MA at ne ed? fleg dy : teh y as bipe ety aby co oF . pat eeer le Felanen tt Besant ar) ‘ t Fie kate Tithe prety ane ; ¥ ' Haleliratad ete +i 4 we sive ca’ . Ay itaten As ce: ar Son Ih Wel de® t “es rude WA a i belie ry Ot oceY vls \ ‘ “6 Tt ee yest + - Ae he ei} | " i ¥ : As by 7" s) : 4 J ty . } i ie wee d ab m ey 3 ial F, ¥ : nH ri re We ; eens! Haynes ali giste te Teh hed i Mae nie a ; , ‘ : tif Pepe ee an “ af Be o Meg ot) tans be vn oe Vo eben was Be gt sf vat Het ne My © temp ere: “1! ea ‘ inyestnes 4 yer Soni yet tle Aaah an ay etunkee 2 = a aS oe Stererpoulaeg- een wehite bao oly bay te J ME eh eg Fae heme bs ay ont! Ghee ‘4 re rl etqaes Hikoedy betes r* Fr} Hyde PPR Hare wee ate | ody REET Wt te Peart of Fe eran: ii Faia Be tee ie Siecle hiss 14 at ‘ slang bg! ap deh thee iene yeahs i ac bes pity ee *'} ily ere ag Vy | Pom id CX b; ' , : Pat Vee ate ie sah ithe ' Pine ! ik pt J eh anne Sipe ae pp ay ay ty a 4 T i Paarl) Ue od “5 ®VE hi 44) eeu eer ery Ute y ar ha " — at i 6d Ob Ge ie pT Y art ty j 77 Sop t4i gis o>. Aries ; zit ny it deta Bf. ae tir Pyhy', ‘ Ta helt ehhh, at a ae ine hie J “bat te eH ¥iN ee Se rempnt Teles Fart Af J THE LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY JOHN JOLY, M.A. D.Sc. F.R.S. F.G.S. ‘ AND WILLIAM FRANCIS, F.L.S. “Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.”’ Just. Lips. Polit. lib. i. cap. 1. Not. VOL. XVIII.—SIXTH SERIES. JULY—DECEMBER 1909. LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD. SMITH AND SON, GLASGOW :— HODGES, FIGGIS, AND CO., DUBLIN; YEUVE J. BOYVEAU, PARIS ;—AND ASHER AND CO., BERLIN. perspicua hehe investigatio inventionem.’ Hugo de S. Victore. “ Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, : Quid toties diros cogat flagrare cometas, aa Quid pariat nubes, veniant cur fulmina ceelo, Quo micet igne Iris, superos Jas conciat orbes Zam vario motu.” J. B. Pinelli e Y Co eee ——VVU_eSV t. This marks the moment at which the wave propagated with velocity 1 reaches the point «. If we were to make m=2, corresponding to the pro- pagation of flexural disturbances along a bar, the cosines in (4) would all vanish, but the lack of convergency indicated by (7) prohibits the conclusion that the disturbance under- goes a finite delay in reaching the point 2. From Fourier’s special solution * we may see that there is in fact no such delay. It would be of great interest to examine the influence on water waves due to a limitation of depth (h), but a complete solution for this case analogous to (1) seems hardly practicable. But without much difficulty we may obtain the first term in the series, viz., the term proportional to ¢”. In general from (2) Ot Rly = oat ao sinat coske dh, dt w Yo * *Theory of Sound,’ § 192. B 2 4 Lord Rayleigh on the Instantaneous Propagation which vanishes when ¢=0, and da? 1 a Toe) ae = —-—] o cosat coske dk, dt vat so that for t=0 d? i m3 — -i{ o cosha dk. i. 0 For waves on water of depth h == Gk tami Mi Wille s . ie passing when & is great (A small) into the simple deep water formula o? =gk, and when & is small (A great) into the shallow water formula o? = ghk*, indicating a uniform velocity of propagation *. When a < 7, we have fT i As aa RE _ (&*—e-*) sinda if ort pas SIM cw At (= ie ete 21a Care If we differentiate this with respect to c and then make a=7, to which there seems to be no objection on the understanding postulated, OO mt. p— me aoe =we { <—*— seoscade = — pa Cala ie TL men RS ie +e Adapting (10) to our present purpose, we have 2 2 mz/2h — 1x/2h ij o cosh dete wan A aes . “(is 0 2 h2 ( emt/2h en me/2h ? ? whence d?n/dt)? is given by (8). The first term in the expression for 7 is acccordingly __ gmt’ cosh (mr2/2h) V7 Bre Sane aaa ae ti We learn from (12) that, no more than in the case of deep water, is there any delay in the commencement of disturb- ance at a finite distance a from the source, and the extension is not without importance, seeing that in truth water cannot * It may be remarked that a modified formula, viz. ao” = gk (1—e-*h), agreeing with (9) in the extreme cases, would be more amenable to calculation. + De Morgan’s ‘ Differential Calculus,’ p. 669. of Disturbance in a Dispersive Medium. 5 be very deep in relation to all the wave-lengths concerned, since among these infinite wave-lengths are included. In the present case all the wave-velocities of simple trains are finite, and thus the sudden propagation to a distance is independent of an interpretation earlier suggested. If in (12) his small compared with x, we may write git? 7 = “Ue BR eh hen ae ele) showing that when 2 is relatively great the elevation in its earlier stages, though finite, is on a greatly diminished scale. As regards the general question, I do not think that the instantaneous propagation of disturbance should be considered paradoxical. It is to be remembered that in (9) the water is treated as incompressible, 7. ¢. that the velocity of pro- pagation of waves of expansion is regarded as infinite. A more complete treatment of the case of finite depth on the basis of (2) and (9) would be instructive, even if limited to selected values of the ratio «:h. So far we have con- sidered only the first stage. When h is small compared with z, an important part of the disturbance arrives under the law applicable to shallow water, viz. a= a/ (oh) » BL BPR i ie yak 14) Writing (2) in the form =e 1 . j. a 1 i 2° a 5 a =) cos (at—ka) dk + oa cos(gt+he) dk, (15) we see that the first integral acquires a specially enhanced value when wz and ¢ are so related that ot —kz is approximately zero for small values of k. The condition is of course Bhat GaR ds jy iene & sans! gh CAB) and the important part of the integral will be ah?\~2 1? loom n= zy. cos (4 zh?k*®)dk = Gn 08 &° rd). (F » (17) large when h is relatively small, but still finite. For larger values of ¢ the most important part of the first integral of (15) occurs in the neighbourhood of such values of k as make ot—kz stationary. This happens when & has a value ky such that eae esters Hath Sing he! chs a, CSS 6 Dr. J. W. Nicholson on the Relation of As Kelvin has shown*, the first integral of (15) takes approximately the form HS cos (aot —k,w«—1 7) TOR oot oldt * n while the second integral is relatively negligible. For example in the case of deep water waves, where o = (gh), (18) gives ko = gt?/Ax, oo = gt /2.2, so that Cot —kye—la = g?/4e—it; and finally a grt gt? = cos 7 Qar2aue Ay If we attempt to fill up the gaps in our solution by applying quadratures to (2), we have to face the difficulty that, as written, the integral is not convergent. Some analytical transformation is called for. One way out of the difficulty might be to calculate the difference between the solutions for finite and infinite depth, for it would appear that the non-convergent part of the integral, corresponding to infinitely small wave- lengths, must be the same for both. Terling Place, Witham, May 4, 1909. ae a ele Il. On the Relation of Airy’s Integral to the Bessel Functions. By J. W. Nicnorson, W.A., D.Se., Isaac Newton Student in the University of Cambridge fF. [* an earlier paper { the Author has indicated a relation between the integral tabulated by Airy in the course of an investigation of the intensity of light near a caustic, and the Bessel functions of high order. This relation is approxi- mate, and is valid only when the argument of the functions — is large. Its main utility depends upon the fact that Stokes has given extensive tables for the integral, which may be quickly transformed into tables of the Bessel functions of high order. But there exists also an exact mathematical connexion, which will now be developed. The integral may be expressed in terms of the Bessel functions of order 4, and certain associated integrals possess the same property. * Proc. Roy. Soe. vol. xii. p. 80 (1887). + Communicated by the Author. t Phil. Mag. Aug, 1908. Airy’s Integral to the Bessel Functions. 7 i] g When these functions of fractional order are tabulated for a small argument, the results may be readily applied to the rapid tabulation of all Bessel functions of very high order, if the order and argument do not differ widely. Airy’s integral may be defined by the formula fio) = (7 a .costt+pe), CY) and it will be convenient to define also two associated integrals’ in the forms | fic) =| dw.sin(w®+pw). . . . (2) 0 x and Ane ( ee ele ey csathe int datas’! Ga) 9 Stokes has studied the properties of 7;(p) in detail, and more particularly its asymptotic expansion when p is not small. He has also given a differential equation satisfied by the integral, but appears to have overlooked a transformation reducing it to a form which was already well known. = DR u =| dp, ree = hit 0 it may be shown at once that u''—} ow =1. where the accent denotes differentiation with respect to p. Accordingly, isolating the real and imaginary portions, SS eos Neel ae 7 fy 1 ) f57 ota = 8:: ah seh Daacl sik d Moreover, 2D fi! — App =| (w= Hp)danen+ ea 0 =_— 1 [ester] ai 3 Be in (ft+fs)—hel(fetfs) =903- - . - @) and f,+/; therefore satisfies the same differential equation as f,;. If f denote fj or At+/,, f f"— gef = 9. so that 8 Dr. J. W. Nicholson on the Relation of Writing foes p 3F, then on reduction Taking a new independent variable y defined by p* = y’, after further reduction, va ee nF =0. This is identical with the normal form of the equation for the Bessel function I,,(<), provided that Bhan 1 S605 407 a A solution of the original equation is therefore a #1,(s 45). oi In this formula, I, denotes the function me {1 a Pee 8 nf TSE l+ontn al 2'21(a+1)(n+ 2) where, if Ja‘x) be the usual Bessel function of order n, La) = 0d ae Oe a or If I_,(@) denote the corresponding function with the sign of n changed throughout, 7; must be expressible in the form A= py AL ( P, /$)+Bh( (Za /'G) b- Similarly, writing p=— i°8) dw .cos (w?—aw) 0 blige Aa( 24 / 5) +BI-a(z/S) A and B may be at once determined. When o=0, Airy’s Integral to the Bessel Functions. 9 expanding the Bessel functions, we obtain or by a property of the Gamma functions. Again, A.(3) 3 3-8 9-3 Jv) = a dwcos(w—pw) with p=0; P Jo d = & w sin wdw = sat (5) v0 2/3 i leading to Way Sg and finally, when o is positive, ( dw. cos (w® —aw) a0 iy) Vic Zo ta [20 fo =3V/ 3154/5) v/5) Moreover, when p is positive, dw cos (w* + pw) 0 “EV 5G /5)-E(S4/5)F- > 09 By the property of f,+/5 indicated above, there exists also a relation of the form na io 8) | dwe-“—o" + i) dw sin (w®—ow) 0 0 = Cog, (4/5) + Ded. ( (S/3) 10 Dr. J. W. Nicholson on the Relation of where | Die aye ai (sin w+ e~™)dw ag Gro) =F CS) 37 (3) ( w(cos w+ e—™)dw oF Jo aie 7 ee =—3 1D (g) 0G) te03)=—5 so that, when is positive, ie.0) and dw . {sin (w*— ow) + e~@-or} = /)-AG/D}s 08 with the associated equation, when p is positive, i} dw - {sin (w* + pw) + e—e+ert ee (n( r/ SG Dh (13) Writing 20 a 8 ot = 2K so that o=3A’, and combining (10) and (12), we obtain the curious result Jx(20*) = = ( dw{3* cos (w? —32w) —sin (w8 — 3d2w) — oe or finally 1 Ji(2d°) = inf dw} 2 cos (w?— 3d2w+4ar)— et (14) In a similar manner, se J_3(20*) = onl dw} 9 cos (w®— 3\2w—4 3) +e —8M OE TS) 1,(243) = = ml, dw{2 cos (w?+3\2w+4 7)—e—m+3wt (16) iL 2 dw 2 cos (uw? + 3X2w—} 7) 4 ot +t (9x3 raya (eS 1220") 27) 4 eS Airy’s Integral to the Bessel Functions. 11 The Evaluation of some Definite Integrals. Some further integrals which present themselves in con- nexion with the Bessel functions of order + will now be considered. The symbols J3, Ja, Ii, I will be used for : : 2a o the corresponding Bessel functions of argument ae 3 Writing s ia : 3—ow utiv = ( GT es ma ag a9 then if accents denote differentiations with respect to a, alt — gv! = — 1 p= Lyo(u 4 wv), so that ul! + tov = 0, 1 + bow =— 53 whence 1 (u+0)"+}o(ute)=—% (u=0)""—Ja(u-0) = 5. Treating the second equation first, we note that a particular integral of Lyf ae pone Sia oars is given by 4 ome) a dw .e~@ teow, 0 Adding the complementary function, it appears that u—v—z= Ao*l:+ Bo? l-1. Similarly, if p= ( ie te ee v0 Then utovty= Co? Ji + Do? J_.. Jt is found at once that 12 Dr. J. W. Nicholson on the Relation of whence Too { dw(cos w+ sin w? + e—) eo" O21 = =3 g(V8+1 {Jat} . . . (18) and a % \ dw(cos w? — sin w®)e~% — { dw .e—@ tow 0 0 TO? = =~) Vv: ASG ° e e 19 3 30¥8—-Dil+L3} (19) By addition and subtraction, we may express the integrals Vo { dw. (cos v3, e—%” — sinh ow . e~*”) 0 (20) @o > —aow — ws | dw(sin we~%" + cosh aw .e~“’) 0 a Again, another particular integral of ic.2) r= dw sin (w®—ow). Jo With the aid of this, we may express the two integrals, c.2) ( dw (e-e” —sin aw) cos w? 0 e ins oa { dw (e—™ cos cw) sin w 0 It may be shown that no other integrals of the linear-cubic type can be so expressed unless they are derived by the processes of addition and subtraction from those already given. Asymptotic expansions. In a previous paper,* the author has shown that when n—z is not very great in comparison with 23, which is itself * Phil. Mag, August 1908. Airy’s Integral to the Bessel Functions. 13 not small, 5,.0=1(°) A) Pier fc thhenti a sine) 7 ote) — Eey § f,(p) cos nw +fo(p) sin nr} | 1 6 1 wi = wf ae cy a aes @) eo” sin naw fe "Pe Pe. alpe |=) t (23) and if 2 be an integer, | 6\t¢ = ts Y¥,4) = -(2) fe ® fi (pe The functions f;, fo have the same significance as_ before, jf; being an Airy’s integral of argument p. Y, (z) is Hankel’s function detined by tm tT iT Ste FAlpe*) f. 2H iG nf cos nd » sin 27r n=integer. or, in series form, 2\n n—2!/2\2 Y, (2) = 2d, (2) {log $2-+°557}— (5) Jamis Se (3) + = a\. Sn 1 it Vs, . iar :) mG A oa S.)(5) +.. .} 3 (26) 1 | Sa =ltot...+-. e e e e (27) where An alternative expression for J_, (2) is | J_,(z)= “(2) \f (p) cos nm +f,(p) sin no} + (:)' ae wien (28) where the latter integral has already been denoted by /; (p). In all these results p stands for =(2) @=2) Metab ie Rustad wom Cece and is positive if n is greater than z. These expressions are asymptotic, but may be verified to three places of decimals when n=z=8. When n differs from z, it is necessary for p to be very small in comparison with z**, the error then introduced being 1 4 ’ ee. gn a 14 Dr. J. W. Nicholson on the Relation of of magnitude (n—z)/z. It follows that all the higher Bessel functions whose order and argument do not differ widely may be asymptotically expressed by means of similar functions of order i. Tn the first place, z may be supposed greater than n. Thus p is negative, and j= ta /5{a+5-1} where o= — p, and the functions J have argument 20 | ey eo? . 30 3 3 oe Moreover, (p) +fs(p) = Vo | J-y—-J) ‘ and therefore on reduction Tie@)= 54 /( penn) {Ty+9- See I= 3, /(22<") Ji cos (nw+47) +J3_1c0s (nw—477) } ae se) Similarly, or direct from the defiaition, in the case of n integral, pA Oe we =n) | rion i Another function of great importance in physical theory may be defined Ue Ki (2) = Mee | gle) ee 2 . (4 2 sin we Many other definitions have been proposed, but this, which is due to Macdonald*, is the most convenient for practical applications. When x is an integer, K,,(2) = Bo Z| dale z) =a (COS nid n(z) } —JenJ,(2)e""2 2 sin ae i ene ~ =—35(¥a(2) +1J,(2) 2 siglo 41 2): evaluating the undetermined form. K,,(z) is the type of function occurring in all harmonic * Proc, Lond. Math. Soc. vol. 32. j Airy’s Integral to the Bessel Functions. 15 expressions of disturbances in wave theory originating from a body and passing off into space. It may be at once shown that K@=s(le {Atha} . . > (8) where the functions f have the usual ar gument, if z and n do not differ widely in eee pn with 23. Therefore, if the Bessel functions of order } have the appropriate argument ¢, whether n be integral or Hob, Kt) =5(¢)e" tea / oy Paha deed | which may be written ee ae a eth ele ae } Sse mre one) But by the selected definition, for any argument and thus when n eee are large, and m—z not very large in comparison with z 2 1 9) ey -1(8 = n) Ky (5.n— Ey eee oe :). PE SS) if z be greater than 2. The modification necessary in this result, as in (31-33), when z is less than n, may be obtained at once. The accuracy of all the formule is as stated above. The following tables have been calculated from the results given by Airy, with the aid of the formula 7, : ey (p) . Airy employs the integral in the form Mo Ton) = / dw cos 5 (w*—muw) eam (39) 2 which is identical with I(m) = (= ney | —m(= =) (40) AS(2)= (2) 1] en. (2 ag a so that 16 Lelation of Airy’s Integral to the Bessel Functions. TaBLE I.—n greater than z. — } | m—z ae ex 2° L125. 23J (Zz). & Jn(2). | | 2 88666 22 04007 | “4 32849 2-4 | 02987 ‘6 ‘27459 26 02208 | 8 ‘24786 2:8 01609 1-0 | 18344 3-0 | 01163 1-2 14684 | 3-2 00833 14 ‘11601 . 3-4 00591 16 09050 ! 36 90416 1:8 “06977 | 3:8 / 100290 | 2:0 ‘05317 : 4:0 00200 TaBLE I].—z oe than 2. | | Bo iy | : = x 7 | 123; 2 In(2). a 23. 1 2 Jn(2). aa | 0 44549 | 2:2 23779 2 50789 2-4 | +07882 “4 56506 2-6 08616 6 61474 2:8 | +24364 8 65228 30 -+37869 1-0 67264 3-9 | -47653 1-2 67093 3-4 ‘52457 14 64282 | 3°6 | *51447 16 | 58528 38 | 44419 18 49714 | 4-0 | 190d 20 | 37982 | _ anager Tables for shorter intervals may be constructed by inter- polation. ‘The first table exhibits the rapid convergence of J,(z) towards zero when » increases beyond 2, even when z is very great. This convergence soon becomes exponential. A formula suitable for this case has been given by the author*. The limitations to be applied to these tables are well defined. Whenzand mare exactly equal, the error in the value of J,(2) is 0007 when z=8, and ‘0006 when z=20. It is, in fact, fairly constant so far as tables have hitherto been constructedt, It may be shown to affect only the fifth significant figure when n= 100, from theoretical considerations. Other portions of the tables have a more restricted application. * Brit. Assoc. Report, Dublin, 1908. tf Ton=24. Vide Gray & Matthews’ Treatise. a a ae Theories of Matter and Mass. ay They involve an error of magnitude comparable with (n—z)/z at most. Thus if z=20, n=18, even the first figure may be wrong. Their utility is confined to the very high values. For example, they will yield Jioos (1000). to two significant figures, and probably more, as \zn—z)/z is actually larger than the involved error. Trinity College, Cambridge. Ill. Theories of Matter and Mass. By LoutsT. More, PA.D., Professor of Physics, University of Cincinnati *. T is perhaps reasonable to associate the name of Newton with speculations regarding the nature of matter and the iundamental principles of mechanics, and those who attempt to dispense with the axiom that mass or inertia is an inherent and unexplainable attribute of matter, are apt to call their systems non-Newtonian mechanics. In fact, the problem is far older than Newton, and goes back as a per- sistent dualism to at least the time of the Greek philosophers, who recognized that cosmic theories could be built up on the axiom of the objective reality of matter, or on the theory that the external world is but a subjective idea mirrored by our sensations. Since Newton’s formulation of the laws of gravitation and motion scientific thought has, for the most part, squarely placed itself on the side of the objective reality of matter, and associated with it an inalienable property, inertia or mass. To be sure, Newton himself, in letters and by queries in his treatises, ventures certain metaphysical guesses as to the causes of inertia and of the force of gravi- tation. But when he discusses mechanies scientifically he puts such speculations resolutely aside with the remark, hypotheses non jingo, undoubtedly feeling that science begins with the simple assumption of some such axioms, and has no concern with their causes. With the discovery of the law of conservation of energy, another apparently invariable property of matter has become available, on which to base theory. As the scientist accepts without hesitation the reality and continuity of space and time, it is natural that a controversy should arise as to which of the two properties of matter, mass or energy, may serve best to make concrete to us the abstractions space and timef. * Communicated by the Author. + The only attempt I am acquainted with, to express time as a function of space, has been made by Bergson in his “ Essai sur les données immédiates de la conscience.” Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. C 18 Prof. L. T. More on Theories As both attributes, mass and energy, are always associated with matter, and as matter apparently is revealed to us only through them, it is possible to take either one as the funda- mental attribute, the “ Ding an sich” of Kant. Thus the postulate of inertia is the basis of an atomic or corpuscular theory, while energy serves in the same capacity for the science of energetics. But the attempt to explain matter and energy has led to the substitution of vortex rings, strains or electric charges in an ether for the hard atom, and has ~ refined the concept of energy to a mathematical symbol. These methods sooner or later lead to purely metaphysical discussions, expressed by mathematical equations in place of scholastic logic, in which a hypothetical universe is sub- stituted for sensible matter. When we assert that matter is an attribute of the zther or a complex of centres of energy, we explain nothing as we merely endow a more tenuous hypothetical fluid with all the properties of matter under discussion. or example, to explain the genesis and growth of a crystal we transfer to each constituent molecule all the properties of the complete crystal ; an evasion rather than a solution of the problem. For a century or more science has tried to explain all phenomena as variations of mechanical force, acting accord- ing to Newton’s law, between atoms and ethers. The attempt has failed, mainly for two reasons, the simple atom proved to be inadequate, and no ether could be imagined which did not. contain irreconcilable contradictions when phenomena were to be codrdinated. When the step was once taken of considering the atom as a complex system of subatoms, the passage to the converse problem, of explaining mass as a variable function of some more fundamental attribute of matter, has been rapid. : By In recent theoretical articles matter is no longer an aggre- gation of concrete atoms or subatoms, places of more or less differentiation in an ether possessing inertia, but a manifes- tation of some more fundamental entity, such as a negative charge of electricity. The argument of these writers is essentially as follows: since it may be proved that a moving body of ponderable matter possesses more momentum when it is electrically charged than when uncharged, therefore we may account for not only the inertia and momentum of matter, but also for matter itself, by endowing something with an adequate electrical charge.and velocity. This con- clusion is, at least with our present knowledge, a non-sequitur; in' the first place we have no experience of the something; and second, the requisite velocity may be an unattainable of Matter and Mass. 19 one. The discussion of these theories is perhaps more readily accomplished by a review of a paper by Dr. G. N. Lewis*. This paper is an ingenious effort to reconcile modern ideas and Newtonian mechanics. In it the writer attempts two distinct things: first, to establish a quasi-corpuscular theory of light, and second, to explain inertia, wholly or in part, as a function of velocity. We may pass over the difficulties ail corpuscular theories of light plunge us into when such phenomena as interference, polarization, diffraction, &c. are discussed, as they are not touched upon. The fallacy of his hypothesis lies in his cardinal assumption “‘ That a beam of radiation possesses not only momentum and energy, but also mass, travelling with the velocity of light, and that a body absorbing radiation is acquiring this mass as it also acquires the momentum and energy of the radiation. Therefore a body which absorbs radiant energy increases in mass’’}. In the first place, the assumption made, that because energy is involved in radiation, and because a black body absorbing this energy is moved mechanically, therefore radiation is due to a mass in motion, is not a necessary one. Maxwell proved that such a mechanical action must occur if radiation were due to electromagnetic waves, and Nichols and Hull measured the effect as a property of such waves. Secondly, the assumption is an arbitrary one, contrary to our experience. As an illustration, if a ball moving toward a man were stopped by his hand he would evidently absorb this energy, and yet no one would claim that the man had increased in mass. Still less would the claim be made if the ball were the mass of a beam of radiation which, according to Dr. Lewis, would have no “mass if it were at rest, or indeed if it were moving with a velocity even by the smallest fraction less than that of light.” The fallacy in the assumption is even more clearly seen in the mathematical deductions, from which I quote: “The momentum of any part of a beam of radiation having the mass m will be given by the equation Bia fie teres kb hla esha ees GOD The increase dM in the momentum of the body absorbing the radiation will, therefore, equal the increase dm in its * Lewis, “On a Revision of the Fundamental Laws of Matter and Energy,’ Phil. Mag. vol. xvi. p. 705 (1908). + L. c. p. 707. C2 20 Prof. L. T. More on Theories mass, multiplied by the velocity of light, aM=Vdm. |... .’ 2 Substituting energy, EH, for momentum we obtain “dma wo. aa By the pure mathematician any quantity of an equation may be considered either as a constant or as a variable, but such is not the case when the equation is an expression of a physical law. Quantities are then fixed as constants or as variables, according as our experience requires them to be. If in equation (5) the velocity of light is said to be a constant and the “mass of radiation” a variable, some necessity, or at least some plausibility, must be given to what is otherwise an arbitrary assumption contrary to our ideas and experience. One might equally well transform the equation for potential energy P=m(gh) into the differential dP=(gh)dm, and declare that a change in the potential energy of a body is due to a variation in the mass of a body maintained in a constant position. From this axiom we may deduce the law that mass is a function of the position of a body, just as readily as Dr. Lewis proves it a function of momentum. The only difficulty is that experience teaches differently. Measurements of the velocity of ligbt all show that it decreases when passing into absorbing media, and Nichols and Hull detected a change in position or motion of a body which absorbs light and not a change in its mass. Nor is it made clear how the quantity of m, which in (5) refers to a beam of radiation, later is the mass of the absorbing body. — Again, other questions arise in connexion with this theory. If a body, emitting radiant energy, loses 1:111x 10-# gramme for every erg expended, a simple calculation, from the estimate that the sun radiates 6 x 10*° calories (pounds per degree centigrade) in a year, gives a mass of 1:2 x10” grammes a year for its loss in mass. Such a quantity should have an influence on cosmic problems. Another difficulty occurs of a more serious nature. The “‘ something possessing mass”? whose momentum is a beam of radiation has no mass while it is a part of the radiating body before it begins its journey of radiation. In the free ether of Matter and Mass. 28 it attains the velocity of light and acquires the property, mass. Now the mass of a body, according to the summary of the writer at the end of the paper, becomes infinite if it has the velocity of light.. To escape this dilemma either light must move with a velocity less than the velocity of light, or else these light-particles must be a new creation of matter, having nothing in common with our ideas of pon- derable matter. Nor do their unusual properties end here. If the energy of the radiation is absorbed the particles again cease to be, vanish, and pass into the unknowable. ‘They are ghosts which appear and disappear at the will of the necromancer. Surely we should pause before adopting so fantastic a view. The second part of the article is an attempt to construct a new system of mechanics. In this system we may retain all the axioms and propositions of mechanics previously held excepting the one which states that the mass of a body is independent of its velocity. For this we should substitute that mass is proportional to content of energy, and therefore changes with velocity. This is not a new idea, or the school of energetics has laboured in vain. In fact any treatise on hydrodynamics arrives at the same conclusion, except that we usually call it effective or apparent mass. But the deduc- tions from this axiom will repay study as they are typical of a new movement in physics. On page 711 we find the equation W437 10 de elimi Si rat aad GF) where EH’ is the kinetic energy, M the momentum, and »v the velocity of a moving body. And as M=mz, dM =mdv+vdm. Since the mass as well as the velocity is to be reckoned a variable, we have by substitution QM GIO OO. se ove” a (LA) Introducing the relation of mass to energy given in equation (7) we may write dH’ =V*dm and combining this equation with (14) gives V7dm=mvdv + v*dm. Here again we have the unexplained duality of the mass m, 9003 | 22 Prof. L. T. More on Theories which in (14) refers to the body, and in the following equation to a beam of radiation. It is also perplexing to understand what (7) has to do with this problem. In a simple discussion of the momentum of a moving body such an attribute as light or radiation is not necessarily involved, nor even the existence of an absorbing medium. Granting this objection is not valid, we arrive by simple transformations to the following equation i (67)? where m, is the mass of the body at rest, m its mass when in motion, and £ the ratio v/V. We may further obtain the expression for the kinetic energy acquired by a moving body in the forms H=mVol aie ee ae - ley N= mV7{5@? +4644 i. J: > For small values of v m/ nig = or == tnw?, and when v= V BH! =mv*. The writer states that this difference for the energy “instead of demolishing our theory actually furnishes a remarkably satisfactory aryument in its favour.” It really does neither, tor the ordinary hydrodynamic equation for energy, given later, expresses precisely the same results without a need for the assumption that mass varies with velocity. If we strip the problem of perplexing details and then compare it with analogous examples taken from other branches of physics, the earlier ideas of inertia should be easier to compare with those of the present time. The problem may be put in the following form:—in all cases where a body is giving or receiving energy its mass is a variable. This inter- change of energy may take place between two bodies or between a body and a fluid in which it is immersed. For the latter the fluid must be of such a nature as to be able to absorb and emit energy, and so be endowed with what Newton called inertia. It is evident that if the fluid cannot absorb energy there can be no loss or gain of energy to the body, and consequently no change in its mass. Does this interchange of energy require a real change in the mass of a body, or does it produce a variation in other of Matter and Mass. 23 attributes of matter such as velocity or change of position ? The fallacy involved is really a question of definition. According to Newton™ the inertia of a body is an inherent and inalienable property of it, independent of the influence of any other body or ether, and forms the connecting link between ourselves and the external world. The inertia referred to by Lewis and other modern writers is a relative property of matter, depending entirely upon the presence of other matter, and has nothing to with the body perse. They generally take some form of energy as the fundamental attribute. But since the absolute nature of matter is entirely unknown to us, it seems reasonable to say that we have no criterion by which we can decide between the two, mass and energy. Undoubtedly those who have maintained the variability of ‘inertia of ponderable matter have been obliged to create some primitive fluid or ether and supply it with inertia in the Newtonian sense. Ponderable matter then becomes merely a place of discontinuity or variation in this primitive fluid, which is to be considered the only actual matter. Now to transfer the essential properties of a sensible body to another, which we have no faculty of detecting directly, is not an explanation, but an evasion of the problem. In any mechanistic theory of phenomena, based on the mutual attractions between atoms, the relations between mechanics and the other branches of physics are expressed in three ways, by hydrodynamic, thermodynamic, or electro- dynamic equations. Because of the contradictions which have occurred when all phenomena are explained by forces of attraction, the converse problem has been attempted ‘of explaining the nature of atoms and their mutual forces, and we have as a result Boscovich’s centres of force, vortices, charges of negative electricity, ztherial strains, the “some- thing in a beam of radiation,” and others. However diverse in appearance, these all have one property in common, they deal with a transfer of energy, and they either tacitly or openly postulate the existence of invariable inertia in some- thing tangible or intangible. An examination of any one of these will answer the purpose, and I have chosen one the least complicated by metaphysical abstractions. If two spheres of radii a and 6 are immersed in a fluid, * Princ. Math. Def. III. Hec (materiz vis) semper proportionalis est suo corpore, neque differt quicquam ab inertia masse, nisl in modo concipiendi. Per inertiam materi fit, ut corpus omne de statu suo vel quiescendi vel movendi difficulter deterbetur. 24 Prof. L. T. More on Theories and are moving toward each other along their-line of centres with velocities u and wu’, the momentum of each sphere is no longer its mass times velocity, but the action takes place as if the mass had been increased. The formula for the kinetic energy™ is OH! = Lu? + 2Muu! + Nw?, where dab? dash® L=2/3 (1+ : 3a i of? ‘i efr(e—fo)*fs° f : M=2 “(1+ 3 ] jae +...) ie jr (6a i fi fs ke = fe | e~ja ae 3a2h? 3a*b§ N=2 ( ee : ) /3mpb*{ 1+ ra a5 37 B(e— fil) fy? +... J, in which the /’s are functions of a, b, and ¢ only. ‘ If the spheres are small compared with the distance between them De: 3 L= 2/3mpa'( 1 + = ) arb? M=27p er 3 373 N=2/37p (1 + ) approximately. And, lastly, if there is only one spkere moving in an infinite fluid . L==2/3arpe®=1/2m, 2 is 6 M=N=0, The quantities L, M, and N are the apparent or virtual increases in the masses of the spheres, and in the simple case of one sphere moving in the fluid reduce to one-half the mass of the sphere. In other words, the introduction of a second moving sphere in an infinite liquid acts as a constraint, in- creasing the kinetic energy for a given velocity, and so virtually increases the inertia of the system. Equation (A) should be a satisfactory answer to Dr. Lewis’s surprise that (17) shows an increase of the energy, HE’, of a moving body. If we compare these equations with (17) developed by Dr. Lewis we cannot but be struck with their similarity. * Lamb, ‘ Hydrodynamics,’ p. 189. of Matter and Mass. 29 In each the kinetic energy of the body in motion is increased, in the one case by hydrodynamic and in the other by thermo- dynamic relations. And yet no one claims that to speak of this increase in mass is anything more than a figurative way of saying that the fluid pressure acts as if it had increased the true inertia of the moving body. Why then should we claim otherwise for a moving body 1 radiating light? The same can be said of the apparent increase of inertia of an electrified body moving in an electromagnetic field. While no one has used the hydrodynamic equations in the above form to explain the cause of inertia, yet it is essentially the foundation of Lord Kelvin’s theory of vortices moving in a primitive fluid. It was a promising and ingenious attempt to explain the nature of matter, and it readily and sufficiently accounted for such fundamental attributes as impenetrability, diversity, conservatism, &c., but it failed because the effective inertia of the vortex ring was not invariable but dependent upon the position and influence of its neighbours. Maxwell* certainly felt this to Hesthes titel depscoanaie theory of the vortex atom as in other similar theories, and has expressed his opinion with such perspicuity that I shall quote from his article at some length :— “ One of the first, if not the very first desideratum in a complete theory of matter is to explain—first mass, and second gravitation. To explain mass may seem an absurd achievement. We generally suppose that it is of the essence of matter to be the receptacle of momentum and energy, and even Thomson, in his definition of his primitive fluid, attri- butes to it the possession of mass. But according to Thomson, though the primitive fluid is the only true matter, yet that which we call matter is not the primitive fluid itself, but a mode of motion of that primitive fluid. It is the mode of motion which constitutes the vortex rings, and which furnishes us with examples of that permanence and continuity of existence which we are accustomed to attribute to matter itself. The primitive fluid, the only true matter, entirely eludes our perceptions when it is not endued with the mode of motion which converts certain portions of it into vortex rings, and thus renders it molecular. “In Thomson’s theory, therefore, the mass of bodies re- quires explanation. We have to explain the inertia of what is only a mode of motion, and inertia is a property of matter, not of modes of motion. It is true that a vortex ring at any given instant has a definite momentum anda definite energy, * Maxwell, ‘The Atom,’ Encyc. Brit. 26 Mr. R. Tabor Lattey on the but to show that bodies built up of vortex rings would have such momentum and energy as we know them to have is, in the present state of the theory, a very difficult task.” Our aspect toward nature and natural law is constantly shifting, but the general principles underlying science remain much the same. No amount of mathematical manipulation will enable us to discover the fundamental property which makes the external world evident to us. Whatever it may be it must remain for us a mere postulate, call it what we will, inertia, mass, or energy. If we abstract this attribute from ponderable matter we assign it to an atom; if we sub- divide the atom it is associated with a subatom; if this is but a discontinuity in a primitive fluid the same process of thought occurs. Not only is this pursuit of no real advantage to us, it is a hindrance, as it apparently confuses the purposes of science which should attempt to express the phenomena dis- covered by experience in general mathematical laws. The discussion of the postulates of science is extra-scientific and disturbs the boundaries between physics and metaphysics. The deductive methods of the pure mathematician are un- suited to experimental science, and however little we may value the discoveries of Bacon, yet he did announce the scientific method which made possible modern science. We should avoid many a pitfall if we kept in mind those things which have obstructed natural philosophy, the wrong use of logic, of theology, and of mathematics,—‘* Mathematica, que philosophiam naturalem terminare, non generare aut pro- creare debet.” If I have seemed to put undue emphasis on this latest of the theories of matter and energy it is not because of its uniqueness, but because Dr. Lewis has presented his ideas without the complexity which eens obscures in such attempts the real issue. University of Cincinnati, January 1909. IV. The Ionization of Electrolytic Oxygen. By Roxpert Tasor Lartey *. i 1897 Townsend + showed that the gases obtained by electrolysis of concentrated aqueous: solutions of potassium hydroxide and of sulphuric acid contain charged paficles which serve as nuclei for the formation tte mist, * Communicated bv the Author. ink ae Camb. Phil. Soc. ix. 1897, pt. Vag Phil. Mae [5] xliv. 1898, P — ee oe Tonization of Electrolytic Oxygen. 27 ' By measuring the total charge qg in a given volume of gas and the number n of drops in the cloud he obtained the value 3x 10-1 for g/n. If all the drops had charges of like sign g/n would represent the charge on each ; experiments on the conductivity of the charged oxygen from sulphuric. acid showed that it contained a mixture of positively and nega- tively charged particles in the ratio of about 4:1, so that the charge on each is greater than g/n in the proportion of 5:3. When this fact is taken into account the value of e would be about 5x 10-1 E.S. units. At Prof. Townsend’s suggestion I have examined the oxygen obtained by electrolysis of a solution of potassium hydroxide of sp. gr. about 1°2, as it appeared probable that an accurate value might be obtained by using the method devised by Prof. H A. Wilson for measuring the charge on each particle in the case of mists produced by adiabatic expansion *. An electrolytic fog of this nature has two advantages over an expansion fog which ensure much greater accuracy of measurement. The radii of the particles are extremely small, and hence their rate of fall is slow (from 1 to 2 mm. ina minute) and easily observed ; also the cloud is stable, while in a fog produced by expansion the velocity is great and it is certain that a more or less rapid evaporation must be taking place, so that it is impossible to know the size of the drop which corresponds to the velocity that is observed. In my experiments observations on the rate of fall were always made over several successive millimetres, and in no case was any evidence of a change in the size of the drops observable during the course of an experiment. A current of about 10 amperes was used for electrolysis and electrodes of platinum foil about 2°5 x 3 ems. were found to give the best results. The oxygen from the anode was passed into an apparatus shown in vertical section in the figure. The gas passed up the brass tube a into the observation vessel 6. This had plane glass slides ; its upper and lower boundaries were square brass plates which could be connected to the terminals of a battery of secondary cells. The upper plate had eight small holes near its edge by which gas might escape, and it was suspended from a slightly larger brass plate by four brass rods. This part of the apparatus was surrounded on five sides by a water jacket c having plane glass slides. In order to prevent electrolysis in this water it was insulated from the base plate by a layer of shellac. On part of one wall of the chamber 6 a scale of millimetres * Phil. Mag. [6] vol. v. 1903, p. 429. 28 Mr. R. Tabor Lattey on the was engraved ; a beam of light from a Nernst lamp passed through this and thence obliquely across the chamber. The upper boundary of the fog could then be distinguished through a telescope by means of the light scattered by the fog particles. as a N asia AT) The shaded portions are of brass, the vertical walls of glass. Water is represented by broken horizontal lines. In some of the earlier experiments a simpler apparatus without a water-jacket was used and difficulties, due to heat convection currents, were often experienced; these results are given in the table on page 29 under the heading “ first set”; not only was the observation chamber different in these, but the electrolytic apparatus was also different, and hence the rate of fall of the fog under the influence of gravity was different from that obtained in the “second set” with the modified apparatus. By this method the charge on a particle is deduced from the change of velocity produced by a known field. Since the charges on the particles vary in sign, the effect of a field is to accelerate some and to retard others in their fall ; this made the outline of the fog somewhat indistinct, but it was found that the boundary of the rapidly falling portion could Ionization of Electrolytic Oxygen. 29 be always followed with fair accuracy and that occasional observations on the more slowly moving particles could he made. If V' is the velocity with which a particle of radius a falls in a medium whose viscosity is 7, then Stokes’ theorem. gives the equation 4a ag=6rnaV'. If an electric field whose gradient is X units per cm. is acting, and if the particle has a charge of E units, then the velocity V with which it falls is given by tr7oeig+HX=6arnav. Combining these equations we get _ 87 ofan E= Aan oe (V’—V). Taking the viscosity of oxygen at about 15° C. as 2°12 x 10~+, this reduces to H=3°94 x10-®V® (V’/—V)+X. _In the following table X is given in H.S. units per em., the sign refers to the potential of the upper plate. V is in cms. per second :— | Ge | V x 10%. Ex 10°, | First Set. | 0-0 2°725 —0:067 3°087 —11°17 +0:067 2°439 — 882 —0°133 2°500 +348 +0133 2-150 — 886 — 0-200 3°030 —313 +0°200 1852 — 899 —0°267 3°788 — 821 Second set. 0:00 1°764 —0°0545 2°415 —19°76 — 00606 2-110 — 9°45 +0°0667 1:961 +4°88 — 00909 2°325 — 9:28 +0°1182 2°174 +574 —01182 2°096 —1865 —0°1485 2525 — 848 +0°1636 3°774 +20°34 30 Mr. R. Tabor Lattey on the In calculating the means the individual values have been weighted according to three factors: (i.) The error caused by 5 secs. in the time to fall 1 cm., (ii.) The error of 1 volt per cm. in the value of X, and (iu.) The number of observations on which V depends. It will be observed that the values of E group themselves about three values, indicating that the positively and nega- tively charged groups of particles are each subdivided into sets of particles carrying charges of differing magnitude. Which set of particles would be observed in any given experiment was apparently a matter of chance. Alterations in the method of illumination apparently caused one set to show up rather than another ; but unfortunately the rela- tionship between the conditions of illumination and the portion of the fog observed could not be elucidated. That the different sets of particles differed only in charge and not in magnitude was shown by the constancy of the rate of fall under the influence of gravity alone. In the case of the fog nuclei produced by Roéntgen rays, Prof. H. A. Wilson was able to observe three sets of particles which fell at different rates under the influence of an electric field, and he concluded that the charges on the more highly electrified particles were multiples of those on the particles on which most of his observations were made. If we assume that this is also the case for the particles in an electrolytic fog, we obtain as the mean weighted submultiple 4°66 x 10-1, and the final mean values of EH x 10?° will be 4°66 O30 and) 13-0. Rutherford and Geiger * obtained 9°3 x 10-!° for the value of the charge on an e-particle, and as they consider that an a-particle probably has two atomic charges, they give 4°65 x 107" as the value of unit atomic chargein H.S. units. The values obtained by observation of the rate of fall of an expansion fog in gases ionized by various methods vary some- what, but are all of the same order of magnitude. 65 x10-%° J.J.Thomson. Phil. Mag.[5] xlvi. 1898, p.528; Go uk 107" 3 ye xivani. LSoae 3°4 x1077° :; » 6]. 1903, pee. poliex dO 2° H.wAy Wilson, i [6] v. 1903, p. 429. 4:06x10-'° Milikan & Phys. Rev. 1908, p. 197. Begeman. * Proc. Roy, Soc, dexxt, A, Lave) p60. Ionization of Electrolytic Oxygen. 31 Though these results are probably not so accurate as those obtainable in the case of an electrolytic fog or by Rutherford’s method, yet they are of greater interest, since they give the charges on ions for which Ne can be found directly where N is the number of molecules in a cubic centimetre of gas. The most recent value of Ne is 1°23 x 10" at 15° C.* Faraday’s experiments show that 1 c.c. of hydrogen at 15° C. is liberated from acidulated water by 2°-44x 10” E.S. units of electric eurrent. Now 1 cc. will contain 2N atoms, and hence we may conclude that Ne for hydrogen ions in solutions is 1/2 x 2°44x ae 12 *22 x 101, a figure which is in substantial agreement with Ne for gaseous ions. Hence it has been concluded that e has the same value for gaseous as for electrolytic ious. If we assume that e=4°'66 x 10-", we obtain for N the value 2°62 x 10°, which may be compared with that derived from other considerations : 2°61 x10! Planck (Theory of Heat Radiation) f. 20010" Perrin {. The last value is of especial interest as it was obtained by the most direct method. The numerical distribution of particles at different depths in a colloidal solution was obtained by direct counting under a microscope ; the osmotic pressures calculated from these numbers gave the actual numbers of molecules corresponding to a known osmotic pressure. Since the experiments here described did not yield results of the accuracy expected, owing to the various causes noted above and since it is sufficiently clear that the charge is the same as that on ions produced by other methods, they were not further pursued. It may possibly be found that the most accurate method of finding e is from the quantities Ne=1-23 x 10” and N as found by Perrin’s method. The author wishes to acknowledge his indebtedness to Prof. J. 8. Townsend for his many suggestions and his sympathetic help in the course of these experiments. University Museum, Oxford. February, 1909. * J. S. Townsend, Proc. Roy. Soc. vols. Ixxx. & Ixxxi. (1908); C. E. Haseltfoot, Proc. Roy. Soc. vol. Ixxxii. (1909). + Wied. Ann. [4] iv. 1901, p. 504. ¢ Compt. Rend. cxlvii. 1908, p- 594, [ 32 ] V. Note on the Theory of the Greenhouse. By C. G. ABBot, Director, Astrophysical Observatory, Smithsonian Institution *. : a paper of the above title | Professor R. W. Wood Il states that he has compared two “ hot-boxes” one having a glass cover, the other a cover of rock salt, but otherwise similar. A glass plate was interposed in the path of the entering sun rays. He observed a maximum temperature of about 55° C. within each box when exposed to the sun. He concludes that the function of the cover is mainly to prevent the loss of heat by convection, rather than the escape of long wave rays, and asks: “Is it therefore necessary to pay much attention to trapped radiation in deducing the temperature of a planet as affected by its atmosphere ? ” It may interest some to know that much higher temperatures can be reached within a “ hot-box” than that observed by Professor Wood, if precautions are taken to diminish the loss of heat by convection from the warmed outer surface of the cover. On November 4, 1897, the thermometer recorded 118° C. within a circular wooden box 50 centimetres in diameter, 10 centimetres deep, insulated in feathers, covered with three superposed and separated sheets of plate glass and exposed normally to the sun rays in the yard of the Astro- physical Observatory at Washington. The temperature outside was 16° C. Agreeing with Professor Wood that the main function of the cover of a “ hot-box”’ or “ hot-house”’ is to prevent loss of heat by convection, it is interesting to see if this could be predicted. Published experiments on the cooling of solids in dry air and in vacuum give the relative rates of loss by convection and radiation under known circumstances. Planck’s radiation formula for the ‘black body” enables computations to be made of the losses by radiation for different temperatures of source and sink. The transmission of glass, salt, and the water vapour of the atmosphere, and the effective temperature of the latter are approximately known. I have attempted to compute from such data the relative hindrance which salt and glass covers would interpose to the loss of heat by convection and radiation combined from a “black” surface at 55° C. For the dependence of the tem- perature of the earth’s surface on the atmosphere, some numerical data can be assigned also, and as shown below there is reason to think that “trapping” is more important perbaps than Professor Wood thinks. * Communicated by the Author. Published by permission of the Secretary of the Smithsonian Institution. - + Phil. Mag. 6th series, yol. xvii. p. 319 (1909). On the Theory of the Greenhouse. 33 From an interesting paper of P. Compan ™* it may be seen that for a blackened copper ball 2 centimetres in diameter cooling from a temperature of 55° C. to nearly ‘ black ” surroundings at 0° C., the rate of loss of heat by convection in still dry air at atmospheric pressure is four-thirds as rapid as the simultaneous loss by radiation. In a breeze of 3 metres per second the convection loss becomes 3 times as rapid as in still air, or 4 times as rapid as the loss by radia- tion. The loss of heat by convection alone is approximately proportional to the difference of temperatures between the source and the sink. If the covers had been absent in Professor Wood’s experi- ments, the boxes would have been exchanging radiation principally with the water vapour of the lower atmosphere. Experiments of Langley, Rubens and Aschkinass, and others indicate + that less than 10 per cent. of the radiation from the earth’s surface can penetrate the water vapour of the atmosphere above a coast station like Baltimore. Hence the water vapour of the atmosphere can be considered as _practi- cally a “black body” for rays of great wave-length. The effective temperature of the water-vapour layers with which a coverless “ hot-box”’ would have been exchanging radiation may be estimated at 0° C. If glass is interposed the radiation is entirely cut off. Ifa rock-salt plate 1 centimetre thick is interposed between the body at 55° C. and surroundings at 0° C., the absorption of the plate is about 19 per cent.f and the reflexion probably nearly 10 per cent. more, so that the transmission may be reckoned at about 70 per cent. In combining the preceding results with those of Compan we will at first neglect the loss of heat by convection from the outside of the cover. We may assume the temperature of the air just outside the “ hot-box” to be 15° C., and also that Newton’s law of cooling is applicable to the convection loss. In still air with no cover the rate of loss of heat towards the front by convection and radiation combined is proportional to : 40 an X 133 +100 = 197. With glass cover: 0+100x0°00= 0. With salt cover: 0+100x070= 70. * Annales de Chimie et de Physique, t. xxvi. pp. 488-574 (1902). +t See Annals, Astrophysical Observatory, Smithsonian Institution, vol. il. pp. 167-172. t See Kayser’s Handbuch d. Spectroscopie, vol. iv. p. 485, and Planck’s formula of radiation. Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. =D 34 On the Theory of the Greenhouse. Thus of the heat which would have escaped toward tha front from a coverless box at 55° C. in still moist air at 15° C., the salt hinders se = 65 per cent, as much as the glass. Remembering, however, that owing to its higher absorbing power for long wave rays the glass will be warmed more than the salt, the convection loss from the outside of the warmed cover will be greater for glass than for salt, so that the efficiency of a salt cover may be much more than 65 per cent. of that of one of glass. The cunvection loss from the front of the cover is a considerable factor, for in the “ hot- box” tried at this observatory the front of the inner glass cover became too hot to handle and often cracked with the heat. In view of these figures we may agree with Professor Wood that a salt cover * is nearly as efficient as a glass one for a “ hot-box,” although it would seem strange that he observed no difference at all. Perhaps in spite of the glass filter the cover-giass obstructed the entering sun rays more than salt. But is not the case quite different with a planet? Let us take the mean temperature of the earth’s surface at 14° C., the mean effective temperature of the water-vapour layers to which it principally radiates as 0° C., the tempera- ture of space as —273° C. Then the rates of escape of heat from the surface by radiation, first with the water-vapour Jayer interposed, and, second, imagining the air to be com- pletely transparent to earth rays, would be in the ratio of 19 to 100 according to Planck’s formula. It is very difficult to estimate how fast the heat of the earth’s surface escapes by convection, because neither the difference of temperature between the surface and the air nor the rate of motion of the air is well known. But if for the sake of discussion we suppose a temperature difference of 10° C. and a velocity of 3 metres per second, the rate of convection loss comes out only 0°54 as great as the rate at which heat would escape by radiation if the air was no hindrance. This assumed convection loss is 2°8 times as great, on the other hand, as the estimated rate of escape of heat by radiation to the water-vapour layers at 0° C. In other words, according to this estimate the con- vection is the main agent in removing heat from the earth’s surface as things are, but would be only a small factor if the air was transparent to long-wave rays. If these figures represent at all the order of magnitudes of the quantities there can be no doubt, I think, that the atmo- sphere is important as a trapping agent to increase the earth’s surface temperature. # A salt cover, however, is better than a perfectly transparent one. Ea — . Steady Flow of an Incompressible Viscous Fluid. 35 A fair estimate of the actual increase of the earth’s tem- perature due to “‘trapping’’ has been made. Imagine a perfectly “black” and rapidly rotating planet of the earth’s dimensions, situated beyond the orbit of the earth at such a distance from ihe sun that the radiation absorbed by it would be equal to that available to be absorbed by the earth, allowing for the reflexion of clouds, et cetera. Such a planet would assume the temperature of —17° C., whereas the real earth has a mean temperature of +14° C.* The difference, 31° C., is attributable to three causes :—(1) The imperfect “blackness” of the earth. (2) The “blanket effect” of the atmosphere. (3) The warming of the earth’s surface by radio-active substances and internal heat. Remembering that the earth is mainly water covered, it must be almost “perfectly black’ for long-wave rays. I myself regard the conduction of internal heat and that of radio-active substances as negligible. This would leave the full 31° as due to the “blanket effect.” If there were no water on the earth, the emissive power of its surface tor long-wave rays would be less. Also, on account of the absence of clouds, its absorption of solar rays would be greater. The two differences would perhaps more than counterbalance the loss of the “blanketing effect,” so that the mean temperature of the earth without water would perhaps be rather higher than now, but much less uniform. ranging from above present temperatures by day to far below C° C. by night. VI. On the Steady Flow of an Incompressible Viscous Fluid through a Circular Tube with Uniformly Converging Boundaries. By A. H. Gisson, M.Sc., Lecturer in Hydraulics in the Manchester University T. f¥XHE general equations of motion for the three-dimensional flow of an incompressible viscous fluid are { :— eo fou , dru PRO u Ou Ou Ow - ou a aah ty Uae tay ta: tae ae 2 Ov, Ov ~ Flat ot oe "de tay tae | (1) Ow ou Ow Ow Ow 0: ws a cPagtse * i : * Annals, eA Ob ervatory, vol. ii. p. 175. + Communicated by the Author. } ‘ Hydraulics, Gibson, p. 665. D2 36 Mr. A. H. Gibson on the Steady Flow of an where yw is the coefficient of viscosity ; w is the weight of unit volume; wu, v, and w are the velocities of flow in directions 2, y, and z respectively ; and p is the pressure (reckoned positive if compressive). Assuming that in a circular tube with uniformly converging boundaries motion takes place in uniformly conveta a lines, so that the pressure is uniform at all points on a spherical shell having the point of convergence as centre, we a WY Ae Nie a hI v=0; w=0; iy = 3 7, = 0: while if the motion is steady oe = 0, so that in the latter case the state of flux along the tube is represented by the single equation ap) 07u GF ar ae Oe oat Sah 45s Oe (2) If r be the distance of a particle from the centre of the tube at a point distant x from the point of convergence OU Oa Mera op Oe OF rer’ and the equation of motion becomes ape. O7u of @ oe . 8) da © Oe" Or rar gO’ while if the angle of convergence of the sides is small, so * Qu Qu or_ Qu OW +7? Ou ei Oe oY | OF, OY), OF |”) Ov a One ade Orr or -2(S)=2(e Ne oy? oy\dy/ or \or 7 / OY =. Pu .(? ()) ys or + ar 2 Ou ou 7 -y¥ aa or or’ or Site Similarly Ou 22 Oru, Ou 72-2? Oz? ~ 72° Qr2 ° @r* 78 Ou ou ow, 1 ou Oy” aT aa a or’ Ineompressible Viscous Fluid through a Circular Tube. 37 that without sensible error r = 26, on converting to polar coordinates 2 and @ the equation becomes dp _ oe > Bote 1 Ou TZ Quy | (4) Bint tn SF tee? PO oe eS Cz Since wu is symmetrical with respect to 6, putting — = =) where 2a is the vertical angle of the conical pipe, and there- fore assuming no slip at the boundaries, we get, on integration, 2A = 2A 2A au ne = du yt \ a 4B me (8-095 "By When p=, v=uU and 2=2%; a Ar 2uy Aug 1 } con geen {2-3 " (2-6) 2g ° a a hie “} : Bra ag a t 95 ak ie L - ©) Again since the volume discharged per second is given by 0: = a 2rrx*bu dé = 20A’ (220 — 6) dO _ wAa* That 9 Fs vis . av _o¢ o9_!1 o ar 08 Or 2 08 ou _ oO Ou _ 2 (: 3") 0a a or or oav\z' de/ ar _1 ou pan 1 Ou ~ a Og? x ~ a? Bg?’ 38 Steady Flow of an Incempressible Viscous Fluid. 2__ 92 while 1, ee = _ 2Q(— 6) Tatx? (6) 1 2Q) 2Q oy i =a. go a — A materu— ratay?ug Substituting this value in (5) we get I NSS aaa i ag ee ae =a ba Tp May Ma Ny?) ee (7) At the boundaries wu = w= 0, so that here Bit eet BP 2 8) ee | CS SS qr Oia wee) she 8uQ Xo a) v s Sire Mla ee giving the difference of head (expressed as the length of a column of the fluid) as measured by piezometers opening flush with the sides of the tube at points distant respectively #, and « from the point of convergence, and where the radii are respectively a) and a. From (6) we have, at the centre where 6=0, Beh Ln = ° razz?’ while the mean velocity over the whole section = —. TWa*aX~ Maximum velocity _ Mean velocity a? + J VII. The Determination of a Constant in Capillanty. By R. D. Kuizemayx, D.Sc, B.A., Research Student of Emmanuel College, Cambridge*. ] HEN the area of the surface of a liquid is increased the increase in the amount of energy in the surface- film of the liquid is equal to the sum of the external work done and the amount of heat absorbed from the surrounding bodies to keep the temperature constant during the process. The relation between these quantities can be immediately obtained by means of Helmbholtz’s free energy equation connecting the total energy with the free energy, which gives dn HE Dg Beals, gailuen | (1) where A denotes the surface-tension and E the total energy corresponding to the temperature T. A is equal to the ex- ternal work done, and ape therefore equal to the amount aT of heat absorbed from the surrounding bodies. This formula was first given by Lord Kelvin. Whittaker + has calculated the values of Hy, the total energy for different temperatures, for a number of liquids, using the surface-tension determinations of Ramsay and Shields}. He found that the energy E per cm. of the film of a liquid is proportional to the product of the internal latent heat of evaporation into the absolute temperature of the liquid, er MSRP UNG! VSR) hk) ae aD) where L is the internal latent heat of evaporation corre- sponding to the temperature T, and K is a constant. The constant K was found to be different for the various liquids. The extent of the agreement of this empirical law with the experimental facts is shown by the following tables taken from Whittaker’s paper. * Communicated by the Author. + Proc. Roy. Soc. A. vol. lxxxi. p. 21 (1908). t Phil. Trans. A. vol. clxxxiy. p. 647 (1893). 40 Dr. R. D. Kleeman on the Ether. Methyl formate. 1 | | | | e108 | Ex 101) SON RT UR tL SOU ie oma AL or or | K104 K104. slo 4o let 7536 20°8 303 | 69:4 |107°49 213 oee | 469 forOr 20°8 818 | 68:8 |103°95 ALS | 833 | 48°9 | 70°79 20°5 1 323 | 682 | 99:51 21-2 343 | 47°8 | 68°35 20°4 goo) OT | 90°59 21-2 353 | 47:1 | 65°85 20°3 343 | 67°3 | 92:16 Pics, 363 | 4671 | 63°31 20°1 353. | 66:2.) 88°03) Yise 373 | 45°5 | 60°33 20°2 363 | 65:5 | 85°10 21-2 383 | 44°7 | 58:07 20°1 373 | 64:6 | 82°43 21:0 398 | 48°83 | 54:9] 20°3 aso.) Gore) F921 21:0 403 | 42°6 | 51°62 20°5 393 | 62°9 | '75°92 pA hi lig 413 | 41:1 | 48°31 20°6 403 | 61°8 | 71:95 Pi ess ae 423 | 39°3 | 44°38 20°9 413 | 60°4 | 68°10 pA G5 423 | 58°8 | 64:03 21°7 Benzene. aaa | Carbon tetrachloride. | Bisset (Las ones Bx 104 4 r eh ee cel Ae ae Me ee 353 | 59°5 | 856 19°7 K104 aoe i 602 4 nSSe7 19°8 SS Se Ee 373 | 60°9 | 82-0 19°9 363 | 57:9 | 40°62 Oost 883 | 61:1 | 80:0 20:0 oo | OTe og eS 38°9 393 | 60°7 | 781 198 083 | 56°8 | 38°64! 388°4 403 | 60:1 | 76:1 19°6 393 | 564 | 37°63} 38-2 413 | 59-4 | 741 19°4 403 | 55°6 | 36°58 one 423 | 588 | 71:9 19°3 413 | 548 | 85°56! 87:3 483 | 58:0 | 69°7 19°23 493) 1} 53°9) || 84°42 37:0 443 | 57:2 | 67:5 19:1 433 |) bol | sa'28 37°9 453 | 5671 | 65:1 19:0 443 26. | 32:07 37:0 463 | 550 | 627 190 453 | 52°2 | 30°83 37°4 473 | 54:0 | 59-9 19:1 463 | 51°7 | 29°52 &7°8 4838 | 52:9 | 57:0 19:3 476: | 50°68.) 28°22) ) oak 493 .| 51:5 | 538 19:4 483 | 50°3 | 26°83 37°8 503 | 49°9 | 50°5 19°7 493 | 49°8 | 25°35 37°8 518 | 48:1 | 46:6 19:1 508 | 4773 |: 23°73) BS | The object of this paper is to find a value for K of a liquid in terms of its absolute constants. Such a determination is evidently desirable. Ramsay, following Eétvos, has shown that the surface- tension of a liquid at the absolute temperature T is con- nected with the absolute temperature and other quantities by a a iy ae ~ ek Determination of a Constant in Capillarity. 4] Chloro-benzene. | | eee na | me hE fh or K104 423 | 598 | 65°81| 21-4 433 | 59:9 | 6412) 21-6 443 | 60:0 | 63:02! 21°5 453 | 60:0 | 61-46! 21°5 463 | 59:3 | 59:97) 21°3 473 | 586 | 58:31) 21-3 483 | 581 | 56:81) 21-2 493 | 57-41 55°29' 21-1 503 | 56-7 | 53°83} 20:9 513 | 55°9 | 5243/ 20:8 523 | 55:1 | 50°81| 20-7 533 | 538] 49:09| 206 the equation gr TE Pei day go i) where v denotes the molecular volume of the liquid, and A is a constant which is practically the same for all liquids, being equal to about 2-1, T, is the critical temperature, and ais another constant which is also approximately the same for all liquids, its mean value being about 5. Substituting for X in equation (1) by means of equation (3), we obtain rT =a) AT 2 (T.—T—a) dv ec y2i3 vy at ee a: Let us suppose that X refers to a temperature much below the critical temperature of the liquid, say near the absolute zero. The value of ou is then a very small fraction, and T(T,—T—a) small in comparison with (T,—T—a). The third term on the right-hand side of the last equation may at_ low temperatures be, therefore, neglected in comparison with the other terms, and in that case K= Sg), ah The molecular volume is given by v= eat where m is the molecular weight and p the density of the liquid. Sub- stituting for v in the last equation we have _ prA(T.— a) * ihe m/s E 42 Dr. R. D. Kleeman on the And since E= KLT, we have _ pA = meLT (T,—a). ol) s)he) (4) The latent heat of evaporation L, of a liquid is given hy the well-known thermodynamical relation d L,=(¥—)T a, where v, and v, denote respectively the volumes of a gram of the saturated vapour and the liquid, and p denotes the pressure. lor temperatures well removed from the critical temperature the vapour behaves approximately as a perfect gas, and this equation may then be written RP de moe? where R denotes the gas constant. If the equation be written in the form Lan algae TD: pe and the temperatures and pressures at the right-hand side be expressed in terms of the critical temperature and pressure, we obtain Lym _ RaT, pe dB Rad a 6p.’ Ve dec maine where al.=T, and 8p.=p. Thus the relation between In, T, and m for different liquids at corresponding states 1s given by els =constant. Since the temperatures of liquids at their boiling-points are approximately corresponding tem- peratures, this relation holds approximately for liquids at their boiling-points ; it is known in this form as Trouton’s law. If the temperature of evaporation is so far removed from the critical temperature that the vapour behaves approximately as a perfect gas, the external work of evapo- ! RT ration p(v;— v2) is approximately equal to ——-. Therefore ne L+p(.—w) =L+— =L1 m lim tim Tae Lm 6 +h = constant; or = 18_ also and therefore a Determination of a Constant in Capillarity. 43 constant for different liquids at corresponding states. Writing Lm =B, where B= Ra eS and substituting for L in 14 B dz equation (4) we obtain Ka". *BA(T.—a)m™s flag Expressing p and T in terms of the critical density and temperature, we obtain “- Ay? p22 (I = a) mis Big t? ‘ where p= Yee Let us write the equation in the form —_ Mm!4(T, —a)p.2? emai cer HUTA 2/3 where M = A Y Bw: Now it is known that K is a constant for a given liquid, therefore M must be a constant for the liquid. Further, in obtaining K for different liquids we may suppose the liquids taken at corresponding states, so that the values of «, 8, y, are the same for each liquid. Then it follows that since M is a function of a, 8, and ¥ only, it must be the same for each liquid. Fr ria since a is equal to about 5 and T, of the order 500, iz » may be neglected in comparison with = We have then, finally, Mm3p,2/3 i oS rane ape). od Meet = (5) where M is a constant which is the same for every liquid. M m'3p22 T. for a few liquids calculated from the data given in the second, third, and fourth columns of the table, the value of M being put equal to 5°57 x10 in each case. The values of 104 IK, contained in the fitth column of the tuible, are the means of the values contained in the preceding tables. It will be seen that the values of K given by equation (5) agree fairly well The following table contains the values of 104 with the values given by the equation K= Li" A better agreement can scarcely be expected since the critical constants cannot be determined with any great accuracy. ef Determination of a Constant in Capillarity. M=5:57 x10-1. i Bes j | 1/3. 2/3 Te. pe. | mm, | K10+ A0Maoee Be | ne Ripon eee 466°6 | -2604 | 74 | 20° 20:4 Methyl formate ......... 487 |°3489 | 60 21°2 22°2 Carbon tetrachloride ...| 356 |:5576 |158°8 | 38:1 36°4 IBENZONE ko wee sateen 561°5 | 3045 | 78°05 | 19°5 19°2 2, DA No es ARC wel daraiels 633 | °3654 ee 2 The value of K given by equation (4) will not apply to polymerized liquids because the value of A is then nota constant, but varies with the nature of the liquid and its temperature. It is also very probable that the relation given by Whittaker does not apply to such liquids. If the critical density and temperature of a liquid is known, and its capillary constants for temperatures differing by a small interval, the internal latent heat can be calculated for these temperatures by the equation Wee (7 adn lee i He — 7) ne oF arom xl Ort? deduced from the equations (1), (2), and (5). An inspection of Whittaker’s results shows that K or LT is very constant for different temperatures, and this equation would therefore give fairly accurate results. If a large number of determinations of A for different temperatures are not available, the values of \ and = in the above equation may be obtained from equation (2), the constants in the equation having first been determined by ~ means of the values of \ for two different temperatures. This, however, will not give very accurate values for L. Equation (5), by writing it in the form BE Mm)*,.28 ea a, may be used to find either of the critical constants it contains if one of them is known. The right-hand side may be evaluated for any convenient temperature. Cambridge, March 20, 1909. Ea] VIII. Theory of the Alternate Current Generator. By Tomas R. Lytz, IA., Se.D., Professor of Natural Philosophy in the University of Melbourne *. T has been usual hitherto to ascribe the distortion of the wave-form of the current given by an alternate current- generator to :— 1. “Lack of uniformity and pulsation of the magnetic field, causing a distortion of the induced E.M.F. at open circuit as well as under load.” 2. “‘ Pulsation of the reactance causing higher harmonics under load.” 3. “ Pulsation of the resistance causing higher harmonics under load also” f. And, as far as I have been able to find out, another cause has been overlooked, namely, the mutual reactions between armature and field, which when the generator is loaded is at least as important as any of the foregoing. If such is the case it can only be explained by the fact that the theory of the simple alternator has not been completely worked out. In the following paper this is done for an alternator with a uniform field by means of a new application of the vector method in which all the harmonics of a periodic function are dealt with simultaneously. In the same is shown how to take account of hysteresis and eddy currents, and the theory of the action of dampers in reducing the heating in the field is also given. The theory of the alternate current synchronous motor is also dealt with. 1. Let two coils be arranged as indicated in fig. 1, one of them, F,, called the field coil, being fixed and having a battery of constant E.M.F. = 7 in its circuit, the other, A, called the * Communicated by the Physical Society : read April 23, 1909. tT Steinmetz, ‘ Alternating Current Phenomena.’ 46 - Prof. T. R. Lyle on the Theory of armature coil, fitted in the usual way with slip rings for connexion to an external circuit and being rotated by power at a constant angular velocity » round a fixed axis which is perpendicular to its own axis of figure and to the direction of the lines of force of F, and which passes through its own centre. It is required to determine completely the currents that flow in both A and F. Let « and & be the currents at any instant in A and F respectively, and let the mutual inductance of A and F when their axes are coincident be m, and hence mcoswt at the time t. Also let r and 7 be the total resistance and self- inductance of the A circuit, and p, » similar quantities for the F circuit. Then, when the armature is being driven at constant angular velocity w, and « and & are flowing, the total number of lines linked on A is lu+m€ cos wt, and the number linked on F is AE+ me cos wl. © Hence d ener {le +m€ cos wt} = 0 | : (1,) pé+ an {rE + me cos wt} = 9 ( where 7 is the applied steady E.m.F. in the F circuit. 2. If we assume as the solution of these equations w= 2 + ay sin (wt +c) + a sin (2wt + c) + 23 sin (3at +e) + &e., a= se + &, sin (wt +;) + €, sin (2+ 72) + & sin (Bt +43) + &e., we can see at once on substitution that p&)=2n, and that %o=0, and it will be shown afterwards, § 15, that when wo=0 then £), xo, £5, a4, £5, &c., vanish, or in words, when #y=0 only odd harmonics appear in w, and only even ones in & Let us therefore take asin (wt +¢;) +23 sin (Bet + ¢3) + 45 sin (Sat + ¢5) + &e.) i (iis v f= 8 4 Bysin ot + 92) +Ersin (dot +45) + be Now any harmonic in either « or &, for instance 9 sl (gat + cy); being completely specified by «,, c,, and 4, —_ —— the Alternate Current Generator. 47 can, when its order g is known, be represented by the vector drawn from the origin in any reference plane to the point in that plane whose polar coordinates are x, cg, twice the constant term in & being er in the same plane by the vector to the point tte 3 The form of solution ar) assumed may now be written v= a,ta,t+a;t+ Ke. IIL. E =D taytatagtie. oe where aj, a3, &C., a, %, a, &e., are vectors whose orders are . indicated by the subscribed numbers. Of these, one only, namely a, is as as it is drawn to the point whose polar 2 co-ordinates are aed 2 where & = = The others have to be determined. Note a.—In the sequel it will sometimes happen that a vector, say 4,, originally assumed of order g, will be used to represent an harmonic of a different order, sayg+1. In such a case it will be written (a,),.1 ; thus ag = Ly Sin (Gwt +c), but (@g)g41 = wy sin {(q+1)wt + cq}. Note b.—The length of a vector « will be written as a (2. e. with the bar) ; thus a; = 23, unless in cases where no ambiguity can arise, when a@ simply will be written for the length of the vector a. 3. If we agree to indicate by ° the operation of rotating any vector to y which it is prefixed through an angle @ in the positive direction, then ia |e sOr 6 = 2— 4, and Tv Ya = (cosO+u2sinO@)a or wo = cosO+e2sin O. 21 Also, if ¢ = D.J, ta is the vector obtained by increasing a in length D times and then rotating the increased vec stor through an angle / in the positive direction. Plane vector operators such as ¢ are well known to be subject to the same rules as ordinary algebraical symbols. 48 Prof. T. R. Lyle on the Theory of Again, the sum of two operators a,e%, ae, can be ex- pressed as a single operator Az’, say, that is | Ala = ala + agu2a, where @ is any vector. Using the expression for e? given above, Tv A(cos Wc? sin yr) cag aif = a;(cos 0, + sin 6;)a+ a,(cos 0,4 v2 sin 0,)2, so that —Acos = a, cos 6, +4, Cos Oy ; A sin = a, sin 6,+ a, sin ,. Hence a eae oa), and jana a, sin 6;+ a, sin 0, a = ye a Cos 8, + dae cos 8B, Again, if ty = e, sin ( pott+Yp), then A = te = eee seeing that d we 4 ‘e rAG) = poé, sin (pe + p+ 5 Hence for 2 and & as expressed in § 2 dx T r i n a= wl? X.Gag, - = wl2> pap. Tw 4, By means of the formula 2sin a cos b = sin (a+b) +sin (a—b) it is easy to show that 2 cos wt, where w is the a series of odd order vectors in § 2, is represented by the series of even order vectors of which the one of the pth order is the vector sum of ay_j and a,144, or that | 2x cos wt = (a), + (a, +43 )o+ (a3 + 5 )4 + (85 +476 + Ke., (a1)9 being the resolved part of a, along the y axis, that is along the direction of vectors of zero order (see Note a, § 2). Similarly 2E cos wt = (ap +a), + (a+ a4)3 + (% + a 6)5 + Ke. the Alternate Current Generator. 49 Again, by means of the formula 2 sinasin b = cos (a—b)—cos (a+b), it is easy to show that Tv vie Tt 2% sinwt =e 2 (ey—ag); +6 2(a,—ay)3 +4 2 (a,—a5)5 + Kc. T —= 6 23 (%q-1 —to41)¢ where g is odd with a similar result for the product 2z sin ot. 5. If we now substitute the vector expressions from §§ 2, 3, 4, in equations I. and equate separately to zero each set of vector terms of the same order we obtain the two series of vector equations TA + gore? lay + 5 (@g-1+ a+1) } = 0, (IV.) T Pm + pak rapt pt == a1) } = 0, (V.) together with £) = 2n/p, where q is any odd number and p any even number. From IV. we deduce a series of equations of the type Tv ny te oth = = 0, or Qy—1 thy ag tag41 = 9, where ¢, is the operator Dgt-“4, in which Y sng Sa D, cos f, = 2-, Dj, sin fy = aa that is 4 ae r OE Bey |) bE See ekg et Se Lhe aa ( + aaa} tan fy = wal Similarly from V. we deduce the series Ap—1+Tp% + apy] = 0 where 7, is the operator A,e~?, in which Xr ‘ 2p Sb a Er, or 4 rae r2 ae ae A» ==(2 + ta :) tan dy = x: Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. 10 50 Prof. T. R. Lyle on the Theory of Note that the vector equations in this paragraph are equations connecting the different vectors, considered purely as vectors, without any reference to the order of the harmonic they originally represented. 6. We have thus obtained the following infinite series of equations connecting the vectors used to represent wand & :— £18 + a = —a% @y + Todo + Ag = (0: Ay + tag 4+ og — 0 (VL) az + T 404 + as = () : atta, +a = 0 &e., &e. And as it is well known that algebraic methods are applicable to plane vector operators of the type here made use of, we obtain the following infinite determinant vector solution for a,, namely, of die) OAD 00S. daa (er 0 Ota? wt 00°00 ae Lee he le Uae ae 1t1000.... 601n10....:o 24S) ee OO eee OF0-1 7, 1 0 ie 00/010 Meret au. O0017m1.... &e., &e. &e., &e. or Pay = —IT,a, where P, is the infinite determinant operator whose leading term is ¢,, and II, that whose leading term is 7». 7. Py, Ile, Ps, Wy, &e., being the determinants whose leading terms are ;, 72, ts, Ts, &c. respectively, we find at once by expanding that P, =— ty II,—P; Il, = T2 P,—I,, &c., hence Py t Psi Armies! 5 ae a te II, /P3 A eee a aoe 2 T, — Xe. I| TNR —" o~ Uh i) SA SS — ———— the Alternate Current Generator. 51 so that ay = 7 5 Yo 1 where §, is the infinite continued fraction operator whose leading term is ¢}. Again, if i = SS li 2 2 5 as Bd One Samer Ac2 : il SS Ae SU are hae suas sh Spe tT — &e 1 Y= ™]— > 9 cf ie Pee and so on, we find in a similar way, or by making use of equations VI., that 1 “2 1 8 = —qa, K&e., &e. S3 Hence for the complete solution we have 245 = —S,a, = Sis@e = —§,>,8,a; = &e., which gives a,, a3, a5, &c., a, a4, %, &e., in terms of the known vector a) provided the eontinued fraction operators S,, 22, S3, &e., are determinate. It is easily seen that they are determinate for when q becomes a large number i= 2 te To41 = eat ie (see § 5) 3 that is, 8), do, S3, 24, &c. are recurring continued fraction operators, and the recurring elements when reached are simple numbers. 8. The form of solution obtained is one very easy of practical application. In computing the continued fraction operators just so many of their known t¢, r elements (see § 5) need be taken account of as are necessary to give the required degree of approximation. Moreover, in the case of a practical alternator, as the re- sistance of the field-magnet coils is negligible relative to EK 2 52 Prof. T. R. Lyle on the Theory of their reactance, all the + elements are practically simple numbers independent of the field resistance, while for the ¢ elements g is never a large number when ¢,49 differs little from ¢,, So that we could obtain 8, with considerable accu- racy by assuming the recurring stage to be reached, and therefore which gives the quadratic in 8, 9 t qg+l from which 8, can be obtained by ordinary algebra. [In solving this quadratic the two operators that come under the square-root symbol will have to be reduced by the addition theorem in § 3 to a single operator, as” say, and the square root of this is “as”.] If Sq obtained in either of these ways be = sus, then as 1 es —_ ab, (oes ea gl!) Sy = ya ga x —1 can be obtained by the addition theorem, and so on for Sg_9, Ses &c., up to 8;. Let the results be written Si = Git hy Ss == owl, Ss = sy OR, &e., and in general Sy = she, Sy = opp Pr. 9. As a is the vector of length 2n/p lying along the axis of y (phase=7/2), and as 1 1] a a S (>) ai ea Gor lle Miees ( T ea ae ( T ao == on sin { wt + 9 +b:) = ae wt a +b). Again, as if 1 OE ae S, Aus Ate zit Cae» ao = 7 sin (20t+ = +b, +82) : 5109p CO ee = —_ the Alternate Current Generator. 53 similarly yy i #7 _ sin (301-5 +b, +A,+bs) ; 5100539 2n CS (Go aa as aE sin(dor+ 5 aa +- b,+8,+bs; +1): $19 9530 49 SANE S1O9837 4850 2 &e., &c. And substituting these values in sin (Swt— bid +b, +8,+Ds+ 6,405) 5 v=a,t+az;t+a;+dc., ExT tata tke, we obtain the armature and field currents in the usual trigonometrical form of expression. It is worth while drawing attention to the fact that the period of the alternating current induced in the field circuit is half that of the armature current, and that it contains all harmonics, both odd and even, relative to its own funda- mental, and so its wave-form will in general be unsymmetrical with respect to the time-axis. 10. The total u.m.r. E generated in the armature circuit being equal to — F (me Cos wt), d = FS pea 1 +941 )o> (see § 4) 7 @n » = oy 2 (eg—1 + %41)¢- Also as Oy ttyay +241 = 0 us H= vee Zgtgay: a And in either of these formulz the trigonometrical ex- pressions in § 9 for the vectors can be substituted. In the first, however, it must be noted that both «,_; and @ 41 are to be taken of order g (odd). Thus the funda- mental harmonic of EH is omn = : sin wt + = s sin (ot-+b, +22) } 54 Prof. T. R. Lyle on the Theory of from the first expression, or omn D, Prive from the second, as t; = Dye“. Similarly the total alternating E.M.F. (H say) generated in the field circuit is given by either sin (wt +b; —f;) T | an > H= — “ge >P(ap—1 +441) p 7 Wir © or H = ak LPT pps so that the fundamental harmonie of H is equal to either somal = sin (2wt +b, + 37) + J sin (2ot +b; +8, +bs +77) | 1 Pp $, 0983 DONG Ne oe oy. — sin (2at +b, + 8.-—¢2.4+ 77). p 804 ( i+ P2— $2+7) 11. The mean value of the product sin (awt + @) sin (bwt + d) being zero when a and > are unequal and 4 cos (@—q@) when a and 6 are equal, we find that the mean value of 2? where w= 2a, 1s or = 22a, 5 a 2 and the mean value of &’, where — = — 4 Lap, is ane 2 aie. USS — wy + 222° Again, for the same reason, if « and 6 be any two vectors representing harmonics of the same order and if S«® be the product of the lengths of « and B into the sine of the angle from a to B measured in the positive direction, then the mean value of the product i t-a into B 18 — 48a => —iSBa. Applying these principles to the determination of the mean value Ee of the product of E and «, that is of the the Alternate Current Generator. 55 electrical power developed in the armature circuit, we find from the first expression for E in § 10 that a wm Ez = — - DS (eg 1 + %y 41) tie Sc {Sa a;— Saja. + 3Sa a3 — 3S aga, + 5Sa,a5;—5Saza_+ Ke.}, and from the second expression for E that === @m wm ee Ba = 3-298 (ta, - Ag») = Go =qD Sle May « ay «) @N’ a2 ° ae Ns = 24,qD, a = 41 >a, er 2r E as b, sin f, = on (see § 5) = the heat developed in the armature circuit. Similarly the total electrical power (H+7)& developed in the field circuit is given by areca AN 6s ] mv (H+ a)§ = 5° — PPS pS(ap_1+ay414 a” wm =p 3 oa {2Sa,a,—2Sa.a, + 4Sa;0,—4S2,a;+ &e.} or by Sa sear a @n (H+n)é eo + 7 UpS(tpap ap -) which reduces to pean bse = PSS a (H+)€ = p= + FaP+ae ta) + ke.) = total heat developed in the field circuit 2 and is made up of two parts, the first = fon due to the direct exciting current and the.second = 5 (aq? +a,’ + a’+ Ke.) due to the induced alternating field-current. Adding the first expressions for Hz and (H+7)§& and Be 2 cancelling 7& against pa we find that Fae @n ‘ ( Ez + Hé —— -- { Saga -+- Saja, +- Sa.a3 + Sag%, -+ &e. } e 56 Prof. T. R. Lyle on the Theory of 12. The torque exerted at any instant in driving the. alternator is. d — yf eed rv —o_ Hoi 7 = ve Tot) {m cos wat} = mx sin wt = 5 aay xt pC toe (see § 4) Tv m 5 : Taking the mean value of this product we find that the mean driving torque T is given by T= — - {Saaz + Sajao+ Sagas + Saze,+ Kc. }, which result, combined with the last one obtained in § 11, gives the power equation ol = He+HEé as it ought. 13. The solution obtained can be represented geometrically in an interesting way as follows :— Take two lines OX, OY, fig. 2, at right angles. Measure Fig. 2. off from OY in the positive direction the angles YO1=b,, 102=£8,, 203=b;, 304=,, &e., where b,, 82, bs, Bs, &e., are the angles determined in § 8. the Alternate Current Generator. 