each wave-surface ; and as the law of this want of uniformity is not yet known, we can only legitimately employ Airy’s method in the cases where this want of uniformity has an inconspicuous effect upon the result of our inquiry. ‘This is the case, for instance, in the treatment of telescopic vision to which Airy applied it. Here the sector of each hemispherical wave that we have to deal with is sufficiently small for the want of uniformity within its small extent to be of negligible amount. Tt has sometimes been supposed that we can investigate microscopic vision by applying Airy’s analysis to the light sent forward to the eye from the image of the microscopical object which is formed by the objective close to the eyepiece. This light as it comes from each point of that image is confined within a cone which is a continuation upwards of the nazrow 442 Messrs. Ayrton and Mather on Galvanometers. cone from the back lens of the objective to that point of the image. Accordingly, if that object which is called the wisual substitute in Part I., § 14, p. 342, could be put in place of this image, sending forward hemispherical waves from each point ‘of it which might be treated as uniform within the limits of the aforesaid cone ; then what the Airy method as hitherto applied has investigated is what minuteness of detail it would be possible to see in this object. . But such an inquiry does not. even touch the main points towards which an investigation of microscopic vision needs to be direcied. It tells us nothing as to what this visual substitute is, how far it can represent something on the microscopic object, and how far it consists of intercostal markings, diffraction-fringes arising from the mismanagement of the illuminating apparatus, or any other misleading effects. And of course it gives us no clue as to how we are either to interpret or control any of these effects. Every legitimate mode of resolution, and there are number- less such, must lead to precisely the same result, if we can succeed in correctly following out its consequences. Where they differ is in our power of handling them. Abbe’s resolution into beams of plane waves recommends itself above all others in regard to this; since it substitutes uniformity for that want of uniformity which exists in all other methods of resolution in just those places where in the present state of our knowledge we are unable to assign the law of this want of uniformity. And even if we ever come to know this law, the resolution into uniform plane waves will still recommend itself in consequence of the law of uniformity being simpler and therefore more easily handled than any law of non-uniformity. (To be continued. | XLII. Galvanometers. By Prof. W. EH. Ayrton, F.R.S., and 'T. MaTHER*, N an article on “The Electric Discharge in a Magnetic Field”? contributed by Sir David Salomons to the Phil. Mag. for September, it is stated on p. 255 :— “T made a large number of experiments with galvanometers built on the D?’Arsonval-Deprez type, and obtained very varying results by modifying the magnetic field. By in- creasing the field a maximum sensibility was reached, which decreased on further increasing the field. ‘“‘ The various experiments described no doubt indicate the cause of this, viz. that the field being made too powerful, less current passes through the coil, and the sensibility begins to * Communicated by the Authors. Messrs. Ayrton and Mather on Galvanometers. 443 fall. I had a special galvanometer-apparatus made to fit my large magnet, converting it probably into the largest galva- nometer of the type extant ; but the sensibility is exceedingly small when the magnet is fully excited, and increases rapidly when the excitation is somewhat diminished.” _ The preceding is gravely given by Sir David Salomons as an illustration of the displacement of the current in a con- ductor by a magnetic field ‘‘ generally known under the name of the Hall effect,” in apparant ignorance of the fact that the “ Hall effect ” is extremely minute. Indeed, had Sir David Salomons tried to compare the current sent by a given P. D. through a coil of insulated fine copper wire when placed in and out of any magnetic field he would have found it practi- cally impossible to detect any difference, and he would have - convinced himself that the great falling off in sensibility of a d’Arsonval galvanometer as the strength of the stationary magnetic field was increased beyond a certain limit could have nothing to do with the “ Hall effect.” - Further, this phenomenon, which is described in the Phil. Mag. for September as new, has for some time past been known to electrical instrument-makers, for it was one of the eauses which prevented the sensibility of the suspended-coil type of galvanometer being increased beyond a certain limit. _ In the discussion which took place after the reading of a paper on a “ Workshop Ballistic Galvanometer”’ before the Physical Society in June 1892, reference was made— perhaps for the first time publicly—to the difficulty ex- perienced in increasing the sensibility of a d’Arsonval galvanometer by increasing the strength of the field beyond a certain point. And it was the investigation of the cause of this phenomenon, and the discovering of a means to over- come it, that caused the publication of the description of this instrument to be delayed until the meeting of the British Association in 1895, as was explained in the account of this latter instrument given in all the electrical journals about September 1895. In the ‘ Electrical Engineer’ for October 5th, 1894, it was mentioned. that ‘“ great difficulties were, however, found to arise when the extreme sensitiveness sometimes required in the laboratory was attempted ... chiefly due to the traces of magnetism found to exist in the silk and other parts of the coil usually considered non-magnetic .... A great number of trials was made at the Central Technical College which showed that .... the purest wire of electrolytic copper or of fine silver, specially drawn and covered, still showed traces, and a method . . . was at length devised whick has practically solved the difficulty. The non-magnetic pro- 444 Messrs. Ayrton and Mather on Galvanometers. perty of the new coils allows a magnet to be used whose field is four times as strong as those ordinarily employed in this type of instrument.” Rather more than a year later, in the ‘ Electrical Engineer ” for December 13th, 1895, further information on this subject is given :—‘t This phenomenon was first noticed by Mr. Mather in December 1891 ... The coil to be tested was suspended in the earth’s field and the period of a complete oscillation was found to be 25:2 seconds. It was then placed in a field of 1500 C.G.S. lines and the period was only 3°5 seconds,” corresponding with a controlling force due to the magnetic action of the coil fifty times as great us that due to the suspension itself... “parts of the coil became magnetic and it can easily be seen that this secondary effect is magnified in the d’Arsonval type of galvanometer, when, with the object — of gaining sensibility, the magnetic field is strengthened ... in fact the magnetic action of the coil will defeat this attempt.” References are also given in the ‘ Electrician’ and ‘ Hlec- trical Review’ of the same date to the limitation in sensi- bility produced by the magnetism of the coil ; and lastly, in the ‘ Electrician’ for January 31st, 1896, Mr. Fisher, in a series of articles on the ‘‘ Crompton Potentiometer,” writes:— ‘‘ whilst up to a certain point the deflexions became greater with increased strength of field, beyond that point the de- flexion gradually fell off as the field was strengthened, this being due, as Messrs. Ayrton and Mather have pointed out, to the presence of iron in the materials used in the construe- tion of the coils. A remedy for the same was found by Messrs. Ayrton and Mather, and it is due to Prof. Ayrton’s kindness in disclosing the process adopted that the sensi- bility of the instrument is to a great extent due.” : We may take this opportunity of replying to an article on ‘Galvanometer Design. Waste Space near the Needle,” published in the Phil. Mag. for December 1895, by Prof. 8. W. Holman, of the Massachusetts Institute of Technology, as a criticism of one of the facts brought out in the 1890 paper on ‘¢Galvanometers” by Dr. Sumpner and ourselves. In that paper it was pointed out that to obtain maximum sensibility with an ordinary reflecting-galvanometer no wire should be wound in a certain space close to the needle, or, if wound, it should be connected up the reverse way to the rest of the coil; and it was shown that the approximate shape of the space in question was “an oblate spheroid with a polar axis about 0°72 | of its equatorial diameter, the latter being, of course, slightly: larger than the length of the needle.” | Messrs. Ayrton and Mather on Galvanometers. 445 Prof. Holman admits the accuracy of our reasoning that there is a certain space in which the wire should either be left out, or be oppositely connected, but he considers that we overestimated the volume of this space because we neglected “the fact that the field over the remainder of the needle is not the same as at the poles, either in direction or strength.” And to support his argument he proceeds to consider what ought to be the boundary of the space in the cise of “a very thin uniformly magnetized prismatic needle” (the italics are ours) without observing that this is exactly the case we dealt with, and, therefore, must lead to exactly the conclusion we arrived at. For no part of such a longitudinally magnetized needle, other than its ends, contributes to the deflecting moment when placed in any weak magnetic field, since no free magnetism exists except at its ends. Hence his objection that the field is not uniform throughout the length of the needle has no weight whatever in the very example he has himself selected. We may also call attention to another error into which Prof. Holman has fallen. He gives as the value of the deflecting moment, produced by a current in a coil on a very thin uniformly magnetized prismatic needle, the expression 1 2| m.f cos @.ds, 0 ““m being the strength of pole of any thin transverse section or shell of the needle, ds the thickness of that section, f the field-intensity at that point, and @ the field-direction angle with the axis of the coil.” But this expression could only be correct if every part of the needle were equidistant from the axis of rotation. And even if allowance were to be made for this not being the case by introducing s, the distance of a section from the axis, the expression l 2| m.fcos@.sds 0 would still only give the correct value for the deflecting moments in the case of “a very thin uniformly magnetized prismatic needle” by making m equal to nought for all points, except at the ends. And when that is done, the conclusions arrived at by Prof. Holman are profoundly modified. As to the confirmation by experiment of his conclusion that the deflecting moment of a coil of diameter about half the length of the needle is nil when the coil is placed close to the needle, that merely proves, we think, that the needle he used in his experiments was not uniformly magnetized. It is, of course, well known that it is almost impossible to obtain 446 Messrs. Ayrton and Mather on Galvanometers. magnets uniformly magnetized, and if free magnetism exists along the length of the magnet as well as at its ends, our conclusion must, of course, be modified. Indeed, we convinced ourselves by experiments made at the Finsbury Technical College as long back as 1884 that with ordinary magnetic needles it was necessary to place a coil of given diameter somewhat nearer to the needle than was indicated by the formula in our 1890 paper before the deflecting moment changed sign. But since by far the greatest amount of free magnetism on very thin magnets exists near their ends, we do not consider that the theoretical deductions contained in that paper concerning the waste space can have been far wrong. We agree with Prof. Holman that uniformity should be observed in describing the sensibility of galvanometers, and we were glad to see that the system for denoting sensibility which was proposed and used by us in our 1890 paper was adopted in the programme of the Naturforscher und Aerzte which met this September in Frankfurt. The ¢, however, used by Prof. Holman in his proposed list of observed quantities should be the pertodic time, and not, as he states, “the time of a single swing.” Further, in addition to the data respecting resistance, periodic time, and current per millimetre deflexion at given scale distance, mentioned by Prof. Holman as essential in descriptions of sensitive galvanometers, we would point out that it is also important to give the moment of inertia of the suspended system, for unless this be done it is impossible to make the comparisons of various instruments complete. As is well known, the smaller the dimensions and mass of the moving parts, the more excellent will such an instrument appear, when excellence is judged entirely by thé deflexion per micro-ampere at constant scale distance and constant period. But for certain purposes it is necessary to compare instruments under conditions of constant controlling moment per unit angle deflexion, because the stability of the zero and trustworthiness of the readings depend ou this quantity, as was pointed out on pages 85 and 89 of our 1890 paper ; so that to make this comparison, a knowledge of the moment of inertia of the suspended system is required. Other useful particulars of galvanometers are the total volume of the coils, and the decrement, or logarithmic decre- ment, of the oscillations. And since this latter depends on the periodic time and on the condition of the galvanometer circuit, whether closed or open, the damping should be observed with the instrument under the same conditions as when the periodic time was taken. Pu Adgin] XLIV. Notices respecting New Books. Anleitung zur mikrochemischen Analyse der wichtigsten organischen Verbindungen. Vol. Ill. By Prof. H. Brenrens. Hamburg: Voss, 1896. HE rapid development of organic chemistry, and more especially the discovery of substances chemically almost identical but phy- sically different, has caused the chemist to turn his attention to physical instruments, with the result that the polarimeter, polari- scope, and refractometer are to be found in every well-equipped laboratory for chemical research. Prof. Behrens now seeks to introduce the microscope to the organic chemist, and in the three parts of his work which have already appeared he describes the behaviour of the more important organic compounds when crystal- lized, or treated with reagents, on the stage of the microscope. The reactions described result in the formation of crystals, the size, shape, and optical characters of which are specified. The present volume deals with the aromatic amines, and is enriched by 77 illustrations of microscopic crystals obtained by precipitation. lt should prove a useful handbook in the organic laboratory. Je la. Es XLV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. {Continued from p. 372.] June 10th.—Dr. Henry Hicks, F.R.S., President, in the Chair. es following communications were read :— ‘On Foliated Granites and their Relations to the Crystal- line Schists in Eastern Sutherland,’ By J. Horne, Esq., F.R.S.E., F.G.S., and E. Greenly, Esq., F.G.S. The crystalline schists of Eastern Sutherland are traversed by great numbers of granitic intrusions, chiefly in the form of lenticular sills. These generally lie parallel to the foliation-planes of the schists, but transgressive junctions are also frequent. Thin seams of granite also occur in such abundance as to constitute with the schists a banded gneissic series; but these seams can often be seen to transgress the schistose folia, and even often to proceed from large masses of granite. The granites contain numerous inclusions of the schists which they traverse, such inclusions retaining, usually, the dip and strike of the surrounding rocks, There are no chilled edges ; and, moreover, the component crystals of schist and granite mutually interlock along the lines of junction. The authors give an account of the foliation of the granite. In some rare cases a foliation parallel to that of the schists traverses granite-veins. It is generally, however, parallel at once to the sides of the sill and to the foliation of the schists ; and many of the structures are the remains of biotite-folia belonging to schists whose quartzo-felspathic elements have been incorporated with 448 | Geological Society :— those of the granite. But many sills or veins, traversing the schists at various angles, are foliated parallel to the line of junction, and so discordantly to the structures in the schists; and foliated granites may even be observed to cut each other’s foliation. These can hardly be anything but original igneous structures; but, if coexistent with the last-named, would be indistinguishable from it. The country-rocks are various types of biotite-schist or gneiss, with quartz-schists at Kildonan, and a scapolite-limestone at Arma- dale. They are almost all holocrystalline, but it is certain that sedimentary rocks enter into the complex. The whole series is powerfully folded. The granites increase in size and numbers north-westward from Kildonan: the intimate intrusive relations above described becoming more highly developed in the same direction. The schists, at the same time, become more and more highly crystalline, sulimanite also appearing in them. About Kinbrace they are coarse silliman- ite-biotite-gueisses, with large striated felspars. Igneous contact is not held to be the sole origin of metamorphism, though the cause which brought about the introduction of the gra- nites has evidently also produced these high types of crystallization, The evidence of powerful movement which the schists everywhere present suggests that such movement was the initial cause of the whole series of phenomena. Movement recurred throughont, though all cataclastic structures (if such existed) have been wholly effaced by crystallization ; introduction of granite being the final stage in the production of the complex, and a high temperature (as shown by the absence of chilled edges) being maintained to the very end. With regard to the granites, the authors find it difficult to believe that they are wholly foreign matter, but remark that it is here necessary to observe the utmost caution. ~ 2. ‘The Geology of the Eastern Corner of Anglesey.’ By E. Greenly, Esq., F.G.S. ‘I'he notes contained in this paper embody the principal results obtained during a survey of Anglesey on the six-inch scale. The schists of the South-east of the island are succeeded uncon- formably by the slates of Careg Onnan, which appear to be separated by a strong unconformity from the Ordovician shales. The Careg Onnan slates appear (pending confirmation from other sections or direct fossil evidence) to be of pre-Cambrian age, and the author records the existence of sponge-spicules therein. The ashy grits and bedded tuffs of Baron Hill near Beaumaris appear to have been moved somewhat from the E.N.E. along a thrust-plane. They are traversed by planes of mylonization, and are much broken and folded. The Ordovician rocks consist chiefly of sparingly fossiliferous dark shales and mudstones, but contain a group of volcanic tuffs on the horizon of the pisolitic ironstone. The Carboniferous rocks appear to be about 700 feet thick, and contain conglomerates, sandstones, and shales, with plant-remains about the middle of the series. Seismic Phenomena in the British Empire. 449 - The Glacial striz sweep round from 8.8.W. at the north, to S.W. and W.S.W. at the south end of the district. In the Penmon area there is cross-hatching with a series running 8.S.E., and it is suggested that this is due to fluctuations in the power of the Car- narvonshire glaciers to deflect the ice coming from the north, combined with the local influence of certain high ground. 3. ‘Seismic Phenomena in the British Empire” By M. F. de Montessus de Ballore, Captain of Fortress Artillery at Belle-Lle- en-Mer. The author gives a brief outline of a plan that he has elaborated for studying Seismology. He has separated his work into four parts:—1. The formation of an EKarthquake Catalogue. 2. Refuta- tion of the empirical laws previously enunciated. 3. Description of the globe from a seismological point of view. 4. Investigation of the characters which differentiate stable from unstable regions. He gives a method by which the relative seismicity (or instability as regards earthquakes) of regions may be obtained and registered, and indicates some of the results which he has derived from his study, including the intimate relationship between instability and surface- relief, and the independence of seismic and volcanic phenomena, The main part of the paper is a section of the third division of the author’s work, and deals in detail with the earthquakes of the British Empire. In this part of the paper, the recorded earth- quakes of the British Isles, India, Australia and New Zealand, British Africa, Canada, and various scattered possessions are de- scribed. June 24th.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read :— 1. ‘Notes on the Glacial Geology of Arctic Europe and its Islands.—Part If. Arctic Norway, Russian Lapland, Novaya Zemlya, and Spitsbergen.’ By Col. H. W. Feilden, F.G.S. With an Appendix by Prof. T. G. Bonney, D.Sc., LL.D., F.R.S., V.P.G.S. The author gives an account of observations made in Arctic Norway which tend to prove that the shell-bearing terraces are true marine deposits indicating uplift since their formation, and that they were not formed by ice-dams. He then describes terraces recently formed in Kolguev Island, which illustrate the combined influence of pack-ice, sea-waves, and snow on the formation of terraces in a risingarea. The glacial geology of the Kola Peninsula is next considered, and the distribution of the boulders noticed. There is no doubt that these boulders have been derived from local rocks, and that no ice-sheet from the North ever passed through Barents Sea or impinged on the northern coast of Europe. The author saw no evidence of the former extension of an ice- sheet over the now frost-riven rocks of Novaya Zemlya. He found wide-spread deposits of boulder-clay with marine shells in this region, which he attributes to the action of floating ice. In the Kostin Schar many of the islands are connected by ridges covered 450 Intelligence and Miscellaneous Articles. with rounded stones pushed up by floe-ice, with solid rock beneath glaciated by the floe-ice. Several minor phenomena connected with the glacial geology of Novaya Zemlya are also described. The raised beaches of Franz Josef Land are noticed, and immense deposits occurring in Spitsbergen, which were originally formed under water in front of glaciers, alluded to. These, as weil as other submarine deposits of glacio-marine origin seen elsewhere by the author, show no signs of stratification. Prof. Bonney describes specimens brought by Col. Feilden from Norway, the Kola Peninsula, and Novaya Zemlya. From an examination of the rocks obtained im situ in the latter region, Prof. Bonney confirms Col. Feilden’s suggestion that the Kolguev erratics may have come from Novaya Zemlya. 2. ‘Extrusive and Intrusive Igneous Rocks as Products of Magmatic Differentiation.’ By Prof. J. P. Iddings, For.Corr.G.8. The author, after pointing out the propositions concerning differentiation of magmas upon which he is in agreement with Prof. Brégger, discusses the points of difference, and describes the relation of the igneous rocks at Electric Peak to all of those which took part in the great series of eruptions which occupied almost the whole Teitiary period, and spread themselves over a vast territory in Montana, Wyoming, and Idaho. In Tertiary times the eruptions were at first largely explosive, and the accumulation of tuff-breccia formed a chain of lofty volcanoes, comparable with the Andes in size as well as in the nature of their material (andesite and andesitic basalt). After considerable erosion of these volcanoes, gigantic fissure-eruptions flooded the region west of the denuded volcanoes. The massive lava-streams which welled from these fissures consisted at first of rhyolite with an average silica-percentage of about 74, alternating occasionally with basalt; but the great bulk of the basalt was poured out immediately after the rhyolite from fissures still farther to the west and south-west. In the case of these extrusive rocks, whose volumes are of such magnitude, the evidence ‘drawn from the succession of their eruptions and from their com- position is of a higher order than that derived from the smaller and more localized eruptions, and it is upon evidence of this order that the author ventured to enunciate the principle that in a region of eruptive activity the succession of eruptions in general commences with magmas representing a mean composition and ends with those of extreme composition. XLVI. Intelligence and Miscellaneous Articles. CARBON MEGOHMS FOR HIGH VOLTAGES. BY W. M. MORDEY*. Ss insulation of apparatus and cables used with high voltages should be tested with high voltages. [or this and many other _ purposes some inexpensive and trustworthy form of high resistance * Paper read before Section A, British Association, Liverpool, Sep- tember 23rd, 1896. Communicated by the Author. Intelligence and Miscellaneous A,'ticles. A5L- is required. The ordinary carbon megohm is very untrustworthy, being subject to considerable variation and unsuited for use with pressures of more than a few volts. The Author having overcome these defects thinks the simplicity of the plan followed no reason for withholding a description of it. A study of some of these carbon megohms, supplied by instrument-makers, showed that, although the loss is very small, being oniy one-millionth of a watt per volt impressed, the delicate conducting film or line of plumbago is too much disturbed by the heat generated. Experiment showed that on increasing the cross- section of the conducting film, and correspondingly increasing its length, it became easy to construct a carbon resistance practically unaffected by any ordinary variation of temperature, and capable of being used with pressures of 100 volts per megohm, or as much higher as may be desired. - Various ways of carrying this out have been tried. Excellent results were obtained by the use of long strips of shellaced cartridge-paper coated on one side to a width of one to two inches with plumbago, well burnished, the edges of the paper strip being folded down over the film to protect it. The strip is then rolled into a loose spiral, secured toa support, and mounted in a suitable box with terminals. Examples of these resistances were shown and particulars given of tests to which they had been subjected. The resistance in one case was 1:315 megohm at 74° F. It was tested at various temperatures up to 150° F., and was practically constant throughout this range, the resistance at the higher temperature being 1°51 megohms. Another resistance shown, which measured 0°975 megohm, had been subjected to a pressure of 100 volts for 12 hours continuously without showing any change. It was stated that these resistances were being supplied by Mr. Paul, of 44 Hatton Garden, London. ee eee SEARCH FOR SOLAR &-RAYS ON PIKE’S PEAK. BY FLORIAN CAJORI. Experiments carried on by M. C. Lea* and others have failed to show the presence of Rontgea rays in solar radiation. If these rays reach us from the sun, their intensity must be ex- ceedingly feeble. The suggestion has been made that Roéntgen rays may exist in sunlight, but are absorbed by the earth’s atmo- sphere. The fact that Lenard rays are stopped by only a thin layer of air made it not improbable that Rontgen rays might be stopped by a thick layer of it. On this hypothesis a mountain- top is the best locality to examine sunlight for the new rays. The writer determined, moreover, to expose the photographie plate to solar rays, not several hours, but several weeks. * Am. Journ. Sci. [4] i. 1896, pp. 3863, 364. 