57 In OY take Oa=2y/p=2x exciting current. Produce | O 10 through O to a so that Oa ee ee ha 2 "take Sy Oa,=Oa,/c,. Produce 30 through O to as so that Oa, = 2% and so on where s,, 0, 53, 04, &¢., are the quantities determined in § 8. Then the vectors to a;, a3, a5, &c., represent completely in amplitude and phase the different harmonics of the armature current, the subscribed numbers indicating the orders of the harmonics ; and those to a», a4, %, &c., represent completely in the same way the different harmonics of the induced alternating field current. Again (see § 10), if we rotate the vector drawn to the middle point of a2 backwards through a right angle, we ee . obtain the vector OH, that represents Sot into the first harmonic of the total e.m.r. H generated in the armature ; and if we rotate backwards through m/2 the vector to the middle point of a, we obtain the vector OH; that re- presents = into the third harmonic of E; and similarly for the other harmonics of E. In the same way, by rotating backwards through 7/2 the vector to the middle point of a ,a3, we obtain the vector OH, that represents — into the fundamental harmonic of the E.M.F. H induced in the field circuit; and so on for the other harmonics of H. Again, as S28 is = twice the area of the triangle whose sides are « and @ and is positive if 8 follows 2 in rotation order in the diagram, the mean torque exerted on the generator by the driver (see § 12) is equal to 3m into the sum of the areas of the triangles a)Oa,, ajc, #20ag, a3Oa4, Ke., these triangles, in the case of any generator, being all taken as positive. 14. When, for any generator, the ¢, tT operators have been calculated for a particular load (see § 5), a geometrical solution can easily be obtained to a high degree of accuracy by aid of a ruler, scale, slide-rule, and protractor. Thus if we neglect the harmonics ag, ag, a9, &c., then, drawing any vector from the origin to represent a; we can construct for a, as ag= —t,a; (see § 6). From ag we can con- struct for tex, and as a; + Te%g+a,;=0 the triangle of vectors 58 Prof. T. R. Lyle on the Theory of gives us a;. Proceeding in this way, we obtain in succession G4, &g, a, &, &, which represent the harmonics of x and & correctly as regards relative phase and relative amplitude. But as « must be equal to twice the exciting current we have a scale for our diagram, and hence obtain a complete solution. The fact that for a practical alternator the tT operators may be taken as pure numbers (see §§ 8, 22), renders this method of solution both easy and expeditious. 15. If a source of constant u.m.F. be included in the armature circuit as well as in the field circuit of the simple alternator indicated in fig. 1, equations I. § 1 become re + si le -+m€ cos wt) = e pé + ss (XE + mz cos wt) = n, and both the armature and field currents will now contain harmonics of all orders, odd and even. In this case we assume that x == + a, + a, + as + &C. = z +a,+a,+a,;+ &e., where a is the vector to the point whose polar coordinates are 2e/r, 7/2, and a, is, as before, the vector to the point 2n/p, 7/2. The other vectors aj, a, a3, KC., a, a, a3, HCe, have to be determined. On substituting for x and & in the above equations it will be found that the odd order vectors in # and the even order ones in & are determined by the same equations (LV. § 6) as when e=0, and are completely independent of the even order vectors in « and the odd order ones in &, these latter depending only on e and vanishing with e. This being so, a1, a», a3, a, &c., are given by the solution already obtained, and «, ay, a3, a4, &c., will be given by a similar solution the equations expressing which may be written down from symmetry. Thus the complete solution is given by a = —8,a, = 8, 2.%. = —S,2,S,a3 = &e., ay = —Dya = 2S a. = —2BS.2,0;3 = Ke., where a) is the vector to 2n/p, 1/2, as before, and @) 1s the vector to 2e/r, 7/2. the Alternate Current Generator. 59 Note.—In the former case (e=() the ¢ operators were all of odd and the rt ones of even orders. In this case the operators of either class are of both orders. The translation from the above vector solution to the ordinary sine form follows as in § 10. 16. In the preceding solutions the magnetic fluxes have been assumed to be in phase with the magnetizing current- turns, and so iron loss due to hysteresis and eddy currents has been neglected. -To take account of the latter the interpretation of the well-known relation B=wH connecting steady magnetizing force and induction produced has to be modified. The induction produced by H=H, sin (w@t+c¢,) is known to be of the form B = mH, sin (wt +¢,—6,) + higher harmonics, and attending only to the fundamental harmonic in B, if H be represented as explained in § 2 by the vector hy, and B by the vector ,, then the above trigonometrical relation may be written ; by = pyly where p, is the operator my—®. In a former paper* by me was shown how these per- meability operators, as they may be called, can be determined. They depend on the character of the iron and the thickness of the lamine, on the amplitude and period of the funda- mental harmonic of the induction oscillation they refer to, and to some extent on the wave form of the latter. For the purposes of the following discussion we will assume that when the magnetizing force H = hi +hz+h;+ &e. produces the induction B => 6,+6;+6;+ &e., then b,=pyhi, bs=psh3, b;=p5h;, &e., where the p’s are operators of the type given by by = mgt 4, [This assumption as regards al]l the harmonics of B but the fundamental is not strictly in accordance with what is known concerning the behaviour of laminated iron under periodic magnetizing forces, for 63, b;, &c., depend, at any * “Variation of Magnetic Hysteresis with Frequency,” Phil. Mag. Jan. 1905. 60 Prof. T. R. Lyle on the Theory of rate for high values of 6,, more on 6, than on hs, hs, &e. At the same time it is hoped that the following discussion may be of some value. L In general if H=ZA, produce B= Xb,, as the total iron loss per c.c. per cycle due to both hysteresis and eddy currents is dB T SWE ce A BG where T is the a the total iron loss per c.c. per second is = ~ . Average value of product Hee i dt = = Av. product Sh, into 22qaby a = {Sb hy + BSdgh3 + 58b;h; + &e.} (See § 11) = g—-Sgbghy hg sin 8. Again, it is well known that if the steady magnetizing current-turns nz act on a magnetic circuit composed of different materials, the flux F produced i is given ne ae Amna si Au where the L, A’s are the lengths and sectional areas of the different. portions of the circuit, and the w’s are the perme- abilities of these portions tor the particular flux densities in them. If now the magnetizing current be an alternating one, that is if z=, sin (wt +¢,) =a, (a vector) the same equation will give the corresponding harmonic of the flux produced, but the p's are now the permeability operators, for the different portions of the circuit. >, can, by the addition theorem in § 3, be reduced toa single operator so that if the flux f, (vector) be produced in any magnetic circuit by the current-turns na, we have always a relation of the form hi Gna, where Gy, is an operator of the form ney which can be determined. the Alternate Current Generator. 61 Hence, following the assumption already made, if the magnetizing current-turns ne = n(a;+a3+a;+ Kc.) produce in a magnetic circuit the flux F=/f,t+f/tfst &. then f, = nGya, fs = nGyaz, Ke. where the G’s are operators of the type given by G,= qt °%. In the above the back E.M.F., € Say, in the magnetizing eoils due to variation of flux is AB ivinsy e= na = now 2aq and the power absorbed, that is the total iron loss per sec. in the magnetic circuit, is the mean value of ez, that is of the product a, into no2d9 fy which (see $11) = = $nw (957) .a,.) = w3(oF sin 9) 17. As an example let us determine the G operator for a magnetic circuit of uniform cross section = 100 cm.?, made up of 40 cm. length of laminated iron and two air-gaps each 1 mm. when B maximum = 5000 and the frequency 30. In the paper already quoted we find for a sample of No. 26 iron well insulated between the laminz when Byax = 5000 and frequency = 30 q.p. that w= 25000-°" (nearly). Now G= “ eyes Ap FU 40 50°, ., | and 2s 100 3500" + af 1 ° = hy 16 +200 } 2106 3°18’ aa Haws G = 5968.-2°18 . 62 Prof. T. R. Lyle on the Theory of 18. Returning to the alternator, if n be the number of armature turns, v the number of field turns, and a — re 0 w=a tagta,t+&c., & = Fta,ta, +t &e., a the armature and field currents respectively, the magnetizing current-turns M, producing flux across the air-gap and through the armature in a direction axial to its windings are given by M, = nz+v€ cos ot, and the current-turns M, producing flux across the air-gap and through the armature in a direction parallel to the planes of the windings, and behind that of M, by 90°, are given by M, = vé sin wt, or in vector notation (see § 4) Vv vS = | na, + 5 (a1 +2941)4 | M Be ee oy) hee A Ng = gq+l/ 2 which produce the armature fluxes A, and A, given by v AL — XGy | na, + 9 (a1 ‘.3 an+-1)o | ee Ay = 36 *2Gy(@q-1—%41)¢ where Gy = oe and g any odd number. [ Note that the directions of A, and = are fixed in the armature. | Now if magnetic leakage be otherwise taken account of, the flux in the stator must be continuous with that in the rotor so that the flux F looped on the field-windings at any instant is given by F = A, cos @t+A, sin ot, which by means of the relations in § 4 can be reduced to iM F=% | rye a 9 (G11 a Pee...) where p is even and 2G, = Gp_1+Gp41. the Alternate Current Generator. 63 19. If l’ be the self-inductance in the armature circuit either external to the armature or due to magnetic Jeakage in it, and if X’ be a similar quantity for the field circuit, the equations for the two circuits are ax d Me retl at ag =() Rae Cees where 7, p, 7, 2, &, have the same significations as in § 1. Substituting in these equations from § 18, and _ then equating separately to zero each set of vector terms of the same order, we obtain the two series of vector equations, us T a) 5 V ra, + gol Pay tng Gy 4 nay + 5 (%-1+ 241) } = (0) ae " p%, + pwr ie, + vp { VG a, + 3 (CG, 13, + Gp 41%)41) } —() with a, = as where q is odd and p even. These reduce at once to the two series, tg —1 + tg Gag +2941 = 0 Gp—1ap—1t Tp%p + G4 141 = 0 . = = ey £ or, after putting a’, for G,a,, to / tg ttay tei, = 0 ‘ / equations of exactly the same form as those for the simple case but in which the ¢ and 7 operators are now given by 2 aie = s : ppl gh q vera ie Got yo } 2 Tv WV pe These operators having been calculated from known data, . 7 ' / ! the solution for a, a’, a's, Uc., a2, a4, &e., proceeds exactly as in the simple case, and as a’; = Gya,, a’; = Gia, ke, a}, a3, a5, &e., can then be obtained, e - 64 Prof. T. R. Lyle on the Theory of 20. In §16 it was shown that the iron loss (2. e. energy dissipated per sec. in the iron) in a magnetic circuit is +2 eh sin 6, ; hence the loss due to the flux A, § 18 is 2 20299, Sin dyna, + 5 (4-1 + 944) and that due to the flux A, is u 5 Vv? —_————.” ZOLT Jy Sin 89-7 (%g-1—%q +1) Adding these we find that the total iron loss in the generator 13 | yas Se ES ; 2 3099, sin By {nay + ¥ (ay 1+ 2941) + 7 (%g-1—#941) He , Expanding and remembering that SED ie ied A ~ atPB =a?+)?+2aB cos «B, and that to [reo = —t Gay (see § 19) we find that the total iron loss is equal to . 2 ma 3 Ez 7 Sin 6g 15 (22_,+ 4s) — n'a } — { sin? 6,+ ql’ sin 6, cos a, } at] where gq is odd. 21. An approximate determination of the effect of iron loss on the performance of an alternator can be obtained by taking all the G operators for its magnetic circuit as equal to Gy, that is, equal to the one for the fundamental harmonic of the armature flux. Making this simplification in the equations of § 19, we find that a,, a3. as, &c., 29, %, &e., are connected by the two series of equations tgp tte tai = 0 .) a&y—1 + Tptp + Apt} = 0 the Alternate Current Generator. 65 with a, = 2m/o, in which 2 Pee See ey ; sere e. yO. 2 w= ogy natl— = epre = 4" + gq. quay J 1 eta 2 S54 Baan P = it Ca me nv inion, y) Bee "Ge paling : for 4 gn’, © for gv’, m for gnv, aad—remembering that 6 is a small angle (see § 17)—unity for cos 6, we find that ty = Duh 9. T) = Apt, where P 4 ne 9? Lae Dp ==9 7 (141)? + = 5 +2—sin 8 m* Go q@ ES oy De D, sin fy = ens sin 6 Ap = aa LOTR) + 2 2 42 ina} 2 Hs : 2p A, sin $y = ner sin 6. The ¢ aha t operators having been calculated from these formule, the rest of the solution for this case follows in every particular the course for the simple case fully ex- plained in $§ 8, 9. 22. In order to illustrate the practical application of the foregoing theory, I will determine the performance of a small two-pole alternator when carrying a rather heavy non- inductive load. The details of the alternator are as follows :— ' ( diameter 12 cm. lenoth 8 cm. Armature ji n=100. resistance *25 ohm. Air-gap =1 mm. turns v= 400 Field resistance p=3 ohms. exciter, three storage-cells ; r=6°6 volts. Frequency 100/z, 1. e. o=200. Magnetic leakage=5 per cent. Flux operator G=5000 i-®. Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. F 66 Prof. T. R. Lyle on the Theory of Let the external resistance in the armature circuit in the case In hand be 4°75 ohms so that r=5 ohms. Hence (see § 21) Vee Dao = 050 = *20 . 10% Pie ob aal Oem he Oo 4 E10! m == 2,108, n=), Oe, p =o. w = 200, C= o- and = 2n/p = ‘44 (absolute). Using these values for the constants and the formule in § 21 we obtain the ¢ and 7 operators which are given in the following table :— tgq=Da — So To=Apt Pp. | Dg Sa p. Ap op 1 “592 24° 51’ 2 84 0° 22' | 3 "535 8 48 4 8:4 8 5 -530 5 18 6 8-4 1' 7 +528 3 45 8 8:4 =P 9 527 2 54 10 8:4 - 11 “526 as | 12 8:4 ae 13 526 T 5y 14 8:4 andl Dee (3 526 1 40 16 8:4 ql | 17 “526 1 28 18 8:4 a7 [Note that the 7 operators are all practically equal and simple numerical multipliers (see § 8). | And from these, by the method explained in § 8 we obtain the S, =, continued fraction operators which are given in followi ing table :— Sg=sqe Pa: Sp=opt Pp: | q Sq bg Pp. op Bp | 1 "457 562 te 2 5°82 7° 46’ | 3 *366 15 32 4 5°63 5 aS Eb *353 9 50 6 5°57 3 40 7 350 909 8 5B 2 54 | 9 "348 5 384 10 Dae 2 18 11 346 4 30 12 5:51 1 bt 13 *346 3. AS 14 5°50 L a And from these as explained in § 9 we obtain the different harmonics of both the armature current and the induced field current. These also are given in tabular form:— the Alternate Current Generator. 67 | | : | r= xq sin (qut—5 -+¢9). £=°224-Dépsin (put += +yp). | | er ae tq | eq Pee NS YP } __ —— —— : 1 ey 0 oOo, Sz 2 ) 166 44° 18 vec the | yee EI A dene Ga 58 | ) | “228 | 74 48 6 O41 78 28 | Pelee iy, | 85-87% | Cras me foc ( cs Nina OFT ae 11 | 9 ee OF oe A: ih SOLE |, 96 28 / ll 032 100 53 S| 12 006 102 44 ) 13 017 | 106 26 | 14 003 107 47 | The virtual armature current in amperes being equal to 10 W327 is 775 amps., and the terminal virtual voltage being 4: 75 times this is 36°8 volts. The no-load voltage for the same exciting current is 62°2. The virtual value of the alternating current induced in the field circuit in amperes being equal to 10 7 32E is 1°34. The copper losses are :— Ll ESE a ee 15 watts. In the field due to exciting current... 12 ,, In the field due to induced current... 5°4 ,, The total iron loss calculated by means of the formula in § 20 is 20 watts. The total losses are therefore 52°4 watts, and as the output is 285 watts the efficiency is 84 per cent. Fig. 3.—Theoretical armature current (x), and induced field-current (&), in a fully loaded alternator. See Se et isd eb ) eee o ee mae OO ee In fig. 3 are plotted the wave forms of both the armature F 2 63° Prof. T. R. Lyle on the Theory of and induced field-currents determined above, correctly as regards both their relative amplitudes and phases. 23. In desi ening the field of an alternator attention should be given to the fact that the conductor has to carry not only the exciting current, but also the induced field-current, which, as we have seen, may at full load attain a relatively large value. In addition it should not be forgotten that in the field-magnet cores there is the associated alternating flux which causes some additional heat. | It is well known that in a case of excessive heating in the field, reduction of the heating is effected by the employment of heavy closed copper conductors, called dampers, embracing the field-magnet poles. EG explain this action, let us consider a two-pole machine on each field pole of which is a damper. Neglecting magnetic leakage and iron loss, if ¢ be the eurrent in each “damper, the magnetic flux through the armature windings 1s gina + (vE +28) cos wt, and that through the field windings and the dampers is g{vE+ 26+ nex cos ot}, so that the equations connecting wz, &, and € are re + gna a: 7, ine +(vE+20) cosat}=0, | pE+ gy -{vE-+ 26-4 ne cos at} =), re « 7( eee 2o+g © (E+ 2f-+ne00s at} =0, ) where < is the resistance of each damper and the other symbols have the same significations as in the previous sections of this paper. Obviously there is no constant term in band considering only the variable terms (harmonics) in &, we see at once that. veb= pé, from which it follows that vet 20=vE(L+«)=vE' say, where pa vz and that the Alternate Current Generator. 69 The first two of equations VII. may now be written . r wt gn S fre aN cos gi 0, n 1+’ / I ns er +05, rata + nv cos aes 7 being divided by ine as the constant term in &' is equal to the constant term in & (€ having no constant term). Now wz and & determined from these equations will be very approximately the same as 2 and & determined from the equations in § 1 for the alternator without dampers ; for a) the given vector is the same for both, as are also all the ¢ operators. The 7 operators differ 1 a that for p, o/(1-+e) i is substituted, but in § 8 and in note § 22 it is shown that the r operators for generators as podem constructed are practically inde- pendent of the value of p the field resistance. Hence we see that & is the alternating field current if the dampers are absent, & its value when the dampers are attached and these currents are connected by the relation f= (1+ «)€. In addition as 2-0? = Kp&, Cian 2 1 Shere ue 2 pe =" 26 eer Hence if H’ be the copper loss in the field coils due to induced alternating current when the generator is without dampers, H the same when dampers are attached, and h the loss in the dampers when attached, H’ KH’ Hl . = te” ES Cae H+h= vas, If we assume that the mean length of a field turn is equal to the length of a damper turn, it is easy to show that « is the ratio of the volume of copper in the dampers to the volume of copper in the field windings when there is no resistance external to the windings in the field circuit. If there is resistance external to the windings in the field circuit, « is greater than the above volume ratio. The magnetic flux in the field coils being equal to give’ tnx cosat} is practically unaffected by the presence of dampers, so that the iron loss in the field-magnets remains the same. 70 Prof. T. R. Lyle on the Theory of 24, If a source of alternating u.M.F. = E where E = By sin (wt +) + By sin Bet +h,)+&e., =e, te;+e,+ Ke. (vectors) be included in the armature circuit, {and if the armature rotate in synchronism with this E.M.F., we have the case of the synchronous A.C. motor. In this case the armature and field currents 2 and & are connected by the equations (see § 1) Ta + £ (le +mé& cos ot) => Kg sin\(gat + hg) pe+ £ (ne +m cos wt) =7. Assuming as in § 2 that v=ataztas+c., E = . + a+ a,+Xe., and proceeding exactly as in § 5, we obtain the infinite series of equations ta, + = —a4)—K, a, + Tt, + ag ==) |) Ag+ f33 + a4 = —K; Ay + Ty, + a5 = 0 a4 +tsas5+ ag = —K5 SIGs, | WCs, in which a=the vector to the point 2n/¢, 7/2, as before 2 3 b Qs qin@ and Kg = where Seg isthe applied E.M.F., and the¢ and 7 operators have the same values as in § 5. Solving for a, we find that Pia = — ITo(a@9 + K)1 —IT,(«3); rt II,(«K;),;—e., where P,, I., Ty, &c., are the infinite determinant operators whose leading terms are t,, T2, Ta Ts, &c., respectively as in § 6. the Alternate Current Generator. 71 Reducing to the continued fraction operators of § 7 we obtain Bi I 1 a= — a Get eoi S38, (2 - 5,5,5,3,5, M1 Ke and using the equations a5 = —)a,—a)9—K, 3 ag = = T 9h, — a, 3 &e., the successive harmonics of the armature and field currents can be obtained. 25. If in the last example the E.M.F. inserted in the armature circuit be sinusoidal and equal to E sin (wt+ h) =e (a vector), the solution will (see equations in last paragraph) obviously be identical with that for the simple generator given in §§ 5 et seq., when in the latter ay+« is substituted for «) where Tv 2 2 kK =— te, am and in this case it is important to know the condition which determines whether the machine will run as a motor and develop mechanical power. In § 12 the driving torque T was shown to be given by T —— 7 {Sapa — Saja + Saoaz + Sasee, — &c.} and T must be negative for a motor. Now, as i ubi a; = —g (+e = ——(a+k); (see § 8) 1 at 1 2 5 +b Saga, = — a { Sag » Pre + as Say .t ; e} i l firs, & 2 56 a ay sin bj + ye eae (b.+i) }. Again, as } 3 Pa a4a=—_—_>-= =—-— — 2 pas 1 Co ls sin By - n Bo Saja, — ed a,” ds (a +4) 5 2 1 %2 similarly Buty Dal, Sa.a5 — : (a + K) ; &e., &e. 3 ae A ame 72 Prof. T. R. Lyle on the Theory of but i (ag-}-K) = ao? +x? + 2a K cos a Sa 52 4 - = ay + ——5 2 + —-mecosh ; wm wm and if > sin Bs 4 ais bs pans + Xe., sy? Oo $1°02"S3 Sj F953 04 we find that EN ks sin 4 “4B ha i + Z = {ee oe +h) +2B cos hha Aye 4m 3 Be? > 1 hich must be negative if the machine runs as a motor. Now, 51, 2, 83, 4, &¢., sinby, sin By, sin bs, are all essen- tially positive and therefore B is so. Also a and e are essentially positive. So,-in order that the machine may work as a motor, h, the phase angle of the applied E.M.F. must have such a value as to make the above expression for T negative. The power supplied by the source e being the mean value of the product of e and wz, that is of e and ay, that is of e and 2 ti (a+) 1S S] = — 5— %esin (h—bi) + 9 : ex sin by (see § 11) a8} 251 Py Eee ae es 95, fo sin (kh—b,)— sor esin by b. It is interesting to note that the armature and aiternating- field currents which flow when an E.M.F. = Hsin (wt+h) is acting in the armature circuit, the angular velocity of the armature is w, and the exciting current C, would be un- changed if the E.m-r. Esin (wt+h) be removed, the speed maintained, and the exciting field-current changed from C toa /C2+ = This follows immediately om the vector lion in § 31 connecting a, a, az, &e., with a,+« when ks, Ks, Kz, &C., are zero. 26. The case of the synchronous motor with sinwounial applied u.M.F., discussed in the last paragraph, can easily be represented geometrically. nee the Atternate Current Generator. 73 In fig. 4, let Oxo, taken in the axis of Y be equal (as in § 13) to twice thie steady exciting current of the machine. Draw Fig. 4. the vector OE! to represent in amplitude and phase 2/wm times the applied E.m.F. ; that is, if the latter =e'sin(wit+h), OH! = 2e/om, and the angle from OX to OH’ measured in the positive direction is = h. Rotating OH’ forward through 90° gives us « of § 25, and completing the parallelograin 2Okx, its diagonal is a) +« in the line OY’. Knowing the motor circuits, we can determine s,, bj, >, Be, $3, 03, &e., and then construct for aj, a, as, 24, Kc., exactly as in § 13, except that in this construction the vector aj+« takes the place of a in § 13 (see § 24). Now the mechanical torque developed by the machine is (see § 12) = 4 ” SSeeoay + Saya. + Sa.a;+ Ke.} m. : = ginto the sum of the areas, attending to signs, of the triangles ajQa,, a,O«, «,0a3, &e. But the triangles a,Oa,, #,Oa;, a,;02,, &., are all essen- tially negative [their sum is = —4Ba)+x? of § 25], so that if the machine is to develop mechanical power and run as a motor, the phase of OE’ must be such that the area of the triangle 2 jVa, is positive (as it is in fig. 4) and numerically greater than the sum of a,O,, «0a; Ke 74 Prof. L. R. Ingersoll on Magnetic The power supplied by the source is _1l oma; =o oe OH’. a, cosa,OH’, ON. — « = ——a,« sin a,Ok, 4 am 2 x area of triangle a,O«, and the power developed by the motor = wT = = x sum of areas of the triangles «Oa, a,;Oa,, «.Oa;, &e., attending to signs. Hence the efficiency is equal to Oa; +8,O0%, + a.0a;,+ Ke. a,Ox« F By rotating the vector from O to the middle point of Goa backwards through 90° and doubling we obtain OK,, which represents in amplitude and phase 2/mw times the first harmonic of the total u.m.¥. of the motor (see § 13). This vector can now be compared with OE’ which repre- sents 2/mw times the applied E.M.F. Fig. 4 easily explains how, by increasing the exciting current of an A.C. motor, the phase of the armature current is advanced relative to that of the applied E.M.-F. IX. Magnetic Rotation in Iron Cathode Films. By U. R. _ | Incersout, Ph.D., Assistant Professor of Physics, Univer- sity of Wisconsin*. [Plate I.] Part I. The Bolometric Method of Measuring Rotations. Part II. Rotation dispersion Curves for the Faraday and Kerr Effects in the Infra-red Spectrum. Part III. Dependence of the Kerr Rotation on the Refractive Index of the Overlying Medium. INTRODUCTION. § ace purpose of the present work has heen an experimental study of certain problems in the magneto-optics of the magnetic metais, viz. the Faraday and Kerr effects for a long range of spectrum ; the thickness of the surface layer which * Communicated by the Author. This work has been aided by a grant from the Rumford Fund of the American Academy of Arts and Sciences, for which the writer wishes to express his appreciation. Rotation in Iron Cathode Films. to gives rise to the Kerr rotation ; and the relation between the Kerr rotation and the optical density of the surrounding medium. These questions have been studied for the simplest typical case,—that of iron in the form of thin films, the cathode film being chosen for reasons which will appear later. | The rotation of plane polarized light on transmission through thin metallic films in a magnetic field has been studied by Kundt*, Du Boist, Lobacht, Righi§, Harris ||, Skinner and Tool{], and others. This effect, discovered by Kundt, has since been measured for light of various wave- lengths by other investigators, and so-called rotation disper- sion curves thus obtained for films of iron, nickel, and cobalt. Recently Harris made some very careful determinations of such curves for iron films deposited cathodically in atmo- spheres of hydrogen, nitrogen, and oxygen, while Skinner and Tool find that, independent of changes in atmosphere, two different sorts of films with different rotatory powers may be produced for some metals by the cathode discharge, and moreover that the rotation for any wave-length bears more or less relation to the absorption for that wave-length. An effect quite similar to this of rotation by transmission through a magnetized film, and which, doubtless, owes its existence to quite similar if not identical causes, is the so- called Kerr effect, or rotation of the plane of polarization upon normal reflexion from a polished mirror held perpen- dicular to a strong magnetic field. The mirror may be of iron, cobalt, nickel, or magnetite, and indeed in the earlier experiments was formed by merely polishing one end of a pole-piece of the magnet. The work of Kerr** was extended by Du Boist+t, who determined the variation of this effect with wave-length for mirrors of the above-mentioned substances. Such rotation dispersion curves resemble those obtained for the case of transmission through thin films, in that they are anomalous, showing in general an increase of rotation with wave-length, as far as the limits of the visible spectrum, instead of a marked decrease, as is the case for practically all transparent * Wied. Ann. xxiii. p. 228 (1884); xxvii. p. 191 (1886). + Wied. Ann, xxxi. p. 941 (1887). t Wied. Ann. xxxix. p. 347 (1890). § Mem. R. Accad. Sc. d. Bologna, 1886, p. 443. || Phys. Rey. xxiv. p. 337 (1907). ‘one Paper read before the American Physical Society, Chicago, Dec. 7. #* Phil. Mag. [5] iii. p. 339 (1877). t+ Wied. Ann, xxxix. p. 25 (1890); Phil. Mag. [5] xxix. p. 253 (1890). 76 Prof. L. R. Ingersoll on Magnetic substances. Moreover, the rotation, while of about the same order of magnitude in the two cases, is opposite in sign, a point not satisfactorily, or at least simply, explained by the theory. Complicated phenomena, which have been studied by many other observers, arise for cases of oblique incidence or of magnetization parallel to the surface, but in the present work we shall consider only the more common case of nearly normal incidence, and of magnetization perpendicular to the surface. A few years ago the writer* developed a method of measuring such magnetic rotation for wave-lengths of the infra-red spectrum, and supplemented the work of Du Bois by extending his curves to about X=3'5y. The striking thing shown by these curves was that the rotation in each case reached a maximum for wave-length about ly, and decreased rapidly for longer wave-lengths. Moreover, in the case of nickel the rotation changed sign for wave-lengths longer than 1:4, while for magnetite the case was still more complicated. It was desired at the time to proceed at once with measure- ments on thin films of the magnetic metals, but the determi- nation of such small rotations was too difficult and uncertain a process withthe apparatus as it then existed. Accordingly, the method of measurement was considerably modified, and thereby greatly improved, and the apparatus almost entirely rebuilt on a more extensive scale, with a more careful working out of details ; this has made possible the handling of the sort of problems it was desired to take up in this investi- gation. Aim of the present work.—This has been: First, to measure the transmission, or Faraday, rotation for iron films of various thickness for as wide a range of wave-lengths as possible (X="6 pw to 2°2 w), thus supplementing the work of Lobach, Harris, and others by extending their curves over a spectral region of greater extent. Second, to determine the reflexion rotation, or Kerr effect, for the same films and in the same magnetic field, with the view of correlating as closely as possible these two rotation effects due to transmission and reflexion respectively. . Third, to study the dependence of the Kerr rotation on the thickness of the film, a problem suggested by Kundt, and left by him after some preliminary observations with the hope of more careful treatment later.. Fourth, to study briefly the effects of oxidation on the forms of the rotation dispersion curves, and the general relation between absorbing or reflecting power and rotatory power. Fifth, to * Phil. Mag. [6] Ixi. p. 41 (1908). Rotation in Iron Cathode Films. 77 investigate the effect on the Kerr rotation of overlaying the surface with liquids of various refractive indices. These questions are discussed in Parts II. and III. of the present paper. Iron has been chosen as a working substance for these experiments as it gives the largest, and hence most accurately measurable effects, but it is intended in the near future to study part or all of these effects with films of cobalt and nickel as well. The cathode type of film has been used chiefly because it may be readily produced of any desired thickness and without a preliminary deposit of platinum, as would be required for electrolytic films and which would be very objectionable for some of the experiments. It is true that cathode films differ somewhat in optical properties from the massive metal, but the same may be said of the electrolytic film which is well known to be granular in structure. In some cases the cathode film appears to resemble fused metal more nearly than the electrolytic. Part [.—Tse BoLtometric METHOD AND APPARATUS FOR MBasuRING MAGNETIC ROTATIONS. This method with the necessary apparatus for measuring rotations for the shorter infra-red wave-lengths has already been described by the writer*, both in its original form and after important modifications had been introduced; but so many changes have been made since then that a brief description of method and apparatus seems desirable here. The essential difference, in the optical system, between this method and the customary process of measurement applicable to the visible spectrum, arises from the fact that any small rotation of the plane of polarization occurring between crossed nicols, or other polarizing agents, causes the greatest change of intensity when the latter are crossed at 45°, a principle recognized and used over half a century ago by Provostaye and Desainst. This, then, is evidently the most effective arrangement when a bolometer or other radiation measuring instrument is to be used instead of the human eye. In the first arrangement adopted, piies of thin glass plates were used as polarizer and analyser. Light trom a Nernst glower, after being polarized by reflexion, passed through the magnet and the rotating substance between its pole-pieces, and after reflexion from the analyser fell on the slit of a * Phil. Mag. [6] Ixi. p. 41 (1906); Phys. Rev. xxiii. p. 489 (1906). Hereafter referred to as Phil. Mag. Joc. cit. and Phys. Rev. Joc. cit. t+ Ann. Chim. Phys. (3) xxvii. p. 232 (1849). 78 Prof. L. R. Ingersoll on Magnetic spectrometer, to reach finally, after dispersion, the strip of a bolometer. On exciting the magnet the rotation of the polarization plane would cause a change of intensity of the radiation passing the analyser and falling on the bolometer, which change, when divided by the actual intensity of trans- mitted radiation of any given wave-length, gave a ratio proportional to the rotation for this particular wave-length. The Compensating Principle.—The foregoing arrangement was capable of yielding very fair results at a great expendi- ture of labour in observing, but difficulty arose from small and unavoidable changes of brilliancy of the glower which would appear as spurious rotations. After trying many ways of compensating for this, there was finally adopted the scheme of using as analyser a large double-image prism, placed so that each of its principal planes made an angle of 45° with the original plane of polarization. The two transmitted beams of equal intensity were carried through the spectro- meter, and after dispersion were allowed to fall on the two strips of a specially constructed bolometer. Any rotation would thus diminish one beam and increase the other by an equal amount—thus producing a doubled effect—while any small change in brilliancy of the glower would affect each beam equally, and hence give rise to no error. This was immeasurably superior to the former arrangement, and more than made amends for the small loss of range of spectrum its use involved; for the thick calcite prisms (the polarizing plates were also replaced by calcite) would transmit little beyond A= 2'5 pw. The very simple mathematics of this method have already been worked out in a former paper*, and we need take from this only the formula §=45/7 . dl/I, which gives for any wave-length the rotation 6 in degrees, when I is the intensity of radiation on either bolometer strip for this wave-length, and dI the relative change of intensity of the two beams. Use of High and Low Dispersion—One of the problems to be met in this work was that of securing, in spite of the many losses, a sufficiently intense spectrum such that the small changes of intensity amounting to perhaps less than 1/10 per cent. would still be readily measurable. Every effort had been made to secure this in the earlier form of apparatus by the use of large apertures and a brilliant source, hence as a still further increase was desired for the present * Phys. Rev. loc. cit. — Rotation in Iron Cathode Films. 79 work, it was necessary to resort to a reduction of dispersion. But this would mean a sacrifice of certainty of wave-length, and would magnify the rather uncertain errors due to the width of the slit image and bolometer strip in the spectrum. To avoid this two distinct sets of prisms and mirrors were used in connexion with the same spectrometer table, giving in the one case a very intense but correspondingly con- tracted spectrum, and in the other a spectrum of several fold greater dispersion, but correspondingly weaker in energy. In practice, then, some film or substance giving a relatively large rotation was tested with each of these combinations, and the two curves compared with a view of determining the effect of the lower dispersion, if any, in distorting the eurve. This correction could then be applied with assurance to curves obtained with films which gave such small rotations that only the lower dispersion arrangement could be used. Tests by Mechanical Rotation.— While in as simple a form as possible, to attain the desired end, the foregoing method is necessarily complicated when compared with the extremely straightforward ways of observing the same phenomena in the visible spectrum. Hence it is desirable to have some way of checking the results, or at least of applying a thorough test. This was done by mounting the polarizer in a divided circle: small and accurately known rotations were then given it, causing of course corresponding rotations of the plane of polarization. These were measured just as if of magnetic origin and checked with the known rotation produced mechanically. The results of this test, as well as of the measurements spoken of in the last paragraph, will be given later. Apparatus. In the matter of general arrangement of apparatus the former order was preserved, as will be seen from fig. 1. The whole was, however, mounted on massive slate slabs which rested on heavy wooden supports. The component pieces, with the exception of the optical parts, were con- structed in the shops of this Department. Electromagnet.—This had proved so satisfactory since its construction some years ago, that the only change necessary was the addition of cooling coils which carried circulating tap-water, and kept the ends of the pole-pieces at a nearly constant temperature. The method of excitation is worth brief mention. The winding, which consisted of about 6000 feet of No. 10 wire, was grouped in eight coils. The four pole 80 Prof. L. R. Ingersoll on Magnetic coils were most effective, and when excited with 16 amps. at 60 volts, gave a field of about 6000 units, which, while not as high as might be desired—on account of the large air-gap necessary—was very satisfactory for present purposes. Now Fie. 1.—General arrangement of apparatus. it was very desirable to have as small an external field as possible, particularly at the polarizer which had to be very near the magnet, and this was secured by a combination of series and parallel connexions of the remaining four coils, with suitable resistances, until a compass-needle remained unaffected at the position of the polarizer. This could be done without material sacrifice of the field due to the pole- coils. Optical System.—Light from the D.C. Nernst-glower G, in its firebrick enclosure was converged by the mirror M, to an image between the pole-pieces, and to another image on the slit of the spectrometer by the mirror M,. A double image prism P of 4°5 cms. aperture served as polarizer, only Rotation in Iron Cathode Films. 81 one of the two beams being used. It was mounted in a massive brass conical bearing B, and could be rotated by a micrometer tangent screw to produce an accurately known mechanical rotation of the plane of polarization, as mentioned above. The analyser, A, was a slightly larger double image prism of 5 cm. aperture. Spectrometer.—The two images (of the glower) from the analyser, each about 1 cm. long, fell vertically over one another on the two parts into which the slit was divided by the diaphragms D, D (fig. 2); and shutters, Sh, allowed Fic. 2.—The slit and its accessories. 2 = EI | Z iA Z 2 I ro Fo) LEA i a Se ee ae ,e ‘y / 1 L aty vs wee I ',? i i ee a eee 8 dey each beam to be cut off separately. The sliding shade, Sl, was necessary for the following reason:—It was required that the initial intensities of the two spectra as they fell on the bolometer strips should be equal. This was accomplished by Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909.° G | 82 Prof. L. R. Ingersoll on Magnetic the two thin wedge-shaped shades, which, when moved across the slits, darkened one image by cutting off a small part of the centre, and at the same time lightened the other until the two beams were of equal intensity. Because of slight inequalities in the bolometer strips this adjustment had to be repeated for each new setting of the spectrometer. Hach of the prisms for the spectrometer was of glass instead of rock-salt as formerly used. There was no need of rock- salt in this case, since there was at best a considerable thick- ness of glass to be traversed by the light, in connexion with the double image prisms; and, moreover, glass has the advantage of giving a somewhat more uniform dispersion than rock-salt. The prism of lower dispersive power had a refracting angle of 25°, and was of ordinary flint-glass with faces 9x9 cms. It was used with mirrors of 35 cms. and 30 cms. focus respectively. The other prism had a 45° angle and was of extra dense flint with faces 9x 7:5 ems. The corresponding mirrors were of 50 cms. focal length each. This arrangement gave a spectrum from three to four times longer than the other. Bolometer and Galvanometer.—The former might be said to be of the differential type, as both strips were exposed, being vertically above one another. Hach strip was °5 mm. by 8mm. The balancing coils and slide wire were all self- contained, and the instrument was remarkably steady and free from drift. The galvanometer, which was of the Thomson astatic type, had a system weighing about 2 mgs., and was worked at a sensibility of from 3 to 5x 107-1 amp. per mm. for 6 ohms resistance. To free it from the influence of the magnet three large concentric cylinders of soft steel were used as magnetic shields, and in addition the coils themselves were embedded in the two halves of a mass of Swedish iron 3x5cms. This combination gave a shielding effect of over 6000 times. Proportionality corrections were applied to all galvanometer deflexions. It was necessary, in the process of measurement, to be able to reduce the sensitiveness of the bolometer-galvanometer combination in some known ratio. This was done by the use of four resistances which could be inserted separately in series with the galvanometer circuit, and which gavea graded reduction of sensibility of from 2°9 to 104°5 times. Control and Operation.——The various parts of the apparatus ‘were arranged to be controlled by the observer in front of the galvanometer scale. This was done by means of the five rods 7,7, 7, which operated respectively the spectrometer table, the sliding shade, the bolometer balancing arrangement, Rotation in Iron Cathode Films. 83 and the two shutters. An auxiliary rod also turned the micrometer screw of the polarizer mounting. Supposing everything in adjustment, the process of making observations was fairly simple. The spectrometer having been set at the wave-length for which it was desired to measure the rotation, the sliding shade was moved by means of its screw adjustment till both beams were of equal inten- sity, as shown by the galvanometer returning to zero. The magnet-switch was then thrown, and in a few seconds the reading taken. The current was then reversed and the new reading noted, and so on until a set of four or five readings at regular intervals of perhaps 15 seconds, had been taken for each direction of the current. The difference between the means of each set of readings would give the quantity dl], but it would also contain the small but still noticeable direct action of the magnet on the galvanometer. To eliminate this the galvanometer connexions were reversed by a suitable switch and the above process repeated, and a slightly dif- ferent value for dl obtained. The mean of these two values gave the true one. To measure the intensity I it was first necessary to reduce the sensibility by a considerable factor——usually 26°6 times—— by pulling one of the switches, Sw, thus inserting a series resistance. Then by closing each shutter separately two nearly equal values of I, or rather of I/26°6, would be given, the mean of which was used. As explained above, the ratio di/1 is proportional to the rotation occurring on reversal of the magnet. By repeating this process for a dozen or twenty wave- lengths distributed over the spectral region, in which it was possible to work, say from X¥="6 w to 2°24, a very good rotation dispersion-curve could usually be obtained. As in the previous work, all the more careful measurements had to be made at night. Large and Small Rotations.—In the determination of large rotations this method has very evident limitations when com- pared with visual schemes, but as the largest measurable angle, perhaps 30°, is many times what would be met with in any work with films, this consideration is of no importance. Of more interest is the question of the smallest measurable rotation. This is largely a matter of the amount of energy incident on the bolometer strips available for measurement, and hence depends on the part of the spectrum; also on the general conditions of steadiness of the apparatus. No especial pains have ever been taken to actually determine the smallest rotation which could be detected, but in practice angles of G 2 } 84 Prof. L. R. Ingersoll on Magnetic less than ‘003° have frequently been measured, and it is believed that, with care, rotations of three or four, perhaps even of single, seconds could be detected. PRELIMINARY MEASUREMENTS. Calibration of Magnetic Field.—It was desired to test the transmission and reflexion rotations of films under exactly the same conditions of field strength. Since they could not be located in the same part of the field for the two tests, this necessitated a calibration of the field. To do this a small flip-coil was used having the same area as that of the cross. section of the beam as it passed through, or was reflected from, a film. From a large number of measurements curves. were plotted showing the variation of field strength with position and with magnet current; and the current was accordingly adjusted in practice to give the same field strength whatever the position of the film. | Sensibility Reduction Factors.—As a very exact knowledge: of the reduction effect of the series resistances on the galvano- meter-bolometer sensibility is required, this was measured in three ways:—by astep by step process ; by the use of rotating sectors; and by computations from the results of mechanical rotations of the polarizer. Four resistances giving reduction factors styled A, B,C, and D respectively, were used ; and in the step by step way these factors were measured by comparing the effect on a certain galvanometer deflexion obtained, with full sensibility of the introduction of the resistance A. This was then similarly compared with B and the process repeated for Cand D. Very careful galvanometer proportionality cor- rections were required for the success of this method, and at best there are certain theoretical objections to it. In the second way, by the aid of a rotating sector which transmitted only ~), of the incident light the reduction factor C was measured by the comparison of two nearly equal galvanometer deflexions. For the energy transmitted by the rotating sector and measured with the highest sensibility gave almost the same throw as the total energy measured with the resistance C inseries. The values of A and B were likewise determined with the aid of suitable sectors. By rotating the polarizer through small and accurately known angles, a third series of values was obtained, for these rotations were measured just as if they were of electromag- netic origin ; and, by computing back, the necessary values to be assigned to the reduction factors were easily found. These values agreed very well with those determined by the last method, as may be seen from the following table. Rotation in Iron Cathode Films. 85 Papen, Values of Sensibility Reduction Factors. A. B. C. (1) Values given by step by step method .. 2°95 9°45. 27°25 (2) Measured with rotating sector........ 2-90 9-20 96°70 (3) Computed from rotations of the polarizer 2°92 9°15 26°45 Accepted values........ 2°90 9:20 26°60 D, which was rarely used, was found by comparison with C to be 104°5. This table is of interest in that it gives an idea of the maximum accuraey which could be expected of this way of measuring magnetic rotations, or rather, of the largest error which is likely to enter from this source. It is true that sets (1) and (2) disagree by 2 per cent., and (1) and (3) by 3 per ent. ; but, as stated above, method (1) is not as free from objection as the other two, whose results differ by less than 1 per cent., and this is estimated as about the probable error. Correction for Errors due to Low Dispersion.—This was determined, as previously indicated, by comparison of the two curves made with the same rotating substance under the two different conditions of dispersion. As might be antici- pated, the error in determining any particular rotation is dependent not oniy on the wave-length, that is, on the position of the point on the curve, but also on the actual form of the curve. Furthermore, the largest error is to be expected when we have the combination of an energy curve rapidiy increasing—as the Nernst-glower energy curve in the early infra-red—and a rotation dispersion curve rapidly falling, as is the case for glass and similar substances. This is well shown by the rotation dispersion curves of fluorite in Pl. I. fig.3. The rotations on the upper curve are 30 per cent. higher at ‘65, and the difference gradually lessens until they are equal at 2°0m. An extrapolation to give the true form of tbe curve as determined with a spectrum of great dispersion would raise the upper curve by only about 1 per cent. That the correction is much smaller, if not negligible, when the rotation increases with wave-length in the early infra- red is indicated in Pl. I. fig. 4. The curve is for rotation on reflexion from a polished steel mirror in a field of 5700 units. Itis essentially identical, though plotted somewhat differently, with the curve as measured for the same mirror with the earlier form of apparatus *. The corrections for a third type of curve—a horizontal straight line—could be deduced at once from the figures in Table II., and are negligible. With * Phil. Mag. loc, cit. p. 65. 86 Prof. L. R. Ingersoll on Magnetic. these three types it will be possible to estimate the corrections with ample accuracy for any of the curves discussed in the present paper. Most of them, as a matter of fact, are of the latter two types. 2 Sources of Error. Accuracy of the Method. The writer has previously discussed t a number of sources of error incidental to this work. In the present case an attempt, at least, has been made either to remove these or make them subjects of special experimentation, with a view of determining the magnitude of the errors they introduce. It would seem then that the accuracy with which magnetic rotations can be measured in the infra-red is largely dependent on the care with which the preliminary experiments have been carried out. Fortunately it is possible, as previously stated, to get a check on this accuracy by making known mechanical rotations of the plane of polarization and measuring them just as if of electromagnetic origin. ‘Table II. shows the results of these tests. The rotation of the polarizer of 1°°178—pro- duced by six complete turns of the micrometer tangent-screw —was measured with the apparatus for a number of wave- lengths and with each of the two sets of prisms and mirrors. Lest it be very reasonably objected that the mechanical rotations have been already used to determine a series of values of the reduction factors A, B, C, and D,—and that if these values are used the table would necessarily show a correspondence,—the series (2), determined by the preferable or rotating sector process, has been used in this computation. TABLE II. Test of Accuracy of Method by Measurement of a known Rotation of 1°178. ; ] Wave-length. With 45° prism. || Wave-length. | With 25° prism. 69 pw *L-LOLS ‘59 1:166° ‘75 *1°158 | "64 1-160 ‘81 1170 ie 1170 88 1.163 "85 1-172 ‘98 | 1174 1:04 1:168 1:23 ) 1169 j 1:31 1:170 161 | 1170 | 1 64 1171 1:84 GO) UE 1:97 1178 2°01 1-189 | * The smaller amount of energy makes measurements in the shorter wave-lengths less reliable. +t Phil. Mag. foc. cit. p. 51. Rotation in Iron Cathode Films. 87 It will be seen from the above table that the actual and computed rotations usually differ by 1 per cent. or less. This, then, may be taken as about the order of the outstanding probable error of rotation measurements in this work. It is about as great an accuracy as may be reasonably expected in almostany spectro-bolometric or radiation work, and is ample for the present investigation. In the matter of certainty of wave-length, as great accuracy cannot be claimed as might be expected in radiation problems where a spectrum of large dispersion and a very narrow bolometer-strip can be used. The spectrometer was calibrated in the present case by double dispersion tests, using a rock- salt prism on the second spectrometer to fix the wave-length scale. Each of the two prisms was tested several times in this way. For the 25° prism the estimated probable error rises from a few thousandths of a micron in the visible and early infra-red to about ‘Ol wat A=1'1ly, and is perhaps three or four times as much at 2°34. For the 45° prism the probable error hardly exceeds ‘024 anywhere. It must be remembered, however, that the bolometer-strip covers a much greater width of spectrum than this ; hence the deter- mination of a rotation dispersion curve which had sharp bends or dips corresponding to sharp absorption-bands would be practically impossible. Part J].—Roratrion DISPERSION CURVES FOR THE FARADAY AND KERR EFFECTS. Deposition of Films.-—The films were deposited cathodically on pieces of microscope cover-glass in an atmosphere of hydrogen, an induction-coil being used as a source of current and a small spark-gap introduced in the secondary circuit to make it practically one directional. A flat coil of pure iron wire, making a disk of 2°5 cms. diam., served as a cathode, and the best results were obtained with a vacuum of a fraction of a millimetre, and with the pieces of cover-glass just outside the cathode dark space and about 1 cm. fiom the cathode. It was possible to use thin microscope-cover glass as a backing for the films, in spite of its poor optical surfaces; for it will be noted that in all cases the film was placed where the beam of light converged to a focus. Hence the loss of light occasioned by the departure from planeness of the surfaces was immaterial, while the advantage of having only a small thickness of glass is evident. Considerable care was required to secure films which were sufficiently uniform over the required area of 4x15 mms., and free from oxidation. With the first induction-coil used— 88 Prof. L. R. Ingersoll on Magnetic one furnishing a high voltage and small current—it was almost impossible to avoid a certain amount of oxidation. This gave place to a smaller coil, furnishing a larger current and taking a much shorter time—half an hour or less—to deposit a film. Still later a 2000 volt generator set was used, but most of the films discussed in the present paper were deposited with the smaller induction-coil. Oxidation, when present, was readily detected by the brownish colour imparted to the film. It was doubtless caused by the minute quantity of occluded air which would still remain even after repeated washings with hydrogen. When, however, the greatest care was taken in getting rid of this remaining air by frequent washings with dry hydrogen, between short periods of electrical discharge, films were obtained which were quite colourless, of a greyish appearance when thin, and looking like smoked glass when thick. This accords with the description of Houllevigue * of the appear- ance of iron films free of oxidation. The films were kept in an atmosphere of dry hydrogen when not being used, and did not deteriorate appreciably for many weeks. When left for some time in moist air they slowly oxidized to a yellow colour. Measurements.—About forty films were deposited in all, in lots of two or three ata time usually, and perhaps half of these tested. Out of this number four have been selected which had suitably varying thicknesses and which showed almost no traces of oxidation; and the curves made from these are shown in PI. I. figs. 6-9. Fig. 5, eee The rotations shown in the “transmission ”’ curve were measured with the film in position A, fig. 5, the pole-pieces * Jour. d. Phys. (4) iv. p. 406 (1905). Rotation in Iron Cathode Films. 89 being in line. The field was approximately 5700 c.G.s. units with a magnet current of 16 amps. For the “reflexion” curve the film was held in position B and a piece of plane silvered glass placed at C. The beam striking the silver surface would be reflected to the film and from this through the other pole-piece, which was thrown out of line to the dotted position to allow the passage of the beam: it would then follow practically the same path as in the first ease. The reflexion at the silver surface did not affect the polarization of the beam and the departure from normal incidence on the film—about 8°—was well within the limits of 15°, for which, as shown by Righi%*, the rotation is prac- tically the same as for normal incidence. This arrangement, then, served the purpose of the customary optical system in which the normally reflected beam is turned aside by a plane glass plate at 45°; such an arrangement would be of difficult, if not wholly impossible, application in the present problem. With a magnet current of 13-7 amps., the field in this position was identical with that in position A. Corrections.—F ollowing the practice of Kundt, the rotations given by the curves and tables of the present paper are for ‘the reversal of the magnetic field, unless otherwise specified, and hence are really doubled values. They were all deter- mined with the use of the 25° prism, and therefore, as has been noted in Part L., some correction may be necessary to ‘the measured values. Butit will be observed that the curves may be considered as partly straight lines and partly of the type of Pl. I. fig. 4; and in either case the corrections are negligible. For the transmission curves, correction has been made for the rotation due to the glass on which the films were deposited. This was small—as the glass was only ‘18 to*22 mm. thick,— but by no means negligible, for in some cases it may be com- parable with the rotation of the film itself. 1t was carefully determined for selected sample pieces (correction being made for the use of 25° prism as indicated in Pl. I. fig. 3), and in each case the correction applied was proportional to the thickness of the paiticular piece of glass on which the film was deposited. In Pl. I. figs. 6-9 the dotted curves give the rotations as measured while the solid line curve has been corrected for the glass rotation. The curve for the glass alone is shown in PI. I. fig. 6. To be certain that no other influence than the magnetized film was causing rotation, trials were occasionally made for rotation on reflexion from two silver surfaces, instead of one * Ann. Chim. Phys. (6) ix. p. 182 (18886). 90 Prof. L. R. Ingersoll on Magnetic silver and one iron. Such rotations were always found to be extremely small. One has been plotted in Pl. 1. fig. 6, and denoted by the letter S. It amounts to only about -002°. It is undoubtedly true that the results as given for the thinner films are somewhat in error because of multiple internal reflexions, but it would be hopeless to try to allow for these until we can separate more clearly the two rotation effects and perhaps localize the reflexion rotation. This error is not considered of importance except in the case of the very thinnest films. It is also a fact, from the work of previous observers *, that transmitted light from a magnetized film is slightly elliptically polarized. This would not, cause any error in the present work; the rotation measured would be that of the major axis of the resulting ellipse. Absorption Measurements.—It was thought to be of interest to determine if the absorbing and reflecting powers of the films showed a variation with wave-length corresponding to: the rotation. Accordingly measurements were made of the transmission of each film, as well as of the reflecting power (by comparison with silver) of the front and rear surfaces. The curves for several films are shown in PI. I. fig. 10, where T, the transmission, is approximately equal to e-“, a being the: absorbing power and ¢ the thickness. No attempt has been made to correct for the complicated system of. internal reflexions : this is in itself an extremely difficult problem for films as thin as some of these. The values of T have been obtained by merely dividing the fraction of radiation trans-- mitted by 1—R, where R is the reflecting power of the air-film surface. While not possessing the accuracy of the rotation measurements they serve very well to indicate the selective or non-selective character of the absorption or: reflexion, which is the only part in which we are particularly interested. It will be noted that the transmission—and therefore also. absorption—for the pure iron films 15, 22, and 24 is almost: non-selective or independent of wave-length. The same is true for film 17 whose curve is not shown. This explains. the greyish colours of these films, and, in agreement with the conclusions of other observers as already pointed out, is. accepted as evidence of their freedom from oxidation. The curve of reflecting power with wave-length for film 15 is incidentally shown in PI. I. fig. 13. It shows a slight increase of reflecting power in the infra-red, as is the case with pure: iron in the massf. Film 17 showsa slightly greater increase- * See Harris, Phys. Rev. xxiv. p. 337 (1907.) + Hagen and Rubens, Ann. d. Phys. vill. p. 1 (1902). Rotation in Iron Cathode Films. OT of reflecting power with increasing wave-length, while films 22 and 24 show a somewhat greater decrease, but on the whole the reflecting power for the pure filmsis also relatively non-selective. Thickness of Films.—The absorption and reflexion data would afford a possible means for determining the relative thicknesses of the various films; but, as Houllevigue and Passa * have shown, it is more accurate +o compute the thick- nesses from the rotation produced, since this is proportional to the thickness. Accordingly the thicknesses of the four films already mentioned, 15, 17, 22, and 24 have been com- puted in this way, assuming Houllevigue and Passa’s data and iron cathode films, as approximately 58 up, 30 wy, 13 wy, for 8 wm respectively f. Kundt’s results for films by electrolysis would give thicknesses about one third smaller. Very Thin Films.—Tests were made also on a number of very thin films, some of them less than 0°5 wp in thickness, but the results are of questionable value, particularly those for rotation on reflexion. For in such thin films reflexion would take place not only at the first or air-film surface, but also at the film-glass boundary and at the glass-air or rear surface, and, because of the small loss on transmission, these three surfaces—or at least the first and last—would each return about the same amount of radiation. The latter part was generally excluded by covering the rear glass surface with an absorbing mixture of the same optical density as the glass, 2. e. Canada balsam and lamp-black; but there would seem to be no way of separating the first two parts. In one case there was tried the experiment of depositing a thick film of platinum, and on this a thin film of iron. The rotation shown on reflexion was positive, as might be expected, due to the preponderance of the rotation of the doubly trans- mitted part of the beam. The only striking feature of the experiment was the enormously varying reflecting power shown by such a film, increasing from almost nothing in the visible to about 50 per cent. at X=2y. In general, the results on very thin tilms indicated a some- what larger reflexion rotation than the transmission. The latter rotation sometimes measured not more than °003°, with the reflexion rotation perhaps twice as large and frequently appearing positive in the early infra-red. Lect of Oxidation —Considerable data on this point have * Comptes Rendus, cxli. p. 29 (1905). t+ This scale of thickness has been checked to within a few per cent. by subsequent measurements, by interference methods, of films deposited on optical glass. See “Addendum.” a2 Prof. L. R. Ingersoll on Magnetic been collected, but the results on different films are somewhat at variance. This is in accordance with the observations of Kundt *, who found very complicated effects when the mirror for which he was measuring the Kerr rotation was oxidized. In general it was found, however, that films of a reddish or brownish colour—indicating more or less oxidation—gave curves similar to those shown in PI. I. figs. 11, 12,and13. The difference between these and the curves for the pure iron films is seen in the rapid decrease of rotation with wave-length after the early infra-red, This is particularly true for the. case of rotation on transmission, and was very marked in a film deposited in air instead of hydrogen, and which was presumably completely oxidized. Furthermore, the curves for rotation on transmission and reflexion do not show the same similarity as in the case of pure iron, and indeed in two of the cases shown the reflexion rotation appears positive for the shorter wave-lengthis. | The change in the character of the rotation curves is seen to be accompanied by a marked variation of the transmission with wave-length, as shown by the dotted curves of Pl. I. fig. 10. For the opaque partially oxidized film 29 of Pl. I. fig. 13 only the reflexion rotation and reflecting power could be measured, but each is seen to change markedly with change of wave-length. As to the effect of oxidation on the magnitude of the rotation, films 7 and 14 show smaller rota- tions than the pure iron films, although film 14 has about the same absorption as film 22. The reflexion rotation from film 29, however, is slightly greater for the early infra-red than that from film 15 or that due to a steel surface as shown in Pl. I. fig. 4. Inscussion of Results—The first fact worthy of note which may be deduced from the curves is that the magnetic rotation, either on transmission or reflexion, of iron, instead of in- creasing indefinitely with wave-length, as might be concluded from observations in the visible spectrum, reaches a maximum value shortly outside the limit of this spectrum. ‘This maximum rotation, which is reached for pure iron at about X= 15, is seen to be on the average a little over one and two-thirds times that for the wave-length of sodium light. In the second place it will be noted that while the Faraday rotation decreases by five times in going from film 15 to film 24, the Kerr rotation is only halved. In other words the reflexion rotation increases less rapidly than the thickness of the film and soon reaches a maximum value. That this has been very nearly reached in film 15 is indicated by the * Wied. Ann. xxvii. p. 199 (1886). Rotation in Iron Cathode Films, 93 agreement in magnitude of the rotations with those obtained with the polished steel surface, as well as the agreement with the results of other observers of the Kerr effect —working visually—reduced for this same field strength, viz. 5700 units. Moreover some later tests made visually with the aid of an ordinary half shade polarimeter on an opaque unoxidized film gave a rotation for sodium light, almost identical with that of this film. The seat of the Kerr rotation is unquestion- ably a thin surface-layer, and the foregoing results allow one to say that a layer of less than perhaps 20 mu thickness contributes considerably more than half of this rotation *. This is of the same order of magnitude as the thickness of the frequently assumed “transition layer” of optical theory. A third point is the great similarity, if we confine our attention to the results for pure iron, of the curves for the two cases of rotation. While for the thinner films the Kerr rotation curve shows a more rapid decrease on the short wave-length side, the forms of the two curves for film 15 are almost identical—at least until beyond 1°8u4—as is shown by the following Table III. The rotation for the wave-length of sodium light is taken as unity in each case. TABLE ITT. Rotation dispersion of the Faraday and Kerr effects for a pure iron film (15). Wave- ‘Transmission Reflexion Wave- | Transmission Reflexion length. | rotation. rotation. length. rotation. | rotation, 589n | 1:00 Let OD hy 14D | eral | —1-70 ‘70 1:20 | —116 1:50 1:73 —174 30 | 133 | —134 | 160 yee hr eee get 90 ) 1-44 | —142 1-70 1-73 —1-76 1-00 1°52 bp bre oH) E80 171 —176 1:10 1:59 | —156 | 1:90 1-70 —176 1:20 1-64 _ —162 2:00 1:68 _ —176 1:30 168 | —166 2-10 165 | —1-76 | 2-20 162 | —176 It would seem from the above that any explanation of the Kerr effect must indicate, more clearly than it does at present, its very close connexion with the Faraday rotation ; but unfortunately for the generality of this statement the * We might also say that practically the full value is given by a layer 60 pu thick, which is about the same thickness as that found by Keenigsberger and Bender (Ann. d. Phys. xxvi. p. 763, 1908) for platinum and gold films which give the same phase change on reflexion as the massive metal. 94 Prof. L. R. Ingersoll on Magnetic results for partially oxidized films show a considerable difference between the two curves. Kundt explained the varying effects obtained when the steel mirror for which he was measuring the Kerr effect was slightly oxidized, by the mutually interfering action of the two beams, one reflected from the air-oxide surface, and the other reflected and rotated by the oxide-metal surface. In the present case, however, we are dealing with a homogeneous layer, not a film of oxide on the metal, and the discrepancies cannot be as ae explained away. The resemblance between the reflexion rotation curve fiir film 29 of Pl. I. fig. 13 and that obtained with a steel mirror, Pl. I. fig. 4, would indicate that the latter, though polished brightly, still had more or less oxide on its surface, perhaps in the minute scratches left by polishing. In the previous work on the Kerr effect (Phil. Mag. l. c.) the rotation dis- persion curves for polished surfaces of nickel and cobalt showed this decrease of rotation with wave-length after about ly, as well as steel. It remains to determine if cathodic surfaces of these metals show a similar effect. If, as shown above, the Kerr rotation takes place in an extremely thin surface film, it is not remarkable if polished surfaces fail to give results identical-with those from the more perfect cathodic surfaces. Some such connexion as is seen to exist between rotator y power and absorbing or reflecting power might reasonably be expected. Thus in film 29 a rotatory power . decreasing with wave-length is accompanied by an increasing reflecting power. The readiest explanation of this—ov erlooking for the moment the somewhat different state of the iron—would be that the Kerr effect is a function of the penetration of the wave on reflexion, and this may on the whole be less for a greater reflecting power. Similarly for the pure films, the flat part of the rotation dispersion curve accompanies a non-selective — absorption or reflexion. But this does not account in either case for the rapid change of rotatory power with wave-length in the visible and early” infra-red spectrum. ‘This accords with the conclusions reached by the writer from a study of the Kerr rotation curves for mirrors of steel, cobalt, and nickel, that this spectral region,—viz. from perhaps Le ‘Au to 1y—hae much the same optical significance in the case of metals that a region of resonance absorption has for a dielectric. As is well known, the refractive indices of metals increase with ‘wave- length j in the visible spectrum. It remains to investi- gate their optical constants for the remainder of this region Rotation in Iron Cathode Films. 95 and as far as possible in the infra-red, for it quite possible that the anomalous character of the dispersion may cease, or at least change—as it does for the rotation dispersion—within the region in which it is possible to study it. Experiments to this end are now in progress. Part IIJ.—DEPENDENCE OF THE KERR ROTATION ON THE REFRACTIVE INDEX OF THE OVERLYING MEDIUM. In connexion with the foregoing experiments tests were made for several films of the rotation from the rear, or glass- metal, surface, and the unexpected result was found that the rotation in this case was more than half again as large as that for the ordinary air-metal surface. Thinking that some con- nexion might be established between the reflexion rotation and the optical density of the overlying medium, experiments were tried with films whose surfaces were covered with thin layers of various liquids, held in place and protected by a slip of microscope cover glass. The rotations measured in this way all proved larger than for the bare surface and by a factor not far ditferent, in most cases, from the refractive index of the liquid. | It can be readily seen that the rotation as measured by the bolometric method for such cases as these, will not represent, without suitable corrections, the actual rotation which takes place at the liquid metal surface. or in the first place a part of the energy would be reflected from the surface of the glass cover slip and would be returned without undergoing any rotation. A smaller part would likewise be reflected from the glass-liquid surtace, while the part which is reflected and negatively rotated by the true liquid-metal surface must also be attected by the positive rotation due to the double passage through glass and liquid. The rotation due to the latter need not be considered since the layer of liquid is so thin, but that due to the former must be corrected for. If we are dealing with rotation trom the glass-metal surtace of the film the corrections are of the same sort, but slightly simpler, since the liquid is lacking. ‘To make the first correction, that is, for the reflected energy which does not penetrate to the metal surface, we must know the combined reflecting power R, of the air-glass, glass-liquid, and liquid-metal surfaces, and also R’ of the air-glass and glass-liquid surfaces alone. The former is obtained by measurement, the latter by calculation from the known refractive indices. Then of every * Phil. Mag. doc. cit. p. 70. 96 Prof. L. R. Ingersoll on Magnetic R parts of energy which are reflected and go to make up the measured quantity I, R’ parts are inactive, having suffered no rotation and hence should be subtracted from I in computing the actual rotation. This is equivalent to multiplying the rotation, measured in the ordinary way as dl/I, by R/(R—R’). When there is added to this the doubled rotation due to the passage twice through the glass the corrected rotation is obtained. ‘To take the first case in Table ]V. as an example, TABLE LV. Reflexion rotations from the rear (glass-metal) surfaces of pure iron films 15, 17, 22. | Double Measured } r Corrected us rotation. R. Ri. ae Wiscre rotation. | Film 15. ‘63p | —*262° 321 7040 | —"299° "143° — “449° 74 — 348 328 | 040 —°396 108 — 504 94 ~-"480 340 *U39 — "543 ‘070 —'613 1:28 —'610 oD "039 — ‘691 037 —°728 171 | —662 | -335 | -038 | — “747 019 — "766 2°14 — ‘656 336 038 — ‘740 "009 — "749 Film 17. 65p eS. Dit 040 —*250° Nar — ‘383° To —°312 259 ‘040 — ‘369 ‘100 —°469 96 — ‘414 "247 039 —°492 ‘066 —*558 1:30 —‘d17 "929 039 —°624 033 —'657 1°74 —'d570 215 038 — ‘693 016 —‘709 2°16 —'567 191 038 — ‘708 ‘009 —717 Film 22. "66p — ‘084° 090 040 —"152° liao” — ‘285° 5 —I181 “088 7040 eS ay "100 — °432 "96 —'314 “080 039 —'613 ‘066 —'679 1:30 —°414 081 039 —'798 033 — 831 1°74 —°459 ‘075 038 — ‘930 016 —-946 2°16 — 430 ‘070 038 —°940 "009 — "949 the measured rotation (=45/adI/I) for X=*63y was found to be —*262°. The reflecting power of the glass and glass- metal surfaces was °321 and that of the glass alone (there being no liquid in this case) was*040. This gives a correcting Rotation in Iron Cathode Films. 97 factor of ‘321/:281 which brings the measured rotation up to a'—°299°. Subtracting from this the glass rotation of +°143° we get the corrected rotation of —*442°. The pro- cess is entirely similar for the case when the liquid is used, save that the glass reflecting power is made slightly larger— perhaps *045—to take account of the additional, or glass- liquid, surface. The cover slips used were of practically the same thickness as the glass on which the films themselves were deposited and hence the glass rotation was the same in either case. The corrected rotations from the above table have been plotted in the curves of PI. I. fig. 14. As in all the cases con- sidered these are the doubled rotations occurring on reversal of magnetization. It will be noted that the curves have the same general form as those of the Kerr effect in PI. I. figs. 6-8, but that the rotations are all considerably larger. The remarkable feature, however, is that the magnitude of the rotations is nearly the same for the three films of very different thicknesses, and that the thinnest film shows the largest rotation. In the following Table V. (p. 98) the results are shown of a number of experiments with liquids ef optical densities ranging from 1°33 to 1°72. Discussion of Results.—In Voigt’s * recent “ Magneto- und Electrooptik,” which contains the most complete treatment of the Kerr phenomenon that has yet appeared, there is reached on p. 316 an expression for the rotation on normal reflexion and for polar magnetization—the case we are considering —which may be written Q(k—2) n(1 + hk?) where Q is a complex which does not contain n, and n and & are respectively the refractive index and absorption index of the metal. The equations have not been worked out for the ease of a surrounding medium other than vacuum or air, and until this has been done it is useless to attempt any satisfactory justification of the above results on theoretical grounds. But it is of interest to note that if we grant two not unreasonable assumptions t—viz. that the refractive index * W. Voigt, Magneto- und Electrooptik, Leipzig, 1908. + Experiments now in progress in this laboratory show that the reflecting powers of metals, when overlaid with various liquids, are in agreement with the well-known formule for metallic reflexion, if assump- tions similar to these are made. In this light they seem extremely reasonable. Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. H Rotation = z = ; 98 Prof. L. R. Ingersoll on Magnetic TABLE V. Showing effect on the Kerr rotation of overlaying iron surface with liquids of various refractive indices. «a is the rotation due to the metal surface in air, and P to the same surface overlaid with the liquid. (1) With Potassium mercuric iodide solution. N,1°72. Film. Wave-length. Rotation a. Rotation f. B/a. Mean. Oe pee comet ae ‘B4u —°357° — 651° 1-82 1-11 — 420 — ‘748 1-78 1-75 1-74 —°462 —763 1:65 WG cc ntaue cess "B4p —°355° — "659° 1-85 (similar to Bae | —°435 — "780 Nye) 1-79 15). 1-74 — 480 — 830 1-73 DO Bae tues ‘67 p — 888° —"704° 1-81 (opaque) 82 — 403 — 691 Pi 71 1-07 — ‘378 —°632 1-67 : 1:69 — 245 — “399 1°63 (2) With Bromnapthalin. N, 1°66. Gigs tenets 84u —+357° —-630° 1-76 1:10 — +420 — 698 1-66 1:67 1-74 —-462 —-737 1:59 (3) With Canada balsam. WN, 1°55. | ere ee 84 — oe — "593° 1-66 1:10 — aa) — ‘686 1°63 1-64 1°74 — "462 —'753 1:63 Polished "B4u —o50~ — °504° 13h steel. 1-41 —°540 — 452 133 13a 1:96 = 261 —°365 1:40 (4) With Glycerine. N, 1°45. Op ak..a8.'. bee "84 —°357° — 556° 1:56 111 — 420 — 630 1:50 (30: . 1-74 —462 —670 1°45 2) Er ‘67 — 388° — 596° 1:53 "82 — "403 —°617 1°53 1°50 1:07 — 378 — ‘557 1-47 1-69 — 245 — 364 1:48 Polished ‘Sty — "385° — 534° 1°39 steel, 1-41 — 340 — 484 1-42 1-42 1:96 —*261 — 379 1°45 (5) With Water. N,1:33. a — “355° —+438° 1:23 Hig Sart 84 PLY —-435 — 523 1-20 1-20 1:74 —-480 —:567 1:18 Rotation in Iron Cathode Films. 99 n may be taken as relative to that of the surrounding medium, while the absorption index & is constant—we reach at once the conclusion from the above equation that the Kerr rotation should increase directly as the refractive index of the over- lying medium. That this is at least the general trend of the facts is shown by Table V. The agreement is by no means good, but, for the experiments with cathode films, the mean values of the ratios—if we allow that a mean has any significance when there is such a decided “drift”? of the results—differ generally by only a few per cent. from the refractive indices. There is no evident explanation of the rapid decrease of this ratio with increasing wave-length ; it is much greater than the decrease of index of the liquid would require it to be. The results with steel mirrors are seen to differ widely from those with cathode films, particularly in case (3) with Canada balsam as the liquid. But a polished metal surface, with all its microscopic scratches, is not to be compared for ultimate smoothness of structure with a cathode mirror on a glass surface. It may be indeed that the viscous Canada balsam did not penetrate to the bottom of crevices of the steel surface. | Passing to the case of rotation from the rear surfaces of films we should expect to find such rotations larger than those from the first surfaces bv a fraction equai to the refractive index of the glass, in this case about 1°49. But ifthe curves of Pl. I. fig. 14 are compared with the corresponding ones of Pl. L. figs. 6—8, it will be seen that the rotations have increased from over 1°7 in film 15 to nearly 3 times in film 22. Two explanations are offered for this: that the state of aggre- gation and physical properties of the metal are modified in the layer next the glass ; or, more probably, that the matter is complicated by internal reflexions in the case of the thinner films. This would possibly explain these results and at the same time not throw discredit on the work of Part II. where the reflected rotation is measured from the thinner films, because the reflecting power of a plain or air-iron surface is much greater than that of the glass-iron. Hence, since by Stokes’ law these reflecting powers also hold for the internal reflexions, the amount of energy returned on the first internal reflexion is much less in a cases of Part II. than in the present experiments. An attempt was made to verify qualitatively these con- clusions as to the variation of the Kerr effect with the overlying medium, by means of visual observations with a H 2 100 Prof. L. R. Ingersoll on Magnetic half shade polarimeter, using sodium light. An opaque film was deposited on plate glass and the Kerr rotation measured with, and without, the use of Canada balsam. ‘The obser- vations were very difficult and not very satisfactory in the latter case, but, when corrected for the doubled rotation of the glass cover slip, came out about half larger. SUMMARY. 1. The writer’s bolometric method of measuring magnetic rotations has been developed until, under favourable circum- stances, rotations of less than ‘001° can be detected, and angles somewhat larger measured with an accuracy approxi- mating 1 per cent. It is applicable to a range of spectrum from the D lines to A=2°2y. 2. The dispersion of magnetic rotation for cases of reflexion from and transmission through, iron cathode films, has been measured. Tor the pure iron films these curves are entirely similar and show a gradual increase of rotating power until wave-length 1-5u is reached, where the rotation reaches a maximum value over one and two-thirds times as great as that for the D lines. 3. After a certain thickness is reached the reflexion rotation ceases to increase further with thickness of film. A layer of iron, of thickness less than 20up, or about that of the assumed “transition layer’ of optical theory, gives rise to considerably more than half of this rotation. | 4, Partially oxidized tilms do not show the similarity between the reflexion and transmission rotation dispersion curves that pure films do. The rotation for oxidized films reaches a maximum in the early infra-red and falls off rapidly with further increase in wave-length. This change in form of the rotation curve with oxidation is accompanied by a corresponding change in the transmitting or reflecting powers as a function of wave-length. ) 5. The Kerr rotation is nearly proportional to the refractive. index of the overlying medium, which, with certain assump- tions, may be shown to be in accordance with Voigt’s theory. 3 Physical Laboratory, University of Wisconsin, Oct. 31, 1908. ; ADDENDUM. Since the above was written, Skinner and Tool’s paper on the optical properties of magnetic films has appeared (Phil. Mag. Dec. 1908). It is a valuable contribution to the literature of the subject, showing very clearly as it does the Rotation in Iron Cathode Films. 101 different types of films which may be produced by the cathode deposit : the writer, however, is obliged to ditfer from them in some of their conclusions. A comparison of their work with the pre-ent shows at once that what are here referred to as “oxidized” films would seem to be identical with their “dark” films, and the ‘“ pure iron” films of the present work, while not produced in just the same way, have the general appearance and non-selective reflecting and absorbing powers which they describe for their “‘metallic’’ type. The chief objection to calling the latter two virtually identical is the abnormally high rotating power (per unit thickness) and extinction coefficients which they assign to these “‘ metallic” films. These are some three times larger than for electrolytic iron, while their determinations of these quantities for electrolytic films are considerably higher than those of other observers. A possible explanation of this lies in their thickness measurements ; for their method,.it is believed, results in a considerable underestimate of the thickness of the film and hence overestimate of its rotating power and extinction co- efficient. Their method—an interference one—involves the assumption that the phase changes on reflexion at glass and iron surfaces are the same, and this they were able to justify for very thin films. But Koenigsberger and Bender (Anz. d. Phys. xxvi. p. 763, 1908) find for the cases of gold and platinum at least, that while this is true for extremely thin films it is by no means the case for thicker ones. To test this for iron, a number of films were deposited on optical glass and their thicknesses measured for sodium light after the manner of Skinner and Tool. The thicknesses were then measured by the method of Patterson (Phil. Mag. ii. p- 692, 1902), whereby the effect of any possible phase change is eliminated by a second cathode deposit, and in every case this gave considerably larger results. The true thickness was from a fraction larger, to more than twice as great as that measured in the first way, and this is more than sufficient to explain the abnormal values above mentioned. Since the magnetic rotation for sodium light as well as the thickness was measured for these latter films, data were obtained for checking the estimates of the thickness of the films used in Part II. of the present work. These were checked to within a few per cent., or within the error of measurement. In regard to the yellow-brown or “dark” films, Skinner and Tool consider that the metal is here in a different state 102 Prof. A. S. Eve on the Amount of of aggregation and deny the possibility of any chemical com- bination of the metal with a gas. The writer, on the other hand, has assumed in common with Houllevigue, that such films are the result of partial oxidation. This view seemed to be supported by the fact, already mentioned, that films deposited in oxygen (air) showed the same decrease of rotation with increasing wave-length after about 7 = lw. To throw more light on this point, a thick film, giving a rotation (Na light) of +2°:°5 before oxidation, was oxidized by moist air and ozone and its rotation then measured bolometrically. When corrected for the glass, the results gave + 014° for A=1:08u, and +°006° for A=1°75pu. the successive measure- ments differing by only a few thousandths of a degree. It will be noted that the rotation is still in the same sense but many times smaller than before, and that it shows this decrease with increasing wave-length after 7~=1yu. These same characteristics are exhibited, in a smaller degree, by the yellow-brown films. In conclusion, it seems to the writer that it is unnecessary at present to explain either of the types of films obtained by the cathode deposit as an especially anomalous state of the metal. or the “ metallic” type, as shown by Skinner and Tool, in general resembles, more or less, electrolytically deposited films ; and in the case of the “ dark” films, while it is admittedly difficult to account for the presence of oxygen in the depositing chamber when one notes the care taken by these experimenters, these films show at least some of the characteristics of oxides. _ X. On the Amount of Radium present in Sea- Water. By A. 8. Eves, M.A., D.Se., McGill University, Montreal*. N this paper measurements will be expressed in terms of Aa (10-1) gram of radium per kilogram of water tested. Three observers have made determinations of the amount of radium in sea-salt or sea-water. : Strutt f found 7°5x 10-1 gram of radium per gram of sea-salt, and this is equivalent to 2°3x10-” gram radium per kilogram of sea-water. ‘This, the first determination, was stated to be approximate only. The writer { examined Inagua sea-salt, and a sample of * Communicated by the Author. Tt Proc. Roy. Soc. A. vol. Ixxxviii. p. 151. { Phil. Mag. Feb. 1907. Radium present in Sea- Water. 103 sea-water collected from mid-Atlantic, and found 0°3 and 0°6, respectively, expressed in the above units. A large number of samples have been examined by Joly, and in his Presidential Address to the British Association, 1908, he stated that the average value found by him was 16. These three observers then give results in the ratios of 4,1, 27. There are several points of special interest in Joly’s paper *. In the first place he found that the addition of HCl tended sometimes to increase the amount of radium determined by his experimental method, apparently through clearing away precipitates, possibly of suiphates. Next, a second deter- mination invariably afforded a higher reading than the first. Thirdly, two samples of sea-water which had stood for two months in bottles, before testing, gave low values. I venture to give a brief summary of the results published by Joly. Samples of Sea-water collected near land. Without Hcl. With HCl. ee AT OUP 85... 0iaiie ia: oan a wae 35°6 40-0 & Hew miles W.of I. of Man ...:..... 3°8 33°6 & 6o miles-Wot Valencia .......... 12°6 31-4 d. 1-5 miles 8S. of Crow Head, Co. Kerry, 15:2 22°6 e. 20 miles W. of Bantry Bay ........ 26°8 39°3 Samples from Ocean between Madeira and Bay of Biscay. Without HCl. With HCl. Oli 5 ee cee Sear 2°9 14°4 eee ae OE ee Ue 15:0, 21°3 ea me ict aps ate = ls US eed on ei 19-3, 27°3 Eee, is. ARS Ie EU EN te 4:4, 8-0 h.. AOE he oe ths, Ae eo. eee oa 2°0, 14°6 (Sees ele sia ae a 8:4 on a iF a is eta, ode 3°5 26-0 Re hes ON) a Deets PN OES ty 30°4 EM roi a eto ein cee Pict e win x eal ea 14:6 Arabian Sea. Pre SO Sei alse 9, ad sie es 9 me 24:3, 31:4 27°8 The range is from about 8 to 40, and the average value of all Professor Joly’s determinations is 16. . * Phil. Mag. vol. xv. pp. 885-393 (March 1908). 104 Prof. A. S. Eve on the Amount of As my published values were so much smaller than the above, it seemed desirable to make some more measurements and ascertain the reason for the difference. In 1908, on a voyage from Liverpool to Montreal, six samples were collected, by myself, in a canvas bucket over the side of the vessel and ‘placed in six clean new glass bottles. The first two samples were collected whilst the water was warm and the ocean currents were from the south, but the second pair were obtained when the sea was cold and the currents were from the north; while the last two were from the Galf of St. Lawrence, and therefore nearer shore. The six samples then together seem to constitute a fair average sample of the waters of the North Atlantic. The sea-water was taken from the bottles and placed in six new glass flasks and, except with sample 1, the bottles were well rinsed with HCl and distilled water, which were afterwards added to the sea-water in the respective flasks. A seventh flask was also filled with distilled water and 60 c.c. HCl, in order to see if there was any radium present in the flasks, water, or acid used. Oh yee Aeemge 2c pa eee 30 August | 56°27’ 26°32’ |29Sept.| 1272 | 500 0 2 ee BLA, 56°6' 33°3' |18Jan.| 1135. | 600 | 60 PRs 1 Sept. | 55°5' 41°32’ | 8Dec.| 1130 ? 30 Cie Dag. 53° 33’ 49°32’ | 2Oct.| 1180 | 600 | 40 peat Meee 51° 34’ 56° 26'*/29 Dec.| 1149 | 149 | 60 ae 1s, Off Gaspe Co.* | 10 Dec. | 1215 ? 50? | * In the Gulf of St. Lawrence. A glass flask, silvered inside, was fitted as an electroscope, and the method followed was that described in a previous paper t. The natural leak was small and constant. Atter the sea-water and acid had been sealed for about a month in the flasks they were boiled for some minutes. All the gases driven off, including the emanation, were collected over water and introduced through a drying-tube into the electroscope. As the method is a comparative one, there appears to be little objection to collection over water. T Eve & McIntosh, Phil. Mag. Aug. 1907. Radium present in Sea- Water. 105 Nevertheless it might be objected that the radium emanation is absorbed by bubbling through water to a variable and unknown extent. Therefore re-determinations were made by collecting over mercury. There was no certain observable difference between the two methods. It is often simpler and it seems perfectly safe to collect over water. To calibrate the electroscope | prepared solutions of radium bromide, using those standard solutions whose history is given in the American Journal of Science, vol. xxii. July 1906. These same standard solutions were those also used by Rutherford and Boltwood in their determinations of the ratio of uranium to radium in pitchblende. As Joly used this ratio for calibration, our standards are practically the same. Moreover Strutt, Joly, Eve and McIntosh all find values for the radium contents of rocks which are in satis- factory agreement, so that the question of relative standards does not arise. One c.c. of the standard solution, containing 1°57 x 10-° gram of radium, was taken with a new and clean pipette and placed in a flask with 99 c.c. of distilled water and HCl. Another new and clean pipette was used to remove 1 c.c. of the well-shaken mixture and to transfer it to a second flask containing 99 ¢.c. of distilled water and HCl. More dis- tilled water was added to each flask, and, after sealing, the contents were in due course tested. Divisions per minute. Gram radium. Collected over water. Over mercury. ag LO"? 8-43 8°43 Pan x 10°! “080 083 The agreement is better than can be expected and is partly accidental. One division per minute of the electroscope is a measure of the emanation from 1°90 x 10-” gram of radium. In testing the specimens of sea-water it was found that the readings by day were larger than those by night. Mr. F. W. Bates has recently proved that the conduction of sulphur is greatly increased by direct sunlight, and also to a less extent affected by daylight. My readings were, therefore, taken between 5 P.M. and 9 a.m., during which time the aluminium-leaf moved about 40 divisions of the scale in the eyepiece of the observing microscope. When samples were tested at intervals of less than a month the necessary cor- rections were made for the incomplete growth of the radium emanation in the flasks. The flask containing distilled water and HCl alone gave the same reading as the “ natural leak.” 106 Amount of Radium present in Sea- Water. The results obtained by me were :— Sample. Collected over water. Over mercury. Mean. #40 ee 10; 0:89; 0-73 0°66 0°82 Baten th An AKG, 1:03 0°38 071 Rec er tot Coe 0-75; 1°74; 1°83 1°67 1:50 Lael Oa ed 0:38 ; 0°28 0°75 0:47 eM aE ee tae 0-71; 0°47 0-51 0:56 LNW AR ee ae 1°83; 1:60 1:25; 1:34 1:50 Mean. ...... 0:94 Range: about 0°5 to 1:5. The high reading for number 3 may perhaps be due to the fact that the HC] and distilled water were left for 6 days in the collecting-bottle. Number 6 was collected but a few miles from land. It will be seen that my result agrees very well with my previous value 0°6, but it does not agree with the value 16 found by Professor Joly. I publish this result, therefore, with some diffidence, but after taking every pre- caution in my power to eliminate error. At first sight it may seem a matter of small importance whether there is 9x 10-!6 or 16x 10-4 gram of radium per gram of sea- water. That is not the case. The amount of radium in the ocean affects the question of the ionization of the atmosphere over the ocean with all the consequent problems of cloud formation, atmospheric electricity, and propagation of electric waves by wireless telegraphy. It also enters into the problem of penetrating radiation. Moreover, it has a direct con- nexion with the interesting results of Joly as to the amount of radium present in deep-sea deposits, and possibly with the amount determined by Strutt in sedimentary rocks such as chalk or limestone. A measurement was also made of the radium present in the water of the River St. Lawrence. This water is supplied to the City of Montreal without any filtration or treatment, and my sample was taken from a tap in the Chemistry Building. No great reliance can, therefore, be placed on the result, 0°25. Joly found 4:2 for the water of the River Nile. Thus we both found only four times as much radium in the ocean as in the rivers named, although our relative values are as 17 to 1. This seems to show that the radium, and presumably the accompanying uranium, find their way some- what rapidly to the deposit on the bed of the ocean, for the ratio of other salts in sea- and river-waters respectively show a vastly greater ratio. Further measurements of the amount of radium in river-water are needed, but the quantity is small and difficult to measure. On the Transformations of X-Rays. 107 If we take the amount of radium in sea-water as 10-” gram per gram of water, and in the soil as 4 x 10-”, a simple calculation * shows that the penetrating radiation from the soil should be about 1600 times as great as trom the ocean, so far as the penetrating radiation may be attributed to the presence of radium. If we follow a calculation of Becker ¢, we find the radium contents of the ocean to be equivalent to the radium found in a very small thickness of the deposits at the bottom of the ocean. Let us suppose the ocean contains 9 x 10-'°, the deep-sea deposits 25x10-” (Joly), and the sedimentary rocks 1:1 x 10-¥ (Strutt), in each case in terms of grams of radium per gram of material. Take the mean depth of the ocean as 3°5 kilometres and the specific gravity of the deposit or soil as 2°5. Then the amount of radium in 3°5 km. depth of ocean, per sq. cm., is about equal to that, also per sq. cm , in 114 ems. of sedimentary rock, or 5 ems. of deep-sea deposit. Summary. 1. Radium emanation may be collected over water or over mercury with about equal accuracy when testing for the quantity present in a given solution. 2. The result of testing six samples of sea-water from the North Atlantic leads to the average value of 9 x 10-18 gram of radium per gram of sea-water. This is about one-seven- teenth of the value found by Joly. Montreal, April 1909. XI. Transformations of X-Rays. By CHartes A. SADLER, M.Sc., Oliver Lodge Fellow, University of Liverpool t. yy BEN a primary beam of Roéntgen radiation falls upon any substance, secondary Roéntgen rays are emitted, the character of which depends both upon the nature of the substance and upon the particular kind of primary beam used. With reference to the latter it has been found that variations in the intensity of the primary beam produce no perceptible change in the character of the resulting secondary, the sole controlling factor appearing to be the degree of “hardness” of the primary §. ‘ Terrestrial Magnetism,’ March 1909. Bull. Geol. Soc. of America, vol. xix. p 115 (1908). Communicated by the Physical Society : read April 23, 1909. Barkla, Phil. Mag. June 1906, pp. 812-828. Matt—+ * 108 Mr. C. A. Sadler on the It has been shown * that if the radiating substance be an element of lew atomic weight—as hydrogen, oxygen, or carbon—it emits a radiation similar in penetrating power to the primary producing it ; its penetrating power varying with that of the producing primary. This type of radiation, which will be referred to as a “scattered” radiation, may be considered as produced by an acceleration of one or more electrons in the atom of the radiating substance, due to the action of forces in the primary pulse. From an element of greater atomic weight than that of calcium (40)—and possibly from other elements of lower atomic weight under very penetrating primary beams—the emitted radiation has been shown to consist of scattered radiation, and superposed upon this, a type of radiation which is characteristic of the radiating element. The pene- trating power of this radiation is a constant quantity peculiar to the substance and is independent of the penetrating power of the primary producing it. Moreover, this radiation appears to be entirely homogeneous in character, and experiments point to the conclusion that the radiating electrons producing this type of radiation are no longer appreciably under the influence of the forces in the primary pulse. This homogeneous radiation is only produced when the penetrating power of the primary is greater than that of the homogeneous radiation characteristic of the radiator. From the group of elements Cr—Ag the ionization pro- duced by the homogeneous portion of the secondary radiation, emitted when any of its members is subjected to a sufficiently penetrating primary, is many times greater than that produced by the scattered portion—in the case of copper as radiator this ratio is as high as 150 : 1. The homogeneous radiation from chromium is very “ soft” much softer indeed than any ordinary primary beam, and from chromium down to silver and probably beyond, the penetrating power of the characteristic radiation increases with increase of atomic weight; the radiation from silver being many times more penetrating than that from chromium. One of the chief difficulties experienced in the investigation of X-ray phenomena has been the heterogeneity of the primary beams hitherto available. ven where devices are adopted to ensure that the current through the X-ray bulb used as a source of primary rays is uni-directional and of nearly constant strength, the primary so obtained consists of a mixture of constituents of different penetrating power ; so * Barkla & Sadler, Phil. Mag. Oct. 1908 pp. 550-584. ae Transformations of X-Rays. 109 there remains the difficulty of ascertaining which particular constituents of the composite beam are principally concerned in producing the phenomena under investigation. It was thought that useful information concerning the nature of X-rays might be obtained if the homogeneous rays previously mentioned were used to excite tertiary radiation in different substances. Sagnac has shown that the tertiary X-rays from metals exited by secondary X-rays are more easily absorbed than the exciting rays. Previous experiments * had shown that if two substances A and B be taken, each of which is found to emit a homo- geneous radiation when a suitable primary beam falls upon it, the homogeneous radiation from A being more pene- trating than that from B, then if a homogeneous beam from A be passed through a thin plate of B, tertiary radiation is excited in B by the radiation from A, while if the process is reversed it is found that the radiation from B excites no tertiary radiation in A. These phenomena were examined in greater detail in the ‘experiments described below. It was found that no trace of a homogeneous tertiary radiation could be detected from aluminium when subjected to any of the homogeneous radiations from the group of metals Cr-Ag, and the amount of scattered radiation pro- duced was extremely small when compared with the secondary incident beam. Advantage was taken of these facts, and the primary and secondary beams were passed through tubes of thick aluminium of rectangular cross-section. This enabled the apparatus to be arranged compactly with comparatively short distances between the anticathode of the X-ray bulb and the secondary radiator, and between the secondary and tertiary radiators respectively, a condition essential to secure that the ionization produced by the tertiary rays in a suitable ioni- zation chamber should be sufficiently intense to ensure accurate readings in a reasonably short time, and that the direct tertiary radiation should produce an ionization large compared with that produced by stray secondary and tertiary rays from the surrounding air and neighbouring screens. The general arrangement of the apparatus is indicated in Plan by fig. 1. A rectangular brass tube B lined with aluminium °2 cm. thick was fitted into an aperture in the lead screen SS sur- rounding the X-ray bulb emitting the primary rays, and the * Barkla & Sadler, Phil. Mag. Oct. 1908, pp. 550-484. 110 Mr. C. A. Sadler on the bulb was so placed relatively to this tube that the axis of the tube passed through the centre of the anticathode A normally. Bion. + 240 VOLTS The rays from A passing through this tube impinged on the radiator R, consisting of a rectangular plate of the metal, the secondary rays from which were to be studied. A portion of the secondary rays so produced passed down the rectangular brass tube D lined as before with ‘2 cm. aluminium, and a plate of any substance placed in this secondary beam provided a source of tertiary rays. The intensity of the primary beam was measured by allowing a narrow pencil of rays proceeding from A through a small aperture O in the lead screen SS to enter an electro- scope H, of the ordinary Wilson type through an opening covered with tissue-paper and aluminium-foil in the wall of the electroscope. The deflexions of the gold-leaf were observed by means of a microscope fitted with a scale in the eyepiece. The intensity of the secondary beam was measured by means Transformations of X-Rays. 118 of a similar electroscope E, placed in the path of the secondary beam passing down the tube D (R, removed) as indicated in the Plan ; the size of the aperture in the wall of this electro- scope being 3X2 cms. It was found that by carefully shielding the electroscopes E, and E, from draughts and sudden changes of temperature very reliable readings could be obtained, the motion of the gold-leaf being absolutely dead-beat. Preliminary experiments also showed that with a given radiator R, in position (It, being removed) the ratio of the deflexions in E, and H, when the bulb had reached a steady state rarely varied by more than 1 per cent. during a series of readings. The ordinary Wilson type of electroscope was found to be quite unsuitable as a means of measuring the tertiary radia- tion ; the type of electroscope described by R. T. Beatty in his paper on “Secondary Rontgen Radiation in Air” * was finally adopted. Briefly described, this consisted of a brass ease having two sliding quadrants insulated from the case and charged to potentials of +240 and —240 volts respectively ; an insulated gold-leaf hung vertically between them and was connected to the wire e, which projected into and was insulated from the ionization-chamber I, which itself was insulated and charged to +240 volis. An adjustable com- pensating-chamber insulated and charged to —240 volts eliminated the normal ionization in the chamber I. The sensitiveness of the electroscope was adjustable by means of the sliding quadrants. With the order of sensitiveness required in all the experi- ments described, the motion of the gold-leaf was dead-beat, and a series of readings of the ratio of deflexions in electro- scopes H, and H, showed that with deflexions up to 20 scale- divisions in EK, this could be obtained with an accuracy of 2 per cent. with certainty. A calibration of electroscopes EH, and E, showed that the value of a deflexion of a scale-division was the same within 1 per cent. throughout the range of scale employed. The sensitiveness of H; was adjusted and then maintained constant throughout a given series of readings, and in all readings a constant deflexion of KE; was used, thus eliminating the effect of the slight change in value of a scale-division which was found to exist in different parts of the scale. Preliminary experiments showed that the secondary radia- tion from air together with other stray effects were very * R. T. Beatty, Phil. Mag. Noy. 1907, pp. 604-614. 112 Mr. C. A. Sadler on ike small compared with the readings obtained when metallic radiators were employed. The portion of the radiator R, exposed to the primary _ beam was limited to that opposite to the tube D by means of a suitable stop placed in the tube B as indicated in the diagram. Nature of the Tertiary Rays. It was perhaps reasonable to expect that the tertiary radiation emitted by any member of the group Cr-Ag when subjected to a more penetrating homogeneous beam from the same group would be identical in character with that emitted as secondary radiation by the same substance when excited by a suitable primary. Direct experiments were carried out to test how far this was true, and for this purpose pure iron was chosen as the tertiary radiator. The radiator consisted of a small rectangle 3 cms. high by 2 cms. broad, formed of pure iron wire interlaced so as to expose as large a surface as possible to the exciting beam. This was placed in the position indicated by R», the centre of the radiator was at the intersection of the axis of the tube D with the normal from the centre of the aperture to the ioni- zation-chamber I, the plane of the radiator making equal angles with these directions. | As a secondary radiator in the position R, a plate of pure copper was used. The aperture YY of the ionization-chamber I in these experiments was 3 cms. high by 2 cms. broad, and the distance from the centre of the aperture to the centre of R,, 4ems. Owing to the obliquity of some of the tertiary rays, it was evident that the absorption coefficients, obtained by studying ihe absorption by thin plates of different substances placed parallel to the aperture YY in the path of the beam, would be greater than would have been the case had it been possible to utilize a pencil of tertiary rays. A control experiment conducted with a fairly soft primary beam falling upon the same iron radiator similarly situated before an aperture of the same size as that in the screen YY in an electroscope of the Wilson type placed in the secondary beam from the iron, gave an increase in the value of the absorption coefficient by an aluminium plate -00297 cm. thick of 6 per cent. over the value found when.a narrow pencil of secondary radiation was used. Transformations of X-Rays. 113 The absorption coefficients of the tertiary beam from iron were then determined by thin sheets of aluminium, iron, copper, and zinc. ‘he values so obtained are compared with those obtained when the same absorbers were used with the secondary rays in the control experiment in the following table. TasE I. X nN Value of — for Value of ~ for Absorber. o p Secondary Rays. Tertiary Rays. Al (00297 cm.) ... 93:8 94:2 Fe (00315 cm.) ... 69-1 69°1 Cu (00298 cm.) ... 101-0 102°5 Zn (‘00132 om.) ... 119-2 120°0 It will thus be seen that within the limits of experimental errors the penetrating power of the tertiary beam is identical with that of a similar secondary beam from the same substance. The Homogeneity of the characteristic Tertiary Radiation. The tertiary beam from iron excited by the secondary homogeneous beam from copper was now cut down by thin aluminium sheets to test its homogeneity. It was to be expected, even were the beam perfectly homo- geneous, that after cutting down by a few plates the beam would appear slightly more penetrating, for the more oblique rays would suffer extinction to a greater extent than those passing through the absorber in a perpendicular direction. It was not found possible to test for homogeneity to an exhaustive limit owing to the smallness of the readings in the later stages, but the results obtained show that for all practical purposes the beam may be regarded as homo- geneous. Phil. Mag. S. 6..Vol. 18. No..103. July.1909. | I 114 Mr. C. A. Sadler on the The results are tabulated below :— TABLE II. Iron as Tertiary Radiator ; Copper as Secondary Radiator. | | Amount previously Subsequent, absorption | absorbed by Aluminium. 2s cacures Al (00297) em. thick. None. 55'6 per cent. 55°6 per cent. 5 SNS) va, DG, Se Uae Sa) ) 25, Previous experiments have shown that associated with the homogeneous secondary radiation from a metal of the group Cr—Ag is a small proportion of scattered radiation, the relative ionizations produced by the homogeneous and scattered portions being about 150: 1. If the secondary beam from iron be absorbed by say 0104 cm. aluminium, then while the homogeneous portion will be absorbed to the extent of about 90 per cent. the scattered portion will only be absorbed by about 30 per cent., giving an absorption of the whole beam of 89°6 per cent. (the absorption being measured by the relative diminution in ionization) ; so that the relative ionizations produced by the residual homogeneous and scattered portions respectively will now be as 21°4:1, and a sheet of 0104 aluminium would now only absorb about 87:4 per cent. of the whole beam, and this increase in penetrating power would become more and more pronounced as further absorptions took place. In a corresponding case of the tertiary beam from iron excited by copper radiation, the amount otf scattered copper radiation in the beam if present at all will not be present to so great an extent since the copper radiation will not pene- trate to anything like the same depth in the iron as an ordinary primary radiation, though on the other hand the ionization produced by beams of scattered primary radiation and of scattered copper radiation conveying equal amounts of energy per second through unit volume of air, will not be equal; the scatiered copper radiation being more easily absorbed will produce the greater ionization. No direct evidence has yet been obtained that when the normal tertiary radiation from iron is excited by homogeneous radiation from copper, any of the copper radiation itself is Transformations of X-Rays. 1h scattered by the iron; its presence in the beam would be ditfivult to detect for a small percentage of copper radiation in the beam would produce a very minute change in its absorption coefficients. The figures given in Table II. there- fore do not preclude tiie possibility of a small percentage of the ionization being due to scattered copper radiation. Independence of the Penetrating Power os the Exciting Radiation. Experiments were made to test whether the penetrating power of the tertiary radiation emitted by a substance depended in any way upon the penetrating power of the exciting secondary beams. In the first test, iron was chosen as the tertiary radiator, copper and arsenic as the secondary radiators. The radiation from arsenic being about twice as penetrating as that from copper. In the second test chromium was taken as the tertiary radiator, and iron, copper, and arsenic as secondary radiators ; the radiations from each of these substances being more pere- trating than that from chromium, the radiation from arsenic being about four times as penetrating as that from iron. The results are tabulated below :— TABLE IIT. Tron as Tertiary Radiator. Absorption coefficient |Percentage Absorption eancary lof the Secondary Radia-| of the Tertiary Radia- ar tion by Aluminium. |tion by (‘00297 em.) Al. LO ee | 128°9 59°6 Lo, ee 60°7 55°4 TABLE LY. Chromium as Tertiary Radiator. . . = Secondary | Absorption coefficient | Percentage absorption : of the Secondary Radia-| of the Tertiary Radia- | en | tion by Aluminium. |tion by (00297 cm.) Al.| MT eke: 6352 2-0. 239 7a1 ge ) 128°9 75°3 | ROTI ie oe asin «5 | 60°7 75°1 116 Mr. C. A. Sadler on the From these results it will be seen that the penetrating power of the tertiary radiations is uninfluenced, so far as can be measured, by variations in the penetrating power of the exciting secondary beams; they further show that if any secondary radiation is scattered by the tertiary radiator, the ionization it produces is small compared with that produced by the tertiary radiation. This result is analogous with that obtained with secondary beams *. ; It has thus been shown that the characteristic tertiary radia- tion from iron is identical with the characteristic secondary radiation from iron in its penetrating power, its homogeneity, and in its independence of variations in the penetrating power of the exciting radiation. Similar results were obtained with copper as a tertiary radiator. Conneaion between the Secondary and Tertiary Radiators. A series of experiments was now undertaken in which the several members of the group of metals Cr-Ag were used as secondary radiators, the tertiary radiators being also chosen from among the earlier members of the same group. By referring to column 1, Table V. it will be seen that the absorption coefficients by aluminium of the radiations from the metals of this group indicate a wide range of penetrating powers, so that it was reasonable to expect that for each tertiary radiator there would be at least some secondary radiations sufficiently penetrating to cause it to emit its characteristic radiation. The method of experimenting was as follows :—The secondary radiators successively placed in the position R, (see fig. 1) were subjected to the primary rays proceeding from the anticathode A, R, being temporarily removed. The ratio of the deflexions of the gold-leaves in the electro- scopes EH, and Hy; obtained from the microscope readings was determined in the case of each radiator ; let 7, be the value of this ratio and 7;/ be the value of the ratio with no metallic radiator in the position R,, the air in its neighbour- hood acting as a source of secondary radiation. Next, the particular tertiary radiator under examination was placed in the position R, (as previously defined), and the secondary radiators were again in turn subjected to the primary rays. Ionization was now produced in the chamber I and deflexious of the gold-leaf in electroscope B3 * Barkla & Sadler, Phil. Mag. Oct. 1908, pp. 550-584. Transformations of X-Rays. bi b/) were obtained. Let the value of the ratio of the deflexions of the gold-leaves in E; and H, be rg, and when the tertiary radiator was removed and the air alone in its neighbourhood acted as a source of tertiary rays, let the corresponding value of the ratio be r,/. The tertiary radiator R, was then replaced and the ratio 7, again found, and then finally removing R, the readings for the ratio r; were repeated. Working with an X-ray bulb, having an auxiliary spark- gap, it was found that in the steady state the two sets of values for 7, and likewise those for 7, showed agreement to within 2 per cent. In no case was the air-effect 7’ more than 1 per cent. of the value of 7, in most cases less than } of 1 per cent.; and in no case was the air-effect 7,’ more than 2 per cent. of the value of 7, when the characteristic homogeneous radiation was excited. In those cases where the penetrating power of the secondary beam did not exceed that of the characteristic radiation from the tertiary radiator employed, the air-effect 7,’ became of considerable importance, being as high as + of r, in some eases. The author hopes to obtain more reliable data in these particular cases in the course of further experiments. Tt will be seen later, however, that an accurate knowledge of these particular data is not essential in the present investi- gation. It was estimated that if in all other cases 4 of the air- effect was taken in addition to the normal leakage, and this subtracted in each case from the direct effect when the metallic radiator was in position, the resulting ratios finally obtained would be accurate to at least 2 per cent. If adenote the ratio of the normal leakage in any given time in the electroscope EK, to the deflexion in H, in the same time, witha primary beam as during the actual experiment, then since the normal leakage is compensated for in Hs, the ratio of the ionizations in the electroscopes HE; and E, due to the homo- geneous radiations Be Eas aks a aan 1% [37 +a] ee tes If the absorption coefficient of the homogeneous radiation from a given tertiary radiator by Al be denoted by Ay, and that of the exciting secondary radiation by 24, then as long as Ay = or is > A, the value of R is quite small and approxi- mately constant. As 2, decreases through the value A, we get arapid increase in the value of R, and for a comparatively 118 Mr. C. A. Sadler on the small subsequent increase in penetrating power of the secon- dary beam, values of R 30 to 40 times as big as the previous steady values are obtained ; this increase corresponding to the excitation of the characteristic tertiary radiation. Let us consider the tertiary radiation emitted normally from a given radiator of area S upon which a uniform parallel beam of secondary rays is incident normally. Let us define a quantity &, such that the fraction of the energy of the secondary beam passing normally through a thin layer ox of the tertiary radiator which is transformed into tertiary radiation is kéz. Thus, if I be a measure of the energy passing normally per second through unit area of the tertiary radiator at a depth 2 below the surface, the energy transformed per second in a layer da=Ikéz. Now Barkla* has shown that when this homogeneous type of radiation is excited, it is practically evenly distri- . buted in all directions : consequently, the energy passing per second as tertiary radiation from the layer 6a through the tissue-paper-covered window of an electroscope of the Wilson type (I being constant over the whole area of the radiator) = 7 Slk8xe-™, 2. where A, is the absorption coefficient of the tertiary radiation by the material of which the tertiary radiator is composed, and w is the mean solid angle subtended by the aperture of the electroscope at ali parts of the radiating area. But if 1p is a measure of the energy incident normally per second on unit area of the tertiary radiator at the surface, I a ean where A, is the absorption coefficient of the secondary beam by the material of which the tertiary radiator is composed, and the whole energy passing into the electroscope per second from the tertiary radiator w it wi = 7 Blok \ Cae eae. . - ") 1 dor b Ay +tAg ( ) If now we remove the tertiary radiator, and place the electroscope previously used in the path ot the secondary beam, with the centre of its tissue-paper-covered window occupying the position previously occupied by the centre of * Barkla, Phil. Mag. Feb, 1908, pp. 288-296. Transformations of X-Rays. 119 the radiator, and with its plane perpendicular to the axis of the secondary beam, the energy passing per second through the window, if its area is A, is I)A. Therefore the ratio of the energy in the tertiary beam passing per second into the electroscope in the first position to the energy of the secondary beam passing per second into the electroscope in its second position oS k sale 8 aay Eh Ae There is considerable evidence that the ionization produced in a given volume of air by a beam of Roéntgen radiation is approximately proportional to the absorption of that radiation by the air. It has been found®* also that the ratio of the absorption coefficients of homogeneous beams of different penetrating powers by any two substances, e.g. carbon and aluminium, in which no radiation of the homogeneous type is excited by the beam under consideration, is a constant. Also it has been found that the absorption of a beam of Roéntgen rays by any substance depends only upon the quantity of matter present and not upon its state of ageoregation. It is assumed on the basis of these results, that the ioniza- tions produced in a given volume of air by homogeneous beams of different penetrating powers are proportional to the absorption coefficients of these beams by carbon or aluminium. Making this assumption, we have the ratio of the ioniza- tions produced in the electroscope by the tertiary and secondary beams oS k B 3, dhe hk et (say) . = itn (5) where 2 and £ are the absorption coefficients by aluminium of the secondary and tertiary beams respectively. From (5) we find that k | 3, @ A Ag Ge ee In the above calculations we have considered the special case of normal incidence and emergence, but, since we are dealing with radiators sufficiently thick to absorb the whole of the incident radiation, it is easy to show that the results (4), (5), (6) are quite general for oblique incidence and emergence, where the incident and emergent beams make equal angles with the normal to the radiating surface. * Barkla & Sadler, Phil. Mag. May 1909. a 120 Mr. ©. A. Sadler on the In order to deduce values of & from the experimental data, it is necessary to know the values of a, 8, A, and A, for each of the tertiary radiators employed. « and £ are readily obtained for the whole series and likewise A, and A, for Zn, Cu, Ni, and Fe. In the case of Cr and Co, being unable to obtain thin plates of these substances, the values for A, and A, could not be obtained directly but were deduced by the following method. If the -values of (where Az, is the absorption coefficient by a substance of its own characteristic radiation and p its density) for the substances Fe, Ni, Cu, and Zn are plotted Bigeze 80 70 D (=) Az ? VALUE OF 3 400 300 . 200 3 100 Oo , ABSORPTION COEFFICIENTS By Al. as ordinates, against the absorption coefficients for the radia- tions from these substances by Al as abscisse, it is found that the points obtained lie on a straight line, as shown in fig. 2. Transformations of X-Rays. 121 The values of = for Co and Cr deduced from this graph are Co (61°3), Cr (83:7). Moreover, a regular relationship is found to exist between the ratios of X, for the radiations from consecutive members of the group Cr—-Se for each of the absorbers Zn, Cu, Ni, and Fe. Taking the values of the absorption coefficients for any three of these absorbers for the radiations from the group Cr—Se, values for the coefficients for the fourth absorber could be deduced, starting with a value of A, as a basis and using these observed relationships. In no case was the discrepancy between the experimental and deduced values greater than 2 per cent. | In a similar manner the remaining values of the absorption coefficients for Co and Cr were deduced, taking the values of A, obtained above as a basis for calculation in each case. TABLE V. of the ratio a el i Values of X used in calculation of £4. | / x Values of X! used in calculation ABSORBERS. } | RapiaTors. | Al. | Cr. | Fe. | Co. | Ni. | Cu. | Zn | Cr.'| Be. | Co. |- Ni. | Cn. | os Chromium...) 367 | 544 | _ ae 239 | 2500; 514 2150 | | Cobalt ......| 193-2) 2076, 521| 545 |1785| 102 Nickel......... 159'5| 1730/2440] sea} 482; | —_| 1490 2090 1340 Copper ae 128-9) 1478 2080 | 2560} 537} 474 1279 | 1798 | 2194; 150 a e 106°3) 227 | 1715 | 2172|2275| 497 361 1072 | 1485 | 1875 | 1936 | 12071 Arsenic ...... 60°7) 755 | 1040 | 1383 | 1422 | 1575 1464. 666 | 915) 1161 wo, Milena. 10 Grams: wc.) Gon ceme ere eempem eee yal te loosens OG ae Basalt, Giant's Causeway, 20 grams | ......0--.o.ceccecserecetsconcees OO yam Gneiss, Simplon’ Tiranel,/ 10 prams). pce tense soe esc eos 1: ia Diabase, Fifeshire, 10 grams _..... BOOMS AIRS Bhs less than O2 ,, Shale, Moffat Dale,’ 1O.crams,\..cc.cccuva tonne tenc serene. tales seh lO. ae Granite,'Co.. Wicklow, 20) crams | cs.. cnet amen tenets vebe ons acsoaie»- 1:1) oe Carboniferous Limestone, Armagh, 22°5 grams ... lessthan O2 ,, Marsupites Chalk, 32 grams ..........c.cesseseeeee ce lessthan O06 _,, Red Clay, N. Pacific, 2°4 arams. .occieguycceenge tas less than O'9 _,, 5 Central Pacific, 10 grams rates. cabal nie de vanes : Oe Radiolarian Ooze, Central Pacific, 6°3 grams ......... less than O4 ,, Manganese Nodule, 8. Pacific, 12 grams............... less than O2 ,, Meteorite fell at Dundrum, 25°6 grams ................cececeeeee sees 0:09 _—,, Sea- Water, Coast of Dublin, 1400 ces. ............... less than 1:4x10-8 S. Atlantic, 790 ces: eee were ie less than I-B ” 9 1500 ees...) eSGr eee poe lessthan 14 ,, am Indian Ocean; 2800 ices.) chee edad lees 0 save |) OPO es In giving these results in the Phil. Mag. for May I regret that 1 was unaware of M. Blanc’s important contributions to the same subject. M. Blanc has been so kind as to send me an account of his results which appears in this present number. The determination of thorium in the meteorite which fell at Dundrum, Co. Tipperary, seems quite certain although the quentity present is small. Two prolonged experiments gave an identical result of a steady gain of little over one scale-division per hour This meteorite is partly nickel-iron, but for the greater part, about 75 per cent., consists of non- metallic minerals. The Rocks of the St. Gothard Tunnel. The experiments which I had previously made upon the radium content of the rocks of the St. Gothard tunnel (Address to Section C, British Association, 1908) left me in possession of solutions of 51 rocks. These rocks had been selected so as to be as far as possible typical of the principal Rocks of the St. Gothard Tunnel. Distance Thorium | F Radium No. | from N. in grams in grams (Stapff). entrance: Description. per gram | per gram Metres. x10-°. | x 10-22. Finsteraarhorn Massif. Be. 0 Gneissic granite............0..4.- 75d grams. 18 52 Bek ci 304 Gneissic mica-schist, taleose . 9°09 Lj 48 Bass. 540 =| Gneissic granite ............4.. 8:76 1-4 38 fF... | 885 i AN Wes ers ore ane 8:93 2-7 55 _ ae 957 Be i. Sete Sea 10°6 0°9 57 19a@...| 1099°5 Grey Pietra sages ase tenes 12-0 32 61 DeDiaya 3 12795 | Grey gneissic granite .. ...... 8°38 15 83 rr 1520 | Coarse gneissic granite ......... 8-98 20 79 a 1600 a ea ER has se 10:0 0-9 Le 28...... 1700 s ‘ ree ERIE 8:43 27 8-1 rR 1900 Pa * eg hele etna 8:27 15 14-1 Ursernmulde. 33a...) 21168 | Ursern pneiss..................00 11°14 grams. 1-4 32 366 ...| 2278°9 | Quartz-schist ................-.000 9°6 iA. o4 ae 2582 Black lustrous slate ..... ...... 8:0 02 6°8 44...... 2605°1 | Grey cipolin ................e eee. 9°47 0-4 2:4 2] oe 2660°6 | Quartzitic cipolin ............... 11°36 0-4 14:3 aS 27658 | Black lustrous slate ............ 10°66 1:0 4:2 ee 2930°0 | Ursern pneiss................-..0. 91 13 21 5 eae 3443°6 | Sericite-schist .................. 8:0 1°7 4-2 i — 37561 | Black lustrous schist ........ 7°84 2-4 59 > ee 4038°8 | Quartz mica-schist ............ 8:16 <0°3 2-8 | oe 4290°0 | Ursern mica-gneiss ............ 8°38 05 7 St. Gothard Masszf. i's 4525°8 | Gurschen mica-gneiss ......... 8:53 grams. 0-9 32 95......, 4882°7 | Hornblende rock ..........-.++ 9-05 boreal SO a 5250°0 | Schistose serpentine ............ 791 a | 31 | 1074 57342 | Quartzose Mihisacs eee 9°02 15 2°6 | 112... EE as, siteeemn aun 10:0 «OS 2°6 Ca = 6204-4 Quartz-felspar mica-gneiss 8°47 oe 57 Mie.) 6G! Gmeies... os edsceceesccnesee: 85 isan al Se Pe... 64269 | Hornblende gneiss ............ 9:02 | 08 8-4 i Bee RED ce. Soc aoe ceva a wenmen sens 8°34 ant ee 3°5 1296...| 7366°6 | Fine-grained gneiss ........... 9°51 07 46 135......| 7695°3 | Fine mica-gneiss ............66 9°17 13 3:2 ae 6741°1 | Quartz-felspar mica-gneiss ... 8°67 1°3 2°1 from S. | entrance. 167......| 6081-2 | Mica-gneiss........0....ceceesc0e. 10:0 | 09 13 166...... ) oss BAND ARRON? 89 venues 18 1G8.. | 5507-2 | Mica-schist poe siecicesse dee 9°58 eves! 25 158... 5267 3 a ER 9-0 Porro 22, RGA. Ce: | 5002-4 Hornblende mica-gneiss See 8°76 ARDeS ioe: 48 15,2... | 4501-9 | Sella-gneiss ...............2.0008 8-96 Ndi as 26 1 abedesp | 4078°2 | eins, LIBR So heut aes Ree 84 Oy | 2°7 ) ey alls | 3353°5 | Quartz-gneiss ..........0-s0000 8:25 <3 8-9 ‘iL ae 3272-4 | Mica-pneiss ..............020+8 » 873 poe eS 9-2 Lessinmulde. | 121 d...| 3049°2 | Hornblende-schist..... ..... ... 864 grams. | <0'3 27 llla...| 2792°8 | Caleareous mica-schist......... 9°02 | 05 7 aff 109....... 26829 | Hornblende mica-schist ...... 7°99 | 0°6 19 ee | 2008'1 | Amphibole garnet mica-schist. 8°38 ga 43 _) | 1528°3 | Quartz-schist ...........-...00:00. 9°5 | <03 6°5 (eee | 10145 | Amphibole mica-schist ......... 9:17 bw OD 2°] _ | 632°2 | Quartz-mica-schist ............ 88 | 05 | at a SOUP EROINE sagen at svedse canes oo 8°66 O-4 4°] a 144 Prot. J. Joly on the Distribution of ‘rocks passed through by the tunnel. The solutions had been prepared with much care and stringent precautions against accidental contamination with radioactive materials. After each radium test the alkaline and acid solutions were put by in corked bottles. The quantities of rock in solution are, indeed, small; in most cases rather less than 10 grams. Notwithstanding this, in all but a very few instances, perfectly definite readings of the increased discharge rate due to the contained thorium have been obtained. The alkaline solutions have not in every case been dealt with. About one third of the entire number of alkaline solutions were investigated for thorium, but with negative results. This is to be expected from the limited sensibility of the method of observation and from the insolubility of both the carbonate and oxide of thorium, a property which must result in the retention of the greater part of the thorium in the residue of the melt after this is leached with water. In one case only was any appreciable quantity of thorium found in the alkaline solution. In this case a very abnormal amount of radium had also been detected in the alkaline solution. The numbering of the rocks and their position in the tunnel are taken from Stapff’s great work on the St. Gothard Tunnel (Annexe Spécial aux Rapports du Conseil Fédéral Suisse sur la Marche de L’ Entreprise du St.-Gothard). The naming of the rocks is based on Stapff’s nomenclature. I add the radium determinations for comparison. They have not before been published in detail. (Table, p. 143.) The means of the determinations of the several geological divisions into which Stapff subdivides the course of the tunnel are as follows :— Thorium in| Radium in |Uranium in grams per | grams per | grams per 2 ram g ram g£ ram L090, x 1O= ls <10=5 Granite and gneiss of Finsteraarhorn Massif .| 1°85 77 2:26 Altered sediments, Ursernmulde ............... 0:97 4°9 1-44 Schists, etc. of St. Gothard Massif ............ 1:18 ey) 1:15 Altered sediments, Tessinmulde ............... MOLL 3-4 1:00 The uranium is computed on Boltwood’s measurement of the equilibrium amount of radium in one gram of uranium : 34x 107% gram. In my address, referred to above, I drew attention to a correspondence between the radium content of the St. Gothard Thorium in the Earth’s Surface Materials. 145 rocks and the distribution of temperature in the rocks as observed during the progress of the tunnel; suggesting that the observed gradients may, in tact, be referable to radio- activity, wholly or in part. It will be seen that the radio- active energy due to thorium must also be predominant in that region of the tunnel in which the gradients were found to be steepest ; that is in the Finsteraar granite. To some source of heat in this granite, Stapff attributed the remarkable gradients obtaining in the first 2000 metres of the tunnel. We see now that this granite is not only richest in radium, but in thorium; for however variable the results from one specimen to another may be, the added testimony of the 22 radicactive determinations in these rocks, and of the 80 measurements elsewhere throughout the tunnel, can hardly be deceptive. As observed in my former paper on the dis- tribution of thorium, the thermal value of this element is not determinable without a knowledge of its rate of transformation or an experimenta! determination of its thermal out-put when in equilibrium with its transformation products *. The quantities of thorium observed in the above experi- ments appear in the mean to come out as roughly proportional to the quantities of uranium. Im individual experiments, however, a comparison of the radium and thorium content shows that very often such a relation is widely departed from. The net result is to ascribe to these rocks quantities of uranium and thorium which are not very different. : As in the case of the collective radium measurements now in our possession, so in the case of thorium according to the foregoing observations, sedimentary materials appear to reveal the denudative loss of radioactive materials. That thorium is a generally distributed constituent of the earth’s crust and enters into the composition of deep-seated materials seems established by its universal presence through- out so vast and complex a region as that traversed by the Alpine tunnel, as well as by its presence in plutonic rocks and lavas of many ages and from many parts of the world, and in the waters and sediments of the ocean. Trinity College, May 22. * I desire, here, to correct a mistake into which I fell when referring in my previous paper to the views of Professor Soddy. A misinterpretation of a passage in his paper of Phil. Mag. Oct. 1908, led me to believe that the writer maintained the probability of equality between the rates of break up of uranium and thorium. I have Professor Soddy’s authority for stating that he had not intended to express that view. Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. L } EAL AS [ 146 ] XV. On the Distribution of Thorium in the Earth’s Surface Materials. By G. A. Buanc, Ph.D. (Lome) *. ' YFXNHE very interesting results communicated by Professor J. Joly in the May number of this Magazine induce me to recall the results of some researches which I have made on the same subject. In a first note published in February 1908 (Rendic R. Accad. d. Lineet, xvii. 1st sem. p. 101, 1908, and also Phys. Zeit. ix. p. 294, 1908) I gave the results of an investigation made by me in order to determine the amount of thorium contained in unit mass of the soil in Rome. The method consisted in comparing the amounts of excited activity of the thorium type which is produced on a negatively charged wire placed under a vessel covering a given area of soil with that produced when the vessel is placed over a layer of the same earth with which a known quantity of thorium hydroxide in radioactive equilibrium has been intimately mixed. | The result was that the Roman soil must contain ea. 1:45 x 10-° gr. of thorium per gram. It is evident that this vaiue must be considered as a minimum, the experiments having been made with thorium hydroxide, 2. e. with the compound which has the strongest emanating power, while we do not know the real state of combination in which thorium is contained in the soil. , In this same note I announced that I had undertaken an investigation with the object of determining, in a more precise and satisfactory manner, the proportion of thorium contained in a certain number of rocks of different nature and origin. The method followed in this second investigation (Rendic. R. Accad. d. Lincez, xviii. 1st sem. p. 241, 1909) consisted in dissolving, after fusion with alkaline carbonates, about 200 gr. of each sample of rock, and collecting the insoluble hydroxides (after having freed the solutions from radium by separating the insoluble sulphates). The hydroxides so obtained showed a noticeable activity when tested by the electroscopic method; this activity increased for a few weeks, until a maximum was reached. This activity could not be due to radium, for the solutions from which the hydroxides were obtained no longer gave any appreciable trace of radium emanation after the insoluble sulphates had been separated ; the test was made according * Communicated by J. Joly, F.R.S. Distribution of Thorium in the Earth's Surface. 147 to the method used by Strutt in his investigations on the amount of radium contained in rocks. It remained to be seen whether part of the activity could not be due to actinium. Although the presence of traces of actinium cannot be excluded in an absolute way for the moment (careful tests are being carried out presently in order to settle definitely the question), it is certain that the greatest part of the activity shown by my hydroxides is due to thorium. In fact, by using a very sensitive electroscope built for researches on the ionization in closed vessels, I succeeded in obtaining quite distinct phenomena of excited activity from the hydroxides, the rate of decay being that of thorium-excited activity, without any sign of an initial rapid fall which could be attributed to the presence of actinium. After the activity of the hydroxides had been determined, a given amount of thorium hydroxide in radioactive equi- librium was added to them, and the activity newly determined. In this way the amount of thorium hydroxide necessary to produce the activity originally shown by the hydroxides could be calculated, and therefore also the amount of thorium that must be present in each sample of rock. The results so far obtained, to which has been added the one obtained in a quite different way for the soil of Rome, are the following :— Vegetal earth (Rome) ............ 1:45 x 10-* gr. p. gr. Syenite (La Balma, Biella)...... 8:28 x 10-5 x - Syenite (Bagni, Biella)............ BBO HOTP 140 y'i9, Granite (Baveno, Lake Major)... 3°14x 10-6 is Granite (Voges, France) ......... 2 Ot x10 “ Finally, in a quite recent paper (Rendic. R. Accad. d. Lancet, xviii. 1st sem. p. 289, 1909), although, of course, the small number of specimens of rocks examined by me does not allow us to draw any definitive conclusions, | have cal- culated the average production of heat due to the products of the thorium family contained in the rocks examined by me, finding that it is about twice the average production of heat due to the products of the uranium-radium family con- tained in the igneous rocks examined by Strutt. Further, as it is easy to calculate, the average amount of y rays emitted by the products of the thorium family contained in the specimens tested by me is over six times greater than the average amount of y rays emitted by the uranium-radium L 2 148 Dr. J. G. Gray and Mr. A. D. Ross on an family products contained in the igneous rocks tested by Strutt. The research described above is being now extended to a large number of specimens of surface materials of the earth’s crust, but the results so far obtained, as well as those now published by Professor J. Joly, allow us to conclude that thorium has certainly a considerable importance as regards terrestrial radioactivity. Rome, Istituto Fisico della R. Universita, May 1909. XVI. On an Improved Form of Magnetometer and Accessories for the Testing of Magnetic Materials at Different Tempera- tures. By James G. Gray, D.Sc., F.R.S.E., Lecturer on Physics in the University of Glasgow, and ALEXANDER D, Ross, 1.A4., B.Se., PRS. Assistant to the Professor of Natural Philosophy in the Unwwersity of Glasgow*. [Plate II.] 5 a the usual form of magnetometer the magnetizing - solenoid is placed with its axis in the magnetic east and west line passing through the magnetometer-needle. The effect of the current is balanced at the needle by means of a compensating coil connected up in the circuit. This latter coil has its axis coincident, or nearly so, with that of the solenoid. When a feebly magnetic specimen is under examination the solenoid, and consequently the com- pensating coil, must of necessity be brought up close to the needle. If large magnetizing currents are employed, any small shift of the coils from their correct positions may be sufficient to seriously impair the balance. In consequence of this the operation of adjusting the position of the com- pensating coil (the solenoid is usually clamped once for all in a convenient position) is a difficult one, especially as the slight inevitable movement of the coil which results from clamping it in position generally results in the balance being interfered with. Even if this adjustment be accomplished with the requisite accuracy for the undisturbed position of the magnetometer- needle, it does not necessarily follow that the compensation is complete for the needle in its deflected position. In * Communicated by Professor A. Gray, F.R.S.: read before the Royal Society of Edinburgh on February 1, 1909. Reprinted from the Pro- ceedis:5s of the Royal Society of Edinburgh. Improved Form of Magnetometer. 149 practice, the axes of the solenoid and compensating coils are im general slightly inclined to one another and to the east and west line passing through the needle. The effect of this is to increase the directive force on the needle for one. direc- tion of the current and to diminish it for the other. That this is the case will be seen from fig. 1, in which the want Fig. 1. N E Ww of alignment of the coil and solenoid has been greatly ex- aggerated. The magnetometer-needle is situated at the point P, and it has been assumed that the solenoid and coil are so placed that they produce fields at P in the directions PS and PC respectively. 1f the intensity of the field due to the solenoid be denoted by F’;. and that due to the coil by F., then since the coils balance for the undisturbed position of the needle it follows that F;cos 6,=F,cos 6,. There are left, however, the components of the intensities in the north and south direction, and it is evident from the figure that if H is the horizontal component of the earth’s magnetic field at P, the total directive force at the needle is H+(F, sin 0, +F,sin 6,). If the current is reversed in the circuit the directions of F, and F, change, and the directive force at the needle becomes H—(F, sin 6,+ F, sin 02). The presence of the effect referred to may be made appa- rent by placing a permanent magnet close to the magneto- meter, and thus deflecting the needle. On reversing a current in the circuit,a change in the deflexion will in general be observed. The magnitude of the errors intro- duced may be determined in this way for various parts of the scale and allowed for in the results, or the coils may be rotated until the effect disappears. If the former method is adopted, the labour of computing the results is much in- creased, and, further, it is difficult to make a proper correc- tion, since the allowance to be made is a function both of the angle of deflexion and the strength of the current. The second method can only be used if the coils are capable of being rotated on their stands, and the adjustments would be difficult and troublesome to carry out. 150 Dr. J. G. Gray and Mr. A. D. Ross on an The necessity for attending-to this source of inaccuracy was first pointed out by Erhard*, who investigated the magnitude of the errors which were involved by neglecting it. In the case of a magnetometer of the usual type ex- amined by him, it was found that with a magnetizing field of 128°3'c.a.s. units in the solenoid there was a change of 6°8 per cent. in the directive force on the needle on reversal of the current. Erhard advised that the magnitudes of the errors introduced should be determined for various parts of the scale and allowed for in the results. While carrying out a research on certain feebly magnetic alloys, the authors found that the elimination of the afore- mentioned sources of error caused very considerable delay in the progress of the work. An attempt was therefore made to design a form of magnetometer which would overcome ~ these disadvantages which are common to instruments of the usual type. In planning the apparatus the following re- quirements were kept constantly in view: (1) the magneto- meter must be capable of accurate and rapid adjustment; (2) there must be no resultant Erhard effect; (3) the instru- ment must be suited for testing specimens at all tempera- tures from that of liquid hydrogen to the critical temperature; (4) it must be alike efficient for testing strongly magnetic and feebly magnetic specimens; (5) the magnetizing solenoid must be capable of furnishing fields up to at least 400 c.@.s. units; (6) the instrument must be rigid, all parts being fitted on one bed-plate, and the coils must be capable of being clamped without danger of destroying the compensation in so doing. Fig. 2. Ss Cc L n 7 ae | LITT Ss Fe | Cc, The general principle of the instrument which has been evolved will be seen from fig. 2. ms represents the magneto- meter-needle provided with a concave mirror, by means of which and a source of light L, its movements are observed .* & Kine oo bei magnetometrischen Messungen,” Ann. der Phys, 1902, p.. 724 Improved Form of Magnetometer. L5Sé on the scale SS. H is the magnetizing solenoid placed due east or west of the magnetometer-needle and clamped in a convenient position.. C, and C, are compensating coils placed with their axes approximately in coincidence with that of the solenoid. In adjusting the apparatus the effect of the current in H on the needle vs is first approximately annulled by means of C,, which is then clamped in position. The final adjustment of the compensation, so far as the undisturbed position of the needle is concerned, is carried out !'y means of C,, which on account of its great distance from the needle contributes only a small fraction of the balancing field, and thus provides an adjustment of great refinement. The position of C, necessary for balance having been obtained, it is clamped in position; obviously, since the distance of C, from the needle is great, any slight movement caused by doing so produces no perceptible effect on the compensation. Tf the axes of C,, H, and C, were coincident and passed through the magnetometer-needle, the adjustment would now be complete. If, however, the needle ms is deflected by means of a permanent magnet, and a large current is reversed in the circuit, in general an alteration in the scale-reading on SS will be observed. A coil Cs, placed with its axis in the magnetic north and south line passing through the needle, is now included in the cireuit. By properly adjusting the direction of the current in C3, and altering the distance of C; from the needle, the compensation can be made perfect for all positions of ns*. In a magnetometer where vs, C,, H, and C, are all carried on stands moving in one channel in the bed-plate, there should be little departure of the axes of the coils from coincidence. Accordingly the resultant mag- netic field, due to the coils and solenoid, in the north and south direction will be small. ~The coil C3 is therefore made of little power, and a small change in its position brings about only a very slight alteration in its effect upon the needle. It can therefore be clamped without any risk of upsetting the balance. The manner of making the adjustments will be tully explained later. The instrument with its fittings is shown in plan in fig. 3 (p.155). The bed-plate is in the form of a cross, and is built of well-seasoned mahogany planks 22 cm. broad and 2°5 cm. thick. The length over all is 350 cm., and the breadth from end to end of the arms 135 cm. The cross-piece is at a distance of 100 cm. from one end of the main length. Like * A side coil has been used by Dr. G. E. Allan in his magnetometric work for giving compensation throughout the scale, but it does not permit of the adjustment here described. 152 Dr. J. G. Gray and Mr. A. D. Ross on an the main portion of the bed-plate, it is formed from one piece of wood, the two lengths being set accurately at right angles and half checked into one another. The junction is made rigid by means of glue and brass screws. A channel 11°5 cm. broad is formed over the entire length of the cross- piece by means of two mahogany strips which are square in section and fixed parallel to the edges of the arms. A similar channel runs down the main length of the bed-plate, being discontinued where it is crossed by the channel already mentioned. The wooden strips forming these channels are permanently fixed by glueing and by brass screws driven in from the under side of the base-board. After they have been constructed they are made of perfectly uniform width by sand-papering, the width being tested from time to time during the process by means of a wooden gauge. A is a mahogany box consisting of bottom, sides, and top, ~ the ends which face east and west being left open. In the bottom is a slot running parallel to the cross-piece of the bed-plate. A brass screw projecting upwards from the base- board of the magnetometer passes thrcugh this slot and is provided with a brass washer and locking-nut. By this means the box can be moved through a small distance in the north and south direction, and securely clamped in position. On the upper surface of the box is fastened a plate of glass on which stands the magnetometer proper. This part of the instrument is also constructed of mahogany. A wooden pillar 20 cm. in height has a narrow hole drilled longitudi- nally down through it. This hole terminates in a small cell with a glass window in front. The cell is just large enough to contain the mirror of the magnetometer—a concave mirror, 1 cm. in. diameter, having a focal length of 50 cm. The mirror has attached to its back a small piece of magnetized watch-spring about 8mm.in length. The needle and mirror are suspended by a fine quartz fibre from a screw at the top of the upright pillar of the magnetometer. By means of this screw, the axis of which is vertical, all torsion can be removed from the fibre when the needle is hanging in its equilibrium position ; and by giving the screw an observed | number of complete turns a determination of the torsional rigidity of the fibre can be made. The pillar of the magneto- meter is attached to a circular base provided with three small brass levelling-screws. ‘The position of these feet cn the glass top of the box-stand is defined by the hole, slot, and plane method. , AA (fig. 5) is the magnetizing solenoid. Two brass tubes 45 cm. in length are connected at their ends by brass rings i mproved Form of Magnetometer. 153 so as to form a water-jacket BB measuring 4 cm. in internal and 6 em in external diameter. On the outside of this is wound 868 turns of No. 15 s.w.G. copper wire in four Jayers (only one layer is shown in the figure). The wire is double silk-covered, and each layer is varnished over after winding. The terminals of the coil are mounted on an ebonite block at one end of the solenoid. D and € are the inlet and outlet tubes of the water-jacket. Although the water-jacket is somewhat narrow it is found to be effective in keeping the helix of wire cool, even though the interior is raised to a temperature of over 1000° C. by means of an electric furnace. The water-jacket is made small in capacity in order to keep down the mean radius of the solenoid, and hence maintain the end effect of the solenoid small. The field at the centre of a coil of length 2/ and radius a is less than that given by O:4anC in the ratio (/?—2a”)/I?, where n is the number of turns in the coil per unit length and C is the magnetizing current in amperes. In the case of the solenoid now de- scribed the reduction in the field from the value 0:4anO due to the finite length of the coil is only 1:14 per cent. The solenoid is carried on a mahogany base-board provided with two vertical supports terminating in V-shaped grooves to receive the coil. The position of the solenoid carrier in the channel of the magnetometer board may be fixed by means of a brass clamp (shown in fig. 3). This friction clamp is furnished with two screws which press mahogany blocks against the outer surface of the wooden strips forming the channel of the magnetometer bed-plate. C, and (, (figs. 2 and 3) are circular coils of 15 cm. radius erected on wooden stands provided with brass clamps as in the case of the solenoid. Hach coil is wound in three sections, the terminals of which are screwed into the base of the stand. The sections in the case of C, contain 5, 7, and 9 turns of wire respectively, and in the case of C, 6, 8, and 10 turns. These sections may be used singly or in com- bination, and accordingly there is a wide range of variability in the powers of the coils.’ C; is a coil of similar construction, but has a radius of only 6 cm., and is built in two sections of 1 and 3 turns of wire respectively. D is acoil having a radius of 12 em., and its function is to prevent loss of time due to the needle vibrating about its position of equilibrium. It is connected up in series with a single cell and a reversing key; and by properly tapping the key a series of impulses is communicated to the needle, which is thus quickly brought to rest. L is a farther sliding stand carrying the object screen. 154 Dr. J. G. Gray and Mr. A. D. Ross on an This consists of a vertical wire placed in front of a window of obscured glass fitted in a metal box containing an electric lamp. By altering the position of this stand, the image of the cross-wire formed by the mirror of the magnetometer can be produced at any distance from 110 cm. upwards. From 150 em. to 200 cm. is in most cases a suitable value. At this distance it is received on an engine-divided glass scale of the usual type. , E is a deflector stand on which a small permanent magnet may be mounted in the “B” position of Gauss. The construction of the stand is similar to that of the stand which carries the magnetometer proper. On the top of it is fixed a rectangular block of wood provided with a groove for receiving the magnet. The bed-plate of the magnetometer is mounted on six pairs of mahogany feet, which are fastened to a rigid table by means of brass screws. The process of setting up the apparatus is as follows. The centre of the magnetometer-needle has first to be placed on the axis of the solenoid. To accomplish this, coil Q, (fig. 3) is removed, and the solenoid H is moved along the bed-plate towards A until its inner end is almost in contact with the back of the magnetometer casing. The stand A is then moved in its channel until the needle is brought exactly on to the axis of the helix, and is then permanently fastened in this position by means of the clamping screw already mentioned. The table carrying the magnetometer is now placed so that the long channel of the bed-plate lies due east and west, the adjustments being carried out and tested by means of the well-known method described in Gray’s ‘Absolute Measurements in Electricity and Magnetism.’ The method is as follows:—A wire is stretched out vertically beneath the needle, and accurately parallel to the short channel of the bench. On passing a current through this wire a deflexion of the needle is produced. If the current is reversed in direction the deflexion will have the same numerical value as before, provided that the wire les exactly magnetic north and south. The table is so placed that this condition is fulfilled, and its feet are then clamped to the floor by means of L-shaped brass brackets, The scale is erected on a separate table in order that the movements of the observer may not set up oscillations of the needle. The coils C,, H, and C, are now connected up in series with the storage-battery, ammeter, and variable resistances, &c., care being taken that the direction of the current in C, and Cy is opposite to that in H. The permanent adjustments of the instrument are pow complete. ‘IOJOMOJOMOVIY Jo urpq a Cn Cn 156 Dr. J. G. Gray and Mr. A. D. Ross on an When a specimen has to be tested the solenoid H is moved to a convenient distance from the magnetometer-needle and firmly clamped. The coil C, is placed at the far end of the magnetometer table, and a current two or three times greater than the maximum to be used in the subsequent test is sent through the complete circuit. Coil C, is then moved until it just falls short of balancing the effect of the solenoid on the needle. It is then securely clamped. Coil C, is next slowly moved up towards the magnetometer-needle until the deflexion of the latter is bronght exactly to zero ; Cy is now clamped, and the accuracy of the compensatien verified by suddenly reversing the current in the coils. No measurable change in the scale-reading should result. The current having been interrupted, a small permanent magnet is next placed east and west on the stand Hj, and the stand moved along the cross channel in the magnetometer bed-plate until the spot rests near one extremity of the scale. The current is again made and reversed, and if any appreciable deflexion of the spot on the scale is observed coil C3 is included in the circuit, the current being so directed through it that the deviations of the needle from its equilibrium position are diminished. The coil is gradually moved closer to the magnetometer until the Erhard effect is completely wiped out, and is then clamped in position. The compensation now holds for all parts of the scale, and the apparatus is ready for carrying out magnetic tests. The several sections in which the three compensating coils are built allow the adjustment to be completely made with the coils in several different positions. This is a great advantage, as it always affords a means of escape from any arrangements of the coils which might prove awkward when specimens are in the solenoid. . With reference to the adjustment of the coils described above, it should be noted (1) that the method is systematic, and that there is no possibility of failure to secure a balance —all the adjustments are carried out in a perfectly definite manner ; (2) that the method is delicate, for, owing to the great distance of coil C, from the magnetometer-needle, it may generally be moved several millimetres without causing any appreciable error in the compensation; (3) that the method is capable of furnishing a high degree of accuracy ; with the near end of the solenoid at a distance of only 12 cm. from the magnetometer-needle it is quite possible to arrange that the change in the scale-reading brought about by reversing a current of 15 amperes in the circuit is only a fraction of 1 mm. with the scale at a distance of 175 cm, Improved Form of Magnetometer, 157 from the needle ; (4) that the operations can be carried out with great rapidity ; unless the solenoid is very close up to the magnetometer, the changing over of the apparatus from one degree of sensibility to another can be carried out within the space of two minutes. The magnitude of the directive force at the needle is easily determined by passing a measured current through one of the balancing coils and noting the deflexion of the magnetometer-needle produced. The value of the directive force is then easily calculated. Fig.4 (Pl. I.) isa photograph of the apparatus when adjusted for the examination of a strongly magnetic specimen ; fig. 44 shows the arrangement when a feebly magnetic specimen is being dealt with. When the solenoid has to be placed very close to the magnetometer-needle to allow of a very feebly magnetic specimen being examined, the coil C, is placed on the opposite side of the needle to the solenoid. For general use, however, it is convenient to have the solenoid and coil on the same side. It is worthy of remark, in passing, that even if C, is placed as close up as possible to the end of the solenoid, it cannot alter the field at the centre of the specimen by so much as } per cent. When used for testing specimens at temperatures higher than than that of the room, an electric furnace of a type similar to that devised by Dr. G. E. Allan *, is placed within the helix. In fig. 5 it is shown in position. A tube E of Fig. 5. A A 0990000009090000000900009900000000000000090009009000000000900009000090 je a! F a= 2 Eee ee ee CC SS = = ee |jo=; [LATTA PERROTT H G CODOSSDSOSCOOOOOCOOOO OOO COO OOUO OOO GOO OOOO O OOO CO OOO COO O CO OO CO 0G0oS00000 Cc unglazed porcelain of about the same length as the solenoid having an internal diameter of 23°5 mm. and a thickness of about 2 mm., is wound non-inductively with fine platinum wire ; the ends of this wire are brought out to two terminals mounted on a slate frame at F. The tube is enclosed in a tube G of Jena glass, which fits as a cartridge within the magnetizing solenoid. The space HH between the glass and porcelain tubes is packed with dry kaolin clay, which per- forms the double duty of supporting the furnace and * Phil. Mag. 1904, vol. vii. p. 46. 158 Improved Form of Magnetometer. preventing the coils of the platinum wire from changing their positions when expanded by heat. A cylinder of electrolytic sheet-copper is placed within the tube E, and assists in maintaining a very uniform temperature over the space occupied by the specimens. In the figure the platinum wire is shown equally spaced over the porcelain tube. In reality this is far from being the case. The proper winding of the tube is an exceedingly troublesome operation, and can only be accomplished by repeated trial. . The temperature of the furnace is measured by means of the ordinary thermo-element or a platinum resistance thermometer, The two wooden stands used for the pyro- meter are shown in position in figs. 4 and 4a. As will be seen at once, the several slots in the horizontal carrier for fitting on the tops of the stands permit of these latter being placed clear of the sliding bases of the compensating coils. Fig. 6, c 00000000.0000000000090000.0000000.00000000000000000000000000006000000)l y B MUI AM Y 1] Til = a Se SS FeO KKK AKO K KK LLANE KKK ALEK HOLL KeKK Ke Keke KK eee KeKeneK Keke reKere rere) For tests at the temperature of liquid air the arrangement shown in fig. 6 is employed. The specimen A is enclosed in a glass tube BCD, of which the end B is closed and the end D is open and bent up. Cork bungs F, F are fitted on the tube so as to bring the axis of the specimen into coincidence with that of the solenoid. A third bung F or a pad of cotton-wool is used to prevent access of warm air into the interior of the solenoid, and a covering of cotton-wool on the portion CD prevents it from warming up and conducting heat to the specimen. Instead of closing the glass tube at B, a cork may be used to stop up the opening. The cork, however, if dry, is liable to loosen and permit the liquid air to leak out, or if it is at all damp it expands and fractures the tube. Where tests have to be made as the specimen slowly warms up from the temperature of liquid air, a Dewar tube is used, with its mouth closed by a cork which has two bent tubes passed through it—one for pouring in the liquid air, and the other for the bringing out of the leads from one or more thermo-elements in contact with the specimen. The Porous Plug Experiment. 159 ' The dimensions given above for the internal diameter of the solenoid will be found sufficient for receiving a double vacuum Dewar tube for tests at —252°C. on specimens immersed in liquid hydrogen. A slightly modified form of the stand supporting the solenoid permits of the latter being carried in an east and west position on one of the arms of the cross-piece of the magnetometer. The apparatus is therefore available for use with specimens in either the “A” or “B” position of Gauss; the methods described in Gray’s. ‘ Absolute Measure- ments in Electricity and Magnetism’ for the determination of the effective lengths of the specimens thus become available. The considerable height of the magnetometer-needle above the level of the magnetometer base-board (18 cm.) would also permit the apparatus to be readily adapted for testing by the “‘one-pole” method *. Several instruments of the above type have been built in the Physical Institute of the University of Glasgow, and aré giving every satisfaction. . XVIf. The Porous Plug Experiment. By W. A. Douactas Runge, M.A., Professor of Physics, Grey University College, Bloemfonteimnt. | HEN a gas escapes through a narrow orifice so that its kinetic energy is nearly destroyed, it either falls or rises in temperature. This alteration in temperature is known as the Joule-Thomson effect. Few experimental determinations have been made of this effect since the original experiment of Joule and ‘Thomson, but the matter has been so fully discussed that any reference to the previous work is unnecessary. | The author has made many experiments on the thermal change occurring during the expansion of a liquid gas, using for the purpose liquid carbonic acid contained in the small bulbs used for aérating water. If one of these is punctured below the surface of water c ntained in a calorimeter, and the rate of evolution of the gas controlled, a reduction in temperature will take place. If we suppose that the gas remains liquid during the expansion, which might be the case if the rate of escape was slow, then the pressure would remain fairly constant, and the gas would thus be driven through the plug under a * See Ewing’s ‘ Magnetic Induction in Iron and other Metals,’ p. 89. + Communicated by the Author. 160 Prof. W. A. Douglas Rudge on pressure whose value can be found from the tension of the gas at the temperature. : The total heat-change occurring in a calorimeter during the escape of the gas will be:— (1) The heat absorbed during evaporation. (2) x “ » change in temperature of the gas. (3) The heat absorbed by the Joule-Thomson effect. (2) is a small quantity in the experiments described. If H=amount of heat absorbed from the calorimeter, L=latent heat of the gas, S=specific heat, M=mass, and K=change of temperature due to the passage of the gas through the plug H=M,L+(KxMxS8), _ H-M, L iS and if P=the difference in pressure on the two sides of the =K, plug Epc chaise in temperature per atmosphere dif- P ference of pressure, the assumption being made that the specific heat remains constant. P. Plug chamber. M. Manganin coil. W. Turbine. T, and T,. Thermometers. The apparatus (fig. 1) used consisted of a small oval-shaped calorimeter made of brass in which the plug was placed. The plug itself was a small brass vessel with a gas-tight cap the Porous Plug Experiment. 161 at the lower end, and having at the upper end a stuffing-box through which passed a hard steel screw for the purpose of perforating the bulb when an experiment had to be made. The vessel was of such a size that the buib nearly filled it, and any free space could be plugged with cotton-wool if necessary. At the bottom of the vessel a fine brass tube 1 mm. in diameter was attached and carried round the chamber in the form of a spiral, the length of the tube being about 1 metre. The gas liberated from the bulb had to pass through the spiral before escaping into the air, and any heat absorbed by the gas during its expansion would be supplied by the liquid contained in the calorimeter. A spiral of “manganin”’ wire was placed in the bottom of the calori- meter so that any suitable temperature could be reached and maaintained by an electric current. A small turbine wheel driven by an electromotor served to stir the liquid; the tem- peratures were read by a thermometer graduated into 5). A second thermometer was placed in the escaping gas in order to ascertain whether the gas differed in temperature - from the liquid in the calorimeter. This was not the case. The calorimeter was suspended inside a water-jacketed outer vessel, the temperature of which was adjusted by coils of wire through which a current was passing. The mode of conducting the experiment was as follows :— The bulb containing the gas was weighed and then placed in the plug-chamber. At first the bulb was packed round with cotton-wool, but experience showed that this was not necessary as the small hole pierced in the bulb, and the fine brass tube, checked the flow of the gas sufficiently. In the first series of experiments the temperature of the liquid in the calorimeter was raised to about 20° C., and a cooling curve constructed over a range of temperature of 5°. A preliminary observation was taken of the alteration in temperature produced during the escape of the gas from a bulb so that radiation losses might be corrected in the usual way. The actual determination was now made with another bulb. The temperature of the calorimeter and its contents being adjusted to the required value, the screw was forced in and the gas allowed to escape slowly, the rate of escape of the gas being regulated by the position of the screw. The thermometer was read every minute and a curve plotted of the results. The time occupied by an experiment varied from 5 to 20 minutes, so that even at the shorter time the kinetic energy possessed by the escaped gas was small. The change of temperature was generally about 2°. After the gas had escaped the bulb was weighed and the Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. M 162 Prof. W. A. Douglas Rudge on amount of gas originally filling it found. This averaged about 4°5 grammes. The internal volume of the bulb was about 5°35 c.c. The heat absorbed was found as usual by multiplying the water equivalent of the calorimeter and its contents by the change in temperature, the water equivalent being found by sending a current of known strength through the manganin coil and calculating its value from H=C?RT. The liquid in the calorimeter was generally water, paraffin was occasionally used, but as different samples showed variations in the specific heat it was considered best to adhere to water. A typical experiment gave the following figures :— Weight of bulb full of eas: [eee a.» 17°31 grms. : git (CRAPO 2 cheat etree loser? ays 12°91 8 ~- GOS once Ss cre ee Ree Ss ss 440 ,, Temperature before escape of gas ........ 22-25 °C. Temperature after escape ...........--.>- 20°35 ,, Palin ‘temperature §.:. 2.0. wee ks os Loe Correction 305, total fall’ 2) saat © oe =: 19575, Duration of expenmient 7... ike... - 25 minutes. Water equivalent ......... BiG OS pa ea 134 units. Heat‘absorbed '°.'5.': genie doom eee sos 261°3 5 Latent heat of 44 ers. of gas ............ 159°6" Heat absorbed by passing through the plug. lly *“Cooling of the gas necessary to account for the absorption of heat... 1 aacs «ss 110" Pressure of gas at commencement of ex- PLUTON Fo ess tice, «chats eee ene ete ele 7a 57°9 atmospheres. Cooling effect per atmosphere .......... 1‘9 nearly. The examples in the following table are selected because they are all about 20° C. : The numbers in the last column are fairly constant, and about 100 experiments have been made which give practically the same range in the numerical differences. * The calculated value of the cooling was obtained by assuming the value of the specific heat of the gas to be ‘21, then H=M x8x (6-2) Fall in temperature (9—7¢) = Mxs: the Porous Plug Experiment. 163 TABLE I. Wo} | 2 | ene 43 E , _ © a ead ne o's e Se i Bae 3 2.4 = “s a ee 2S, Sq x ap 2 2, | ee eS FE Seer = ES ee ee. es be) ss = = se 4 br 5 Ay a 185 4:8 283-5 | 1824 | 1026 | 102 yah. | l org |. 