452 | Intelligence and Miscellaneous Articles. During preliminary experiments made in Colorado Springs, it was found that a sheet of aluminium would allow certain solar rays to pass through. These were not Roéntgen rays, for the reason that black paper placed between the aluminium and the ~ photographic plate seemed to cast as deep a shadow as did a strip ot iron. A different mode of exposing the plate was necessary and a plan similar to Lea’s was finally adopted. The first 100 leaves of an unbound book were turned over, and a rectangular trough of the dimensions of the photographic plate (7-5 by 13 cm.) cut into the next 55 pages. Seven pages above this trough, thin metallic plates, from 5 to 20 mm. wide, were placed between two leaves, and held in position by gumming the two leaves together. Care was taken to let the mucilage dry before shutting the book. After the photographic plate (Seed, 23) was placed in the trough, the book was closed, wrapped in black Ba paper, then in paraffine paper, and finally put into a tin Ox The box was prepared as follows :—Its lid was placed externally over its bottom and a rectangular window, 7°5 by 13°5 em., cut through them both. Thereupon a sheet of aluminium, 13 by 23 cm., and :29 mm. thick, was placed between the lid and the bottom, so as to screen the window. The wide margin of the - ec. lying between the sheets of tin, was united to them above and below by thin layers of bees’-wax. Externally the edges of the rectangular window were covered with sealing-wax, to which a thick layer of paint was finally applied. A new lid was provided for the open side of the box and both lids were soldered on. Prepared in this manner, the box could be left exposed to all kinds of weather without danger that moisture would reach the photographic plate. To touch the plate, rays had to penetrate the sheet of aluminium, a few layers of paraffine and black paper, and 100 pages of the book. Roéntgen rays of intensity ordinarily met with in the laboratory penetrate at once very much greater thicknesses of these materials. Through the kindness of Mr. F. Blackmer and Mr. D. Rupp, of Colorado Springs, the box was taken to the suinmit of Pike’s Peak (elevation 14,147 ft.) and fastened by wires upon a roof sloping southward. The box was left in that position from June 27 to August 10. When subjected to the usual process of development, the plate failed to show any action of rays and presented a uniform surface, without traces of shadows from the metallic strips. Another plate, similarly exposed from July 7th to August 28th in Rosamont Park, near Pike’s Peak, at an altitude of 9200 ft., gave the same result. Thus even in high altitudes no evidence of the presence of Rontgen rays in solar radiation was obtained.—Am. Journ. Sct. [4] 11. 1896, p. 289. Pin Maem. So Velce eile GLOW LAMP IN SERIES WITH BACK E.M.F. A | 5 4 a © > RNY, Ss 4 z “7 r g@; _| sles 4. 5 G 7 8 c) AMPERES. Mintern Bros: lith . OHMS xXI10. Phil. Mag.S.5.Vol.42 Pll. GLOW LAMP IN SERIES WITH BACK E.M.F. AMPERES. Mintern Bros.lith . Pinal Maso. Volusia ab ey * SS ,- fone * | -— 2G +> | | j + ——— - - ———— ———— wo — |}. ~~ SS — : —— — aa ‘ | ees aoa STA i aa EEoaliaa ald a 8 6 ay eee ce Ae este tee SS a os Se _ Dept ptt mmm A His ly _— Cie erty. (ae ee —_— LAA bd oa (Be ie So re a — la |e D Paine = Pena fe | See ! - Soe ae LN sh paced oe Sf] ee ea ea i / eh eae or JOURNAL OF SCIENCE so, [FIFTH SERIES.] Kos DECEMBER 1896. XLVII. On some Experiments with Réntgen’s Radiation. By RicwHarD THRELFALL, W.A., Professor of Physics, and JAMES ARTHUR PoLLocK, Demonstrator of Physics in the University of Sydney, N.S.W* | a experiments to be described were performed during April and May of this year, and were made with the object of elucidating the nature of the radiation. It was thought that the following possible explanations should be tested :— ‘1. The radiation consists of a swarm of material particles projected through the glass of the generating tube, Electrical changes taking place at the glass surface are invoked to explain the differences between Rontgen’s and Lenard’s rays. 3 2. The radiation consists of an “ sether wind.” Adther is sucked through the glass towards the source of radia- tion and then blown outwards. The question as to whether the radiation observed by Rontgen is the expression of the motion of sether to or from the source remaining open. 3. The radiation consists of zther vortices moving to or from the source. 4, The radiation consists of sther waves: that is waves of regular or irregular zether motions. 5, The radiation consists of electromagnetic waves of either * Communicated by the Physical Society: read November 13, 1896. Phil. Mag. 8. 5. Vol. 42. No. 259. Dee. 1896. 2K 454 Messrs. Threlfall and Pollock on some yery small wave-length or having longitudinal com- ponents. This is probably a special case of (4)—at least if we are to look to the zether to explain electricity and magnetism dynamically. 6. The radiation is a phenomenon of a new order entirely unconnected in any way with anything in our past experience. | Source of Radiation. Being thrown entirely on our own resources for means of production of the radiation—all the Crookes’s tubes in our possession being almost useless—we arrived at the form of tube shown in fig. 1. These tubes are easily made; the surface Fig. 1. opposite to the kathode being spherical, can be made very thin, and the electrodes are kept well apart. The kathode is best made very nearly plane—if concave it will easily fuse the thin glass against which its rays are projected ; we have lost many tubes from this cause. We have found that the bulb may be conveniently about three or four centimetres in diameter and the main tube as little as 1°5 to 2 cm. in diameter. ~The expansions round the electrodes are intended to obviate local heating, for it is not always easy to prevent oscillatory discharges and consequent ‘‘ kathoding” from the “ anode.” The chief merits from our point of view, however, were that the tubes were very easy to make out of comparatively small glass tubing. Their volume is small, so that they can be exhausted quickly, and they give very intense action. In fact one tube—the bulb of which ultimately fused under the Experiments with Réntgen’s Rays. 455 influence of the kathode-discharge—gave quite as intense if not more intense radiation than a “ focus ”’-tube made in our laboratory, which appeared to act perfectly, so far as we could judge. Experiment to test Hypothesis 1, When a vacuum-tube is prepared with electrodes of alu- minium-wire whose ends are about 1 centimetre apart, and exhausted until the discharge will rather jump across three or four centimetres of air between balls of 1°5 cm. diameter than pass in the tube, it is generally noticed that the dis- charge, when forced to pass by the tube, goes rather more easily in one direction than the other. By placing a spark-gap with spherical electrodes in parallel with the exhausted tube and properly adjusting the distance of the balls from one another, it is easy to so arrange matters that the sparks pass mostly by the spark-gap when the current is in one direction and by the tube when it is reversed. An arrangement of this kind is exceedingly sensitive to small changes of pressure in the exhausted tube. In the experiment to be described, the spark-gap was generally so adjusted that when the coil-com- mutator was in one position the whole of the discharge passed over the gap—only the faintest glow being discernible in the tube in a dark room. When the current was reversed, however, the. discharge was about equally divided between the gap andthe tube. No very delicate adjustment of the gap seems to be necessary, at all events when the discharges follow each other rapidly. Having thus obtained a means of testing the vacuum in a discharge-tube more rapidly and probably much more deli- cately than by any kind of gauge, we thought it worth while to try whether Rontgen’s rays would project particles into the exhausted tube.» If hypothesis (1) be correct, then particles must be carried into the exhausted tube if it is thin enough to be transparent; and if in addition it contains a piece of platinum-foil which stops the radiation, the particles would also be stopped; also if the particles are not wholly entangled in the platinum, some change in the vacuous state of the tube is to be expected. A tube about 12 cm. long and 1°5 em. in diameter, and having a bulb about 4 cm. in diameter in the middle of its length, was prepared of German glass. It was provided with electrodes fused in from either end, and extending to within 1 cm. of each other in the centre of the bulb. A bit of platinum- foil lay in the bulb, and the tube was fused on to a Sprengel pump through about a metre of tubing some millimetres in 2K2 456 Messrs. Threlfall and Pollock on some internal diameter. A phosphorus-pentoxide tube was included just above the fall-tube. The whole apparatus, including the pentoxide tube, was repeatedly heated by a Bunsen burner and exhausted until the discharge preferred to pass through 3 cm. of air-gap rather than through the tube. So sensitive, however, was this means of testing the vacuum that for the first few days, despite frequent heatings and pumpings, the vacuum would not remain constant for more than some minutes. After about a fortnight of heating and pumping, however, the vacuum became so steady that the change in twelve hours, which was sufficient to entirely stop the discharge in the spark-gap, could be rectified by the fall of at most 50 drops of mercury in the fall-tube—~. e. by about 30 seconds’ pumping. The change of vacuum occuring during an hour could still be easily detected by testing with a current in alternate directions. ) Under these circumstances, experiments were made by urging Réntgen tubes to their utmost, almost in contact with the bulb of the exhausted tube, and directing their radiation on to the platinum-foil. Though many very active tubes were fused or otherwise destroyed, yet during an hour’s action on several occasions no change of vacuum in the exhausted tube could be detected when due allowance for the slight progressive deterioration was made. This exper'nent was repeated several times, and a tube which had successfully exhibited the fluorescence of a screen of tungstate of calcium through an aluminium plate -7 mm. thick to an entire audience, was melted down in the operation’; but no effect whatever was observed. Professor Wright, of Yale, has given some reasons for thinking that Rontgen rays when passing through gold-leaf carry particles (of gold?) off with them ; so that if a positive effect had been obtained in the experiment described it would not have been quite conclusive ; neither is the negative effect observed conclusive against any particles being carried for- ward ; it only shows that the particles so carried (if any) either refuse to behave as gaseous particles, or are exceedingly few in number. : FE The experiments of Professor Minchin which are now available have, however, rendered the solid particle theory so unlikely that it is hardly worth while pushing the investiga- tion further—at all events until much more powerful appli- - ances are to hand. In case the experiment appears worthy of repetition, we would call attention to the fact that it appears desirable to use specially purified phosphorus pentoxide in the drying-tube ; for the presence of the vapour of phosphorus Experiments with Réntgen’s Rays. 457 or its lower oxide fouls the mercury when impure pentoxide is heated. Experiments made to test whether Réntgen’s Radiation is associuted with ether currents in any way. With regard to hypothesis (2) Michelson has put into our hands a comparatively simple method of obtaining the inter- ference of two beams of light which may be used for detecting the presence of ether currents by their influence on the velocity of lignt travelling through the moving ether. ' The arrangement employed in fig. 2 was made use of for Fig. 2. the purpose of determining whether Réntgen’s radiation is associated with zether movements. In this arrangement the light from L is divided into two beams at A which travel round from mirror to mirror in opposite directions, eventually reaching the telescope T. When the adjustment is correct, interference-bands are seen on looking into the telescope. In this experiment it was estimated that a shift of the bands equal to one tenth of the width of a single band, or a widening of the bands by one fifth of the same amount, 458 Messrs. Threlfall and Pollock on some could not have escaped our notice. In some experiments the Ro6ntgen tube was placed so that the line of kathode discharge made an angle of about 30° with the path BC, and in others made an angle of 90° with the same line. No disturbance of the bands could be detected when the coil was started or while it was working, which shows at once that within the limits of accuracy imposed by the experimental conditions, the Réntgen radiation is unaccompanied by ether streams. This conclusion refers, of course, only to air, and it therefore appeared desirable to make an additional experiment, replacing the air by a substance of greater density. Pure benzene was selected as a suitable liquid, and a glass tank 16°4 cm. long, and several centimetres wide and deep, was placed in the path BC. The radiating tube, which was placed above the free surface of the benzene, was arranged te radiate on to the path in all directions, and in some cases was actually immersed in the benzene so that its active surface was in the field of view of the telescope. ; No disturbance of the bands commencing when the coil started, and stopping when it stopped, was ever detected, though a great many excellent observations were made. Of course, effects due to the heating and electrification of the glass can be easily distinguished from those we are in search of in view of their persistence after the coil is put out of action. ‘The tube employed gave quite visible fluorescence by barium platinocyanide at a metre’s distance and through aluminium *7 mm. thick. We can get an idea of the order of the minimum ether velocity which could be detected by this means. The path BC being some 25 cm. long, we will suppose that only 10 cm. of it are influenced by the tube and that the radiation is along the path. The sen- sitiveness of the method was the same whether we employed air or benzene. A shift of the bands amounting to a fifth of the distance from band to band would be produced by an ether velocity sufficient to change the time of passage of light over the path by one tenth of a period. As sodium light was employed, we may call this 5:9/3 x 107"* seconds. But the time required for light to travel over ten centimetres in alr is about 1/3 x 10~° seconds ; or the velocity is not changed by the radiation by more than six parts in ten million, say. This is about 177 metres Experiments with Rontgen’s Rays. 459 per second, so that the conclusion to be drawn from the experiment is that the Rontgen radiation is not associated with ether velocities greater than, say, one fifth of a kilo- metre per second, or about a thousand times less than that of kathode rays as measured in a vacuous tube by Prof. J. J. Thomson (Phil. Mag. vol. xxxvili. p. 364). Experiment to test whether Réntgen Rays produce any change in ether affecting the velocity of light. An experiment (fig. 8) was arranged on Michelson’s Fig. 3. principles. In this case the sodium light from L is divided at the partially silvered mirror A, one beam travelling to C and thence to T, the other travelling to B and thence back to T. The path AC is operated upon by the tube, and the path AB is screened by a heavy cast-iron screen. The active 460 Messrs. Threlfall und Pollock on some surface of the tube is brought up to the path CA, and the Rontgen radiation allowed to traverse it in a variety of direc- tions from parallelism to normality, and is even thrown on to the mirror at OC. For experiments on benzene, troughs of that liquid as similar as possible are inserted in both paths, the one in the path AB acting merely as a compensator. This experiment is much more difficult than the one previously described, and the benzene requires to be well stirred if good definition is required. In the experiments in air a shift of the bands by ;!, of the width of a band could be observed, while in benzene a change of about half the distance from band to band only could be seen. A widening of the bands to about half the above amounts could have been detected in each case. When the benzene was used the fringes were unsteady, and opportunities for observation had to be waited for. Of course, when the active surface of the Réntgen tube dipped into the benzene so as to appear in the field of view of tne telescope great disturbances due to thermal and electric changes became visible. These, however, did not appear instantaneously on starting the coil, nor did they disappear on stopping it. In no case was any real effect observed. The chief interest of this experiment lies in tue fact that if the Roéntgen radiation consisted of longitudinal ether waves, 2. €., waves of longitudinal ether displacement, some effect was to be expected. If the waves are long compared with the path AC (the path AB being screened) a widening of the fringes, or in the extreme case a total disappearance of the fringes, is to be anticipated. ‘This can easily be realized by blowing an organ-pipe in the neighbourhood. If the waves are short compared with the dimensions AC then all will depend on the azimuth of the tube, or rather on the inclination of the Roéntgen-ray path to the path of the light rays. This appears from the fact that wuole waves would produce no effect in the case contemplated—everything would depend on the fractional parts of the waves included in or projected on AC. The conclusion to be drawn from the experiment is that neither in air nor benzene are the light-transmitting properties of the ether interfered with. The limits of observational accuracy are of the same order as in the case of Experiment II. Action of Réntgen’s Rays on a Selenium Cell. It so happened that one of us was engaged early in the year in experimenting with photo-resistance cells made of selenium which had been laboriously purified and which was probably as pure as any that has ever been obtained. Con-- trary to expectation, such cells showed a quite normal light- Experiments with Réntgen’s Rays. 461 sensitiveness whether the electrodes were of platinum or of aluminium. The cells were made according to the directions given by Mr. Shelford Bidwell* in his paper read before the Society last year—the only difference being that purified selenium was employed. The result of a good many observations was to show that a certain selenium cell with platinum electrodes was acted on to about the same extent and in the same direction whether it was exposed to the radiation of a “standard” candle ati a distance of three metres, or to the Rontgen radiation at a distance of ten centimetres and passing through*7 mm. of aluminium and about 3 mm. of wood. ‘The tube was working so as to cause visible fluorescence in a barium platino- cyanide screen—not of quite the best quality—at a distance of rather over a metre in a room nearly but not absolutely dark. This is of course a very rough way of stating the degree of activity of the tube, but when the experiments were made Professor Minchin’s work had not reached us, and consequently the simple scale of tube intensities which it implies was not available. In order to test whether the action of the light differed in kind from that of the Rontgen radiation two experiments were made—in one the rate of resistance-recovery of the selenium cell was carefully studied and compared with the rate of recovery of the cell after exposure to candle-light ; in the other tests were made in the hope of discovering that a permanent electromotive force was established by the radia- tion, and that it persisted after the radiation was cut off. Neither of these experiments led to positive results. The rate of change of resistance during the twenty seconds of exposure to Réntgen’s radiation was, so far as could be seen, exactly the same as when the candle-flame was substituted at the proper distance. The recovery curves, extending over about half an hour, were also very similar on the whole (several tests were made), though both curves themselves exhibited great irregularities. In order to obtain effects as little complicated as possible by previous history the sensitive cell was kept in circuit on the bridge, and was traversed by the testing current for two or three days before the observations. It was for the same reason that exposures were limited to 20 seconds, for the rate of recovery of resistance with the cell employed was very slow. On one occasion when an accidental exposure for several minutes to Rontgen’s radiation * Phi Mag. vei. xb. p. 233. 462 On some Experiments with Réntgen’s Rays. was made the cell had by no means recovered four hours afterwards. The resistance of the sensitive cell employed was reduced from 1209 ohms to 1185 ohms in 20 seconds by the radiation under the conditions mentioned. The testing battery consisted of two “Obach”’ cells, and the bridge was made up of two equa! arms of 1000 ohms each—the selenium and the variable arm. We mention this in case it may ever turn out that the effect depends on the testing current. With regard to the electromotive force which it was supposed might be set up. The cell was kept at rest and undisturbed for three days before the final trial; it was placed three centimetres trom the active tube, which was, as before, in a metallic box, together with the coil. The tube was shut off from the cell by an aluminium plate *7 mm. thick. A very sensitive high resistance galvanometer in our possession, which has been described in a paper read before the Royal Society but as yet unpublished, was employed to test for any electromotive force which might be set up. An exposure to the radiation was made while the cell was in series with the galvanometer, and it was found that the cell always exhibited a small electromotive force whether it was exposed to the rays or not. This prevented the test from being very sensitive, but inno case was any electromotive force attributable to the radiation discovered, though if a a voltage of 10~7 volts had come into operation its effect could probably not have escaped observation. At the time these experiments were made we were unin- formed as to the discharging action of the rays, which has since been so copiously studied. As soon as we saw an account of some of this work we felt that the change of resistance of the selenium cell was no longer an isolated phenomenon to be worked out by itself, but must be studied in conjunction with the similar phenomena observable in other substances, and it is for this reason that the experimental work was not extended so as to include other cells. These notes may, perhaps, be summed up as follows :— (1) It is easy to make a Rontgen tube of great activity by the most elementary glass-blowing. (2) The Roéntgen radiation does not consist in the pro- jection of gaseous matter, or if it does the amount of such matter involved is extraordinarily small. (3) The Roéntgen radiation does not consist in the projec- tion of sether streams having a velocity above a couple of hundred metres per second: this is true whether the radiation takes place in air or in benzene. (4) The properties of ether regarded as determining the On the Diurnal Periodicity of Earthquakes. 463 velocity of electromagnetic waves are not greatly changed (2. e. not at all within our experimental limits) by the Rontgen radiation, and this applies alike together in air and in benzene. (5) A selenium cell composed of platinum electrodes and highly purified selenium is affected by Rontgen radiation to an extent which is comparable with the effect produced by diffused daylight. (6) No permanent or temporary electromotive force is set up in a selenium cell by the Rontgen radiation. XLVI. On the Diurnal Periodicity of Earthquakes. By CHaruESs Davison, Se.D., F.G.S., Mathematical Master at King Edward's High School, Birmingham*. L W ITHIN the last seven years, two important memoirs have appeared dealing in part with the diurnal periodicity of earthquakes. In a paper published in 1889, M. de Montessus de Ballore + considers the question from a negative point of view, his object being to show that the diurnal period is apparent rather than real. More recently, in 1894, Prof. F. Omori f, in a valuable investigation on the after-shocks of earthquakes, points out that there are various periodic fluctuations in their decline of frequency, three of the periods being a day or less in length. I will first give a brief summary of the methods and conclusions of these two writers before proceeding with the immediate object of this paper, which is to subject the records used by them, or similar records, to the more rigid process of harmonic analysis. 2. M. de Montessus’s statistical inquiries are based on a great catalogue of more than 45,000 earthquakes. The separate entries being of unequal value, he divides them into seven classes, according to the nature of the district and the mode of record. The first six classes include all registers obtained without instrumental aid, the seventh those of the Italian geodynamic observatories. For every region of each class he gives the total number of shocks during each hour of the day. Representing by d the number of shocks occurring in the twelve day-hours (6 a.m. to 6 P.M.), and by x the number in the twelve night-hours (6 P.M. to 6 A.M.), he then evaluates the ratio d/n for each region. Tor the first group, excluding the fifth or volcanic series, the mean value of d/n * Communicated by the Author, with some alterations, after being read before the Royal Society on March 5, 1896. + ‘ Etudes sur la répartition horaire diurne-nocturne des Séismes et leur prétendue relation avec les culminations de la lune.” Arch. des Sc. phys et nat. vol. xxii. 1889, pp. 409-430 and tables. yi t “On the After-shocks of EKarthquakes.” Journal of the Collé of Science, Imp. Uniy. Japan, vol. vii. 1894, pp. 111-200. ea AG4 yo Be, Ci Davison on the Diurnal varies from 0°75 to 0°82, and increases with the scientific character of the record. Also, the value of d/n being small for moderate shocks and approaching unity for severe ones, M. de Montessus infers that earthquakes in reality occur just as frequently by day as by night. - The seventh class comprises the records from thirteen geo- dynamic observatories in Italy, all obtained by means of con- tinuously recording instruments. The value of d/n varies from 0°50 for. Corleone to 2:06 for Bologna and 8. luca, being on an average 1°49. If all shocks are excluded but those of intensity I. of the Rossi-Forel scale, the mean value rises to 1:80. This seems to imply the existence of a true diurnal period, but M. de Montessus interprets the inequality otherwise, referring the more numerous slight shocks of the day-time to ‘“mouvements dus a l’homme, roulements de voitures et de trains de chemins de fer, explosions de mines, &e.” The suggestion is a useful one and deserves careful consideration. At the same time, it should be remarked that the phenomena admit of another explanation, for we might expect that slight earthquakes would be subject to periods of greater amplitude than violent shocks*. With regard to the non-instrumental records, however, M. de Montessus’s analysis leaves little doubt that the more frequent observation of earth- quakes at night is due to the conditions being then more favourable for the detection of weak tremors. 