44 262 1596 | 1026 | 112 57-9 1:93 21-85 | 4:39 260 146 114 123 58-9 2:08 | 93 4-4 | 244 140 | 104 112 | 60-4 1:84 233 | 368 | m0 | us | s | im 609 «| 1:82 The latent heat of the whole mass of the gas was calculated by the usual formula dk the values of V, V,, and = being taken from Amagat’s table *,—the values of the pressures were also taken from the same source. It may be objected that the pressure varied during the experiment, and this of course is true; but dealing with such small amounts of liquid gas, it would be extremely difficult to measure the alterations in pressure occurring during an experiment. If, however, we assume that the gas is boiling steadily, as is probably the case, the pressure inside the bulb will remain fairly constant until about § of the gas has evaporated, and then the remainder of the gas would be in the gaseous condition, and during its escape the pressure would fall from the steady value down to that of the atmo- sphere. With a larger bulk of gas it would not be difficult to stop the experiment before all the gas had evaporated. There is also a small change in the temperature of the gas, and this will influence results slightly. The mean result deduced from these experiments is that carbonic acid in passing through the plug is cooled by 1°894 C. per {atmosphere difference of pressure, at a temperature of * Preston’s ‘ Heat,’ p. 394. M 2 164 Prof. W. A. Douglas Rudge on about 21° C., and under a difference of pressure of 57 atmospheres. A second series of experiments was undertaken in which the gas was heated to a point above its critical temperature, so that the latent heat of evaporation did not require con- sideration. The same apparatus was used, the necessary temperature being reached by sending an electric current through the coil. The usual temperature was from 36° C. to 40° C. The experiment was carried out as follows :—A constant current measured by a Siemen’s milliampere metre provided with shunts, was sent through the manganin coil, a carbon rheostat being included in the circuit so as to keep the current at a steady value, and this could be done to about 0:5 per cent. Observations were taken of time and tempe- rature from about 32° to 40° and curves plotted : (1) When the calorimeter containing the bulb was heated and the gas not allowed to escape ; (2) When the gas escaped during the heating. The rate of rise in temperature was greater in (1) than in (2), and by comparison of the curves the fall in tempera- ture during the escape of the gas was found. The following table gives the result of one experiment. Tase IL. (1) ie When the gas not allowed During the escape of to escape. the gas. Time. Temperature. Time. Temperature. 0 31°15 18 31:3 2 33'1 20 33°05 4 34°8 Ghee 34°75 6 36°4 23 35°35 8 38°0 24 30°95 10 39°95 25 36°7 12 41-0 26 373 14 42-4 27 379 16 43°8 28 38°5 29 39°15 30 39°85 32 41:2 34 42°6 36 43 * G indicates when the gas is liberated. These two curves (fig. 2) become parallel after the evolution of gas has ceased, and the difference between two points on the Porous Plug Experiment. 165 the same ordinate during the escape of the gas gives the reduction in temperature caused by the escape, and this Fig ° 2. am co) Tem PERA TURE. cop) ip onieee er Ps 2G. 2B SO 32.1. 34. 36 TIME. (1) Without escape of gas. (2) With escape of gas. multiplied by the water equivalent of the apparatus gives the heat absorbed in the process. In this particular case the cooling amounted to 0°926 G., and the heat absorbed in the process to 215 units nearly. Since the gas during escape was at an average temperature of 37° C. it was above the critical temperature, and the pressure was calculated by finding the volume occupied by the gas, and dividing this by the capacity of the bulb. The volume of the gas at 37° C. and 760 mm. was 4°56 x 22320 x 310 14 x2973 = 2630 ce., and since the capacity of the bulb was 5°35 c.c. the pressure was 9 ake =492 atmospheres. D°39 Amagat’s curves show that at this high pressure Boyle’s law holds for carbonic acid. As the gas escaped the pressure fell, and it was assumed 166 Prof. W. A. Douglas Rudge on that the fall was uniform so that the average pressure was 49 - = 246°5 atmospheres, hence the cooling effect per atmosphere was 215 4°56 x 21 x 246°5 Other experiments gave similar results, six typical ones being tabulated below. = (07-911 ©. Weight | Fall in Heat Calculated | Pressure | Cooling per of gas. | Temp. | absorbed. fall of gas. | atmosphere. 456 | 962 | 224 | 993 492 | O-911C. 4:14 "926 215 247 445 115 4:13 ‘910 212 244 444 1:09 4°57 1:04 242 252 492 1-025 4°68 1:03 240 245 504 967 4:59 | 104 % 242 251 494 1:015 * Caiculated as on page 162. These results are fairly consistent, and do not differ very ' much from the value originally given by Joule and Thomson. The temperature, however, did not remain constant during the experiment. As there was some uncertainty as to the exact value to be taken for the fall in temperature, an attempt was made to conduct the experiment under such conditions that the tem- perature remained constant during the escape of the gas. This was done by so regulating the flow of the gas that the temperature remained constantly at 34° C. “After many trials the best rate for the gas to escape and’also the most suitable current to heat the calorimeter were determined, and it was found possible to keep the temperature constant within about 3!,° C. The amount of heat absorbed was found from the rate of rise of temperature just before and after the evolution of the gas. The results were not very different from those obtained in the previous experiments, but as the flow of gas was not free the variations in pressure were probably very con- siderable, and this may account for the variations in the value, and also for the higher numerical result. the Porous Plug Experiment. 167 Tasze III. bares Temperature Hxperiments. Time. Temperature. i yh deal 31:6 | Bed scatiocsu.! | 34-42 | ides ee: | 33-23 | i | G 340 | Mats Gi uc. cue 34-0 | 24m. 108. «2.0... G, 340 ... 29m. 108. we. 34-65 The average rate of rise of temperature during the escape of the gas was 0°-142 per minute. G and G, mark the commencement and cessation of flow of the gas. Tas_e LV. Constant Temperature Experiments. Weight | Time of | Heat Calculated | Pressure | Cooling per of gas. | escape. | absorbed. fallofT. | of gas. | atmosphere. me | —— | 4:52 | 7m. 45s. | 260 2673. "| -4T3 1-128 | 452 | 7m. 5ds. | 296 312 473 1:31 467 |9m.303.; 308 314 487 1:29 | 453 | 5m. 20s. 249 262 474 A103). | The numbers in the last column do not agree very well, but the values are very much of the same order as those of the other experiments, and the variations indicate the order of the differences met with in about 50 experiments. No very great accuracy can be claimed for these experi- ments, especially for those conducted below the critical temperature, as there is some uncertainty as to the correct value to be taken for the latent heat, and also the value of the specific heat must be continually changing under the great changes in pressure; but the method seems promising it carried out with more refined apparatus than is at present at the author’s disposal. A piece of apparatus is now under 168 Mr. W. Duddell on a construction for carrying out the experiment at 0° C. There should be no difficulty in using large quantities of liquid gases as a means of obtaining constant high pressures provided a strong enough vessel is used. =the author has great diffidence in expressing any opinion as to the value of these experiments, but as very few deter- minations of the Joule-Thomson effect have been published, — he thinks that these may be of some interest. University College, Bloemfontein, O.R.C. XVIII. On a Bifilar Vibration Galvanometer. By W. Dupve11, Fellow of the Physical Society *. he a paper read before this Society in May 1907, Mr. Albert Campbell drew attention to the great advan- tages of vibration galvanometers in the measurement of mutual inductances, and he further described a new type of vibration galvanometer which he had designed. During the last few years the use of vibration galvano- meters for the measurement of capacities, self and mutual inductions has greatly extended, and in the near future they may be expected to supersede the telephone and possibly the secohmmeter, for these purposes. As there are very few published data about the sensibility, etc., of these instruments I think it may be of interest to describe what I believe to be a new type and a series of tests made on it. ) Vibration galvanometers like ordinary galvanometers may be broadly divided into two classes,—those in which the moving part consists of a piece of iron or steel and the current to be measured flows round fixed coils as in the case of the Thomson galvanometer,—those in which the current to be measured flows round a moving coil placed in a fixed magnetic field on the siphon recorder principle. The vibration galvanometers of Max Wien and Rubens belong to the first class, while Mr. Campbell’s moving coil vibration galvanometer belongs to the second, and so does the new bifilar instrument described below. Generally speaking, when one requires to build a sensitive instrument having a short periodic time it is necessary to reduce as far as possible the mass of the moving parts in order to combine high sensibility with short period. Further, in the case of a vibration galvanometer, it is also necessary to keep the damping forces as small as possible, as * Communicated by the Physical Society : read May 14, 1909, Biilar Vibration Galvanometer. 169 the sensibility to alternating currents depends very greatly on the magnification one can obtain by bringing the instru- ment into tune or resonance with the alternating current to be measured. These considerations have led me to construct a vibration galvanometer in which the mass of the moving parts is reduced to a minimum, the moving coil being reduced to the two wires forming its two sides, similar to a bifilar oscillograph, but with this difference :— Whereas the bifilar oscillograph is designed so as to make the damping aperiodic, the bifilar vibration galvanometer is designed so as to keep the damping as small as possible. The design of the instrument* is shown in fig. 1, in which a, b, c, d,is a fine bronze wire passing over a pulley p, and stretched tight by means of a spring, the tension on the spring being capable of variation by a milled head. The wires carry a mirror M in the centre and are placed in a strong magnetic field between the poles N and 8 of a magnet. The wires pass over two bridge pieces B, B, which limit the length of the wires which is free to vibrate. These two bridge pieces can be moved nearer together or further apart by means of a right and left handed screw as required. The current to be measured passes up one wire and down the other, causing one wire to tend to move forward and the other back in the magnetic field and so tilts the mirror M through a small angle. The periodic time of the wires depends on their mass, length, and tension, as well as upon the moment of inertia of the mirror. In a completed instrument the moment of inertia of the mirror and the mass of the wires are fixed, but their length and tension can be altered in order to adjust the periodic time. Fig. 2 shows the relationship between the free length of the wires and the frequency of the free vibrations of the instrument for different tensions, and fig. 3 gives the relationship between the frequency and the tension for a series of different lengths. It will be seen from the curves that the total range of frequency obtainable with the instru- ment is very large, namely, from about 90~ per second up * Messrs. Nalder Bros. are manufacturing the instruments. 2000 =| 1] | ee NS met +++ ons” Frreourncy == A, PER SEC (MMA 170 On a Bifilar Vibration Galvanometer. to 1900, though the wires are rather too loose below 100~ per second, Fig, 2. 4 RS gee. Fee pe OF Wires — C entimernes. aa 3. eraeesaee — | a OE . ‘ gs! am LU yee z¢ ei i Loh, 25 cE ” = og oo! a N a — RS + : : a art >< v2 e. ae uh wu & » im os 2 —— \ Fe 2 ry x of Fi 0 2 4 6 Te te! | a "Wension GRAMMES As the damping in this instrument is very small the resonance is very sharp. Figs. 4 and 5 show the amplitude | a eRe eeee eS BusjIw ] LV 'SWW = NoIL931439q7 40 IGALNAW YT 500 600 700 400 200 100 > fe PER SECOND Freevenc ¥. Fig. 5. ee 60C O_O 0 300 400 900 Fr EQUENCY: “Ns PER SECOND 200 172 Mr. W. Duddell on a of the deflexion where an alternating current, having a constant R.M.S. value, is passed through the instrument, the frequency of the alternating current being varied. In fig. 4 the instrument was set so as to be in resonance at a fre- quency of 595~ per second, and in fig. 5 at a frequency of 290~ per second. The small irregularity in the curve fig. 5 at a frequency of 240~ per second was not an error of observation, hut was, I think, due to the intrument resonating one of the higher harmonics of the wave form of the alternator. To measure the sensibility of the instrument the following method was used :—A current generally 0:1 ampere from a small high-frequency alternator, having a very nearly sinu- soidal wave-form, was passed through a small non-inductive resistance and an accurate dynamometer. The vibration galvanometer in series with a high non-inductive resistance was connected as a shunt to the terminals of the small resistance in the main circuit. The current of 0-1 ampere flowing through the main resistance produced a small known difference of potential applied to the galvanometer circuit from which the current through the galvanometer could be calculated. The vibration galvanometer it must be remem- bered, has when in operation a back H.M.F., so that it is very important to keep the resistance in series with the instrument very high to prevent the back H.M.I’. from falsifying the calculation; 25,000 ohms was used for most of the tests. This method of testing the sensibility of the vibration galvanometer really calibrates the vibration galvanometer in terms of a standard dynamometer and known resistances. The vibration galvanometer is practically insensitive to any- thing except the fundamental of the wave-form of the alternating current for which it is tuned, whereas the dyna- mometer reads the mean squared current which is equal to the sum of the squares of the amplitude of all the harmonics including the fundamental. The two instruments are there- fore not strictly comparable unless the amplitude of all the upper harmonies is zero, that is to say, that the current used has a pure sine wave-form. With an instrument giving a very sharp resonance there is some difficulty in determining the exact value of the maximum amplitude, a fact which prevents such consistent results being obtained as would otherwise be the case. When the instrument is tuned so as to be in resonance with the alternating current to be measured the amplitude of the vibration is practically proportional to the R.M.S. current, as is shown by the tests recorded in fig. 6, hence it is | METRE 2 ui © Aimpuruve or Derrecrion eer rer) 150 200 100 Bijilar Vibration Galvanometer. 172 permissible to quote the sensibility in millimetres of amplitude at a metre per R.M.S. microampere. I have theretore adopted this method. 6) 3 10 15 20 25 52 9) oo PGi icro —Amreres In fig. 7 (p. 174) the relationship between the sensibility of the instrument in millimetres of amplitude per R.M.S. micro- ampere, and the frequency of the alternating current is given. The different curves refer to different free lengths of the wires. One interesting point of this figure is that where it is possible to tune this vibration galvanometer to a given frequency, using various combinations of length and tension, the sensibility so obtained is very nearly the same as long as the wires are longer than the pole pieces. The practical result of this is that if at any given length of wire or tension, one can tune the instrument to suit the frequency of the alter- nating current, then no further adjustments need be made in the hope of finding a better combination of length and tension for the purpose. 174 Mr. W. Duddell on a With each adjustment of the instrument in fig. 7 to suit the various frequencies, the sensibility of the instrument was wae) ) w cn = © 3 s Ss ) Mins. Pre Mi icro-Amrcré AT | Mi erre rS) Frequency $ PER SECOND PA LTERNATING Current tested with direct current as an ordinary galvanometer (fig. 8). It will be noted that the sensibility to alternating current decreases very nearly inversely as the frequency for which the instrument is adjusted, whereas for direct current the sensibility decreases approximately inversely as the square of the frequency for which the instrument is adjusted, which is what usually takes place with direct current galvanometers. By dividing corresponding ordinates in figs. 7 and 8 a new curve is obtained (fig. 9), which | have called the magnification, which shows for a given adjustment of the instrument, how much more sensitive it is to an alternating current of the proper frequency than to a direct current. The highest value obtained in the curves is about 460. Had the vibration Bijilar Vibration Galvanometer. 175 Fig. 8. 0 100 200 3CO 400 500 600 700 Frequency : ~ PER SECOND Direct Current galvanometer been aperiodic and of sufficiently short period to follow the alternating current then the alternating current sensibility would have been only 2,/2=2°82 times the direct current sensibility. The practical applications of the vibration galvanomeier nearly all involve using the instrument in some form of bridge or null method for determining when a small difference of potential vanishes, that is to say the instrument is generally used as a sensitive detector for small alternating voltages. The resistance of the instrument used in these tests is 136 ohms, but owing to the back E.M.F. of the instrument its sensibility as a voltmeter must not be calculated on the basis of this figure. This resistance could be easily reduced by employing a more conducting material than hard phosphor 176 Mr. W. Duddell on a bronze for the wires. There would be no objection to doing this except that the upper limit of the frequency to which the instrument could be tuned, without risk of breaking the wires, would be some somewhat reduced. Fig. 9. GTA Piacnirication Dut ro Heesonance. O 100 200 300 400 500 600 700 F'reowency = Avs PER SECOND In view of the importance of the fact that the back E.M.F. reduces the sensibility of the instrument, I have made some tests to determine its value, using the same connexions as before :-— Biilar Vibration Galvanometer. 177 Let E = the R.MS. value of the E.M.F. impressed on the circuit consisting of the vibration galvanometer and its added resistance ; d =the corresponding amplitude of deflexion in millimetres ; yr = the total resistance of the circuit ; e =the back E.M.F. (R.MLS. value per millimetre of deflexion) ; ¢ =the true value in microamperes of the current through the vibration galvanometer ; k =the true sensibility in millimetres per micro- ampere ; | then. = d = ck. If the mechanical friction of the instrument is small, then, when it is tuned to resonance, the motion of the wires will be nearly 90° out of phase with the force, 7. e. the current ; and the E.M.F. induced in the wires due to their cutting the magnetic field will also be 90° out of phase with their motion, so that the back E.M.I’. will be approximately at 180° to the current. The E.M.F. sending the current through the Vibration galvanometer may therefore be approximately taken as E—ed, and the current H—ed , whence c= r+ek= ke. If therefore 2 be plotted against r the resistance of the vibration galvanometer circuit, the graphs obtained should be straight lines which should not pass through the zero but should cut the zero line at a point ek which gives the apparent resistance of the instrument due to its back E.M.F. This test has been carried out and the graphs are given in fig. 10. From these graphs the following results were obtained :— Back E.M.F. in | a ae Frequency. poe : microvolts per | millimetre. Rice (Se en a ee | 5 538 | 30 4-8 10 592 | 130 14:8 13 530 | . 165 18-4 | 16 28 205 8:4 | Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. N 178 Mr. W. Duddell on a The very large amount that the apparent resistance of the instrument is increased by its back E.M.F., over 200 ohms in one case, shows how very important it is to try to keep 100 ApeitieD E.M.F Microvo.ts AMPLITUDE or IDEFLECTION =: MMS Ratio 400 200 © 200 400 600 800 1000 1200 Onnms Torat Resistance or Instrument Circuit. DcaAte Distance = 89 CMS. IN THIS Case this back E.M.F. as low as possible, and how little can be gained by reducing the real resistance of the wires themselves. sy The fact that the back E.M.F. of the instrument is practi- cally proportional to the deflexion and hence to the current ; Bijilar Vibration Galvanometer. 179 through it, and so appears, as far as the outside circuit is con- cerned, like an addition to the resistance of the instrument, indicates that no arrangement of condensers is likely to improve matters as one might at frst expect. Tt will be seen that the intercept in the above table decreases for a given frequency with the length of the wires in use, and as the current sensibility does not change at all rapidly with the active length of the wires there is some advantage in using the wires as short as possible when measuring small P.D.’s in a low resistance circuit. I have not had an opportunity of testing the back H.M.F. of other vibration galvanometers. In the case of the moving coil vibration galvanometer I should expect that it would be considerably larger than in the bifilar owing to the coil having a number of turns. I trust that the discussion on the paper may bring out some information on this point. All the sensibilities so far given for the vibration galvano- meter correspond to the use of a permanent magnet for the field. The instrument has, however, been tried in an oscillo- graph electromagnet, and the current sensibility was found to be increased threefold. This corresponds at a 100 frequency to a sensibility of not Jess than 160 millimetres per microampere; as a_ small fraction of a millimetre movement of the spot is noticeable we may reckon that at a 100 frequency with this instrument we can detect a current as low as 2 or 3x 10-° ampere. The advantages of the bifilar galvanometer may be summarized as follows:—Simplicity—ease in tuning—wide range of frequency for which it can be tuned—high sensi- eee, oeeible self-induction—comparatively small back Its main defect is the small size of mirror that it is neces- sary to use on the instrument. With a carefully adjusted optical arrangement, and using a small 4 volt metal filament lamp, one can work with comfort at a scale distance of a metre in a roum which is not too well lighted. In conclusion, I wish to express my indebtedness to my assistant Mr. Neale, for the painstaking way in which he has made the experiments recorded in this paper. N 2 } et ey XIX. Note on Kénig’s Theory of the Ripple Formation in Kundi’s Tube Experiment. By J. Rosiyson, B.Se., Pemberton Fellow of the Armstrong College, University of Durham*. jC apetcrertperres so evidence f has been given by different investigators in support of Koénig’s theory of the ripple formation in a Kundt’s tube. A point will here be brought forward which at all events is not in opposition to this theory. Konig { showed that when two spheres of the same diameter are in a tube in which stationary sound-waves are set up, there is a force of repulsion between them in the direction of the axis of the tube of the magnitude, 3 wa R®w, 4 24 2% where o=density of the gas in the tube, R=radius of each sphere, 7)= distance between the centres of the spheres, §=ancle between the line joining the centres of the spheres and the axis of the tube, Wy = 2rvay, Where 7, is the amplitude of vibration of one of the spheres, and vy is the frequency of the sound-wave. cos 6 (3—5 cos? @), Now this force of repulsion between the spheres depends ON Wo, which varies along the tube when stationary waves are set up. If we consider that the amplitude is a) at an antinode, it is zero at a node, and at a distance x fromthe antinode it is ih 7 2 a=, Oy 7 5 where 2/ is the distance between two consecutive nodes. Therefore in the expression for the force- exerted by one sphere on the other, we must substitute w for w) where ie 2 W=Wy COSZ +7 he wy being the value of 2ava at the antinode, and w its value at a distance x from it. | * Communicated by Prof. H. Stroud, M.A., D.Sc. + W. Koniy, Wied. Ann. xlii. pp. 3853, 549 (1891); S. R. Cook, Phil. Mag. May 1902, p. 471; J. Robinson, Phys Zeit. 1908, p. 809. t W. Konig, loc. cit, Ripple Formation in Kundt’s Tube Experiment. 181 A consequence of this would be that for equilibrium the arrangement of the particles is not the same at all parts of the tube when a stationary sound-wave is set up. We may find how the distance between the ripples varies at different parts of the tube in the following way. For the equilibrium of a particle in one ripple, the forces of repulsion acting on it from all the particles in the ripples to one side of it, must equal those from the particles to the other side of it. Now as the forces considered vary in- versely as the fourth power of the distance between the particles, we need only consider consecutive ripples, and we get an approximate result as follows:— We consider three consecutive ripples, a, 6, ¢ (fig. 1), and for the equilibrium of the particles in the middle one 6, we calculate the iotal force of repulsion exerted by the particles in each of the ripples a and ¢ on a particle in 0, and equate these forces. Fig. 1. abe The cross-section of a ripple perpendicular to the axis of the tube is a segment of a circle (fig. 2). We get an approxi- mation to the result if we consider the particles in this cross- section as uniformly distributed over a rectangle whose length is the same as that of the chord. This simplifies some inte- grations which follow. Now consider the total force of repulsion exerted by one whole ripple A B of length 2b on one particle at O, at the centre of the next ripple (fig. 3, p. 182). Let the distance apart of the ripples =a. In the ripple A B, suppose there are n particles per unit length, all the dust particles in the tube being supposed to be of the same size, i. @., of vat R. These particles are of course supposed to be small. 7. ea 0, q g ] 182 Mr. J, Robinson on Kénig’s Theory of the a The force exerted by one particle at C on the particle at O = pa eels .cos @.(3—5 cos* @). 1° \ Now in the length dz of the ripple there are n dw particles and the force exerted by these on O 3. nro R®w? = —2* =~ cos (3 — 5 cos? 8) da. %0 B Vv Therefore the total force exerted by the whole ripple on O, +0 bay =r=-{ aug cos 6 (3—5 cos” @) dx ° —b ro" S Oo 5? = —2rraRe? | sat At ee i 0 ro ax. Now ro=asec 8, x=a tan 6, dx=asec?@.d0; and therefore _1b 6 ‘ @ ite 2 tan ans { oF a= | cos? 6 (3—5 cos? 8) 0 Tt) i Oe aan Les: q ca) 0 a? dé tan = al 3 cos’ 8—5 cos’ 0)dé. 0 a? Ripple Formation in Kundt’s Tube Experiment. 183 Now f5 cos’ 6. d@= cost Osin 8 + 4{ cos? 0. dé, and 3 j cos® 6. d= cos? 6. sin @ +2 sin 6, r. 1 { cos 6(3—5 cos? 9) d0= — asin 6(2+ cos?6+3.cos' @) tan—1 5 a and F=n7reR*w? i z (2+ cos? 6+ 3 cos’ 9) | aT Sa es a 0 Now if the ripples are wide, as they are when wide tubes are used, we can have conditions so that b is large compared with a, and then Bt is nearly a right angle. Then we a can neglect cos? § and cos*f, and we find F=nroR*w? [ b se =i! — 2 sin at, a — as ele > a’ ; which we can put approximately 2naro Row? is We will now consider three consecutive ripples A;, Ay, A; Fig. 4. A, As A3 (fig. 4) so arranged that A, is distant from the antinode, A, is distant aj. from Ay, and Az, do; from Ag. The values of n and w at A, are n, and w, ” ” ” 3 Mg 59 Wee Then the forces exerted by the ripples A; and A; on a 184 Mr. J. Robinson on Kénig’s Theory of the particle at the centre of A, are I’; and F; respectively, where 2 nya R8w,? 3 Ay F\= 2n,7r0 Rew,” 5 3 433 i= For equilibrium of this particle in A we have F, =F; and therefore zis __ N3w3* era 3) ‘ A3 1. é. cs) awa Ay9 NW)?” which gives the ratio of the distances between successive | ripples. Now W, = Wo COS — T Diu, Tw h+a,+a ie l 7 h+2a = Wp COSS 2 eae 2 (where a is the mean of a; and ay), (5. h+ =“) 3 COS ee ab a Aye Th De Ny COS ; ph If we consider nj =73, 2. e., that the distribution of powder along the ripples is the same ‘for all of them, then And we see that. a,3; is smaller than aj, 2.e., that the farther we get from the antinode the smaller is the distance between the ripples. We can find the ratio of the distance apart of the rth and 7+ 1th ripples, and of that between the Ist and 2nd ripples a Ripple Formation in Kundt’s Tube Experiment. 185 (the 1st being supposed to be at the antinode) as follows, if we consider Ny =Ng=Nz= «2.00... = Np zy as (2 ; Qy9 Ww} 4q Q}a | £ 2 (3 w w oo | | S|s 8\s i bw ye ts to R|8 ho oi is) [=r} eer, | ae Ha» aD WS tae bho ecersee = es eee8 Ar, = a) ae ee ef” Forming the product of all the terms on the left, and of — those on the right, and equating, we get f 2 Ar rt igh Wr Ur+l a1 .2 W, - W2 Now W,41 1s approximately =w,, and W. IS Ag5- Some experimental results in connexion with this point have been obtained. The distance between two nodes was divided into three parts, left, middle, and right, and the mean distance between the ripples in each part measured by means of a travelling microscope. It would be desirable to make such measurements whilst the tone is being emitted, but as I used the ordinary method of producing the figures * by means of stroking a glass rod, this was not done for the results here given. The results are given for different powders and for different frequencies, and in every case it is seen that the distance between the ripples is greater at the antinodes than near the nodes, which is quite in agreement with the above investigation. Distance between consecutive ripples. Distance tex i * F Fre- Fine iron Coarse iron Emery powder Sand : © a quency. powder. powder. wo nodes. Left./Mid.) Right.) L. | M.| R. | L. | M.| RB. | L. | M. | mm.)mm.; mm. |mM.)/mmMm.)mMmM.)mmM.;mmM.| mm.) mm.|mm.) mm 3°63 4545 |0-90| 0-94] 0:86 | 1-11] 1-50] 1 31] 1-43) 1-91) 1°57) 1-23) 1-72! 1-06 cm. 5:03 3208 | 1:01) 1:25) 1:07 | 1°64| 2°33) 1-64) 1-68) 1°76) 1°48) 1-34) 1-82) 1:22 cm, * Phys. Zeit. 1908, p. 808. s Selective Reflexion of Monochromatic Light. 187 No objection can be made to these results on the ground of varying intensity of sound, as the measurements of each of the parts, left, middle, and right, are for the same set of ripples, and thus no doubt remains that the distance between the ripples diminishes in going from the antinode to the node. My thanks are due to Prof. Geh. Rat Riecke for his kind advice and encouragement during the progress of this work, which was carried out in the Physical Laboratory of the University of Gottingen. The Physical Laboratory, . University of Gottingen, \ / / April 22, 1909. \/ / XX. The Selective Reflexion of Monochromatic Light by Mercury Vapour. By R. W. Woon, Professor of Experimental Physics, Johns Hopkins University*. {Plate IIT. ] alga present paper forms the first of a series now in pre- Pp aration upon the optical properties of mercury vapour, which has yielded results quite as interesting as those which have been obtained with the vapour of metallic sodium, though of a somewhat different nature. The vapour of mercury has a strong and narrow absorption line in the ultra-violet at wave-length 2536°7, not unlike one of the D lines of sodium in character. I have already published some observations of this very remarkable asym- metrical band in the Astrophysical Journal f. There are a number of other absorption lines and bands, but it is with the one above mentioned that we are chiefly concerned in the present paper. There is a fainter line at 2539°3, which fuses with the stronger line as soon as the vapour acquires any considerable density. Planck’s theory of absorption is based upon the supposition that the energy, taken from the oncoming waves, is re-emitted laterally by the resonators. Though it is my opinion that this re-emission only occurs in exceptional cases, we do find it in some instances. As I have shown in a previous paper, sodium vapour, when illuminated with sodium light, emits the absorbed wave-lengths without change. The emission is ditfuse, however, that is, it is scattered in all directions. Radiation of this nature I have called resonance radiation, to * Communicated by the Author. T “Change in the appearance and apparent position of an absorption band caused by the presence of an inert gas.” 188 Prof. R. W. Wood on the Selective Reflexion distinguish it from fluorescence, in which case there is a change of wave-length. I predicted some years ago that if the molecular resonators were packed closely enough together, the secondary wavelets which they emit, having a definite phase relation, would unite into a single wave, and the scattered light would dis- appear, regular reflexion of the absorbed light taking its place. Repeated efforts to discover the phenomenon with sodium vapour yielded negative results, since it was impossible to obtain the vapour at great density with a sharply defined surface, on account of its corrosive action upon the trans- parent walls of the containing vessel. In the course of a long series of experiments, which I have been making upon the fluorescence, dispersion, magnetic rotation, &c. of mercury vapour, it occurred to me that this substance was well suited to the study of the phenomenon, if it existed, for it is not difficult to obtain the vapour at a pressure of 20 or 30 atmospheres, in bulbs of fused quartz. To separate the images formed by reflexion from the inner and outer surfaces of the bulb, the necks were made of very thick-walled tubing, so that the walls of the bulb were prismatic as shown in fig. 1. These bulbs were made especially for the work by Heraeus of Hanau, and were found most satisfactory. A good-sized globule of mercury was placed in a bulb which was then highly exhausted and sealed. It seemed best to begin by using light of exactly the right frequency, that is of a wave-length identical with that of the absorption line. The light from the mercury arc in a quartz tube shows a strong line of exactly the right frequency. The bulb was mounted in a small tube of thin steel provided with an oval aperture in the side: the ends were closed with disks of asbestos board, one of which supported the neck of the bulb, as shown in fig. 1. The steel tube was heated by two Bunsen burners, usually to a full red heat, and the mercury arc placed as close as possible to the aperture and a little to one side, so that its image appeared reflected in the tapering neck of the bulb, as shown in the figure. The flame of Monochromatic Light by Mercury Vapour. 189 of the burner must play over the aperture to prevent con- densation of mercury drops at the point where reflexion occurs. By properly choosing the direction in which the bulb was viewed, the reflexion from the outer surface disappeared, and the slit of a small quartz spectrograph was directed towards the bright image of the are reflected from the inner surface of the wall. A number of photographs of the spectrum of the reflected light were taken, the first with the bulb cold, the succeeding ones at gradually increasing temperatures. It was found that the relative intensity of the 2536-7 line in the spectrum of the reflected light increased rapidly as the temperature of the bulb increased. A series of these photographs is repro- duced on PI. III. fig. 1. The time of exposure was less in the case of the red-hot bulb, in spite of which the line 2536 is very strong while the other lines do not appear at all. Previous work having shown, however, that .mercury vapour emits scattered resonance radiation, when stimulated by the light of the 2536 line, it was next necessary to prove that it was not a diffuse radiation which had caused the increased intensity of the line. A very nice method was found of proving this. If our eyes were sensitive to the ultra-violet light, we should see, in the case of the diffuse emission, the entire surface of the bulb glowing with light, while if the radiation was regularly (7. e. specularly) reflected by the vapour, we should see merely the small image of the are increase in brilliancy. The steel tube was mounted vertically in such a position that the two images due to reflexion from the inner and outer surfaces of the front wall of the bulb appeared one above the other. Inasmuch as the mercury arc consisted of a narrow vertical column of light, these images appeared as narrow vertical lines of light, and could be used in place of the slit of the spectrograph. The arc in this case was placed at a distance of about a metre from the bulb. The slit tube of the spectrograph was removed, and the instrument placed in such a position that the two reflected images occupied the position previously occupied by the slit. On exposing a plate we obtain two spectra one above the other, the one that of the light reflected from the outer surface, the other that of the light reflected from the inner surface. Two photographs were taken, one with the bulb cold, the other with the bulb red-hot. The latter showed that the image of the arc as seen in the 2536 light had been increased 190 Prof. R. W. Wood on the Selective Reflexion tremendously in brilliancy by the presence of the mercury vapour. The two photographs are reproduced on PI. III. fig. 2, the spectrum image formed by the light of wave- length 2536 being indicated. The light reflected from the inner surface is not as intense as that reflected from the outer, consequently one of the spectra is weaker than the other in each case. The 2536 line is, however, many times brighter in the spectrum of the image formed by the inner surface of the bulb when hot. This experiment shows that the mercury vapour reflects light of this particular wave-length in much the same way as would a coating of silver on the inside of the bulb. Experiments were next undertaken to ascertain how nearly the frequency of the light must agree with that of the absorption band in order that metallic reflexion should take lace. j It was found that the spectrum of the iron arc showed a group of closely packed lines exactly in the region required, and it was accordingly put in place of the mercury arc. The slit was replaced on the quartz spectrograph, and photo- graphs of the reflected image of the arc were taken with the bulb cold and heated to different temperatures. A very remarkable discovery was at once made, for it turned out that the iron line which was metallically reflected (2535°67) was about one Angstrém unit on the short wave-length side of the absorption line. As the temperature and vapour density increased a second iron line was strongly reflected, this one coinciding almost exactly with the absorption line. It is in reality a double line, with wave-lengths 2536-90 and 2537-21. To make absolutely sure that no error had occurred, I photographed the spectrum of the iron arc, passing the light through mercury vapour at different densities. - The iron line which first disappeared was the double one, which was not reflected until the mercury vapour was at its greatest density. The line which was metallically reflected by the vapour at a lesser density was not absorbed by the vapour even when its density was so great that four or five lines on the long wave-length side of the line first absorbed, were completely blotted out. This can be better understood by reference to fig. 2 (p. 191). In the upper line we have the group of iron lines in question. The next line shows the absorption by Hg vapour when its density is small, the fourth iron line (double, mean \ 2537) having disappeared. Just below is the absorption by dense vapour, the absorption having extended towards the visible region of the spectrum (much of Monochromatic Light by Mercury Vapour. 191 farther than can be indicated in the figure), the third iron line being still transmitted, however. Below this is the reflexion from Hg vapour at about ten atmospheres, the third iron line being strongly reflected. In the lower line : . aenser » (C5 htm) | Fositcon of Wg. Line tr HG. irc. - we have the reflexion by vapour at 25 atmospheres, the third and fourth (double) iron lines appearing strongly reflected. This figure isa diagram, of course. Photographs are reproduced in figs.3,4,5,&6(PI.IIL.). Fig. 3 ais enlarged from fig. 5, and was made with a concave grating of two metres radius. The powerful reflexion of the third and fourth iron lines (indicated by arrows) is well shown. Fig. 36 shows the absorption of the fourth iron line by the vapour at small density, while fig. 3 c shows that the reflexion of the third line is much stronger than that of the fourth by vapour at about ten atmospheres. In fig. 4 we have the same thing shown by the quartz spectrograph, the upper spectrum reflected from rare, the lower from dense mercury vapour ; third and fourth lines indicated by arrows. Fig. 5 was made with the grating, and shows a wider range of the spectrum than the enlargement ; the powerful selective reflexion of the two iron lines is beautifully shown. Fig. 4 was enlarged from fig. 6 (quartz spectrograph). It is useless to speculate about the cause of this surprising apparent shift of the reflexion band until the absorption of a very thin layer of the vapour at very great density has been studied, for the absorption band may be shifted towards the short wave-length region as the density increases, though this is precisely the opposite to what we should expect. I have attempted to study this with small-bore tubes, but the thickness of the layer was too great. 192 Prof. R. W. Wood on the Selective Reflexion It will be necessary to have a cell made of two thick plates of fused quartz separated by a distance of say 0°01 mm., and capable of standing a pressure of at least ten atmospheres. I have ordered the cell, made in prismatic form, with the plates in contact at one end, and separated by a distance of 0-3 mm. at the other. They will be fused together along the edges, a tube being provided for the introduction of the mercury and exhaustion. This cell will also be very useful in the further study of the reflecting power of the vapour in connexion with the state of polarization of the light. There are still many interesting points to investigate, and I am at the present time devising methods and apparatus for studying the gradual transition from diffuse scattering of the radiation, to metallic or specular reflexion. It seems probable that a good deal of new information regarding the mechanism of reflexion can be obtained in this way. I have already made a preliminary investigation with a polarizing prism. The mercury are was placed in such a position that the reflexion from the inner surface of the bulb took place at the polarizing angle. The image from the outer surface was hidden by a screen. The narrow line of light was then photographed with a quartz lens in combination with one half of a quartz Rochon prism. This prism gives two superposed spectra of an unpolarized source, one polarized vertically, the other horizontally. The light reflected from the inner surface of the bulb, being polarized by the reflexion, yields only a single spectrum. It was found, however, that when the bulb was heated red-hot the mercury line 2536 appeared double, showing that the vapour reflects unpolarized light. This is shown in Pl. III. fig. 7. The upper spectrum is of the light reflected from the hot bulb, the lower from the cold. In the latter the line to the extreme left is the 2536 line. In the upper spectrum we find this line not only rela- tively much stronger, but appearing in duplicate (indicated by the arrow). It must be remembered that the two spectra given by half of a Rochon prism with an unpolarized source are superposed, the deviations being different, however. As wiil be seen, the 2536 line is the only one which appears twice, that is in the two spectra which the prism is capable of forming. The metallically reflected light being unpolarized is equally divided between the two spectra furnished by the prism. Both lines are therefore much brighter than the one in the lower spectrum. One yery import.nt point in connexion with the specular of Monochromatic Light by Mercury Vapour. 193 reflexion from an absorbing vapour is the very great density necessary before the phenomenon is exhibited. In a gas at atmospheric pressure the molecules are so close together that there will be about 80 to the wave-length, z.e. 6400 in a square the sides of which are equal to a light-wave in length. This would appear to be more than sufficient for the appli- cation of Huygens’s principle: experiment shows, however, that the reflexion does not occur until we increase this density tenfold. Iam inclined to think that it is a question of the suddenness with which the wave is stopped, rather than of packing the resonators close enough together to make the application of Huygens’s principle possible. It appears to me probable that if the wave-train can penetrate to a depth of several wave-lengths into the medium, there will be no regular reflexion, regardless of the proximity of the resonators. An analogous case is that of two media of very different refractive indices, between which the transition is gradual instead of abrupt. Some authorities hold that reflexion will ‘occur in this case, arguing, if I understand them correctly, that we can divide the transition layer into a large number of planes, each one of which will reflect a small amount. Even if this were the case it appears to me that we should have complete destructive interference, for the wave-trains reflected from the hypothetical planes would be gradually and progressively displaced with reference to each other and give us zero for a resultant. The same thing may be considered as taking place in the case of the resonators. ). e4 cos 7 sin G 5) —#sin yy cos (0-5) | wxp { (e+ 3) } =sin («+ 5 )(cos5 —t sin) : 2 2 FC Elliptic Polarization. 19% whence Soh R cosy cos ( O— 5) tesinysin(6— .) cos y sin (6- )=« sin cos O— >) zs cot( a + 3 (cos +zsin A), which gives cos2ysin(20—R) _ R 1—cos 2 cos (20—R) ee (2+ 2 ) e0s s (2) sin 2 aheeed =cot at 5) sin A 1—cos 2y cos (20—R) | 2 Irom these we obtain the equations tan (20—R)=tan (22+ R) cos A, ? sin 2y=sin (22+ R)sinA, s Nan ah) tan? y=tan («+ 6) tan (a +R—8@) that determine the character of the stream emerging from the quartz, 8 and § and consequently R and A being supposed to be known. 2. For the discussion of the elliptic polarization it is more convenient to express tan 2(@—a) and sin 2y in terms of tanR. Solving for tan 2(@—«) we obtain tan (2a +R) cos A—tan (2e - R) tan 2(9—«) = oe) 1+tan (24+ R) tan(2«—R) cosA _ sin 2R cos’A/2 —sin 4a sin? A/2 cos 2R cos? A/2 + cos 4a sin? A/2 A sin 2R—sin 42 cot? 28 sin? R ~ eos 2R+ cos 42 cot? 28 sin? R __ 2 tan R—2 sin 22 cos 2 cot? 28 tan? R 1+ (cos 4a cot? 28—1) tan? R Also sin 2y= sin 22 cos Rsin A+cos 2esin R sin A ae sin 24 cot 28 tan R+2 cos 22 cot 26 tan? R 1+ (cot? 28 +1) tan? hk 4 2tanA/2 2 cot28sinR 1+tan?A/2~ 1+ cot? 2@sin?R’ These expressions have the form y =2(ar+ bex?)/(1+ ca’), sin A= 198 Mr. James Walker on and the maximum and minimum values of y are y=a&m occurring when | v= ty = (b+ Vb +a°c) |(ac). 3. First considering sin2y, we see that sin 2y=0, or the light is plane polarized, when tanR=0 and when tan R= — tan 2a, the corresponding values of tan 2(@—«a) being 0 and —tan4da. Sin2y attains its maximum and minimum values sin 2e cot 28 tan7,,, when lect + tan? 2e/ sin? 26 . | tan 2«/ sin? 28 ‘ writing tan 2a/sin 28=tanw, W being a positive angle less than 7, tan R= tanr,= tan ?m= sin 2B cotyy/2, or —sin 2B tan W/2, and since tan R= sin 28 tan 6/2, the maximum and minimum values of sin 2y occur when 6=n4— yp. The values of tan R corresponding to the maximum and minimum values of sin 2y may be written tan R= sin 28.2, where «= coty/2 or — tan y/2, and tan 2a= —2 sin 28 cot W/2/(1— cot? ¥/2) = 2 sin 8 tan W/2/(1— tan? y/2) = —2sin 28 2/(1—2?); substituting these values in the expression for tan 2(@—a), we find eG a )(1— cos 48 ae (1—w?)(1+2?)(1— cos 48. x?)’ tan 2(0—a)=2sin2 8 and unless x?=sec 48 tan 2(0—«)=2 sin 28 32 7 tan 2a. But when «?=sec 48 tan 2a=,/ cot? 28—1, or tan? 28= cos? 2a; hence corresponding to the maximum and minimum values of sin 2y, we have tan 2(@—a)=— tan 2a, unless cos 2a= + tan 28, a case that will be considered later. Further, sin 2y= +1, only if tan y/2= sin 2a cos 28, or cot y/2= sin 22 cos 28, that is if cos 2a=-+ tan 28, and consequently, except in these cases, @ determines the plane of maximum polarization. Hence, reserving for future consideration the cases in Elliptic Polarization. 199 which cos 22=-+ tan 28, we see that as R increases from 0 to 7, corresponding to a change of from 2n7 to 2(n+1)7 according as 8 is positive or negative, the light is initially plane polarized in the primitive plane of polarization; it then becomes elliptically polarized of a sign, the same as or opposite to that of the plate according as sin 2e is positive or negative: the ratio of the axes of the elliptic vibration attains its maximum value, the plane of maximum polariza- tion being then either parallel or perpendicular to the prin- cipal section of the quartz, when tan R=sin 28 cot w/2 or =-—sin 28 tan y/2 according as # is positive or negative ; when tan R= —tan 2a the light is again plane polarized in an azimuth symmetrical to the primitive plane of polarization with respect to the principal section of the plate; the sense of rotation then changes, and the ratio of the axes is again amaximum when tan R= — sin 28tan W/2 or =sin 28 cotw/2, the plane of maximum polarization being again either parallel or perpendicular to the principal section; and finally, when R=z. the light is plane polarized in the original plane *. 4, Turning now to tan2(@—«a), we see that this attains its maximum and minimum values tan R,,, when tan R=tan R., __ —sin 2a cos 2a+,/(cos? 22— tan? 28)(sin? 24+ tan? 28) as cos? 2a— sin? 2e— tan? 28 This, however, only gives a real value for tan R, if cos? 2a> tan” 28, and when this is the case, writing cos? 2«— tan? 28= cos’ y, where y is a positive angle less than 7/2, we have tan R,,= tan (y—2a) or — tan (y+22), the value of sin 2y in these two cases being tan 28/ cos 2z. Thus if cos? 2«< tan? 28, the plane of maximum pola- rization rotates continuously as R increases; while if cos’ 24> tan? 28, it oscillates between two extreme positions, making an angle y/2 on either side of the principal section of the plate or the perpendicular plane according as cos 2a 1S positive or negative ft. * The changes in the value of sin 2y may also be conveniently traced from the formula sin 2y=2 sin 2a cos 28 sin 6/2 sin (+ 6/2)/ sin W. + This oscillation of the plane of maximum polarization was deduced by Croullebois (Ann. de Ch. et de Phys. [4] xxviii. p. 382 (1873)) for the special case of light initially polarized in the principal section of the quartz. He appears to have overlooked the fact that it requires in this case that tan 23 should be less than unity or 8<7/8, a condition found by Monnory (J. de Phys. [2] ix. p. 277 (1890)). The condition for the general case does not appear to have been previously given. 200 Mr. James Walker on The following | tables give some of the principal cases of the changes of the plane of maximum polarization and of sin 2y as R increases from 0 to 7, 8 being taken as positive. TABLE I.—cos? 2a> tan? 28. O +a 00 tTlk |, a i a 10 ae April Ist ...; 8£7 ,, 2 apr tst ..! 45-4. ,, Fe ‘18 a 1:87 ae. | oe eae arg | ae It was found in all cases that the change in fia ratio cold/hot was not sufficiently decided to show that the rate of produc- tion of Uranium X at 1000° C. was sensibly different from that at ordinary atmospheric temperatures. In conclusion, I wish to thank Professor Strutt for suggesting these experiments and for his help and interest throughout. XXIV. The Motion of Electrons in Solids. Part I1.— Radiation of all Wave-lengths in a perfectly Rejlecting Enclosure. Natural Radiation. Dependence of Natural Radiation on the Law of Force. By J. H. Jeans, IA., 1 ll a Tg A general Formula for the Emission of Radiation of all Wave-lengths. 25. ie the first part of this paper we discussed radiation of great wave-length only: our first task in discussing radiation of all wave-lengths must be to find general analytical expressions for the radiation emitted by moving electrons, which shall be valid throughout the whole spectrum. Consider an element of volume dv, so small that its linear dimensions may be neglected in comparison with the wave- length of any radiation under discussion. We regard the motion of an electron in this element as the creation of a series of imaginary electric doublets. Let M (components * Communicated by the Author. Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. Y 210 Prof. J. H. Jeans on the M,, M,, M:) be the moment of the doublets in dv at any instant, then in the notation already used, oe Seed. Here &, which in the previous paper denoted summation over a great number of electrons, will now, on account of the smallness of dv, represent (except in special cases) a sum over zero or one electron only. Taking the element dv as origin, the components of mag- netic force at x’, y’, 2’ arising from the motion parallel to Ow of any electron or electrons which may happen to be in dv, will be * i | To ae ne dt or, by equation (46), Zing vod wil... (0, —— ee ra dr is be dw), ° ° ° . (47) - where, in calculating the field at time ¢, M, and 7, are to be evaluated at time t—7/V. | 26. Consider now a small prism of infinitesimal cross section dy dz extending from «=—l to e=l. The small piece dx dy dz of this prism is to replace the former dv. The total current parallel to Ox which flows through this prism at any point will be 7,da dy. Let us call this ),. The value of j, at any point of the prism can be expanded in the form 3) Nagel J = q=a0 as icy cosge+B,singa)dg,. - « - (48) q=—0 where l A, =| Je COS Gx dx, 1 le (i. sin gw du. = =) Ultimately, when the elements of current are identified with individual electrons, these equations become | A, = eu cos gx, By 2eu sin gz, 2 eee the summation being through the prism of length 21. The values of A,, B, of course vary with the time. Again using Fourier’s theorem, we put p=a2 ‘ A,= z ( (on cos pt+a'g,sinpt)dp, . . . (50) p=0 * Larmor, ‘ Aither and Matter,’ p. 223. fotion of Electrons in Solids. y 3 WD x t pene top = ("s, Pewee ett ol) 20 | "t “a= | Absin gt Abang ye| yh vl) ee +h (2) 0 The value of B, can be similarly resolved into harmonic terms, with typical coefficients Byp, B’qp. The whole motion is now resolved into regular waves. ‘There are waves of all possible frequencies, and the waves of any single frequency are of all possible wave-lengths. Consequently these waves travel with all possible velocities. 27. The magnetic force at time ¢ produced at a sufficiently distant point 2’, y’, 2’ in direction l', m’, n’ by the 2 com- ponents of velocity of the electrons Pie re prism, is, by expression (47), a? ee tk, Lie a (0, —n', m’) rs Ge de), Pe gay e's z=—l in which j, is evaluated at time t—7/V. From Sean (50) the value of A, at time t—7/V is mf ooson('-t aH y) + 2’, sin p (t-t0— v) be Ww ee t) is the time required for radiation to travel from the middle point of the prism (e=V) to 2’, y’, <’. aa gives, as the value of the integral in expression (53), cj p=n2 q=oa f Te dz = at dx \ : on COS GL COS P(t) wep dq csi p=0 g=0 + similar terms in 2',,, ee 2 Bal p=~x q=o0 be 2 car sin { ptt) +(9 - a+ vt} Dap? p=0 g=0 g ee same (+40) na Sn A: oy eee + ...—asimilar function of —J, pax ome = (4op)q=u'p/v COS p(t—to) dp + (G+ 6 wa? COS j) (t—ty) + (a! o,—Bqp) sin p(t—ty) |dp, . (54) Pz 212 Prof. J. H. Jeans on the in which g may now be regarded as simply an abbreviation for l’p/V. We have in effect imagined the motion of the electrons. parallel to Ow to be resolved into a doubly infinite series. of regular waves corresponding to all values of p and g. Analysis has now shown that the only waves which con- tribute at all to the radiation are those for which p and q are: connected by the relation g=l'p/V. Thus the only waves in the prism parallel to Ox from which the radiation is appre-- ciable are those with an exponential factor ¢?-"?/", It follows that when the whole three-dimensional motion of electrons is resolved into waves of electrons travelling in all directions with all possible frequencies and wave-lengths, the only waves which contribute to the radiation in the- direction J’, m’, n’ are those having the exponential factor eip{t—(Uz+-m'y+n'2)/V}, These are waves of electrons travelling in the direction l', m', n’ with the velocity of light, In fact it can easily be- shown, by direct physical reasoning, that the disturbances. sent out in the direction 1’, m’', n’ by the different elements of a wave of electrons which is not of this kind, must. annihilate one another by interference. 28. Putting 17° =CptB el + Ceo)? ae (55). we see that equation (54) can be expressed in the form tT [oo) fi dx =|» cos p(t—e) dp. T z=—l 0 On replacing g by pl'/V, we have (cf. equations (51), and (49)) V so that, from this and similar equations, t Tas toy + foes = J > eu cos p(t v) dt 0 ' : : Le 2 on» —Bop = | Yewsin p(t v) dt. 0 Squaring and adding, we obtain t (rt i Yr" =|. i, D> e?uyu's cos (ts —t,— aa dt; dtz,. (6) the summation extending over all possible pairs of electrons, one being taken at instant ¢, and the other at instant tp. ¢ l' nx ohh ={ > eu cos pt cos sae dt, 0 Motion of Electrons in Solids. 213 From the law of distribution of velocities there is known to be no correlation between the velocity-components of two different electrons, either at the same or at different instants. Hence in equation (56), the whole value of y,? must arise from terms in which the two electrons concerned are iden- tical: we must have t(t (ie "Yp -( { > e? uy tt, cos p(t —to— ar) dindiget tw (OT) ovo 29. In dealing with radiation of great wave-length we neglect p/V, and therefore replace ol t —tk— ——— by p(t:—te). The value of y,2 now becomes tpt Yn" -( { > e2 UyUg Cos P(r ty) dt, dto, . ° “ « (58) 0/0 and this is readily seen to be identical with the value obtained in our previous analysis for the corresponding quantity *, as of course it ought to be. Formula (58), in which p/V is neglected, may also be interpreted in another way: it is a formula for radiation of all wave-lengths, in which the finiteness of the velocity of propagation is neglected. It is of interest to notice that from formula (58) which had already been obtained, we could have deduced the more general formula (57) by an appeal to the principle of relativity. Still another meaning can be given to formula (58): it is a general formula for radiation of all wave-lengths, in which the Doppler-effect is neglected. In all observed radiation the influence of the Doppler-effect on the partition of energy in the spectrum is insignificant T, so that we may take (58) to be a formula for radiation of all wave-lengths under natural conditions. Formula (58) is independent of the direction I’, m’, 7’. Adding to it the corresponding quantities which originate in the velocities of the electrons parallel to Oy and Oz, we obtain, as in Part I., for the total emission per unit volume in time ¢, p=o ia 3 2 nV p?( \(= e(uyue a U1V2 = WW) cos p(ty —t,)dt, dt, ap. (59) p=0 = 0.0 * The present p*yp? is identical with the previous Ay’+B,’. : ft At OPC. u/V=+52,,; in the sun, at 6000°C., u/V=73,. It is easily shown that the error introduced by neglecting the Doppler-effect is of the order of u?/V?. 214 Prof. J. H. Jeans on the This formula can be used, as in Part I., for the calculation of radiation. It is of interest to notice that it can be readily transformed to another known formula. If we replace cos p(t; —t:) by cos pt, cos pty +sin pt; sin pte, and integrate by parts with respect to ¢, and ty simultaneously : we obtain for the emission ie. duty i. | in in| { (3 js a di 177 )&008 pls C08 pty + sin pt; sin pt,)dt, dt, \ dp = 25 {(foetoon (fein fam which is the formula used by Sir J. J. Thomson*. On integration with respect to p, the total radiation per unit. volume per unit time is verified to be ae ap a Radiation in a Perfectly Reflecting Enclosure. 30. Hvery material substance ought, on the electromagnetic theory of light, to be perfectly reflecting for waves of infinite wave-length, while all actual substances are transparent for waves of very short wave-length. It follows that in any actual enclosure, the radiation of great wave-length will be retained indefinitely , so that equi- librium (7. e. equipartition) of energy must be established between this radiation and the matter in the enclosure (a consequence of general dynamical theory which we have already verified), but the radiation of short wave-length will escape without ever attaining to energ gy-equilibrium. On the other hand in an ideal (but i in practice unattain- able) enclosure, from which no radiant energy can escape, no matter how short its wave-length, there ought to be equi- librium of energy between matter and radiant ener ey of all wave-lengths. The law of partition of radiant energy in such an enclosure ought, therefore, to be that given by the theorem of equipartition of ener gy, namely, 8H REA eo * Phil. Mag. (6) vol. xiv. p. 217. Motion of Electrons in Solids. 215 The formule which have now been obtained not only enable us to verify this last conclusion, but also give us an insight into the mechanism by which equipartition is arrived at and maintained. 31. In §§ 2-7 of Part I. an expression was obtained for ec, the conductivity, on the supposition that the motion of the electrons was checked or modified only by the forces acting upon the electrons from the matter. We must now con- sider also the possibility of the motion of the electron being modified by the pulses and waves of radiation through which it passes on its path. If, as will be found to be the case, the partition of radiation is that given by formula (61), the expectation of electric force arising from the radiation at any point is infinite, or, more strictly, is limited only by the imperfections in the reflecting powers of the walls or by the imperfect homogeneity (coarse-grainedness) of the ether, both of which disturbing factors we have agreed to neglect*. Thus the forces produced by the radiation preponderate over those originating in the matter. We must still picture the electrons as checked in their motion by the molecules of matter, but must also regard them as being continually buffeted by waves and pulses of free radiation. 32. Whatever forces act, it is clear that the general argu- ment of §§ 2-7 may still be used, provided we take account of encounters with pulses and waves of radiation as well as with molecules. The value of « will then depend on the partition of energy in the ether, but, whatever its value, the relation expressed by equation (10) will still be true, namely, K Kp? Net (62) e= eS Also, provided this same value of « is still used, equation (38) is also true, namely ee ia ke AS C7 where e= Ne?/mx. These equations are still subject to the limitation that they are true only if the time intervals 27/p and t,—t, are great * Let A, be, roughly speaking, the shortest wave-length which can exist in, and be retained by, the enclosure. The radiant energy per unit voiume obtained by integration of (61) is 8m RT/3\,*. Half of this must be the mean value of E*/8z, where E is the electric force resulting from the presence of the radiation. Thus the values of E are arranged (and it can be shown that they are arranged according to Maxwell's law) akout the mean square value E?=32n? RT/3),°. * 216 Prof. J. H. Jeans on the compared with the time of a complete rearrangement of the velocities of the electrons. But when the ether is filled with pulses and short waves of sufficient intensity, this latter interval may be treated as infinitesimal, and equations (62) and (63) may be supposed true for all values of p and t)—to. 33. Proceeding as before (§ 19), we integrate expression (59) with the help of relation (63) and obtain for the emission per unit volume per unit time, 2 i I Kn? m? nV(1+ N?’e# ) For simplicity suppose the enclosure (of volume A) to be completely filled with homogeneous matter (K,). Let the radiant energy per unit volume, analysed into waves of different frequencies, be jE, dp. The total radiant energy of frequency between p and p+dp in the whole enclosure is AH, dp. The rate at which this disappears owing to absorption by matter is as in Part I. (8 18), ain? pAR, dp,... 1 0). eGo) K*p?m N?e# “in which V?u replaces C?/K. The rate at which the energy in question is added to by new emissions from the matter is at once obtainable from formula (64). Combining loss and gain, we find for the complete rate of change in H,, i alin KM An? RT , “ae = pm? * ey — AaV B, } othe (66) 1+ Niet 34, The steady state is given by dE,/dt=0, and therefore b 4 1 7 V? = Or RIA ds, » + «oven which is exactly the value required for equipartition of energy. Moreover, it will readily be found that formula (67) exactly expresses the steady state even after allowing for the corrections required by the Doppler-effect, which in our present analysis have been neglected. Thus the steady state is one of absolute equipartition of energy. BE, dp = 7g RT p? dp, Motion of Electrons in Solids. 217 35. Equation (66) shows further that if E, has not the value required for equipartition of energy, it will always move towards that value. The total energy, if not equally distributed between the different vibrational degrees of freedom, must pass towards this state. The “time of re- laxation ” for radiation of frequency p is 1 l K el evil ea For long waves this becomes K/47C?«, which is equal to the “time of relaxation”’ for the dissipation of irregularities of electric charge inside the same conductor *. In other words, the energy of great wave-length adjusts itself to equipartition exactly as rapidly as electric charges adjust themselves to the equalization of potential: the radiation of shorter wave-length adjusts itself at a slower, but still comparable, rate. There is one reservation, a very important one, to be made to all this. Equation (66) assumes the ether to be already filled with an adequate number of “pulses” and waves of short wave-length. If this condition is not at first satisfied, progress towards a state of equipartition of energy of short wave-length will begin slowly, for the creation of pulses and short waves is known to be a very slow process (§21). The theorem of equipartition shows, however, that the final state must be one of equipartition. Natural Radiation. 36. If the reflecting powers of the walls of the enclosure fall short of perfection in any degrec, the system may no longer be treated as conservative, and there is no justification for expecting equipartition of energy (of. § 21). To find the partition of radiant energy we fall back on our detailed analysis of § 28. Natural radiation, whether examined when streaming freely from a hot body or when taken from an enclosure with the most perfectly reflecting walls obtainable, is found, as a matter of observation, to be almost totally devoid of waves of the shortest wave-lengths. This is what we should in any case expect from our knowledge of the slowness with which energy of short wave-length is generated, and of the imperfect retaining power for such waves of all actual sub- stances. The analysis of §§ 30-33 assumed the presence in abundant quantity of waves of short wave-length: this analysis must now be modified to suit natural conditions. * Jeans, ‘ Electricity and Magnetism,’ § 396. 218 Prof. J. H. Jeans on the The symbol « has already been regarded as dependent on the partition of radiant energy. In passing to the new conditions now under consideration, « acquires a new value but not a new meaning; it stands in the analysis just as before, and equation (62) remains true for the new value of « as well as for the old, except that, as in Part L., its validity is confined to small values of p. Equation (63) also is no longer true except for certain sufficiently great values of the time-interval t,—¢,. As a con- sequence, equation (64) no longer expresses the emission of radiation except for waves of great wave-length. Let us replace this formula for the emission by the perfectly general formula { Ap sidctcal On dp, 6 san) en v(1+ “" ) ai N?e* which will be supposed true from p=0 to p=a. Here @, is a function of p and of T, and the constants of matter. The formula (68) is perfectly general because Op may be a perfectly general function of p and of these other quantities. Our analysis has already proved that ©, must become equal to unity.when p is small, and must fall off exponentially with p when p is great. | Formula (65) will give the absorption provided p is small. Thus at sufficiently low temperatures the formula will give the absorption accurately through those parts of the spectrum in which the energy is appreciable. To avoid too great com- plication, we shall assume formula (65) to be accurate for all values of p with which we are concerned. Our results will therefore be strictly true for low temperatures, but will be only approximations for higher temperatures. 37. Using the assumed value (68) for the emission, it is found that equation (66) must be replaced by dbp _ Kh ( Ape kee 5 Laces 14 «n'm? | o7rV ant ae } Te Ne" so that instead of equation (67) for the steady state, we have i Ey dp= yi RT p?’ O,dpHer ee = 8e RE AOL dK. Me on er - From what has already gone before (§ 16), it will be clear that the known qualitative properties of radiation will be accounted for if, on actual calculation, @, is found to be a function only of T/p and of constants which are the Motion of Electrons in Solids. 219 same for all kinds of matter. Any other form for ®, would be contrary to experience: a form in which T and p entered otherwise than through the single variable T/p would be in opposition to Stefan’s law and to Wien’s displacement-law, while a form of @> which varied for different kinds of matter would coniradict the fact that the radiation in a cayity is independent of the substance of the walls. It should be noticed that we are at present concerned only with facts about ©, which are deducible from experiment; these facts are undoubtedly true, quite apart from any theories we may hold as to why they are true. 38. We shall first consider what are the conditions, in terms of the electron-theory, that ©, shall have the required functional form. If these conditions are found to be such as we can readily believe to be satisfied in actual matter, then we shall be able to apply a further test to the electron theory by actually evaluating the function ©, and comparing the value so found with experiment. The functional form required for ©, can be expressed by the equation (Tr), - e+ + 2) in which a isa constant, the same for all matter, of which the physical dimensions are those of T/p, and @ is a function which may involve other constants, but must be the same for all kinds of matter. Let us assume @, to be of this form and examine what inferences can be drawn from equation (72). Let us put ap=ul, so that uv is a pure number, and ©» is a function of w only. Expression (68), which represents the total emission per unit volume per unit time, now becomes > dpe ART? x Ne? | Ne*a a —- u) udu aw V mu? Kum \2 $ (u) u—0 — 3 Ne?a ART’ pNe? amT Sis a Vma? si Ger 6K) where ® is a new function which is the same for all matter. The total emission per unit volume per unit time is, however, known to be (c7, equation (60)) INe*n — 2Ne*u = BV 7? where /? is the mean value, at any instant, of the squares of 220 Prof. J. H. Jeans on the the accelerations of the electrons. Hence, as a condition that equation (72) may be true, we must have — 6RT ‘KmT 2 es a i amma? (Sa. Cm 39. We wish to evaluate both sides of this equation in terms of electron-motion. Let wu, v, w be the components of velocity of an electron at any point wv, y,z at which the potential is V. The equations of motion ‘of the electron are du _ @ OV dt mon’ =2{(<) (5;) (Se) ae Hence, if E? denote at any instant the mean of the squares of the electric intensities at the points occupied yy electrons we have 5 Ce ve BA (75) -so that — eH? -—... Me The evaluation of the right-hand member of equation (74) is more difficult, as it involves the evaluation of k. If we denote by 3 the operator fo) fo) fo) fo) 51 ee oy es? we obtain from (75) a” {ea ,0V hi ae ap? (77) where, on the right, 5; operates only on u, v, w, and 2, 2 = operate only on V. Let aN, electrons in unit volume move so that the small departures from Maxwell’s law produce an infinitesimal current i; parallel to Ow, this being given (¢f- equation (2)) by ia Dd eu. The summation of equation (77) over all electrons in unit volume leads to “ , n—] ¢ 1 4 (5) 0 m ae ry ite) If we take the expectation of value of each term on the Motion of Electrons in Solids. 22t right, we of course obtain the expectation of the value of the term on the left. In taking these expectations of value, we put Suije, jo=Zw=0. ree ell in,, west ....i= 0. VI=d3= ... =0, Ke. Also there is no correlation between velocities and position,. ‘and we may put BBY YOY ug On py > p20 and the same for all differential coefficients of odd order. Equation (78) now assumes the form >> i ThE expectation of G:) 1.=pnlz y pte 1 CID) where Dna depends only on RT/m, e/m, and on averages of differential coefficients, and of products of differential _ coefficients of V*. Corresponding to a definite value 7, of i, at time t, the expectation of 7, at time ta, say za, is given by ETE di, fi ben tg=1; + (te—t,) = " +t (t,—t)? (3 i) a ce in which the expectation of every term has to be taken. Thus from equation (79) tg=h + (t2—ty) pity +5 (ta—th)? pot) +... - (80) also, for great values of ty—t,, the relation is known to be ip=e a4) 1 =7;—(f,—-t eth (Q—t)? e+, . . . (81). where, as before, e= Ne?/mx. For great values of (t,—t,), equations (80) and (81). * Relation (79) can be derived more simply, and by a method which some may think more rigorous, by an application of statistical mechanics. Let all possible states of the electrons in a unit of volume be repre- sented in the appropriate generalized space. Let S denote the region or regions of this space for which }«=7z/e, where zz has a definite given value. Equation (78) is true for the configuration represented hy every oint in the generalized space: it is therefore true throughout %. Multiply it by the element of volume in the generalized space, integrate throughout S, divide by the volume of S, and we obtain equation (79). at once. 222 | Prof. J. H. Jeans on the . become identical. It follows that, as regards the quantities involved, and the algebraic dimensions of these quantities, «” must be similar to p,—we can evaluate e”, to within numerical constants, by evaluating p,. Or, again, e? must be given, except for numerical constants, by the value of Pn+2/ Po But the difference between pnr+2 and pa lies in operating, before averaging, with 9”. It follows that ¢? is similar, as regards the quantities involved and their algebraic dimensions, to 3”, regarded as a multiplier. The operator 3? consists of sixteen terms of which typical terms are Df "Cees | OF Ow’ Ot Ox’ O° Regarded as multipliers, the dimensions of these terms are those of : OVV Ian) ee du\? ; 2(S—) [¥* ih a) Ju . em The potentials and velocities of the different electrons are arranged according to the law of distribution Ae eV emit... 2RT ge dy dz du dv du, so that the average values of eV and mu? are each of dimensions RT. We know that the average value of mu? is RT, and can take the average value of eV to be aRT, where a will, in general, depend on the — of the particular Uu dt (75). Substituting in the terms (82), we find that all the q ; e fOov~w j terms are of the same dimensions, namely, aa , which substance involved. The value of — is given by equation may be expressed as the dimensions of e?H?/RTm. We must accordingly have an equation of the form — Ne? Bek «= mic of RT’ Si where @ is a numerical constant which may depend on the stracture of the particular substance, 40. The values of /? and « are given by equations (76) and (83). Substituting these values in equation (74) we obtain eh? 6RT? V RI m ( Baek ), m2? ~ ama? «~vhich is satisfied if @(g= 3 +. Motion of Electrons in Solids. 223 Since ® is to be the same for all substances, 8 must be the same for all substances. | 41. Going back to equation (73), and substituting this form for ®, we find that we must have (writing v for cumT/Ne?a) v Uv T ue ~ | eer dh (u) udu= o(-)= aa lia (85) u=0 The fraction v/u does not depend on p, and is therefore independent of u. Calling it y, the equation becomes ra ve v T ' | ab (2)d0=— ae ‘iene iS) v=0 and since ¢ is the same for all substances, this can only be satisfied if y is the same for all substances. It must clearly be a pure numerical constant. We now have Ms tld Yu Neva so that pom aee Goniy gag Rigo (8) cone oss Oe or, in simpler form, Nb K= 7. 5 . . 4 5 . e s (88) where 0 is a universal constant. 42. For pure metals « is known from experiment to be approximately proportional to the inverse temperature, and it is natural to expect « to be proportional to N. There is, therefore, nothing inherently improbable in equation (88). We see that the observed differences between the temperature coefficients of x and the values which they would have if « varied exactly as T~' must be attributed either to variations in N as the temperature changes, or to differences between the value of « measured and the value with which we are here concerned. Such a difference would arise, for instance, if the resistance of a solid was not entirely made up of resistances such as we have been concerned with—as, for example, if the solid were not homogeneous, but had a crystalline structure. In any case equation (88) ought only to be true for very low values of T. 224 Prof. J. H. Jeans on the The Law of Force. 43. To reconcile experiment with electron-theory, we have found that at low temperatures the value of « must be of the form given by equation (87). But actual calculation has. shown that « must have the form given by equation (83). Comparing these two values for «, we find P=RPajeeey. -.. . (. 1.) Thus the average square of the force (e?H?) acting on an electron must be of the form gT?, where g is the absolute constant Rm/a?8’y?._ We can easily see why e?H? increases with T ; at higher temperatures the kinetic energies of the electrons are greater, and the electrons consequently penetrate to regions at which the force is greater. The knowledge of the exact relation between EH? and T enables us to find the law of force under which the electrons move. 44. Consider first a temperature T=0. The electrons have no kinetic energy,and so fall into positions of equilibrium. Thus K?=0, in accordance with equation (89). Considering next small values of T, we can find the nature of these positions of equilibrium. Suppose, first, that these positions were represented by ordinary minima of potential (if such could exist), then at a small temperature T the electrons would oscillate about these positions. The average squared force (H*e*) would be proportional to the average square of the displacement, and therefore to T, and equation (89) would not be satisfied. Thus the zero value of H? which indicates rest in a position of minimum potential is. not a limiting solution of equation (89). There is only one alternative— EH? must vanish when T=0, on account of the electrous being at infinity, or being so far removed from the centre of force that the forces acting on them are negligible. Suppose, first, that each electron is acted on by only one centre of force of law y/r*. The potential is (n—1)p/7—", so that at temperature T the law of distribution of distances is e—("—)e/RIr"—* 52 dy, and the value of e?E? (the average value of y?/r?") is found to be proportional to T?”/"-1, This gives relation (89) if n=3, and if w is the same for all kinds of matter. If the electrons are acted on by more than one centre of force, it is readily found that H? will not vary exactly as any power of T,and must moreover involve the distances between the different centres of force; these would be different for different kinds of matter. 45. Thus we must suppose that, in all kinds of matter Motion of Electrons in Solids. 9a alike, the radiation proceeds from electrons describing orbits about centres repelling as the inverse cube of the distance, these centres being of equal strength in all kinds of matter. The influence of forces varying as other powers of the dis- tance, and of the presence of centres of force other than that primarily involved, must be looked for in departures from the laws of Stefan and Wien. It will be remembered that Sir J. J. Thomson, in his paper already referred to, comes to the conclusion that Stefan’s and Wien’s laws point to collisions with molecules which have to be similar for all matter, and repel according to the law p/r®. The present writer ventures to think that the similar centres of force may be found to be the positive electrons. The ultimate test of any such conjecture must, however, be the calculation of the radiation function and comparison with experiment. Conclusion. 46. It may be of value to collect and summarize those of the results obtained which have reference to the radiation problem, arranging them in their logical order. I. It has been verified, by analysing the motion of the electrons, that radiation in a perfectly reflecting enclosure, when in a steady state, must be distributed between the different wave-lengths according to the law of equipartition (§ 34). We have found formule for the rate of progress towards this state, and for the “ time of relaxation ” (§ 35). II. It has been shown that when the walls of the enclosure are incapable of retaining radiation of short wave-length (as all actual substances are) an entirely different partition of energy is to he looked for. We have supposed this new partition to be such that the energy: of frequency p has ©, times its equipartition value. III. It has been verified, by analysing the motion of the electrons, that ©,=1 when p is small, and that ©? must fall off exponentially with p when p is great. Both these results are in agreement with experiment. | The first result @p=1 had been obtained by Lorentz* on the suppositions of undisturbed free-paths and instantaneous collisions, butit seemed desirable to have a further calculation free from these suppositions f. | IV. The various results obtained have given some insight as to why @, starts with unit value and gradually falls off as p increases. We have found t (§ 26) that the irregular * Amsterdam Proceedings, 1902-3, p. 666. + Phil. Mag. xvii. p. 253. t Cf. also Phil. Mag. xvii. p. 254, Phil. Mag. 8. 6. Vol. 18. No. 103. July 1909. Q 226 i Motion of Electrons in Solids. motion of the electrons can be resolved into regular trains of waves. Only those waves contribute to the radiation which travel with the velocity of light (§ 27). These waves emit and absorb radiation with a frequency equal to their own, and there will clearly be rapid interchange of energy between the waves of electrons and the radiation of the same trequency in the ether. So long as we deal only with waves of wave- length great compared with the distances of adjacent electrons, the collection of electrons can be treated as a continuous electric medium. The degrees of freedom of the electrons may be supposed to be the waves in this medium, and these are in energy-equilibrium both with the matter and with the waves in the ether. We see at once the dynamical necessity for the result that ©, =1 when p is small. As we advance up the spectrum we cannot suppose that there are waves of the electric medium for all values of p, for if this were so the finite number of electrons would possess an infinite number of degrees of freedom. If p, and Po are two adjacent values of p, there may be only one degree of freedom of the electric medium for the values p, and po of p, and for all the values between. The vibrations of this degree of freedom may at one instant exchange energy with the vibrations in the ether of frequency »,, at another instant with those of frequency p2,and so on. If the various vibrations of the ether are retained indefinitely there must ultimately be partition of energy between all (result I.), but if not there must be a falling off from equipartition values. V. The dependence of ©, on p will vary with different structures of matter. All the known phenomena of radiation are accounted for if @p is a function only of T/p and of universal constants. According to the thermodynamical theory, ©, must neces- sarily have this form. The thermodynamical! theory, however, applies (if at all) only to the radiation inside a perfectly radiation-tight enclosure. Then ©, has the required form, for it is equal to unity for all values of T and p (result I.), but this does not give any assistance towards finding a formula for natural radiation. VI. The required form of ©, is obtained only if the law of force acting on the electrons is that of the inverse cube of the distance. VII. Since it is known that there are terms in the law of force which fall off as the inverse square, and since the electrons must always be acted on by more than one centre of force, it follows, if our analysis is sound, that Stefan’s and Wien’s laws must be only approximations. April 28th, 1909. ieinese | XXV. Notices respecting New Books. Cours de Physique. By H. Bovassz. Vols. II.,1V., & V. Paris: Librairie Ch. Delagrave. ° compile a new textbook of physics at the present day is no light task, since the subject is being enriched in so many ways in consequence of modern discoveries on both the experimental and the theoretical sides. M. Bouasse himself has felt this especially in connexion with the development of Thermodynamics (Vol. IT.). The happy time is past when the lot of a professor was merely to explain certain general principles and apply them to some stereo- typed examples; or rather, as we should prefer to say, the happy time has come when that is no longer necessary. The present textbook is one which deals mainly with the theoretical side, though the results of theory are usually illus- trated by numerical calculations applied to particular experimental eases. M. Bouasse possesses the quality of most French writers ot being a very lucid exponent of his subjects. The general im- pression conveyed by these volumes is that they are very tightly packed ; there is nothing prolix, at any rate, in their style; and yet we do not know of any clearer exposition than we are here presented with. Our own preference is that the experimental side should be considered side by side with the theoretical, and the absence of experimental details may be thought by others as well as ourselves to be a drawback. On the understanding, however, that the book is not intended to be used alone, we can confidently recommend it. The parts of the subject which are dealt with in the volumes at present before us are: Thermodynamics, Theory of Ions, Optics, Electro-optics, Hertzian Waves. The Theory of Valency. By J. Newron FRIEND. Longmans, Green & Co. 1909. Price 5s. Tuis forms one of the Textbooks of Physical Chemistry edited by Sir Wm. Ramsay. The fact that a special volume should be needed dealing with a peculiar part of a subject like this, is sufficient evidence of the very rapid progress of knowledge. No volume on this subject exists prior to this one in English, and only one in German; consequently it practically opens new ground in the way of separate publication. The subject is avery fascinating one, and our author, who can speak with weight, has put it forward in an interesting and thorough fashion. In spite of the many difficulties which the subject presents, there can be no doubt that the idea of valency is a valuable one, especially in the light of modern electrical developments. At the same time the present reviewer wonders whether it is not being pressed too far. The possibility, at any rate, of the existence of fractional valencies is certainly suggested by the phenomena of loose aggregates such as in the formation of hydrates. It also is suggested by such results as those of Ternent Cooke (p. 57), according to which the vapour 228 Intelligence and Miscellaneous Articles. density of zinc is found to be some 12 per cent. higher when in an atmosphere of argon than in one of nitrogen. Such facts as these make one pause contemplatively, and sympathise more completely with the ideas of Lodge expressed on p. 137 rather than with the main ideas underlying this volume. Transactions of the International Unien for Co-operation in Solar Research. Vol. Il. Manchester University Press. Tu1s volume, which is edited by Prof. A. Schuster, contains the verbatim report of the Third Conference of the International Union held at Meudon in 1907. Amongst the papers communi- cated and printed here are one on the determination of the wave- length of the red ray of cadmium as a fundamental standard of wave-lengths by MM. Benoit, Fabry and Perot; the work of MM. Fabry and Buisson on measurements of wave-lengths made to establish a system of spectroscopic standards ; the measurement of Solar Photographs made with the spectroheliograph by George E. Hale; and the report of the Committee on Sun-spot spectra drawn up by the Secretary (A. Fowler), including a list of publi- cations referring to Sun-spot spectra. The volume is crowded with interesting and valuable matter. XXVI. Intelligence and Miscellaneous Articles. To the Editors of the Philosophical Magazine. GENTLEMEN,— [% a paper of April 1909 in this Magazine, the Earl of Berkeley and C. V. Burton treat the problem of finding the influence of gravity upon a binary solution. I wish to call the attention of the authors to the fact, which they seem to have overlooked, that a complete solution of the problem is to be found in a paper * by the writer published Oct. 1906. The cases of a rotating solution and a solution subject to the earth’s field were specially treated, and in the latter case numerical calculations were carried out for solutions of cane-sugar and potassium hydrate. Further, the following equation was found :— (Ot et r= (55 pan KP Op This important relation connecting the concentration gradient with the variation of osmotic pressure with hydrostatic pressure is identical with the relation expressed in equation (7) in their paper. I am, Gentlemen, Yours faithfully, L. VEGARD. * Christiania Vid. Selsk. Skr. No. 8, 1906; Phil. Mag. May 1907. Phil. Mag, Ser. 6, Vol. 18, Pl. I. pp thickness. Cert ESOT deal | n on reflexion from ste “Gupaae and low dispersion arra; ee ae Peer ia (a7 Se eee avelength 43 eRe bee Se ess a es 2.0m aa ).—Curves showing the variation of transmission | with wave-length for the various films. a) | : Jas A & rel oe a eee ee a Sco | > in 22So2 =a HH CER REEEEEECAHE EERE EEE me EEE 13 Fig. “PY Wavelength” a 18) yl as a | Curves showing the rotation on reflexion from the rh = al glass-iron surfaces of films 15, 17, 22. cx REE 18 ic ee c-2 TASS —— Ba 2 || | See g SS SSS oe a z Bieter titi. c 2.0% Lop os Wavelength. Rotation On Refiection . TyeERsOLL, Ira. 3,—Curyes for rotation on transmission through Fluorite, showing effect of using high and low dispersion. Fria. 4.—Curves for rotation on reflexion from steel, showing measurements with high and low dispersion arrangements, Phil. Mag, Ser. 6, Vol. 18, Pl, I. Fig. 6.—Ourves for film 15, of 58 He thicknoss, Si ioe eee a fees JL 25 - Rotation On Transmission Rotation 1 a op to 156 Wavelength Frc. 7,—Curves for film 17, of 30 yp thickness, L C1 ® On Transmission R, a i [ | 5 K) 1s 2.0 Ze o Wavelength, a ar Fra. 11.—Curves for partially oxidized film 7. Transmission curve On Transmission. Rotation On Reflection has been corrected for the rotation of the glass. On the reflexion curve, points plotted as triangles were deter- mined with the rear glass surface covered with Canada balsam and lamp-black. | GRRe Br (SESS ea g ? Wavelength. Rotation On Reflection. On Transmission 1 Nn, », JL 5 19 15 2.) te We Wavelength. us zy Fie. 12.—Curves for partially oxidized film 14, Transmission curve has been corrected for rotation due to glass. I6% lo ean ic} al al 3 le! 2 : IL = 1 = 08;— i— 5 | 3 ae =] © go 4 I $+ ° = le 2 ° ° Oc oO > Sela vo ia 6 A | al | 08 ae Loe rr _t ZOE Wavelength Rotation CoE eS cn E : sereeee mo : estecatiianeat zy Ey aL + 2 ° Rotation On Reflection ie 19.05 5 Wavelength, | e Pia, 10.—Curves showing the variation of transmission with wave-longth for the various films, 2 LI “29 ee Mee eld fe ve T cin percent) 13, Wavelength Fre. 13.—Curves for rotation on reflexion and for reflecting power of opaque, partially oxidized, film 29. The reflecting power curye of pure iron film 15 is shown for comparison. I'ra. 14.—Curves showing the rotation on yeflexion from the glass-iron surtaces of filma 15, 17, 22. Ref!, Power, Eig et a Re ea a a M4 : g SSE a 3 SS nee 5 a = Deeoeesian ety A = ¢ a ane ne Ce ci - Wavelength BE ws 1onte ~~ ae Lie t ~ . “ qg o oP ag + , y ‘ ~ > ‘ ‘ ‘ ! aa ote a % . i | eee H é * ms 4 i f = ree a a3 ~~ REY 5 ' re) ae ao ae ie Pewee d ss ait ea 7 ‘ ‘4 as r . 2 ‘ Ff - he) ree © Tae | n re ry Se a Le t * ‘ » ; ~ ‘ 7 4 y ‘) y he ya’ ree J 7 4 ‘ ‘ > . “ ru . - 1 uw —. Lass ; ‘ me | 4G ‘ " - F } 4 - je x . i) a 7 t o , \ 4 ‘ oi mg , " wy —- Oe P ay dee ie _ ‘ . “ 7 - . 5 aes La * . ‘ F , + y E mu wu 2 ; y. ‘ | t Y > a i : : ; , i \ ; t ' a ' : 2 ' i= y . ‘ 4 { Ly ~ i a ” ve > o <= . é Scat. yew tong = i ‘ 7 aS «J ; s «oe wees i +’ ’ oe . ‘ * Lik ie ‘ . 2s & ey 8 t ta & . ' ‘ , PI , te 1‘ £0 - r . eM ate i ; ded AAAS Hike ; ite = e ‘ . ’ “ ar hene ee Vise ae Be ' sas on te we — a ee = > ~~ Hy L ! ‘ £ r a . * - ' , by ’ GRAY & Ross. Phil. Mag. Ser. 6, Vol. 18, Pl. IT. Fig. 4. Rie. 4x, WwoopD. Phil. Mag. Ser. 6, Vo). 18, Pl. ITI. = e 2 2 = Ss iS RS x S N > CoLD. outer Hor saaee'y CoLp. RED-HOT. } outer inner § Hor. Fia. 1. Figs?) hie. 5. ie. 3: Pic. <7. Fre. 8.—Mercury Waves. THE Pn, ’ LONDON, EDINBURGH, anp DUBLIN —* AND JOURNAL OF SCIENCE. wan ah, [SIXTH SERIES.] . ~~, 4 se) AUGUST 1909.\ *. qn 2 L Se ie de XXVIL. The Discontinuity of Potential at ‘the Sud Glowing Carbon. ByJ.A. Pottockn, A. BL BeRanciaups and EB. P. Norman *. @ . WING to the projection of ions by hot substances, a discontinuity of potential will occur at the surfaces of the electrodes in any circuit in which these latter are formed of heated materials. The value of potential discontinuity has been calculated by Professor Richardson f from considerations connected with the gas theory of metallic conduction, and has been found in the case of carbon by Mr. Duddell ¢, who observed at the surface of the cathode of the ordinary carbon are a forward electromotive force of 6°1 volts, and a back electromotive force of 16°7 volts at the surface of the anode. In a circuit with one heated electrode in air at ordinary pressure, the projection of ions from the hot surface necessitates the establishment of a _ potential-difference between the electrodes if the current in the circuit is to be zero. If electrons alone were projected, a layer of gas close to the hot surface would become negative to the solid and the potential-difference between the electrodes for zero current might be taken as a measure of the surface discon- tinuity of potential. When positive ions are emitted as well as electrons, owing to the differc.se in the distances from the electrode at which the two classes of ions are stopped by * Communicated by the Authors. Read before the Royal Society of New South Wales. + Richardson, Phil. Trans. A. eci. p. 497 (1903). { Duddell, Phil. Trans. A. ccili. p. 305 (1904). Phil. Mag. 8. 6. Vol. 18. No. 104. Aug. 1909. R yt. —_ 1m, *E , 4 ; fe PHILOSOPHICAL MAGAZINE ~~. “ 230 Messrs. Pollock, Ranclaud, and Norman on the collision with the gas molecules, the electric force may change sign in the near neighbourhood of the heated surface. In this case the potential-difference between the electrodes for zero current, with appropriate sign, must be less than the value of the surface discontinuity which would be due to the projection, alone, of that class of ions which conditions the sign of the potential-difference. With the apparatus described in a previous paper™ the potential-difference for zero current has been found in the case of glowing carbon at various temperatures, The experi- ments were a continuation of the work already described, and in the paper just mentioned will be found full details of the method of investigation. The observations, which fulfil the condition that the values should be independent of the ~ distance separating the electrodes, are shown in the figure. For zero current the hot carbon was positive to the cooler electrode in all cases. Potential-differences for zero current. 18 T | | | | i | sl when distance between| carbons|= 2m: (O) a“ “u “a ” “u H + a“ ” ” “ 1 | ae OR eee Bae a: | ee le a) tae leh pa | a eel S00 760 i900 2100 u) 200 2700 2900 3109 3300 3500 woo 500 Temperature Absolute. i2 -] 2 a es = o Ly & = between The heated electrodes were cored carbon rods, 0°5 centi- metre in diameter, supplied by Messrs. Siemens Brothers for use with their Lilliput arc lamps, with the exception of the one employed for the observation at 3040° absolute which was a squared rod, 0°5 centimetre on the side, of solid Conradty carbon Marke C. As the measure with this material agrees well with the other results, it may be concluded that * Pollock & Ranclaud, Phil. Mag. March 1909, p. 366. Discontinuity of Potential at Surface of Glowing Carbon. 231 values of the potential-difference for zero current with hot electrodes of different makes of carbon do not seriously differ. At 3120° absolute, with 50 volts between the electrodes, the ratio of the flow of negative electricity from the hot carbon to the flow of positive, when the sign of the potential- difference was reversed, was as 20 to 1. On the assumption that at high temperatures the potential- difference for zero current measures the surface discontinuity of potential, as the number of electrons then projected per second far exceeds that of positive ions, the curve in the figure has been continued to the value, 16:7 volts, found by Mr. Duddell (loc. cit.), for the back electromotive force at the anode of an are between solid Conradty horis carbons. This measure has been plotted for the temperature of the crater, 3690° absolute, determined by Messrs. Waidner and Burgess* from observations with a Holborn-Kurlbaum optical pyrometer, a similar instrument to that with which we have estimated the other temperatures. Mr. Duddell gives 6:1 volts as the measure of the forward electromotive force at the are cathode ; this value corresponds, on the curve of potential-differences for zero current, to a temperature of 3375° absolute, which, if the assumption already stated is legitimate, may be taken as an estimate of the temperature of the cathode of the carbon arc. With a heated iron wire in the place of the hot carbon of the previous experiments, the potential-difference for zero current was 0°85 volt at 1410° absolute and 0°25 volt at 1570°, the hot wire being, in both cases, negative to the cooler electrode. The potential-difference with a platinum wire, not specially treated, at 1580° absolute, was 0°40 volt, the hot wire being again negative. With a Nernst filament, designed for 0°25 ampere at 90 volts and used under these conditions, the potential-difference for zero current was 0°25 voit. In this case the filament was positive to the cooler electrode, and with a potential-difterence between the elec- trodes of 45 volts, the ratio of the flow of negative electricity from the hot filament to the flow of positive, when the sign of the potential-difference was reversed, was as 33 to 1. Professor Richardson (loc. cit.) gives, for the number of corpuscles shot off from unit area of a hot conductor per b second, the expression A@e ®, in which A depends on the number of corpuscles per unit volume of the conductor, and b on the work done by a corpuscle in passing through the * Waidner & Burgess, Phys. Rey. xix. p. 255 (1904). R —_ 232 Discontinuity of Potential at Surface of Glowing Carbon. surface layer, 8 being the absolute temperature. The formula, considering A and 6 as constants, very well represents the observations of its author and others on the saturation currents from hot bodies through the range of temperature for which it has been employed ; from such observations the values of b for certain substances have been determined. In the theory by which the expression is deduced, b is equal to ®/R, where ® is the work done by a corpuscle in passing through the surface layer, and R a gas constant, equal to p/N@, p being the pressure and N the number of molecules per cubic centi- metre. The discontinuity of potential is thus represented by b/Re, where e is the ionic charge. The following are the values of the discontinuity of potential as calculated by Professor Richardson :— | Temperature Discontinuity of absolute. potential. Podium ay ee. 490°-700° 2°45 volts. Platina en 1378 -1571 AST Te Carbon), J. 2300 1520 -1770 61" ee These results, which are not appreciably altered by recal- culation with the new value of the ionic charge determined by Professor Rutherford and Der. Geiger *, seem singularly high. If bR/e really represents the discontinuity of potential, the fact that the discontinuity varies somewhat rapidly with temperature for higher values shows that b cannot be con- sidered altogether constant. In a recent paper Professor Richardson and Mr. Brown + originate the theory of a method for finding the kinetic energy of the electrons projected from heated materials, and they have experimentally determined the component, per- pendicular to the hot surface, of the velocity with which electrons are projected from glowing platinum, the result for a temperature of 1650° absolute being 1°5 x 10’ centimetres per second. This velocity of projection, in the case of glowing carbon, may, on certain assumptions, be estimated from the results already given in the present paper. As suggested by one of ust, a point of view is possible from which the work done in connexion with the passage of the electrons through the surface-layer may be considered as represented by their translational energy when they emerge into the gas. In such a case the surface discontinuity of potential, V, may be * Rutherford & Geiger, Proc. Roy. Soc. A. xxxi. p. 162 (1908). t Richardson & Brown, Phil. Mag. xvi. p. 355, Sept. 1908. t Pollock, Phil. Mag. March 1909, p. 361. Vibration Curves of Violin G String and Belly. 233 expressed by the equation nr é where m is the mass of the electron, e the ionic charge, and v the component, in the direction of the field, of the velocity with which the electrons are projected from the hot surface. If this equation holds, on the assumption previously stated, we may deduce from the curve in the figure that the velocity with which electrons are projected from glowing carbon varies from 1°5 x 108 centimetres per second at 3375° absolute to 2°5 x 108 centimetres per second at 3690° absolute. In a similar way, from the result previously given, a lower limit to the velocity with which electrons are projected from the Nernst filament may be calculated as 3 x 10° centimetres per second. The Physical Laboratory, The University of Sydney, November 28th, 1908. XXVIII. Vibration Curves of Violin G String and Belly. By H. H. Barton, D.Sc., F.RS.E., Prof. of Experimental Physics, and T. J. Ricumonp, B.Sc., Research Scholar, University College, Nottingham*. ; [Plates IV.-VI.] T the end of 1904 it occurred to one of us that it would be of interest to trace the various changes in vibration form experienced as the motion passes from a vibrating string to the ear by means of the bridge, belly, and air in the sound-box. For although the string is the source of the vibrations concerned, and the pitch of all those vibrations depends on the dimensions, nature, and tension of the string, yet it is only after the occurrence of the modifications referred to that the ear receives the impression and affords the hearer any evidence of the quality of the tone produced by the instrument as a whole. Hence, although both by theory and experiment the vibrations of a string have been investi- gated and their character known, whether excited by plucking, striking, or bowing, there still remains much to be done before we have full information as to the qualities of sound actually received from any musical instrument. Or, in brief, though we have theoretically a sufficient knowledge of * Communicated by the Authors. 934 Prof, E. H. Barton and Mr. T. J. Richmond on the quality of tones emitted by vibrating strings, we have not the like knowledge of the quality emitted by stringed anstruments. The preliminary work was done with the monochord and dealt with the belly *, the air f in the sound-box, and the bridge f respectively. The present paper is the first instalment of work on the violin and is in the main confined to the g string. Speaking generally, perhaps the chief distinction between the curves here obtained for the violin belly and those for _the monochord lies in the fact that to the eye the violin-curves appear simpler and smoother. Often that means, however, that they have a fuller retinue of upper partials, but without undue prominence of any one of them, as was sometimes noticeable with the monochord. But perhaps it is still too soon to draw such conclusions safely. Incidentally the pitch of best resonance was found by use of the French-horn, and a wandering of the vibrations of the belly over its surface was detected. Optical Arrangements.—The general arrangement of the apparatus for the experiments may be understood from fig. 1 (PLIV.). Inthis Ty:and T, indicate the two tables, the first carrying the lantern L and the lenses, the second holding the violin V. These tables were each mounted on pieces of rubber and lead to cut off the vibrations of the one from communication vid the floor to the other. Since together with the vibrations of the belly, those of the string were to be recorded also, the light coming from the electric arc-lantern needed dividing into two parts. One part passed through the vertical slit 8, then through a lens Ly (with diaphragm), which focussed a real image of the slit on the string. The light then passed to the plane mirror M, held just behind the string. This reflected a diverging beam of light to the lens L., which was thus focussed upon the photographic plate P, the light passing through the opening of the door D to the dark room. Since the first real image of the slit was focussed unon the string the second image on the plate was crossed by the shadow of the string. Thus, as the string rises and falls in its vibration, the shadow of it falls and rises on the plate. This of course would only produce a blur if the plate were at rest. But the plate is shot in horizontal rails by a catapult of indiarubber cords, so arranged that the velocity * Barton & Garrett, Phil. Mag. July 1905, pp. 149-157. + Barton & Penzer, Phil. Mae. Dec. 1906, pp. 576-578. t Barton & Penzer, Phil. Mag. April 1907, pp. 446-452. a Vibration Curves of Violin G String and Belly. 235 is uniform as the plate passes the doorway and receives the light. Quarter-plates were used and generally those called “ Warwick Rainbow Isochromatic Fast, Backed,” though sometimes “ Imperial Process.” | Consider now the second portion of the light from the lantern. This was deflected by the plane mirrors M, and M., and so directed to the small hole H in a copper plate. It passed thence to the concave mirror by Hilger, 1*2 cms. in diameter (fixed on a lever), and marked m in the figure. This mirror focussed the real image of the hole on the plate just below the image of the slit crossed by the shadow of the string. Hence, as the string and belly vibrate, and the plate shoots past, we obtain a photographic negative, the positive print of which gives the string’s vibration in black upon a white ground in the upper half, and the belly’s vibration in white on a dark ground on the lower half. The precise arrangement of the concave mirror will be dealt with in connexion with fig. 4. The distances M to Ly. and Ly, to P in fig. 1 were respectively of the order 52 and 132 cms. Hence, on the negatives, the string’s motion is magnified 132/52 = 2°54 times nearly. Mounting the Violin—The method of holding the violin for the experiments (and in a way intended to imitate the actual grip of a player’s shoulder, chin, and left hand) is shown in fig. 2 (PI. IV.). Two blocks screwed on the table supported a stout brass rod, carrying a board which was thus capable of turning about a horizontal axis. The board was turned to a suitable inclination and then clamped in position on a block as shown. This board carried two other blocks, that to the right having a groove, lined with wash-leather, to admit the neck of the violin, which was then held down by the indiarubber cord passing over the peg-box, as seen in the photograph. These arrangements imitate the player’s left. hand. Near the tail-piece of the violin, 7. e. at the left end of the figure, wash-leather lies under the back of the violin, which was held down by a swinging block over which an indiarubher cord passed. These pieces imitate the player’s shoulder and chin; the ordinary chin-rest was left in position. In order to be able to photograph the motions of the single string, although all four were present, the finger- board was removed from the violin, the mirror M (fig. 1) placed just behind the string under examination, and the other strings kept out of the path of the beam. Thus, when the g string was being dealt with (which is the one farthest removed from the lantern and plate) the d’ and a’ strings 236 ~=Prof. E. H. Barton and Mr. T. J. Richmond on (occupying the middle positions) were raised on a specially prominent part of the bridge, and the e’’ string (nearest to the lantern and plate) was held down by a cord passing round the neck of the violin. Thus, although three of the strings were kept out of the way the conditions were but slightly altered from those of actually playing the violin. All the strings were there and in tune, two were on a rather higher part of the bridge, which would slightly increase the pressure on the belly, and one was tied down, which is only the same as its being pressed down by the performer’s finger when “ stopping ”’ it for a particular note. Optical Lever for Belly Vibrations.—The violin used was. an old English instrument without any name or date, but. full size and of ordinary model, as seen by fig.3 (PI. IV.) . It is easily found by scattering sand or only touching lightly with the finger-tips, that the belly of the violin is very dead near the edges where supported by the ribs which attach it to the back. But spots just inside the f holes are specially lively and were accordingly thought preferable as places whose motion should be recorded. A spot on the right hand of the belly was chosen and a little wedge of soft wood fastened upon it, so that the upper surface of this wedge was level when the violin was mounted. On this upper surface a piece of microscope cover-glass was then fastened by shellac so as to form a support for one leg of the three-legged optical lever used to record the vibrations. The other two legs rested upon a conical hole and V-groove on a small table or disk of brass carried by an adjustable bracket. Thus the optical lever was carried on the geo- metrical arrangement of the “hole, slot, and plane,” and turned about the hinge formed by the hole and slot as the plane rose and fell. The lever was of aluminium provided with steel legs and with the mirror had a mass of 1:124 gram. Jt was held firmly down by an indiarubber ring obtained by cutting a slice off a tube. The lever, mirror, and rubber ring complete weighed 1:254 gram. The adjustable bracket which carried the optical lever can be seen better in the detached view of fig. 4. In both views the hole and slot are shown in white. Magnification of the Belly’s Motion—The distance of the moving foot of the optical lever from the axis through the hole and slot was 6 mm., and that from the mirror to the photographic plate was 176 cms. (see m. P in fig.1). Hence the magnification of the belly’s motion on the original negatives was 2x 176+0°6 = 587 nearly. Thus, on the original plates, or any prints reduced from them, the Vibration Curves of Violin G String and Belly. 237 magnification of the belly’s motion is (587+2°54 or) say 231 times that of the string’s motion. The General View of Experimental Arrangements is shown in fig. 5, which gives ata glance the scale and disposition of the various parts, optical and acoustical. Results —The chief results obtained are shown in the curves 1-40 on Plates V.& VI. These are partially explained by the marginal letterpress ; other necessary details may be noted here. PuatE V.—The whole of the curves 1-20 on this first plate deal with the g string at concert-pitch (about 203-4 per second). This is the fourth or so-called silver string, and always elicited a sufficient motion of the point of the belly under examination. Curves 1-3 show the vibrations of the string and belly when the string was bowed at one-sixth, one-seventh, and one-eleventh respectively of its length from the bridge. The string had a vibrating length of 32°5 cms. from bridge to nut and was usually illuminated at a point 14 cms. from the bridge, z. e. at 0°43 of its length. The speed at which the plates were shot can be inferred from the number of periods or complete vibrations occurring in the length of the plate (43 inches). Thus, three vibrations occupying 3+203°4 of a second were photographed on the length of 44 inches, which gives about 24 feet per second for the speed of the plate, which was the normal usage in all the curves except Nos. 4 and 5. Curves 4 and 5.—It was noticed that in plucking the g string at 2 of its length from the bridge (or at other places like + or } &c.) the vibrations of the point of the belly under examination speedily rose to a maximum, died away again, attained a second maximum, and so on, for about five successive maxima, occurring at intervals of about one second or rather less. By placing one ear close to either of the f holes the same effect of successive maxima or “beats” could be heard. When the observer’s ears were about a yard away from the violin this effect of beats was practically gone, thus showing that the maxima previously observed were merely maxima of the vibrations occurring at that spot, and that when the vibrations there diminished, those of some other part of the belly increased ; so that at a moderate distance the total effect from the various parts of the belly was devoid of these successive waxings and wanings. To record these fluctua- tions of amplitude on a single plate necessitated its exposure for several seconds, and thus the motion would be tar too 238 Prof. E. H. Barton and Mr. T. J. Richmond on slow to show the thousand vibrations, or thereabouts, then occurring. It was accordingly moved quite slowly by hand, all trace of the individual vibrations being therefore lost, but the successive swellings and subsidences of the vibrations being well shown. e ve 4 shows about half these effects in its entire length. Curve 5, in which the plate was moved still slower, comprises the w hole series of waxings and wanings in its length. The sudden, almost instantaneous, reponse of the belly at the start is specially noticeable. Curves 6-10 show the effect of plucking the string with the fleshy finger-tip as is usual when the violin is Lipase ss pect | ; the points of attack being respectively at 2, 4, 4, 1 and + of the string’s length from the bridge, the plates pens g shot quickly with the catapult as at first. Curves 11-13 show the vibrations obtained when the string was struck with a hammer consisting of an ordinary lead- pencil wrapped at the end with several thicknesses of wash- leather, the places of striking being respectively 4, 3, and 4 the string’s length from the bridge. Curves 14-17. give the effects of plucking the string with the point of a lead-pencil, which may be aly a Be the points of excitation being respectively at 2, 1, 4, and tof the string’s length from the bridge. Curves 18-20, concluding the first set, show the vibrations elicited by ae the string with an unpadded lead-pencil at the points 2, 4, ‘and 1 from the bridge. It is very noteworthy that all these cases of plucking and striking give vibrations of the belly and of the string itself of a very ‘smooth flowi ing character, being quite different from those with the metal string and the monochord belly *, &e. Prats VI.—The curves 21-40 on this plate show vibrations at various pitches from the g string and the other strings. As before, the chief points are indicated by marginal notes ; but some further details are given here. Curves 21-22 show the vibrations elicited by the g string sounding its octave harmonic or second partial. It was touched at the middle with a finger 4 the oe hand, and bowed with the right at the points 7) jz and 5, of the whole length of the string from the bridge. The large amplitudes of the belly’s vibrations are noticeable in contrast with the very small motions of the string. Curves 23-24 show the vibrations from the g string “stopped” or held down by a clamp at three-fourths of its * See Plate I. fig. 10, Phil. Mag. July 1905; also others in Phil. Mag. Dec. 1906 and April 1907. Vibration Curves of Violin G String and Belly. 239 length from the bridge, so as to sound middle c’ (say 271°1 per second). Curves 25—28.—As the strings of a violin are occasionally tuned to other pitches, either to agree with accompanying instruments or for special effects, the g string was tuned a semitone down and up, also a tone and a tone and a half up. The effects obtained are shown in curves 25—28 respectively, the bowing throughout being at one-seventh of the string’s length from the bridge. Itcan be seen from the prints that, when the string was sharpened more and more, the belly responded so powerfully that, to avoid an undue amplitude, the string needed bowing more and more gently. In fact, for the bp the string’s motion is barely visible in the original plate, though the belly’s motion is so large. (See also notes on curves 38-40.) Curves 29-30 show the vibrations from the g string when flattened and sharpened a semitone and plucked with the finger at one-seventh. Curves 31-33 show the vibrations from the combined effect of the g string at concert-pitch and the d! string (normally at 305 per second) tuned to 6, ¢ and at concert- pitch respectively. The excitation is by bowing both strings at one-seventh. The curious character of these curves, amounting in one place to an undercutting (curve 31) is due to the fact that the vibrations of the d’ string caused the mirror to rotate slightly about a vertical axis, thus moving the spot of light horizontally on the photographie plate. Hence these curves have not the true character of displace- ment-time curves. Accordingly, no curve is given, with the present arrangement, from the vibrations of the d’ string alone. But it is easily seen that a small motion, whether vertical or horizontal, superposed upon a displacement-time graph of much larger amplitude gives very similar results ; these combined effects are therefore included now. Curves 34-35 show the combined effects of d’ string at concert piteh, (i.) with the g string, also at concert pitch, and both plucked at 4, and (ii.) with the g string sounding its octave harmonic, and both bowed at +5. Curves 36-37.—Since the d! string vibrating alone failed to act satisfactorily with the present arrangement, it was at first thought that the same would apply still more to the a! and e' strings, which are thinner and higher in pitch. It was indeed true of the e" string. But the a’ string, on the contrary, evoked, by bowing, such powerful vibrations of this particular spot of the belly that it was very difficult to bow so lightly as to keep these vibrations within reasonable 240 Prof. R. W. Wood on the Absorption limits on the plate. The bowing at 71; was out of the ques- tion, and we were driven to adopt the positions 1 and 4 from the bridge, which produce softer passages. Curves 38-40.—It was noticed in connexion with curves 26-28 that, as the sound of the string approached 0p, the response of the belly was very powerful. This led to the idea that bp, or some note near it, was the pitch of best resonance of the instrument. A French-horn was accord- ingly tried with its bell just over the violin belly and the notes af, 6), and bf sounded in succession, a plate being shot each time. The string, of course, did not respond, being tuned to g ; it therefore shows asa straight black line on the prints. The belly’s motions are, however, shown by curves of moderate amplitude in prints 38 and 40 for the extreme pitches and by one of greater amplitude in print 39 for the intermediate pitch of bb (say 244 per second). This is accordingly the pitch of the instrument as a resonator, when we judge it by the vibrations of the spot of the belly under examination. University College, Nottingham. May 11th, 1909. ES XXIX. The Absorption, Fluorescence, Magnetic Rotation and Anomalous Dispersion of Mercury Vapour. By R. W. _ Woon, Professor of Experimental Physics, Johns Hopkins University *. [Plates VII. & VIII.} indent after Hartly’s observation that the vapour of mercury exhibited fluorescence under the stimulus of the light from the electric spark, I commenced a careful study of the optical properties of the vapour, in the hope that phenomena analogous to those which have been observed in the case of sodium vapour might be found. Though the vapour has proved disappointing in some respects, a number of very interesting observations have been made, some of which appear to be quite new. I have already described the remarkable absorption-band at wave-length 2536, which is probably the most unsym- metrical band ever observed, and the modifications produced in its appearance caused by the admixture of any chemically inert gas (‘ Astrophysical Journal,’ 1907). In the present paper I shall briefly review the results set forth in the above note, as they have some bearing upon the * Communicated by the Author. and Fluorescence of Mercury Vapour. 241 other observations. The study of the vapour has been attended with great difficulty, since all of the interesting things are in the ultra-violet, and can be picked up only by the aid of photography. ; The work has been suspended from time to time, and then taken up again as new methods of attack have suggested themselves. I have at last succeeded in devising a satisfactory piece of apparatus for the study of the anomalous dispersion of the vapour. This is much to be desired, for the vapour, unlike that of sodium, does not attack the quartz vessel in which it is contained. It is thus possible to work with prisms of known angle, and vapour of known and uniform density. If we work with prisms we shall need a cement capable of resisting the vapour and of standing a temperature of say 300°. I have some hopes of a mixture of the fused haloids of silver and am now making experiments in this direction. A quantitative determination of the dispersion would be of very great interest, on account of the asymmetry of the absorption- band. The absorption spectrum of the vapour is shown on PI. VII. fig. 1. A small globule of mercury was placed in a quartz bulb 3 ems. in diameter, which was thoroughly exhausted and sealed. The spectrograms were taken in succession, the temperature of the bulb being gradually raised. There are three distinct absorption-bands, all in the ultra-violet region. The one at wave-length 2536 appears first as a pair of fine lines, not unlike the D lines in appearance, one of them (A=2539°4) relatively much weaker than the other (A= 2536°7). As the density of the vapour increases they fuse together, forming a single band which then widens in a remarkable manner towards the region of longer wave- length, its boundary on the other remaining almost fixed in position. In addition to the absorption-band at wave-length 2536, there is a group of narrow bands just above the three bright cadmium lines further down in the ultra-violet. These bands do not appear until the vapour has acquired a con- siderable density : they form a series, the head of which is turned towards the visible spectrum. The individual bands which make up the group decrease in intensity with decreasing wave-length and lhe closer together, resembling a Balmer series on a very small scale. The wave-lengths of the four bands which make up the group are as follows :— 2346°1, 2339-4, 2334-4, 2331-2. They can be seen in figs. 1 and 7of Pl. VII. They are sonearly fused together that it is 242 Prof. R. W. Wood on the Absorption doubtful if they will appear separated in the reproduction. There is also a general absorption further down in the ultra- violet, which wipes out the last cadmium line first, and then the others in succession. The apparent absorption-band at the extreme right of fig. 1, Pl. VII., is merely the region of minimum sensibility in the blue-green region of the ortho- chromatic plate. If the buib contains air or any other chemically inert gas at atmospheric pressure, the band (2536) widens sym- metrically at first, attaining a width of about 8 Angstrom units. Beyond this point a further increase in the density of the mercury vapour causes a widening in one direction only, as is the case when the vapour is in vacuo. If, instead of sealing the mercury up in a bulb filled with air, we place it in a quartz flask provided with a long neck and gradually raise the flame below the flask, we get a remarkable series of spectrograms (Pl. VII. fig. 4). The band widens and then appears to drift towards the longer waye- lengths, without further increase in width. This apparent drift is due to the expulsion of the air by the boiling mercury, the band contracting on one side more rapidly than it widens on the other. This action of the air in modifying the appearance, and in some cases the apparent position of the absorption-band, cannot be attributed to chemical action, for the same effect was found with hydrogen, nitrogen, and helium. As we shall see presently, the vapour is deprived of its power of fluorescing when it is mixed with another gas. It was tound, by making a more careful study, that the effect of air upon the band at 2536 was a little more com- plicated than was at first supposed. Jn vacuo the broadening is almost entirely in the direction of longer wave-lengths. Itfair is present Fig. 1. a hazy band appears on the short wave-length side of the line, and if the time of exposure and vapour density are just right the band and line are separated by a narrow strip slightly lighter than the band. The form of the absorption curve in the two cases is indicated in fig. 1. A photograph is reproduced on Pl. VII. fig. 3, short wave-lengths being to the left. It is difficult to obtain an enlargement which shows the lighter region between the line and the band, though it is not difficult to make it out in the negative. The appearance of the band suggests that mercury + air gives us some sort of a molecular aggregate and Fluorescence of Mercury Vapour. 243. which broadens the 2536 line and shifts it towards the shorter wave-length region. The shifted and broadened band and the narrower 2536 band appeared to be dis- connected, and it occurred to me that it might be possible to obtain the broadened band alone. It seemed as if we might be dealing with a molecular aggregate mixed with free mercury molecules, in which case it might be possible to get the effect of the aggregate alone by employing a very long column of air containing but very little mercury vapour. I accordingly fitted up a steel tube 3 metres long, containing 20 small porcelain boats each containing a few drops of mercury, and closed at the ends with quartz windows. The appearance of the two bands was the same as before how- ever. The tube was surrounded by a second tube heated by a line of very small flames obtained by drilling pin-holes at intervals along a long piece of gas-pipe. ‘The very in- teresting observation was made that the 2536 line was quite distinct in the photograph of the absorption spectrum, even when the tube was at room temperature. This gives us a means of studying mercury vapour at low temperatures, and determining whether it can be prevented from entering an exhausted receiver by any of the absorbing devices (e. 9. gold-leaf) frequently suggested. It will also be possible to determine its vapour density at lower temperatures than has hitherto been possible. It was found that if the tube at room temperature was exhausted, the line became much fainter, almost disappearing. On readmitting the air it immediately resumed its full intensity. No trace of the broadened and displaced band appeared at room temperature, owing to the insufficient density of the vapour. The effect of admitting the air is precisely analogous to the observations made by Angstrém on the CO band in the infra-red. It is a pressure effect, the effect of admitting the air being equivalent to compressing the actual amount of mercury vapour present until it is at atmospheric pressure. Ang- strém’s paper should be referred to in this connexion. [ have observed the same thing with sodium vapour for many years, but never felt quite sure as to the interpretation of the phenomenon. The D lines widen and fuse together the moment nitrogen or hydrogen is admitted to one of the steel tubes. In the case of sodium vapour, however, I could not feel sure that the actual number of sodium molecules per cubic cm. had not been increased by the admission of the gas, for the gas would hinder diffusion to the cooler parts of the tube, and it might easily be possible for us to have the metallic vapour at the centre of the tube at a pressure as. g Prof. R. W. Wood on the Absorption ° great as that of the atmosphere in the tube. I have long since abandoned the viscosity theory which I first proposed to explain ‘the apparent peculiar behaviour of the vapour, and now believe that even in the highly exhausted tubes we can never have the vapour at a greater pressure than that of the residual gas. The error resulted from an over-estimate of the density of the metallic vapour, based upon its optical properties. | This pressure effect is not to be confused with the phenomenon studied by Humphreys and Mohler, for it occurs at pressures below one atmosphere, and there is no shift, the band merely becoming wider and blacker, precisely as if more mercury vapour were present. Fluorescence. The fluorescence of the vapour is best shown by enclosing a drop of the metal in an exhausted quartz bulb, heating the bulb over a Bunsen burner turned down very low, and passing a powerful spark between zinc or cadmium electrodes placed as close as possible to the bulb. The colour of the fluorescent light is a bluish green mixed with a good deal of white, i.e. it embraces a region of the spectrum extending from the red-yellow well down into the ultra-violet. The colour of the fluorescent light varies somewhat with the nature of the electrodes used. The spectrum appears con- tinuous even with a concave grating of 2 metres radius. Photographed with a small quartz spectrograph, the spectrum is found to be continuous, extending roughly from the yellow down to wave-length 3000, with a very pro- nounced minimum at wave-length 3600. It was at first suspected that the visible band and the ultra-violet band might be excited by different radiations, and a week or more was spent in photographing the spectrum emitted by the vapour when stimulated by lines isolated from the spark- spectrum by an auxiliary quartz spectrograph. Very little, if any, difference could be detected however. It was found that if air was in the bulb it was impossible to excite any fluorescence. If, however, we boil the mercury in a flask it fluoresces brightly as soon as it is in brisk ebullition, and if the absorption spectrum is photographed at the moment at which fluorescence appears, we find that the absorption-band has contracted on its short wave-length side to its position when the vapour is in vacuo. The fluorescence spectrum is shown on Pl. VII. figs. 2 & 5, excited in this case by the light from the cadmium spark. The cadmium lines appear as well owing to diffused light. As will be seen, there is in addition '* and Fluorescence of Mercury Vapour. 245 to the continuous spectrum, a bright line (indicated by an arrow on fig. 2) which is not present in the spark spectrum, and which coincides in position with the sharp absorption- line 2536°7, shown by vapour of small density. It was at first thought that this line was excited by the bright cadmium line which falls within the region of the expanded part of the absorption-band. The zinc spark had a bright line which lies even nearer the mercury line, and it was expected that the emission line would be stronger in the case of zinc excitation. To my surprise it was impossible to obtain any trace of the line using the zinc spark as a stimulus. The fluoresvence spectrum was then photographed when excited by the cadmium lines in succession but in no case was any trace of the line found in the spectrum. This seemed quite bafiling, and much time was spent in repeating the work using longer exposures. The results were all negative however. It was then found that when the image of the spark was thrown upon the bulb with a quartz lens and the bright spot of fluorescent light photographed with the spectrograph the line was absent in the spectrum. The aluminium spark was found io be even more efficient than the cadmium in bringing out the line. (See fig.6. The aluminium spark spectrum is recorded below for comparison. Fluorescent line 2536 marked with arrow.) This at once made me suspicious that the bright line might be excited by the very short waves, which penetrate quartz with difficulty, and I arranged my auxiliary quartz spectrograph to deliver the light of the last aluminium line which can be observed with ordinary apparatus. This light excited a feeble fluorescence, and by giving a very long exposure I was able to secure its spectrum. The line appeared in his photograph, faint but unmistakable. I then focussed the spark upon the bulb with the quartz lens, placing the lens much nearer the bulb than before, after having made a rough calculation of its focal length for these very short waves. Again the line appeared. As a final test I placed the spark close to the bulb and took a series of spectra, interposing in succession quartz plates of increasing thickness. It was found that a plate 8 mm. in thickness reduced the intensity of the fluorescent line fully one half, while a plate 18 mm. caused its disappearance from the spectrum entirely. The mystery was thus completely solved. The cadmium spectrum has lines of much shorter wave-length than any shown by zine. The cadmium lines which excite the 2536 Phil. Mag. 8. 6. Vol. 18. No. 104. Aug. 1909. S 246 Prof. R. W. Wood on the Absorption and line in the fluorescent spectrum are more refrangible than any which appear in the photographs. | The difficulties which accompanied the solution of this problem were still further complicated by the fact that even with the aluminium spark placed close to the bulb, the line was often found to be absent in the spectrum. The cause of this was eventually found. The line only appears when the vapour is quite rare, 7.e. when the temperature of the bulb is comparatively low. The best density is that at which visible fluorescence first appears and is quite faint. The line then comes out strong. If the temperature is raised a trifle and the density of the vapour increased, the visible fluorescence becomes very bright, but no trace of the line 2536 appears in the spectrum. This circumstance gave a great deal of trouble in the labour of securing the line with the monochromatic aluminium radiation (shortest wave- length) as the vapour density was at first arranged so as to give the brightest fluorescence. In fig. 2 are reproduced tour spectra taken under identical conditions as to time of exposure, position of the cadmium spark, &c. The upper was taken with highly attenuated vapour, and while showing ‘the bright line distinctly (see arrow) exhibits only a very faint trace of the continuous spectrum fluorescence. In the third spectrum the line is barely visible, while the fluores- cence is much brighter. In this case the vapour was denser. In the fourth the bright line has disappeared, and the continuous spectrum is at its maximum brilliancy. # The fluorescent line is double like the absorption-line, 2536°7 strong, 2539°3 faint. Both appear in fig. 2. Lifect of Temperature upon the Fluorescence. If a very small drop of mercury is sealed up in an exhausted bulb it can be completely vaporized. The temperature can now be raised to a bright red heat without danger of bursting the bulb. It was found that as the temperature was raised the fluorescence diminished gradually in intensity and finally disappeared entirely. On removing the flame the fluorescence presently reappeared again. No effect of temperature on the appearance of the absorption- bands could be detected. If a quartz flask with a long neck is filled to a depth of several millimetres with mercury, and the flame of a Bunsen burner is made to play around the bulb heating it red hot, fluorescence can be detected only close to the surface of the Fluorescence of Mercury Vapour. 247 boiling metal. The appearance is quite striking, a layer of glowing vapour clinging close to the metal, reminding one of the discharge at the cathode in a vacuum-tube. The temperature of the vapour when it leaves the metal is about 360, consequently it fluoresces brightly: as it rises its temperature is speedily raised to the point at which fluores- cence disappears. A still better way of showing the effect of temperature upon the fluorescence is illustrated in fig. 1, Pl. VIII. The exhausted bulb previously described is used. It is heated from below by a small flame from a Bunsen burner until the fluorescence excited by a cadmium spark placed as close as possible is at its brightest. The small pointed flame from a blowpipe is then directed against the side for a few seconds. The fluorescence promptly disappears at the super-heated spot, reappearing again as soon as the local heating is stopped. If the ultra-violet light of the spark is focussed at the centre of the bulb, a narrow cone of brilliant green light extends from the point at which the light enters the bulb nearly to the opposite wall, as shown on PI. VIII. fig. 2. The flame of a blast-lamp directed against the wall of the bulb at the point where the fluorescence begins causes the luminons cone to retreat from the wall to a distance of several millimetres, much as the positive column separates from the cathode in a vacuum-tube discharge. A photograph of the effect is shown on Pl. VIII. (right-hand figure). The failure of the 2536 line to appear in the fluorescence - spectrum except when the vapour is at comparatively small density is very remarkable. It occurred to me that it might be due to disappearance of diffuse radiation by the combina- tion of the secondary waves from the molecular resonators into a regularly reflected wave. I have shown in a previous paper (“Selective Reflexion of Monochromatic Light by Mercury Vapour” in this Journal, supra, p. 187) that this takes place when the vapour is illuminated by the light of the 2536 line from the mercury arc, and its density increased to ten or more atmospheres. It is possible that something of the same nature might explain the failure of the line to appear when the vapour was excited by the very shortest ultra-violet waves. It must be remembered that in this case there is a change of wave-length involved, and it is hard to see how the necessary phase relations for selective reflexion could hold. Experiment showed that the hypothesis was , 248 Prof. Wood on the Fluorescence, Magnetic Rotation, untenable. The spectroscope was directed so as to view the image of the aluminium spark reflected at the inner surface of the bulb, everything else being screened off by closing the iris diaphragm of the instrument. The vapour was given the density which showed the brightest visible fluorescence. If the 2536 radiations were present, going off as a regular (7. e. not diffuse) wave, the line ought to appear under these conditions, but no trace of it appeared on the late. ‘i I see no way of explaining its failure to appear by absorption, for the whole surface of the bulb on one side is illuminated by the light of the spark, and the spectrograph receives the light from the outermost surface of the vapour mass. I have not yet determined whether an elevation of tem- perature causes the disappearance of the line, as it does of the continuous spectrum, for the bulbs which I now have are not well adapted to the complete investigation of the temperature effect. I am having two connecting bulbs made, one of which can be raised to a very high temperature, the other being held at a lower temperature, the density of the vapour being the same in both. This bulb should furnish more precise information. : The failure of the 2536 line to appear in the fluorescent spectrum when the vapour has a considerable density, and the complete destruction of the visible fluorescence by the elevation of temperature, I regard as the two most important points brought out by the work. The 2536 line is connected in some way with an absorption- band in the vicinity of the wave-length 1860, for it appears only when the vapour is stimulated by the last aluminium line, and the cadmium lines which are completely stopped by 2 ems. of quartz. It is not brought out by stimulation with the other brilliant cadmium and zinc lines, which excite a very powerful visible fluorescence. Stimulation by the 2536 line from the mercury arc probably brings out the 2536 fluorescent line, though I have not proved this as yet, for it is difficult to be sure that we have removed all possibility of diffused light. The fact that we get selective reflexion of this light when the vapour is dense, indicates that in all robability we have a diffuse radiation at lesser densities. If the ultra-violet spectrum of the cadmium spark is focussed upon the bulb, it is found that the brightest fluorescence is excited by the lines which are most strongly absorbed, which is what we should expect. and Anomalous Dispersion of Mercury Vapour. 249 Anomalous Dispersion and Magnetic Rotation. Strong anomalous dispersion has been found at the 2536 line, as shown in fig. 8, P]. VII. These photographs were made by the method of crossed prisms in the manner which I have employed in the study of sodium vapour. The mercury was placed in a long steel tube, closed by quartz windows and heated along the under side by a row of small flames. As will be seen from the photographs, the curvature of the spectrum is much more marked on the short-wave- length side of the band, which is the steep side. A quanti- tative study of the dispersion of the vapour will be made next year, by an interferometer method, which will doubtless be of considerable value in connexion with the theory of dispersion, for it will be possible to determine the exact density of the vapour, the length of the column, and its temperature, which was never possible in the case of sodium vapour. The determination of the dispersion curve will also be extremely interesting on account of the asymmetrical -nature of the absorption-band. The magnetic rotation of the plane of polarization was also investigated in the vicinity of the 2536 line. The effect of the absorption-band upon the rotation was very marked on the short wave-length side, but there was little or no increase on the other side, doubtless due to the broadening of the band in this direction. The light from the cadmium spark was passed through a polarizing prism (Foucault), then through the quartz bulb between the poles of the electro- magnet, a Fresnel biquartz parallelepiped, and a second polarizing prism, the image of the fringes formed by the Fresnel parallelepiped being focussed on the slit of the quartz spectrograph. Nicol prisms cannot be used for the ultra- violet on account of the absorption by the film of Canada balsam. The direction of the rotation resulting from the 2536 line was the same as for the D lines of sodium, from which we may infer that the line is due to negative electrons. A further study of the dispersion and magneto-optics of the vapour will be commenced as soon as the necessary apparatus of fused quartz has been constructed. A wide tube with plane-paralle] end-plates also of fused quartz weided directly to the tube is being made by Heraeus. E 2500] XXX. On the Flow of Energy in a System of Interference | Fringes. By R. W. Woon, Professor of Experimental Physics, Johns Hopkins University *. [Plate VIII. fig. 3.] cigars interference minima formed by two similar sources of light form a system of confocal hyperboloids, and the question of the flow of energy in this case, or any similar case, does not appear to have been discussed. Energy is obviously flowing out from both sources at its normal rate, but the direction of flow is perhaps not quite obvious. Suppose the minima equal to zero, which is nearly correct at the centre of the system. Energy evidently cannot cross a plane along which there is no disturbance. In stationary waves, if the nodes are absolutely at rest, which is the case if the two wave-trains are of equal ampli- tude, we cannot speak of a flow of energy across them. A node may be considered as having the properties of a perfect reflector, that is to say the point acquires the power of reflecting as a result of the arrival of a wave travelling in the opposite direction. We are thus forced to the conclusion that the flow of energy in the case of the interference-fringes must be along the hyperboloids, that is along curved paths. We can show this experimentally by means of ripples in mercury excited by two needles mounted on the prong of a tuning-fork. If we view the mercury surface through a narrow slit opened and closed by the vibrations of another fork slightly out of tune with the first, we see the waves (stroboscopically) creeping slowly along the surface, and following the lines of the hyperboloids. Two questions now naturally occur to us. How does the energy get into the bright fringes, if the dark fringes are supposed to act as barriers ? and what is the nature of the wave that is travelling along a bright fringe? In regard to the first question : the dark fringes are never absolutely black, as no one of them is equidistant from both sources. The amplitudes are there- fore slightly different, and there will be a flow of energy in the direction of the disturbance having the larger amplitude. Though it may be very slight at any given point, it is ample to account for the flow along the hyperboloid. We can take as an analogous case two parallel sheets of cloth tightly stretched, and very close together. Consider water forcing its way into the space between the two sheets from both sides. A very small flow across unit cross-section will give us a * Communicated by the Author. Flow of Energy in a System of Interference Fringes. 251 large flow across unit section taken perpendicular to the sheets. We may, however, have a fringe which is absolutely black, for there is nothing to prevent us from considering the sources as vibrating with a difference of phase of 180°. This makes the centre of the system dark, and equal to zero, and it must act as a barrier to the flow of energy from both sources. In other words, the central fringe can be considered as acting as a perfect mirror, and we can regard the fringes as formed by the interference of these reflected waves with the direct. If the flow of energy is along the hyperboloids, it is evident that in the region between the sources the flow is in a direction nearly perpendicular to the rays. We can watch this flow with the mercury ripples and tuning-forks. (I find that a ring of castor-oil or glycerine poured around the edge of the mercury surface prevents disturbing reflexion from the walls, and to a large extent waves due to jars from the table.) The bars of light perpendicular to the line joining the vibrating sources slide out sideways, each one of them forming one of the waves which travel along the hyperboloid. We can perhaps get a better idea of what happens if we con- sider what is going on in a bright fringe outside of the region between the sources. What is the type of wave, and is it capable of showing us both of the sources if it alone is allowed to enter the eye? If we regard the dark fringes as absolutely dark, that is as perfect reflectors, we must regard the waves as travelling between them as between two silver walls. The incidence is very oblique, i.e. the wave is nearly perpen- dicular to the reflecting plane ; and if we consider the wave as a portion of a sphere with its centre at one of the sources, the wave after reflexion from the interference plane wili bea portion of a sphere with its centre of curvature at the other source. This process will repeat itself over and over again, a given portion of the wave-front appearing to come first from one source and then from the other. The bright fringe will then contain two groups of wave-fronts inclined to each other at a small angle. These can be seen with the tuning- fork waves, and on looking over some of Mr. Vincent’s photographs, published in this Journal some time ago, I found one which showed the phenomenon very clearly. An enlarge- ment of a portion of this photograph is reproduced on Plate VIII. fig. 3, the inclined wave-fronts showing especially well above the point marked X. Though each bright fringe contains two wave-fronts, we cannot “resolve” the sources with them, for calculation shows that their width will be insufficient. In other words, 252 Mr. B. Hodgson on the Conductinty of if we screen off the other bright fringes, passing the waves in the one through a slit, the slit width necessary turns out to. be just what is needed to prevent resolution. In the region between the sources we must regard the same thing as going on, the only difference being that here the incidence is more nearly normal. The waves are stationary on the line joining the sources, but as soon as we get off this line we must regard the stationary waves as oozing out in all directions, the velocity of the oozing increasing with the distance from the line. I realize that the language which I have used here is not very exact, but it is not easy to visualize exactly what is going on, and still harder to put it into words. If this note serves to direct attention to a new view-point of a well-known phenomenon, it will have accomplished all that I had intended it to do. EN or # ! = z. XXXI. The Conduchniey of Dielectrics under the Action of Radium Rays. By B. Hoveson, B.Sc., Prize Demonstrator in Physics, Armstrong College, Newcastle-on-Tyne*. A STUDY of the conductivity of dielectrics under the action of radium rays is extremely important in view of the fact that the work already done on this problem is throwing light on the nature of dielectric conductivity itself, and perhaps also on the nature of polarization in dielectrics. The early investigatorst were inclined to look upon dielectric conductivity as electrolytic in action, but recent work seems to point to a conduction similar to that occurring in a dense gas. The conductivity acquired under the action of radium rays was demonstrated by P. Curie, Bécquerel, and Becker, and recently the phenomena have been studied in great thorough- ness by Jaffé f. | Curie §, Bécquerel ||, and Becker { showed that dielectrics under the action of radium rays increase in conductivity, and noticed some departure from Ohm’s law. Jaffé divided the current into two parts : (1) obeying Ohm’s law, (2) an ionization current. * Communicated by Prof. H. Stroud. + Von Schweidler, Ann. d. Phys. xxiv. p. 711 (1907). t Jaffé, Ann. d. Phys. xxv. p. 257 (1908). § Curie, Comp. Rend. cxxxiv. p. 420 (1902). || Bécquerel, Comp. Rend. cxxxvi. p. 1173 (1904). 4] Becker, Ann. d. Phys. xiii. p. 894 (1904). Dielectrics under the Action of Radium Rays. 2953 The Ohm’s law current was exceedingly small for pure substances, and it was subtracted from the observed effect and the remaining ionization current studied. This latter shows evidence of consisting of two parts: 7 (1) due to mobile ions similar to those existing in an ionized gas ; (2) due to slowly moving ions which appear to be of the nature of electrolytic ions. (1) is saturated by a field of 1000 volts per cm. (2) shows no signs of saturation in fields of 7000 volts per cm. , Jaffé took extraordinary care to obtain pure dielectrics ; but even with the most elaborate precautions it appears im- possible to get an absolutely pure specimen. In the work described below substances were obtained as pure as possible, and only experimented with if the ordinary conduction current was of the order of 10-% ampere with an applied field of ead 100 em The method used was to measure first the current through the dielectric without the radium near and then with the radium, the difference giving the ionization current. Apparatus. One of the many difficulties was to eliminate all possibility of leak through air ionized by the radium, which would give either a spurious effect or cause such leak as to mask any effect which might exist. After many trials the following simple form of apparatus had the desired effect. The substance under examination was placed in a thick lead box A (fig. 1), 11 cm. square and of sides 2 em. thick. Fig. 1. ie ei os ea -<--- +S e-- - S ee e Two electrodes B and C were supported inside by means of ebonite stems, B being connected during an experiment to one terminal of a set of storage-cells, and C to one set of quadrants of a Dolezalek electrometer, by means of the spring D and the wire E, both held in a cylinder of ebonite F. 254 Mr. B. Hodgson on the Conductivity of To prevent leak across the ebonite supports the following arrangement was employed. The electrode B (fig. 2) was © Fig. 2. supported by ebonite stems N N, and C by similar stems PP, from an earthed plate Q. This avoided effectively any spurious effect due to defective insulation. The radium used contained about 5 mg. of pure radium bromide and was sealed in a glass vessel with a thin mica cover. When acting on the dielectric it was placed in the lead box L and the rays passed through 2 cm. of liquid before reaching that between the electrodes. K, (fig. 1) was a key which enabled the electrode C and electrometer to be “ earthed” or insulated at will. G was a capacity added when necessary to lessen the rate of movement of needle. To prevent any leak due to ionized air the following arrangement was used. The wire E was passed through a glass tube T covered with tinfoil and earthed, and filled with heavy paraffin oil of high insulation. By this means air was removed from all connexions right up to the electrometer, and so chances of leak due to air-ioniza- tion were eliminated. This oil proved a splendid insulator, and when the system was charged up to 1 volt no leak could be detected in 6 min. The electrometer, keys and condenser were enclosed in earthed tin boxes M, M. R, R was a large earthed wire cage. In performing an experiment the electrode B was connected to a set of storage-cells and the key K was lifted, insulating the electrode ©. The needle then began to move, and scale readings were taken every } minute. A knowledge of the capacity of the system and the sensitiveness Dielectrics under the Action of Radium Rays. 255 ef the electrometer enabled the current to be found. When no E.M.F. was applied no current could be detected, so that the radium rays themselves did not charge up the system appreciably. In all cases given the resulis were got by applying a +E.M.F., as Jaffé showed that the ionization current was the same on applying either a + or — E.M.F. The following substances were experimented with:—heavy paraffin oil (density -89), solid paraffin, vaseline, glass, and ebonite. The oil and vaseline were poured into the lead box, and in the case of the iatter it was allowed to solidify. For the solid paraffin an additional piece of apparatus was used (fig. 3). Molten paraffin was poured round the electrodes C, B, held in a tin vessel T. (C was supported by a stem D passing through a hole in the vessel, and insulated from it by a layer of sealing-wax S. This vessel was placed in the lead box A, the stem D touching the spring E, and so making contact with the electrometer. Oil was poured into the lead box to exclude air. At this stage the radium was put in position and allowed to ionize the dielectric and the current again measured. The 256 Mr. B. Hodgson on the Conductivity of following results show the increase of conductivity imme- diately after insertion of radium. In the cases marked thus * Fig. 4. in Table I. no deflexion was got after some minutes. The sensitiveness of the electrometer throughout the experiments. was about 200 scale-divisions per volt, and the capacity of the electrometer and connected electrode 0:000096 micro- farad. The capacity G (fig. 1) was 0:002454 microfarad. TABLE i. Sabnnoye, |. Ouest | nest) a Heavy paraffin oil...) *0°0 10-13 amp.| 5'1xX10—13 amp. | 190 = ; + + spugaie Oris PUN ee iC ic Pau ess 43 90°, Solid paraffin ...... *0-0 $5 ve (apie area ke hay » | 260 ,, PEDENILS ips. ccneeess *0:0 a, (eesti Raa aes + 520 _,, WiASBNING, gence. 00098 1K 10=22) eh aexos 190 ,, If the radium was removed and the current measured from time to time, the E.M.F. being continually applied, it was. found that the current diminished, and finally reached its initial value (Table IT.). Dielectrics under the Action of Radium Rays. 257 TABLE II, | Solid Paraffin. [Dine sect ececesess ome.) 10:40 11.0 112-119" 111.13 11.24 11.40 } Current (10-13 amp.) | 0:0 0-0 2-2 8 5 3 Radiat. sccsceced.. out out in out out out Heavy Paraffin Oil. PG Fee tee sees se 12.5 12.10-12.33 12.42 2.15 3.52 Current (10-13 amp.) | 0:0 dl 3°3 2°5 18 pc ae eee out in out out out * ra io Samyps: Fig. 6. The complete recovery took a considerable time, one specimen of paraffin having a conductivity equal to that before the action of radium only after the lapse of 13 hours. If the radium was allowed to act continuously and the current measured from time to time, it was found that the 258 Conductivity of Dielectrics under Radium Rays. conductivity increased. This is shown in the case of paraffin and vaseline in Table ITI. TABLE III. Vaseline.) Osh ene ee oe Rae 20 CO CP a oa » oA 10.36 10.52 11.18 12.46 3.08 Current (10—12amp.)| 1:8 18 2:2 35 4°9 Hadi Ve Me eee out out in in in Pimp 44.2. eetess: 10.30 10.47 11.18 11.48 12.18 12.36 12.55 Current (10—-amp.)| 48 124 170 174 178 182 191 ERGUUM |, savecoveendencane out in in im. . aD in in Fig. 7. Lil = —-O =a Poe er (x) eee ae 4 ’ HkEAVY PARAFFEINV \IN O/L- t 10"amps. g ra) 1 hours 2 3 The curves obtained, showing the behaviour of dielectrics under the action of radium rays, are similar in character to those obtained by Jaffé with very pure substances. The immediate increase due to radiation was observed in benzene, toluene, aniline, and carbon disulphide, in addition to those mentioned above. The vaseline used was the unpurified commercial sort, and it was rather irregular in its action. Its conductivity proper decreased very rapidly, so much so as to mask completely the increase due to radiation, if snfficient time was not allowed to elapse to produce its own minimum conductivity. These experiments have been conducted in the Physical Laboratory of Armstrong College, Newcastle-on-Tyne, under Prof. H. Stroud and Mr. H. Morris-Airey, to whom my best thanks are due. XXXII. Note on the Psychological Accommodation of the Lenses of the Eye. By A. L. HopGes*. [Plate IX.] F one chances to look at a picture or drawing showing in perspective a road leading off into the distance he can feel the lens of his eye changing focus, as if the object were really getting a greater distance away. Now of course all parts of the picture are practically the same distance from the eye and no such change in shape of the lens should occur. I append a simple perspective drawing to illustrate (Pl. [X.). Run the eye rapidly from the seemingly nearest part of the track to the farthest. The eye consciously and by will accommodates itself to the seemingly increased distances. This is readily perceived by trying it. This should throw it out of focus. I have found that it does with some people and does not with others. Dr. Horace Richards, to whose attention I called the phenomenon, seems to think that the eye is fooled into changing its focus, and immediately on coming to rest again at the end of the line finds out its mistake and re-focusses. I have tried this myself and feel a perceptible jerk on letting the eye come to rest. But on .several students whom I persuaded to try it, the final re- focussing effect was not noticed, they claiming that they could see equally well along the whole line but still perceiving the change in the accommodation. I think it a rather interesting little effect and one not devoid of interest to physicists. The question is: If the brain can see an upright image where the eye sees an inverted one, why cannot the brain fool itself into seeing a clearly defined object where the eye sees a blurred one? Because it certainly pursues the method that always gives a clearly defined image in real life, and the sub-conscious reasoning—if such there be—possibly proves to the brain that the blurred image falling on the retina is really a sharply defined one. * Communicated by the Author. ’ ec Uae XXXII. The Viscosity of Water. By Ricnarp Hoskrne, B.A. (Camb.), Physics Master, Sydney Grammar School*. ; ie a paper recently published+ in the Philosophical Magazine I explained how I had obtained three absolute values for the viscosity of water at different temperatures. I have since examined my reductions more carefully, and have found that the values are, in ©.4G.S. units, 005500 at - 50° C., °008926 at 25° C., and °017897 at 0°05 C. The last value reduces to ‘017928 at 0° C. Knibbst has deduced the absolute value :013107 at 10° C. from Poiseuille’s observations, and has shown that the data of every other experimenter whose work was published earlier than 1895, including Thorpe and Rodger, were not satisfactory for absolute values. So far as I have been able to examine the work published since 1895, I have reached a similar conclusion with regard to it. In order, therefore, to obtain, if possible, a complete table of absolute values between the temperatures 0° C. and 100° C. I have revised all my earlier work §, and reduced my obser- vations again by applying in the reduction formula, as given in my last paper, the value m=1°158 ||, instead of m=1-000, which I had previously used, and the value n=1:649. My results obtained in this way are contained in Table A. Hach value is obtained by the reduction of double sets of observa- tions. The table contains also the kinetic-energy correction in each case. The values are reduced to even temperatures by means of the formule to be given in Table B (p. 262), which reproduce the observed values with remarkable closeness, It is this fact which justifies the method. These values agree with the absolute values at the tempe- ratures 0° C., 10° ©., 50° C., and also (by interpolation) at 25° C., and it is reasonable to suppose that at the other temperatures also they are the correct absolute values. From the graph, values at the odd 5 degrees, for which there were no experiments, were obtained very carefully. _ * Communicated by the Author. Read before the Royal Society of N.S. Wales. + Phil. Mag. April 1909. ¢t Journal and Proceedings of the Royal Society of N. S. Wales, vol. Xxx1. § Phil. Mag. March 1900, May 1902, May 1904. || Boussinesq’s theoretical correction is 1:12, but experimentally I obtained the average value 1:158 for four tubes, which had been treated in exactly the same way as those used in these earlier experiments. 4 For these tubes n seems to have the value 1°64, for with that value inserted, the reduced values for viscosity at 0° C., 10° C., and 50° C. agree with the absolute values at those temperatures as given at the beginning of this paper. . The Viscosity of Water. 261 TABLE A. Viscosity at even Temp. |K.E. term x 105.| Viscosity x 10°. [Reduction x 10°. temperature. 0-100. 65 1785 6 01791 0:25 9-5 1780 Seige) LOLGOR Pt ae 4 0-21 11-0 1780°5 413 (01793 ¢ O1793 at O° ©. 0-21 11-0 1779'5 +13 [01793 571 7-6 1489 433 ~—«*(-01592) - 6:53 104 1452 Nt) Acie Ee 9-89 11-0 1314 fy 01310) 10:05 125 1310 49 01312 12:44 11-9 1221 +87 —_|-.01308 7 18105at.10° C. 12°51 92 1223 439 ~—‘*|-01312 17-07 9-9 1083 459 —*|-01142 we 17-10 99 1082 +60 foray f “Oll42at 15 20:37 11-2 997 49 91006 20-44 11-2 998 410 |-01008 25 20-72 14-4 989 417 |-e1006 ¢ 01006 at 20 20-72 14-4 988 417 _|-01005 30-25 13-7 798 +4 ce | 30-40 13°7 793 46 00799 se 30-78 171 787 413 00800 ¢ 00800 at 80 30°78 16-0 736 413 |-00799 40-07 16-2 658 41 0U659 40-00 16:0 657 40 00657 a6 41°74 19:3 636 +21 00657 00657 at 40 41-74 19:3 635 491 00656 50-10 18-4 550 41 00551 50°30 18-9 548 43 00551 51-82 21-9 533 +16 00549 ¢ 00550 at 50° C 51-82 21-0 532 416 —‘|-00548 59-90 18:4 468 cs 00167 60°13 183 470 ty 00471 | : 60°67 23-0 463 5 00468 ¢ 00469 at 60° C. 60-67 99-8 464 ae Oos69 65°30 210 434 42 00436) . 65°38 21-0 434 42 00436 | ‘00436 at 65° ©. 6991 19-7 410 05 |+-004095 10 20-8 405 +05 |-004055 | . 71°58 25-3 396 49 00405 ¢ 00406at70° C. 71°58 253 396 49 00405 8027 295 357 ay 00358 ] 79-90 20:8 356 +0 00356 |... 81-19 26-6 350 +5 00355 , 00856 at 80° C. 81°19 26-6 250 45 00355 90:00 225 316 +0 00316 29° 314 ey That eee 90:10 293 316 Py 00316 95°8 3: 298 43 00301) 97-7 23-6 291 +8 09299 f ‘00300 at 95° C. 97-7 23-6 291 ae 00284 at 100°C. Phil. Mag. 8. 6. Vol. 18. No. 104. Aug. 1909. T 262 The Viscosity of Water. The formula which best represents the results is of the type m=n/1+«t+ket?, but it is found that the range of temperature for each set of constants must not be greater than 25 degrees. In Table B are given the constants and the temperatures to which they apply, in connexion with the above formula. Taste B.—Constants in the formula y;=7/1 + yt + Ket. Formula. mie. le ae Ky. Niel Cee. 0° C.— 25° C.| -03445 | -000285 | -017928 (2) eae 25° C.— 50°C.) -03544 | 000195 | -017998 (ae 50° C.— 75° 0. | -0864 ‘000175 | -017928 (4); See 75° 0.—100° C. | -0390 000142 | -017928 Knibbs * has tabulated the relative fluidities (reciprocal of viscosity) of Poiseuille, Graham, Rosencranz, Slotte, Noack, — and Thorpe and Rodger, as redetermined by himself; and if — my results be treated in the same way and compared with the mean values, it will be seen that the agreement is very close as far as 50° C. These relative values are given in Table ©. | TaBLE C.—Relative Fluidities of Water 0° C.—100° C. Temp. | Poiseuille. Graham.| Rosencranz. | Slotte.| Noack. Tiodee| Aree Hatin 1846. 1861 1877. 1883. | 1886.| 1894. aes 0°C° 1000 1000 1000 1000 | 1000 1000 1000 1000 Sree 1177 1183 ei 1181 | 1178 1176 1179 1178 BOK. 1363 1369 We 1372 | 1875 1365 1369 1369 ae 1557 1580 Ms 1574 | 1575 1562 1570 1569 2) ae 1771 1796 Ae 1785 | 1796 1772 1784 1782 Bip 1992 | 2021 Be 2005 | 2020 1992 2606 2008 BO veces: | 2296 2240 iA 2933 | 2233 2995 2231 2941 Be 3) 2479 2493 be 2473 | 2484 2466 2479 2477 AO... 2738 2758 2730 2717) 2726 2716 2731 2730 ASR 3010 3018 3020 2961 | 2974 2976 2993 2988 7 ie 3308 3270 3214 | 3214 3246 3260 3260 ee 3549 3540 3477 | 3479 3517 3512 3530 tL See 3834 3720 3744 | 3763 3797 3772 3823 65 ...... 4165 3980 AON a: 4086 4062 4112 71 See 4461 4210 AMA N 4385 4338 4414 Ties ve 4430 A571 4693 4565 4719 BO vcicyt 4620 4849 5003 - 4824 5037 Bh ee a 5128 5316 5222 5852 90 ...4.: 5460 5409 5633 5501 5674 : 5 sieges Ae 5695 5955 5825 5977 100 3 ep 5983 6282 6132 6314 * Journal and Proceedings of Royal Society of N.S. Wales, vol. xxx. Proposed International Unit of Candle Power. 263 Table D contains the absolute values for the viscosity of water at 5 degree intervals from 0° C. to 100° C. as deter- mined from the whole of my experiments on water. The Taste D.—Absolute Viscosity of Water. Absolute Viscosity Thorpe & Temperature. | Viscosity. | (Computed). | Rodger’s (Hosking) | (by formula) Values. Goo. 017928 | -017928 (1) 01778 NO a 01522 | 015218 01512 TT caer a 013105 | -013107 01303 Pena 01142 |: -011422 01138 SPO CCW) 01006 | -010055 01004 = eee 008926 | -008926 (2) 00893 Shane aaa 00800 | “00801 09799 | Beem Muri) 00724 | -00723 00721 ee es 00657 | -00657 00655 “2 ne 00600 | -00600 00597 ee 003500 | -00550 (3) 00548 See. 00508 | -00508 00506 | EN. 00469 | -00470 00468 Ae ce, 00436 | -00436 00436 eh deel 00406 | -00406 00405 2 a 00380 | -00380 (4) 00379 ot, a 00356 | ‘00356 00355 “5 ae 00335 | -00336 00334 oe eg al 00316 | -00317 00316 16 85 "99 aii 10°2 ie The last three values of X are not exact. The values of \ and of A/density for thicknesses between 2 to 3 mm. and 5 to 6 mm. were also found for various substances. | SECONDARY. . Primary. | Absorber | | lo Be ae a | d/d. ft Ld Pa a age ee a eer OY Bie ee Seabee “S6 "121 28 | 039 Copper ......... 1-09 | 122 | jo Sa a “84 118 | | Aluminium | 21 : (i ea | 039 In the right columns are values for the more easily absorbed primary y rays as found by McClelland; these serve to illustrate the relative softness of the secondary. The secondary y rays were next investigated by the method of reversal of pairs of platesat A and B, precisely as described earlier in this paper when using primary rays. Taking the mean values for brick or iron radiators, on wood, iron, and lead platforms, the following results were obtained. Emergent secondary radiation using secondary y rays. Pee. 1 RN PE LO SPRANG 64:5 oc Serer ree era ay ee 70-0 pS oa aha SASHA Aa Ciao tailed 75°0 Care) Go's 4 The curve obtained, shown in fig. 5, is typical of easily ahsorbed vy rays. 286 Dr. A. 8. Eve on Primary Gamma Rays from Uranium X. About 13 kilograms of uranyl nitrate were placed in a cylindrical glass vessel so as to form a layer about 6 cm. thick. This was placed beneath the vertical cylindrical electroscope described earlier in the paper, plates were fixed close to the electroscope and the emergent secondary radiation was observed by the reversal method. The y rays from uranium X are teeble, and the measurements were difficult and uncertain ; but the results obtained were :— Uranium, y rays. Emergent secondary radiation. Pp poe 100 Ke ) ye 0 HV, * L008" and Ke _Vi-V.! te NaN sg 93 2 B= Woe 10)? B= V,) 100 The readings p, and q; on the scales cannot be less than 1, and the readings po, #3, dz, and g3 cannot be greater than 10. Hence, remembering that (V, — V2) /(H— V;) cannot be greater than (V—V3)/(E— Vj), we see that if (V;— V3;)/(E—Vj,) be equal to or less than 1/53, Ap is not greater than the hundredth part of p,+p2/10 + 3/100. Similarly, if (V;—V,')/(H— Vj) be equal to or less than 1/53, A, is not greater than the hundredth part of q;+ q2/10+ 93/100. We have therefore to arrange the relative values of the resistances of the slides and the bridge wire so that this may be true. As we have pointed out above, however, the inaccuracy in the value of « depends on the relative values of # and p; + po/10 + p;/100 + Ay. When these quantities are nearly equal, approximate methods of computation fail. By Ohm’s law, we see from fig. 6 that V,-—V,_ E-V, 1 Sm 10° and Ves ee oot 9 ‘ — Ry oe em y) (2) Device for evaluating Formule and solving Equations. 299 where R, and R, are the resistances of the circuits: RP, and RP... Hence it readily follows that a a) 81 rN H=3 > 10°R, 100 \R, R,/. 1000° RB, If R be the resistance of a slide, the minimum possible value of both R, and R, is R/10. Hence the maximum possible value of (V,— V3)/(E—YV) is ii R and this is less than 1/53 when 27/R is not greater than 1/287. Similarly. if p, R,’, and R,’ be the resistances of the slides, the readings on which are 2, g;, and gq, respectively, we see that " » \? 97 +18 E48 1(R) = ee 5 (2 ? =| Hav, = 10 (ty) +1005 +R By hod BN mes ot dah RM * 7000 Gar) iar In the very unlikely case when p = R,'= sh Ry’, (V,—V,/)/(E—V,) has its maximum possible value, and in this case it will be less than 1/53 if 7/R be not greater than 1/1100. Hence the desired accuracy can be attained by making the resistance R of each slide 550 times greater than the resistance of the bridge wire. It is to be noticed that the effect of connecting a slide resistance with P, instead of P, is to divide its value by 10. Hence, if we were adding 8°8 to 0°75, we would put the contact-finger of one slide on 8°8 and connect it with P,, and the contact-finger of another slide on 7-5 and connect it with P,. Suppose also that the value of 2 was 123. In this case we could only obtain a balance when it was connected with ().. VIII. Cubic Equation. Let us suppose that the cubic equation is © + a,0°—a,v+a,=0, where a», a;, and ay are positive numbers. The arrangement of the apparatus for solving this equation 300 Dr. Russell and Mr. Wright: The Wright Electrical is shown in fig. 7. The bridge-wire is the same as in fig. 6. We move the slides AB, A,B,, A.B,, and A,B; so that the ra} readings 1, a2, a, and a on their logarithmic scales are on the index-line II’. The ends of the contact-fingers touching AB, A,B., and A;B; are connected with P; and the finger touching A,B, with Q;. The fingers through N, N,, N,, and N; make angles tan—10, tan-'1, tan-* 2, and tan-!3 with the index-line. The battery and galvanometer-keys being closed, the bar to which the fingers are connected is gradually lowered. When the galvanometer deflexion is zero let us suppose that x is the reading on the logarithmic scale 8. In this case we have H-V; (Hey; seein, eee eS -— RB 3 Re ee Rn Device for evaluating Formule and solving Equations. 301 and thus 2?+a,27—a,%+a=0. Hence z is one of the roots of this equation. When a contact-finger, N, for instance, reaches the end of its slide N,B, will be R/10. If we now move the slide A,B, so so that A, is on the index-line, unclamp the contact- finger and move it parallel to itself until N; is over A, and then reclamp it, the resistance of N,B, will be R. If, then, we disconnect the finger N, from Q; and connect it with Q, the deflexion on the galvanometer will not be altered, and so we can continue to increase x. It will be seen that as # increases from 1 to 10 the contact-tinger N; traverses A;B; three times. ‘The first time N; gets to the end of its scale it is connected with P, and moved back to A;. The second time it reaches the end it is connected with P, and again moved back. The device enables us to find any real root of the equation, greater than 10” and less than 10"*1. All we have to do is to find the root of the equation x* + (a,/10")x? — (a,/10?")a + ay/10*"=0, lying between 1 and 10, and multiply the result by 10”. By solving a similar subsidiary equation we can find the approximate values of the roots of the equation which are less than unity. We may use Newton’s rule to find more accurate values of the roots. If a, for instance, be an approximate value of a real root of f(«)=0,a—/(a)/7'(a) gives usually a very much closer approximation 2,. The failing case is when we have two roots very nearly eqnal to one another. The device always indicates when this occurs. If two roots are each equal to a, or if they are approximately equal to a, the galva- nometer deflexion instead of passing to the other side of zero when z becomes greater than a returns to the same side. In practice if 7’(a) is large when f(a) is zero the device is very sensitive, but when /'(a) is small and in general, there- fore, when the roots are equal the device is unsensitive. To find approximate values of the negative roots of the original equation we find by the device the roots of 3 The imaginary roots* are most readily found by first finding as accurate a value w, as possible of the real root. We then divide the cubic expression by «—«, and equate the dividend to zero. The roots of this quadratic equation give the approximate values required. * Cf. C. P. Steinmetz, ‘Transient Electric Phenomena,’ p. 136. 