3. Prof. Omori’s investigation is based for the most part on seismometric records. He makes use of the valuable Tokio register from 1876 to 1893, that for all Japan from 1885 to 1890 (which is only in part a seismometric record), and especially the lists of after-shocks at Kumamoto, Gitu and Nagoya, and Chiran, during the thirteen or fourteen days following the Kumamoto earthquake of 1889, the Mino-Owari earthquake of 1891, and the Kagoshima earthquake of 1893. The shocks are grouped in hourly, two-hourly, and six-hourly intervals, and curves are drawn, not through the points corresponding to the numbers so obtained, but by some process of smoothing which is not explained. The periods which are brought into prominence by this method are 24 hours, about 8 or 9 hours, and about 4 hours, in length. In the case of the Mino-Owari earthquakes, while both the eight- hourly and four-hourly periods are shown on the Gifu and Nagoya curves, the former is more marked at Gifu and the latter at Nagoya. The diurnal period for these two stations appears to have its maximum about 1 a.m., for Tokio in the évening, and for all Japan early in the morning. 4, The method adopted in this paper is that of harmonic * See Phil. Trans. 1893 A, pp. 1116-1120. Periodicity of Earthquakes. 465 analysis. As the absolute frequency of earthquakes in different districts is extremely variable, the average number of shocks per hour in each case is represented by unity, so that the results may be directly comparable. The epochs are given in the mean local time of the place of observation, with two exceptions, namely, Japan and Italy, in which the standard times are those of 135° HE. and 15° E. respectively. In the Table, however, the figures for Japan refer to mean Tokio time, for Japanese after-shocks to mean time of 135° H., and for the Italian stations to mean Rome time. Japan. 5. Tokio—Japan Seismol. Soc. Trans. vol. ii., 1880, pp. 4-14, 39; vol. vi., 1883, pp. 82-35 ; vol. vul., 1885, pee 100-103; yel. x, 1887; pp. 97-995 vol. xv., 1890, pp- 127-134: Brit. Assoc. Rep. 1886, pp. 414-415 ; 1887, pp: 212-213 ; 1888, pp. 435-437 ; 1889, pp. 295-296 ; 1890, pp- 160-162 ; 1891, pp. 123-124; 1892, pp. 93-95 ; 1893, pp. 214-215. Duration of record, 1876-1881 and 1883-1892. Number of earthquakes, 1204 ; in winter, 661 ; in summer, 543. This valuable record begins in the latter half of 1872, and, up to the end of 1892, contains 1304 entries. From the end of 1875, the earthquakes were registered by means of seismo- graphs, Palmieri’s being in use until April 1885, and the Gray-Milne seismograph after that date. Towards the close of 1882 the list is incomplete, owing to the removal of the instrument to a new station. For general purposes this would he of little account ; but as I wished to compare the results obtained from the six winter months (October to March) with those obtained from the six summer months (April to September), this year has been omitted. Whole year. Winter. Summer. Harmonic Component. | Ampl. | Epoch. | Ampl. | Epoch. | Ampl. | Epoch. h m h m hm A.M. A.M. tae Ist (24 hours) ...| 130 | 10 14 093 | 10 39 "176 9 58 2nd (12 hours)...| ‘082 | 10 22 "123 9 26 ‘085 0 12 ord (8 hours) ...! °098 6 28 "086 6 31 ‘111 6 25 | 4th (6 hours) ...) °118 3.7 "148 2 56 ‘096 3 26 5th (44 hours) ...| *030 Ls ‘059 1 49 060 4 2 | 6th (4 hours)...... "024 3 27 ‘097 ott “058 0 58 466 Dr. C. Davison on the Diurnal 6. Japan.—Prof. J. Milne, ‘‘ A Catalogue of 8331 Harth- quakes recorded in Japan between 1885 and 1892.” Seismol. Journ. of Japan, vol. iv. 1895, pp. 1-xxi., 1-367. Duration of record, 1885-1890. Number of earthquakes, 1175 ; in winter, 578 ; in summer, 597. Prof. Milne’s great catalogue includes all the earthquake- records collected by the Imperial Meteorological Office at Tokio. A large number of these were obtained by means of seismographs, but unfortunately the particular shocks so recorded are not indicated. For my present purpose, I have made use only of those in which the time of occurrence is given in hours, minutes, and seconds: for these, Prof. Milne informs me, were certainly registered by seismographs. As many others may, however, be omitted by this mode of selection, it is obvious that the results will not compare in value with those obtained from the Tokio record. I have excluded the shocks occurring during the last two years em- braced by the catalogue on account of the great number that followed the Mino-Owari earthquake of 1891 (see §§ 7, 8):— Whole year. Winter. Summer. Harmonic Component. | | | Ampl. | Epoch. | Ampl. | Epoch. | Awpl. | Epcech. h m m h m mi : ) A.M. Ree P.M Ist (24 hours) ...| °147 11 53 "239 1l 50 ‘061 Op A.M. 2nd (12 hours)...| -004 9 8 7035 9 48 ‘028 3 58 3rd (8 hours) . 064 6 31 045 6 12 ‘083 6 40 4th (6 hours) "100 2 ao O67 al o2eS "146 2 53 After-Shocks of Japanese Larthquakes. | 7. Prof. F. Omori, Journal of the College of Science, Imp. Univ., Japan, vol. vii., 1894, pp. 126-188, 157, 178-191, 194, I am indebted to Mr. K. Nakamura, Director of the Central Meteorological Office, Tokio, for the hourly numbers of shocks recorded during each month by a Gray-Milne seismograph at Gifu from October 1891 to December 1893, and at Nemuro from March 1894 to February 1895. Duration of records: Kumamoto, July 81—Aug. 13, 1889; Gifu and Nagoya*, Oct. 29—Nov. 10, 1891; Chiran, Sept. 8-21, 1893 ; Nemuro, March 1894. Number of earthquakes: * It should be mentioned that a few of the hourly numbers of shocks at Gifu and Nagoya given in the table differ by one or two units from those given by Prof. Omori. The figures in the table are obtained from the lists of shocks given in Prof. Omori’s tables xi. and xii. Periodicty of Earthquakes. 467 Kumamoto, 148; Gifu, 1258; Nagoya, 572; Chiran, 238 ; Nemuro, 345. _ The Kumamoto earthquake occurred on July 28, 1889 ; the Mino-Owari earthquake un October 28, 1891 ; the Kago- shima earthquake on September 7, 1893; and the Nemuro earthquake on March 22, 1894. Kumamoto. Gifu. Nagoya. Chiran. Nemuro. Harmonic Components. | Ampl. |Epoch.! Ampl.|Epoch.| Ampl. |Epoch.| Ampl. |Epoch.| Ampl. |Epoch. h m h m hm hm h m | AM. A.M. A.M. A.M, ras! AM. Ist (24 hours) | 623 | 0 3 | 163 | 2 19 | 505 | 0 15 | 096 | 4 35 | 204 | 4 12 2nd (12hours).| 456 | 2 35 | 089 | 5 29} -171 | 1 25 | 069 | 3 58 | 200 | 8 27 pta(s Hours)...| 430 | 2 57 |.-229 | 3 58] 111. | 1 17 | 075 | 6 52 | 327 | 5 53 Ath (6 hours)...| ‘214 | 1 56 | 069 | 1 12 068 | 1 41 | ‘086 | 2 18 | 052 | 4 42 5th (44 hours) .| ‘239 | 1 12 | 051 | 0 50 | 072 | 1 83 | 121 | 0 40 | -148 | 3 10 6th (4 hours)...| 088 | 0 52 | 121 | 0 32 | -210 | 0 37 | -239 | 1 57 | 293 | 0 55 The numerous slight shocks which follow a severe earth- quake are subject at first toa rapid decline in frequency ™~. Now, if a simple harmonic series be superposed on a declining linear series, the harmonic analysis of the compound series shows that not only are the amplitude and epoch of the function of the same period changed, but minor harmonic components are also introduced. Jt is clear therefore that the epochs given above cannot be supposed to agree exactly with those of their physical equivalents. At the same time, the omission of the first one, two, three, and four days in succes- sion from the Gifu and Nagoya records produces no important change in most of the components. Moreover, as will be seen in the next section, the different conditions introduced by the occurrence of a great earthquake endure even when the decline in average frequency of the after-shocks ceases to be sensible, The results for Gifu and Nagoya confirm those obtained by Prof. Omori by a different method of analysis, the 8-hour component being more marked at Gifu, and the 4-hour com- ponent at Nagoya. Prof. Omori gives the time of each shock recorded at both places until the end of Noy. 10, those at Nagoya to the nearest second, and those at Gifu generally to the nearest minute. Out of 1257 shocks recorded at Gifu * F. Omori, Journal of the Coll. of Science, Imp. Univ. Japan, vol. vii, 1894, pp. 111-126 ; Seismol. Journ. of Japan, vol. iii, 1894, pp. 71-80. See also Natural Science, vol. vi, 1895, pp. 891-887, 68 Dr. C. Davison on the Diurnal and 572 at Nagoya there are only 175 whose times of oc- currence differ by less than a minute; and it does not follow that even all these are identical, for, during the first day or two, shocks were frequently felt at Gifu for several minutes in succession. Though the two stations are less than 14 miles apart, and both are close to the great fault-scarp, it would seem, from the above analysis, that their after-shocks do not originate under quite the same conditions. 8. Gifu: Nov. 11-Dec. 31, 1891, number of earthquakes 839; 1892, number of earthquakes, 865; 1893, number of earthquakes, 272. Nemuro: Apr. 1894—Feb. 1895, number of earthquakes, 347. Gifu, ’ ’ : Nemuro, Nov. 11-Dec. 31, 1891.| “fu, 1892. | Gifu, 1893. |4. 1894 Feb, 1895. Harmonic = Com ponent. | Ampl. Epoch. | Ampl.|Epoch.| Ampl.|Epoch.| Ampl. | Epoch. hm hm hm hm 4 ea A.M. fag “Sie A.M. | Ist (24 hours) ...) :205 111 | -007 |5 3{-106 |3 20] -062 0 29 A.M Qnd (12 hours)..., “119 255 |-171 19 0| -087 |10 43 | -099 4 44 3rd (S hours) ...| °156 029 | +154 | 558] -078 |126| -217 315 4th (Ghours) ... 018 338 | 048 | 033] +188 |149| -053 1 31 5th (44 hours) .... “076 052 | -049 | 438] 085 | 341] 169 2 42 6th (4 hours) .... °187 159 | 133 | 2 33 | -095 | 159 | -205 0 16 Philippine Islands. 9. Manila—P. Miguel Saderra Masd: La Seismologia en Filipinas (Manila, 1895), pp. 100-108. Duration of record, 1869-1889. Number of earthquakes, 210*, Harmonie | Ampl. oe Component. h m A.M. Ist (24 hours) ......... ‘273 10 49 2nd (12 hours) -,..3-..2 136 2 20 ord (8 hours) ......:.. 210 6 38 Ath (6 hours) ......... 310 4 22 * The total number of shocks in P. Saderra’s catalogue is 218, but three of these the exact time is not given. Periodicity of Harthquakes. 469 Italy. 10. M. F. de Montessus de Ballore, Arch. des Sei. phys. et nat. vol. xxii. 1889, tables. | Duration of record: Acireale to Verona, Dec. 1872-1887 ; Vesuvius, 1863-1884. Number of earth-tremors: Acireale, 364; Bolognaand 8. Luca, 636 ; Cascia, 505; Corleone, 584; Rocca di Papa, 388 ; Rome, 2346 ; Velletri, 1491 ; Verona, 700 ; Vesuvius, 547; Italy, 8177. In the same table M. de Montessus gives the hourly num- bers of tremors at four other observatories (Alvito, Belluno, Narni, and Spinea di Mestre), but the total numbers of tremors are so small (123, 180, 144, and 159) that I have have not made use of them separately. They are, however, included in the total for all Italy. Ist comp. 2nd comp. 3rd comp. 4th comp. (24 hours). (12 hours). (8 hours), (6 hours), Observatory. ee 1 Ampl. |Epoch.| Ampl.|Epoch.| Ampl. |Epoch.| Ampl. Thee. 1 m hm hm hm oa P.M. A.M. A.M. A.M. CREAN (onc). 40.3632 Hod | O49 (cM, 45) O40) FOG | 143 | 2Por Bologna & S. Luca .|| ‘705 | 0 8 | -166 | 6 56 | ‘081 | 7 41 | 009 | 5 25 A.M, IU F210 ihe cidceres 259i 2h O91, Sekt) 166)" 4 Sis -280 eons @arleone ............ 3957) 0 1d) s0on le 2S 1G OOS esses Rocca di Papa ...... 523 |11 22 | -159 j11 22 | -342 | 410 | 103 | 2 44 P.M. lig 2 oe ae 613 | 0 36 | 143 |10 25 | 097 | 1 37 | -150 | 4 6 MeMetrt......cxeeca- 307 | 0 25 | 113 {11 O | 164 | 0 43 | 060 | 2 25 A.M. WECM BUA a secu csacen 2ooy Li of e270 NOP 130 iO 5S | “s66eiponaG P.M. WeamtyIUS: © 6..605.000.. AAO Wiles ie37 lei bob.) :052.7)-5) 59) |2:038) aa LDL) ener eee ‘o24y | O25 | AIZ IE 14 | O45" | i461 Lis) arag The nine Italian records thus agree in exhibiting a marked diurnal period, the epoch in seven cases being about noon, and in the other two cases not far from midnight. Reference has already been made to M. de Montessus’s explanation of the preponderance of slight tremors during the day. There is much to be said in favour of this explanation. The obser- vatory on Vesuvius is only a few yards from the main road, along which there is a great deal of heavy traffic about mid- day. During the interval embraced by M. de Montessus’s Phil. Mag. 8S. 5. Vol. 42. No. 259. Dec. 1896. 2.1L 470 Dr. CG. Davison on the Diurnal catalogue the observatory at Rome was situated close to a much-frequented street. At the various observatories of the second order the arrangement of the recording instrument, I am informed, was not then irreproachable. On the other hand, at Rocca di Papa, Dr. Cancani tells me that the appa- ratus could not be in any way influenced by accidental or artificial movements on the ground outside. He does not, however, attribute the movements of the tromometers to seismic causes so much as to the action of the wind either near to, or at a distance from, the observatory. This one case, therefore, being free from doubt so far as artificial disturbances are concerned, it becomes un- necessary to reject entirely the results obtained from the other records, especially when the epochs of the principal harmonic components agree so closely, as some of them do, with those derived from the Rocca di Papa register. More- over, while some variability might be expected in the epoch of the diurnal period if it were due to natural causes, it is difficult to understand how, according to M. de Montessus’s explanation, the epoch could ever occur near midnight. Summary of Results. 11. The following conclusions may, I think, be drawn from the results of the above analysis :— (1) The reality of the diurnal variation of earthquake- frequency seems to be proved by the approximate agreement in epoch (mean local time) of the first four components for the whole year at Tokio and Manila, and for the winter and summer halves of the year at Tokio. (2) In ordinary earthquakes there is in nearly every case a marked diurnal period, the maximum generally occurring between 10 A.M. and noon. The semi-diurnal period, though less prominent, is also clearly marked, the maximum occurring, as a rule, between 94.m. and noon and between 9p.m. and midnight. Other minor harmonic components are also occasionally important—the first maximum of the eight-hour component probably occurring about 6.30 A.M. and that of the six-hour component about 3 or 4 A.M.; but in these two epochs the results are not always concordant. (3) Though the materials are insufficient for any general conclusion, a comparison of the results for Tokio and Rocca di Papa seems to show that the slighter disturbances at the latter place are subject to a more marked diurnal periodicity. (4) In the after-shocks of great earthquakes the diurnal periodicity, as a rule, is strongly pronounced. The maximum of the diurnal period occurs within a few hours after mid- night, but the epochs of the other components are subject to Periodicity of Earthquakes. Aq1 wide variation. A special feature of after-shocks is the prominence of the eight-hour and four-hour components. After a year or two there is some return to ordinary con- ditions; but even when the average hourly number of shocks is reduced to one-hundredth of that during the first few days, the characteristics of after-shocks are still per- ceptible. Origin of the Diurnal Periodicity of Earthquakes. 12. The pressure of the atmosphere, either at rest or in motion, has for some time been regarded by seismologists as a cause of earth-tremors. Prof. Milne, who has made a detailed analysis of tremors recorded at Tokio, concludes that they are more frequent with a low than with a high baro- meter, and with a high than with a low barometric gradient ; also, that a majority of the tremors were produced by the action of either local or distant winds upon the surface of the earth, and possibly by their pressure against a neighbouring mountain-range *. ! My object is now to inquire how far the larger disturbances considered in this paper are subject to similar laws. If there is any intimate relation between the diurnal variation of earthquake-frequency on the one hand and that of barometric pressure or wind-velocity on the other, it is evident that the epochs of their respective harmonic components should not differ widely ; since any distortion of the earth’s surface by changes in the distribution of atmospheric pressure must be propagated, both along the surface and downwards, with great velocity. | The records of most value for the purposes of this com- parison are: (1) those of ordinary earthquakes at Tokio, Manila, and Rocca di Papa; and (2) those of after-shocks at Kumamoto, Gifu, Nagoya, Chiran, and Nemuro. 13. Taking, first, the diurnal variation of barometric pressure and seismic frequency, it will be seen that the only approximate agreement in epoch is in the second and fourth components at Tokio and the second at Rocca di Papa. The epochs of the first component differ by as much as eight or nine hours at both places. * “Karth-Tremors in Central Japan,” Japan Seismol. Soc. Trans. vol. xi. 1887, pp. 1-78, vol. xiii. 1890, pp. 7-19; “ Karth-Tremors and the Wind,” Roy. Met. Soc. Journ. vol. xiv. 1888, pp. 64-72. It should be mentioned, however, that P. Camillo M. Melzi has arrived at different conclusions from his analysis of the tromometric records at Florence. See especially his memoir, “ Nuove osservazioni sull’ independenza dal vento nei moti tromometrici nei pendoli isolati,”’ Pontif. Accad. det Nuovi Lincet, Mem. vol. v. 1889, pp. 3-39. 2L2 In the ease of wind-velocity the agreement in epoch is A7T2 Dr. C. Davison on the Diurnal Ist comp. 2nd comp. 3rd comp. 4th comp. (24 hours). | (12 hours). | (8 hours). (6 hours). Barometric Pressure. | Ampl. |Epoch.| Ampl. |Epoch.| Ampl. |Epoch.| Ampl. |Epoch. mm. | hm |-mm.| hm | mm. | h m | mme} gee A.M. A.M. A.M. A.M. | Tokio. (whole year).| ‘52 | 122 | 54 | 9 5] O7 | 243) 03 | 3 37 Cwinter) ace. ..: 67 | 0 54) 61 8 56) *19 | 1 25 OS raw » (summer) ...j/ “41 |} 2 2|-48 | 9 22) -03 | 5225 ROR gore | “Milan (whole year).| ‘18 | 3 7/| °36 9°59) OL 2 40 a: nak Naples __,, $5 ‘09 | 0.57 | -31 /10 13) 03> | 2-280) ] Oi aaa Eur: 9; 3 25° |2 3) 38 | 9 59) 04 | 1 34) O02 R tee 1st comp. 2nd comp. ord comp. 4th comp. (24 hours). (12 hours). (8 hours). (6 hours). Wind-Velocity. Ampl. |Epoch. mee Epoch. ee Epoch. ge Epoch. nm. per sec.| h m a sec.| h m esate hm were hm P.M, ice res Tokio (whole year).| ‘86 | 0 42} -24 | 1 52} 02 | 6 23} 05 | 3 48 A.M. » (winter) ...... 48 |11 56) -25 |1 7] 04 | 5 23} 06 | 3 34 P.M. » (summer) ...| 1:25 | 0 59} 26 | 235] 03 | 025| 40 |4 6 Manila (whole sean) 201 | 0 44) 51 | 150] 06 | 1 49] 08 | 3 53 much closer, especially for the third and fourth components at Tokio. The epochs of the first and second seismic com- ponents at the same place, however, precede those of wind- velocity by as much as two or three hours. At Manila the epoch of the first component of seismic frequency precedes that of wind-velocity by about two hours, and the epoch of the second component of the former follows that of the latter by half-an-hour. The diurnal variation of barometric gradient between Tokio and Nagano (112 miles W. 30° N. of Tokio) seems too slight to produce such important effects, though the epochs of its harmonic components do not differ widely from those of wind- velocity *. * IT am indebted to Prof. Omori for copies of the tables of the hourly means of barometric pressure at Tokio and Nagano published by the Periodicity of Harthquakes. 473 Ampl. Epoch. Barometric Gradient. mm. per 112 miles. h m P.M. Ist component (24 hours) ... 106 0 50 2nd “a (12 hours) ... "057 10 5 3rd = ( 8 hours) ... 010 5 3. 4th = ( 6hours) .. 006 4 0 With regard to the after-shocks of Japanese earthquakes, the records are of such short duration that satisfactory results can only be obtained by a detailed comparison during the intervals over which they extend. It is worthy of notice, however, that the epoch of the first seismic component occurs with some persistence early in the day, and does not differ very greatly from that of the first component for barometric pressure. It seems evident, therefore, that we cannot attribute the diurnal variation of seismic frequency exclusively to that of barometric pressure or of wind-velocity. But it is not im- probable that it may result from a combination of both phenomena ; that the diurnal periodicity of ordinary earth- quakes may be due chiefly to that of wind-velocity, and the diurnal periodicity of after-shocks chiefly to that of baro- metric pressure. In support of this suggestion, it may be mentioned that the amplitudes of the first component of wind- velocity and earthquake-frequency at Tokio are both greater in summer than in winter, and that the same amplitudes for the whole year are both greater at Manila than at Tokio. In the case of after-shocks, a reason may be given for the efficacy of barometric pressure if, as seems not improbable, the principal earthquakes were due to the sudden elevation of one rock-mass adjoining a fault. In a movement so abrupt as this must be, the disturbed mass would almost certainly overshoot its position of equilibrium, and immediately after- wards would begin to settle back to it by a succession of minor slips, at first numerous but gradually becoming less frequent along the whole line of displacement. In such a condition the elevated rock-mass would, in some part or other, be constantly on the point of giving way, and a slight increase of barometric pressure would probably be sufficient to pre- cipitate a slip resnlting in an after-shock. Imperial Meteorological Office at Tokio. The hourly means for the Italian stations are given in Buchan’s ‘Atmospheric Circulation,’ pp. 17,18. The hourly means of wind-velocity for Tokio are obtained from the ‘ Report of the Meteorological Observations for the ten years 1876-1885 made at the Imperial Meteorological Observatory of Tokio’; those for Manila from the ‘ Osservatorio Meteorolégico de Manila, Observaciones verificadas’ (1890-93). Dr. GC. Davison on the Diurnal A474 83 OT $e Gs g 61 02 68 CG 9% Bie ca ee orenT 8 Gl LG Gh P 86 gS 19 1G gg One es Se TL OL 86 8 GG 1¢ ‘a +S SI Ag 9G 18 Gop ater “HO T=6 9G 8 CG 8g G GZ GG SP 0G 9G Or a Ge 6-8 OT II $6 Lb P 61 86 LY 91 6G Oper aa ee ee ES ey GI OL on 1g 8 8% 83 OF ar aa Soke a ha eG 6 P ST Li 8 GZ #6 6P Di SI CR Me ee 050 6 OL 91 9§ P FG £3 L¥ 61 LG Oe Taree G=p ral 8 63 9¢ I *8 98 OL 8G 08 BOY SAAR The i SI GT 8s G GS GG GG GS 8G OR. a hteenGa L oL I OP G SI 68 1g 0% Whe bps Dt i eer, LT P SI GG vir 9% LG eg 6S Des 09) S|) eet) FI IL 1G 6g g 0Z 0% OF 61 LG OR) Se U; 9 a GP P 86 GS eg GS +8 6G Teo 6 CT 0% IP j 06 1G Li 8G GG OG [ero TeG el OL LG 6h f 9G G3 6P 6G OF 69 catch pales Bre pai ol GG eg 9 18 9G Lg 0% 9¢ 60 eae aay SI 6 91 LP g $6 LG 1g 02 0g (Gas se ee 0% My cS ey Il Zo 61 IP LG ST (GN CEE at lial 9) —18) 83 6 as a6 Il BG Fall 25 PG 0G OOF arts! Sans Ger ST 6 rs 19 Zl GG 86 GP 61 0G Gp sm y[PN earidh, eras OL ral GG 8g SI 18 PG 19 IZ LZ o) aa is eons 1 Ls; GI PP +9 $I 91 06 9€ ST LG Che Ave all GT g 1g gg L GZ ial Ks 8% OT 6e of CRY T-0 ; 168T “LOUUMING *LOFUT AA “avo * TOU ung *LOJUT AA ‘aod : "Iv & "A : ‘ nade “UBILYO ONO ANE He mae ‘oyOUVUIN | Geils ero iy Jae PLOtL AA “ANOTT YL ‘undue ‘OLYOT, ‘soyenbyyaeg jo saoquinyy AyinopzyT 475 of Karthquakes. culy a Period 9¢ 8 0G 6 OL OL GI GT GT Gh OT 8G 1G GG 8 OL 9 ST 68 GL vE GP II SI 8 g 8 6 66 6G 8G 8G 1G ¥ LT &T 194 61 96 IL ks &T 9 GT al Cort all SI GL 8¢ 61 T LT 61 O&T 6 iat GT LE al 4 91 CT LET 91 FI oT GE 1G LI IT 6 6FT SI 6I GI Gg &G 6 0G 8 LET IIL on GT 96 1 IT Ht ST LIT 96 GT iT cg SG IT OT GT 19 vé SI GT IP 61 él I ead PrL 6&6 6G 1G 1S 1G 9 GG OT PLL &G 1G 16 9¢ CG OL LT 8 S9T GG OT 8ST 96 GG SI | GL GT CIT oT 6I 96 LE 91 L GT GT 18 Ol él IG GS OL 8 9T OT C9 OT L ial 6Z GI L iat OT G9 Gl GG Of GG G él ne L 6S 61 eP 08 Sil 4 Or 06 8 OF cil 6E Ig 9) 9 Il at 8 LY OT OF 86 6 L g 1G al &Y Or SP 06 9 6 ¢ IIL I vP 6 6g 0G 8 Gt 4 Gl L mee 8X "e681 “A OA of ‘aMO9TION] “elOst,D F ee ‘Q[VodIOW | ‘“epLUeyy Leeet ‘ce Pel ‘ou yy |: MH —— ‘C68T ~~ eS) pee teal Tg 0d IT A0N ——_--_—"" oeeeee oeeeee eeeeee evecee eeevee eoecce Mo So GOSS 66 ‘N'd [-0 ues mA 2 | CO ee eal mG OD SH ud) CO E00 66 oe "WY 1-0 “Moy, a ee re ae A ee en ee ‘soyenbyjaieg jo stequinyy ATInoF] 476 Mr. W. Sutherland on Thermal Hour. Velletri. Verona. | Vesuvius. Italy. | Qs Aw oo ee 258 21 14 264 | s Ee ess 52 15 21 238 DB cee hee 42 19 23 264 SA ere 46 20 21 250 Aa Gh 4) eee 34 20 14 248 pee ek oS 36 24 14 257 G27 eee. 65 27 16 260 (2S) es ears 66 30 19 308 B=) em 8 96 29 17 407 ONO. hee 97 59 17 482 TOL Se 87 81 35 527 1S ee ee 715 33 37 436 Oia 83 2a 40 452 je eee 78 29 ao 388 Deo: vag wees 82 3l 47 443 DA. Ae ee 7d 49 32 A54 Aa keene 68 33 32 385 Gri nee warns ane 718) 23 19 347 Ba firs presen 48 18 13 294 {oe ee 48 13 15 276 SOR ey pee oon 5l 25 13 346 SEOe eee 34 33 17 318 TOE: et ake 52 29° ya | 1S el eee 1 ES ee. 45 23 25 247 XLIX. Thermal Transpiration and Radiometer Motion. By WituiaAM SUTHERLAND*. (Continued from p. 391.]| Part I].—Radiometer Motion. I HYNOLDS, in treating of radiometer motion in con- nexion with his discovery of thermal transpiration, showed that fundamentally both phenomena are traceable to the same general cause: the object of the rest of this paper is to bring out this fact more clearly, and to establish theoretically the general laws of radiometer motion for comparison with the experimental results of Crookes and Pringsheim. ln the theory of thermal transpiration, we have seen that under suitable conditions the variation of temperature along a passage through a porous plate can produce a certain difference between the pressures at its hot and cold ends, and iherefore the solid wall of the passage must be exerting a tangential force F from cold to hot, such that, R being the mean radius of the passage, P= 7R*(pe—pi), and, accordingly, the gas in the passage exerts a tangential * Communicated by the Author. Transpiration and Radiometer Motion. ATT force F on the solid from hot to cold. If then a porous plate had one face heated and was hung on to a string with this face and the opposite cool one vertical, the tangential force F acting along all the passages would deflect the string from the vertical, a case of radiometer motion ; if two such plates were mounted in a vertical plane and free to revolve round a vertical axis lying between them, and one face of one was warmed by irradiation, it would move away from the source, and thus a continuous rotation could be kept up as in an ordinary radiometer. In discussing thermal transpiration we confined our atten- tion to fine tubes, such as might represent the passages in porous plates; but as we saw that the phenomena depended for the most part on the ratio of the radius of a passage to the mean free path of the gas, it follows that our deductions for fine tubes will hold for tubes of any size with rare enough gas to give a free path as large as may be necessary ; thus with the means of getting high enough vacua and with delicate manometers it should be possible to demonstrate thermal transpiration along an ordinary gas-pipe or the largest gas main ; in the radiometer we have generally to do with thermal transpiration going on in spaces of ordinary size. We have already obtained in (5) an expression for the traction exercised on the gas in the tube by the whole surface of a tube along which the temperature varies ; thus EF =nmu’rR’ ; a curious result that the traction on the surface should be proportional to the square of the radius, but it is to be remembered that the tube is supposed to be long enough in comparison with its diameter, and of sufficient thermal capacity, to dominate the temperature of the gas so thoroughly that the temperature throughout any section of the tube is the same as that of the wall. ‘his traction has been found for the case when the motion due to thermal transpiration along the tube has become steady ; but in connexion with radiometer motion it is necessary to consider the traction before the steady state is established. Imagine a solid surface over which the temperature varies to be suddenly introduced into a mass of gas at rest and uniform in temperature, and let us determine the traction which the solid immediately exerts on the gas. The first effect is to make the layer of gas in contact with the solid take the temperature of the solid at every point of the surface, and therefore each molecule that encounters the surface acquires on the average the velocity u given by 478 Mr. W. Sutherland on Thermal (4), and the number that encounter unit surface in unit time being nv/4, the total momentum imparted to the gas in unit time by a surface S is given by F=Snnwu/4. . 