302 Dr. Russell and Mr. Wright: The Wright Electrical IX. Equations of Degrees higher than the Third. The device can be usefully employed to find the values of the roots of equations higher than the third with sufficient accuracy for practical work. When calculating, for example, the requisite resistances for the motor controller of an electric ear, the following equation * has to be solved LVO—Y) 4 Qe@7—ay=0, where n is the number of steps in the rheostat. To solve this equation three only of the slides shown in fig. 7 are required. AB is connected with Q;, and A,B, and A,B, are connected with P;. The finger making contact with A,B, is inclined at an angle tan—!n/(n—1) with 1’, and the fingers on A,B, and AB are inclined at angles of 45° and 0° respectively. The value of « is then increased until a balance is obtained. When solving equations containing large numbers of terms it is sometimes convenient to divide the equation by a suitable power of x. In this case the fingers making contact with slide resistances representing terms containing negative powers of x are inclined to the left of II’ (fig. 8). Let us consider, for example, a sextic equation. As shown above, we alter it so that the required root or roots are multiples or submultiples of the equation v® —a5a° + aye* + a3v* — apt? — av + ay=0, which lie between 1 and 10. Dividing this equation by 2° we get a — asa? + age + 3 —agu-1— ayu—* + ana = 0. In general, seven slide resistances will be required, but if when 2 is put equal to unity any term is less than the - hundredth part of the sum of the terms of the same sign preceding it, that term can be neglected. The slide resis- tances are first moved until the readings on the index-line ATe do, dy, Ag, ... &c., as shown in fig. 8. The contact-fingers are next turned round to the requisite angles tan—’3, tan—!2,... tan-1—3, respectively. The ends of the contact-fingers are then connected with suitable points on the arms of the bridge. At first sight it might be thought thst two extra pairs of contact-points P,, Q, and P;, Q; would be required in the bridge arms. If a one per cent. inaccuracy, however, is * E. Wilson, ‘ Electrical Traction,’ vol. i. p. 42. Device for evaluating Formule and solving Equations. 303 permissible this is not necessary. To illustrate this point, and also the method of using the device in this case, let us consider the numerical equation e—5727 +0122+8'6—0:0427 + 1:32-7=0. Fig. & Putting « equal to unity we see that the term 0-04 can be neglected compared with 5.7, only five slide resistances therefore are required. We connect A;B, with Ps, A,Bo with Q,, A,B, with P, and make the reading on it 1:2, AB with P, and A'’B’” with P,. The finger on the slide DAE 5 gets to the end A’ of its scale first. We then disconnect it from P, and connect it with P;. We also alter the reading 3804 Dr. Russell and Mr. Wright: The Wright Electrical on the slide resistance A’’’B’’” to 10. When the fingers on the resistances A,B, and A;B; get to the ends of their scales we connect them with P, and Q, respectively. When, how- ever, the finger on the resistance A;B; gets for the second time to the end of its scale we disconnect altogether the wires connected with P;, and move the wire connected with P, to P, and the wire connected with Q, to Q.. In working the device these operations seem quite natural and little thinking is required. It is also easy to see that if a one per cent. inaccuracy is permissible it is unnecessary to have more than three pairs of terminals on the bridge arms. X. Imaginary Roots. In solving certain engineering problems in connexion with finding the amplitudes, the damping factors, and the periods of certain mechanical and electrical oscillations, a necessary step is finding the imaginary roots of certain algebraic equations. Quadratic equations present no difficulty, and we have already shown how approximate values of the imaginary roots of cubic equations can be found. With the biquadratic equations, however, which occur when discussing the theory of the parallel running of alter- nators*, the oscillations set up in coupled electric circuits in wireless telegraphy+, &c., both pairs of roots are sometimes imaginary. In this case we proceed as follows:—Let 2+ ye be a root of the equation f(<)=0. Then f(#+ye)=0, and hence, expanding by Taylor’s theorem, we have fe) Bi @)+ taf fOr" e+. b =0, and thus we must have a Op ys iv Fa)-FF a+ ont (=D) ei(a) and as (2) — © f(a) =0... @) From (6) we get y’ in terms of «, and substituting this value of y*? in (a) we get an equation of the sixth degree to find z. The two real roots of this equation can be found b the machine arranged in the manner shown in fig. 8, and the pairs of corresponding values of y are given at once by (6). Approximate values of the four imaginary roots can thus be rapidly found. If a higher degree of accuracy be required we can either use Newton’s method of approximation, or better apply Horner’s method to the auxiliary sextic. * A. Russell, ‘ Alternating Currents,’ vol. ii. p. 184. t J. A. Fleming, ‘ Electric Wave Telegraphy,’ p. 209. Device for evaluating Formule and solving Equations. 305 Theoretically we can always obtain approximate values of all the roots real or imaginary of an equation of the nth degree by the device, as y” can always be easily eliminated from the equations corresponding to (a) and (6) by Sylvester’s method* . XI. Solution of Equations containing Miscellaneous Functions. For this purpose some of the coniact-fingers are made from wires bent into the shape of certain curves. Suppose, for example, we desire to find the roots of the equation a b — 4+ -—~ =ca" +d (x gn Tf (x) ( )s where the values of f(x) and F(z) have been computed, or found experimentally, for values of «. Fig. 9, The wire passing through the point N; (fig. 9) issbent so * Burnside and Panton, ‘Theory of Equations,’ p. 296. 306 Dr. Russell and Mr. Wright: The Wright Electr ical that if y bea horizontal ordinate and w the vertical abscissa on the logarithmic scale, y=h log f (x), where h is the length of the scale on the slide resistances. Similarly the equation to the wire through Np is y=h log F(2). The contact-fingers through N,, and N, are set so that their , inclinations to the vertical are fixed at —tan-! m and tan—! n respectively. The rod II’ is then gradually lowered and the readings on the logarithmic scale 8, when the deflexion on the galvanometer is zero, give the roots of the equation lying between 1 and 10. The use of a bent contact-finger to take into account the “hysteresis loop” of iron would be of use in certain electrical problems. XIT. Solution of Transcendental Equations. Fig. 10. o Let us suppose that the equation we have to solve is yl," a> ala? —_ Ag) 403” aie Gal OQ? == Q. Device for evaluating Formule and solving Equations. 307 In this case (fig. 10) the scale S is an ordinary scale, the length KL being equal to hv. The various contact-fingers are adjusted so that the angles they make with the index- line II’ are tan—! (4, log 1,), tan! (by log ly), tan—! (83 log J3) and 45° respectively. We connect the contact-fingers as in fig. 10 and vary z. The values of x for which there is no. deflexion on the galvanometer are the roots of the given equation lying between 1 and 10. By altering the given equation to one whose roots are ten times smaller we find the roots lying between 10 and 100, and proceeding in this way we can get approximate values of all the roots. By similar settings of the contact-fingers, and by using both logarithmic and ordinary scales, approximate values of the roots of very complicated equations can sometimes be. easily found. XII. Tracing Curves Electrically. Suppose we desire to find the graph of the curve Y= a2? + dgt?—apv + ... = f(z), where p, q, 7, ... may be positive, fractional, or negative indices. We set the contact-fingers at angles tan! p, tan-1g, ... with the index-line, and move the slide resistances until the readings on the scales are ay, dg,.... The contact-. fingers on the slide resistances representing the positive terms are then connected with P, and the other contact-fingers with Q. In addition we have a slide resistance Y with a vertical finger, which is also connected with Q. The fingers are. moved down through a given distance 2 on the logarithmic scale, and the value of the reading y on the slide resistance Y when there is no deflexion of the galvanometer is then found. In this way simultaneous values of 2 and y can be rapidly obtained, and hence we can readily plot the curve. The curve could also be traced automatically by making the spot of light from a mirror galvanometer, connected between P and Q, fall on a strip of sensitive paper which is constrained to move so that its velocity is always proportional to the rate at which w is increasing. The points where the trace cuts the line of zero deflexion would give the roots of the equation f(7)=0, and the turning points of the trace would give the roots of 7’ (z)=0. In the same way the integral curve y=( fe) dz, 0 could be drawn automatically. 308 Prof. L. T. More on the Localization If the slide resistances were made of large size so that they could carry appreciable currents, recording ammeters and voltmeters could be employed to trace the curves. XIV. Conclusion. * We think that if engineers and physicists recognize that approximate values of roots of very complicated equations can be easily obtained, it may considerably extend the use- fulness of theory. Authors are often diffident to publish results which can only be utilized when the roots of equations of degrees higher than the third can be found, or when equations involving miscellaneous functions can be solved. In these cases we hope that a knowledge of the methods of using logarithmic slide resistances described above may be of practical value by showing how the theoretical results can be immediately utilized. We hope also that this preliminary sketch will induce others to improve the method, and to apply it to other and possibly more practical uses. It seems, for example, par- ticularly suited to harmonic analysis as the integrals repre- senting the coefficients of sin nv and cosnx in the expansion of f(z) can be readily found. In conclusion, we shall quote from the quaint but spirited preface to Seth Partridge’s book on the slide rule (1671). “ T am sure here is a good Subject, a good piece of Cloath, if the Garment be not marred in the making ; if it be, the fault is in the botching Taylor, not in the stutfe.” XXXVI. On the Localization of the Direction of Sounds. By Louis T. Mort, Ph.D., Professor of Physics, The Uni- versity of Cincinnati *. A a paper, written with the co-operation of Dr. H. S. Fry +, I published some experiments which indicated that the phase relations of sound-waves played a part in our determination of the direction from which sounds were heard. The experiments had been made some years previously and laid aside until further work could be done. They certainly showed that, by altering the phase difference of the waves entering the two ears and without appreciably changing the intensity, the direction of the sound could apparently be made to change. The weak point in our results was that the sound did not return to the medial * Communicated by the Author. + More and Fry, Phil. Mag. [6] xiii. p. 452 (1907). of the Direction of Sounds. 309 plane of the head, shift to the other side and back again as the cycle of phase difference was completed. In the mean- while, this was shown to be attainable by the experiment of Lord Rayleigh *. Later Professors Myers and Wilson f, using an improved form of our apparatus, made the sound shift from right to left and back again several times, as the phase difference was steadily increased, and they plotted curves from their results showing agreement between the observed and theoretical directions based on this idea. They also advanced an ingenious theory to account for the effect of the phase. Our knowledge of this subject has recently been increased by other investigators. Mr. T. J. Bowlker f records observations, in which he found this influence of phase difference, and that the direction of the sound shifted over to the opposite side, but the value of his results was diminished by the form of his apparatus. By the use of short metal tubes, attached to the ears and with the open ends a very considerable distance from the source of the sound, too much importance was given to disturbances due to the direct transmission of the sound to the ears and to the effects of resonance. Apparently these, at times, were more evident than the effect sought for. Dr. Knight Dunlap § has brought out the curious fact that each person has a preference in locating the direction of a sound, which is independent of the position of the source and which varies from time to time in the same individual. The cause of this preference has not been discovered. In the same journal Mr. Joseph Peterson || has a monograph on com- bination tones and allied problems, in which he has collected a large amount of information on this obscure subject, and he has added a critical review of the various theories extant. The experiments in this paper were made with an apparatus similar in principle to that in my former work, but with the improvement introduced by Myers and Wilson, which permits of a continuous variation of the difference of phase at the two ears. The apparatus (fig. 1, p. 310) consists of a brass tube, 260 cm. long and 1°5 cm. in diameter, with * Lord Rayleigh, Phil. Mag. (6) xiii. p. 214 (1907). + Myers and Wilson, Proc. Roy. Soc. vol. lxxx. p. 260 (1908). See also the Brit. Journ. Psychol., vol. xi. p. 363, where a more complete account is given. t Bowlker, Phil. Mag. (6) vol. xv. p. 318 (1908). § Dunlap, Psychological Rey. vol. x. no. 1 (1909). || Peterson, Psychological Rey. vol. ix. no. 3 (1908). Phil. Mag. 8. 6. Vol. 18. No. 104. Aug. 1909. Y +o es a 310 Prof. L. T. More on the Localization a short brass T-piece soldered to its middle point. This tube slides freely in two other brass tubes, AC and BF, each 140 cm. long. The ends of these are extended by SS ———————————————— — i ED a B 7 A e glass tubes, C to G and F to K, of the same diameter, and joined together by rubber tubing. In the early part of the work, two ear-caps were attached at Gand K. The ear-caps were made of wooden disks, 9 centimetres in diameter, stuffed with soft annular pads of cotton-wool covered with silk. But in all the observations recorded two long rubber tubes, each 800 cm. in length and of a diameter equal to that of the other tubes, were attached at G and K and the ear-caps added to their free ends. The tubes A to G and B to K were clamped to the top of a table, and the long tubes GR and KL were laid side by side on the floor to an adjacent room, where the listener sat with the ear-caps attached to his head, H, as shown. Much care was given to making the whole system symmetrical and the two branches of exactly the same length. An examination of the results shows that this was obtained. The position of the T-piece of the slider was read from a scale, graduated in centimetres, fastened near it, the middle or symmetrical point fixed at 100. The tuning-forks used in the experiments were clamped vertically in a box covered with wadded cloth to deaden the of the Direction of Sounds. 311 sound on the outside and were struck with a constant force by a soft hammer operated by a lever outside the box. A glass funnel, with its shank protruding through the side of the box, collected the sound which then entered the slider tube by a rubber tube connected to the shank of the funnel and to the T-piece. If rubber stoppers were inserted in the orifices of the tubes at the ear-caps, and the latter placed over the ears, no sound from the fork could be heard, but with the tubes free it could be heard clearly and the intensity was sufficient to locate its direction accurately. I found this arrangement to be much better than to have both listener and the fork in the same room, for two reasons. In the latter case the sound passing through the outside air directly to the listener caused confusion with the sound passing through the apparatus, when decisions were made. Also the listener involuntarily tried to guess the position of the slider independently of the sound heard, even though a large screen concealed it entirely from sight. The desire of the listener to guess the position of the slider was also lessened by seating him so that the line through his ears was at right angles to the sliding tube. Unmounted Koenig tuning-forks were used as sources, and by sliding the T-piece back and forth, any difference of phase was obtainable at the two ears. In the series of observations which follow, I noted the apparent direction of the sound and, after recording it, my assistant, Mr. P. B. Evens, who managed the forks and slider, told me the position of the latter by the scale. The sequence of the positions was quite irregular and not known to me previously. The apparent direction of the sound was recorded as: middle, when the sound seemed to lie in the medial plane of the head; right or left when directly from either side; anda fourth, half, or three-fourths right or left as the angle increased by 224° from the middle to the sides. Figs. 2 to 11 (p. 312) show the results of such a set of observations. They have been plotted in the convenient manner adopted by Myers and Wilson. The abscisse represent the position of the T-piece in centimetres and the ordinates the apparent direction of the sound, above the axis to indicate from the right, and below it, the left. The points plotted are not means of several readings taken for the same position of the slider, but separate judgements. The dotted lines show the theoretical positions of the points. Vs 312 Prof. L. T. More on the Localization Fig. 2. a ss Fig. 4. (n = 192), Big, ), (# = 256). Fig. 6. (n = 320). Fig. 8. (n= 512). ee ae cr a anc a ~ id i. at * of the Direction of Sounds. 313 Fig. 9. (n = 640). we [Swe Same Fig. 10. (n = 768). Fig. 11. (n= et R \ we ¥ \ 4 / Re \ "3 . i \ \ / %. Jaen h i \ ene: - ee N RIOT If the phase does influence the location of the sound then no difference of phase or a difference of any whole number of half wave-lengths should cause the sound to come from the front or back and as the difference of phase increases to one fourth a wave-length, the sound should swing around to the side, and then go back to the middle as the difference _ increases further to a half wave-length. From a half to a whole wave-length the cycle is the same, but from the opposite side, and so on to any number of wave-lengths. The curves show this clearly, the sound apparently coming from the side whose phase is in advance. Since the shifting of the slider doubles the phase-difference, the wave-lengths | have been divided by two, so that they would agree when the scale-readings were plotted instead of phase-differences. In the series of observations given, it is unnecessary to record them in tables as they can be read easily from the curves, which are plotted from individual readings. The observations on the direction were made by myself in all of them and the close agreement to the theoretical curves which are shown dotted, I attribute, not to any keenness of hearing on my part, but to the precaution of having the sounds made in a different room and muffled by striking the forks in a padded box, thus entirely eliminating the distraction caused by hearing the sound otherwise than through the tubes. We may conveniently divide the curves into two groups. Figures 2 to 7 inclusive, showing records of forks OC, (n = 64 dble. vib.) to g' (n= 384 d.v.), give almost perfect \ 314 Prof. L. T. More on the Localization agreement between the experimental and theoretical curves. In figures 8 to 11 inclusive there is a progressively increasing discrepancy between the curves. In all cases I noted changes of direction which followed a sinusoidal curve, but there was besides an increasing difficulty of locating sounds which theoretically should be from the right. When the frequency 1024 d.v. was reached in the series, all the sounds apparently came from the left in varying degrees. The judgement for these high frequencies was also somewhat further confused, as shown by an inclination to locate sounds near the middle or slightly to the left. With practice the regularity of the curves was improved but they invariably showed this decided preference in location. On trying the judgement of Mr. Evens in locating directions, I found that he had an even more decided preference, but his was for the right side, and also that 1024 d.v. was practically the limit of his power of determining direction in this manner. The cause for this preference, which agrees with Dr. Dunlap’s conclusions, is unknown, but there are some facts which apparently have a bearing on it. My own hearing is about normal, although my right ear is a little more acute. Mr. Evens is not normal, as he heard with considerable difficulty with his right ear. In both cases then the region of preference lies on the weaker side. In the next place the half wave-length for frequency 1024 is about 16 cm., the average distance between the ears. For waves of such length the head must cast a very appreciable sound shadow and so make possible the determination of direction by an immediate comparison of the intensities at the two ears. The mind would then have no training for phase-differences with these waves. But these facts are possibly only coincidences. We may judge then from these experiments that c” (n = 512) is near to my limit for accuracy of judgement by phase-differences and that accuracy decreases for higher pitches, becoming untrustworthy at a pitch of about 1024 d.v. Although no detailed investigation was made with sounds of a higher pitch, yet a qualitative trial with a fork of pitch 3000 d.v. approximate, showed that absolutely no sensation of direction existed. The fork was struck and then held close to the orifice of the T-piece, while the latter was slowly moved to the right or left. The only result was the sensation of a very shrill uniform sound a long way off, whose direction was impossible to locate. It has not yet been shown whether the perception of of the Direction of Sounds. 315 direction requires the use of two ears, and it is hard to determine because total deafness in one ear alone is rather rare. Experiments made on Mr. Evens and others who are hard of hearing in one ear, prove that they locate directions about as readily and as accurately as those whose hearing is quite normal. But these do not answer the question as the auditory nerve in each ear is usually unaffected, the trouble being with the drum or some other mechanical defect, and sufficient sound reaches the inner ear to produce some sensa- tion. I was fortunate in finding a person whose physical ears were perfect but who was totally deaf in one ear, and normal in the other, in fact the good ear was abnormally acute. Miss §., after an attack of spinal meningitis at the age of four years, entirely Jost the sense of hearing in the left ear. Examination by aurists showed that the nerve of this ear was atrophied, and the power of hearing gone. She tells me that she experiences no difficulty except that she has no faculty of telling the direction from which sounds come. On hearing a sound she turns her head indifferently in either direction until the object making the sound is seen. eo test her statement the following experiments were made. 1. The ear-caps were applied to the head and a fork sounded, as in the previous experiments. The right (good) ear was stuffed with cotton and the orifice of the tube into the ear-cap closed with a rubber stopper. The tube to the left (deaf) ear remained open. No sound was heard. 2. Same arrangement as in 1, except that the fork was mounted on a resonator and held directly to the T-piece. In this case also no sound was heard. The intensity of the sounds used in these and in the previous experiments was evidently too feeble to produce sensation by conduction through the head. 3. A test of locating sounds was made in the same manner as described earlier in this paper. In all positions of the slider, Miss S. merely heard a uniform tone issuing from the right tube. She apparently could not understand what I meant by asking if she noted any shift or change in the direction of the sound, as it seemed to her to be without direction. 4, Lastly, a test was made to see if she could determine direction without the use of the apparatus. She was seated blindfolded in the centre of a room. As a source, a fork with frequency 256 d. v. was used, mounted on its resonator. She apparently could determine direction to an extremely 316 Prof. L. T. More on the Localization limited degree when the sound was made on her right, but she was quite in error for sounds from the medial plane or from the left. This inaccurate power of determining direc- tion I attribute entirely to changes in loudness. If the fork was held well to the right side and the mouth of the resonator gradually and slowly closed by the palm of the hand, she stated that the fork had been moved to her left side. | The use of two ears for comparison is probably necessary for any but a most rudimentary determination of directions of sounds. What power there is, seems to be due to the increase or decrease in the intensity of the sound produced by a decided lateral position of the sounding body. There is no faculty of locating by phase relation in such a case. Combination of Two Tones. The tone given by a musical instrument usually consists of a fundamental combined with several overtones of rela- tively feeble intensity, and we undoubtedly locate their position by the fundamental wave, ignoring the higher tones. This, for example, was found to be the case when an organ- pipe was used, as no confusion occurred from the presence of its harmonics. But the conditions are altered when two forks of different pitch are struck with equal force, or still better the shriller one a little harder, and held to the T-piece simultaneously. 1. Forks c’ (n=256) and c’ (n=512) were tried in this manner. ‘The two tones combined so that the separate notes were heard with great difficulty. At 100 the direction was middle, at 40, 1/2 lett, and at 160, 1/2 right. Comparison with figs. 5 and 8 shows that the lower tone exerted the greater influence. The results obtained with chords of less perfect harmony were not so simple. 2. Forks c’ (n=256) and e! (n=320).—At 100, the tones combined in a chord, whose direction was middle, and the component tones were not heard. At 40, e’ was heard distinctly and by the right ear only with a location of full right ; c’ was heard by the left ear only with a direction of half left. Besides these, the combi- nation chord was noted as being rather indistinct and near the middle. At 160, e’ full left, and c’ one-half right. The chord, indistinct and one-fourth right. of the Direction of Sounds. 317 Figs. 5 and 6 show that the direction of the separate notes followed the curve as if each were alone present, and that the location of the chord was rather more influenced by the lower tone. 3. Forks ec’ (n=256) and g’ (n=384).—In general, the lower tone was completely blotted out, the chord was heard either to the right or left, and the higher tone was usually quite distinct and its direction clearly indicated. For the most part the direction of the chord was most strongly influenced by the theoretical direction of the higher com- ponent. But at certain positions of the slider, the sound g' became quite feeble and even inaudible, leaving only the chord. The positions where this occurred were when the theoretical directions of the two component waves, taken separately, were both in coincidence, either right, left, or middle. Professors Myers and Wilson have offered an ingenious theory to explain the effect of phase-difference on hearing. According to this theory the difference of phase is a primary cause of the changes in locating sounds, and acts by pro- ducing an inequality between the intensities of the sound inside the ears. For example, a sound-wave enters the right ear with a certain phase, and at the inner ear encounters and combines with a portion of the sound which entered the left ear and passed through the head to the inner right ear. Similarly, the sound-wave enters the left ear but at a dif- ferent phase, and there meets sound passing through the head from the right side. They assume “That the displace- ments in the internal ear due to the two sets of waves are in opposite directions. It should be said that the principal reason for making this assumption is that it enables an ex- planation of the lateral effects to be given.” Now the phases of the waves entering the ears from without are different, therefore the diminution of the intensities of these waves by the combination with the waves conducted through the head is unequal in the two ears. And we are supposed to judge the direction of the sound by comparing the two unequal intensities of the combined waves in the internal ears. In further explanation, they say, ‘“‘The distance between the ears through the head is small, and the velocity of sound through the bones probably very high, so that we should not expect a reversal of the effect due to this cause, unless the frequency were very great. But with high frequencies the lateral effects cannot be obtained. The amount of sound which must get through the head to produce an appreciable 318 Prof. L. T. More on the Localization difference between the intensities at the two internal ears is not large, because since the two amplitudes are added, an imperceptible amount getting through might produce an appreciable difference of intensity.” The theory is very ingenious at first sight, but it does not seem adequate when considered closely, as there are a number of facts which contradict it, and others which are not ex- plained by it. In the first place, the head always casts something of a sound shadow, even with deep tones, and the intensity at the averted ear is always a little less, no matter what the length of the sound-wave may be. This direct difference of intensity is probably as great, if not considerably greater, than the difference of intensity caused by the interference of the sound in the internal ears. If so, why is it not simpler to refer localization of sound always to differences of intensity of this kind at the outer ears? This opinion is supported in several ways. In my experi- ments the sounds were purposely made feeble, so feeble that sufficient sound did not travel through the head to produce any sensation. It is possible that even if they did not pro- duce a direct sensation, yet they might cause an appreciable effect by interference. But this is hardly likely when we remember that these feeble tones were as readily affected in direction as loud ones. Certainly such minute interferences should at least render the effect less obvious. Also if one tube were suddenly pinched, so as largely to reduce the direct effect of intensity at one ear, no confusion was caused to the judgement, yet the relative intensities of the compound tones in the two internal ears must have been as suddenly and as greatly altered, and this should by their theory shift the direction of the sound. This is not the case. An ex- periment was devised which makes this objection very forcible. A thick felt pad was inserted between one ear-cap and the head. In the pad a hole was cut the size of the opening of the passage into the ear and in line with it. The direct sound entering the ear was thus decreased but slightly while the amount of sound conducted through the head from this side was much diminished, since the sound which would have struck the skull in the neighbourhood of the orifice of the ear was stopped. Now if the pad was suddenly removed the resultant intensity of the sound in the opposite internal ear was decreased, because the sound conducted through the head was increased and relatively much more than the intensity at the inner ear on the pad side, consequently the direction of the Direction of Sounds. O19 of the sound should shift unmistakably. No such effect could be detected. So far we have discussed only the simplest case, when the sounds approach through tubes and impinge only on the ears. But if the theory is to hold for the practical locating of sounds in the open air, the idea of interference in the inner ears becomes still more inadequate to account for the facts. Leta musical note be struck behind a person and at an angle of 20° with the medial plane, then besides the sounds travelling through the head from one ear directly to the other, we have the entire back part of the head struck by the waves of sound. These waves travel through the head to the inner ears with different lengths of paths, at varying angles, and together make an intensity certainly much greater than the waves going from one ear to the other. It would be extremely difficult to predict what the resultant amplitude would be when all these motions with their differing phases compounded with the sound entering the external ear. Locating sounds would be to say the least a complicated matter. It is also readily understood that this theory would lead us to expect that simple musical tones would be easier to locate than noises which have not so simple a wave form, while the contrary is proved by experiment. None of these objections applies to a simple and direct influence of phase relations on our hearing, as they do not affect the phase of the waves. The only objection to the idea that the ear is capable of detecting the phase of a sound or at least the difference between the phases of two sounds, is that it is difficult to reconcile with our theories of audition. But is it not a fact that we know extremely little about the mechanism of audi- tion, and still less about the resultant nervous stimulation ? The experimental facts to me, at least, seem irreconcilable to the theory of locating sounds in all cases by intensity varia- tions, and none of the objections made in this paper are pertinent to the appreciation of phase-differences. It is of course possible that neither of these is the direct cause, which may be something in the sound-wave affecting us by some unknown psychological influence. University of Cincinnati, April 1909. [300 7 XXXVIII. A Method of producing an intense Cadmium Spec- trum, with a proposal for the use of Mercury and Cadmium as Standards in Refractometry. By T. Martin Lowry, Was, fF .C.8 | F' the different line spectra that are available for spectro- scopic standards—hydrogen, mercury, cadmium, &&.— the simplest and purest is undoubtedly the cadmium spectrum. The visible spectrum is made up of four strong lines (red, green, blue, and dark blue), which are so narrow and of such a high degree of purity in respect of the absence of satellites. _that they have been used by Michelson to produce interference- bands of an order of retardation that has apparently never been reached in the case of any other lines. Michelson’s. racemes of the wave-lengths of the three chief Cadmium ines :— Wdered 72) 6438°4722 10-1 metre. Cd green...... 5085°8240 xf 4 Gdwolne § 2c. 4799°9107 ie . have indeed formed the standards from which all other wave- lengths have been deduced. It is therefore evident that the cadmium spectrum is destined to play an extremely important part in optical determinations of all kinds. Unfortunately, the difficulty of producing a cadmium lamp which shall burn steadily and give out light of high intensity has been so great. that the four cadmium lines have been used only very occasionally in optical experiments. Sodium. The standard monochromatic light employed aimost uni-- versally for refractometric and polarimetric measurements has been the yellow flame-spectrum of sodium, which has the advantage of being produced with very great readiness, but with all the drawbacks inseparable from the use of a doublet, instead of a single line, asa standard. Thus in determining the refractive index ny of a liquid, the Pulfrich refractometer gives readings for the less refrangible constituent, whilst a hollow prism mounted on a spectroscope gives an average value for the two constituents, unless indeed the resolution be sufficient to read them separately. In polarimetric work the double character of the sodium line renders it impossible to secure a proper extinction for large values of a,, since one * Communicated by the Physical Society : read June 25, 1909. Method of producing an intense Cadmium Spectrum. 321 wave-length is transmitted with considerable intensity when the other is extinguished, and in addition there is always some uncertainty as to the “ optical mass-centre ” of the doublet, which may indeed vary in different types of sodium-lamp, on account of changes in the relative intensity of the two con- stituents *. It should also be noted that the sodium flame emits a considerable amount of light of other colours, which in accurate work, or in reading large rotations, must be removed by filtering through a coloured screen, or, better, by means of a spectroscopic eyepiece (Perkin). Hydrogen. The hydrogen lines, Ti, (red), w.-l. = 6560°04, Hg (blue), w.-l. = 486149, H, (violet), w.-l. = 4840-66, have been universally employed with the sodium doublet in refractometric work when dispersion-values were required. The choice has been wholly one of convenience and has no other merit to recommend it. The vacuum-tube, though easily fitted up, can hardly be seriously considered as a source of light. The red line is by far the strongest, and has been used with advantage to produce interference-fringes in measurements of length ¢, but would be utterly useless for polarimetric work in which the source of light must be viewed through a Nicol’s prism set within 2° or 3° of the extinction position, The violet line is unpleasantly weak even for refractometric measurements, and demands the use of the full power of a six-inch coil, with an efficient optical condenser, before readings can be made with any degree of comfort. The hydrogen spectrum has the further dis- advantage of showing, at least in an ordinary vacuum-tube, an almost continuous back-ground of weak lines. Although, therefore, refractometers are regularly sent out with tables for the sodium and the three hydrogen lines—and no data whatever for light of any other wave-length—it is evident that this position is radically unsound and cannot be perma- nently maintained. * Compare Landolt, Optische Drehungsvermdgen, 1898, pp. 362 et seq. +t See, for instance, Tutton’s measurements of the coefficients of expansion and of elasticity of crystal-plates (Phil. Trans. 1903, a. 202, p. 143). Compare also Tutton, Proc. R.8., June 10, 1909. 322 Dr. T. M. Lowry on a Method of Choice of Standards. The essential properties for a standard source of light are, (1) that it should be of sufficient intensity to be used for all the various types of optical measurements, so that, for instance, refractive indices and optical and magnetic rotatory powers may be determined for the same wave-lengths, (2) that it should be strictly monochromatic and as far as possible free from satellites, and (8) that it should be pro- duced with sufficient readiness to render it generally avail- able. These requirements, as has been shown, are only partially fulfilled by sodium light and fail completely in the case of the hydrogen spectrum. ‘The purpose of the present communication is to suggest that the spectra of mercury and of cadmium fulfil most of the essential conditions outlined above, and to describe a method by which the cadmium spectrum may be rendered more generally available for spectroscopic work. The suggestion—which is made on the basis of practical experience in the actual measurement of optical and magnetic rotations and of refractive indices for a large range of wave- lengths (see for instance Proc. Roy. Soc. 1908, 81. p. 472) —that sodium should give place to mercury and cadmium as a chief standard source of light, is fully supported by the theoretical considerations recently advanced by Bates (“Spectrum Lines as Light Sources in Polariscopic Measure- ments,” Bureau of Standards, Bulletin, 1906, 11. p. 239) and by Nutting (“ Polarimetric Sensibility and Accuracy,” ibid. p. 249, “Purity and intensity of Monochromatic Light Sources,” ibid. p. 439). The former author has worked out a formula showing the errors due to the use of a doublet in polarimetry, and has redetermined the ratio of the sodium- yellow and mercury-green rotations for quartz ; the latter has developed formule in reference to polarimetric sensi- bility, and spectral purity. The two points in these papers that bear directly on the practical problem now under con- sideration are, (1) the confirmation by Bates of the purity of the mercury green line, which gave very sharp readings in the case of a quartz plate of about 54 mm. thickness ; this point is, however, seriously discounted by the fact that he professes to read the sodium doublet to 0-0001°, and gives the ratio of sodium to mercury to six significant figures (0°850944: 1), (2) the statement by Nutting that on one basis of reckoning the “spectral purities ” of cadmium green, mercury green, and sodium yellow, are represented by the : i Lg $ ‘ We a ratios 79,5009 i0,0007 204 7p, Whilst on another basis the “ specific producing an intense Cadmium Spectrum. 323 ‘impurities ” of the mercury green and sodium yellow lines are given by the ratios iu xp 3 these figures serve to show that the change of principal standard now proposed on the basis of practical polarimetric work is fully justified by minute spectroscopic tests on the lines themselves. Mercury. The use of the enclosed mercury arc as a source of light in spectroscopy dates back to 1860 (J. H. Gladstone, “ On the Electric Light of Mercury,” Phil. Mag. [4] xx. pp. 249-253), but its use in polarimetric measurements was apparently intro- duced by Disch (Ann. Phys. (4) xii. p. 1155) in 1903, who made use of the Arons lamp. The Bastian mercury lamp, which has been in use in my own laboratory since 1906, and at the Central Technical College since 1907, has the advantage. of being a commercial article of much lower cost; it is con-. structed with a suitable resistance in the holder, so that it can be plugged into the ordinary lighting circuit without using a resistance-frame or any special leads. This lamp is unfortu- nately no longer on the market, though it is still constructed to order by the Brush Electrical Engineering Company ; but silica lamps of moderate price are promised which may prove to be as economical in working as, and even more. efficient in illumination than, the earlier glass lamps. Of the six chief mercury lines, aCe a yellow doublet, 5460°97 a splendid green line, 4358'°58 a strong violet line, tokens at the extreme limit of the visible spectrum, | two, the green and the violet, have already proved to be of the utmost value in polarimetry, and are likely in the future to prove of equal value in the measurement of refraction and dispersion. Their use in polarimetry has been due to the following considerations. For accurate measurements of the specific rotatory power of a substance, and to any even larger extent for tracing the course of chemical changes (isomeric change, sugar-hydrolysis, &c.) by polarimetric observations, it is essential to use an intense source of light in association with a very small half-shadow angle, since only thus can a maximum of sensitiveness be secured : it is also desirable to use a light. 324 Dr. T. M. Lowry on a Method of of relatively short wave-length, in order that the actual readings may be large *, without incurring the loss of optical intensity and the fatigue which result from the use of blue light. The intense green mercury line, which can be read with a considerably smaller half-shadow angle, and gives readings about 15 per cent. larger than the sodium doublet, is therefore much superior to the traditional standard, apart altogether from the question of spectral purity. In the latter respect the contrast is extreme ; in the case of quartz I have been able, without any noticeable loss of accuracy, to secure readings showing a total rotation of 50 right angles for the mercury green line, two independent series of determinations giving average values 4487°78° and 4487°79°; sodium under similar conditions gave no extinction at all. The green mercury line promises, indeed, wholiy to replace the sodium doublet as a chief standard in polarimetric work, and it is highly desirable that it should acquire as quickly as possible a like predominance in the measurement of refractive indices, and in all other optical determinations. The violet mercury line has proved indispensable in the measurement of rotatory dispersion on account of its extraordinary brilliancy. In spite of the low sensitiveness of the eye for light of such small wave-length it has been found possible to read this line with a half-shadow angle of only 6°, and to secure series of readings (each an average of 10 settings) which only differed from one another by a hundredth of a degree. The violet line is less pure than the green, as it is accompanied by two satellites of smaller wave-length, but these are so weak that they cannot be seen at all in the polarimeter, and cannot, therefore, produce any appreciable disturbance in the readings. The yellow doublet is made up of two lines separated by about three times as great an interval as in the case of sodium ; for small rotations they may be read as one line, but I have also been able, by using a-narrow slit, to read them separately; they are, however, altogether unsuited for general use. For refractometer work the mercury lines are at least as easily available as those of hydrogen; a warmed vacuum- tube containing a drop of mercury gives the lines with greater brilliance than those of hydrogen, and it is therefore not unreasonable to suggest that—as a minimum concession to the correlation of optical measurements of various kinds— the use of Hg 4861 and Hy, 4341 shall be abandoned in favour of Hg 5461 and Hg 4359 in future refractometric work, and : Asa rule the specific rotation is doubled on passing from yellow to violet. producing an intense Cadmium Spectrum. 325 that tables for these wave-lengths shall be supplied as a matter of course with instruments of the Pulfrich pattern. It may be noted that the mercury and hydrogen violet lines differ by only 18 Angstrom units, the mercury line having the longer wave-length: in a Pulfrich instrument the two lines are indistinguishable, but the edge that is read with a hydrogen-mercury vacuum-tube (such as is sometimes sent out with the instrument) is due to mercury and not hydrogen. The adaptation of a polarimeter for use with mercury light costs about £2, with a further £3 for the lamp. Cadmium. The cadmium spectrum is much less easy to produce than that of mereury. Michelson made use of a strongly heated vacuum-tube with aluminium electrodes connected to platinum wires passing through the glass. This was improved upon by Hamy (Comptes Rendus, 1897, exxiv. p. 749) who used a copper heating-jacket and external electrodes, thus avoiding the risk of cracking the hot glass by wires passing through it. Ihave had no personal experience of such lamps, but am doubtful whether they would give a sufficiently intense light for use in polarimetry. The amalgam lamp with an are enclosed in silica can be made to give a splendid series of lines for use in spectroscopy, but I have found that it is useless for polarimetric work, since even the green cadmium- line can only be read with a half-shadow angle of nearly 20°. Apparently the current is carried mainly by the mercury, and the other metals show only weakly in the spectrum. I have not been able as yet to find any description of an enclosed cadmium arc, though I believe they have been tried —evidently not with complete success, or the results would be more widely known. The method set out below is not put forward as the ideal way of producing an intense cadmium spectrum, but rather as an intermediate stage in the development of the perfect cadmium lamp of the future. It was found that brilliant speciral lines could be sent into the polarimeter by using an are burning between metallic poles rotating in opposite directions. Copper, for instance, gave a valuable series of lines, and brass electrodes were found to be very efficient for developing a zine spectrum, the red line Zn 6364, and the three blue lines Zn 4811, Zn 4722, and Zn 4680, standing out very distinctly from the copper lines. A brilliant cadmium spectrum could be produced by melting the metal onto copper electrodes, but it soon burned off, and in any case it Phil. Mag. 8. 6. Vol. 18. No. 104. Aug. 1909. Z 326 Dr. T. M. Lowry on a Method of was difficult to avoid a displacement of the readings by the appearance of the copper line Cu 5106, as a ghostly partner of the green cadmium line Cd 5086. After many unsuc- cessful attempts a workable method of producing the cadmium. spectrum was found in the use of an alloy of silver and cadmium. It is perhaps not very widely known that these metals are isomorphous, and form an excellent series of alloys. These have the advantage that no eutectic is formed, the melting-points throughout the series lying above that of cadmium and over a considerable range approximating some- what closely to the melting-point of silver. Thus whilst the addition of 28 per cent. of copper (mp. 1082°) lowers the melting-point of silver from 960° to 780°, the addition of 28 per cent. of cadmium (mp. 322°) only lowers the melting- point to 860°. Nearly 50 per cent. of cadmium must be added to lower the melting-point to 780°, and even a 60 per cent. alloy melts as high as 700°. These alloys, which can be turned up like pure silver, were supplied by Messrs. Johnson and Matthey in-the form of rods + inch in diameter and 12 inch long. _ For spectroscopic work a tiny arc can be burnt. quite steadily between the points of the rods, in great contrast to the behaviour of pure cadmium, which splutters very badly and gets choked up with oxide, even when the current is kept so small as not to melt the metal. For polarimetric work a greater intensity of light is desirable, and this is obtained by using a heavier current, and rotating the electrodes in opposite directions (compare Baly, Spectroscopy, p. 370) in order to maintain the are in a central position. The rods of alloy were screwed for half their length into copper cylinders 2 inch in diameter, which served the double purpose of cooling the electrodes—a point of some importance—and connecting them with the iron spindles by means of which the rotation was produced. When run at the highest intensity both rods become red hot, and one of the copper cylinders is usually luminous, but it is not desirable to over-run the are since even if the electrodes do not melt the cadmium distils out irregularly and causes a certain amount of spluttering. The electrodes are filed up before the arc is started, and are carefully adjusted so as to run true to centre; alternatively they may be allowed to burn until the ends are flat and then used without further attention except to adjust the length of the arc from time to time. The cadmium spectrum thus produced is of great brilliance—the green line is even brighter than that of mercury, and can be read with a half- shadow angle of 3° or less. From some points of view producing an intense Cadmium Spectrum. 327 it would be a better chief standard than mercury green, as it is considerably brighter and gives readings about 15 per cent. higher, but in view of the greater trouble involved in producing the light, and persuading it to burn steadily, it is better to use it as a secondary line for the study of rotatory dispersion. The red and blue lines are also very bright and can be read quite easily. The dark blue line is of much less intensity, and is not likely to be widely used, as it is difficult to read, and does not differ sufficiently in wave-length from the light blue line to justify the extra trouble involved ; this observation applies, however, only to the existing arrangements, as it is quite possible that when a more powerful source of steady light is available the dark blue line may prove to be of considerable value in shortening the gap between Cd 4800 and Hg 4359. Unlike copper the silver spectrum does not clash at all with that of cadmium ; the brilliant silver green lines “ah nor doublet (compare sodium) 5209°25 are separated from the cadmium green, Cd 5086, by an interval nearly as great as that which separates the two cadmium blues, and the only other line that shows at all strongly in the spectrum is a line in the far-violet, perhaps Ag 4055. In conclusion: It is suggested that the mercury line Hg 5461 should be used as chief standard in optical work of all kinds, and that dispersion should be measured from this line to Hg 4359 instead of from Ha6561 or Hg 4861 to H,4341. As secondary standards are suggested the flame spectra Li6708 and Na 5893, purified spectroscopically, together with the three cadmium lines Cd 6438, Cd 5086, Cd 4800, giving a well-distributed series of seven wave- lengths. 6708, 6438, 5893, 5461, 95086, 4800, 4359. Red red yellow green green blue violet. 130 Horseferry Road, Westminster, 8.W. Note added July 1909.—I am glad to find that the desirability of a change in the standard wave-lengths for use in refractometry is appa- rently recognized by other workers: in particular, Dorn & Lohmann in their measurements of the refractive indices of liquid crystals (Ann. Physik, June 10th, 1909, [4] xxix. pp. 5385-565) have used the series Li 6708, Na 5898, Hg 5461, He 43859, which is identical with a series that I am using for the measurement of the refractive dispersions of the alcohols and acids of the aliphatic series, and differs from the series of seven lines used in the measurement of rotatory dispersion only in the omission of the three cadmium lines. aes a met f) 328") XXXIX. The Recombination of the Ions in Awr at Different Temperatures. By Henry A. Erikson, Assistant-Professor of Physics, University of Minnesota ™*. [ this paper are given the results of an investigation, as far as it has progressed, of the recombination of the ions produced by the y and @ rays of radium in air at different temperatures, the density of the air remaining constant and equal to that of the normal atmosphere. It is now known that the previous experimental results obtained in this connexion were rendered uncertain by diffusion, owing to the fact that the electrodes were too close together in the case of some of the densities involved f. It was shown experimentally by L. L. Hendrent, in connexion with his work on recombination at different pres- sures, that the effect of diffusion upon the coefficient of recombination («) in the case of air 1s very small when the electrodes are 2 cm. apart and the density and temperature of the air are those of the atmosphere. It was concluded from this that, with the electrodes 4 em. apart and a similar density, the eftect of diffusion would be so small, even at different temperatures, that whatever variation was found in « would be mainly due to causes other than diffusion. If the effect of diffusion may be neglected at room-temper- ature, it may be neglected with more safety still at lower temperatures. At higher temperatures one cannot be so certain. The Ionization-Chamber. The final form of ionization-chamber decided upon was a copper sphere 11 cm. in diameter, having at its centre a sphere 3 cm. in diameter. This inner sphere, with its attached tube, was of glass covered with copper, electrically deposited. These two spheres formed the electrodes and were therefore 4 cm. apart. Any irregularity due to the connexion with the inner sphere was avoided by means of a cone, as shown in fig. 1. The radium was contained in a small glass sphere and placed at the centre of the two spheres forming the chamber. This makes a very regular arrangement, for which the * Communicated by Sir J. J. Thomson. J Phil. Mag. vol. vi. p. 655 (1903). t Physical Review, vol. xxi. p. 314 (1905). Recombination of Ions in Air at Different Temperatures. 329 constant, on the assumption that the ionizing effect of the rays varies inversely as the square of the distance from the source, may be readily obtained as follows: i ( sean |” 4 (40 w)rdr=o(r2—7;) (447 —@) a7: Ty (A) eS ("ade= ("4/ Bae —w)r iT gape [os —7r”)(A7—«) eT) — oe —r2)?(4r— w)?. But from equation (A) In= Q Jo (r2—7,)(47—w)’ _ +7 )(r? —r,’)(47 —w) Q Q Sees giid vl sun os Nee NE where Q is the total number of ions produced by the rays per second, N the number existing in the gas when equilibrium is established, and o the solid angle of the cone. It is seen that K is a constant which depends only upon the dimensions of the chamber. Experimental Method and Arrangement of Apparatus. The method used in this investigation was essentially the same as that employed by Hendren (loc. cit.). Fig. 1. PAAAAARALG! SLL LTITT/ AULA i i?) TULL The arrangement of the apparatus was as shown in fig. 1. 330 Prof. H. A. Erikson on the Recombination of Q was measured in the ordinary way by obtaining the time (T) required for the leaf of the electroscope to move a certain number of divisions when the key A was open, 1000 volts being applied to the outside of the chamber. During this measurement the capacity (C) was added to the capacity (C,) of the electrode system. was obtained by measuring the total charge in the gas when equilibrium had been established. This was accom- plished by means of the contacts made by the horizontal slide 8, which could be released and made to move by means of a suspended weight. When the slide was in the position shown in fig. 1 everything was connected to earth. When the slide is released contact is made at a openin the key B, thus insulating the inner electrode of the chamber. A little later the slide makes contact at 6, which connects the ionization-chamber to a high potential H. Considerable difficulty was here experienced in preventing a partial loss of the free induced charge through leakage to the guard-ring G. It was found, however, that this could be overcome in a very satisfactory manner by applying a voltage of about 2 E to the guard-ring G at the same instant that EF was applied to the chamber, and then connecting the guard-ring to earth again at the same time that the chamber was earthed. This was accomplished by the relay D when the slide made contact at ¢ and broke contact at d. Atethe slide disconnects the chamber from the high potential H and an instant later earths the chamber through contact at f. When the slide makes contact at g the key A is opened, thereby insulating the leaf of the electroscope. At h the inner electrode is connected to the leaf by closing key B, the charge C,V, collected on the electrode causing the leaf to deflect. Contact at 2 opens the key B again and insulates the leaf. From the deflexion the potential V, to which the charge has raised the capacity C, of the electrode system is determined. The collected charge ©,V, requires two corrections : During the time (¢) that EH was applied to the chamber, the rays produced a quantity Qet which must be subtracted. Also during the time (¢') from break of contact at e to make of contact at ia back-leak took place which must be added. The leak per second (L) was readily determined by charging the electrode system to a potential a few divisions higher and noting the time (T,) required for the leaf to move to a point the same number of divisions lower than the the Ions in Air at Different Temperatures. 331 deflexion caused by the charge C,V;. The amount of loss due to the back-leak then is : C,(V;3 Ae V4) t’ t Li’= T, From these determinations we have: @= (C+C,)V me tae.” be) (C+CO)V , (V; we t! ee LC; rae ae i 3000" a=K elisa | sh, (C+C,)V,. (V3—V4)C1 7” T| Gv, -S4y* t+ aE oe | The times ¢ and ¢' were readily obtained from the tracing of a tuning-fork on the surface of a smoked glass placed upon the slide. Care is necessary at this point ; t must be sufficiently large to allow all the ions to pass to the electrodes, and E must be so high that the time required for an ion to pass the distance between the electrodes permits only a negligible amount of recombination. These points are readily tested experimentally by using different values for E. It was found that with H=600 volts and E=1000 volts, the same value for « was obtained. This test was applied at the temperature of liquid air as well as at room-temperature. The value of E used throughout the entire work was, however, 1000 volts. In order to be certain that the deflexions obtained are due to the ions produced by the rays it is necessary to have the apparatus so constructed that the radium may be removed and the manipulations described above repeated without the rays. The inner spherical electrode was therefore constructed so as to open to the outside through the tube serving as its support. It was found to be possible to get all parts so perfect that no motion of the leaf was obtained without the rays, and care was taken to have this as the working condition throughout the entire work. The capacity C consisted of two circular plates placed 2mm. apart. The capacity of this condenser was computed according to Kirchhoff’s formula (Abhandl. p. 113) giving 700 cm. The capacity ©, was obtained from comparison with C by method of mixtures. 332 Prof. H. A. Erikson on the Recombination of The value of each deflexion in volts was obtained from a> potentiometer, a cadmium cell being used as the standard. The lowest temperature was obtained by immersing the chamber in liquid-air. The next higher temperature was obtained by packing CQ, snow about the chamber, the liquid- air tube being used as the containing vessel. Temperatures higher than that of the room were obtained by inverting the chamber and heating it by means of a concentric electric coil, the whole being imbedded in dry sand. Results. In order to show the magnitude of the different quantities involved, a set of observations with their substitution in the expression for « is here given. Time in seconds required for the leaf to move 10 divisions (== "bil volt) TOS 979, 10:2, 104, 10, 10, 102 10, Ay, ae The: deflexion in scale-divisions due to charge C,V,: 23°6, 24:4, 24°5, 24:4, 24°3, 23°8, 23°8, 24:2, 24-4, 24-6, 24°5, Avy.= 24°23 (=1°56 volts). K=F(1%+11) (19? —11’) (447 —@) =4(5°8441:55)(5°84?— 1-55”) (4—-561) = 710. Me Ci eer 0027): 771. Lae : = mie 10 300e nee (e=3'4x 10-), ni SO O)V,. V3—ViC+C,) aa N= [GVi— "pe T | 50% is ne TAT X°771 30°2 i | 47x 1-56 mei 3, 120 (1:60—1:37)747 12-47 1 | as 13°56 120 | 3002 = 0 * Oly bp aOR %: ply ae . In the following Tables are given all the results obtained up to the present time. 09 oy £0.¢ g—-01X00-ST AS 12-8 ,-O1X 28.11 z-OLX2G-01 | ,-O1XGrIT | “AV aw) SS ee ES —— ee tar eS ee ae “got )} S eg mo | wn © Space Loe oe Sawer rion «OF ‘“ C8.5T seein “ SEIT || s “ 9B.F “10-01 A ee aS oe ee ae “ 90-11 } P eee ee te, cen none Be icine > Meese eee lh vad satay : ecg nae “gy oT “— go.cT | aie ¢ I “ 984 “ 88-91 eS pas ee geen ee. ala age “ O18I = eeeeee stamfetetet Re ecetaterere eR eet a Ge eatimeisieipipre 6c CE-OL “ PLIT } S , oT Hea Se ee ee a ee fF 5 68:9 18-FI 28-11 | So ee ae eres ogee eesti Spee te ge eal ae SEPTEMBER 1909. XLUI. The Ions of Gases. By WitL1aM StTHERLAND *. [| fapanite accumulations of experimental work on this subject show the need of a more comprehensive theory than has yet been advanced. The following is an attempt to state the fundamentals of a theory wide enough to contain the chief phenomena now known. The simplest theoretical ion in a gas is an atom charged with an electron, just as in electrolytic solutions. But the calculations of J. J. Thom- son, Langevin, and others, seem to show that the smallest ions in gases consist of a few molecules, say two or three. P. Phillips in his experiments on Ionic Velocities in Air (Proc. Roy. Soc. xxviii. 1906, p. 167), with a wide range of temperature finds the number of molecules in a gaseous ion to vary apparently with the temperature. It will be shown immediately that this variation of the size of the small ion in gases is only apparent, that the experimental ion is the simple ion of theory and electrolysis, and that the seeming change of size is due to the same cause as the seem- ing change of size of molecules with temperature in the viscosity of gases and allied phenomena before the effects of cohesional force were allowed for in the kinetic theory of gases. When the electric force of the simple ion in a gas is introduced into the calculation of the ionic mobilities to be expected at the different temperatures in the experiments of * Communicated by the Author. Phil. Mag. 8. 6. Vol. 18. No. 105. Sept. 1909. 2A 342 Mr. W. Sutherland on Phillips, it removes all necessity for ascribing varying com- plexity to that ion. Wellisch (‘ Nature,’ lxxix. 1908, p. 148) has already shown by reasoning which is not supported by the present investigation, that by considering the electric force of an ion in the same way as cohesional force in the theory of gaseous viscosity, it becomes no longer necessary to hold that the linear dimensions of the smallest ions in gases betoken a complex structure for them. But in the larger ions formed by spraying electrolytic solutions into flames and hot gases we find on a more elaborate scale just such a variable gaseous ion as the simplest has hitherto been supposed to be. As an extreme case of this type we have the large ion discovered by Langevin in the atmosphere. Of this ion we know little more than its small mobility except the demonstration by Pollock (Austr. Assoc. for the Ady. of Sci. 1909) that this mobility varies considerably with the humidity of the atmosphere. Premising that the mobility of an ion is its velocity in cm. per second under an electric force of a volt per cm. we shall for convenience divide gaseous ions into three classes, those having at about 15° C. mobilities of the order of magnitude 2, 0°02, and 0:002. No doubt these types merge continuously each into the next. ‘They can be specified more accurately according to the following definitions. Let the ion formed of atom and electron be called a nucleolus, such an ion surrounded by molecules forming a solid or liquid mass be called a nucleus, ‘and let a collection of molecules in the form of a vapour round a nucleus or nucleolus be called an envelope ; then the three types of gaseous ion are (1) nucleolus alone, (2) nucleolus and envelope, and (3) nucleus and envelope. The third type merges into the visible drop of fog and rain, though it is probably distinguished from these by the fact that the majority of the molecules in the nucleus and envelope are more directed by central electric force from the electron than by the mutual cohesional forces. The present theory will be divided into three sections, each devoted to one of these types of ion with a reference to theories of condensation and a summary. 1. The Lon formed by Atom or Radical with Electron. Let the ion of charge e move with velocity wu in the direc- tion # under uniform fall of potential whose rate is dH/da, then, if the viscous resistance of the gas to its motion with unit velocity is F Fused eo... 3e ) the Ions of Gases. 343 If cohesional and electric force were neglected, the mole- cules of gas being treated as forceless spheres of radius as, mass m3, and number per cm.? Ns, suffix 1 allotting the cor- responding quantities to the ion, the expression found for Fu in the kinetic theory of “ perfect” gases is | 1g 9 Fag ee fe mak (a) Fu=4N3(a +43)? { 2m(v)? + v;°)/3}? The immediate problem is to find how we must modify this expression to provide for the greater frequency of collisions caused by electric and cohesional force. The treatment can proceed almost exactly on the lines of my paper on the Viscosity of Gases and Molecular Force (Phil. Mag. [5] xxxvi. 1893, p. 507). Select an ion anda molecule which are initially far enough apart to exert negligible force on one another and are each destined to have their next collision with one another. Let 7, and 7; be their distances from the centre of mass of the two, so that _ mr,=mszr; and let 7,+73 their distance apart be denoted by v. Let the cohesional force between them be —d¢(r) /dr and the electric force between the electron of the ion and the molecule be —dw(r)/dr, then using z for 1/r we have for the motion of the molecule relative to the centre of mass the usual equation Af Spel (SF? + FO) <0 manent) Mshg”23" dr in which hg is twice the area swept out by 7 as it describes the angle 6. From this for the equation of relative motion we get Pe atts (E04 HO) Ko, | (a) ae ** mym;h?z*\ dr and then the first integral of this gives the equation of energy a? { (35) +2 b apr 2™ fb) ye) L4av? 6) MyzMz in which v is the relative velocity when ion and molecule are at distance r apart, and V is the relative velocity when r is so great that the relative orbit nearly coincides with its asymptote. let 6 be the length of the perpendicular from the ion on the asymptote so that h=bV. When the relative orbit is such that there is no collision, we can determine the 2A2 344 Mr. W. Sutherland on minimum value of r by the? condition dz/d@=0. Denote the reciprocal of this distance by w which is given by Sitrot = EMS ar) apt) fav? a Msg or mee S o(r) +4p(r) f — WV VERO. 147M There must be a collision if 1/w is less than ajy+a3. Hence the greatest value of b ‘for which a collision is possible is given by aati 2 NES ne { s(ar+a) +4(u+a) ay Fas) 1 or (4 laa t( eer me ola 0) plea Thus it is proved that to adapt (2) to the case where electric and cohesional forces are operative (a,+ a3)? is to be replaced by the right hand of (7). Just as the correspond- ing result in the theory of the viscosity of a gas applies strictly only to gases above their critical temperature and at moderate densities, that is to say, under conditions which allow the relative orbit of a pair of colliding molecules seldom to consist of a curve of finite range, so the result just obtained is strictly applicable only when the relative orbit of ion and molecule is seldom a curve of finite range. Tor the resist- ance to an ion we now get from (2) with m,v,2=mz3v;?, V2= 0,7 + 037. 27r = mms 2 ‘1 (a1 + a3) + (a, +43) EMA a cote 2 Bu=gN3(a1 + 43) 3° mytm; °° ) ha m3v3"/2 . (8) To adapt this for comparison with experimental results we put m3v3” proportional to T the absolute temperature, and remembering that N; varies as 1/l’, we get F proportional to T-2(1+C’/T) where C’ is proportional to (a, +43) +W(a, +3). If then in (1) we make dH/dz a volt per cm., we get for the relation between ionic mobility wu and temperature T the equation A’Tz = —_ ioe \ u BT, \> ak see (9) in which A’ and C’ are parameters having values character- istic of each gas, the dashes being used to distinguish them ye the Ions of Gases. 345 from the corresponding parameters in the similar equation for the viscosity of a gas. We can test the validity of (9) by means of the experiments of Phillips (loc. cit.). In air _for the positive ion A’=0°222 and C’=509°6, and for the negative ion A’=0°222 and C’=333°3. These give the following calculated mobilities for comparison with the ex- perimental. TABLE I. T 411 399 383 373 348 333 285 209 94 Pos. (uwexp. ... 200 1°95 185 1°81 1°67 1:60 1°39 0:945. 0:235 ion. i eal. ... ZOL, 395 1°86 1:81. 168 1°60 1:34 0954 0336 Neg. (wexp. ... 2-495 2:40 230 2°21 2°125 2:00 1:785 1:23 0:235 ion. mel, 4) Saupe eee oes 227 FIZ 20S 173, 124 O474 Down to T=209° the mobilities of both ions are given with satisfactory accuracy by the theoretical formula (9), but at 94° the formula fails, as theoretical considerations led us to expect that it would, because 94 is about 30 below the critical temperature of air. It is notable that at this lowest temperature the experimental mobility is the same for both ions. This shows that at this temperature some rather . profound change has occurred in the conditions of movement of the two ions. From the values of A’ and C’ it appears that at high temperatures the mobilities of the two ions will tend to become equal again. It appears also that the differ- ence in the mobilities is caused by the difference in the values of ©’ which are proportional to the potential energy of ion and molecule in contact. If we compare these values, namely 509°6 and 333°3, with 113 the value of C the similar parameter in the viscosity of air, which is proportional to the potential energy of two molecules of air in contact, we see that in both cases the potential energy of ion and molecule is larger than that of molecule and molecule. This is what we should expect from our knowledge that the potential energy of molecule and molecule is like that of two electric doublets of charges e and moment es in which s is less than the diameter of a molecule. It seems then we must trace the remarkable difference in the mobilities of the two ions to differences of their potential energies when in contact with a molecule of air. Unfortunately we do not know experimentally what the ions are. In pure gases we may infer that the ions are atoms charged with a positive or a negative electron, but we do not yet know whether in the 346 Mr. W. Sutherland on presence of impurity there may be a tendency for one or both sorts of electron to associate specially with the impurity. But in spite of these remaining uncertainties the interpreta- tion of the experiments by (9) proves that the small ion in air does not attach to itself satellite molecules whose number varies with temperature. The electric force of the ion accounts for the facts just as cohesional force accounts for the corresponding facts in the viscosity of gases. I may mention that for the negative ion in air the result at 94° can be expressed as well as all the others by changing (9) to a A’T2 Sis Cl where T= 107 A’ =0'1704, C =e: In the further investigation of (8), until experiment informs us definitely as to the atoms or radicals which torm the ions, we shall be forced to make assumptions. Tor the diatomic element gases we can write m;=2m, if the ions are formed of their atoms, and we may also put a;?=2a,’, although we must be on the watch lest the atom when made an ion may undergo change of volume. Possibly the change caused by the positive electron is different from that caused by the negative. In such a compound gas as CO, we shall assume an average ion of mass m;/2 and of volume 27a,°/3, and shall consider the average of the nearly equal mobilities of the ~ positive and negative ions. Then (8) becomes dh eé-=—- = 3°59 N3a3?mgv3 (a + 21d(ay + a3) + vr (ay + as) }/m3v3" | u . (10) dx For air at 0° C. the left side of this equation has the value 10-4 because e=3x10-! and dH/dx=volt/em.=1/300. To evaluate the right side we put N3m;=0-°001293, and N,mv,2=3pV in the usual notation of the gas laws, with V=1, and p=1,014,000 dynes/cm.’, and 2a;=2°38 x 10-° (Phil. Mag. Feb. 1909, p. 321), while [1+ 2{b(a,-- a3) + W(a, +43) }/mgv3?]u=u(1+ C7T) : = A’T?=0°222 x 2137 oon for both the positive and the negative small ion in air at 0° C. With these values the right side of (10) is 1:18x 10-%, whereas the left side is 10-1. Here we meet, even in a more pronounced form, the discrepancy which has led previous writers to suppose the small ion to be a cluster of molecules, for which 2a; would be large enough to make the r a x ——-S. | YY ae oe the Ions of Gases. 347 right side equal to the left. It shows that Wellisch’s theory does not give the right reason for the difficulty. The fric- tional resistance expressed by the right side of (10) must be made 8°6 times as great to make the dynamical theory of the small ions in air correct. The additional resistance is in- troduced if we take account of the two new types of viscosity (Phil. Mag. [6] xiv. p. 1) shown to be fundamental for the motion of ions in liquids. We shall find these to be as important in the dynamical theory of ions in gases. The first of these viscosities, whose coefficient is ¢, has its origin in the mutual potential energy of the opposite electron charges of the two kinds of ion. The second has its origin in the mutual potential energy of an ionic charge, and the polarization which it induces in the neighbouring molecules of the surrounding medium. Its coefficient was denoted by @. As the causes producing ionization and maintaining it in a liquid solution are different from those acting in a gas, it will be necessary to make a special calculation for € and @ in a gas, though similar to that furnished for liquid solutions. In the paper just mentioned it is shown that if q positive and gq negative ions of charge e are uniformly distributed through a cm.*, of a medium of dielectric capacity K, they possess a rigidity If they are strained by electric force so that each positive electron is displaced in one direction and each negative in the opposite, a corresponding stress is developed. Now the presence of molecules may cause this strain to relax by forcing the ions back to uniform distribution ; they will convert the rigidity N into a viscosity NT, where T is the time required to reduce the stress to 1/e of its initial amount, e being the base of natural logarithms. When the ions are those of an electrolytic solution, the relaxing action of the molecules of solvent is due to their ionizing force, that force which pulls the ions of the solute apart and keeps them uniformly distributed. In the paper just cited this ionizing force is taken to be proportional to q’* as it overcomes the direct electric attraction between neighbour opposite ions. But in a gas we do not regard the molecules as direct ionizers. What then are the actions ina gas tending to keep ions uniformly distributed? The chief one is the following. According to the principle of the electric origin of molecular attraction each molecule behaves like an electrically polarized 348 Mr. W. Sutherland on or electrized sphere, similar to a uniformly magnetized sphere, and its electric axis tends to set itself very readily along the lines of electric force. In the absence of external electric force the axes of neighbours so adjust their mutual directions as to produce cohesion. But when the powerful central electric force of an electron acts upon neighbour molecules, it forces their electric axes all to pass nearly through itself. Those molecules next to the nearest neigh- bours have their axes caused to converge towards the electron, but not so accurately, and so on. Thus the cohesive forces of the molecules are deranged, and the surrounding molecules are attracted towards the electron. We shall consider the law of this attraction soon, but just now we must recognise that near the electron the gas will be compressed by this attraction to a greater density than the average. The ten- dency of this denser gas to diffuse outwards from the central electron is just equilibrated by the inward electric attraction. Let 7 be the distance between two neighbour electrons, then we may take the average value of the force of diffusion per em.” of section to vary as 1/r. Hence, when two neighbour electrons have r between them changed to r+dr by electric force, the unequilibrated force of diffusion called into action — will be proportional to dr/r?.. But d7/r is the strain to which the associated stress F'’ is proportional, so the force restoring uniformity is proportional to F’/r ; but in Maxwell’s theory of transition from rigidity to viscosity this is proportional to f’/T, therefore in a gas T is proportional to r. It must also be proportional to the resistance offered by the gas to the motion of the whole ion with unit velocity, which we have denoted by F. Thus we have T « Fg-1/3 and therefore ¢ the viscosity NT derived from N, varies as Fge?/K. For a gas we may put K=1, We have now to obtain an expression for 6. The electric polarization consists in the directing of the axes of electriza- tion of the molecules towards the nearest ion. Let R be the distance from an ion to the six nearest molecules. Though this is less than the average distance between two molecules because of condensation due to attractive forces round the ion, it is proportional to that distance. The mutual potential energy of an ion and a neighbour molecule is ¢(R)+W(R). The rigidity N of the system ion and molecules is equal to the potential energy per unit volume and is therefore pro- portional to {@(R) +W(R)}/R?. We have now to find the time of relaxation T. The force between ion and molecule is d{o(R) +¥(R)}/aR. the Ions of Gases. 349 Per unit area it is proportional to R-2d{$(R) + (R)}/aR, and the change of this for change dR is dRd[ R-*d{o(R) + 7(R)} /dR]/dR. But the associated stress F’ is proportional to dR/R, so in this case the force restoring uniformity when the system of ion and molecules is strained is preportional to F’/Rda[R-d{¢(R) + W(R)}/dR]/dR and also to F’/T, so that T-! is proportional to Rd[R-*d{(R) + ¥(R)}/aR]/aR. Now we know that for two electrons the potential varies as 1/R, for an electron and an electric doublet as 1/R?, and for two doublets as 1/R%. In the actual case at distance R the form of ¢(R)+(R) is almost that of 1/R?, as will appear in Table II.: hence in the product NT we get a result pro- portional to R°/R*, that is,a constant. Thus in a gas this factor of @ is independent of the density, just as the ordinary viscosity of a gas is. In the previous reasoning we have considered only the molecules which are immediate neigh- bours of anion. Similar reasoning applies to the next more remote lot of neighbours and so on. It is important to notice that the argument by which this factor of @ was proved independent of density makes it also independent of the nature of the gas; it is a universal constant. To the above reasoning we must add the statement that T is proportional to F, so that NT and therefore @ is proportional to F, which varies from one gas to another. In applying these new viscosities € and @ in the study of the motion of ions through gases we treat @ as acting just like F, while as regards € we consider it to act over area q-7* with a relative motion U,—U, between two neighbour ions at distance g—'* apart, wu; being the velocity of the positive ion and uy of the negative, so that the resistance experienced by an electron is f(y — up) la: aia Sle For the motion of the ions in a field of intensity dE/dx we have the equations oF = Su — ug? +(O4F In | (11) , e £( B+(O@+F )u. ; 350 Mr. W. Sutherland on The easiest case is that in which q is so small as to make ¢q-*° negligible. These equations then take the same form as (1) with F replaced by 0+ F. We found that in the case of air the right-hand side of (10) must be made 8°6 times as large as it is to give the facts of experiment. Thus for air then we have 0=7°6F, and in forming the theory of 6 we found that this same relation must hold for all gases. ‘Thus then we have found that the small ion in gases does not consist of a cluster of molecules, but that its electric charge causes it to experience a viscosity of electric origin and also to behave as if it had an enlarged radius. Introducing the factor 8°6 into the right-hand side of (10) we get as the general equation for the mobility of a small ion the equation di é a = 30°9N 303730, [1 + 2 ip(ay + a3) ~e W(ay + az) 1 /mgv3” ju Pete ONT) A’. In establishing this we have confirmed the theory of electrically induced viscosity by finding that it is the chief factor in determining the mobility of ions in gases. We have also found that the potential energy of ion and molecule in contact in gases plays the same part as the mutual potential energy of molecules in contact in the theory of the ordinary viscosity of gases. Investigations of C in the theory of gaseous viscosity and of C’ in (12) enable us to study the ‘potential energy of molecules under ideally simple conditions. To find C’ directly for any substance experiments like those of Phillips on air will be necessary. But from the known values of wu for different substances we can make a preli- minary indirect determination of C’ and therefore of (a1 + a3) +a + ag). From (12) we have, when dH/dx=volt/cm., and the tempe- rature and pressure are fixed, um'a?(14+C/T)=constant... Jaume This is the origin of a roughly approximate law announced by Lenard that wm’? is constant for several gases. For both positive and negative ion in air at 15° C. we have seen that atts O/T) AT = 0:222: 28817, a= Aah NOs It is rather more convenient at present to use B?? instead of a?, B being the limiting volume of a gramme-molecule, and to use the ordinary molecular mass M instead of m, namely 28°86 for air. The relation between B and a is B=4 x 10" x 22430(2a)3. (12) —————————K— ee the Ions of Gases. 351 Thus we transform (13) to uM a (285) 1069 0 ee ais. C4) which is the desired equation for finding C’ from a single measurement of u for a substance and its known values of M and B. The values of u have been collected by J. J. Thomson in his book on ‘The Conduction of Electricity through Gases,’ and by Wellisch with new determinations of his own for a number of vapours, in a paper read before the Austr. Assoc. Ady. Se. Jan. 1909. There isa difficulty in comparing the values of B when these are arrived at by different methods for different substances. This can be seen by comparing the results of two methods for one substance, for example, Cl,. or this gas its viscosity gives 2a=3°13 x 10-8, and so B=27-4, whereas in the inorganic chlorides as well as in the organic B for Cl, is 38 (Phil. Mag. [5] xxxix. p. 1). Itcannot be assumed that the value of B for Cl in Cl, is necessarily the same as that for Cl in compounds, but I think the chief part of the discrepancy between 27-4 and 38 is to be traced to the assumption that molecules of a gas can still be treated as spheres while they are in collision. The kinetic theory of gases gives us 2a as the distance between the centres of two molecules while they are in collision, which may be less than the mean diameter of either. For this reason I shall present the data for discussion in two ways, first using only the values of B derivable from the kinetic theory of gases, and second only those derived from the apparent limiting volumes of liquids and solids. Tans, Ll; Bowtie.) Wy. OMe Wl, CO; OO:2)) NO: 2ax1010 ........ ic, SemettGD P46) 225.813 228 241 OTT a aemeaes . 1230 1096)" 2742.) 1066 ©) 1254... 