2. > This is the initial yalue of the traction ; but as the velocity u is carried out to the remoter parts of the gas, a molecule which encounters the surface having come from a region where it had already acquired a fraction of u does not receiye the whole of u from the solid, and therefore the traction diminishes with time. To determine the final value when the motion of the whole gas is steady we may consider the simple case of two parallel planes the variations of temperature over which are such as to produce velocities u, and w in a fixed direction in the gas in contact with the two surfaces ; then in the steady state we may suppose the transition from wz to u, to occur linearly, so that the velocity u at distance x from one of the planes is wy—(uj—w,)a/D, where D is the distance between the planes ; then the mass of gas that flows in unit time along any layer of width 6 and thickness dz is nmbu dz, and the momentum imparted in unit time to the layer is nmbu? dz, and therefore the total momentum acquired by the gas between the planes is ninbu? da =nmbD (u,? + uta + U2”) /3. 0 Obviously the planes impart the respective fractions uy?/(uy*+Us”) and wy?/(u,?+us”) of this, so that the traction per unit area of the first plane, if its length in the direction of motion is J, is mmDrey? (ry? + Uytty + Up") | dL (uy? + uy”) “ but it is really a useless artificiality to consider the traction per unit surface, as most of the traction is really exerted on the gas near its entrance to the space between the planes, and we will therefore confine our attention to the total tractions. As before in the case of the tube, the result that the traction should be proportional to the sectional area between the plane is peculiar, but it is true only when the planes dominate the temperature of the gas in such a manner that w is a linear function of the distance from either. Thus the initial total traction on the first plane is Snmvu/4, which is proportional to the surface S, that is to both width and length, but inde- pendent of distance from neighbouring surfaces; and the final traction in the steady state is nmbD (iy? + uytts + Ug”) Uy?/3 (uy? + U2”), Transpiration and Radiometer Motion. 479 which is independent of the length but proportional to width and distance from neighbouring surface. To bring out the full signification of these we had better introduce the value of uw, and let us suppose w, to be 0; then the initial and final total tractions exerted by a plane of varying temperature at distance D from a plane of constant temperature are —Snmv®A(n![n+v'/0) 24, (21) dnmDv*A%(n//n + v//v)9/108. J When the conditions are such that the pressure can remain constant between the surfaces, n//n-+2v’/v=0, and then these become Snmvav’/24 and bnmDdr?2v2/108, both acting from cold to hot, and therefore the equal and opposite reaction of gas on the surface is from hot to cold. But when the conditions are not such that the pressure is kept constant, but that a difference of pressure is established by thermal transpiration which goes on till a steady state is established, the effect of the difference of pressure may be much greater than that of the traction, as the following example will show :—A piston is inserted into a cylinder which it does not quite fit, and is fixed immovable so as to leave a clear space of sectional area a between itself and the cylinder, and the cylinder is closed ; when one end is heated a fall of temperature gets established along the cylinder, and the gas at the cold end begins to transpire through the narrow space into the hot end until the difference of pressure p.—p, sufficient to stop the flow is established; then the total traction of gas on the side of the piston is a(p,—p,), while on the area A of the hot end of the piston there is a total pressure A(p.—Pp1) in excess of that acting on the cold end, so that the total force urging the piston from hot to cold is (A + a)(p,—p), which may be made as much more important than the total traction as we please by diminishing a. If the piston is freed it will begin to move under the force (A+a)(p,—), and become an exaggerated instance of radiometer motion. This example makes clear the lines on which to formulate a general theory of radiometer motion; we have only to adapt our transpiration formulee established for circular tubes to the case of any space bounded by solid walls over which the temperature varies. In the general problem of radiometer motion we have to do with a solid surface over which the temperature varies and which therefore is subject to a traction from hot to cold, and also establishes a higher pressure in the gas towards its hot end than at the cool end; the relative importance of traction and difference of pressure in producing motion of the body to which the surface belongs depends 480 Mr. W. Sutherland on Thermal entirely on the relative position of the movable surface and the fixed surfaces surrounding it. We have seen that for a tube the total traction is nmu?mR?, and for a passage bounded by two parallel planes of width b and distance D apart with the same variation of temperature along both, it is nmu?)D/2 along each plane, and as wR corresponds to 6 and R to D/2 we see that the traction exerted between the walls of a cylinder of any section and the contained gas may be written in the form nmu?sD/2, where s is the perimeter of a right section of the cylinder, and D is a mean value of the distance between opposite parts of the perimeter. For the difference of pressure established by thermal transpiration along a tube of any section we may use the equations (14) and (17) if in them we interpret 2R as a mean value of the distance between opposite parts of the perimeter ; and in the case where there is a variation of pressure across only a fraction of the perimeter, as for instance in the case where one plane wall has a varying temperature and the opposite one a uniform temperature, we must multiply by a fraction not greatly different from that fraction (1/3 instead of 1/2 in our example). We can there- fore state the fundamental equations of radiometer motion as follows:—If across a length 0 of the perimeter s of any cylinder a variation of temperature is suddenly established whose average rate is v’ over a length J, then the initial total traction between solid and gas is approximately blnmdoy'/24..- "'. 9 eee When the steady state is reached the total traction is approximately bDamd2v? (n’//n + v’/v)?/108, or bDamar?v?(p'/p —v'/v) 2/108,(23) and the difference of pressure between the two ends of / is _ bv — ry 1 PrP see A at pl/t t+ B+ 1/(Pat Ph where the values of A’ and B’ are those given in (19), with R,=R,=R. No proof has been furnished here that the introduction of the fraction b/s rigorously adapts our expres- sion (19) to the case where only a fraction b/s of the boundary is operative in producing thermal transpiration, but it is a _ reasonable enough approximation for experimental results at present available, closer approximation could easily be caleu- lated if required. If in (23) we write (p,—p1)/l and (ve—v,}/l for p’ and v’ we can express the total traction in the steady state entirely in terms of v, and v, which completes the solution. » » (24) - OF Transpiration and Radiometer Motion. A481 With these results we can now state what ought to be the behaviour of a radiometer, and as Crookes and Pringsheim found the best form of instrument for investigating the laws of the radiometer experimentally to be one in which a single vane of mica blackened on one side was attached with its planes vertical to a horizontal arm attached to a vertical torsion fibre, the whole being suspended in a glass bulb capable of being filled with any gas at any pressure, we will discuss the theoretical laws of such a form. Let D be the mean distance of the edge of the vane from the glass wall immediately opposite it, b the perimeter of the vane, s—6b the perimeter of the glass wall opposite, Hi the area of each face of the vane, H +S the sectional area of the bulb (8 being small compared to H) in the plane of the vane, and @ the thickness of the vane; when the black face is irradiated let its tempera- ture become 6,, that of the clear face being 6,, then there is a fall of temperature 0,—6, through the thickness of the vane, and thus the thickness of the vane becomes a surface capable, along with the surface of the bulb opposite it, of starting thermal transpiration from the cold edge to the hot, with elevation of the pressure in front of the hot face to po, and depression of that behind the cold face to p,;; when a steady state is established the total traction on the surface of varying temperature must be approximately equal to S(p.—p,)b/s, and the excess of total pressure on the black face over that on the clear face is E(p,—p)6/s, so that the total force deflecting ' the vane whose moment is to be balanced by the torsion couple of the fibre is (H+8)(p,—p,)b/s. Thus the total deflecting force is ay OM 1 (E+8) SU +% 9 D?v9?( po + 71) 3aDv Ste (25) 1679?(v2+ v1)* No(Vet+r;)*> Pot Pr c/{A’p + B’+1/p}, where p is the mean pressure (p.+ ,)/2. This equation contains all the theoretical laws of radiometer motion when 8 is very small compared with H. If everything is kept constant except the mean pressure (p2+ ;)/2 there is a value of the mean pressure of the gas in a radiometer for which the deflecting force is a maximum, a very important point in radiometer construction. When the pressure is high enough the last two terms in the denominator may be neglected and the deflecting force is inversely proportional to the pressure, and when the maximum is passed and the pressure becomes small enough the first two terms may be neglected and the deflecting force becomes proportional to the density 482 Mr. W. Sutherland on Thermal and dies away indefinitely with increasing exhaustion of the bulb. It will be seen that the deflecting force depends on the dimensions of the apparatus in a somewhat complicated manner, but that the most important principle is that (as regards the denominator) it increases with diminishing dis- tance D between vane and glass wall, except at pressures so low that the first two terms are negligible ; and as diminish- ing D means in general an increasing value of b/s, we see that in general at all pressures the efficiency of the radiometer is increased by bringing the edge of the vane nearer to the glass wall. Other things being equal the deflecting force is proportional to the total sectional area H+S of the bulb. As regards the effect of the nature of the gas on radiometer motion the equation shows that at pressures low enough for neglecting the first two terms of the denominator all gases give the same deflecting force, a theoretically interesting result, but not of much practical importance: the practically important matter is to determine how the different gases com- pare, each at its maximum effectiveness; now when the deflecting force is a maximum p+ p,=4%(v2 +v;)7/3DuQ, or D=2n where A is the mean path at (p.+>p,)/2, and the deflecting force becomes proportional to 4n9(v,+v,)?/3Dv, so that the most effective gas is that for which (v,+1,)?/v is largest, that is to say, for which )/m? is largest ; compare for instance hydrogen and oxygen, 7 for H, is °44 of that for Og, while m? is 1/4, and thus at the pressure of maximum efficiency H, is 1°76 times as efficient as O,, and at higher pressures the advantage of H, increases till its efficiency is 1:76? that of Ox. From Rayleigh’s measurement of the viscosity of helium as ‘96 of that of air (Proc. Roy. Soc. Jan. 1896) while hydrogen’s is about ‘5, and with 4 as the molecular mass of helium as against 2 for hydrogen, it would appear that helium ought to be nearly 22 or 1:4 times as efficient in a radiometer as hydrogen. The equation (25) contains the laws of the dependence of radiometer motion on the temperatures of the faces of the vanes, although as these temperatures have never been measured experimentally, we cannot verify them as they stand ; but to a certain extent we can bring them within the range of experimental verification in the following manner. When the black face of a vane is suddenly irradiated the tempera- ture of the black face suddenly rises, while that of the clear face is unaltered, and the fall of temperature is confined for the first moment or two to the thickness of the layer of lampblack ; the first deflexion of the vane takes place in Transpiration and Rudiometer Motion. 483 accordance with these conditions, but if the vane is steadily irradiated, conductivity soon establishes a steady distribution of temperature through the vane from front to back with permanent temperatures 0, and 6,, so that the first deflexion alters until it attains the fixed value due to these steady con- ditions. Suppose the black face to be irradiated by a candle, and let Q be the amount of heat it absorbs per unit area per unit time, and E the corresponding amount emitted by the clear face ; then if we ignore loss of heat by the edge, and denote the conductivity of the substance of the vane by &, Oh (Co— Ooi aye ee (ZU) Now in (25), (v.—v,)/(v2+%) may be written (v9? — v;7) /(ve +01)’; (82.—4;) / (03+ 63)’, in which the denominator is nearly 4(@,+,), since the diffe- rence of 6, and @, is small ; and as in the experiments (0, + 6,)/2 was always an ordinary temperature it may be taken as con- stant, so that (v,—¥v,)/(ve+,) was always closely proportional to 6,—6, and therefore to Q6/k; but Q is inversely as the square of the distance of the candle from the vane and directly as the number of candles at that distance (the candles being as nearly as possible in the normal to the centre of the vane), thus the deflecting force varies as the number of candles and inversely as the square of their distance from the vane, which is the experimental result (Crookes, ‘ Nature,’ xiii.) ; the deflecting force is proportional to the thickness of the vane and inversely proportional to the conductivity of its material, hence the advantaye of using a substance such as mica for the vane, and the disadvantage of using metal. To show that this theory of the radiometer is in harmony with the experimental facts, we will briefly describe the general results of Crookes’s numerous experiments, and it will be seen that they accord with the deductions from our formule. Crookes obtained his most valuable quantitative results with an apparatus such as the one of which we have just considered the theory. The bulb was continued into a vertical tube for containing a torsion fibre nearly a metre long, and the rectangular plate of roasted mica was attached directly to the fibre so that its plane was vertical and its centre at the centre of the bulb; a continuation of the line of the fibre divided one face of the plate into two equal halves, or 484 Mr. W. Sutherland on Thermal one of which was lampblacked. For all the experimental niceties reference must be made to the original paper (Phil. Trans. elxxii.) It is obvious from the description of this apparatus that it does not comply with the conditions under which (25) was established, as the mica plate is probably only a fraction of a millimetre in thickness and between 5 and 10 millim. from the glass bulb where it is nearest, so that the length of the region in which thermal transpiration occurs is much less than its width, whereas in (25) the contrary is supposed to be the case. The chief effect of the difference in these con- ditions will be that thermal transpiration, instead of going on over the whole distance between edge of plate and bulb, will extend to a distance from the edge of the plate which will depend on the conductivity of the gas; in fact, if we move along the shortest distance between plate and bulb we shall find the fall of temperature across that line grow less as we leave the plate and become negligible before we reach the bulb ; but the better the conductivity of the gas the farther will the dominating influence of the edge of the plate extend; there- fore in our formule, when applied to Crookes’s experiments with the torsion radiometer, D must be interpreted as a function of conductivity kh’. Then b being the length of the edge of the black half of the plate, the area S over which thermal transpiration is effective may be taken to be 6D, over which at the front and the back of the plate there is an average difference of pressure pg—p,, which, however, will not be maintained over the whole front and back of the plate, because there is so much facility of escape for the gas, but only near the edge, so that probably H varies as 6D; thus (H +8)6/s will be replaced by 0K, where K is a function of k’. Another effect of the fact that thermal transpiration occurs only to a certain distance from the edge of the plate will be to reduce the effect of slipping, seeing that the velocity of transpiration dies away to zero in the gas. To indicate that slipping has not its full theoretical effect we had better change B’ to B”, and to remind ourselves that in A’ and B/ the symbol D or 2K now means a function of k’, we will change A’ to A” and B” to B” and put bK(v.— v)/(ve o- V1) = Be then (25) becomes deflecting force=c'/(A”p+B”+1/p). . . (27) There is no need to take account of molecular force in altering density at edge of plate because so small a fraction of the free path lies in the condensed gas. Transpiration and Radiometer Motion. 485 The last point to be attended to in applying our equations to the experimental results is that when one side of the mica vane is irradiated the glass bulb is also warmed in such a manner that it is hottest where nearest the candle, and there- fore there is thermal transpiration along the inner surface of the bulb tending to raise the pressure near the hottest point with diminution towards the coldest point ; now we can afford to neglect the effect of this near the vane until the pressure gets so small that the mean free path of a molecule becomes, say, nearly equal to the radius of the bulb, for then the walls of the bulb, on account of their much greater area than that of the effective edge of the vane, must dominate the distribution of temperature and pressure in the gas even quite close to the vane, and there- fore at the highest exhaustions the relation between pressure and deflecting force must tend to a limit determined rather by the bulb than by the vane. With these explanations (27) is now applicable to the experiments of Crookes. With his apparatus Crookes was able to study concurrently the viscosity of a yas and the forces at play in the radiometer at pressures from one atmo down to the lowest measurable by the M‘Leod gauge. The form of his vibrating system renders the mathematical problem of obtaining an expression for the viscosity of the gas from the constants of the apparatus and the observed decrement per vibration of the logarithm of the amplitude of the vibrations of the mica plate intract- able ; but it is obvious, from the theory of the vibrating disk method of measuring viscosity, that the motion of the mica plate when oscillating must be retarded by the viscosity of the gas in such a way that the difference of the logarithms of successive amplitudes is proportional to the viscosity of the gas, so that although absolute values of viscosity are un- obtainable with the apparatus, approximate relative ones can be got with it. Ata number of different densities of the gas Crookes measured the logarithmic decrement and also the re- pulsive effect of a candle-flame radiating towards the blackened half of the mica plate from a horizontal distance of half a metre, the latter being measured by a reading of the permanent deflexion of the plate from its position of rest in darkness. Now from Maxwell’s well known discovery that the viscosity of a gas is independent of its pressure it follows that the logarithmic decrement is independent of the pressure so long as slipping of the gas on the solid surfaces is negligible ; but, as already indicated, Kundt and Warburg showed experimentally, with some support from theoretical reasoning, that slipping ceases to be negligible when the mean free path Phil. Mag. 8.5. Vol. 42. No. 259. Dec. 1896. 2M 486 Mr. W. Sutherland on Thermal of the gas beconies comparable with the linear dimensions of the containing vessels; they did this by pushing the rare- faction of the gas so high in a vibrating-disk apparatus for measuring viscosity that the logarithmic decrement diminished measurably—for example, with air and a distance of ‘11 em. between the fixed and moving plates the log. dec. at 1 atmo was 132, at ‘01 atmo it was °129, and at :0008 atmo it was "111; now at 20° C. and at these pressures the mean free path in air is about ‘00001 cm., :001 cm., and ‘012 em. respectively, this last value is nearly 1/10 of the distance between the plates, so that when the distance between the plates is only 10 free paths the log. dec. diminishes by 16° per cent. of its limiting value when the distance is a large number of free paths. Thus we see how the measurements made by Crookes of the log. dec. in his apparatus give valuable information as to the relation between the free path of the gas and the distance from the edge of his mica plate to the glass bulb. In the following table the first row contains the pressures of dry air at 15° C. in terms of the atmo as unit, the second gives 10* times the log. dec., the limiting value of which at higher pressures is 1000, and the third contains the deflecting force of the candle in an arbitrary unit :— IECSS: sein g3i ase 736 495 300 100 72 39 LO oe dees a..25.: 975 966 952 876 824 710 3°5 aes) 10-0 27:0 | S250 eee def. for. he ne = eal. 4-0 59 96 250. 3-3 presse falreeGl te. 36 29 19 13. 0 10* log. dec... ..... 605. «657 TT 500 460 OXp. §--5 goo 42-6 38'8 30:9" =27ek def. for. Weal. =... 407 40:8 36'8 30°70 =. 268 Thus at a pressure between 36 and 29 millionths of an atmo the repulsion rises to a maximum, say at 30 millionths, at which the mean free path is 00001 x 10°/30, that is one- third of a centimetre. The actual distance between the edge of the mica plate and the bulb is not given by Crookes, but from the figure he gives one would imagine that the distance might be between *5 cm. and 1 cm., and thus the experi- mental result corresponds to our theoretical one that the maximum effect is to be expected when D=2); before the maximum is reached the repulsive effect ought, according to (27), to vary inversely as the pressure, so that the products of the numbers in the first and third rows above ought to be approximately constant, and the first four products are 2600, Transpiration and Radiometer Motion. 487 2700, 3000, and 2700, which verify the equation. Beyond the maximum, according to (27), the repulsion is ultimately to vary directly as the pressure, so that the numbers in the third row divided by those in the first are to tend towards constancy : the last three values are 2:0, 2:4, and 2°5, while at lower pressures the value 3 is reached; but the results at these lower pressures have not been reproduced in the last table, because the M‘Leod gauge with air becomes less re- liable towards 1/10° atmo, and therefore Crookes’s results at the lowest pressures will be discussed in a separate paper on the measurement of pressures in the highest attainable vacua. From Crookes’s experiments we can calculate ce’, A”, B’” in (27), for with 1/10° atmo as unit of pressure and Crookes’s arbitrary unit as the unit of repulsion, we have just seen that e/A” is about 3000 and ¢ about 3:0, so that A”=-001 ; now the deflecting force is a maximum when p?=1/A”, so that the maximum value of the deflecting force, namely, [f(2+B" VA"), gives a convenient method of finding B’” when A” and c’ are known ; thus for air, B'’’=-0l and we have all the data for calculating the deflecting force at any pressure by (27) for comparison with experiment: the calculated values are given in the fourth row of the last table, and show that we have the correct form of equation to represent the experimental facts. But according to the meanings of A” and B’, B?/16 should be nearly equal to A”, whereas B”’”/16 is only the 1/160 part of it. } Now the term in B’” expresses the effect of slipping, and our results for air show that in Crookes’s apparatus the effect of slipping is only 1/160? or 1/13 of what it would be under the ideal conditions for (25), indeed (25) with the given values of A’ and B! stands for one limiting case, and with B/= 0 it stands for the other where slipping is of no account, and the conditions of Crookes’s experiments are nearer to those of the latter limit than of the former; indeed, with slightly different values of c’ and A” we could put B’/”=0 and get nearly as good a representation of the experimental results for air as that just obtained. For nitrogen the values of the repulsive force are about two-thirds of those for air at the same pressures, except in the case of the small values, which are somewhat unreliable, thus for nitrogen A’ and B/”’ have about the same values as for air, while ¢’ is about 2:0; now according to equation (27) c’, as it depends only on the dimensions of the apparatus and the temperatures of the two 2M 2 488 Mr. W. Sutherland on Thermal faces of the mica vane and conductivity, ought to have nearly the same value for two gases so closely alike as air and nitrogen ; that is of course on the assumption that the value of c’ for oxygen is not much different from that for nitrogen, but we had better delay the discussion of this curious point - until we have considered the data for oxygen. For CO, and CO the parameters are :— ce ee ie COME meee 1°25 000625 0-0 COME tom. 1°32 "000625 0-01 In the case of CO these values give values of the repulsion or deflecting force agreeing closely with the experimental over the whole range of pressure, but for CO, the calculated values are larger than the experimental at the higher pres- sures; but the matteris hardly worth going into more closely, especially as oxygen and hydrogen show exceptional behaviour of the highest interest to which we will proceed. For oxygen Crookes obtained the following, the pressure unit being 1/10° atmo, and the unit of repulsion the same arbitrary one as before :— Sia SS OUCOORE NEE 1000 803 658 623 613 HOt logsdec. 2a. 1102 1093 1088 1086 1085 def. force ......... 12 12 13 13 13 Dees Sees eee 369 297 190 171 110 1.0% log: dee:)-7.-.. 1070 1058 1038 1033 988 deiiOrce as seee 13 14 20 21 3l where the deflecting force remains almost constant from a pressure of 1000 down to 297, after which it rises, and at lower pressures than those given attains a maximum and then dimi- nishes. Now Bohr (Wied. Ann. xxvii.) discovered 2 remark- able discontinuity in the compressibility of oxygen at about 921/10° atmo, which has been corroborated by Baly and Ramsay (Phil. Mag. [5] xxxviil.), and obviously the above anomaly must be traced to the same cause as the discontinuity. These phenomena are so important for the chemistry of oxygen that I will discuss them in a separate paper on “ Sponianeous Change of Oxygen into Ozone, and a remarkable type of Dis- sociation.” Meanwhile we will go on to the region of pressure in which the repulsion in oxygen is not exceptional; here we have e’=3'0, A”’=:0007, and B’”=-:0182, which give the following comparison with the experimental results :— Transpiration and Radiometer Motion. 489 gate en 297 190 VTE 110 70 48 Basi eee 13 20 22 30 40 44 exp. 14 20 21 Sh 13g Ais pri Werte 31 28 22 16 12 f cal. 45 44 40 34 29 JES UECGE 44 44 40 35 30 The perfection of the agreement here emphasises the distinct- ness of the exceptional behaviour at the higher pressures. In the case of hydrogen we have at the higher pressures the following values, the numbers in the third row being the products of repulsion by pressure, which ought according to (27) to be tending to a fixed limit :— Beata once 1000 921 526 421 330 def. force ...... 1] 1 3 4 5 1000 921 1578 1684 1650 (i ieee eee 314 234 205 179 def. force ...... 8 ll 14 18 2512 2574 2870 3222 The products do not show the same approach to a limit as was the case with air, and there is a jerkiness in their variation which points probably to experimental uncertainty. At the lower pressures the quotients of repulsion by pressure, which ought to be tending to a limit, are given in the third row of the following :— 55 eee 16 14:5 12 8 6:5 5 4 def. force ...... 52 49 45 37 3l 29 26 3-2 3°4 3°7 46 4-8 58 6°5 Here again the convergence to a limit is not satisfactory, a state of affairs which will be traced in the separate paper on measurement of low pressures to inaccurate values of the lower pressures ; and in that paper it will be shown that hydrogen exhibits a peculiarity which expresses itself in our equation (27) by dividing A” by (1—ap) where & is another parameter, thus for hydrogen the deflecting force is e'/{Ap/(L—ap) + BY” + 1/p}, - « (28) which makes the deflecting force 0 when p=1/a, a result to be extended to all higher pressures ; the values of the parameters ako, —O00G, a——-0016,, BY’ =-01,, and ¢’=4-16.. whien give the following comparison :-— 490 Mr. W. Sutherland on Thermal Phe oe 2 eee -4000 - 526 380 914 205 Tape Foals ae: 0 2 510 “41 > 218 Some Bek force | eee 1 3 5 8. 14 ogee pees 59. 4 41. 28265 900 | ee eee ness ee Le 63 . 70 >) 64 <8 +449) —eaneeeee exp: tee 64 70 66 58 45 of. ze in view of the experimental uncertainty already pointed out at the high pressures and that which is to be proved at the lowest pressures, this comparison shows that the modified formula represents the facts for hydrogen about as well as possible. We will now compare the theoretical values of the para- meters c’ and A” with the numerical ones just obtained; ¢ stands for bK(v.—7,)/(ve+1v;), in which K is proportional to D and is a function of k’; also (v,—v,)/(ve+v,) is the same for all the gases, so that c’ is proportional to D. But A” =9 D2u,?/167?(v.+,)4, and v varies as m-?, and therefore (A’’y?/m)? is proportional to D, which now means distance from edge of vane to which transpiration extends. The following table contains 107K’, c’, and (A’’7?/m)? for com- parison ; 7 in terms of that for O, as 1, and min terms of that for H, as 2 are appended :— H,. Air. O.. N,. CO. Cas Titan a eats 3324 480 563 524 510 317 eee SO 416 3-0 3-0 2-0 1:32 1:25 (A"'n?/m)? 0... ‘762 520 468 “520 ‘411 284 Bete eee 44 90 1-0 ‘87 ‘87; is Rae ne eY 2 28°8 32 28 28 44 It can be seen that on the whole these numbers confirm the theoretical conclusion that thermal transpiration near the edge of the plate is effective to a distance which increases with the conductivity. The smallness of ¢ for N, as com- pared to its value for air and the smallness of c’ for CO are points that require confirmation by experiments with an apparatus lending itself better to quantitative calculations than the torsion radiometer of Crookes. The values of B’’, as they represent only a small amount of slipping, and are not given very definitely by the experiments, are not worth further consideration. So much for what may be called the static form of the radiometer ; of the results obtained from a great variety of moving radiometers constructed by Crookes the following are the most important. In a radiometer containing two flies, one pivoted above the other, and haying their blackened Transpiration and Radiometer Motion. 491 sides facing in opposite directions, the radiation from a candle causes the flies to revolve in opposite directions, which proves that the driving action is chiefly localised close to the flies ; this result is of course involved in our theory according to which the action of the fall of temperature through each vane is to raise the pressure near its hot face and lower it near the cool face, but the region of lower pressure of the upper fly being just above the region of higher pressure of the lower fly, and, with no obstruction between, ought to produce dissi-- pation ot the driving power of both flies, so that although they move in opposite directions they hinder one another in this direct manner as well as through the viscosity of the gas. Another radiometer contained only one pair of vanes at the ends of a single arm, and each vane carried opposite to its black face, at a distance of a millimetre, a large disk of thin clear mica; the action of a candle on this was to cause rotation in a direction opposite to the usual, that is, the black face moved towards the light. When another disk of thin clear mica was attached opposite the other side of each vane a candle ceased to have any effect. The theoretical reason for these facts is clear; in the first case the region of high pressure set up near the edge of the black face of the vane has more effect on the clear plate than on the vane and in the opposite direction, so that there is a resultant differential pressure driving the vane and its attachments in the opposite direction to the usual ; when the other clear plate is attached there is an equal opposite resultant differential pressure due to it and so there is equilibrium ; in short, when the two clear plates are attached the whole action is confined to the space between them, so that there can be no motion of the whole system. In another radiometer the four vanes were left clear, but at the side of the bulb a plate of mica blackened on one side was fastened in a vertical plane passing through the centre of the bulb, so that a vane in passing it would leave a clear space of a millimetre: when light is thrown only on the clear vanes there is no motion, but as soon as it is allowed to fall on the fixed plate the fly revolves as though a wind were blowing from the black surface. ‘This follows from theory at once, as the edge of the black face becomes a region of higher pressure and therefore a source of wind. On replacing the pith or mica vanes by metallic ones Crookes encountered some new phenomena; perfectly flat aluminium vanes were found to be much less sensitive to the light of a candle than mica or pith ; they move in the same direction, that is with the black surface away from the light, but when the candle is replaced by a source of dark heat their 492 Thermal Transpiration and Radiometer Motion. motion is reversed, which is not the case with mica and pith (of course we are speaking of forms in which two or more vanes are arranged symmetrically with regard to the pivot) ; this reversal simply shows that the metal is a better absorber of dark heat than the lampblack. But in working with vanes made of gold-leaf Crookes noticed that while the blackened side of one vane appeared to be repelled by a candle, that of another appeared to be attracted, and on examination it turned out that while the former vane was flat the latter was crumpled and bent in such a manner as to present a concave surface to the light. Following up this clue by constructing radiometers with bent and curved vanes Crookes was able to prove that in radiometer motion shape of the vane exercises even more influence than the absorbing power of the surface, so that a convex bright surface appears to be strongly repelled by a source of light, while a black surface if made concave to the light is actually attracted by it. The theory of curved vanes is simple: consider a convex vane irradiated by a source on the normal through its middle point ; then, as the amount of heat that a surface absorbs depends on its obliquity to the incident radiation, the farther a part of the convex surface is from the middle the less is it directly heated, and thus there is a continuous fall of tempera- ture from the centre of the surface to the edge; conduction, if allowed time, tends to reduce the amount of the fall but does not obliterate it, and conduction also establishes a fal! of temperature along the back from centre to edge; now the traction of the gas on the solid is trom hot to cold, so that both on the front and the back of the vane there is a traction from centre to edge whose resultant effect is to drag the vane away from the light when the vane is convex to it, so that the light appears to repel a convex surface ; when the surface is concave the same reasoning applies, the gas exerts a traction from centre to edge, and therefore the light appears to attract it. There is hardly any need to reproduce any more of Crookes’s facts or Pringsheim’s skilful experimental analysis of the parts played in radiometer motion by bulb, vane, and gas ; enough has been given to show that the kinetic theory can account qualitatively and quantitatively for all the essential facts of radiometer motion and furnishes general principles for the design of apparatus of the radiometer type. An illustration of the application of these principles will be given in a separate paper on “Two New Pressure-Gauges for the Highest Vacua.” Melbourne, August 1896. po aoa L. Theoretical Considerations respecting the Separation of Gases by Diffusion and similar Processes. By Lorp RayueieH, Sec. R.S.* ae larger part of the calculations which follow were made in connexion with experiments upon the concen- tration of argon from the atmosphere by the method of atmolysis +. When the supply of gas is limited, or when it is desired to concentrate the lighter ingredient, the conditions of the question are materially altered ; but it will be con- venient to take first the problem which then presented itself of the simple diffusion of a gaseous mixture into a vacuum, with special regard to the composition of the residue. The diffusion tends to alter this composition in the first instance only in the neighbourhood of the porous walls ; but it will be assumed that the forces promoting mixture are powerful enough to allow of our considering the composition to be uniform throughout the whole volume of the residue, and variable only with time, on account of the unequal escape of the constituent gases. Let x, y denote the quantities of the two constituents of the residue at any time, so that —dw, —dy are the quantities diffused out in time dt. The values of dx/dt, dy/dt will depend upon the character of the porous partition and upon the actual pressure ; but for our present purpose it will suffice to express d y/da, and this clearly involves only the ratios of the constituents and of their diffusion rates. Calling the diffusion rates pw, v, we have dy _vy eae is oe eee In this equation z, y may be measured on any consistent system that may be convenient. The simplest case would be that in which the residue is maintained at a constant volume, when 2, y might be taken to represent the partial pressures of the two gases. But the equation applies equally well when the volume changes, for example in such a way as to maintain the total pressure constant. The integral of (1) is pee C ar eee!) ys where C is an arbitrary constant, or tl Ome at uid iat ane tee (3) * Communicated by the Author. + Rayleigh and Ramsay, Phil, Trans. clxxxvi. p, 206 (1895). 494 Lord Rayleigh on the Separation of Gases If X, Y be simultaneous values of a, y, regarded as initial, le <) Sl ViX= x so that ao B/Y— pK ee x ($e — In like manner a/y \v/(u—v) y= Y (xy) ee If we write Xv = —- =f7T, . A ‘ : - ; - (7) yr represents the enrichment of the residue as regards the second constituent, and we have from (5), (6), ety = x Bi (vB) x iY/e—P) yy Xey" +xgy? ee an equation which exhibits the relation between the enrich- ment and the ratio of the initial and final total quantities of the mixture. From (8), or more simply from (4), we see that as 2 diminishes with time the enrichment tends to zero or infinity, indicating that the residue becomes purer without linut, and this whatever may be the original proportions. Thus if the first gas (wz) be the more diffusive (u>v), the exponent on the right of (4) is negative ; and this indicates that 7 becomes infinite, or that the first gas is ultimately eliminated from the residue. When the degree of enrichment required is specified, an easy calculation from (8) gives the degree to which the diffusion must be carried. In Graham’s atmolyser the gaseous mixture is caused to travel along a tobacco-pipe on the outside of which a vacuum is maintained. If the passage be sufficiently rapid to preclude sensible diffusion along the length of the pipe, the circumstances correspond to the above calculation; but the agreement with Graham’s numbers is not good. Thus in one case given by him * of the atmolysis of a mixture containing equal volumes of oxygen and hydrogen, we have ¥/X=1 50 ye 92-18) G22. so that r=13 nearly. Thus, if in accordance with the view * Phil. Trans. vol. cliii. p. 403 (18€3). by Diffusion and similar Processes, 495 usually held w/v=4, we should have from (8) : BY Pals so that a reduction of the residue to °229 of the initial quantity should have effected the observed enrichment. The initial and final volumes given by Graham are, however, 7°5 litres and °45 litre, whose ratio is ‘06. ‘The inferior efficiency of the apparatus may have been due to imperfections in the walls or joints of the pipes. Such an explanation appears to be more probable than a failure of the law of independent diffusion of the component gases upon which the theoretical investigation is founded. In the concentration of argon from a mixture of argon and nitrogen we have conditions much less favourable. In this case =}x13 °+4x138 = 229; p/v=V20// 14=:077. If an enrichment of 2:1 is required and if the original mixture is derived from the atmosphere by removal of oxygen, the equation is ee ee —613 ae ae Je 2 oe Ol KZ = 0142 +0029 = 0171, expressing the reduction needed. The results obtained experimentally (doc. cit.) were inferior in this case also. When the object is the most effective separation of the components of a mixture, it is best, as supposed in the above theory, to maintain a vacuum on the further side of the porous wall. But we have sometimes to consider cases where the vacuum is replaced by an atmosphere of fixed composition, as in the well-known experiment of the diffusion of hydrogen into air through a porous plug. We will suppose that there are only two gases concerned and that the volume inside is given. ‘The symbols z, y will then denote the partial pressures within the given volume, the constant partial pressures outside being a, 8. Our equations may be written 5 ae a AG (9) dy=v(B—y)dt or on integration ta + Ce, y=B+De-, ahr Scare (10) C, D being arbitrary constants. After a sufficient time 2, y reduce themselves respectively to a, 8, as was to be expected. 496 Lord Rayleigh on the Separation of Gases The constants w, vy are not known beforehand, depending as they do upon the specialities of the apparatus as well as upon the quality of the gases. If we eliminate t, we get y— B=E(z—a)"", . 2 in which only the ratio v/p is involved. As a particular case suppose that initially the inside volume is occupied by one pure gas and the outside by another, the initial pressures being unity. Then in (10) ae—0,. B=). C= 12 pee we have . g=e#, y=1l—e", .. 42 and ety=lteH—e" . | 2 eee gives the total internal pressure. When this is a maximum or minimum, e“—”¥=y/v, and the corresponding value is es ae b ITY Dc = et+y=1+(F) {1 ae i es Thus in the case of hydrogen escaping into oxygen, p/v=4, and 2 +y=1—3x 4-#=-528, the minimum being about half the initial pressure *. Returning now to the separation of gases by diffusion into a vacuum, let us suppose that the difference between the gases is small, so that (v—y)/w=«, a small quantity, and that at each operation one-half the total volume of the mixture is allowed to pass. In this case (8) becomes Nee ve K ae ey 7 xy Ss nearly ; so that roa (a). . » a This gives the effect of the operation in question upon the composition of the residual gas. If s denote the corres- ponding symbol for the transmitted gas, we have AY Sp (Xe felt es * (X—a)/K 7 P2a/K~ 1 ax B (l—r)a/X anh 1—a/X * The most striking effects of this kind are when nitrous oxide, or dry ammonia gas, diffuse into the air through indiarubber. I have observed suctions amounting respectively to 53 and 64 centimetres of mercury. =2—r approximately, by Diffusion and similar Processes. 497 since 7 is nearly equal to unity. Accordingly ee 1] ‘oo I—r =r nearly, so that approximately s and 7 are reciprocal operations. For example, if starting with any proportions we collect the transmitted half, and submit it to another operation of the same sort, retaining the half not transmitted, the final composition corresponding to the operations sr is the same (approximately) as the composition with which we started, and the same also as would be obtained by operations taken in the reverse order, represented by 7s. A complete scheme * on these lines is indicated in the diagram. Representing the initial condition by unity, we may represent the result of the first operation by ar+3s, or 3(r+8), in which the numerical coefficient gives the quantity of gas whose character is specified by the literal symbols. The second set of operations gives in the first instance dy? 4 dsr 4+ drs +457, or, after admixture of the second and third terms (which are of the same quality), 4 (7? + 278+’) = ( Etsy 2 e In like manner the result of the third set of operations may 3 be represented by (=): and (as may be formally proved by ' * It differs, however, from that followed by Prof. Ramsay in his recent researches (Proc. Roy. Soc. vol. lx. p. 216, 1896). 498 On the Separation of Gases by Diffusion. “induction ”’) of x sets of operations by (3): , . ae When we take account of the reciprocal character of ¥ and s, this may be written = { oe Ep? SE a ey ea” +o > eds) the number of parts into which the original quantity of gas is divided being n+J. If n is even, the largest part, corre- sponding to the middle term, has the original composition*. It is to be observed, however, that so far as the extreme concentration of the less diffusive constituent is concerned these complex operations are entirely unnecessary. The same result, represented by (4)",7" will be reached at a single operation by continuing the diffusion until the residue is reduced to (4)” of the original quantity, when its composition will be that denoted by 7”. And evenas regards the extreme member at the other end in which the more diffusive con- stituent preponderates, it will be evident that the operations really required are comparatively simple, the extreme member in each row being derived solely from the extreme member of the row preceding f. If we abandon the supposition, adopted for simplicity, that the gas is divided into equal parts at each operation, we may still express the results in a similar manner. If p, o be the fractions retained and transmitted, then p+oa=1, and in place of (15) we get yop’. . .04.5 3a The relation between r and s is prtos=1;...: . «rn and the various portions into which the gas is divided after n sets of operations are represented by the various terms of the expansion of (prtas)").03 . . the Greek letters and the numerical coefficients giving the quantity of each portion, and the Roman letters giving the quality. But it must not be forgotien that this theory all along supposes the difference of diffusivities to be relatively small. * There is here a formal analogy with the problem of determining the probability of a given combination of heads and tails in a set of 2 tosses of a coin; and the result of supposing ~ infinite may be traced as in the theory of errors. + Possibly a better plan for the concentration of the lighter constituent would be diffusion along a column of easily absorbable gas, e. g. CO,. The gas which arrives first at the remote end is infinitely rich in this constituent. P) 499) 0 LI. Meroscopic Vision. By G. Jounstone Stoney, M.A., D.Sc., FBS. [Continued from p. 442. ] [Correction in Part I—Instead of the first line of the footnote on p. 336, read as follows:— If the number of replicas is not absolutely infinite, the luminous effects produced in the definite directions spoken of in the text are each a maximum of marvima, &e.] Parr che CoNnTENTS. Page PrP ETON GIS 2 gers Alaa ahaa Alheg, hie ce diab: ea xy ordiey ea ASQ a Numerical Aperture, or Graspi. cancel. +s aides oe 500 34. Information supplied by Imagex .....,...... 503 Foie LESS CL TEN CID eae ie Uae eR ah Ma i 507 36. Significance of what is seen in the Microscope .. 512 37. Explanation of why, when the focus is changed, bright specks may become dark, and fine detail may seem to shift upon an object .......... 513 388. Illustrations of these Phenomena.............. 516 39. illustrations of Illusory Colouration .......... 518 AQ. Illustrations of Fictitious Markings............ 520 Mim Onrrcal COMpaciend. Whit) varias giles deed Geyss ) 524 Ae tlowato See bie EuWlimes) . 1.25. Yas. .ne teat, uy 525 PPE oneniaiie IVCIMATES™.. Jo)... 2 se 2 fc) tee he ee 527 Definitions.—It is convenient to collect here for reference the definitions of some terms we shall have to use. Image « is that image which is seen on removing the eyepiece and looking down the body of the microscope. It is seen without distortion if the iris diaphragm below the condenser occupies its proper position. (See p. 435.) The X scale is one of the radii of image « divided into a scale of equal parts, with zero at the centre, and on which the number G (the NA of the objective) is at its outer end. (See p. 506.) A punctum means a luminous point in image x. It is what a beam of parallel light becomes after passing through the objective. (See p. 903.) A macula is a spot of light of any size and shape in image x2, and corresponds to a sheaf of beams emitted from the object. (See footnote on p. 510.) If kg, in the figure on next page, be the front of the objective, and o the middle of image C, then the radiating lines represent the axial rays of a fan of beams as they emanate from image ©; and the feet of the perpendiculars are in the relative positions in which the puncta of those beams will present themselves in image w. (See p. 504.) 500 Dr. G. J. Stoney on Microscopic Vision. The X scale may be conceived as lying along the line ép, its zero being at o, and the number n (the index of refraction & Z g O P of the air or oil that is in front of the objective) being at the point p on the scale. The zmage plane means the plane in which image OC lies. (See p. 504.) 33. Numerical Aperture, or Grasp.—The microscopic object, the illumination supplied to it, the cover-glass placed over it, and the media on both sides of this cover-glass—yviz. : the medium between the cover-glass and the object on the one side, and the medium between the cover-glass and the objective on the other (which latter is usually air or oil)—are what between them determine the condition in which light enters the objective. It will be convenient to call the three media between the object and the objective a, b, c; a being the medium in which the object is mounted, 6 the glass of which the cover-glass is made, and ¢ being the oil or air which intervenes between the cover-glass and the objective. The surfaces of demarcation between these media are always planes perpendicular to the axis of the microscope, so that we need only consider this simple case. It has already been proved that the light immediately in front of the object, 2. e., as it exists while in medium a, may be resolved into beams of uniform plane waves. These beams con- tinue to be beams of uniform plane waves in travelling across media } and ¢, since the surfaces separating the three media are planes. Hence the light immediately before entering the objective, i. e., as it exists in medium c, may be resolved into beams of uniform plane waves. We may regard this light as suffering reversal, as in § 8, and at the same time conceive medium c¢, the oil or air in front of the objective, to be extended downwards, all other apparatus beneath * being removed. * For convenience of description we suppose the microscope to be pointed downwards, as it usually is more or less. It should be noted that what is commonly called the front of the object is what is then its upper side, the side turned towards the observer, while what is called the front of the objective is its under end, that end which receives the light. Dr. G. J. Stoney on Microscopic Vision. 501 Under these circumstances the light after reversal will form image OC, 7. e. standard image No. 2, in the extension downwards of medium c. If the light be allowed to advance farther down, and then to suffer another reversal, it will in its subsequent upward journey re-form standard image No. 2, and ther centinuing past it, will fall upon the front of the objective in exactly the same state as the light that came from the microscopic object would have done. We shall find the state of things which is here sketched te be much the most conveniert fer our purpose. We may accordingly remove everything that lies below the ebjective except medium c¢, which is te be extended down- wards, and we may substitute image © (¢. e. standard image No. 2, formed as above described in medium ¢ after two reversals) for everything so removed. We have thus only to picture to ourselves image C as present in its proper position in medium c and as emitting its light upwards. This light is resolvable into beams of uniform plane waves, each of which has its own axial ray, viz.: that ray of the beam which starts from o, the point where image C is pierced by the axis of the microscope. Accordingly all axial rays diverge from 0, and after passing through the objective they all converge to, or rather nearly to, another point s on the optic axis, at D. If aand 6 are the angles which one of these rays (or one of these beams*) makes with the optic axis at o and s, then Lagrange’s theorem states that ecina— Nisin 6° OF NO) Se eR where M is the number of times that the linear dimensions of image D are larger than those of image OC, and where n sin a is that which Abbe calls (when applied to the most inclined ray from o which the objective can admit) the “ Numerical Aperture ” of the objective, symbolizing it by the letters NA. These—the name and the symbol—are a too limited name, and an inconvenient symbol. I therefore propose instead to * We may speak of a and £ as the inclinations either of the axial ray, or of the beam to which it belongs. With some objectives image x hes inside the objective, with some eyepieces J) lies inside the eyepiece; and the diagram &c. will need to be modified accordingly. Phil. Mag. 8. 