1912 ae ian 57 16 16 10 10°7 79 8-2 We ak. ine 2 4 28 32 71 28 44 44 see 288 ...i.0i..... Stirs 125) 183 39:5 290 278 175 1000’ (2a)*/288 ...... fol uueee,, «9702, 708% 359%" > 1404") >: 1501 1251 The values given for 10u are 5(u,;+u,), that for He being obtained by Franck and Pohl (Ann. d. Ph. Beibl. xxxi. 1907, p. 1133), namely u, = 5°09 and u.= 6°31. To this monatomic gas the formula (14) for diatomic and compound 352 Mr. W. Sutherland on gases has been applied without change. The values calcu- lated for 100C’/288 belong to an imaginary mean ion. For the positive and negative ions separately they can be found by using uw, and us, instead of their mean w. In the last line 100C’(2a)?/288 has been given. Tor four out of five element gases it is nearly 710, the exceptional value for Cl, being 359. For the three compound gases the values are not far from 1385, which is nearly 2x710. At 15° C. both CO, and N.O are a few degrees below their critical temperature, so that their actual condition does not comply with the stipulations made in obtaining the theoretical equations. Probably the error introduced is not great. But in the case of the more easily liquefied gases with higher critical tem- perature like NH3, SO,, and HCl, and of the vapours of liquids the orbit of the relative motion of ien and molecule after collision will be too often a curve of finite range to allow the theory founded upon infinite range to hold. Nevertheless, for the sake of information I shall apply (14) to the data for easily liquefied gases and vapours Jor these the values of B can be obtained from “ Further Studies on Molecular Force ” (Phil. Mag. [5] xxxix. p. 1). Tasue IIT. NH,. 8O,. HCl. C,H,Cl. C,H... CH,CO,. CH,(C,H.),0,) Ch GG ae 2a anes See BL 83d 27 57 93°5 62 82 80 ROO or acec's = (os, WAL 127 31 34 31 29 28 SDS a Ai) C4380. 620 72 74 74 88 100C'/288 ... 366 204 53 190 80 156 127 119 10B2/8C’/288. 274 218 48 281 165 244 240 221 CH,Br. CH,I. CCl, C:H,;i Aldehyde. # Alcohol: Aestone 2 47 57 84:5 ie: 395 48 56°5 DC Ae ae 28 21 30 16 29 29 29 EGR slop eai's a 95 142 124 156 44 46 58 100C‘/288.... 201 188 47 203 376 311 229 10B2/8C’/288. 262 278 30 358 436 411 337 In this table we notice that when much the greater part of the mass of a molecule consists of chlorine as in HCl and CCl, the potential energy measured by 100C’/288 is con- the Ions of Gases. 353 spicuously small, as in the case of Cl, and so also is 10B?8C'/288 conspicuously small. But in C,H;Cl this effect does not appear. In aldehyde, alcohol, and acetone, which are known to be associative liquids, the potential energy and its product by B?* are both large. The other substances of the table give values of 10B7°C’/288 near to 240, except C;H,., which has the value 165. This 240 is nearly double 138°5 found for compound gases in the last table. We learn then, that on the whole B??C’ increases with the liquefiability of a substance. For the substances of Table III. the values of 100C’/288 are only apparent values of the potential energy, since our theory would apply to them strictly only at temperatures above the critical. Probably the values of 100C’/288 in Table III. are roughly proportional to the desired potential energies. As stated above, the Table has been drawn up to give only preliminary information. Returning to the more definite facts of Table II., we see that constancy of B?°C’ would imply that the potential energy of ion and molecule in contact varies inversely as the square of the distance between their centres. Now one of the main results found in my studies on molecular attraction is this, that molecules attract one another as though each were a uniformly electrized sphere of total electric moment HK. If an ion of charge e and volume half that of the molecule were in contact with the molecule in the position of minimum potential energy, that energy would be proportional to —He/B??. This shows the probable origin of the constancy of B?*C’. But I have shown that in most cases H is proportional to B. So it appears that, if the ion were able to turn the whole field of electrization of the molecule so that its axis passes through the ion in the position of minimum potential energy, C’ would be propor- tional to B/B?*, that is to B43, instead of to 1/B?/, as we have found above to be the case for H,, He, No, and O,. It appears then that instead of the EH which is proportional to B we have to do with another electric moment H’ which is the same for these four element gases. An ion does not turn the whole electric field of a molecule so that its axis passes through the ion, but on the average it turns that electric field so that its component along the line joining the centre of ion to centre of molecule is that arising from an electric moment EH’ which is the same for four out of five element gases in Table I]. The absolute magnitude of this moment can be found by means of the following data for H, at 15° C., using 4x10” for the number of molecules 354 Mr. W. Sutherland on inacm.’ at 0°C. and 1 atmo. Nmv? = 3pV288/273 with p = 1,014,000, ee N= 45 2{h(a,+ a3) + (a, +a3)}/mv? = C'/288 = 2°41, h(a, +a;) + (a,+ 43) = 916 x 10-*, If E! were due to two opposite electrons of charge e at distance x apart, we should have (a, + a3) + (a, +43) = e2/4a?, whence x = 0°0352 x 10-8. I hope to show in a future communication that the fundamental mode of motion determining the structure of all spectra is that of two opposite electrons vibrating within each atom about positions at a mean distance apart of the order 0°05 x10-%. It seems very probable then that this electric moment KH’, which we have been investigating here, is the moment of this pair of electrons which at the same fixed distance apart in all atoms determine all radiation and the structure of all spectra. The further investigation of C’ must be a matter of special experiment, just as in the case of C in the viscosity of gases. The coefficients of diffusion D of ions in gases are propor- tional to their mobilities, being a measure of their mobilities under the driving force of a certain space-rate of change of partial pressure, instead of the electric force of a volt/cm. Their values have been investigated chiefly by Townsend, and have been found to be some such fraction as a fifth or a tenth of those for comparable uncharged molecules. This difference has been generally ascribed to the formation of molecular clusters round each ion. From the foregoing it is plain that the difference is due to the operation of the electrically induced viscosity @ on the ions. In making a useful comparison of the two types of diffusion coefficient we must remember that we are assuming the ion in a pure gas to be of half the mass and half the volume of the molecule. Townsend has determined D for the positive ions in CO, as 0°023, and for the negative 0°026, mean 0:0245. For comparison with this we must choose the value of the diffusion coefficient for a gas which has about half the molecular mass 44 of CO, and half its molecular volume. The nearest we can get to this is to take the case of CO whose molecular mass is 28 diffusing into CO, with a. coefficient 0°131, or that of O, with coefficient 0°136. In these cases the molecular volume of CO and Q, is nearly the Ions of Gases. 355 equal to that of COQ,, a difference which could be approxi- mately allowed for by a short calculation, but it is hardly worth making, as the point under consideration is well enough presented by comparing the mean of 07131 and 07136 with 0°0245. Thus we find the resistance to the diffusion of the ion 5-4 times as great as the corresponding resistance to that of the molecule. This result isin general agreement with the demonstration given that the new viscosity @ increases the resistance of ordinary gaseous viscosity to 8-6 times its amount. The hypothesis of molecular clusters is unnecessary to explain the slow diffusion of ions in gases. We must also discuss another quantity closely related to u, namely a, the coefficient of recombination of ions in gases | according to the very simple formula introduced by J. J. Thomson : mM fides —aN 7h! Ae Oh ele E85) There are certain fundamental objections to the excessive simplicity of this formula which makes the recombination - take place according to the chemical law of mass action, notwithstanding the large range of the electric forces of attraction and repulsion amongst ions. Langevin has given (Ann. de Ch. et de Ph. [7] xxviii. 1903, pp. 289 & 433) the now generally accepted proof that this simplicity is justified. The essence of his argument is this: that the electric force at the surface of a sphere surrounding an ion being e/r?, and the number of opposite ions that can be drawn across the surface of the sphere :being proportional to 4ar?N,w,, the number entering the sphere in unit time is proportional to AvreN ,u;, and is thus independent of the radius of the sphere and of the range of the electric forces of the ions. If we take account of the mobilities of both sorts of ions we get Langevin’s formula Bea Ae Uo cn) «jue arht 3 pom Se) where ¢ is that fraction of the ions drawn into a sphere which combine to form neutral molecules. Langevin has inves- tigated values of e€ experimentally, and Richardson (Phil. Mag. [6] x. 1905, p. 242) has applied considerations of probability to the calculation of e«. But it seems to me that, though Langevin’s theory gives as a first approximation the justification of J. J. Thomson’s equation (15), a second approximation is necessary to bring the theory of ions in gases into agreement with experimental facts and the kinetic theory of gases. Experimental proof of the insufficiency of (15) has been given by Barus (Ann. der Phys. xxiv. 1907, p. 225), using J. J. Thomson’s condensation method of counting Nj. 356 Mr. W. Sutherland on The results of Barus will be discussed soon in connexion with the following attempt to carry the theoretical equations of Thomson and Langevin to a higher degree of approxima- tion. If the ions were always distributed symmetrically, each would be in statical equilibrium as regards the electric forces, and the beginnings of recombination would never arise. Recombination depends chiefly upon the rate at which unsymmetrical positions are formed during the motion of the ions. Let us start, then, with a convenient specification of the symmetrical positions. Suppose the space divided into equal cubes of edge R with an ion placed at each corner which is common to 8 cubes, the ions 3 occurring alternately negative and >: oy patie positive along the straight lines formed by the edges of the cubes according to a : : the specimen plan of fig.1. Likeions b # b # b are arranged along diagonals. If any ion is displaced from a diagonal, it will t+ bt b + be attracted. most strongly towards the nearest diagonal. ie us then b # bee replace the electrons by lines of ele- 4 p # p # tricity of density e/2'?R along diagonals running downwards from left to right. Then in fig. 2 let us make a section of these parallel lines by a plane at right angles to them, the intersections of the lines and plane being marked # for the positive lines and b for the negative. Fig. 2. Again # ranges in diagonal lines, + and so does ». These diagonalsare % at distance R/3? apart, while the df distance between $ and its neighbour b b + is R(3/2)¥*. Spread the lines of # +f density e/2"? R so that they become b planes of surface density e/31?R?, these planes being alternately $ and pb. In this way we have substituted for the original point. distribution an equivalent laminar one. We can now treat the problem of recombination of ions as one of leakage in our laminar distribution. Writing the intensity of the electric force between two lamine as 47re/3"?R?, we consider the rate of leak proportional to this force and to the mobility U1 OY Uy of the ions, and to N,. But N,R?=1,s0 withAa parameter we have finally dN, /dt = — Ae er This factor of proportionality A is proportional to uj+%., =P the Ions of Gases. 357 and to the rate at which unsymmetrical distributions arise to produce the motion which we have treated asa leak. This equation can be written eee et — 2 ACN) ey ap eeg ie (LS) and its integral is | Me = O-F 2AT/3s SY B02 G19) where C isa constant. Thus we have N,~? a linear func- tion of the time, whereas the integral of (15) makes N,-!a linear function of the time. From the tabulated data of Barus for ions in air, I find with second for unit ¢ MeN = 52461... 1). |. 2.2. (20) with the following comparison :— Seconds ............ 0 5 10 20 30 60 120 10—2N, exp. ...... Pe 27) lee Se By ay I 10~2N, cal. ...... $4) 9) 35 27 Muse Side 4 15 Barus gives five other sets of data in graph form, and in these 10° x 2A/3 hasavalue about 4:5. The comparison just given covers a range of N, large enough to show that (17) is to be preferred to (15). Butas (15) has been taken by J.J. Thomson to be proved by various experiments origi- nating in the Cavendish laboratory, it is necessary to look rather more closely into the evidence. In the paper of J.J. Thomson and Rutherford on the passage of electricity through gases exposed to Rontgen rays (Phil. Mag. [5] xlii. 1896, p. 392), the experimental results can be expressed with a slightly smaller average error by the N,’ formula than by the N,°* one, but they can be expressed with a still smaller average error by a formula using N,°?. These early experi- ments are therefore not suitable for deciding between the two formule. In Rutherford’s paper on the rate of recom- bination (Phil. Mag. [5] xliv. 1897, p. 422) the experi- mental results are represented with ithe following average errors per cent. :— On page 423 427 429 With the N,? formula ...... H hl 6:0 67 AS by ie le 2°2 ro ar The theoretical handling of McClung’s experiments (Phil. Mag. [6] iii. 1902, p. 283) on the rate of recombination of Phil. Mag. 8. 6. Vol. 18. No. 105. Sept. 1909. 2B 358 Mr. W. Sutherland on ions in gases under different pressures has been subjected to some criticism in the Phil. Mag. (see G. W. Walker, vill. - 1904, p. 206, Robb, x. 1905, p. 237), and by Langevin (Journ. de Phys. [4] iv. 1905, p. 322), who shows that on the basis of the N,? formula it can be proved that in the experiments at a pressure of one atmo diffusion would cause one-tenth of the effect recorded as recombination by McClung, ile at one-eighth of an atmo at least eight-tenths of the recorded effect is to be credited to diffusion. Diffusion must also have produced a large effect in the large apparent varia- tion of « with temperature in later experiments of McClung’s. We can take McClung’s experiments at 1, 2, and 3 atmos to be complicated with not more than 10 per cent. of diffusion effect. I find that his results can be represented as well by the N,° formula as by the N,?. The reason for this fact is that the residual experimental error in these difficult measurements is such that when N, is graphed as ordinate with ¢ as abscissa, the points lie on an area which is traversed just as well by the curve which makes N,~? linear in ¢ as that which makes N,~! linear in ¢. Thus I think I have shown that the experimental evidence upon which J. J. Thomson relies for verification of the N,? formula (15) is on the whole a little more favourable to the N,°* formula (17). But (15) fails to apply to the experiments of Barus given previously in verification of (17), which is therefore the better approximation to the truth. In this connexion it would be important to make a full review of Langevin’s own experiments, which, on account of wide variations of the conditions, he considers to verify the two laws that ionic velocity is proportional to strength of electric field, and that the rate of recombination of the two sorts of ions is propor- tional to the product of their numbers per c.c., or the two electrical densities which he denotes by p and n. Thus Langevin holds that his experiments verify the N,? formula. The theory of his method of experimenting is rather elaborate, so he contents himself with giving only final results and samples of his data which are not sufficient to allow me to investigate how the N,*°? formula would apply to his experi- ments directly. But the theory by which the N,°? formula is established receives indirect support from Langevin’s results, if we work it out in greater detail. We must inves- tigate A in (17) more closely. Imagine the two sorts of ions for an instant uniformly distributed, alternately at the corners of a uniform cubical subdivision of the volume which they occupy. On account of its thermal velocity each ion will move away from this imaginary position, and the amount the Ions of Gases. 399 by which it moves away will determine the degree of irregularity which causes the recombination which we suppose to go on as asort of leak. To determine A as a function of the density of the gas containing the ions is a problem in the calculus of probabilities known as that of the random walk. A man walks a distance / in any direction from an origin O, then he walks the same distance in any other direction, and sv on till he has taken n walks. It is required to find the probability that his final distance from O lies between r and r+dr. Evidently this is the same as our ionic problem, for the ion after 2 free paths of average length / is at some required average distance from QO, its original position in the initial imaginary uniform distribu- tion. The solution has been given by Rayleigh (‘ Nature,’ Ixxii. 1905, p. 318; Phil. Mag. [5] x. 1880, p. 73, xlvil. 1899, p. 246) for the case when n is large. The required probability is, when / = 1, 2 Se mI Ota Sitilkh ae Oa Lh GQIb) nr and the probability that the distance from O is greater than r is e-”". If we introduce / explicitly the exponent becomes —7?/l?n. In comparing results for different sub- stances or for the same substance at different pressures, we ought to take n to be the number of paths described in unit length, because, though the departures from uniformity recur with a frequency proportional to the molecular velocity, each lasts a time inversely proportional to the velocity. For this reason the element of time does not enter into the com- parison. Thus ml is to be constant for the same substance at different pressures and also for different substances. We have now to find how r is to be chosen in order that the comparison may be statistically correct. The agencies maintaining uniformity are proportional to / the mean free path, for instance, D the coefficient of diffusion is propor- tional to/. But the same agencies produce departures from uniformity temporarily, while they are maintaining average uniformity, just as the thermal velocities, which keep the average pressure of a gas constant and also its average density constant, at the same time cause those temporary local variations of pressure and density which occur when two molecules collide. As regards departures from uni- formity, then the proper unit for measuring its amount linearly is the mean free path of a molecule. Thus r must be proportional tol. Accordingly r°/l?n takes the form cl where ¢ is a constant. Let l, be the value of J when the 2B2 360 Mr. W. Sutherland on pressure is ) = 760 mm. of Hg, then 1 = Iyp)/p, and we now have A in (17) proportional to (uj + w,)e—PoP, log A/(u;+uy) is lmear in I/p. . . (22) If we compare (15) and (17), and suppose them applied to the same set of experiments over a certain range of values of N,, we see that for the average value of N, we must have approximately A =aN,’*. But in Langevin’s experiments N, was the number of ions generated by a single flash from a Rontgen bulb, so that on the average for gas at different pressures. we may take N, proportional to». Thus then A is proportional to ep’, and so from (16) A/(w,+u,) is proportional to ep’, and so from (22) log ep’? is linear in 1/p. Thus from Langevin’s experiments I find with p in mm. of Hg . for air logo ep? = 1°35—745/p for CO, logy ep? = 1°35—509/pJ ° which furnish the following comparison with experiment :-— (23) Air. TELE ONES 152 375 760 1550 2320 3800 edexper. gui! ..38 ‘01 06 “OT 62 80 90 eiealeml ss. sive ‘00005 03 ‘26 64 81 “91 CO,. | EO SED 135 352 550 758 1560 2380 BCR POE. (0 cwice Saeias "O01 13 "27 ‘D1 "95 ‘97 MICU fie cecuse *0007 ‘11 *O2, 50 91 1:02 It is to be remembered that the whole theory and working out of Langevin’s experiments is based upon (15) and (16) with the condition that e must be less than 1. In these circumstances the very simple law e-%, which has been worked out above for comparing departures from uniformity of distribution favourable to recombination, is verified as well as possible. From the values found for a in (15) for various gases it is easy to obtain A in (17). For instance, Townsend (Phil. Trans. cxcili. 1900, p. 129), by an electrical method, in which during 0°93 second N, diminished in the ratio 77 to 46 for air, found « = 3420e, where e is the electron charge 3x10-% So by this electrical method A = 0°0000832. cay the Ions of Gases. 361 We have already seen that the experiments of Barus by the entirely independent condensation method yield 6 and 4°5 for 10° x 2A/3, so that the mean value of A is 0:0000787, with which the result obtained from Townsend’s work is in excellent agreement. With the N? formula Barus found that in his experiments « ranged from 3 to 10 times that given by Townsend’s and similar experiments. McClung and Langevin found values for « in air in close agreement with that of Townsend, though they used entirely different electrical methods. The experiments of McClung when used to give A yield for air the value 0:000176, which is about double those just calculated. The data of Langevin do not contain all the particulars necessary for a calculation of A absolutely. We shall now consider the values of A for the four gases of Townsend’s experiments, obtained from his data Air. Os, CO.. Hy. ees 342() 3380 3500 3020 2A. od 832 769 800 922 It is remarkable that each parameter has a value that changes but little from one gas to another. McClung and Langevin by their independent methods get nearly the same value as Townsend for « for CO,, and McClung’s value in the case of H, agrees with that of Townsend. We have now to see how the values just given for A accord with the theory of it. In (23) the coefficient of 1/p is to be propor- tional to the mean free path of an ion through the gas at a pressure of 760 mm., which is inversely proportional to the square of the molecular diameter with appropriate allowance for the attraction between ion and molecule. Thus we have the coefficient of 1/p in (23) inversely proportional to (2a)?(1+ C’/288), which can be calculated from the data of Table II., which yield the following value for the coefficient :—air 745, O, 860, CO, 462, and H, 908. The value 462 thus obtained for CO, is to be compared with 509 obtained in (23) from Langevin’s experiments. These enable us to calculate for each gas at 760 mm. this coefficient divided by 760 which is the part of log ep’/* we require. The corresponding factor of — ep’® multiplied by w,;+u, or by u from Table IL., according to the theory of A, is to be proportional to A. Here are the values of A divided by this product :—air 50, O, 65, CO, 41, 362 Mr. W. Sutherland on and H, 20. If with CO, we use the coefficient 509, the result is 47. If in (2a)?(1+0’/288) the effective diameter of H, were increased by 16 per cent., the low value 20 for H, would be brought up to 50. Such uncertainties must be cleared up by new experiments and by fresh interpretations of those already on record, which have been worked out by their authors on the basis of the insufficient N,? formula. The foregoing theory of A may be summarised by its results in the following way. Let / be the mean free path of an ion in the gas, being °‘677/N37(2a;)?(1+C//288) which for nitrogen (say, air) has the value 0:000004, then A ='0002484 (uy + uy) e—78 |, ,(24) where ()/2°2565 is the constant length 0:000001754, which seems to be a fundamental constant in the physics of ions, related to a similar one in the statistics of molecules. In concluding the present discussion of the recombination of ions it may be helpful to notice that the formula (16) of Langevin can be derived from our method of lamineze in the following way. Suppose the ions in cubical order at distance © R apart. In a laminar distribution we get density e/R? and force 47re/R* between the lamine. A pair of oppositely charged ions experiencing this force would acquire relative velocity 47e(u,+u,)/R? and would travel R in time R3/A7re (uy + Ua). The ions begin to move so that N per unit volume would disappear in this time. In the actual process the N positive and the N negative ions do not suddenly disappear by coming together simultaneously, but their instantaneous rate dN/dé is 47re(u, + uz) N/R? and since NR*=1, this is (16) with e=1. This brings out the assumption involved in (15) and (16). 2. The Large Ion without Liquid or Solid Nucleus. If the small ion investigated in the previous section is placed in a gas whose molecules it attracts so strongly that it carries its immediate neighbours with it as satellites, some profound changes in the conditions are brought about. The induced viscosity @ almost disappears, because the central small ion has but little relative motion to its immediate neighbour molecules in which it has induced electrization, and the molecules relative to which it is moving are so far away that the induced electrization in them is small. We have here a beautifully simple instance of the way in which a rigidity may merge into a viscosity. It is probable that a the Ions of Gases. 363 small ion in a moist gas tends to attach molecules of H,O to itself as satellites and to surround itself with an envelope of vapour of H,O. Tosuch anion we shall now apply equations (11) with the supposition that @u can be neglected and also Fu as a separate term, though Fu, as the cause of fu, will be investigated immediately. In large ions it has been found that u,=—u,= —vw, so that the two equations reduce to ee Fini, wun € is proportional to g, so that when dE/dx = volt/cm., the last equation makes ug?* constant for different values of g at a given temperature. Thisis the result discovered by Moreau in his experiments on the cooled gases of flames sprayed with electrolytic solutions (Ann. de Ch. et de Ph. [8] viii. 1906, p- 201, Compt. Rend. cxli. 1905, p. 1225). He found that in the cooled gases the number of ions per cm.° varies as the square root of the concentration of the electrolyte in the ‘solution, in agreement with the law of Arrhenius for uncooled gases of flames at ordinary flame temperatures. H.A. Wilson has pushed the temperature up till the ionic dissociation in gases sprayed with electrolyte is complete. If in Moreau’s experiments we denote the concentration of _ the sprayed electrolytic solution by n, we have g« n'? and so from (25) we get un’® constant at a given temperature. He found u,=—wz, and g of the order 10°. We shall take his results with solutions of KCl as typical, their strengths being normal N, N/4, and N/16, which we shall express by putting n=1, 1/4, and 1/J6, giving his values of wu in em./sec. for dE/dx = volt/cm. TABLE LV. Temp. C. 170° | 3100 100° 70° 30° 15° 100u 100un1/2 100u 100un1/2 100u 100un1/3|100~ 100u71/3;100u 100un1/3)100% 1001/3 na=1 39 39 16 16 16 10 10 45 45 oy ae ‘16 m=1/4 65 41 27 17 24 15 15 94;—- — 24 415 a=1/16 90 36 47 19 40 16 24 95 | 72 29 51 20 . ! The departures from constancy in un? are irregular. Moreau sought to give a different explanation for the origin of the constancy of un in his various solutions. 364 Mr. W. Sutherland on The main feature of (25) being verified, we shall now apply it to investigate the remarkable variation of w with tempera- ture. So we must consider € more closely. The first business is to find the number of H,O molecules kept captive by an electron, or rather by our nucleolus. We have already seen that an electron in air increases the density of the air round it. In the same way, but to a greater extent, it increases the density of the H,O round it, because H,O has an exceptionally large electric moment es. For this reason an electron can constrain molecules of H,O to describe orbits of finite range round it. In the sequel, as before, let suffix 1 refer to the nucleolus, 3 to the gas such as air in which the ion is moving, and 2 to H,O. The electric moment of H,O IS és, and if an electron ¢ is at distance r along the axis from the centre of H,O, their mutual potential energy is e?s,/7”. Now when the nucleolus has captured one or two H,O molecules, its velocity of translation may be neglected in comparison with that of the air molecules and of the free H,O. So we treat the electron as at rest, and the free H,O molecules as if moving with velocity v, past it. The dynamical con- dition that a molecule of H,O with velocity v, at distance r should just be able to travel to infinity is m v,"/2=e?s9/r*. Within this radius r the electron gathers a number of H,O molecules whose axes all tend to pass through it, so that radially these molecules will attract one another, while each will repel its lateral neighbours which are at the same distance from the electron. Thus we have a highly charac- teristic field of force in our cluster of H,O molecules. The lateral repulsions will nearly equilibrate one another, so that we can treat all the H,O molecules as revolving round the centre with constant average linear velocity v,. So it is necessary to take account of the radial cohesion. The cohesional potential energy of a molecule of H,O just retained on the outer surface of radius r by the combined effect of attraction from electron and of cohesion may be assumed to be approximately constant and be written in kinetic form ma,w,7/2. Hence to determine 7 we have the more complete equation im, (v." — w,")/2=e?s/77. . & . Tee Now that we have taken account of the cohesional energy, we can make a correct enough average case by treating all the water molecules as gathered on the surface of this sphere of radius r round the nucleolus and all moving with the average velocity of the ion. We shall take the number of H,O molecules per unit surface of this sphere to be propor- the Ions of Gases. 365 tional to N, the number per unit volume in the air. The total number on the sphere is proportional to N,r’, say equal to AN.?. We wish to find the resistance F to the motion of this sphere through the air with unit velocity. Just as in the theory of the viscosity of gases we may say that on account of the electric force of the nucleolus and the cohesional force of the sphere, the number of molecules of air encountered by the sphere will be increased in the propor- tion 14+ (2e?s./7?m,_+ w,”)/v.2: 1. Unless the number of H,O molecules in the sphere is great, the tendency will be for each molecule to experience as much resistance as if the others were absent. It is not a case of a compact sphere of radius r, but of AN.7? spheres of radius a,. If the H,O liquefies into something like water, we shall have to deal rather with a single large sphere formed by the liquid. For the resistance to one molecule of H,O moving with unit velocity through the air we get from the kinetic theory of diffusion 3N3(a@2 +43)? {2ar(v,” + v3") /3 i *mgms/ (mg+ms3) (26 a) Strictly we ought to write down the resistance offered to the nucleolus, but, as it would be quite similar to this, we shall merge it in the resistance offered to the AN,?r* molecules. Thus F=SAN,Ngr{ 1 + (2e%59/77mg + 1,7) /v2? } (dat a)? x 4 Qar (ve? + v5”) /3 be myms/(my +m). Replacing mgv,”/2 by T the temperature and mw,?/2 by Ta a constant temperature, we find from (26) that 7? « 1/(T—T,) and 1+ (2és)/7?m. + w,”) /v.2=2, while (v9? + v4”)? oc T?, Re- turning to (25) remembering that 8 is proportional to Fg, we get dk Ei date where C is constant. This is the general equation for the motion of an ion consisting of nucleolus and H,O molecules in an electric field. To apply it to the case of Moreau’s experiments we put n’® for g??, and have N., Ns, and n all varying inversely as T, so that wu the mobility when dH/dx = voltjem. « T'/*(T—T,). From Table IV. the mean value of un? at each temperature gives a useful mean value of u for the case in which the solution sprayed into the flame was normal, and from these I find that T,=270. In the next Table the first row gives temperatures, the second 5 Sigg ON eH) GE) ea 2 366 Mr. W. Sutherland on mean values of w in cm./sec. for dE/dx = volt/em., and in the third 10'/T'*(T—270) which by (27) is to be constant. TABLE V, Mama. Ol! iL: 170° 110° 100° 70° 30° 15° Oe hate 39 17 16 10 37 17 317 276 300 308 317 292 This theory of the slower ion in gases leads to the revela- tion of an error in the ordinary experimental method of measuring their mobilities, the true values in the limit being only half of those assigned. Let AB and CD be two electrodes giving an electric field from AB to CD between which a Fig. 3. stream of ionized gas is led in the A bs direction of the arrow. It is assumed that, when all the ions —~ are just caught as the stream flows uniformly, a positive ion entering C D at A travels along AD, and a negative ion entering at C travels along CB. But, if this were so, the positive ion after it had crossed the intersection of AD and CB would have no neighbour negative ions, and would be free from the viscous resistance ¢ of electric origin, it would finish its path more swiftly under the resistance F only. The paths of electrons entering at A and C are AOD and COB. If uz is the mobility along AO and wg along OD at right angles to AB, we have AC/w=AC/2u,+ AC/2uq or 2/u=1/ugt+1/ua Thus when wg is large, uz the desired mobility is only half of « which is usually assigned as the experimental measure of uz. Moreau’s values of wu quoted in this paper should be divided by 2, as should also Langevin’s mobility for the very slow ion in air, namely about 1/3000, which should be nearly 1/6000, and a similar remark applies to many other determinations of u. Since, so far, we have been considering only relative values of u this correction is not needed for the purposes of the previous part of this section. It is important in absolute calculations concerning these ions. This error does not affect the velocities of the small ions considered in section 1. | 3. The Large Ion with Liquid or Solid Nucleus. To account for the very small mobility of the large ion of Langevin I have imagined the structure already described, the lons of Gases. 367 namely a nucleus of (H,O), or (H,O); or both in a state very similar to that of a liquid surrounded by an envelope of H,O vapour which is kept highly concentrated close to the nucleus. This envelope is similar to the surface film of vapour of HO deposited on the grains of fine powders. The number of H,O molecules per cm.? close to the nucleus will have a value N,, like a saturation value, and the number will diminish with increasing distance from the nucleus till it becomes N, where its influence has ceased. The thickness of this transition layer may be taken to be constant for a given value of N;, or we can replace it approximately by a constant length J such that 47r7/ is the volume of the transition layer, in which the mean value of N, is not (No,+N,)/2 but E'N.,+ H'N, where E’ and H'are constants. The resistance to the motion of all the vapour with unit velocity through the air will be 4ar7l/(K'N.,+H'N,) times (26a). We can use (26 a) also to give the resistance to the motion of the nucleus by replacing ag+a; by r. We neglect the resistance of the nucleolus and write the total resistance to unit velocity in the form N3T?(E'No+G’+H'N,) . . . (28) where G’ is the constant for the nucleus. This is F, and neglecting it in comparison with €g—? which is proportional to F¢?? we obtain from (25) — =r@?N;T?(HN,+G+HN,)u . . (29) where E, G,and Hare constants. Thus the reciprocal of the mobility for dE/dz=volt/em. is linear in N, which is pro- portional to the humidity. This is one of Pollock’s results for the Langevin ion. He finds 1/w=1200+107-5h, where h is the humidity in grams/m*. The constant term 1200, being not far from half the 2500 to 3000 usually found for the Langevin ion in ordinary air, shows that the resistance associated with N,, is about equal to that associated with No, a result which necessitates the stipulation above that the mean value of N, takes the form E’N;,+ H’N;. Equation (29) shows that the mobility of a Langevin ion in a gas should be inversely proportional to the density, so that refined observa- tions in the atmosphere ought to be reduced to values for standard atmospheric pressure. But the most striking result in (29) is that 1/u should be proportional to g?*, varying rapidly with change of concentration of the large ions. Moreover, as before in (27), 7? is probably proportional to 1/(T—T;), so that (29) gives a fairly complicated dependence of w upon the natural variables. 368 Mr. W. Sutherland on Further experiments must elucidate many of the points raised in the foregoing sketch of a theory. According to the theory the experimental values of the velocities found hitherto for the large Langevin ion ought to be doubled for the same reason as that for doubling the ionic experimental mobilities discussed in section 2. Very interesting questions present themselves as to the equilibrium of these three orders of the ion in the atmosphere. Radioactive substances generate the small ions, most of which disappear through re- combination in such a way as nearly to keep the number of small ions constant under a given set of conditions. But some of the small ions will gather envelopes round them and so build up the ion of the intermediate type. This will be liable to destruction through neutralization of its charge by a small ion. ‘The difficulties of building up the large Langevin ion must be great, but once it is formed, the following principle will act favourably to its permanence. The ionizing power of water comes into play. Consider a very small drop of water in which there is ene molecule of NaCl. This will be ionized into Na¥ and Clb, which will be driven as far apart as possible by the ionizing action of the water, whose tendency is favourable to the splitting of the drop into two parts charged with the opposite ions. Thus then the nucleus of a large Langevin ion by its ionizing action will tend to keep its charge unneutralized by opposite ionic charges. So we can account for the permanent existence of the Langevin ion in the atmosphere. These large ions some- times carry 50 times as much electricity as the small ions in the atmosphere at the same time. lLusby has shown that when the Langevin ions are removed from air, 22 minutes are required for the formation of the same number. If the large ion contains a nucleus of quasi-liquid H,O, its structure merges into that of the drop of water in cloudy condensa- tions. Something similar to the large ion ought to appear in the condensation of H,O on smallions, and in the evaporation of a drop surrounding an ion. ‘The theory of large ions is closely connected with that of cloudy condensation. Now J.J. Thomson in ‘ Conduction of Electricity through Gases” and Langevin (Bloch, Ann. de Ch. et de Ph. [8] iv. 1905, p. 25) have given a theory of cloudy condensation upon ions, which in both cases seems to furnish a remarkably successful explanation of the experimental fact that fourfold saturation is needed in vapour of H,O to produce cloudy condensation on small ions. But they use quite different expressions from those developed here concerning the potential energy of an electron and surrounding molecules. It seems to me that the Ions of Gases. 369 their expressions are not the right ones for the purpose to which they apply them. For example J. J. Thomson writes e’/2Ka for the electrical potential energy of an electrified drop of radius @ surrounded by a medium of dielectric capacity K, which is put =1, and Langevin also uses e?/2a. They then apply this to an electron surrounded by water. But, unless the electron spreads itself over the surface of the drop in much the same way as a large number of like electrons would, this expression is no longer valid. The electrical energy of an electron and an envelope of molecules is a mutual affair, tending to take the form e’s/a? for a central electron and a molecule at distance a, so the total electric energy of electron and drop must be expressed by a form quite different from the e?/2a used by both authors. Then again they carry the conception of surface tension and surface energy even into the dynamical specification of the smallest drops. The directive effect of the central electron on the few molecules of the smallest drop must profoundly modify their cohesional forces. For these reasons the theory _of Thomson and Langevin appears to me to be quite illusory in its details and to give its remarkable result concerning fourfold saturation by a concealed compensation of errors. They give a theory of what is essentially a molecular affair by means of purely molar considerations and data. Their theory applies to drops which are large enough to have a surface tension like that of ordinary water and which carry a surface charge of electricity. It can give no account of the real happenings when vapour of water begins to gather round a small ion. SUMMARY. In a dynamical theory of the ions of gases the two new types of viscosity previously investigated for ions in electro- lytic solutions are found to be of paramount importance. The induced viscosity, namely that which arises from the electric action of the ion upon surrounding molecules, produces in all gases about 7°6 times as much resistance to the motion of the small ion as ordinary gaseous viscosity does. The other type of viscosity, namely that which arises from the mutual energy of oppositely charged ions, is not of large enough amount to make its appearance in the experimental study of small ions at the low concentrations in which these are usually employed. In the case of the small ion there is another result of the electric action between it and surrounding molecules, for this causes collisions to occur more frequently, as cohesional force does in the theory of the effect of temperature on the viscosity 370 Mr. W. Sutherland on the Jons of Gases. of gases. In a gas above the critical temperature and at ordinary pressures the mobility of a small ion varies with temperature according to the formula u=A’TY?/(1 + 0’/T) in which A’ is a parameter characteristic of each gas, and C’ is proportional to the mutual potential energy of ion and molecule when in contact during a collision, being similar to C, the corresponding quantity in the theory of the viscosity of gases. On the principles of the kinetic theory of gases A! is found for any gas in terms of the number, diameter, mass, and velocity of its molecules, by an analysis which leads finally to (12). The theory is verified by means of the experiments of Phillips on the effect of temperature on the mobility of small ions in air, and by means of the data so far obtained experimentally for the mobility of small ions in gases and vapours. It leads to values of the potential energy of ion and molecule in cuntact which are given in Tables II. and III., and these furnish evidence of the presence in Hy, He, N,, and QO, of an electric doublet of constant electric moment. By taking account of the new induced type of viscosity and also of C’ it is shown that the small ion has no molecules attached to it. It is like the ion of electrolytic solutions. The smallness of the coefficients of diffusion of ions is traced to the induced viscosity, the hypothesis of molecular clusters being unnecessary. As regards the rate of recombination of small ions in gases it is necessary to replace the first approxi- mation expressed in the formula of J. J. Thomson, namel dN /dit=—aN?*, by a second approximation dN /di= —AN®, which is deduced theoretically by regarding recombination. as a leak in laminar distribution of the ionic charges. This formula is verified over a wide range of values of N by the experiments of Barus and also by the experiments adduced by J. J. Thomson in support of the N? formula. From statistical considerations formula (24) is established for A and verified by the experiments of Langevin on the effect of pressure on the rate of recombination of ions in air and CQ,. But although the small ion is not associated with molecular clusters, there are cases in which the small ion attaches molecules to itself and becomes a large ion. These are divided into two classes, the large ion consisting of an envelope of vapour, such as that of H,O, surrounding a small ion which is the central nucleolus, and the larger ion in which a liquid or solid nucleus forms round the ionic nucleolus, the whole being surrounded by an envelope. With these large ions the induced viscosity becomes of negligible importance, because the moving electric charge is too far from the molecules of the surrounding gas. But the direct electric i) i aoe , The Echelon Spectroscope. 371 viscosity arising from the rigidity belonging to the evenly mixed ions becomes of paramount importance because of the greatly increased time of relaxation for large ions. The theory of the large ion without nucleus leads to (27), an equation connecting the mobility of this kind of large ion with con- centration and temperature. This is verified in Tables LV. and V. by means of the experiments of Moreau on the slow ions formed by spraying solutions into flames and cooling the resulting gaseous mixture. For the large ion of Langevin, on the supposition that it has a nucleus of water, equation (29) is worked out to show the connexion of mobility with concentration of the ions, density of the air, humidity and temperature. This shows general agreement with the results of Poilock as to the effect of humidity on the mobility of the large ion of Langevin. Experimental data are lacking to test it otherwise. To account for the permanence of this large ion it is pointed out that the ionizing power of water tends to keep it intact. Certain objections are raised to the theory of J. J. Thomson and Langevin to account for cloudy condensation of H,O vapour on small ions at fourfold saturation. During the working out of the foregoing I have had the advantage of correspondence with Prof. Pollock while engaged in his experimental inquiries on large ions. Melbourne, June, 1909. XLIV. The Echelon Spectroscope, its Secondary Action, and the Structure of the Green Mercury Line. By HErpert STANSFIELD, D.Sc., Demonstrator in Physics, Manchester University *. Thesis approved for the Degree of Doctor of Science in the University of London fF. [Plates X.—-XIT. ] Part JI.—THE ECHELON SPECTROSCOPE. The Echelon and its Mounting. < (in echelon spectroscope described in this paper was constructed by Messrs. Adam Hilger for Professor Schuster, a modification, which has proved to be very valuable, being made in the usual design. A front elevation, * Communicated by the Physical Society : read June 11, 1909. + The following alterations have been made :— Equations 2, 3, 4,9, 9a, and the section on the spectrum given by a hot lamp have been added ; also the faint lines previously described as doubtful are shown to have their origin in the echelon. 372 Dr. H. Stansfield on plan, and two end elevations of the echelon are reproduced on Plate X., the plan being drawn with the cover removed. There are 33 glass plates. The smallest plate is 13 mm. wide, and they increase in width by steps of 1 mm. until the last plate is reached, which is 12 mm. wider than the last but one, the aperture being reduced to 1 mm. by the screen 8. The effective aperture of the first plate is similarly reduced in width to 1 mm. by the block B. All the plates are 40 mm. high, and the common thickness is 9°48 mm. The plates are pressed together by the two nickel steel rods marked T, which are intended to have the same coefficient of expansion as the glass. The plates are in very close contact, in most cases the greater part of an interface being taken up by a patch of definite but irregular outline that appears “ black” by reflected light. The remaining part of the interface generally shows white of the first order, but here and there the film of air may be thick enough to show the yellow or even the red of the first order. The common thickness of the glass plates is 9°48 mm.; their refractive index, deduced by a Hartmann formula from the values given by the makers of the glass, is 1:5802 for the green line 5461; and the dispersive power, = is —918 per cm. for this wave-length. ) Optical Effects due to clamping the Plates. The echelon produces a slight cylindrical convergence in a beam of light, altering the focus of the observing telescope by 1mm. (the focal length of the object-glass being 53 cms.). This effect is probably due to the clamping, as Twyman * states that when the clamping pressure is applied a change of focus is produced. He attributes the effect to a uniform increase in the compression of the plates from the largest to the smallest ; but there is direct evidence (see p. 378) that the echelon plates become slightly prismatic, and this effect, increasing towards the smaller end, would also produce — convergence. The focus is altered by rotating the echelon about a vertical axis. The convergence is increased, as would be expected, by turning the echelon so as to reduce the width of the emergent beam (see fig. 3 A), and diminished when it is turned so as to make the beam broader (fig. 3B). Changes in the focus are also produced by covering some of the step- faces at either end of the echelon. * Twyman, Proceedings of the Optical Convention, 1905, p. 53. the Echelon Spectroscope. 373 Use of Auxiliary Prism. Auxiliary spectroscopes have generally been employed to pick out the particular line in the spectrum to be examined by the echelon, the slit of the echelon spectroscope being illumi- nated with the selected line; but a modification in the design of this instrument was made for Professor Schuster so that the prism from the auxiliary spectroscope could be mounted next to the echelon, as shown in fig. 1, the prism being made larger than usual in order to take the full width and height of the echelon beam. This arrangement, which appears to have been originally contemplated by Professor Michelson, has been found to have important advantages. The dispersion produced by the prism, which is 2 per cent. of that given by the echelon, is subtracted from the echelon dispersion when the echelon is in the usual position shown by full lines, and is added to it when the echelon is in the reversed position shown by the dotted lines. The change of 4 per cent. in the dispersion obtained in this way produces the alteration in the spectrum shown in fig. 1. The distance apart of successive orders of the same wave-length is not altered ; but when the dispersion is reduced by the prism, all the lines belonging to the same order approach one another and draw away from the neighbouring orders. It is evident from fig. 1 that all but two of the lines Fig. 1. Echelon MQ Se Wg ~ Kg 4 S [—— i —— represented belong to the same order, and that these two lines, marked 1’ and 1’a, belong to the next higher order. Phil. Mag. S. 6. Vol. 18. No. 105. Sept.1909. 20 374 Dr. H. Stansfield on With the prism on an auxiliary spectroscope, no evidence of this kind is obtained ; and it has simply been assumed in some cases that the companion lines belonged to the bright central line nearest to them. Primary ACTION OF THE ECHELON IN THE DIRECT AND REVERSED POSITIONS. Equations for the Principal Maxima. The theory of the echelon given by Michelson* for the case of light falling normally on the larger end, has been extended by Galitzin t, who has investigated, both by caleu- lation and experiment, the motion and changes in the dispersion of the spectra when the echelon is rotated through small angles within the limits of two or three degrees on either side of the normal position. As the theory of the echelon in the reversed position has not, as far as I know, hitherto been considered, a comparison will be made below with the theory of the ordinary action. Fig. 2. In fig. 2 the reversed and direct cases are represented diagrammatically. The rays and wave-fronts drawn with full * A. A. Michelson, Astrophysical Journal, viii. pp. 36-47 (1898). American Journal [4] v. pp. 2165-217 (1898). Journ. de Phys. [8] viii. pp. 805-314 (1899). : + Furst B. Galitzin, Bulletin de ? Académie Impériale des Sciences de St. Pétersbourg, 5 série, t. xxiii. pp. 67-118 (1905). i in a en Ore a a ee i te ed ee Os “Sa ele oe the Echelon Spectroscope. 375 lines are those regularly refracted, the dotted wave-fronts are drawn perpendicular to the directions in which a maximum of order n is formed. The angle between this direction and the normally refracted rays is called y in the direct: case and yf’ in the reversed case. The distance apart in the air of regularly refracted rays passing through corresponding points E and F of neighbouring step-faces is called fat the end of the echelon and e on the step side. The condition for a principal maximum is that the sum of the distances of EK from the incident wave-front on one side and the dotted wave-front on the other, shall be m wave-lengths greater than the sum of the distances of the corresponding point F from the same wave-fronts. When the angles ¥ and W’ are sufficiently small, we may employ Fermat’s principle and measure the optical paths along the regularly refracted rays. This gives the general equations in the form Serials Wi atewlye| att GE) Bea et BO. 2 Ge iGnA) where R is the retardation produced in a regularly refracted ray by its passage throughasingle plate. Here the equations referring to the reversed case are distinguished by a letter A. The values of R, e, and fare given below, and are plotted in fig. 4 (p. 38U). sin? Rat(na/1— 322? 0s 6), sak MAME 5 e-==s'e0s'@-F i sim 61-404 cos @ oe fer wes ay Sete te Vee Here sis the width of the step-faces, ¢ the thickness of the plates, and @ the angle of incidence of the light on the plates. This angle is in practice generally kept within the narrow limits of + 2°, and it is sufficient to retain only the lowest powers of 0. These expressions then become f =s cos 0+ aaa be R=R,(1+ 5), . A SGM ey esa Cay aE) he Ae Val tally +, RO) faeees, ig a Mee) So, Se ae R, (the value of R when 9=0) is (u—1)t. The parabolic expression for R—R, in equation (5) gives a very close C2 a 376 Dr. H. Stansfield on approximation to the value given by (2), the difference, which depends on 6*, being only 1 part in 800 when 0=5°. The slight deviations of e and jf from the linear expressions (6) and (7) may be detected in fig. 4. Substituting the approximate expressions for R, e, and 7 in equations (1) and (1 A), we obtain the general equations i in the form: Ro(14+ 5) —sy (14+ 5 0)=mr,. «tales [2 Hf Ro(14 57) —sy(14 £2) =m. eae Equation (8) is in agreement with Galitzin’s calculated values and has the support of his measurements which were made on orders close to the position of greatest brightness so that the angle w was always small. If the principal maxima several places removed from the direction of the regularly refracted rays are considered, it becomes necessary to take into account the terms depending on ¥*, which were neglected in applying Fermat’s principle. When the path of the diffracted light is measured along the diffracted rays, the equation for the direct case may be written R—esin W+(t cos 0—s sin @)(1—cos w)=nr&. . (9) If we now suppose the light to retrace its path, the angle of incidence, 6’, on the step-faces is equal to 0—v (see fig. 2), and the angle 6’ +’ at which the diffracted rays leave the end plate is equal to 86. Hence the equation for the reversed case may be found by substituting 6'+' for 0 and W for in equation (9) after substituting for R its value from equation (2). The equation thus obtained may be written in the form: t(/ p2—sin? (6' +h’) —cos 6’) —sf{cos 6! sin yr’ —sin 0’(1—cosy’)t=nnr. . (9A) If the terms whose order in @ and yw is higher than the second are neglected, equations (9) and (9 A) reduce to Ro(1+ epee llai 3, (10) Ro(1+ ¢.)-sW(14 £6 +5<% te the Echelon Spectroscope. 377 These equations only differ from (8) and (8A) by the addition of small terms depending on w? and wW’?, whose values are given in Table I. below. Position of the Orders in the Field of View and Dispersion. According to the first approximation formule (1)and (1A) se R—nxr an ee —". R, e, and f depend on @ but not on wy; so the orders are equally spaced and the dispersions, given by _ de _ de “Cada Po ae MTN... she aon, 7 2 do not vary along the spectrum. The second approximation formule (10) and (10 A) give ~ —nXr Bs aa ult a sod: spit: an n ny If the echelon is rotated a little, so that one order, say the mth, is in the position of maximum brightness where vr or W’=0, el m—n r —e m—n i pd Exgit Bt ( een yc ig ia ae earac i) 2s v : 3 sp! Table I. gives the values of the small nary in the denomi- nators depending on y and w’ for the first five orders on either side of the central order. TABLE I. Rain gid WB Sy ley. | 28 2s p UNGER 003 002 SS ane: 238 005 003 Be 008 005 SF) gts eee | 013 008 378 Dr. H. Stansfield on The Wave-Length Intervals between the Orders. The repetition of a line in a number of orders provides an echelon spectrum with a wave-length scale of nearly equal divisions, and the wave-length value of these divisions, AX, is a constant of the echelon which can be calculated for any wave-length from the thickness of the plates and the re- fractive indices given for the glass. The expressions for AX for the direct and reversed cases may be obtained from the general equations. Neglecting the terms depending on 6”, which do not affect the values by more than one part in ten thousand, they both reduce to nN du ag aoe Ler ave Arx= The changes that are made in 7 by rotating the echelon are so small compared with its whole value (10,070 for this echelon and the green mercury light) that AX is sensibly constant for all positions. On the other hand, AX may be increased or decreased by 2 per cent. by means of the auxiliary prism, as described on p. 373. NovTEs ON CHANGES PRODUCED BY ROTATING THE ECHELON ABOUT A VERTICAL AXIS. Changes in brightness, and the position of greatest brightness. — As an order is moved across the field of view by rotating the echelon, it crosses the lateral maxima of the distribution of light due to the individual step apertures, disappearing as it crosses the diffraction minima, and having its greatest brightness as it crosses the central diffraction maximum. This position of greatest brightness corresponds to the direc- tion of the regularly refracted rays, and is the origin from which the angle y is measured. It does not quite coincide with the position of the image of the slit when the echelon is removed, the position of greatest brightness being displaced towards the side on which the step-faces of the echelon lie. This displacement indicates that the echelon-plates are slightly prismatic. Changes in dispersion and retardation.—Some of the effects produced by rotating the echelon about a vertical axis are represented in fig. 3. The echelon is shown at A rotated so as to make @ negative; in this case eis smaller and therefore (see p. 377) the dispersion is larger than in the Echelon Spectroscope. 379 the normal position. B shows the echelon rotated in the opposite direction so that e is increased and the dispersion decreased. The way in which R, e, and / change with @ is represented in fig. 4. The scale for R is given in wave-lengths, m being the number of wave-lengths in the retardation of the order which is nearest to the position of greatest brightness on the lower retardation side when 02=0. The positions of the row of marks on the 6=0 line represent, by their distances from the apex of the curve, the distances of the orders near the mth from the position of greatest brightness when 6=0, and the abscissee of the curve passing through the marks which lie within it, give the angle through which the echelon must be turned in either direction in order to bring orders higher than the mth up to the position of greatest brightness. The reciprocals of e and f are also plotted to show how the dispersion is changed by the rotation in the direct and reversed eases. These changes in dispersion are simply changes in magnification, as they are not accompanied by any sensible change in the wave-length intervals between the orders. The way in which the effective width, w, of the individual step apertures is reduced when the echelon is rotated so as 380 . Dr. H. Stansfield on to make @ negative, is represented in figs. 3 and 4; w? is also plotted in fig. 4, to indicate the falling off in the intensity of the light on this account. Fig. 4. tet e feu 1 oe ale 1 s1 Ney, UNA ed Ze” te -3 -2° -1° 0 +1° +2° +3° +4° +5 Angle of rotation 8 Width of the difraction-bands.—lt will be seen from fig. 4 that both e and f are greater than w, except when 0=0. Hence, the angular interval, e between the equally spaced diffraction minima is in general greater than or Hy the angular intervals, in the direct and reversed cases, between successive orders. Light reflected from the ends of the plates—The step ends of the echelon plates, which are finely ground, scatter some of the light falling upon them and also give regularly reflected beams, represented in fig. 3. The reflected beams produce echelon spectra ; but as the ends are not polished, the spectra we a me yr "yy re the Echelon Spectroscope. 381 are poorly defined and the spreading of the light brings into greater prominence the broad diffraction-bands corresponding to the narrow sources represented by the illuminated end- faces of the plates. When the echelon and prism are used together, as in fig.1, the reflected spectrum of the green mercury-line may be made to overlap the direct spectrum of the violet line by giving 9 a small negative value. I think it would be an advantage to have the ends of the plates polished or blackened. The position of minimum deviation.—As the echelon is ro- tated from one side of the normal position to the other, the orders first move across the field of view in the direction of decreasing deviation (measured by y) and then turn round and go back again. If the value of R happens to be a whole number of wave-lengths for normal incidence, say mA, then the mth order will come to its position of minimum deviation in the position of greatest brightness when 6=0, but higher and lower orders will not then be quite in their positions of minimum deviation. Consider, for example, a lower order: vf (or in the reversed case wy’) will be positive, and its value when 0=0 can be reduced a little by increasing @ (an the positive direction), as at first the value of R is almost stationary, while e is increasing, and therefore the dispersion is decreasing. By differentiating the general equations (1) and (1A), it will be found that the conditions for the turning-points in the direct and reversed cases are, dR, de dR, df Hci dBy Gude ae: Substituting the values of the differential coefficients and calling the minimum values of the deviation in the two cases wy, and yj, and the corresponding angles of incidence 0,, and i, oy. fe LE pee th and RH i Hence as the echelon is rotated, so as to increase 6, the orders higher than the mth come to their minimum deviation positions before the echelon is normal to the light, and the lower orders have their minimum deviation after the normal position is passed. The central orders are very nearly in their positions of minimum deviation when 0=0. If Wo and yf,’ are written for the values of w and wy’ in this case, 382 Dr. H. Stansfield on it may be shown that and the values calculated from these formule show that, when this echelon is in the direct position, o—p,, is ‘7 per cent. of y,, for an order one place from the position of greatest brightness, 1-4 per cent. of ,, for an order two places away, and so on. The corresponding values for the reversed position are ‘4 per cent. and ‘9 per cent. Effects produced by Temperature Changes. The position of the various orders in the field of view when the echelon is in a definite position, such as the normal position, depends on the temperature of the echelon and on the refractive index of the surrounding air. Records of the temperature of the echelon and micrometer readings of the position of the orders in the field of view, taken from day to day, show that a rise of temperature of 8°6° C. moves the spectrum through a distance equal to the interval between neighbouring orders, indicating an increase of one wave- length in the retardation, R, for this rise of temperature. Curving of the Spectrum Lines. The echelon spectrum lines, like those of a prism spectrum, are curved with the concave side toward the violet end. The curving is due to the variation in the angle of incidence, and therefore in the retardation, R, of light from different points along the length of the slit. The theory has been given by Laue*. Consider the simplest case, in which the slit is vertical and the plates are normal to the axis of the collimator: then light from points above and below the centre of the slit will have a vertical plane of incidence on the plates. Writing i instead of @ for the angle of incidence in equation (3), 1 pl, R-Ry)=5 ee but from equation (1), R—Ro = ep—yY) ; * Physikalische Zeitschrift, vi. pp. 283-285 (1905). i dae | a ~ ; 2 nai the Echelon Spectroscope. 383 and in this case e = s, so that vowo=5()e - 8) Hence, for small values of 7, the spectrum lines are parabolas. The curvature is very small. If, for example, the extreme values of 7 are ten times the angular separation of the orders, Avr, then the top and bottom of the curved image of the slit, representing one order of the spectrum, will be 2 per cent. of Av to the violet side of the centre of the image. Hifects produced by Rotating the Echelon about a Horizontal Axis parallel to the Plates. The echelon can readily be tilted in this way by placing a block under the foot at the small end. The block which I employ tilts the echelon through an angle of nearly 3°, and the photographs Nos. 1 to 3 in Plate XI. of the green mercury -line were taken with this angle of tilt. The horizontal axis of the parabolic lines, which passes through the normal to the plates, has been raised much above the field of view of these photographs, so that the lines where they cross the field of view are considerably inclined to the vertical. The reproductions in Plate XI. have the centre of the curves below them, as they have been turned round in order to put the shorter wave-lengths on the left. Part JJ.—SEconDARY ACTION OF THE ECHELON. Secondary Bands in the Primary Spectrum. The inclined spectrum lines of photograph No. 1, Plate XI. are broken up and have a ropy or screw-like appearance because they are crossed by a secondary system of bands. This screw-like structure of echelon spectrum lines was observed by Gehrcke*. He does not explain how the new bands are produced, but shows that the appearance can be imitated by tilting an echelon with only two apertures, so that the echelon bands slope across the central vertical diffraction band. When the echelon is in the ordinary position the secondary bands are parallel to the spectrum lines, and so their effects, though very important, are not so easily recognized as they are in this photograph taken with the echelon tilted. * Annalen der Physik, xviii, p. 1074 (1905). 384 Dr. H. Stansfield on Character of the Secondary Bands. The secondary bands are superposed on the echelon lines and resemble them in appearance; they are also affected in the same way, but to a greater extent, by adjustments of the echelon. When the echelon is rotated, for example, the secondary bands move faster than the spectrum lines in the same direction and so move across them. When the echelon plates are vertical, the secondary bands, like the echelon lines, are vertical in the centre of the field ; they are also curved in the same direction but more strongly. Their width is about the same as that of the finer spectrum lines, and so, in the ordinary position of the echelon, they are not easily recognized ; but when the echelon is tilted they become more inclined than the spectrum lines in the same direction and can then be seen as in photograph No. 1, Plate XI., intersecting all the spectrum lines. The behaviour of the secondary bands suggested the idea that they might be spectrum lines of a higher order, such as might be produced by the reflexion of light in the echelon. Fabry and Perot Spectrum produced by the Secondary Action. The secondary light, which has been twice reflected in the echelon, is by no means negligible. The echelon was tilted as shown in fig. 5, screens SS being arranged to cut out the ANRRBRRRRBRARERL primary light, and it was found that the echelon was bright with secondary light coming out below the second screen, the brightness extending down to the bottom of some of the step apertures. Suppose that each interface reflects a very small proportion of the light falling upon it and leave out of account for a moment the step structure of the echelon. There will be a secondary beam produced by the combination of the n faint secondary beams which have gone back through one plate, n being the number of plates coming into action; let the the Echelon Spectroscope. 385 retardation of this beam be A. There is another secondary beam whose retardation is 2A, made up of n—1 faint beams which have each gone back through two plates, and so on. Hence the secondary action of the pile of plates in the echelon is similar to that of a Fabry and Perot spectroscope, and, under suitable conditions of illumination, the secondary light by this action would be thrown into a ring spectrum of a high order. The retardation is 2u¢ for normal incidence, so 2 2p it is ai times as great, in this case about five and a half times as great, as that of the primary spectra. The secondary light also undergoes the ordinary echelon treatment as it leaves by the step-faces, and it is therefore confined to the primary spectrum lines. The photograph No. 2, Plate XI., which shows short portions of the rings of the Fabry and Perot spectrum crossing the echelon spectrum, was obtained by stopping the primary light in the way described above, and making the echelon lines broad by widening the slit. The spectrum lines pro- duced by the primary action of the echelon upon the secondary light are inclined because the echelon is tilted as shown in fig. 5, and the centre of the ring system is above the field of view for the same reason. The echelon has also been rotated (in the positive direction of 6), so the centre of the ring system is displaced laterally as well as vertically. The Fabry and Perot spectrum lines are not dependent for their definition, like the echelon spectrum lines, on the narrowness of the slit ; their want of clearness in this photo- graph is partly due to the overlapping of lines belonging to different orders, which is produced by the orders overlapping four deep. The Secondary Point Spectrum. If the slit, instead of being opened wide to show portions of the rings, is made narrow enough to give good definition to the primary echelon action, the secondary light which has undergone both actions is confined to dots indicating the position of the points of intersection of the spectrum lines in one system with corresponding lines, that is lines representing the same wave-length, in the other system. The horizontal dispersion of the dots, given by the ordinary echelon action, now prevents overlapping, as the wave-length interval between the orders in this system is a little greater than the length of the spectrum, and the secondary light 386 Dr. H. Stansfield on gives in this point spectrum, therefore, the advantages of a very high order without the usual overlapping. Gehrcke and Baeyer * obtained similar spectra which they call interference points, by crossing plane parallel plates, and have pointed out the advantages of combining two independent high dispersions. A photograph of the secondary point spectrum, obtained with an exposure of one hour, is reproduced in Plate XI., No.3. The echelon had the usual tilt, about 3°, and the echelon table was rotated about 2° in the positive direction of 8 from the normal position. The dispersion in the Fabry and Perot system is, in this ease, twelve times that in the echelon system, so the wave-length intervals can be best determined by the position of the dots in the former system, while the dots can be recognized and their wave-lengths can be roughly fixed by their position in the latter system. There was no difficulty in recognizing the dots marked 1, 2, 3, 4, 5, 6, and 7 in the photograph, which represent well-known lines in the green line spectrum. In order to determine the wave-length intervals, it is necessary to calculate /\X, the wave-length interval between neighbouring orders of the Fabry and Perot spectrum. It was found from the formula Ax = ee p—2tcosr eA where 7, the order of the spectra, is given by _ 2ptcosr rt haeaione r being the angle of refraction of the light in the plates, and t their thickness. The value found in this way for the centre of the photograph is 96°5 m.A. The wave-length intervals between the components deduced from the measurements of the photograph and this value of AA are given in Table IIL., p- 393; most of them agree closely with the values which have been found by other methods. * EK. Gehrcke and O. v. Baeyer, Annalen der Physik, xx. p. 269 (1906). the Echelon Spectroscope. 387 Character of the Point Spectra produced by the Secondary Light. Fig. 6 is a diagram representing the type of spectrum produced by the secondary light when the echelon is in the direct position and tilted about a horizontal axis, that is, the Fig. 6. : type represented in the photograph of the secondary point spectrum No. 3, Plate XI.; but in order to make the diagram clearer, the ratio of the dispersion in the Fabry and Perot system to the dispersion in the primary echelon system has oeen made much smaller than it is in the photograph. In this case all the rays of light from a given point of the slit are parallel to one another during their passage through the plates, as the lateral diffraction does not take place until the light leaves the echelon by the step-taces. The spectra, or lines of constant retardation, in the Fabry and Perot system are therefore drawn in the diagram as horizontal lines. When the photograph was taken the echelon had been rotated (from the normal position about a vertical axis) as well as tilted, so the plane parallel to the axis of the collimator and the diffracting apertures would not be quite vertical, but the deviation from the vertical is a small angle of the second order (equal to the product of the small angles of tilt and rotation), and it will be seen that lines joining two dots representing the same wave-length and of the same order in the Fabry and Perot system, would be sensibly horizontal, 388 Dr. H. Stansfield on although if the slit had been opened wide so as to show portions of the Fabry and Perot rings, they would have been inclined about 45°, as in photograph No. 2. , When the echelon is reversed, the lateral diffraction takes place as the light enters the echelon and the lines of equal retardation in the Fabry and Perot system will be represented by circles whose centre is the point in the image plane corres- ponding to the direction of the normal to the plates. The four long inclined lines in the diagram (fig. 6) | represent spectra in the primary echelon system; they are inclined to the vertical because the echelon is tilted. The orders of a wave-length dA, are represented in the two systems by full lines, the dotted lines representing similarly the spectra of a second wave-length A, greater than d,. The order of the spectra in the two systems is indicated at the ends of the lines. The points where the full lines of the two systems intersect give a series of points (marked by the larger circles in the diagram) which represent , in the joint system, each point being defined by two orders. The top left-hand point in fig. 6 may be described for example as the np order of wave-length \;. In the same way the intersections of the dotted lines give the positions where A, is represented in the joint system, and the shorter inclined lines joining the Ay and A, points of the same denomination represent the appear- ance of the joint spectra corresponding to a spectrum continuous between these limits. It will be seen that there is no chance of spectra of different denominations overlapping in the joint system as long as there is no overlapping in one of the two systems which are combined. The spectra in the two systems may be regarded as forming an oblique system of coordinates ; the echelon system giving horizontal dispersion may be called the X system and the Fabry and Perot system the Y system. Then the slope of the spectra in the joint system, ay , 1s the ratio of a the dix Ps) ; ee OA ) dispersion in the X system, keeping y constant, to ae the dispersion in the Y system, keeping constant. One important feature of these point spectra is that they give a system of lines whose definition depends in general on the defining power of the two systems which are combined, but does not depend on the smallness of the range of waye- length in the light examined, so long as that range does not exceed a certain relatively large limit. the Echelon Spectroscope. 389 If the definition is poor in one of the two systems, a mono- chromatic radiation would be represented by dots elongated in the direction of the spectrum lines of the other system, and this would in general spoil the sharpness of the lines representing in the joint system a spectrum continuous between narrow limits ; but if these lines are nearly parallel to the spectrum lines of one system, the want of definition in the other will not spoil the definition of the lines, as each dot representing a single wave-length will be drawn out in a direction nearly parallel to the length of the joint spectra. This special case is realized when the echelon is in the direct or reversed normal positions. The diagrams A and B in fig. 7 represent the conditions Bie fe 135 135 735 135 in these cases. They are similar to fig. 6, but spectrum lines have been drawn in the Fabry and Perot system for a series of five wave-lengths whose values increase by equal increments from A; to A;. In the primary echelon system the lines repre- senting alternate wave-lengths have been omitted. B represents the case in which the echelon is in the reversed position, the radii of the circles, representing the spectra in the Fabry and Perot system, being chosen so that their squares increase by equal increments. The horizontal lines in diagram A repre- sent the same spectra when the echelon is turned round into the direct normal position. For convenience in drawing the diagrams, the dispersion in the Fabry and Perot system has been represented as only about ten times as great as that in the primary echelon Phil. Mag. 8. 6. Vol. 18. No. 105. Sept. 1909. 2D 390 Dr. H. Stansfield on system. It should be several hundred times as great even for those parts of the diagram farthest from the centre. It will be seen that in both diagrams the secondary point spectra, drawn through the points of intersection of lines representing the same wave-length in the two systems which are combined, are curved so as to be concave towards the side of shorter wave-length in the primary echelon system; the curvature has been much exaggerated by taking the ratio of the dispersions so much smaller than it actually is. Origin of the Secondary Bands. There is no doubt that the secondary bands which are observed when the echelon is employed in the usual way, that is, with the secondary light superposed on the primary, are very closely connected with the point spectra produced by the secondary light. All the characteristics of the secon- dary bands described on page 384 may be explained by supposing that they are, like the point spectra of the secondary light, the loci of the points of intersection of lines repre- senting the same wave-length in the primary echelon and Fabry and Perot spectra. Another characteristic which may be explained in the same way, with the help of fig. 7, is that when the echelon is in the direct normal position the secondary bands affect each order of the spectrum in the same way, while, when the echelon is reversed, there are marked differences between the different orders. The secondary bands have other characteristics which may find their explanation in interference taking place between the secondary light and the primary. The dark secondary bands appear to cut through the bright primary spectra. This is shown to some extent in photograph No. 1, Plate XI., but it is much more marked when the secondary light is made relatively stronger by covering half the echelon aper- tures so as to stop all the light which has passed through less than half the plates in the echelon. The brightness of the primary lines is no doubt increased above and below the dark bands, making them appear darker by contrast, but I think there is little doubt that there has been an actual reduction in the brightness of the primary light in the dark secondary bands. Another feature of the secondary bands, which may be seen in photograph No. 1, Plate XI., where they cross the line 1, is that they always appear in pairs, fainter and stronger bands alternating with one another. This may be connected the Echelon Spectroscope. 391 with the difference in phase between the primary and the secondary light produced by the two reflexions of the latter. Apart from these phase changes at reflexion, the primary and secondary light would be in phase at the points of intersection of their maxima, as the retardations in both systems are whole numbers of wave-lengths in the direction in which the maxima are formed. There are two cases to be considered for the secondary light, according as it has undergone both reflexions at interfaces or one reflexion at an interface and the other at an external surface. In the former ease, as the air-films are very thin, it is possible that a change of phase of = may be introduced at each reflexion which would give the best phase conditions for interference between the maxima. The latter case may account for the second set of bands shifted relatively to the first. Part [I].—Structure oF THE GREEN Mercury LIne. (5461.) Description of Spectrum given by an Arons Lamp, and Comparison with the Results obtained by other Observers. This spectrum consists of a bright principal line, which is a close double, with six companion lines, three on either side. A photograph of the primary echelon spectrum is reproduced in Plate XII. together witha diagram of the spectrum. The photograph shows, in addition to the genuine components, a number of faint lines which have their origin in the echelon. The genuine components are numbered from 1 to 8, and the false lines are marked 1a, 16, 3a, &. The lines 1a, 1b, 1c, &., mark the positions of the secondary diffraction maxima on the longer wave-length side of the principal diffraction maximum 1, and the lines 3a, 5a, 6a, 7a, and 8a represent the first secondary maxima on the longer wave-length side of the lines 3, 5,6, 7, and 8. When the aperture of the echelon is reduced by covering the first ten step-faces at the smaller end, the faint lines move away from their parents into the new positions of the secondary maxima corresponding to the reduced number of apertures. The numbers in Table II. and Table III. give the distances of the various components from the component of shortest wave-length. I adopted this method of measuring the positions because the bright central line appeared to be the most variable component, while the component of shortest wave-length is a good reference fine. The results of the other observers, given in the Tables, are not convenient for 2D2 392 Dr. H. Stansfield on comparison in their original form, because Gehrcke and Baeyer*, Janicki+, and Galitzin and Wilipt, give the dis- tances from the centre of the principal line, while Fabry and Perot§, Baeyer|| (in a later paper), and Nagaoka §, divide the principal line into two components and measure the distances from the brighter one. Another difficulty in the comparison is that the values obtained by Gehrcke and Baeyer, and later by Baeyer, by the use of crossed plane-parallel plates, are systematically higher than the values obtained with echelon spectroscopes, which agree fairly well amongst themselves. I have reduced all Baeyer’s intervals 5 per cent., and the earlier values of Gehrcke and Baeyer (the means of three sets of measurements given in their paper) by 3 per cent.; and it will be seen that, apart from these differences in the constants, the two inde- pendent methods are in close agreement. TaBLE IJ].—Measurements of the Green Mercury-line Spectrum. The distances of the component lines from the component of shortest wave-length are given in milli-Angstrém units. Crossed Plates. Kchelon Spectroscopes. Reference Fabry & ak Phe ae Numbers, Perot. ehrcke , ae alitzin ie Enevar Baeyer. Janicki. & Wilip. ‘01 A. units | reduced 3 p.c. | reduced 5 p.c. Dat 0 0 0 0 0 1 15 126 136 133 137 2 17 169 169 166 168 3 189 ase 189 Bis. (| 28.) W) ee ae | Central 23 j ee 238 ! pee 236 5 Pea 31 318 320 320 sat. ea 36 364 363 365 365 is 449 8 The brightest component in each case is underlined. * F. Gehrcke and O. Von Baeyer, Annalen der Physik, vol. xx. p. 269 (1906). + L. Janicki, Annalen der Physik, vol. xix. p. 86 (1906). + Furst B. Galitzin und J. Wilip, Mémoires de ? Académie Impériale des Sciences de St. Pétersbourg, sér. 8, vol. xxii. no. 1 (1906). § Astrophysical Journal, xv. p. 218 (1902). | O. v. Baeyer, Verhandlungen der Deutschen Physikalischen Gesellschaft, ix. no. 4, p.84(1907). 4 Nagaoka, ‘ Nature,’ vol. lxxvii. p. 582 (1908). the Echelon Spectroscope. 393 - Tasie IIJ.—Measurements of the Green Mercury-line Spectrum (continued). Nagaoka. Author. | Reference Numbers. Echelon Primary | Secondary Point Width Spectroscope.| Spectrum. Spectrum. : 0 0 0 is aa | 31 | 72 105 ba | 137 135 141 13 2 163 164 167 13 3 189 2. 223 (217) 217 16 Nagas) 247 —= (243) 243 24. 5 | Band. 280 Be 315 319 322 17 6 356 363 365 12 7 390 een ae Le tee 448 448 ae 14 8 477 Fabry and Perot’s values* given in the Table are those published by Zeeman} in 1902. They help to confirm the accuracy of the constants employed in the echelon calculations. The results obtained by several other observers are given by Janickif. The series of faint lines given by Nagaoka resembles the series of false lines in my primary echelon photographs. { published my measurements for comparison with his before discovering that the faint lines in my photographs were not genuine §. * M. Perot informs me (in a letter dated Oct. 13th, 1908) that they have not published any particulars of this line since then. + Astrophysical Journal, xy. p. 218 (1902). t Loc. cit. p. 61. § ‘Nature,’ vol. lxxviii. p. 8 (1908). 