5. Vol, 42. No. 259. Dec. 1896. 2N 502 Dr. G. J. Stoney on Microscopic Vision. speak of the grasp of a beam, and of the grasp of the objective. This designation is justified, since, as we shall presently see, the quantity designated by it, when it is applied to an ob- jective, is the proper measure of its resolving power, 2. e. of the minuteness of detail which that objective can reach ; and when applied to an individual beam or to its axial ray, it indicates the farthest that two rays of that obliquity can go in the representation of detail, in other words their utmost grasp. When applied to the most inclined beam in any meridian plane whose axial ray can be caught by the ob- jective, it measures the grasp of the objective, and may conveniently be represented by G, and it may be symbolized by g when applied to any less inclined beam. When the beams are in the same meridian but differently b b’ as inclined, we may proceed as follows :—Let kg be the front of the objective, o the middle of image C, and ob and ob’ the axial rays of two beams lying in the same meridian plane. These beams, if reversed, will under ordinary circumstances (i. e. if the transversals are not in altogether discordant positions) produce a ruling* inimage C. The spacing of this ruling is given by the formula =o (sina+sin a’), where o is the spacing of the ruling, X/ the wave-length in medium c, and where @ and @’ are counted as positive when on opposite sides of the vertical. Multiply both sides by n, the index of refraction of medium c. Then nN =o(nsina+n sin a’), * To prevent misapprehension it may be well to call attention to the circumstance that this ruling may have a very brief existence—lasting for something like one foot of time in cosmic measure, see footnote, p. 425— and may be succeeded on the image-plane by other rulings parallel to and equally spaced with the first, but perhaps shifted in the direction perpen- dicular to the ruling. Such rulings would be unseen by us. They only become visible when the two beams have some common origin so that their phases maintain the same relation to one another in successive small intervals of time. This prevents the shifting spoken of above. Dr. G. J. Stoney on Microscopic Vision. 503 which is the same as Xr a g+g” (2) where X (=n)’) is the wave-length in air, and g and 9/ the *“‘ grasps’ of the two beams. Hence o and g+q’ are in- versely as one another: in other words, the ménuteness of o is proportional to g+g’. Of course at least two beams have to be associated with one another to produce aruling. If, however, the two beams are equally inclined and on opposite sides of the vertical, 9’ becomes equal to g,so that in this case Xr Beil ia 2 Kaas whence the appropriateness of calling g the grasp of beams that have this obliquity. If ob and ob’ are the most inclined axial rays on opposite sides of the vertical that can be taken in by the objective, formula (3) becomes o— Xn re ee aie al) where > is the spacing of the finest ruling which can be seen by that objective transmitting light of wave-length 2. Whence the appropriateness of calling G the grasp of the objective. The case of two beams which are not in the same meridian plane is dealt with in the next section. 34. Of the Information supplied by Image «. In any of the cases we have to deal with, the angle @ of the figure on page 501 is so small that its tangent may be written for its sine. In fact the two do not differ,in the cases we need consider, by one part in a thousand, a difference which may legitimately be disregarded. Now look down the tube of the microscope. The beams of parallel light emitted from the objective field are concentrated into the points of the luminous image # which is then seen. Let us direct our attention to that one of these beams which is represented in the diagram on p. 901. Its light is concentrated in the point p of image wz. It is convenient to have a name for this concentration of a beam in image a, and we shall call it the punctum of the beam. Let 7 be the radius from the axis of the microscope out to this punctum, and let f be the distance from image v to the focal image of the microscope at D. Then tan B=r/7, whence finally equation (1), Lagrange’s theorem, may be 2 N 2 504 Dr. G. J. Stoney on Microscopic Vision. written oes | I= Bh. te and G (called by Abbe NA)= SR, Be. = R being the radius to the border of the disk of light seen on looking down the tube. It appears from these formulee that the grasp of any particular beam is simply proportional to the radius in image 2 out to the punctum into which that beam is concentrated ; so that we may put the above formule into the simple form of words—g zs proportional to r, on the same scale on which G (the numerical aperture of the objective) ts represented by Kt (the radius of the disk of hght seen on looking down the tube of the microscope). This excessively simple rule will be found of great use in earrying on practical microscopical work. It may be symbolized by the equation * gapr Image C isin the medium e¢ continued downwards. It therefore lies in a plane parallel to and close to the objective plane, but not necessarily coincident with it. Let us call this plane the image plane, in order to give ita name. We have spoken of the image as lyzng in this plane, but the phrase must here be understood in a generalized sense. What is meant is, not that the image is flat, but that the image plane is related to image C in the same way that the objective plane is related to the microscopic object. Consider now one of the beams that form image C. The positions in that beam that are in the phase @ at the time #, are a system of parallel planes transverse to the beam and separated by intervals of X’ from one another. These planes intersect the image plane in a system of parallel lines, which are separated from one another by intervals 6=2/'/sin 2, a being * In dealing with such matters as are discussed in this section, the reader should note that g, g', &c., the grasps of individual beams, though of cypher dimensions are not mere numbers, They are directed quantities, each standing out in some definite longitude, perpendicularly to the optic axis. Each accordingly consists of a vector combined with a scalar. It is thus that they can be fully represented both in direction and magnitude by the radii v, 7’, &c. in image 2, the radii from the optic axis out to the puncta of their respective beams. It is otherwise with G, the grasp or numerical aperture of an objective, the direction of which is immaterial, and of which, therefore, the scalar part is the only one to which we need pay attention. G is adequately represented by R, where R is the length of a radius of image x irrespective of its direction. Dr. G. J. Stoney on Microscopic Vision. 505 the inclination of the beam to the optic axis. All points of these lines are in the phase @ at the time ¢. Proceed in the same way with another beam whose inclina- tion to the opic axis is e’, and which lies in a plane of incidence inclined at an angle ¢ to the plane of incidence of the first beam. It produces on the image plane a system of parallel lines in the phase @ at the time ¢; which lines stand at intervals 6’=2!/sin «’, and are inclined at the angle ¢ to the first set. Let fig. 1 represent the image plane with the two systems of lines drawn upon it. They form parallelograms ; and if we draw the dotted lines of the figure, which are diagonals Fig. 1. to these parallelograms, we find that the one beam is always in the same phase as the other at every point of these dotted lines—in other words, these dotted lines are the middle lines of the equidistant luminous bands which constitute the ruling produced by the two beams on the image plane. Let o be the spacing of this ruling, 2. e. the interval 506 Dr. G. J. Stoney on Microscopic Vision. between the dotted lines. Then co, 6, and 6! are the three perpendiculars of one of the triangles of fig. 1, both in actual magnitude and in position. Now the lengths of the perpen- diculars of a triangle are inversely as its sides. ‘Take then the reciprocals of o, 6, and 6! without changing their positions and fate ie GO AO: and are in the positions of the three perpendiculars of fig. 1. Draw the triangle of fig. 2 with its three sides parallel to the perpendiculars of fig. 1. Its sides will then be proportional to a,b,andc. Again 6=)//sina=)/qg ; and 6/=)//sina’=A/q’ : therefore ax a, b; e, Xr Ig & 4, be and are in the positions of the three sides of fig. 2, in addi- tion to being represented in magnitude by the lengths of those sides. Observe that A/e, g, and g’ are numbers, z. e. their scalar parts are of cypher dimensions. Now if p and p! of fig. 3 are the puncta in image « of the two beams, their radii represent g and g’ both in position and in magnitude estimated on the X scale, which means that scale which prevails throughout image z, and on which the length of the radius of image a represents G, the grasp or numerical aperture of the objective. The X scale is one in which lengths mean numbers. We thus learn that the triangle in fig. 3 is in the same position as the triangle in fig. 2, and is similar to it. Therefore d, the line joining the puncta p and p', represents A/o in magnitude on the X scale, and represents it also in position. In other words, Pe d, or more simply o=A/d, + “> eames if we identify G and R. Hence o 7s equal to X divided by the number represented by d on the X scale; and, further, the ruling of which o is the spacing has its luminous bars perpendicular to the line d. This is a very important proposition, far reaching in the use that can be made of it in the interpretation of microscopical phenomena. We should, however, when employing it, bear this caution in mind—In every attempt to draw an inference from image 2, we must recollect that the inform- ation it gives, though great, is limited. It tells us the intensities and the positions of the beams of uniform plane waves into which the light is resolved—beams which are thrown off from the whole extent of the objective field ; it also telis us the directions and the spacings of the rulings produced by these beams ; but it is silent in regard to every- Dr. G. J. Stoney on Microscopic Vision. B07 thing that is determined by the positions of the transversals of these beams, or the phases of the luminous waves. 35. Resvlution.—Onur first illustration of the great assistance which is rendered to the practical microscopist by Abbe’s theory will be taken from the guidance it gives him when he wants to set up his apparatus so as to resolve an unusually difficult “ test-object.”” That which we shall take is Amphi- pleura pellueda. This cigar-shaped diatom is less than the tenth of a millimetre in length, and about a tenth of that again in width. With ordinary objectives the only detail seen on it is the ridge surrounding it and a longitudinal midrib which dilates into loops at the two ends. Between the midrib and the sides of the diatom are what seem to be two mere uniform plains ; but when adequate arrangements are made each of these plains proves to be covered by trans- verse rows of specks so close that Mr. Nelson in one specimen counted 96 of these rows in the thousandth of an English inch; and the specks of which the rows consist are somewhat closer still. Hence, the spacing of the rows, is the 96,000th part of an English inch, which is the same as o=0°265 p, where mw stands for the micron, the thousandth part of a millimetre. This is a good deal shorter than the shortest wave-length of the most extreme ultra-violet light which can reach us from the sun. The wave-lengths of the visible part of light are much larger, ranging from 0°38 uw to 0°76 pw. | The diatom was one mounted by Professor Van Heurck in a medium containing arsenic disulphide (As,S,), the refractive index of which is said to be 2°4; so that the relative refractive index between it and silex is about 1°7, thus affording both the advantage described in Theorem 6, p- 348, and what is in the present case the still greater advantage described on the same page, in the paragraph which follows the enunciation of that theorem. Moreover, the result seems to show that this medium has also a relatively low dispersive power, which adds to its value. It is unfor- tunate that a material possessed of these important properties is so difficult to manipulate, or so risky, that no one seems to have succeeded in mounting objects in it except Dr. Van Heurck himself. : The apparatus employed were an immersion objective of which the nominal G (numerical aperture or grasp) was 1:35, and a dry condenser of which G’=0°9. ‘To be on the safe side it was thought well to reckon only on being able to make 1°25 of the grasp of the objective available, and 0°85 of the grasp of the condenser. Putting these values for g and g’ into equation (2), viz. :— AN=a(9+9’), co ol ge oe 508°. De Gee Stoney on Microscopic Vision. and putting e=0°265 p, we find A= (0-265) x (1°254 0°85) =0:'56g; which is the wave-length of a ray between the lemon-coloured part of the spectrum and the green. We thus learn that light of the above wave-length is the least refrangible which can help us to see the detail we are looking for. We ought accordingly to exclude all red, orange, and yellow rays since, if present, light of these colours would throw a uniform glare over the plains upon which the detail lies. This condition is best complied with by setting up prisms to limit the range of wave-lengths that we employ. ‘Two two-inch equilateral prisms of dense glass brought into their position of mmimum deviation were found to answer well. The light to be chosen should be of a colour for which the objective is specially well corrected, more particularly as regards aplanatism; and for eye observations it must be in a sufficiently luminous part of the spectrum to supply brightness enough. It should obviously consist of the rays of shortest wave-length that fulfil these conditions ; and on trial the best light was found to be bluish green of about A=0°52y. This wave-length is nearly that of the great magnesium triplet in the spectrum. No collimating-lens was employed to prepare the light for the prisms, but the slit (a coarse one) was adjusted to such a distance from the prisms as enabled the condenser to produce a disk of light in image z of the full size corre- sponding to its grasp, when the condenser was itself adjusted at such a distance from the microscopic object as to produce one uniform colour throughout that disk of light. Upon the slit the image of an incandescent gas-burner had been thrown, which was thus the source of light. The mirror of — the microscope was then turned until the colour seen in image « was bluish green. With these arrangements we know that the wave-lengths we are using are in the neigh- bourhood of A=0°52 p. We are now in a position to determine what size of stop it will be advisable to introduce under the condenser, so as to block out most of those direct beams whose diffracted light does not come within the grasp of the objective, and which accordingly would be not only useless but prejudicial. Since A=0°52 w and c=0'265m we find by equation (2) that gt+g'=1:96. Hence when g has its largest value, which is 1:25, g’ will have its smallest, which accordingly is g =0-71. Dr. G. J. Stoney on Microscopic Vision. 509 We should therefore put in a stop which will block out all beams that have a grasp less than this*. The image at w will then have the ap- pearance represented on a large scale in the annexed diagram. An annulus of bright light will be seen in it between the edge of the stop, which lies at g/=0°71, and the limit of Image a, with X scale. the grasp of the condenser at G’=0°85, and faint light will be seen farther out to the limit of the grasp of the objective at G=1°25. We may, however, with advantage block out still more of the light. For the specks upon the diatom are numerous, and although not quite regularly disposed, they are approxi- mately in straight vertical rows, and less regularly in some- what wavy horizontal rows. In this description we suppose c é 75 0 O | Z BOQ © On Image x. * To get the stop accurately into its place it should be mounted so that it can be centred relatively to the condenser. Provision for this adjustment is always useful and sometimes essential for accurate work ; and Messrs. Watson and Sons, at the request of the writer, made an adjustable cell for holding the stops which is entirely satisfactory. 510 Dr. G. J. Stoney on Microscopie Vision. the length of the diatom to be placed horizontally. Now the nearest of the diffraction-spectra which such sources of light would produce are disposed round a direct ray z, as in the first of the diagrams on p. 509. Accordingly, when z is in the neighbourhood of a’ of the second figure, it produces one, and only one, diffraction-spectrum, that at a, which comes within the grasp of the objective. Similarly the direct beams which have their puncta near 0’ produce diffracted beams with their puncta near 6. And in the same way the beams which are concentrated into those puncta of image x which lie near ¢’ and d’ will produce diffracted light which reaches ¢ and d. But the direct beams that reach the intermediate positions at e’, f’, g’, and h’ throw all their spectra too far out—vertically sideways or diagonally—to be caught by the objective. Hence this intermediate light cannot help to show the specks, and only produces diffused light tending to veil them from view. The image will therefore be cleared by blocking this light out. This is easily done by cutting a cross out of card, and placing it over the central stop. What is then seen at x is depicted in the annexed figure, for in fact the diffracted light is so faint, and the direct light so strong, that to see each macula * of diffracted light it is best to shut out all but one of the macule of direct light; and even then the diffracted light at ¢ and d is faint and diffuse enough to be difficult to see. It now only remains to adjust the draw-tube with extreme care (since the objective is fully corrected only for one length of draw-tube) and to apply a compensating eyepiece of sufficient power. A suitable magnification is 2000, for eyes that see very minute objects with ease; and if there be in the observer a slight defect in this respect, the power 3000 + will be found better. The power 2000 causes the vertical rows—those which stand at right angles to the mid- rib of the diatom—to appear with the closeness of lines ruled at intervals of half a millimetre from one another when viewed * A macula or spot in image z is the representative in that image of a sheaf of beams emitted from the microscopic object. It may be of any size, and the sheaf of beams it represents are those beams of which the puncta are the points of the macula. Bt + The objective made use of had an initial magnifying-power of about 80, and the higher power was reached by a 40 compensating eyepiece which the firm of Carl Zeiss were good enough to make for the writer, and which he has found to be of great service. Dr. G. J. Stoney on Microscopic Vision. 511 by the unassisted eye from a distance of ten inches. When all the foregoing precautions are taken the observer is rewarded by seeing something like 17 or 18 specks in each row where the rows are longest, and fewer in other places. The specks are fainter than the rows, because from their being some- what closer, the diffracted light at c and d lies farther out than that at a and 6, and less of it is grasped by the objective. It is also'more diffuse, and therefore less easily seen in image «, partly because the specks are disposed in wavy lines longitu- dinally while they are arranged in nearly straight lines across the diatom. Another reason why it is fainter is that the longi- tudinal rows are much less numerous than the transverse. On all these accounts it is very difficult to see the maculee at c and d in image a. Another point is well illustrated by this experiment. The larger features on the diatom require a certain moderate aperture to show them well. Now beams so divergent as those that have their puncta in macule so separated as a’, b’, ce’, and d’ cannot concur to show these larger features unless in co-operation with intermediate beams that have been blocked out. The larger features are accordingly only seen by the light of these maculz, each acting separately; and the sheaf of beams that reaches one of them has too small an aperture to show those features well. They present accordingly that clumsy blurred-out look familiar to all microscopists who have worked with annular or oblique illumination. Again, the specks themselves look very much like little molehills viewed from above. This is because they are due to the intersection of rulings which are of the jirst order, and which do not differ much from one another in their spacing. Rulings of the first order mean such as are pro- duced by interference between only one pair of beams. The law of intensity in rulings of this simplest kind is that repre- sented in the accompanying figure, and therefore the specks which are produced by the intersection of rulings of the first order must have the same kind of rounded appearance. Two other appearances are likely to be seen in making this experiment. One is that the bright specks will become dark specks on a slight change of focus; the other is that they may perhaps seem to shift their positions relatively to the larger features of the object when the focal adjustment is dis- 512 Dr. G. J. Stoney on Microscopic Vision. turbed. These are both of them phenomena more conspicuous in others of the experiments which we propose to make, and will more appropriately be explained in connexion with them. (See § 37.) It has appeared desirable to go very minutely through the successive steps of this example in order to show clearly that Abbe’s mode of dealing with microscopic vision does success- fully and in the most instructive manner guide every step of our preparations, and that it renders a full explanation of every phenomenon we encounter whether in the course of the preparations or in the final result. 36. On the Significance of what we see in the Microscope.— As to the significance of these specks. Their spacing along each row is somewhat less than the spacing of the rows, and may be taken to be about 0°24. From the way in which their image is formed by the intersection of rulings of the first order, it appears that they, like rulings of this kind, will appear larger or smaller according to the amount of the illumination; and that they will be best seen when the illumination is such that the apparent diameter of a speck, and the apparent interval between it and the next, are about equal. Accordingly the portion of the object which corre- sponds to it when best seen is that which is contained within a sphere whose diameter is 0°12, and whose radius is there- fore 0°06. Now if we make the probable hypothesis (see ‘On the Internal Motions of Gases,” § 9, in the Phil. Mag. for August 1868, p. 140) that the average spacing in solids and liquids of the chemical atoms of which matter is made up is somewhere about a tenthet-metre*, which is the same as 0:0001y, then there has needed about 900,000,090 of these chemical atoms to build up a portion of the object of the volume of our little globe. If, on the other hand, we suppose that the spacing of the atoms is about a ninthet-metre, 2. e. 0:001~—and it can hardly be more than this—the number of atoms in our little sphere becomes 900,000. The actual number probably lies somewhere between 900 thousands and 900 millions. There is therefore this vast number of chemical atoms in the tiniest part of an object which can be dis- tinguished from another part by so good a microscope, when handled with extreme care. We ought further to reilect that each of these chemical atoms is itself highly complex, and that within every one of them all those events are in progress * A tenthet means a unit in the tenth place of decimals. And as a quarter pound means the quarter of a pound, so a tenthet-metre means the tenthet of a metre. Dr. G. J. Stoney on Microscopic Vision. 513 that are betrayed to us through the spectroscope. In the face of such facts as these it is in vain for biologists to talk as if anyone had at any time seen such a thing in nature as “undifferentiated protoplasm,” or as if any speck of matter that can be seen by the best microscope is other than a body of large size from the molecular standpoint, within which there may be a vast amount of structure and an inconceivable flow and variety of events continually in progress. The finest flagellum of a saprophyte, the tiniest rod in karyokinesis, may, consistently with every lesson taught us through the microscope and by molecular physics, have quite as elaborate a structure as that part of the structure of the limb of a quadruped which can be seen by the human eye. Coarse rulings are usually produced by a fan of numerous beams. It is thus that the shape of the bars of which they consist is brought out. But the finest rulings are of the first order, 7. e. in their case the fan has been reduced down to two beams. Now the intensity of the light in rulings of this kind follows the law [1—cos (27rx(g+9')/X)] *, which is represented by the diagram on p. 511; and the microscopist should constantly bear in mind that every speck or band upon the object which is sufficiently minute to have its image formed exclusively out of rulings of the first order must accordingly have the appearance of a little hillock or little ridge wholly devoid of detail and with blurred outline: and that notwithstanding this there may be any amount of detail, variety of outline, and intricacy of motions present upon the actual object within the limits of the part represented by that speck or band. 37. Propositions 8 and 9. Cause of bright specks becoming dark ; and Cause why fine detail often seems to shift upon an olject.—The finer detail in image C is formed by the inter- lacing of beams that are inclined at a large angle to one another. Let wand u’' be two such beams in one meridian plane, and let the unbroken lines of fig. 1 represent those wave-surfaces in them which at the instant ¢ are in phase @. Then it is easy to see that the two undulations reach every point of the planes represented by the dotted lines in the same phase. Hence if minute markings are seen by the ruling produced by these beams cooperating with rulings produced by other pairs of beams which are but little sloped to w and * If the two beams are not in the same meridian plane, g+g' should be replaced by d, i.e. by the number on scale X which is represented by the length of d, which is the distance asunder in image w of the free ends of g and g’. (See § 34, p. 506.) 514 Dr. G. J. Stoney on Microscopic Vision. u'—a case which occasionally happens—then if we put the object a little out of focus these markings will appear to travei Pigs: along the inclined dotted lines and will appear to shift side- ways if the dotted lines are inclined, which they will be if, as usually happens, the angles of incidence of u and w’ are unequal. This shifting need not extend to the larger features of the object, since they are seen by light that is quite differently circumstanced. In the case represented by the figure the markings that are seen do not pass from bright to dark. Their definition merely fades continuously into a haze while they are being put out of focus inwards or out- wards. But a case which is much more frequently met with is represented by fig. 2. Here two pairs of undulations wu, u/ and v, v’, both in the same meridian plane, cooperate to pro- duce one of the rulings by which the markings are seen*. To avoid complication the wave-surfaces are not represented in this figure, but the dotted lines sloping up to the left repre- sent, as in fig. 1, the planes over which uw and w! are in the same phase. The lines sloping up to the right represent the same for v and v!. Hence if the objective be focussed upon the horizontal plane through s everything is in confusion and the image disappears, whereas on removing the focus a little farther out to p the ruling reappears, but now dark * The case where v and wu’ coalesce and form the dioptric beam, while w and v' are diffracted beams, is that most frequently met with. Dr. G. J. Stoney on Microscopie Vision. 515 lines occur where bright ones were before. At q all is again in confusion, to be succeded on drawing the focus farther out Fig. 2. Image plane. by the reappearance of the ruling at 7, with its bright and dark lines in the same positions as on the image plane. This is what happens to beams wu, wu’, v, v’, all of which lie in one meridian plane. If, as usually happens, the corre- sponding undulations in all the other meridian planes that contribute to form the minute marking have their dotted lines (the lines shown in fig. 2) about as much sloped, then at about the height p they too will produce rulings in all of which dark lines will now occur where bright ones did on the image plane. Hence at the height p dark specks will be produced, by the cooperation of all the beams, where bright ones were produced on the image plane; and light will be distributed over the intervening spaces where on the image plane the darker shades prevailed. The effect depends on the inclinations of the dotted lines being sufficiently nearly the same in different longitudes. Usually they approximate sufficiently for at least one of the alternations from bright to dark spots to be well seen, and not unfrequently a second or third may be imperfectly traced. If, as in fig. 2, v' and v are at the same inclinations as u and wu’, then the dotted lines are equally sloped to the right and left, and the dark specks at level p are directly over the bright ones on the image plane. But this adjustment seldom happens to be accurately secured, and the dotted lines in 516 Dr. G. J. Stoney on Microscopic Vision. consequence slope more one way than the other. The dark specks will then not be vertically over the bright ones, but will have shifted a little in the direction of the more inclined dotted lines of the figure. From all which we may enunciate the two following propositions :— PROPOSITION 8. When the image of minute detail is produced by a triplet of beams, or by two pairs of beams, in each meridian, then the conditions are usually such, especially when the detail presents the appearance of round specks, that it will suddenly change from bright to dark, or vice versa, upon a slight change of focus ; and under special circumstances which are occasionally met with more than one of these alternations may occur. PROPOSITION 9. The conditions are likely to be such, unless special precautions have been taken, that on a slight change of focus the minute detail upon the object will appear to shift its position relatively to the general position and broader features of the object. 38. Experiments illustrating the last section—All the con- ditions spoken of in the first paragraph of the last section can be reproduced if the objective be a good half-inch apochromatic with G=0°65, and if the object be the large variety of Navicula lyra which is frequently met with in slides of diatoms from St. Peter, Hungary. We shall suppose the diatom to lie horizontally in the field of view, ¢. e. with its length in the direction sometimes called Hast and West. Now insert a stop under the con- denser, which will allow the sheaf of beams u to pass. The figure re- presents image «z, which is seen by taking out the eyepiece and looking down the tube of the microscope. Jt is well to use a blank eyepiece to keep the eye central—that is, the mounting of an eyepiece without the lenses, and with a small eyehole. The transverse rows of specks upon the diatom, which lie vertically in the field of view, produce the vivid spectrum v; the longitudinal rows, which are fewer, closer, and more wavy, produce on these accounts the fainter, more distant, and more diffuse spectrum w. On replacing the eyepiece the specks are seen on the diatom with great distinctness. If the stop is in the position represented in the Dr. G. J. Stoney on Microscopic Vision. 517 figure, so that 1 and v are at equal distances on either side of the vertical diameter, then on slightly changing the focus the specks will not shift sideways. But on account of the diffuseness and the one-sided lateral extent of w, the adjust- ment of « and w cannot be the same for different parts of w, nor can it be the same for different colours, and it may be found impossible to find any position of u in which there will not be some shifting of the specks vertically. In this experiment only two of the macule in image # (corresponding to two sheafs of beams) lie in the horizontal direction, and two vertically. Accordingly in each direction there is (as in fig. 1 on p. 514) only one of the two sets of the dotted lines in fig. 2 upon page 515. In this case there- fore the conditions for the passing of bright specks into dark do not exist, and accordingly on putting the microscope slowly out of focus the image grows indistinct but no black specks appear. The case is otherwise if we use a stop with a hole in it as at w in the accompanying figure of image vw. Here there are three maculz, corresponding to three sheafs of beams in the horizontal position and only two vertically. Ac- cordingly on putting the microscope out of tocus the vertical rulings (which are caused by three sheafts of beams) will change from bright to dark while the horizontal ones (caused by only two) will not, and the resulting specks in the microscopic image will become imperfectly dark. Diatoms which show the transition from bright specks to dark in perfection are those known as Actinoptychus, of which a good example is almost sure to be found ona St. Peter slide. With the half-inch apochromatic and with the iris diaphragm below the condenser nearly closed it gives in image w a ring of strong diffracted light. ‘Two opposite puncta in this ring and a punctum in the central macula belong to three beams which produce one of the very numerous rulings which conspire to form the specks in the microscopic image. Hach such trio of beams furnishes both sets of the dotted lines in fig. 2 on p.515. And as the ring is a tolerably circular one the other similar trios, whether in the same or in other longitudes, furnish dotted lines in fig. 2 that are not very far from being equally inclined. These are conditions that will produce black specks at the height represented by p in Phil. Mag. 8.5. Vol. 42. No. 259. Dec. 1896. 20 518 Dr. G J. Stoney on Aicroscopic Vision. fig. 2 on p. 515. Now open the iris diaphragm, insert the eyepiece, and look at this diatom : it will be found to exhibit the phenomenon with great distinctness. A modification of this experiment is to cut a piece of card of the annexed form and to place it over the back of the objective. It allows only two of each trio of beams to pass. These proceed to form the rulings which are competent to form specks in the micro- scopic image ; and accordingly that image will still exhibit the bright specks, which, however, will now go out of focus without any dark specks appearing. Notice that the specks now appear to traverse in a direction perpendicular to the diameter of the semicircular stop, while the microscope is being put out of focus. This is because the dotted lines of fig. 1, p. 514, are here necessarily oblique. 39. Haperiments exhibiting Illusory Colouration. See Pro- position 4, p. 845.—The half-inch apochromatic, of which the grasp is 0°65, answers admirably for these experiments. It should be furnished with a Davis’s shutter, z.¢. a small iris diaphragm interposed between the objective and the mierc- scope tube, by which the aperture may be reduced when desired. We shall also want asmall central stop about 8 mm. in diameter, which can be put over the back of the ob- jective, and which may be cut out of card. This wil enable us, at one stage of our experiment, to exclude the sheaf of dioptric (2. e. undiffracted) beams, while leaving a free passage to others. The object which perhaps most strikingly exhibits the phenomenon we are now occupied with is the diatom known as Actinocyclus Ralfsw. 1°. Select a valve of this diatom which looks blue when the Davis’s shutter is partly closed. 2°, On then opening the Davis’s shutter the colour is for the most part but not altogether discharged, and at the same time a quantity of detail comes into view which was not visible or’ was seen imperfectly when the colour was present. It consists of specks variously distributed over the valve. 3°. Now introduce the central stop over the back lens of the objective, and open the Davis’s shutter. The image is thereby con- verted from biue to red, and there are added to the image dark grooves and bright lunes distributed over the intervals between the legitimate specks. 4°. Finally examine tle diatom with the immersion objective, which has a much greater grasp than the half-inch. It has now become absolutely colourless, and new detail has come into view Dr. G. J. Stoney on Microscopic Vision. 519 consisting of from two to five little points within each of the specks which are visible with the half-inch. Now a study of image 2 enables us to trace the cause of every one of these effects. Focus the diatom with the half- inch. Take out the eyepiece and look at image w. Nearly close the iris diaphragm under the condenser, so as to reduce the incident light to a narrow central sheaf of beams. Then the macula of this sheaf of beams will be seen in image 2 as a central spot of bright light. Faint light is visible about it, which is scattered pretty generally over image [this is light which helps us to see the larger features of the object ],.and at about the distance from the centre where g=0°5 there is a ring of much more intense light which has been diffracted oe in all directions to that distance. ‘This ring Bae of diffracted light is mainly red, owing to the unequal distribution of colour spoken of in § 16, p. 345. As so much red has been thrown into this spectrum, there is an equal deficiency of red in the light which forms the central macula and the faint diffracted beams by which the larger features on the object are seen. Hence it is that when the marginal ring is shut out by partially closing the Davis’s shutter, the diatom will appear blue: blue being the colour which lamplight becomes when much of its red is withdrawn from it. The exclusion of the diffracted red light has another effect—it prevents the formation of a number of the rulings which are necessary for the formation of a good image; and accordingly much of the detail on the diatom which is visible when the Davis’s shutter is open, is lost to sight when it is sufficiently closed to render the image blue. That the image is not quite colourless with the full aperture of the half-inch is because there also exist other dittracted beams which lie beyond the reach of that objective. We know that they exist and that they are coloured, because the image seen with the immersion objective is colourless, and because more detail is seen in it. It has rendered the image colourless by adding some coloured beams to the slightly- tinted image which the half-inch, fully open, presented, and it has brought out further detail by transmitting these additional beams in directions which furnish new rulings. Return now to the half-inch objective. When the central stop is put over its back lens, the central macula of image w is coveredup. ‘This shuts out the dioptric beams. The image 202 520 Dr. G. J. Stoney on Microscopie Vision. is then formed by the ring of red diffracted light along with the fainter and apparently white diffused diffracted light. Accordingly the image in this case is preponderatingly red. At the same time the red diffracted light is now obliged to act without the cooperation of the part of the light of the dioptric beams with which it before produced rulings. What was before a triplet of beams producing a ruling has now become the two extreme beams left to operate without the middle one, and they produce a ruling that is twice as fine It is thus that black bands and bright patches are produced between the legitimate specks. These are very conspicuous in the image, notwithstanding which they are quite foreign to the object. They are produced very much in the same way as intercostal markings, to the illustration of which the next section will be devoted. Similar experiments may be made with innumerable other objects. Thus the familiar diatom, Pleurosigma angulatum, becomes buff-coloured when viewed with the Davis’s shutter sufficiently closed to exclude all but dioptric beams and that inner portion of diffracted light which has its origin exclu- sively in the larger features of the object ; whereas it becomes of a delicate blue when seen with the dark-field illumination obtained by putting a stop of the proper size under the con- denser. In this case the object is seen by its diffracted light only, much of which is coloured. Similarly the tubercle bacillus when stained with fuchsin is intense red when examined through the half-inch in the ordinary way, but becomes a bluish white when seen with black-ground illumination. The study of a variety of cases like the above will be found instructive. 40. Intercostal Markings and allied phenomena. See § 15, p. 3845.—Light which does not contribute to delmeate any- thing upon the object is apt to intrude in three forms— either (a) concentrated into patterns which are superposed — upon the microscopic image, or (b) scattered in patches over parts of it, or (¢) spread in the form of a luminous haze over everything. We shall endeavour to exemplify each of these. (a) The first is well shown in the image of Peristephania eutycha when examined through the half-inch apochromatic objective. ‘he real detail upon this diatom seems to consist of divisions into hexagonal cells which make it look like a honeycomb. Adjust the draw-tube accurately. Now nearly close the lower iris diaphragm, and look at image z. ‘The dioptric light makes a central white macula, and round it are displayed, as in the figure, a beautiful array of coloured macule, each of which is a spectrum, blue inwards and red Dr. G. J. Stoney on Microscopic Vision. 521 outwards, To make the following experiment, the lower iris diaphragm should be opened to so moderate an extent as will cause these macule just to come short of touching one another. When now the Davis’s shutter is gradually opened, which increases the aperture of the objective, a succession of images present themselves. If it covers up all the maculz except the central one, the diatom is indeed seen, but with no detail upon it. In all subsequent enlargements of the aper- ture, the honeycomb structure of the Imuge wv. diatom is visible ; but with the ad- dition of spurious effects which vary * while the grasp of the objective is being enlarged. In fact, they depend on what spectra are permitted to pass and what spectra are excluded. Let us consider three of these images, 1, 2, and 3, of which 2 is formed with a larger aperture than 1, and 3 with a larger aperture than 2. If we start with image 1 and open the Davis’s shutter so as to pass to image 2, we may regard 2 as being image 1 modified by adding to it the new rulings which are formed by the newly almitted light cooperating with a part of the dioptric sheaf. And on the other hand, if we start with image 3 and close the Davis’s shutter, we may regard image 2 as ; being image 3 with the rulings added to it which would result if light equal in intensity but opposite in phase to the excluded light were allowed to cooperate with part of the dioptric light. In fact, these rulings fill the gaps between whatever rulings 3 has and which 2 has not. Sometimes the one of these processes and sometimes the other helps us to a better conception of what is going on. The first process needs no elucidation, and of the second the following is a very neat illustration. Keep the same diatom on the stage; then look at image a, and open the Davis’s shutter till the inner hexagon of six spectra is seen. On _ re- placing the eyepiece a few intrusive mark- ings will be perceived, including a_ bright pateh of light occupying the middle of each honeycomb cell. This is image 1. Next look again at image wv, and open the Davis’s shutter farther until the succeeding hexagon of twelve spectra is also allowed to pass. The image. which is then * With the half-inch apochromatic, two, three, and four intercostal markings can be produced along each side of each hexagon, the last number when we employ black-field illumination. 522 Dr. G. J. Stoney on Microscopie Vision. seen on replacing the eyepiece is image 3. One of its honeycomb cells is represented in the diagram, from which it will be seen that there are 19 deceptive markings upon it. The central one is bright, but by a slight change of focus becomes dark. Adjust the focus so as to make it dark, and then close the Dayis’s shutter into an intermediate position, which shuts out the whole of the red of the outer twelve spectra, while it allows their blue halves to pass. This produces a new image— image 2—which will be seen on replacing the eyepiece. It will be found to be nearly like image 3, but with a red central speck instead of a dark one. The reason of this is that the hexagon of twelve spectra produces, along with some of the dioptric light, rulings which formed the dark central speck, as is proved by its being present in image 3 and not in image 1. Now when we shut out the red of those spectra, we produce the same effect as if we added red light in the opposite phases, and half of this with half the same dioptric light (which has not been excluded) produces rulings the same as before, except that the bright and dark bands are interchanged. These accordingly change the dark into a bright speck at c. The effect is somewhat startling, since we change the specks from dark to. red by shutting out red light! This gives one a lively picture of how it comes to pass that the exclusion of light from image C can lead to the intrusion of unauthorised markings. Another matter may here be adverted to. As explained in § 39, these spectra need not be equally intense for every wave-length: sometimes the less refrangible light pre- ponderates in them and sometimes the more refrangible. Accordingly some of the intercostal markings to which they give rise will have a preponderance of red, others a prepon- derance of blue. The first will seem buff-coloured, the others — whiter than the lamplight we use as our illuminant; and upon scrutinizing the fictitious markings this difference in tint between them is plainly visible. When the dioptric macula is placed excentrically the resulting intrusive markings become in some degree both different and differently situated. Hence when we give a large aperture to the dioptric sheaf of beams by opening the iris diaphragm below the condenser, its macula becomes large ; one part of it is central, others are excentric in different degrees and different directions. Hach part gives rise to its own set of false markings, and these where they overlap interfere and may occasion a general illumination at the place where they are situated instead of distinct markings. This Dr. G. J. Stoney on Microscopie Vision. 523 is illustrated on our diatom by the whole inside of each cell becoming full of a nearly uniform sheet of light instead of a group of definite markings, when the iris diaphragm is suitably opened. It is easy to see from this that there is no one opening of the iris diaphragm which will, in all cases, give the best effect—the etfect most free from intercostal markings. In each case it depends on the way the spectra are disposed, and will therefore differ from one object to another. Its success, so far as intercostal markings are concerned, depends on the circumstance that when a small dioptric macula is shifted about in image w, the illusory effects undergo rapid change, while the image of true detail is but little affected. Hence the real features of an object are well seen with a considerable illuminating cone ; and they may even be better seen on account of the admission of oblique rays, as these will both add to the visible detail and will diminish that defect in images which consists in the rounding off of sharp edges. On the contrary, the false effects produced by the several small sheafs of beams in the cone are so diverse that when jumbled together they become undistinguishable. This is the next best thing to their being got rid of. It is evident that anything which intensifies the strength of the more inclined beams wil! give rise to brighter inter- costal markings. They are, therefore, of exaggerated strength when the object has been mounted in a medium of extra high refractive index, owing to the effect which is described in § 18, p. 346. (6) The diatom employed in the foregoing experiments has the detail upon it disposed with the regularity of a honey- eomb. It therefore concentrates most of the light diffracted by it into definite spectra, and this has led to the formation of intercostal markings of equal definiteness and regularity. Where, however, less symmetry prevails in the disposition of the detail upon an object, the light it diffracts is not distri- buted according to any simple law, and a corresponding want of regularity ensues among the spurious markings, which may become shreds, lunes, and patches, black, white, or tinted, usually twisted about, and sometimes flickering (from slight movements of the observer's eye), and which are chiefly conspicuous where there is some flat space in the microscopic image unoccupied by real detail. Numbers of diatoms exhibit these phenomena. (c) Another frequent event is the presence of a haze of light over everything. It will occur when, from want of a central stop, there is dioptric light w hose corresponding diffracted light is abundant and hes beyond the grasp of the 524 Dr, G. J. Stoney on Microscopic Vision. objective. This has been sufficiently illustrated in § 35. The remedy is to insert a stop of the proper size. A similar fog of light will occur if, by opening the iris diaphragm too far, diffracted light has been rendered too copious in situations where it is beyond the grasp of the objective. Hach part of it will then produce its own body of intercostal markings ; these get massed together and produce a haze. The remedy is of course to lessen the opening of the iris diaphragm ™*. A case which should be specially noted is that of a bar on the object with sharp edges. These produce highly inclined diffracted beams ; and if the objective cannot take these in, the beams —Bd of p. 344 which must then be added to standard image No. 1, round off the edges and add thin appendage-lines which are often mistaken for diffraction- fringes though they have a different appsarance and a quite different origin. Al. “ Optical Contact.” See § 19, p. 348.—An excellent illustration of the effect produced by Stokes’s layer—the effect which microscopists call optical contact—may be obtained as follows :— Focus a valve of Pleurosigma angulatum, mounted dry, under an immersion-lens of, say, G (or NA) =1°3. Adjust the draw-tube. Then set up the apparatus described in § 35, p- 12, for furnishing monochromatic light, and select green light of about wave-length X=0°55 w. Now 0°55 w is also the value of o upon this diatom, 7. e. it is the spacing asunder y LZ» Image x, with X scale. of its rows of markings. Hence from the formula o=)/(¢+ 9’) we find that g+g’/=1, where g’ is the grasp (or radius in image 2 out to the punctum) of a dioptric * A haze of light may have a different origin when the section is too thick. In this case the parts that are out of focus produce it, and it may often be cleared up without detriment to the observation we want to make by partially closing the Davis’s shutter. Dr. G. J. Stoney on Microscopic Vision. 525 beam, and g is the grasp of the associated diffracted beam. [The regularity of the detail on this diatom throws nearly all the diffracted light into definite spectra.] We have made the convention that g and g’ shall be positive when on oppo- site sides of the centre. Accordingly, when on the same side we must regard g/ as negative. Now open the iris diaphragm until the macula of the dioptric sheaf of beams has expanded so as just to touch those of the diffracted sheafs of beams. Then what is seen on looking at image 2 is either what lies within the greater or what lies within the less of the two large circles of the figure, of which the outer one corresponds to 1:3, the grasp of the objective, and the inner one to a grasp=1. If the diatom is “ in optical contact,” that is if the layer of air between it and the cover-glass is less than the thickness of Stokes’s layer, then what is seen extends to the outer circle. Whereas if the chink between the diatom and the cover-glass is more than the thickness of the Stokes’s layer, no light can get into the cover-glass except such as passes up through it and the oil at less than the “ critical angle,” and this supplies light in image «, only within the smaller circle which corresponds to G (or NA)=1. The reason of all this is obvious from what is stated in § 19 ; and very interesting appearances may be obtained by traversing the slide sideways and thus bringing diatom after diatom under the objective. With some the light will extend in its full intensity to the outer circle. These are they thai are in good optical contact. With others nothing is seen beyond the smaller circle. These are they that lie beyond the thin Stokes’s layer which lies like a varnish on the under side of the cover-glass. And now and then one may be found in which the outer ring of light is present but dim. This is one the interval between which and the glass is nearly the full thickness of the Stokes’s layer. The whole experiment, if made with green monochromatic light, is one of exceeding beauty. WG. Flow to See the Rulings.—Ilt has been explained that the microscopic image is produced by the interlacing and mutual interference of luminous rulings, each of which extends over the whole image field ; and that each ruling is due to the concurrence of two or more beams the puncta of which are situated at equal intervals along some straight line upon image z. In order, however, to get light enough to see a ruling, we must be content to use small sheafs of beams instead of individual beams, and these in image x become small maculz instead of points. This in practice may be accomplished by putting a disk of card over the back of the 526 Dr. G. J. Stoney on Microscopic Vision. mounting of the objective and making a pinhole in it where we wish a sheaf of beams to pass. Make one such hole in the centre and examine a slide containing a variety of diatoms, as for example one of the show slides made with diatoms from St. Peter, Hungary. In order to be able to predict the result, we must deal with a specific case. Let, then, our objective be the. half-inch apochromatic with which R, the radius of image wz, is about 8 millimetres. Let us further suppose that the hole in the card is 1 mm. across. Hence the sheaf of beams the puncta of which lie within this hole, contains beams of which d, the distance between their puncta (see § 34, p. 506) may on scale X be as much as one-eighth of 0°65 (the grasp of the objective), i.e. d is nearly 0°08 on scale X. Put this into the equation C=n/d; and put %=0:6h, which is close to the wave-length of the brightest rays in lamplight. We find then C= Cop for the spacing of the finest ruling which can be produced by the light passing through the small hole. ‘This would admit of detail upon the object being seen down to about the size of a speck half the diameter of a disk of human blood. Accordingly all the large features upon most diatoms can be seen through this small hole, as may be verified by passing a slide containing a variety of diatoms under the objective. Now make another similar hole at some distance from the centre, suppose in a position corresponding to g=0'6 ; or, still better, make two holes at that distance on opposite sides of the centre. ‘This gives us three holes in a straight line at equal intervals. Then close the iris diaphragm under the condenser until the sheaf of dioptric beams just fills the middle hole. Only diffracted light will then appear in the other two. Now pass the diatoms again under the objective, and on many of them a ruling will be seen, viz. : on all those which furnish diffracted light of sufficient strength in the positions of the two lateral holes. This ruling will have a spacing calculated by Here then we have actually in view one of those rulings which go to build up the ordinary microscopic tmage—that image Dr. G. J. Stoney on Microscopic Vision. 527 of the object which is furnished by the microscope when the card is removed. Note that the ruling as seen does not extend across the whole field of view, but only a little beyond the boundary of the diatoms. This is because the ruling we see is made by sheafs of beams instead of by individual beams. The more we can reduce the size of the holes without making the ruling too faint, the more diffuse will the image of the diatom become, and the farther out will the ruling extend ; until at the limit it would extend over the whole field of view and be perfectly uniform everywhere *. It is instructive to make this experiment with a specimen of Actinocyclus Ralfsi, selecting one which is blue when seen through a small aperture. Here we found the diffracted light to be red, see § 39. This red light cooperating with some red out of the dioptric light produces a ruling which if seen alone would consist of alternate red and dark bands. But there is an excess of dioptric light beyond what is employed in contributing to form this ruling, and this excess throws a wash of blue light over everything. Where it falis on the red it turns it white, where it falls on the dark parts it turns them blue. Accordingly what is seen is a ruling of bands which are alternately white and blue. Similarly on other diatoms the ruling is found to consist of white and coloured bands instead of merely light and dark. The colour which takes the place of the dark bands is in each case what- ever colour the diatom, or the part of the diatom, presents when seen through a very small aperture. * What has happened may be clearly apprehended from the following considerations:—If instead of three individual beams with puncta at a, d, ¢ to produce a ruling, we suppose two such sets as in the figure, and all under such circumstances that they can interfere, then @ and a’ produce a coarse ruling with its luminous bands and dark intervals lying vertically. Rulings in exactly the same position are produced by 0 and U’', and by cand c’, so that these all reinforce one another—they together produce one ruling ; and the consequence is that all light from aw’, bb’, cc’ is extinguished at the middles of the dark bands of this ruling, At the same time the beams with puneta at a, b, ¢ produce a fine ruling which lies hori- zoutally, and, @, 0’, ¢. produce an identical ruling which reinforces it, and all ight from Imave 2. ad’, bo, ce’ must disappear at the middles P of the dark bands of this ruling. Hence we have two rulings that co-exist, a coarse vertical ruling and a fine horizontal one; and the outcome is that we see a horizontal fine ruling, which however is visible only across the bright bands of the coarse vertical ruling, and which fades out in the intermediate dark spaces, 528 Notices respecting New Books. 43. In our study of microscopic vision no consideration has been given to the consequences of imperfections in the mounting of the instrument, or in the objectives and eye- pieces. To have entered on these branches of the subject would have been to open new ground, and ground which has been rendered of less importance by the extraordinary per- fection both in the stand and in the objectives which may be secured by a careful selection from among the best that are available. It is truly astonishing with what accuracy the chromatic, and especially the even more important spherical aberrations have been successfully corrected in some speci- mens from among the best objectives on sale. Objectives are not unfrequently to be had which, when the draw-tube is adjusted with sufficient care, will bear an eyepiece mag- nifying 40 times without observable defect. However great their degree of perfection, it may he earried one step further by a skilful use of monochromatic light; whereby adjustments can be made by the observer with a completeness which with light of mixed wave-lengtlis is unattainable. This is indicated “by theory, and abundantly confirmed in practice. In whatever branch of microscopic work the obser may be occupied he will find it of advantage to train himself beth in the intelligent manipulation of his instrument and in the interpretation of results, by making a large body of experi- ments such as those of which a few selected examples have been described in the foregoing pages; being careful at every step to understand the reason for everything he does, and to Jind out the cause of every effect he perceives. To enable him to do this has been the object of the present memoir. LIT. Notices respecting New Books. e * Studies in Chemical Dynamics. By J. H. van ’a Horr, Revised & and enlarged by Dr. Ernst CoHEn, translated by THOMAS Ewan, W.Sc., Ph.D. Amsterdam : Peodenice Muller and Co.; London: Williams and N orgate. ne PICs translation of Professor van ’t Hoff’s work will come as a surprise to many English chemists who are not aware of the eae and importance of his researches on some fundamental problems of chemical dynamics. In Britain there are but few workers in the same field, and, as the translator tells us, scarcely any text-book in our language deals with the subject. The reason is, we believe, not far to seek; it 1s, however, a most lamentable one. Notices respecting New Books. 529 In this country it is at present one of the disadvantages of any science which has important industrial applications, that the treat- ment of it in the universities proceeds upon lines which are more appropriate to the technical schools. In the course of a few years the technical schools may afford a partial relief to the universities ; but we cannot help thinking that the necessity of adapting their lectures to the student of technology will always tend in some measure to draw the attention of the university teachers away from the development of the theory of their subject. Professor FitzGerald has, on more than one occasion, claimed for the university teacher increased opportunity for “useless” research, that is, for investigations of a theoretical character without any visible practical applications. This claim is worthy of most serious consideration at the present time. While the future of our higher technical schools is trembling in the balance, could not a division of labour be effected which would relieve the university of some of the teaching at present assigned to it? In the work at present before us Professor van ’t Hoff does not tell us anything new concerning the nature of molecules ; he pos- tulates the existence of reacting molecules just as in ordinary dynamics force and matter are accepted as facts. But, by assuming that the rate of decomposition of the substances involved in any reaction is proportional to the concentrations of these substances, he shows how a knowledge of the degree of complexity of the reaction (as measured by the number of different kinds of molecules taking part in it) can be obtained. The assumption is justified by experiment in a few cases; in many reactions, however, disturbing influences cause a departure from this simple law. The author was thereiore led to investigate the nature and magnitude of the more obvious forms of disturbance, such as the action of the medium in the case of liquids and of the walls of the containing vessel in gaseous reactions. The influence of temperature on chemical change is next discussed, and is naturally followed by an inquiry into the conditions of chemical equilibrium, with special reference to the relations between temperature and equilibrium, The volume concludes with a chapter on affinity. The subject is one which affords much scope for research, and we hope that the appearance of this translation will serve to direct attention to it. Both the reviser and the translator have per- formed their duties with care, while the printing of the volume is a good example of what Holland can produce—very different from some of the specimens of English and typography which occasionally reach us from that country.—J. L. H. Bees LILI. Intelligence and Miscellaneous Articles. ON EXPERIMENTS WITH RONTGEN RAYS. T'o the Editors of the Philosophical Magazine. GENTLEMEN, LLOW me to avail myself of your Magazine to make some re- marks about the Memoirs of Messrs. Oumoff and Samoiloftf (Phil. Mag. October), and of Messrs. J. J. Thomson and Ruther- ford (Piil. Mag. November). The experiments of Messrs. Oumoff and Samoiloff do not, in my opinion, resemble very closely those of my own experiments on electrical shadows to which they refer, but they have rather much likeness with those, concerning the production of Rontgen’s shadows with the electrical method, which I published in two Notes on the 1st of March (Rendiconti della R. Accad. der Lincei). They have therefore the same analogy with those afterwards published by Prof. Silvanus P. Thompson (Phil. Mag. August). No doubt that Messrs. Oumoff and Samoiloff had no knowledge of the previous publications above mentioned. As to the Memoir of Messrs. Thomson and Rutherford, I beg to observe that the fact proved at pages 395 and 396 (viz. that a thinner layer of air may offer a greater resistance than a thicker one) has already been described by myself in a Note on the 3rd of May (Rend. della R. Accad. det Lrncei). In that Note I recalled also some experiments I had formerly made, which proved that an analogous phenomenon may be produced by ultra- violet rays, and also without the action of any radiation at all. In the complete Memoir read before the R. Academy of Bologna on the 3lst May (“On the Propagation of Electricity through Gases traversed by Rontgen’s rays”), I have described with more particulars all these phenomena, and also others that I obtained with Rontgen’s rays. ? I am, Gentlemen, Yours faithfully, Atveusro Rieu, Professor of Experimental Physics, in the University. Bologna (Italy), November 1]th, 1896. —_—__—_ VOLUME MEASUREMENT OF AN AIR THERMOMETER BULB. BY WALTER G. CADY. In all constant volume air thermometry where high tempera- tures are involved, it is frequently necessary to determine the volume of the glass bulb used; such a bulb softens at a low red Intelligence and Miscellaneous Articles. 531 heat sufficiently to have its volume, considerably altered by any difference between the atmospheric pressure and that within the bulb. Thus it is important to know at the end of an experi- ment to what extent, if any, the volume of the bulb may have changed, as any such change must be taken into account in calculating the temperature. The usual method of volumetry by weighing with water is long and arduous, involving as it does the taking apart of the apparatus. Below is given a simple and sufficiently accurate method of calculating the volume at any time without disconnecting the bulb. In addition to the usual apparatus it is only necessary that the manometer tube in which the air is confined be graduated for 9 or 10 centim. from the top, so that the volume of air in the tube may be computed. In the figure, B is the bulb, PP a capillary connecting tube, T the graduated manometer tube, the gra- duated portion of which is about 1 centim. in diameter, connected in the customary manner by flexible rubber tubing with a reservoir. The scale in question is shown at T and is graduated in 0-1 centim. beginning with the fiducial mark. Assuming the whole apparatus to be at constant temperature during the operation, the required volume V is easily found as Woes Py seins 2 pep when v, and v, are volume excesses measured by means of the scale on T, correspending to pressures P, and P, respectively. It will be observed that V is not the volume of the bulb alone. Still, since the bulb is the only variable factor, the above formula indicates what change it nay undergo. The following is an example of a number of observations leading to the volume of a glass bulb used; in each case the first reading is combined with the third, the second with the fourth, in findmg the values of P,v,—P,v, and P,—P.,. Reduced atmospheric pressure =74:76 centim. i P(cm.) u(c.c.) Vice.) 15:17 0:16 239-0 74°63 1°80 241-1 73°79 4-477 To2l 6°20 d32 Intelligence and Miscellaneous Articles. The method is equally serviceable when a long capillary of irregular and appreciable volume joins the buib with the mano- meter, a condition sometimes unavoidable in practice; the volume of the capillary may then be separately found by temporarily plugging up its detached end.—American Journal of Science, (4) i. p. 341. ON THE INFLUENCE OF TEMPERATURE ON THE REFRACTION OF LIGHT BY METALS. BY ©. PULFRICH. About five years ago LI published a research in the Annalen*, in which the influence of temperature on the refraction and dispersion of several transparent solids (glasses &c.) was the subject of an extended experimental investigation. In this research, I was able to show by a series of arguments, that the (positive and negative) variations of the refractive indices observed in those bodies could be regarded as the result of the combined (or opposed) action of two causes, change of density and change of absorption. This explanation would not at that time apply to the metals For the encrmous increase in the refractive indices with tem- perature (about 0°0037 for 1° C.) found by Kundtt, could only be asclibed to a great change in the absorptive power of the metals. Observations have, however, so far revealed nothing of such a change in the absorption of metals. They show rather that the metals have only a small variation of absorption. It is in agree- ment with this that the dispersion of metals experiences almost no alteration with the temperature. The contradiction arising out of this is solved since Pfliiger , in a research which has lately appeared, has proved that the value given above for the variation in the refractive indices of the metals must be ascribed to a source of error neglected in the apparatus used by Kundt, and that, as shown by his own measure- ments made with Kundt’s apparatus and the same form of experiment, both the refractive index and also the dispersion of the metals undergo no demonstrable changes with temperature. The behaviour of the metals can therefore no longer be looked upon as in disaccord with the explanation I have given.— Wiede- mann’s Annalen, no. 11, 1896. * Wiedemann’s Annalen, vol. xly. p- 609 (1892). t+ Jbid. vol. xxxvi. p. 824. t Ibid. vol. lviii. p. 493. [ 333 | INDEX to VOL. XLII. ADMITTANCE loci, on, 300. - Air, on the thermodynamic pro- perties of, 1. Air-thermometer bulb, on the volume measurement of an, 530. Alternating currents, on the measure- ment of, 271. Aluminium, on the melting-point of, 37. Appleyard (R.) on dielectrics, 148. Are, on the resistance of the electric, 407. Aston (Miss E.) on an Alpine nickel- bearing serpentine with fulgurites, 116. Atomic theory, on the genesis of Dalton’s, 350. Ayrton (Prof. W. E.) on galvano- meters, 442. Ballore (F. de M. de) on seismic phenomena in the British Empire, 449, Barr (L.) on the melting-points of aluminium, silver, gold, copper, and platinum, 37. Bedell (F.) on admittance and im- pedance loci, 300. Books, new :—Goodwin’s Azimuth Tables for the Higher Declinations, 116; Glazebrook’s James Clerk Maxwell and Modern Physics, 205; Williamson’s Integral Cal- culus (7th ed.), 205; Whetham’s Solution and Electrolysis, 206; Benjamin’s The Intellectual Rise in Electricity, 368; Brown’s In- troductory Treatise on the Lunar Theory, 369; Behrens’s Anleitung zur mikrochemischen Analyse der wichtigsten organischen Verbind- ungen, 447 ;_ van’t Hoff’s Studies in Chemical Dynamics, 528. Phil. Mag. 8. 5. Vol. 42. No. 259. Dec. 1896. Bucherer (A. H.) on the action of magnetism on electromotive force, 288. Buckman (8. 8.) on the geology of Dundry Hill, 2865. Burstall (Ff. W.) on the use of bare wire for resistance-coils, 209. Cady (W.G.) on the volume mea- surement of an air-thermoineter bulb, 530. Cajori (F.), search for solar X-rays on Pike’s Peak, 451. Campbell (A.) on new instruments for the direct measurement of the frequency of alternating or pul- sating electric currents, 159 ; on the measurement of very large and a small alternating currents, ZANE Carbon megohms for high voltages, on, 450. Cooke (J. H.) on the stratigraphy and paleontology of the Globigerina- limestones of the Maltese islands, 122. Copper, on the melting-point of, 37. Crookes’ tube, on a rotational motion of the kathode disk in the, 123; on electric images in the field of a, 308. Crosfield (Miss M. C.) on the eeology of the neighbourhood of Carmar- then, 122. Current, on the magnetic field due to an elliptical, at a point in its plane within it, 107. Currents, on the measurement of the frequency of alternating or pulsat- ing, 159, 271. Dalton’s atomic theory, on the genesis of, 350. Davison (Dr. C.) on the diurnal periodicity of earthquakes, 463. yA = 534 Debus (Dr. H.) on the genesis of Dalton’s atomic theory, 350. Diathermancity, lecture experiment on, 208. Dielectrics, on the effect of tempera- ture on the resistance of, 148. Diffusion, on the separation of gases by, 493. | Duane (W.) on a damping action of the magnetic field on rotating in- sulators, 288. “Ducks and drakes,” ona theory of, iBEE Dundry Hill, on the geology of, 285. Dynamics, on the hypotheses of abstract, 240. — Earthquakes, on the diurnal periodi- city of, 463. Edison effect in glow-lamps, on the, 52. Elastic constants, on the number of, 240. Electric arc, on the resistance of the, 407. currents, on the measurement of the frequency of alternating or pulsating, 159, 271. discharge in a magnetic field, on the, 245. images in the field of a Hittorf’s (Crookes’) tube, on, 308. waves, on the refractive indices of some substances for very short, 207. Electricity, on the passage of, through gases exposed to Rontgen rays, 392. Electrolytes, on the degree of dis- sociation of, at 0°, 102. Electromagnetic medium, on the wave-surface and rotation of po- larization plane in an aeolotropic, 224. Electromotive force, on the action of magnetism on, 288. Electrons and electric charges, on the theory of moving, 201. Elements, on the analytical repre- sentation of the periodic system of the, 277. Feilden (Col. H. W.) on the glacial geology of Arctic Europe, 449. FitzGerald (Prof. G. F.) on the longitudinal component in light, 260. Fleming (Prof. J. A.) on the Edison effect in glow-lamps, 52. TN DAR X. Fourier’s series, on the convergency of, 125. Frequency of alternating currents, on new instruments for measuring the, 159. Frith (J.) on the resistance of the electric arc, 407. Galvanometers, on, 442. Gardiner (C. I.) on the Kildare in- lier, 372. Gaseous state, on the continuity of isothermal transformation from the liquid to the, 231. Gases, on the passage of electricity through, when exposed to Rontgen rays, 392; on the separation of, by ditfusion, 493. Geological Society, proceedings of the, 116, 206, 283, 371, 447. Glow-lamps, on the Edison effect in, 52. Gold, on the melting-point of, 37. Goldhammer (Dr. A.) on the analy- tical representation of the periodic system of the elements, 277. Granites, on the foliated, of Eastern Sutherland, 447. Greenly (E.) on the foliated granites of Kastern Sutherland, 447; on the geology of Hastern Anglesey, 448. Harmer (F. W.) on the Pliocene de- posits of Holland, 286. Hittorf’s tube, on electric images in the field of a, 308. Holland, on the Pliocene deposits of, 286. . Holman (Prof. S. W.) on the melt- ing-points of aluminium, silver, gold, copper, and platinum, 37. Horne (J.) on the foliated granites of Eastern Sutherland, 447. Hyperphosphorescence, on, 103. Iddings (Prof. J. P.) on extrusive and intrusive igneous 10cks, 450. Impedance loci, on, 300. Insulators, on a damping action of the magnetic field on rotating, 288. Isothermal transformation from the liquid to the gaseous state, on the continuity of, 231. Jamaica, on the geographical evolu- tion of, 288. Jones (Prof. J. V.) on the magnetic field due to an ellipt cal current at : point in its plane within it, i07. INDEX, Kathode disk in the Crookes’ tube, on a rotational motion of the, 123. Lake (P.) on the Lingula-flags and igneous rocks of the neighbour- hood of Dolgelly, 371. Lampa (Dr. A.) on the refractive indices of some substances for very short electrical waves, 207. Lamps, on the Edison effect in glow, 52. Larmor (J.) on the theory of moving electrons and electric charges, 201. Lawrence (R. R.) on the melting- points of aluminium, silver, gold, copper, and platinum, 37. Light, on the longitudinal compo- nent in, 260; on the influence of temperature on the refraction of, by metals, 532. Liquid state, on the continuity of isothermal transformation from the, to the gaseous state, 231. Liquids, on high tensions in moving, pel. Lussano (Dr. 8.), a lecture experi- ment on diathermancity, 208. McAulay (Prof. A.) on the wave- surface and rotation of polarization plane in an aeolotropic electro- magnetic medium, 224. MacGregor (Prof. J. G.) on the hypotheses of abstract dynamics and the question of the number of elastic constants, 240. Magnetic field due to an elliptical current at a point in its plane within it, on the, 107. , on the electric discharge in a, 245; on a damping action of the, on rotating insulators, 288; on the hypothesis of participation of matter in the motion of the, 314. Magnetism, on the action of, on electromotive force, 288; on the possibility of explaining the phe- nomena of, by the hypothesis of participation of matter in the motion of the magnetic field, 314. Mather (T.) on galvanometers, 442. Megohms, on carbon, for high volt- ages, 450, Melting-points of aluminium, silver, gold, copper, and platinum, on the, o7 —— Metals, on the melting-points of various, 37; on the influence of 530 temperature on the refraction of light by, 532. Microscopic vision, on, 167, 382, 423, 499. Miller (Dr. G. A.) on the operation groups of order 8p, p being any prime number, 195. Merdey (W.M.) on carbon megohms for high voltages, 450. Nipher (F. E.) on a rotational motion of the kathode disk in the Crookes’ tube, 123. Operation groups of order 8p, p being any prime number, on the, 195. Optical images, on the theory of, with special reference to the mi- eroscope, 167, 332. Osmotic pressure, on, 289. Oumoff (N.) on electric images in the field of a Hittorf’s (Crookes’) _ tube, 308. Pavlow (Dr. A. P.) on the classifica- tion of the strata between the Kimeridgian and the Aptian, 120, Periodic system of the elements, on the analytical representation of UNE, AN The Platinum, on the melting-point of, oT. Polarization plane, on the rotation of, in an aeolotropic electromag- netic medium, 224, Pollock (J. A.) on some experiments with Rontven’s radiation, 453. Poynting (Prof. J. H.) on osmotic pressure, 289, - ipreller (Dr: C. S. Du R2)jeonsthe Pliocene glaciation, pre-glacial valleys, and lake-basins of Sub- alpine Switzerland, 117. Preston (T.) on the continuity of isothermal transformation from the liquid to the gaseous state, 231. Pulfrich (C.) on the influence of temperature on the refraction of light by metals, 532. Radiometer motion, on, 373, 476. Rayleigh (Lord) on the theory of optical images, with special refer- ence to the microscope, 167; on the separation of gases by diffu- sion and similar processes, 493. Refractive indices of some sub- stances for very short electrical wayes, on the, 207. 36 Reid (C.) on the Eocene deposits of Dorset, 207. Resistance of dielectrics, on the change in the, with temperature, 158. Resistance-coils, on the use of bare wire for, 209. Reynolds (S. H.) on the Lingula- flags and igneous rocks of the neighbourhood of Dolgelly, 371; on the Kildare inlier, 372. Righi (Prof. A.) onexperiments with Rontgen rays, 530. Rodgers (C.) on the resistance of the electric arc, 407. Rontgen rays, some experiments with, 162, 453, 530; on the passage of electricity through gases ex- posed to, 392. Rosing (B.) on the possibility of explaining the phenomena of mag- netism by the hypothesis of parti- cipation of matter in the motion of the magnetic field, 314. Rutherford (E.) on the passage of electricity through gases exposed to Rontgen rays, 392. Salomons (Sir D.) on the electric discharge In a magnetic field, "245, Samoiloff (A.) on electric images in the field of a Hittorf’s (Crookes’) tube, +08. Silver, on the melting-point of, 37. Skeat (Miss E. G.) on the geology of the neighbourhood of Carmar- then, 122. Spencer (J. W.) on the geographical evolution of Jamaica, 283. Stoney (Dr. G. J.) on microscopic vision, 332, 423, 499. Strahan (A.) on submerged land- surfaces at Barry, 119; on a phos- phatic chalk with Ho/aster planus at Lewes, 119. INDE X. Sunlight, on the absence of X-rays from, 461. ; - Sutherland (W.) on high tensions in moving liquids, 111; on thermal transpiration and radiometer mo- tion, 373, 476. Switzerland, on the Pliocene eglacia- tion, pre-glacial valleys, and lake-- basins of Subalpine, 117. Talmage (Prof. J. E.) on certain linear marks in a sedimentary rock, 118. j Thermal transpiration, cn, 373. Thermodynamic properties of air, on o they le Thompson (B.) on the junction-beds of the Upper Lias and Inferior Oolite in Northamptonshire, 121. Thompson (Dr. 8. P.) on hyperphos- phorescence, 103 ; on some experi- ments with Rontgen’s rays, 162. Thomson (Prof. J. J.) on the passage of electricity through gases ex- posed to Rontgen rays, 392. Threlfall (Prof. R.) on some experi- ments with Rontgen’s radiation, 453. Transformers, on the use of air-core, for testing purposes, 271. Vision, on microscopic, 332, 423, 499. Wave-surface in an_ aeolotropic electromagnetic medium, on the, 224. Wildermann (Dr. M.) on the degree of dissociation of electrolytes at 0°, 102. Williams (W.) on the convergency of Fourier’s series, 125. Wilson (E.) on the geology of Dundry Hill, 285. Witkowski (Prof. A. W.) on the thermodynamic propertiesof air, 1. X-rays, on the absence of, from sun- light, 451. END OF THE FORTY-SECOND VOLUME. Printed hy Taytor and Francis, Red Lion Court, Fleet Street. 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