394 Dr. H. Stansfield on Width of the Components. The mean values of the widths of the photographic images of the components are given in Table III. If the echelon acted perfectly, the width of a principal light maximum constituting one order of the primary echeion spectrum of a monochromatic radiation, with a narrow slit, would be 2/33 of the interval between the orders, which corresponds in this case to a width of 30 m.A. The narrowest lines in the pho- tographs which still have a measurable width, are about 10 m.A. wide. The widths of the brighter lines vary consi- derably with their exposure, while the width of the com- panion line 8, which is too faint to be overexposed, is the same on each of the three plates on which its width could be measured. Measurement of Secondary Spectrum. The results obtained by measuring the secondary point spectrum are also entered in Table III. The photograph measured was exposed for an hour, and is the one reproduced in Plate XI., No. 3. It will be seen that the agreement of these results, obtained by an independent method, with the ordinary echelon values, is fairly close, except for the com- ponent 2. The methods agree very closely as to the position of the central line. They both give the centre of the double line at 232 and the dividing dark line at 228. The two components of the central line were not measured separately. in the primary spectrum photographs, but the position of the dark dividing line was sometimes recorded. The positions of the centres of the components given in brackets in the second column of Table III., are deduced from the position and width of the whole line and the position of the dark dividing line (neglecting its width). Speetrum given by a Bastian Lamp. A striking variation in the spectrum of the green line was observed with a Bastian mercury arc-lamp. ‘The glass tube through which the discharge passes is bent nearly into the form of an S in a horizontal plane, so that when one part of the discharge is parallel to the slit plate, another part may be normal to it. When the image of the “ end-on” portion of the discharge is put on the slit, the change in the spectrum is so great that it is difficult at first to recog- nize the components. On measuring a photograph of the ‘“‘end-on” spectrum, however, it was found that the companion lines keep their relative positions, although some become the Echelon Spectroscope. 395 broader and brighter, but the dark space between 4 and 5, the two components of the principal line, is greatly increased (from 6 to 26 m.A.) and, being no longer brighter or broader than the rest, they look like ordinary companion lines. - The “side-on” spectrum of the Bastian lamp resembles more nearly that given by the Arons lamp. The separation of the components of the principal line in the “end-on” radiation has been investigated by Galitzin and Wilip*, who observed the phenomenon first in the case of a Geissler tube arranged so that the axis of the discharge was normal to the slit plate. Spectrum of the Green Mercury line given by a hot Mercury lamp. Janickif describes the broadening of the components of the green and yellow mercury lines which takes place when a mercury lamp is allowed to become sufficiently hot, and a peculiar system of five equidistant bands which he observed when the original components of the lines were lost in a continuous spectrum. Galitzin and Wilipt, who give measurements of the bands, suggest that they may be due to a reversal of the lines, or perhaps to some peculiar property of the echelon spectroscope. The theory of the secondary echelon spectra (see page 388) indicates that the secondary bands would be well detined in a short continuous spectrum, and it seemed probable that they were the bands which Janicki and Galitzin & Wilip observed. I have tested this point with a quartz-lamp fitted with an air-manometer, similar to that described by Galitzin and Wilip §. When an arc is started with the lamp cold, the central line (4 and 5 together) and all the companion lines are at first plainly visible, but the pressure in the lamp increases rapidly and the broadening and coalescing of the lines soon takes place. The position occupied by the bright central line in the various orders is now marked by a dark line, probably due to absorption. As the companion lines become merged in the general brightness the fine secondary bands become clearly visible in all the bright parts of the * First B. Galitzin und J. Wilip, “ Ueber die Eigenschaften einiger Emissionslinien des Quecksilberdampfes,” Mémoires de I Acudémie Impériale des Sciences de St. Pétersbourg, sé. 8, yol. xxii. no. 1 (1907). T Loe. cit. pp. 49-55. t Loc. cit. pp. 34 & 76. § Loc. cit. p. 4. 396 Prof. J. Joly on the field, the fact that they are secondary bands being shown by their motion relative to the primary spectrum when the echelon is given a slight rotation. The secondary bands show clearly on the green line when the pressure in the lamp is about one atmosphere. This research was commenced at the request of Professor Schuster, and I have much pleasure in acknowledging the help I have received from the interest he has taken in its progress. I wish to thank Mr. H. Marsden for assistance in my first experiments on the secondary effects, and Mr. W. A. Harwood, B.Sc., for measuring several of the photographs. My thanks are also due both to Professor Schuster and to Professor Rutherford, for placing the resources of the Physical Laboratories at my disposal. MLV. On the Radium-Content of Sea Water. : By J. Jouy, F.RS.* i his interesting contribution to the subject of the radium- content of sea water t, Dr. Eve quotes the results given in a former paper of mine{. The general results of my subsequent experiments have appeared elsewhere §, but not under conditions permitting their statement in detail or any discussion of their claims. Although incomplete they may serve to define more fully the nature of the difference between Dr. Eive’s observations and mine. But first I would wish to call attention to certain points of agreement. The fact of very considerable differences in the radium- content of sea water from one locality to another, seems to find increased confirmation as experiments multiply. In my paper referred to by Eve these variations range from 8 to 39°3 (1 adopt Hve’s notation, and express the values in billionths of a gram per litre). This variation is found among only 11 samples. It is true that they are from very various localities and include harbour water, coastal and oceanic waters, and extend to the Arabian Sea. Hive finds even wider differences. Here I must point out that by an oversight Hve * Communicated by the Author. + Phil. Mag. July 1909. t} Phil. Mag. May 1908. § ‘ Radioactivity and Geology,’ p. 46. Radium-Content of Sea Water. 397 appears to have misquoted his own earlier results. In his paper of Feb. 1907 * he gives his result on Atlantic water as 0-3 and on sea-salt as 0°6. These figures he interchanges in his last paper. When correction is made for this we find that among seven experiments on Atlantic water only he obtains variations ranging from 0°3 to 1°5. Thus all reported results agree in showing that wide differences in radium-content are observed in samples of water from various localities. I have presently to quote instances of even more striking variations. Karly in my observations upon this subject I sought to find if the variations also obtaining from one test to another of the same sample, might not throw light upon the differences from sample to sample; the possibility suggesting itself to me that these latter might only be apparent and really dependent upon the conditions attending the liberation of the emanation. The fact of variations in successive tests and the conditions controlling these variations became, therefore, of special interest, and I sought by altering the conditions of experiment to investigate the circumstances affecting the liberation of the emanation. I have found in the course of my experiments that where conditions of acidification by hydrochloric acid vary, con- siderable variations in the amount of liberated emanation may arise, more especially where there has been concentration of the sample. But where the acidification and other treat- ment remain unchanged the variation from one test to another is, in general, relatively small. The effect of the acidification is to increase the quantity of emanation liberated, but beyond a certain degree of acidification small additions of acid seem ineffective in producing further change. Dr. Eve’s mode of tabulating my earlier results does not bring out the change of conditions. Thus under the heading “ With HCl” he cites a difference of reading of 2:0 and 14°6 obtained on the same sample ; there is nothing to show that here the first reading was obtained on a sea water concentrated from 2500 ces. and acidified with only 10 ccs. of HCl while the second reading was obtained after the acidification had been increased to 60 ccs. So also in the case of the variation from 19°3 to 27:3 obtained upon another sample. The greatest variation which I have as yet noticed in successive boilings, where there has been no difference of treatment, is from 4°4 to 80. This was on an unconcentrated sea water. The general fact of variations from test to test, even under similar * Phil. Mag. Feb. 1907. 398 Prof. J. Joly on the conditions, seems fully brought out by Eve’s recent experi- ments, which read from 0°75 to 1°85 &c., &e. The following table contains all the results which I have up to the present obtained upon sea water. ‘Those given in my earlier paper are summarized in the entries (1)—(5) and (6)—(10). (19) has also been already dealt with. An arith- metical error in computing the constant of a recently constructed electroscope affected the original values given for (15) and (16). A misprint (‘ Radioactivity and Geology,’ p- 46) siehtly affected (23). The last experiment (25), has not hitherto been published. In the table they are not generally listed in the order in which they have been made; (15) and (16) are two of the latest. TABLE I. Radium per litre. (= (@) Coast round Ireland (5)... . i235). 02 denis oe. a 34 (6)-(10) Atlantic Ocean; Madeira to Bay of Biscay (5) ...... 17. (11) Atlantic, New York to Ireland, Arctic Current ...... 14 (12) Ws - i Gulf Stream)! ).!. /sha 14 (13) A 4 a Mid Atlantic {osha 11 (14) y 260 m. W. of Ireland. 8 (15) 3 lat, 0° 0’, long. B19 261 Wn. kes ee a (16) ¥ lat. 16° 54 S., lone. 877 20 OW oii (17) Mediterranean .......... ia LN ERA SU eee 14 (iS) Malpelk Seah, oo. lswieeie s)s Skee tee ee Roe ee F( {19} Arabian Sea, lat. 10° 40’ N., long. 58° 0’ E. ........ 7 (20) Indian Ocean to Mediterranean ; Sandheads to Madras. 4 (21) fs ¥ off Colombo, .).).. 28 i (22) “ 5 Minicoy to Sokotra . 4 (23) , si Red Sea off Jiddah.. 6 (24) , Mediterranean...... 2 (25) Milena ies sc “sia ese ipl’s Tayahep vata nny es le ee 4 As regards the precautions taken in carrying out these experiments the following remarks apply to all alike. When- ever evaporation was required it was carried out in the recently opened Botanical Laboratory of Trinity College. In this laboratory all the apparatus and fittings are new and no radium work has ever been done in the building. The acid used was a ‘re-distilled’ HCl which I tested at intervals. Allowance was made for a very small trace of radium— almost negligible. The final testing was carried out in flasks of (R) glass, which were procured for the purpose and not used for any other. The rubber stoppers were also new and reserved for this special use. In effecting the experiment the increased rate of discharge of the electroscope was Radium-Content of Sea Water. 399 observed about 15 minutes after the introduction of the emanation and again in three hours. The characteristic gain in rate is an assurance that the effect was indeed due to radium and not to any loss of insulation, &. The constant of the electroscopes was from 0°5 to 0°7 : in other words this was the radium-value in billionths of a gram for a gain of one scale-division per hour. It will be seen that working with so low a constant resulted in quite unmistakable incre- ments of rate even in the case of the lowest values obtained. Ebullition is in every case carried on under reduced pressure and for from fifty minutes to one hour. A quantity of powdered tale (tested for radium) averaging 50 milligrams is added to improve the ebullition. With regard to the nature of the bottles in which the water was collected, their proper cleansing, and the time in which the water was retained in them. In the case of experiments (20)—(24) the bottles were new, of white glass, and stoppered. They were carefully washed and were filled from the canvas buckets. The water was stored in them for periods varying from six weeks downwards, according as the homeward journey of the friend who acted for me was accomplished. The bottles for (15) and (16) were supplied, and specially washed, by me. No pains were spared in their thorough cleansing. A third, similar bottle, was sent out on the same voyage. This brought back water from the Rio de la Plata. ‘The three bottles were in appearance alike, and were new, closed with rubber stoppers. The collector in this case was a gentleman of considerable scientific training who quite understood the importance of care in guarding against contamination. Owing to some negligence in their delivery they did not reach me till about three months after they were filled. Sample (25) was also in a bottle supplied and washed by me. It reached me in a few hours after filling. In all the other cases the bottles were purchased by the collectors or supplied on board ship. I have received every assurance as to the precautions taken in obtaining these samples. The Atlantic series were in black glass bottles. The water was enclosed for from twelve to five or six days before reaching me. The details of the experiments are contained in the table which follows. Owing to the method adopted in boiling off the emanation about 200 ccs. of distilled water are added upon each experiment (to expel all residual gas from the flask), and, hence, between each experiment this is again removed by evaporation. 400 Prof. J. Joly on the TABLE I]. No. Concentration. | HCl. pie me III. ccs. 11. | Arctic Current ......... 2090 to 1600 | 50 6:0 57 | 141 12)" |) Gulf Stream °........... 2200 ,, 1500 | 50 {spoiled} 2°6 | 136 13) )\ Mid Atlantic ..:.2:.:...; 2170 ,, 1800,) 70) |,10:0) 4 106 14. | 260 m. W. of Ireland.| 2120 ,, 1850 | 50 8:0 8:0 15. | Atlantic, lat. 0° 0’, long. 31° 26’ W. ... 1625 50 | 22:8 16. | Atlantic, South......... 1790 50 40 17. | Mediterranean ......... 3015 to 1200 |. 72 Lz 14:0 even) dalack Seas... hes. ceone 2800 ,, 1600 | 50 4:7 2 20. | Sandheads to Madras.| 2950 ,, 1700 | 80 37 36 wee VO Colombo.. -.2505.: 2500 ,, 1500 | 84 2-9 68 22. | Minicoy to Sokotra ..| 2400 ,, 1700 | 50 4-4 4:0 vive ite lied ere (RAST ct, Regan a A 2500" 23 EFO0G, oO 2:5 6:0 24. | Mediterranean ......... 2500 ,, 1600 | 50 2°2 wf 2:2 Papal Valentian-..) aP=(ber’2)2+(bei2)?, —| 8P=ber z ber’ x+ bei z bei’ z, ' ade ar Ud) yP=ber z bei’ z—bei x ber'z. J Then Bz?/P=a(1—p2) +22 2ye, F2/P=2n8, Da?/P=a(1—p)? + «?—2ay(1—p), where ry a ne las aN an Pee (11) For the special case w=1; D=P, so that Ag=t—2(y— iP) /7, . - « « «= C2) a very simple result, which is true in practice for all but iron wires. Again, on reduction, log a/e—p o/kaJ 9’ =log a/c—w(B—ty)/ax, log ha— ps o/haJ .' =log ha—p(B—ty)/ax, and their quotient becomes (A +.B)/C, where 2’ A=«2’ log ha. log a/c—pBe log ha?/c+ p’, 2B=py log he, gy GUS) 2°C=ax* log? ha— 2u8z log ha+ p?, and it has been noticed that 6?++?=« identically. With these values, it is found that, M and N being given by (3), 2&CD(M+.N) =402(E+.F)(A +.B). Thus M=40*(AE—BF)/2CD, N=4a2(AF + BE)/e2CD.S 420 Dr. J. W. Nicholson on Inductance and Moreover, CD 2 —— 2y —— | > = («log? pe oe HE og ha+ E)\(SI-0 + 1— - T=n). (15) 9 AK—BF a By he? oP’ foe — 3 = (« log log ha— = log —— + =) | G ¢ 9) ‘ +1— 7) Wy leas ul loghe . (16) # a The succeeding reduction depends upon the particular circumstances of the wires. We now write w=1, and suppose that the wiresare of copper. The only case needing separate treatment is that of iron, where y is very large. Inductance when w=1. High frequency. Quoting the value of M in (14), the inductance becomes, when p= 1, “aN c 46 4a?(AH—BF) t lit log | toe to gee (17) where ng 2 See wlog “log ha— “log “~ + 5) , 2 2 (1-27) hog he, >. (18) CD 28 —,- =a log? ha— iP Asymptotic formule for the functions (a, 8, y) have been developed by Dr. A. Russell *. When the argument 2 is not less than 8, then to four significant figures, if A=x2”2+, so that, in terms of the characteristics of the two wires, i log ha+ ae 5 wv na=2a(*2*) Oi ea we may write Sete BVI=1-<— Fs, So. a yVI=14 pat oe * Proc. Phys. Soc. vol. xxii. 1 This modification is more convenient for purposes of printing. Resistance in Telephone and other Circuits. 421 and after reduction AE—BF aS 3 ay ) = = (1-5 + 527 Fs) os flog ha | ee ee rae 15 aa + log he-+ <3(1—5), (21) oD cL OR gu Osa 3 | oe dl-gtaet os Reha (1 | 1 a 2 5 — He) log hat 2° J We proceed to examine the limiting frequency for which the four-figure accuracy of these results is preserved. For a copper wire of low resistance as ordinarily used, the _ resistivity may be takenas 1696 C.G.S. If/be the frequency of alternation, n=277/, leading to «= = af ? approximately. Thus r=8 leads to the determining relation 7 oes. eae TM es} If af? is less than 40, the four-figure accuracy, in so far as it depends on 2, is lost. When / is only 400 per second, the limiting diameter of a wire becomes so large as 4 centi- metres, so that the formule are unsuited for practice until the frequency is really great. The usual range of diameter for wires applied to such purposes as telephonic communi- cation is from 1 to 3 millimetres in the case of cables, and to 5°7 millimetres in that of overhead wires. The frequency in cases of transmission of speech will not be greater than 2000. Taking f=1600 as perhaps the real maximum, the limiting radius of a wire becomes 1 centimetre. The results there- fore cannot have a great accuracy in such a case, and the formula (43) below must be used. But it will appear that the corresponding formula for iron leads can be so employed. The present results have a two-figure accuracy even when z=3, leading to a radius of 3°75 millimetres, and therefore will apply to many cases even of telephony when thicker wires are used. In such cases, their use is preferable to that of (43), in that the calculation is more rapid. It is necessary not to overlook the other sources of error. Firstly, in the proof of (1)*, h?a* was neglected in com- * Phil. Mag. Feb. 1909. Phil. Mag. 8. 6. Vol. 18. No. 105. Sept. 1909. 2F 422 Dr. J. W. Nicholson on Inductance and parison with unity. In the most unfavourable case furnished by the telephone, f=1600, a=3 millimetres, leading to h?a?=10-14 approximately. ; Thus this source of error needs no further consideration in such a case. But in fact, the neglect of this quantity is always legitimate. Forif f be the frequency, h?a?=4f710-” for a wire of a centimetre radius. It can only therefore affect the fourth figure if f=20 million, and the second if J=200 million, and such a frequency is never used in combination with so thick a wire. Secondly, a*/ct was neglected in comparison,with unity. Now even in ordinary telephone construction there is usually about 24 millimetres of paper and air between the wires, so that in the case of the cable, taking an extreme radius of 1:3 millimetres, c=4a, and only the third figure is affected. For overhead wires, the distance apart is about 30 centimetres. The limiting practical closeness of the wires, when a knowledge of the self-induction is required, is, I believe, attained in Mr. A. Campbell’s experiments on variable mutual inductances *. The error may then be so great as one or two per cent. Effect of a Small Capacity. Heaviside T has divided circuits into five classes, with the following determining properties:— (1) Submarine cables proper, in which the capacity is the main factor, and whose treatment must tollow the electro- static theory. (2) Short lines of low frequency, in which self-induction and resistance determine the effects. This class includes the majority of short telephone circuits. (3) A class in which capacity and self-induction are equally important. These circuits are very difficult in theory. (4) Circuits of high frequency, but small capacity and resistance, and with the inductance so chosen that signals may travel without distortion. or this class the electro- static theory cannot be applied however long the circuit. (5) Cireuits in which distortionless propagation is obtained by allowing an electric leakage. The effect of leakage is small in all but the fifth case, and will be ignored. Let an impressed force He” act at one end of a cireuit consisting of two parallel wires, with terminal apparatus * Phil. Mag. Jan. 1908. t ‘ Electrical Papers,’ vol. ii. Resistance in Telephone and other Circuits. 423 whose inductance, capacity, and resistance are neglected. Let z denote distance of a point P from the end at which the force acts. If R, L, C be the resistance, inductance, i ‘a ( ) be ne and capacity per unit length, and (4, V) the current and potential at a point P ; then COV/dt = —04,/02 L 0u,/d¢ + Rey = —dV/dz p where 0/0t = in. The solution of these equations is found to be m= (H/De9 dy (23) ~ where I = L2C-2(1+ R?/n?L*)? (cosh 21Q, —cos 21Q,)? Q1, Qo = n($LC)2{ (1+ R?7/n?L? BF 1}. | vig With the value of « we are not concerned. For the effect of leakage, reference may be made to Heaviside’s paper *. cEay = 0, ct He te Pr) ay ol.” (26) which is the ordinary impedance assumed to be valid in the previous paper. In the electrostatic theory, we write L=0, which is obviously unjustifiable if R is small or n very great, so that circuits of the first kind lose their character in these cases. We proceed to estimate the correction to be made in the value of L, to take account of a small capacity, regarding only the first order term. Writing Ay, Ao? = (14+ R?/n?L?)? = 1, then on reduction, cosh 21Q; — cos 21Q, = LOn7? (A? +. A,”) {1+ 4 LOCAL — No”) } = 2Cnl?(R? + L?n?)?(1—40n2LC), 25) so that =e. (R? + L?n?)?(1—1Pn?LC). * Loe. ctt. 22 424 Dr. J. W. Nicholson on Inductance and If L’ be the equivalent induction when this small capacity is taken into account, R?+ Ln? = (R?+ L’n2)(1—}Pn2LC) or (L/—L)/L = —PC(R?+L?n?)/6L approximately. (27) This equation serves to limit the types of circuit to which — the uncorrected inductance formule may be applied, in so far as error due to capacity is concerned. For example, if a three-figure accuracy is required, it is necessary that POR? + Ln?)/6L 10-4, .. 2) eee where J is the length of either wire of the circuit. We have also neglected 1 1 5p lit L20*Qaat +a! — Phe?) = gp Unt 2C°(4 + R2/L?n?) in comparison with unity. This restricts the capacity for which the correction (27) may be used. Thus, for low resistance, Al*n?C? > 9. 107°. This equation will ordinarily supply the Jower limit for C. Thus for frequencies such that mC + (52)-110-2? . |) the uncorrected (for capacity) formule may be used provided that C is also so small as to make Gn’ > 61-7 10-4, |) 1 again neglecting R. For a capacity of one microfarad per kilometre, C=10-*. In a case like that of the Atlantic cable the capacity is about. a quarter of this amount, and the limiting frequency, with 1 in centimetres, is about /-?10'%. This excludes such a cable altogether from the investigation, although a shorter cable of the same radius of wire and capacity gradient can be within its scope. For example, a frequency of so much as 10 million can be treated if / is not greater than 1:2 kilo- metres, for a suitable range of inductance given by (80). The range of inductance is of course dependent mainly on the distance between the wires. Obviously all short telephone circuits satisfy both (29) and (30), and their capacity needs no consideration. Resistance in Telephone and other Circuits. 425 Copper Wires with High Frequency. With the above restrictions as regards capacity and frequency (the latter being of little practical import), writing in (17), . - (1 -5-3 5 a)(1-5 +53) 1 Br RS =, (1-5 +55). ey MSR at) Then with the values of (21), Cay L = log. © +4 eee +53 aS (AE—BF), where X = 2a(Qrpn/o)? = 47ra(8/c)?, - with a four-figure accuracy so far as X% is concerned, if A> 8/2. But a further simplification may be introduced. Since ha is a very small magnitude in actual cases, its logarithm is large and negative. Thus if p = loge ha, the functions may be expanded in a descending series of powers of p, and OP ass lt dof? 5(5 z =) =(; : pea toa(lts)teGtst a) teat or ae =( eae a (aah oD. A 1+ )+sa(g+5+ +3)— what 9 =) ) whence, after considerable reduction A @ oh fp (AB-BE) = plog?—~ (p+ 4plog® + 3log*) 1 a The vanishing of the coefficient of \~? is curious. Finally, for a pair of copper wires, the main error being of relative magnitude a‘/ct when they are close together, if A>8¥v 2, N= 4ra(fic)t, . . » » « (33) 426 Dr. J. W. Nicholson on Inductance and if f is the frequency, then » log = pie ere bh) Bhs ATR L = 4log + 5(I- 54+ pp e log ha 4a? a S pet 4plog ® +3 log ; a? a A igi 1 8P—8P°+ 1p" — (8— Bp 3p? log? t (34) where p=log, ha, and the limiting capacity is given by (29). For most useful purposes it may be greatly shortened, according to the value of 2. Iron Wires with High Frequency. When iron is used, there is no object to be served in obtaining so accurate a formula, on account of the vagaries in the magnetic behaviour of the metal. But the approximate value of w is known, for Lord Rayleigh * has shown that for feeble magnetizing forces of periodic character, w usually lies between 90 and 100, and becomes much greater as the forces are increased. It is therefore lawful to take p as of order 107. In the formule (20), (a, 8, y) never become large, and therefore whatever the value of «x (or A), the approximation may be conducted by expanding the functions in inverse powers of p. Thus if p = log ha as before, OD © tae oie “)( =( ye = att > = 4(1 oe oe ae 1 Cis 1— - +5) pia -*( ~%) =( 2,2 24% a a = + 1+ap7x . x? a?) a +5 +48p2—48yp<) | or Pate 14 2(14 9-7) 4 1(s4dorptet stapes SAH zap = 1+ {1+ Ape— + a(3+48%p% + 4Bpe+ a? Be Oge Ae. ay —ABryp oF Gig pie ). | (35) This neglects the ratio #°/u*. Taking a wire of gauge 4 cm., an approximate practical limit for overhead wires, and * Scientific Papers, iii. ~ Resistance in Telephone and other Circuits. 427 writing, as an ordinary value for iron, o = 10,000 c.as., Dens = 50f : 4 ; e Si “ (36) if «= 100. Thus even when f= 10,000 per second, neglect of x°/u? only affects the third figure of CD, and therefore at most the fourth of L, when the ratio a*/c? is noticed. This process is justifiable whether the ascending or descending series are used for (a, 8, ¥). Ina similar manner, AE—BF 4 a atas?—Qyx — Sea E(1-F a log “* © + SS log halog’ ¢\(1— "+2 ) auf + 1g) he ; and after some reduction, AE—BF i Qeya ¥ << Sarat ee Le © qo ett hia 2D a CD + ( + Spa Be log”) 2 rn2 i ae 1a(2+2Bp2—ap'a? + 2B%pta? + eae ee) id wi fe soe, 1 -- 2 log ; . (ax?p —2B’x’?p —2Bx). In the extreme case above, © => = , and the final error consequent upon its neglect is “of order (6000) -? relative to unity even when the wires have limiting practical closeness. Accordingly, Jas 5 = 14 (2+ Bex — Bo log * =) An? ome 3 a > “a (28%p%? —apto* ae L— rag + 2’p(a—2") log"). Consider now the case in which e>8. In the coefficient of uw”, the first order values of (a@y) may be used, with the second order in that of w-1. Under these conditions, the coefficient of w-? is found to vanish, leading to the very simple result, to order u-°, a ae 1 1 1 i = 1+(A—-1)(log he—2)/2 yu, 428 Dr. J. W. Nicholson on Inductance and and thus for iron wires with 1 >8,/2, ei: apne 4a? Qa? f L = 4 loge + <(1—5 + -)) ra ==5 aie he—2), (37) where : 2 dX = 47a (4) ayaa, oe —; is neglected. o Cm On account of pw, this formula may be applied, for any given frequency, to a wire of only about a quarter the corre- sponding limiting radius in the case of copper. For example, for a frequency 800, and radius 2 millimetres, the value of x becomes 5, with ~=100. Thus a three-figure accuracy is obtained for the most unfavourable case of the telephone circuit. Accordingly, for a telephone circuit of iron wires not twisted together, this result is of universal application. Tron Wires with Small Frequency. This case is not very important, but the result may be given at once. Thus if 2 is not greater than 2, we may neglect the term involving «~*, and write, to three significant figures, 48 Aq? XO (oe c 4a? Qyux L = 4log® + ae (Balog he+2——"), (38) The values of (a, 8, y) suited to this case have been given by Russell *. If ea 9 san (HY, Bi ea3 |. | Ree 207) ||) an a aaa: 12 i a(1 ie 790° r7i*") | Pea ti 473...) OER | Saat (1 om! 3 Gl” Samoa [ (39) ‘oe Beg ORT 2) yae(logett sy 7. 6F° J Moreover, £=5¢(1- ae aa 8 647 2) a 34” * 4390° — 197,360.56 1 1 11 (40) tu = 771 fa ee, Ee 8 re 12) a (14+ 752 180° * 12.98.30" * Loc. ett. Resistance in Telephone and other Circuits. 429 Heaviside * has also given the value of B/e, and Lord Rayleigh + that of y/e, by different modes of proof. Thus finally, when rr ES 2 ER aan C2) ai ig Pte EO ig GAY ie oe i= 4log? +1— 94*"+ q3907" ~ 197360058" An? __ Aeta WE fe BTSy cg SOFIE. a Ou log, he {1-3 Peete | Maden a / ED, en on tan? MERA aa: Smail Frequency, Copper Wires. In the notation of (18), with p = log. ha, ae = = 1—28zp + a2"p’. The frequencies for which this formula will ordinarily be required lie between 200 and 1600, and the radii between 1 and 3 millimetres. These values cause p to vary between about 13 and 16 only, and z between + and unity, so that P/CD cannot be expanded in ascending or descending powers of p or zin general. The result may be most simply written in the form 2 L=4 log= Me 8 a “S-(1—28p-— 1) [(1—4Bp2+ 4ap*2") a Za C a 8a? _ 2 log — . (2ap2?—Qapyz— Bz + 2By)/(1—4Bpz+4ap*2"), (43) where («By z) are given by (39), and p=log-.ha. The two final terms in the last numerator are only about A, of the other two, and may be ignored. * Elec. Papers, ii. p. 64. + Phil. Mag. xxii. p. 381 (1886) ; Scientific Papers, voi. ii. 430 Dr. J. W. Nicholson on Inductance and Il. Errective RESISTANCE. Copper Wires with High Frequency. The limitations of all the formule below, except when otherwise stated, are the same as in the corresponding induc- tance formule. With the previous notation, the effective resistance per unit length of the two wires is os Any ber x bei’ « —bei x ber’ x ~~ (bet z)? + (heey? ao Y_ 22 apap. ae —nN Rife, €OD where CD/P has the value in (15), and on reduction 2 2 eerieae a =P (a log ha log _ BP tog =F ‘) iP x j 2 as, } a log he [ieee alr). . (45) When » =1, and the frequency is high, so that, if #./2=), the formule (20) may be employed, then after further reduction, AF+BE 2, a a 4 =, p= 5, log Slog ha (1— 5 + ix) — 5g log ha (1—5 1 15 + + x log he (1— Gps) + 5 and with the help of (32), we ultimately obtain 2 7g a5 (AF +BE)=2p log = +p—log” — 55 {P+ logs — p+ 2p?) : ] pel a : | + ip? 8° 8° + 3p" log “(8—Sp-+3p?+ 2p!) b where p=log, ha. “@ Finally, for a pair of copper wires, with high frequency, and with the limitations of (34), 4n if 3 4a?n a we a ise oy sal Ac a R= x (1+ 4 ) = Pp 1) log t 4a?n AN a aren ger SS { 8p—8p? + 3p*—(8—8p + 3p? + 2p!) log” }. (46) _ aps an Resistance in Telephone and other Circutts. 431 Iron Wires with High Frequency. When up is large, we may write from (45), ee sa K(28—ay log he— 26° log a (47) and by (35), Pere... y ie 3 so that = BE = (= —y log he) 22 | ie (1 + Bpx—y- *\(28—ay log hc) + B’x log te Neglecting z/u? as before, and writing the first approxi- mations to (a#fy) in the second term, and the second in _ the first, we finally obtain AF+BE 2X a ? iB the term in \°uw~-! vanishing identically. Thus the effective resistance becomes _ Anu Neri 2a°nX (5 “) Be SE (145 = Saas log? te nr? oe 2— —p* +p log® ). . (48) This result is much more accurate than the corresponding formula (37) for inductance, owing to the presence of mw in the numerator of the first term. Moreover, » here denotes the previous X multiplied by p#. It is applicable to all iron circuits of importance in practice, for a frequency greater than about a hundred with a radius of 1 millimetre. Iron Wires with Low Frequency. This result has little interest, but may be obtained at once. For («Bry) are all comparable with unity in this case, and # is not greater than 2. We therefore ignore 2?/u’, and obtain ae ae =(= —y log he). Dies." Gee This term also may be ignored unless a very high order of 432 Prof. C. H. Lees on Vaschy’s or Pirani’s Method accuracy be desired, which can rarely happen owing to the uncertainty as to the value of uw. But if it be retained, the resistance becomes the | lois is 8na*z? Lg ee R= SA(1- 5p— Gy“) - (1 + BON aide ne N24 a) + (o—log “)(1— 5 <4 ne . Ce where z has the vaiue in (39), and the brackets may be shortened except when z is nearly unity. When the frequency is smaller, this makes R = 2c/qa?, the value appropriate to steady currents. Copper Wires with Low Frequency. The formula suited to this case is, writing 6? +y? = a ae (zaBry) are defined as in (39), and under the same limitations, tna? = = : z — — (B—2apz + 2ypz”)/(1—4 pz + 4ap?2?) 8na? led again reducing to 20/7a* for steady currents. Trinity College, Cambridge, April 21, 1909. L. On Vaschy’s or Pirani’s Method of comparing the Self- Inductance of a Coil with the Capacity of a Condenser. By Cuarues H. Luss, D.S¢., F.RS., Professor of Physies in the East London College, University of London ™. q* a recent number of L’Eclairage Electrique, M. O. de A. Silva examined in detail the validity of Vaschy’s or Pirani’s method of comparing the self-inductance of a coil with the capacity of a condenser for the case in which the * Communicated by the Author, + O. de A. Silva, L’Eclairage Electrique, 50. p. 113 (1907). —— 7 log - (Y- 2 —y2+ 2aBpz)/(1—4Bpz+4ap’z), (51) ee ee ee of comparing the Self-Inductance of a Coil. 433 discharge of the condenser was non-oscillatory. In the June number of this Magazine Mr. E. C. Snow * completed the examination by dealing with the oscillatory case. In treating the problem Messrs. Silva and Snow write down the Kirchhoff equations for the currents in each branch of the resistance-bridge, and from them deduce a differential equation of the third order for the current through the galvanometer. This equation they solve and find the quantity of electricity discharged through the galvanometer by in- tegrating the expression for the current as a function of the time between the limits 0 and. On equating this quantity to zero, there results the well-known equation for the method L=Ky?*. The investigations are therefore very detailed, and if the object were to determine, for example, the time which must elapse before the quantity of electricity which has passed through the galvanometer amounts to say ‘999 of its final value (a question which might arise in connexion with the condition that the discharge must have passed through the - galvanometer before its moving part has moved appreciably) such detail would be unavoidable. But if we start, as do Messrs. Silva and Snow, with the assumptions that the galvanometer satisfies the above condition, and that the needle starts from a symmetrical positionf, the investigation may be simplified considerably. The method of using the Hlectro-Kinetic Energy and Rayleigh’s Dissipation Function { for the treatment of problems of this kind, first introduced by Maxwell §, and extended by Fleming || and Niven 7, has proved so powerful, and it is so much in keeping with modern dynamical methods ** that a brief statement of it may not be out of place here. If a network of conductors consist of branches having resistances R,, R,, R;, &c., self-inductances L,, L., L;, &c., mutual inductances M,,, M.3, Ms, &c., and capacities K,, K,, K;, &., and if the quantities of electricity which have flowed through the various branches up to a given time ¢ are * E. C. Snow, Phil. Mag. vol. xvii. p. 849 (1909). + See Russell, Phil. Mag. vol. xii. p. 202 (1906). t Lord Rayleigh, Proc. Lond. Math. Soe. iv. p. 857 (1873), and Scientific Papers, 1. p. 176. § Clerk Maxwell, ‘ Electricity and Magnetism,’ 2nd edit. vol. ii. p. 365 1881). | ? A. Fleming, Phil. Mag. vol. xx. p. 242 (1885). q J.C. Niven, Phil. Mag. vol. xxiv. p. 225 (1887). ** See E, T. Whittaker, ‘ Analytical Dynamics,’ pp. 226, 228 (1904). 434 Prof. C. H. Lees on Vaschy’s or Pirani’s Method Ly, La, 3, &e., respectively, then if we write down the Electro- kinetic Energy ; TS33L,27+2M,Miwintn, 6 ) se the Dissipation Function Di SeR.2,- so (et ty ce and the Electrostatic Energy 2 Vee Dh 22, 0 i ony n the equations for the flow of electricity through the various branches of the network may be written in the form : 0 (oly 0De 1nOF silag,) t 3a, + aa ot te In this equation there is no reference. to electromotive Forces due to cells or other causes present inthe system. To extend the method to cover such cases, we make use of a device well known to readers of Heaviside *, that is we consider a constant electromotive force Ei as due to the presence of a condenser of large capacity K possessing an initial charge X=HK. The Electrostatic Energy of such a condenser when it has given up a finite quantity of electricity # is equal to }(X—~)?/K, z. e. to 3 KE’ — Ez since «/X is small. As we are only concerned with changes of Energy, the term contributed to the Electrostatic Energy by the cell reduces to —Hwx. The extended form of the Hlectrostatic Energy becomes therefore V = 3i07/K, —SE.c, . . se Although in stating these propositions it has been con- venient to take a simple symbol for the quantity of electricity which has flowed through each branch of the network, it is more convenient in applying the method to the solution of a problem to follow Maxwell’s plan of assigning a simple symbol to the quantity which has flowed round a mesh of the network. Kirchhoff’s first law for the distribution of currents in networks, 2. e. that the currents leaving a node have a sum equal to zero, is then fulfilled automatically. The following figure gives the arrangement of the circuit * See for example, O. Heaviside, Electrical Papers, ii. p. 216 (1892). of comparing the Self-Inductance of a Coil. 435 known as Vaschy’s or Pirani’s method, and the arrows show the currents in the various meshes. The following are the expressions for the Hlectrokinetic Energy, the Dissipation Function, and the Electrostatic Energy respectively, the mutual inductances being taken ZeTO :— tg? PINON priv hss Sap ell uooluo wh yaya) D = $Bi? +P (9-22 + 4QG GP + ROH? 4$4C—P? SG 8) a eae ar are | GOD) 0 ES AOS Rc mont a eC ee Differentiating these expressions to find the terms of the equations of type (4), or applying Kirchhoff’s second law directly to each mesh of the network, we have Be+ E(2—Y—z) FQ(t@—9) HE, fe ee oe (8) Ly —P(#—y—z) -—Q(«—-y) + RY 4+2)4+8y—ri=0. (9) Ree (eb -9— 2) PRG +-2)+G2=0, ©.) y)*.) (10) eg) 48 = Oa gh 4) eigearwe ne) aw) drmealmwecs) eu(11) 436 Method of comparing the Self-Inductance of a Coil. Rearranging equations (8), (9), and (10) we have (B+P+Q)®—(P+Q)y—Pz = HE, .\ 2 —(P+Q)a+(P+Q+R+8)y+(P+R)z =ru-Ly, . 9’) —P2+(P+R)g+(R4+G)z | =—hz.. , (10) In the steady state when w, y, and z are each =0, the current z will be =0 if the minor of E in the determinant for z is zero, that is if P/Q=R/S. Integrating the above equations with respect to the time between the limit 0, at which the currents and quantities are zero, and the time ¢,, at which the currents are steady and the | quantities of electricity which have passed have attained the values 21, Yj, 2;, we have :— (B+P+Q)2,—(P+Q)y—Px =| “Bar, . oe) —(P+Q)a,+(P+Q+R+8)y+(P + R)z;=(Kr? -L)g, (13) —P2,+(P+R)y+(R+G)a =)... 7 From the second of which the relation u.=Kry, given by (11) has been used to eliminate 2}. From these equations it is seen by inspection that z,;=0 if ty Kr?—L=0, and the minor of } Edt in the determinant for 0 z, is zero, that is if P/Q=R/S, 7. e. the condition for a steady balance previously obtained.. Since the only conditions assumed to hold in the above proof are that the current in each mesh of the network is initially zero and finally steady, the question whether oscillations take place in the interval or not, does not influence the result. Whether ¢, can be so chosen that the currents throughout the network have become sufficiently steady, without the condition that there has been no motion of the galvanometer- needle or coil during that time being violated, is quite another question. With a modern ballistic galvanometer of the type recently constructed by Prof. B. O. Peirce*, of Harvard, having a period of 10 minutes, there will be very few cases in which there is any doubt that both conditions are satisfied. It is well to remember that even then, the needle or coil should start from asymmetrical position if the absence of reflexion is to be taken asa proof that the time integral of the current throughout the instrument is zero f. * B. O. Peirce, Proc. Amer. Acad. xliv. p. 283 (1909). + A. Russell, Phil. Mag. xii. p. 202 (1906). - Shar acadieasbeiess — par LI. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. _Continued from vol. xvii. p. 772.] February 10th, 1909.—Prof. W. J. Sollas, LL.D., Sc.D., F.R.S., President, in the Chair. — following communications were read :— L. ‘ Note on some Geological Features observable at the Carpalla China-Clay Pit in the Parish of St. Stephen’s (Cornwall).’ By Joseph Henry Collins, F.G.S. An east-and-west fault traverses this pit near its southern wall, with a downthrow to the south of more than 50 feet. North of the fault there is china-clay rock or‘ carclazyte,’ at one point underlying granite not sufficiently altered to yield china-clay, and sometimes containing embedded lenticles or irregular masses of partly-kaolinized granite. The carclazyte is often traversed by veins of secondary quartz, in most instances associated with schorl. It also contains lepidotite, gilbertite, topaz, fluor, and schorl. South of the fault there is nearly horizontal tourmaline-schist, at one point 50 feet thick, and thinning off southwards and eastwards. This, like the rock of the north side, is overlain by subsoil or ‘ growan,’ covered in turn by soil or ‘ meat-earth.’ Underlying the schist there occurs also china-clay rock to a distance of many fathoms from the fault. This occurrence of china-clay under a thick schistose overburden is unique in Cornwall, although the other features of the pit are reproduced elsewhere. The author considers that this example is strongly in favour of the pneumatolytic origin of carclazyte, the gases producing the change being possibly in part carbonic acid, but probably to a more important degree chlorine, fluorine, and boron. 2. ‘Some Recent Observations on the Brighton Cliff-Formation.’ By Edward Alfred Martin, F.G.S, The author records in his paper certain features presented by the face of the cliffs between successive falls at Black Rock, Brighton, during the past eighteen years. As the cliffs have worn back, the base-platform of Chalk grows in height, and the layer of sand which Prestwich found above the Chalk grew thinner and thinner until finally it completely disappeared. At the same time, the Phil. Mag. 8. 6. Vol. 18. No. 105. Sept. 1909. 2G 438 . Geological Society :— raised beach has grown in thickness from 14 to 12 feet. In 1890 there were six feet of sand, with a foot and a half of beach above it. There was practically no protection at this date in the shape of — groynes. In 1892 the sand had decreased to between 3 and 4 feet, but the beach remained as in 1890. Many falls of cliff took place between 1892 and 1895, and at the latter date the beach had increased to between 4 and 5 feet. The eastern limit of the beds had become more clearly defined, the trough in the Chalk in which they had been defined taking an upward direction about 300 yards east of the Abergavenny Inn. Many blocks of red sandstone had become dislodged, and were lying on the modern beach. In 1897, 10 feet of chalk formed the lower portion of the cliff, with 8 feet of raised beach above it in places, but there was a mere trace of sand left. The rubble-drift above was seen to be distinctly stratified. Many masses of red sandstone had fallen out of the cliff, the largest measuring 5 feet in its greatest dimension. In 1899 the raised beach had reached a thickness of 10 feet. Great masses of moved and reconstructed chalk were observed on the eastern boundary embedded in the beach. Two rounded lumps of granite were extracted from the beach. In 1908, the beach was but a little over 8 feet thick in the exposed parts, but the platform of Chalk was 14 feet thick. The upper portions of the beach, which were the least consolidated, had fallen away in such a manner as to leave cave-like gaps beneath the rubble. The number of red sand- stone blocks which lay on the modern beach was remarkable, forty. such blocks being counted in a space of 50 yardssquare. In 1906, the raised beach had increased from 15 to 20 feet: farther west, however, the thickness was not so great. In 1908, there were 17 feet of Chalk, 12 feet of beach. It is noteworthy that as the degradation of the cliff proceeds, the material is rapidly carried away by the sea. No talus remains for any length of time, and if the material is to be prevented from disappearing into deep water, some such contrivance as chain-cable groynes seems to be demanded, fixed somewhere between low and high tide-marks. The only organic remains observed in the cliffs were some fragments of shells, found at the top of the raised beach. February 24th, 1909.—Prof. W. J. Sollas, LL.D., Sc.D., F.RB.S., President, in the Chair. The following communications were read :— 1. ‘Paleolithic Implements. etc., from Hackpen Hill, Winter- bourne Bassett, and Knowle-Farm Pit (Wiltshire).’ By the Rev. Henry George Ommanney Kendall, M.A. nm’ a The Karoo System in Northern Rhodesia. 439 2. ‘On the Karroo System in Northern Rhodesia, and its relation to the General Geology.’ By Arthur John Charles Molyneux, F.G.S. : In 1903 (Quart. Journ. Geol. Soc. vol. lix.) the author described the occurrence of deposits, that have since been recognized as of Karroo age, in Southern Rhodesia. The present communication traces their extension across the Zambesi, where their boundary follows the foot of the remarkable line of escarpments that divide the plateau, nearly 4000 feet in altitude, from the low-lying (1500 feet) regions of the Zambesi Valley. Karroo deposits also form the floor of the peculiar trench-like valleys of the Luangwa, Lukasashi, and Lusenfwa (or Luano), the walls of which are similarly steep, and of metamorphic rock-gneiss, schist, and granite. The Luano Valley is described. Its northern precipice is known as the Machinga (native meaning ‘a fence’), and the Lusenfwa and Molongushi rivers are followed in their mature courses across the flat plateau-plains. They reach the Luano by waterfalls into deeply incised gorges, cutting back 15 and 8 miles respectively into the plateau. Rivers that join the Luano from the south, on the contrary, descend into open valleys of Karroo floors, that are divided one from the other by tongues from the southern highlands, and suggest ‘ rolled-out’ folds. Between the Kafue junction and Feira, the Zambesi River also occupies a trough-valley, lined by steep escarpments; that on the south side rises 2000 feet in less than a mile, being formed of a flexure of altered sediments. The Danda flats show Karroo beds. The Lufua River runs parallel with the strike of the gneiss of the locality, and crosses two synclinal basins of clastic deposits, separated by Archean ridges. The Losito has also a deep strike- channel. The Karroo deposits are grouped into basal conglomerates, coal- measures, Upper Matobola Beds, and Escarpment Series. No effusive basalts were seen, but there is an area of Forest Sand- stones near the Losito-Zambesi confluence. In the Luano Valley, the conglomerates are made up of resisting quartz - quartzite boulders and pebbles—all having dimpled or concave depressions on one or more sides; they possess no orientation, are unsorted, and exhibit a varying matrix. Though they form the base of the Karroo System there is no certain evidence of glaciation, but the beds seem to have originated as scree-deposits on an uneven floor. The grinding of the pebbles into one another is accounted for by the soft nature of the schists and limestones, which would have been removed in the internal movement before consolidation. In the Lukasashi and the Luano there is a general dip of the strata north-westwards, that is, towards the escarpment, and evidence of minor anticlinal and synclinal folds along east-north- east axes. By a combination of these the Karroo deposits become 440 7 Geological Society. lowered from plateau-level on the sonth, towards the north-west ‘ culminating in a great downthrow fault along the foot of the— Machinga. Nowhere on the plateau in the immediate vicinity of the valley- walls have Karroo beds been found, and if they did once extend there, it is remarkable that they should have disappeared. But it is certain that the valleys were at one time filled almost to plateau- level, as the rivers pass through Archean inliers by deep clefts, and must thus have laid out their courses before such hard masses rose from the Karroo beds by erosion of the latter. Also the compara- tively late times in which the Machinga escarpment was laid bare, and the rejuvenation of the Lusenfwa River, etc., suggest a complete filling of the valleys. It is thus possible that the Karroo beds extended over a part of the plateau, and were included in the folding and faulting movements already mentioned. Subsequently, by some continuous agency the whole surface was planed off to a plateau of remarkable monotony; and on a further radical change of conditions taking place, erosion of the softer Karroo strata set in by which the present valleys are again reaching a plane of denudation. The facility with which atmospheric waters and acids attack the sediments is notable, and decomposition extends to 100 feet in depth over the fiat regions of the plains. ae * The author suggests that the trough-valleys of clastic rocks merely ~ follow the axis of pre-Karroo and post-Karroo movements—trending, in three directions. The Luano and part of the Zambesi course agree with that of the folds and cleavage of the complex, certain ranges of hills, and the Machinga Fault (east-north-east) ; a second (south-easterly) trend is that of the Kafue, Losito, Inyanga range, and Lufua, and the folds and cleavage of the complex in these regions ; while the third follows the dominant direction of the great tectonic movements of South Africa (north-east). Mr. L. A. Wallace has noted that the Luangwa and mid-Zambesi are on this strike, and Mr. G. W. Lamplugh has suggested a northerly extension of his Deka Fault. A distance of 800 miles thus displays movements that commenced in pre-Karroo periods, and have repeated themselves since the Karroo time. Fossils from the areas described support the previous allocation of the deposits to the Permo-Carboniferous, and to the Karroo System of South Africa. Notable specimens are members of the Glossopteris-flora, including pith-casts of Schizoneura ; carapaces of Estheria; ostracods; and fragments of bone, fish-scales, and teeth. Paleolithic stone-implements (axe-heads) were found at separate localities on the surface, about the latitude of 14° 50’ S. Phil. Mag. Ser. 6, Vol. 18, Pl. X. SSS “Tift QQ WS G60 AG WN CRC CG RRB BWAE BAY q _— Phil, Mag, Ser, 6, Vol. 18, Pl. X, | SA FIFI: FLD ELH, 7 ZZAZZ IZZIE A Gee eh, Tae hts CSA Ufa NLLS 4 a > < a ot eo ~. 7~ eo , Vol. 18, Pl. XI. 6 Mag. Ser. il Ph STANSFIELD NW 00s osh 00+ ose oot ost 00% os! oot os © vos 47 Hu2- =v Fee Ss ley eee apr eee Mer ety See el Oe ae sang Noe a eee eC eT $q1un wosspuy- unujoeds fo wrsfvig Phil. Mag, Ser. 6, Vol. 18, Pl. XII. aay ~ETIPIL ws STANSFIELD. BEVAN. Phil. Mag. Ser. 6, Vol. 18, Pl. XIII. Bre. |: Hie. 3. Fie. 4. WL pALD dea THE LONDON, EDINBURGH, ann DUBLIN- PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES. ] Q: » oS ea. 5 Rh ee <> ** OIE O 3 Fh Fe: 1909: LI. On Striations in the Electric Discharge Cp By Sir J. J. THomson, IA., F.R.S* | NE of the most conspicuous features of the electric dis- charge through gases, when the pressure is within certain limits, i is died exceedingly well-marked alternations of light and darkness which occur in the positive column. These alternations, which are called striations, are so varied and beautiful that since their discovery by Abria in 1843 they have attracted the attention of many physicists. Grove, Gassiott, Spottiswoode and Moulton, De la Rue and Miiller, Crookes, Wood, Skinner, H. A. Wilson, and Willows have published important researches on the conditions under which the striations are produced; on the influence upon them of such things as the nature and pressure of the gas, the size of the tube, the current passing through it; and on the dis- tribution of the electric force in the neighbourhood of a striation. The investigations described in the following paper relate for the most part to the last of these questions, and were made with the object of testing a theory of the striations which I gave in my Treatise on the Conduction of Electricity through Gases. For these experiments I used tubes fitted with Wehnelt cathodes, 7. ¢. the cathode was a * Communicated by the Author. A Discourse given at the Royal. Institution on Friday evening, April 2, 1909. Plul. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 2H 442 | Sir J. J. Thomson on strip of platinum-foil heated to redness, and having on it a spot of lime or barium oxide™*. With these cathodes large currents can be sent through the tube, and remarkably bright and steady striations obtained at lower pressures and with smaller potential-differences than with the ordinary type of discharge. The pressure has, however, to be low, considerably less than 1 mm. of mercury, to get the full advantages from these cathodes. The first point to which attention was directed was the distribution of electric force along the line of the discharge. Investiga- tions on this point have already been made by Skinner and H. A. Wilson, but it seemed to me that the steadiness of the striations with the Wehnelt cathode made this method of investigation particularly suited for these investigations. The first method used to measure the variations in the electric force along the discharge was to find the variation in the difference of potential between two platinum wires 1 mm. apart as the wires were moved from the cathode to the anode. Several devices were used for this purpose: in some the platinum wires (surrounded up to about a millimetre from their tips with glass rods) were carried ona sort of railroad and moved from cathode to anode. The electrodes in the discharge-tube in this case were fixed. The measurements of the potential-differences made by this method at low pressures gave the very remarkable result that just on the cathode side of the bright part of a striation the electric force was negative (7. e. that the force ona positive charge was in the direction from cathode to anode): on crossing over the bright boundary to the anode side the electric force at once became positive, and rose to a high value. It soon, however, began to diminish, and went on diminishing up to the cathode side of the bright part of the next striation on the anode side. The distribution of the electric force in the striation is represented in fig. 1, and the corresponding distribution of positive and negative electricity in fig. 2, the ordinates representing the distribution of the electri- fication both as to magnitude and sign. Thus if these measurements of the electric field can be relied on we have intense negative electrification at the bright head of a striation (by head is meant the side next the cathode) and a weak positive electrification through the rest of the field. The * My assistant, Mr. Everett, has found that these cathodes can be very easily made by letting a drop of sealing-wax fall on the foil, and then burning away the combustible matter by heating the foil to incandescence. Sealing-wax seems to contain large quantities of some salt of barium. Striations in the Electric Discharge. 443 transition from positive to negative force was very abrupt and well marked, so much so indeed that the position of the Electric Force Fr} i) 3 bo Density of Eleckri/cabion. platinum wires in the striation could be ascertained with great accuracy without looking at the discharge, by observing the deflexions of the electrometer by which the potential- difference between the wires was measured. Many changes were made in the way in which the wires used as detectors were arranged: thus, to prevent any screening of the one wire by the other, an apparatus was used in which the two platinum wires were brought in from opposite sides of the tube, so that there should be no overlapping; exactly the same results were obtained with this apparatus as with the other. Again, another arrangement, similar to one pre- viously used by Professor H. A. Wilson, was tried, in which the exploring electrodes were kept fixed, and the anode and cathode kept at fixed distance apart were, by means of a float, moved relatively to the exploring electrodes a, b, so that these could oceupy all positions from the anode to the cathode. The arrangement is represented in fig. 3 (p. 444). The ex- ploring electrodes in some of the experiments protruded about a millimetre beyond the ends of the glass tubes into which they were sealed; in other experiments very fine hollow glass tubes were used to cover the wires, and the wires instead ot protruding beyond the glass stopped short at about a millimetre from the end of the tube; this arrangement was adopted with the idea of protecting the wires against streams of corpuscles coming down the tube: these by giving up their charges to the wire might cause this to acquire potentials different from those of the gas at the tips of the wire. The results obtained with all these modifications were exactly the same as those obtained with the first type of apparatus, 7. e. there was always when the pressure of the gas was lowa ral s Nip - A444 Sir J. J. Thomson on ite ' negative electric force just in front, 7. e. on the cathode side of the bright part of a striation; this changed to a large Fig. 3. SN positive force as soon as the bright boundary of the striation was passed; at a short distance from the front of the striation this force began to diminish and went on di- minishing until the front of the next striation on the anode side was reached. Though the indications of all these wire explorers agreed in pointing to the existence of a negutive force in front of these striations, yet I felt that the existence of a negative force could never be proved by the use of wire detectors. For let us consider what the existence of a negative force implies. The electric current is always in the same direction throughout the tube, and therefore the average Striations in the Electric Discharge. 445 movement of the ions is in the same direction at all parts of the tube; thus, whenever the electric force is negative, there must be ions moving against the electric force instead of with it. Now the validity of the method of the wire elec- trodes depends upon the assumption that the ions in the neighbourhood of the tip of these electrodes follow the lines of force, that if, for example, the tip were at a higher poten- tial than the gas so that the force on a positive ion were away from the tip, negative ions would follow the direction of the force acting upon them, and run into the tip and lower its potential until it became the same as that of the gas in its neighbourhood. But if the ions do not follow the electric force, and the existence of a negative force implies that some of them at auy rate do not, we have no right to assume that the potential of the wire is the same as that of the gas. Jn some simple cases it is evident that it would not be so. Thus suppose the wire were exposed to a stream of cathode rays, and that there were no positive ions in its neighbour- hood, then it is evident that the wire would acquire the potential of the cathode from which the rays started and not that of the gas around the wire. For these reasons I felt that the existence of a negative force could not be established by means of wire electrodes, aud I adopted an entirely different method of measuring the electric force along the discharge-tube. The principle of this method is as follows: imagine a very fine pencil of cathode rays, travelling at right angles to the line joining the cathode and anode, to pass through the discharge-tube. As it crosses the discharge at any place it will be acted upon by the electric force at the point of the discharge, and will be deflected by an amount proportional to the electric force. The defiexion will be from the cathode of the discharge-tube if the force is positive, towards it if the force is negative. If very small pencils of cathode rays are used the disturbance of the electric field in the discharge-tube due to the negative charge on the rays is quite insignificant, and there is none of that distortion of the striations which, to a greater or less extent, always occurs when exploring metallic electrodes are used. The arrangement by which this principle is carried out in practice is shown in fig. 2. The cathode and anode are fastened together by a piece of glass-rod and fastened to a float, floating on the top of amercury column. By raising or lowering the column the anode and cathode can be moved up and down the discharge-tube. This arrangement is the same as that used with the wire detectors and shown in fig. 3. 446 Sir J. J. Thomson on The wires a, b (fig. 3) were replaced by cathode rays gene- rated in the side tube 8 (fig, 4) by a small induction-coil: Fig. 4. the cathode C is at the end of the tube, the anode is the metal plug A connected with the earth; a very fine hole was bored in this plug and through ita pencil of rays passed across the discharge and then entered the side tube T. In this tube there was a screen W, covered by a phosphorescent substance, in some cases willemite; in others the screen was a zinc sulphide one procured from Mr. Glew. The place of impact of the cathode rays against the screen is marked by a luminous spot, and by measuring with a cathetometer the deflexion of this spot the magnitude and direction of the electric force acting on the cathode rays as they pass across the discharge-tube can be determined. Tinfoil was wrapped round the outside of the discharge-tube to neutralize the effect of electric charges on the glass walls of the tube. The use of cathode rays not only avoids the disturbance due to the presence of the wires, but inasmuch as the cathode rays are negatively electrified particles it enables us to measure the effect of the field on such particles, and as it is the corpuscles which carry practicaily all the current in the discharge, the method enables us to observe in a very direct way the most important factor in the discharge. The method is, however, limited to the case where the pressure in the discharge-tube is low, as it is only at low pressures that the cathode rays produce a well-defined spot on the screen. Observations made with this method showed unmistakably the existence of negative forces in certain parts of the dis- charge, and in fact the distribution of electric force along Striations in the Electric Discharge. 447 the tube as determined by this method agreed remarkably well with that determined by the method of the exploring wire. When the discharge was striated it was generally found that where the cathode rays passed underneath a striation, 7. e. on the cathode side of the bright part of the striation, there was a small deflexion of the cathode rays towards the cathode of the discharge-tube, showing that in this part of the discharge the electric force is negative, while when the path of the cathode rays passed through the bright part of a striation there was a large deflexion of the cathode rays from the cathode of the discharge-tube, showing that in this part of the discharge the electric force was strongly positive. The change from the small negative deflexion to the strong positive one was exceedingly abrupt, so much so that when the anode and cathode were moving downwards, owing to the sinking of the float supporting them, and one striation after another was thus being brought across the path of the cathode rays, the phosphorescent spot moved as abruptly as if it had been struck by a blow when the bright head of a striation crossed its path. At the low pressures at which these observations are made the potential-difference between the electrodes when the current is large encugh to produce striations is exceedingly small, often not exceeding 60 or 70 volts. Under these circumstances the negative forces although unmistakable are small: when, however, the current through the tube is reduced until the discharge is no longer striated, the potential-difference between the electrodes is very much increased, and now large negative forces can be observed in the neighbourhood of the anode. Sometimes the region in which the force is negative extends a con- siderable distance from the anode: in one case I observed a negative force for two-thirds of tke distance from the anode to the cathode. As the corpuscles in the cathode rays have an exceedingly small mass they are able to follow very rapid variations in the electric field; by means of them we can observe the gradual establishment of the steady state of the discharge and the change in the direction of the electric force at certain places from positive to negative. Thus suppose the steady current through the tube is small and the potential-difference is considerable, and that the pencil of cathode rays is passing through the discharge near the anode, then if we watch the behaviour of the phosphorescent spot in the interval immediately following the application of the potential- difference to the tube, we shall find that when the current first starts through the tube the spot is repelled from the cathode, 448 Sir J. J. Thomson on showing that at this stage the electric force is positive throughout the tube. This repulsion of the cathode rays is however only momentary: the spot jumps back, and after a very short interval the spot is attracted towards the cathode, showing that the force in this region is now negative. Thus during this interval the ions in the gas and those clinging to the walls of the tube have rearranged themselves in such a way as to reverse the force in the field. This momentary deflexion is much more perceptible near the anode than some distance away from it; the rearrangement seems to spread from the cathode, and to be established so rapidly close to that electrode that there is no time to observe it, while as we travel away from the cathode the steady state is reached after longer and longer intervals, and there is time to observe the initial distribution of the electric field. We see that the result of the experiments with the cathode rays is to confirm the indications of the wire detector, even when the main current is travelling against the electric force. That the wires in this case should indicate the potential is very remarkable, and must be due I think to the pre- sence in the discharge of slowly moving ions in addition to the swiftly moving ones which carry the main portion of the current, having acquired in other parts of the field sufficient impetus to carry them for some distance against an opposing electric force. The slowly moving ions would be produced by the collisions of the quick ones, and those produced near the tips of the wire electrodes would follow the lines of electric force near the wire and equalize the potentials between the wire and the gas. The great change in the electric force which occurs at the bright fronts of the striations shows that in these regions we have a great accumulation of negative electricity, while the distribution of the electric force in other parts of the striations and in the dark parts between two striations shows that in those regions there is a slight excess of positive electricity. The magnitude of the charges in the electric force is shown by the following numbers which indicate the electric force in volts per centimetre at different parts of the striation. z in the following table is the distance in millimetres from the bright head of the striation: 2 is taken positive when measured towards the anode, negative towards the cathode, thus «= —1 denotes a place 1 millimetre from the bright head of the striation on the cathode side. X is the electric force in volts per centimetre at # The gas was hydrogen ata low pressure. Striations in the Electric Discharge. 449 Hs x. — 9 +67 -++ 33 +30 +10 —10 The last reading was at a point just in front of a second striation. The distance between the bright heads of successive striations was 9 mm. and the thickness of the dark space 2 mm. From the preceding table we see that in the space of 1 mm. at the head of a striation we have a change in the electric force of 76 volts per cm. By means of the equation aX -|- -}- es Rae (oy (eb fn bg | +++ we see that the density of the negative electricity at the head of the striation is about 4 of an electrostatic unit per c.c. The density of the positive electricity in the other portions is very much less than this. With Wehnelt electrodes there is frequently only a small potential-difference between cor- responding points in adjacent striations: in some cases this difference was only 2:7 volts. The changes in the electric force are much more abrupt at low pressures than at high ones; though there is always a large increase in the force at the bright head of the striation. i have not observed the existence of the negative forces when the pressure was more than a fraction of a millimetre of mercury. I have found other cases in which the negative forces are even more pronounced than those I have already considered ; perhaps the most striking of these is one where the anode and cathode are connected together and with earth by stout metallic connexions, so that the two are at the same potential, and therefore the average negative force between them is as great as the average positive force. The anode is perforated by a very fine hole, and through this hole a stream of Canal rays, 7. e. positively electrified particles, passes into the tube: this produces when the pressure is suitable a fully developed discharge, with striations, Faraday dark space, a well-developed negative glow and dark space; and in spite of the anode and cathode being at the same potential there is in this case the normal cathode fall of about 300 volts at the cathode: the negative forces ina tube of this kind must be very considerable, as they have to balance the cathode fall. 450 | Sir J. J. Thomson on The heaping up of the negative electricity at the head of the striations seems to me to be the most important factor in the production of striations. This concentration of the negative electricity at regular intervals along the discharge may be explained as follows. Consider a stream of negative corpuscles projected from the neighbourhood of the cathode with considerable velocity : they will collide against the molecules of the gas, and thereby lose velocity: if the electric field acting on them is not sufficiently intense to restore the velocity lost by the collisions, the corpuscles will lose velocity as they travel through the gas, thus the corpuscles in the rear will gain on those in front, and therefore the density of the corpuscles and there- fore of the negative electricity will be greater in the front, and by the equation =47p, when X is the electric force. x the distance from the cathode, and p the density of the electricity, the electric force will increase rapidly in conse- quence of this concentration. This increase in the force will increase the velocity of the particles in front. If the increase in velocity is not sufficient to make the corpuscles ionize the gas by collision, the congestion will be relieved by the gradually increasing velocity of the corpuscles in front, and there will be no periodicity either in the density of the electricity or the electric force. If, however, the force in- creases so that the corpuscles produce ions by collision quite a different state of affairs will occur; suppose that when the corpuscles get to a place P, their velocity is sufficient to produce ionization. On the anode side of P positive and negative ions will be produced, the positive ones will crowd towards P, the negative ones will move away from it; the consequence will be that there will be an excess of positive elec- trification on the anode side of P: now positive electrification implies a diminution in the electric force as we move towards the anode, thus the electric force will fall. When it has fallen below the value required for ionization the negative electricity will as before begin to accumulate in the front of the stream, and the electric force will again increase to the value required for ionization when the process will be repeated. We shall in this way get a periodicity in the electric force such as is observed in the striated discharge. Thus on this view the concave side of the bright head of the striation acts as a cathode, the corresponding anode being the convex side of the bright head of the adiacent striation on the anode side. Between these two places we have a complete discharge, forming a unit by the combination of which the whole dis- charge is builtup. The ions which carry the current through Striations in the Electric Discharge. 451 any unit are for the most part manufactured in the units themselves, so that these units will behave, as Goldstein and Spottiswoode and Moulton have observed the striations to behave, as if they were to a considerable extent independent of each other. The effect of pressure on the distance between the striations can easily be understood from this point of view, for the lower the pressure the greater will be the dis- tance which particles projected with high velocity will travel before their velocity isdestroyed. Again, the variations in the electric field are due to the accumulation of electrical charges in the tube. These accumulations may be regarded as elec- trified disks whose cross-section is that of the tube; the distance from the disk at which these forces fall to a certain fraction of their maximum value will depend upon the diameter of the disk ; the larger the diameter the greater this distance, so that when the diameter of the tube is small the fluctuations in the intensity of the electric force will be much more rapid than when it is large, and thus we should expect the striations to be much nearer together in a narrow tube than in a wide one. To explain the variations in the luminosity which accom- pany these fluctuations in the electric field we must consider the variation in the kinetic energy possessed by the positive ions when they recombine. The recombination of ions does not in general seem to be accompanied by luminosity, unless the ions possess a definite amount of kinetic energy. We certainly can have a gas with great electrical conductivity, and in which a large number of ions are recombining without any visible luminosity; it seems as if the ions must have a definite amount of kinetic energy for visible light to be de- veloped on their recombination. Now in the space between two striations the electric field in the part near the cathode side of the bright head of a striation—the dark part—is weak; here the ions have not got the minimum amount of energy requisite fur them to be luminous when they recombine; in the bright part of the striation the electric field is strong, and here the ions get sufficient kinetic energy to enable them to give out light when they combine. If the energy required for an ion to give out visible light is greater for light at the blue end of the spectrum than at the red, we might get blue light at one part of the striation, red at another, an effect often observed when we have a mixture of mercury vapour and hydrogen in the tube; a similar separation of the spectra of the two gases in a striation might also be produced if one of the gases were more easily ionized than the other. I wish to thank my assistant, Mr. Everett, for the assistance he has given me in these investigations. ea LI. On the Lateral Defleaion and Vibration of “Clamped- Directed” Bars. By JouN Morrow, AL.Sc. (Vict.), D. Eng. (L’ pool), Lecturer in Engineering, Armstrong College (Uni- versity of Durham) *. Section I.—Jntroduction and Contents. § 1. THE vibrations of a bar under the terminal conditions which are probably most frequent in engineering practice, appear to have hitherto attracted but little attention. These conditions occur when one end of the bar is clamped, and the other is constrained to retain its original direction. Such conditions may be realized by having two initially parallel bars, CA and DB (fig. 1), each clamped at one end, with the otherwise free ends connected by a rigid bar AB. Figs. 1 and 2 show two distinct ways in which such a ie, 1. D B system inay vibrate. In the former case we have pure lateral vibration, whereas in the latter there is a necessary accompaniment of longitudinal vibrations in each bar. The former case is the more important since in it the frequency of the fundamental type wiil, in general, be the lower. I propose to refer to a bar under the end conditions of fig. 1 as a “ Clamped-Directed ” bar. . Although there exists a considerable literature on the theory of the lateral vibration of thin rods, the practical application of the results is extremely limited. The explanation of this is to be sought, not in any lack of enterprise on the part of * Communicated by the Physical Society : read June 12, 1908. Dejflexion and Vibration of “‘Clamped-Directed”’ Bars. 453 the technologist, but rather in the fact that the problems that have been solved are not necessarily those of which the solutions are most required in practice. § 2. As an important example, in which the terminal conditions here considered occur, one might mention the case of the cylinder of a steam-engine supported on two or more mild steel standards. It will be recognized that the upper ends of the standards must be treated as “ directed.” it is worthy of notice that these terminal conditions are mentioned by Lord Rayleigh in his ‘Theory of Sound’* but that the directed end is at once dismissed from con- sideration with the remark that ‘there are no experimental means by which the contemplated constraint could be realized.” § 3. Notation and End Conditions.— Let y, y:=deflexions at points # and < in the length of the bar; w, [=area and moment of inertia of cross-section, the cross-dimensions being supposed small compared with the length ; l=length of bar ; p=density of the material ; E= Young’s Modulus for the material (when there is an axial pull P in the bar, E stands for P/w+ Young’s Modulus) ; t=time, measured from any instant at which y is everywhere zero.; N=number of complete vibrations per second. The symbol y is written for d?y/di? ; and if y, is the in- stantaneous deflexion at some particular point in the length of the bar, we have, for simple harmonic vibrations, ~jly=—iln=F (ay), . 2. where N=hk/27. _ The curve assumed by the elastic central line at any instant 1s given in terms of y;. If a is the amplitude at the point in the length at which y, is the instantaneous deflexion, the value of y; is given by Mere is we! Why my os Ge) The origin will always be taken at the clamped end. At z= we have, therefore, y=dy/dz=0 ; whilst at the directed * See Rayleigh’s ‘Sound,’ vol. i. p. 259, 1894 edition. 454 Dr. J. Morrow on the Lateral Deflexion and end, 2=l, dy/dz=0, and, if there be no concentrated load there, d’y/dz?=0. Section [].— Unloaded Massive Bar. § 4. In the ordinary case of a bar vibrating under the effect of its own mass only, the form of the elastic central line and the frequency of the lateral vibrations are to be determined from the well-known equation d*2 ; das = KY; in which ete OI El Yi é and of which the general solution is y=Asin pet+B cos we+C sinh px + D cosh pa. The end conditions give four equations whose compatibility requires that tan l= — tanh pl, ia of which the least root is pl=2°360902 22 oa Vee Sr The frequency of the fundamental is therefore cos..../ fol 2a pawl? § 5. It can be shown that the values of 0 satisfying e0s.@ cosh 0=1,'.") .° . a are the same as those which satisfy N= @ red te = — od where f= (5 Nie whence . G22 = 1p 1 PP and 4 HI P ae tll ie aug) La peed is ft =(2) ont a3 ee upon (15) Section [IV.—WMassive Bar, Load at Directed End. § 13. When a massive clamped-directed bar carries a load concentrated at its directed end, the frequency and type of lateral vibration can be found to any required degree of accuracy by the method of continuous approximation *. Fig. 4. Fie ss 2. In figure 4, let the origin be at the clamped end and * See Phil. Mag., July 1905, pp. 113-125, and March 1906, pp. 354-3874. Vibration of “Clamped-Directed”’ Bars. 459 assume for the first approximation to the vibration curve y = 44 43(a/l)?—2(x/l)*}, . . » -. (16) which, at the clamped end, satisfies y _ = (; and, at the directed end, y = 21, a ==10): Let m= the mass concentrated at the end, M = the couple required to maintain the direction at that end. Then the ordinary approximate theory leads to ay yi (" . Bl hee yz(e—a)dz—my,(l—x#)+M. (17) Inserting the value of y, from (16) and performing the integrations, Jz ah eee x® pee -Ely = puijs (7557 a" i 120 ? 305) a la? 23 +mij(4-— =), - (18) the constants of integration and the value of M having been determined by the end conditions. This expression is the second approximation to the vibration type, and is often sufficiently accurate. Putting « = / we have KI kh? = —————_—-. . . . . (19) 13 790 Pee + sym § 14. Proceeding to a still closer approximation we can insert in (17) the value of y: given by (18) and again integrate. In the resulting expression for y, we can again put #=l and get 0! | Sale e fr 3832 pwlt+m\ 13 js Pee tie His) ee ‘3714 pol+m 420°" + iz The portion shown in brackets is the correction which this result gives to that first obtained. When the mass of the load is equal to that of the bar, (20) reduces to = 8°730 EI yal 460 Dr. J. Morrow on the Lateral Dejlexion and Section V.—Loaded Bars; Mass of Bar Neglected. § 15. When the mass of the bar is neglected and vibrations occur under the action of a concentrated load only, the exact solutions can be determined directly. If there be no longitudinal force and the mass m be at the directed end, the equation of equilibrium is Bes = —miy,(l—a«) —M. Ely = —my,(dle? — 42’), 12 El —a a ee oueue ° . ° ° e ° (21) § 18. Longitudinal Thrust.—If in addition to the load m there be a longitudinal thrust T acting on the massless bar as represented in figure 9, and k? BT SY = — mj, (l—2) + T(1—y)—M. Fig. 5. 7 ; — us d By virtue of the conditions that atz=0, y= = 0, and, at « = 1, - = 0, the solution may be written my COS nl—1 : Te LA AN Barc a @! —cos NX) +nv— sin na } tN ga sin nl in which n? = T/EI ; and putting # = 1, Ae nl sin nl 2 (22) This result might have been deduced from that for a bar clamped at each end with a load at the centre~. ~ ml 2—2 cos nl—nl sin nl” * Phil, Mag. September 1906, p. 243. Vibration of “Clamped-Directed” Bars. 461 Equation (22) shows that £? = 0 and vibration ceases when nl = v7, that is, when P=] hi /l. After expansion, (22) becomes e= ae (1-5 ee ee _ ml agreeing with (21) when T, and therefore x, is zero. When nl = 2im (i being an integer) the right-hand side of (22) is indeterminate but has the limit —T/ml, vibration being impossible if T is positive. | § 17. The result may also be written T tnl ~ mi tan 4 nl—+ nl’ from which (nl being positive) the expression for the frequency is real when tan 4nl>4 nl, that is, for values of nl between 0 and wz, and for decreasing intervals in the neighbourhood of Sar, ar, oc. : vibration alw ays ceasing when nl =(272—1)z. The first of these intervals is from nl=8-9868 ... to nl= 37, and this corresponds to the first harmonic. With the massless bar harmonics are impossible with low values of T. As T is increased the frequency falls, becoming zero when nl=7,'y being then zero. Between + and 89868 vibration is impossible, “the deflexion increasing with the time. If this region be safely passed that between 8°9868 and 37 is reached, during which vibration may again occur, T being now sufficient to enable the bar to assume the curve of the first harmonic type. Fig. 6, > —77y, § 18. If the mass be situated at any point in the length, let it divide the bar into segments a and 8, as indicated in fig. 6. Then for 2a the equation is My BIS =Ty,—/) —M, and the solution y'=A, sin nv + B, cos ne eee where the dashed symbols refer to values of y in the region b. The conditions at z=0 and w=1 lead cep ee to y= —sin not (Spt at =e sn)( 008 NL — 1) +78 mya, M (23) Mi fo. : Ya 7 (sin nl sin nv + cos nl cos ne )+y — 7 The conditions of continuity of y and - when #=a give an expression for the couple at the directed end, namely Putting w=a in the expressions for y and 7 we find ~~ = = { sin na(2—cos na) — cot nl(1—cos na)?—na . (24) When a=, this reduces to the result of § 16. It can be shown, from equations (23), that the amplitude is a maximum at the directed end. Section VI.— Deduction of the Results of some Statocal Problems. § 19. The calculations in Section V. are similar to those required for the corresponding statical problems. Thus if a clamped-directed bar be subjected to a force W at and per- pendicular to the directed end, the centre-line assumes the form (see § 15) y= ag! xv eae 3) Vibration of “Clamped-Directed” Bars. 463 Similar transformations may be made in $§ 16 and 18, and important results obtained. In each case the maximum defiexion is at the directed end. When the bar is subjected to a force w per unit length acting normally to the «-axis, its deflexion curve is y= ni =P. - la? + ae). We notice that, for a force concentrated at the end, the maximum deflexion of a clamped-directed bar is one-quarter of that for a clamped-free bar; whilst when the force is uniformly distributed the ratio is one-third. Section VII.—Some Experimental Results. § 20. The experiments described in this section were made merely to compare, in a few cases, the frequency calculated by the methods given in this paper with that obtained by direct observation. Care was taken that the accuracy should reach certain limits. The composite beams used for the experiments consisted of two flat wrought-iron bars, each 3°00 cms. broad by 0°315 cm. thick, the latter dimension being in the plane of Fig. 7. i) aT vibration. The bars were rigidly connected together at their ends by being securely screwed to massive cast-iron blocks, as shown in fig. 7. The effective length was measured between the blocks, and this, as well as the distance between the bars, was varied. A striking feature of the apparatus is the certainty with which the end conditions can be relied upon. When this is: the case, the distance between the bars is immaterial ; some of the experiments may, in this respect, be taken as a veri- fication of the absolute rigidity of the ends. § 21. The flexural rigidity of a piece of one of the bars was determined by supporting it on knife-edges at each end of a span of 58:42 ems. (23 inches), and applying loads at the centre. The observed deflexions are given in the following table. 464 Deflexion and Vibration of “Clamped-Directed”’ Bars. onde, | Dalasion. | Piers OG: eee 627 -047 PARC Ee Ramee 580 048 2 ta ees) WS 532 we SSS. ea Me ee 483 ‘050 Ibe CS, ae 433 “050 “2 itpe Nee col geek eee 483 “048 AAR LR ne 531 049 thy eae heh ee ie “580 049 Og ec rece 629 Average difference per pound -0488 The average deflexion at the centre was thus found to be 0:0488 inch per pound, corresponding to a flexural rigidity of 15°20 x 10° grammes weight-cms.? The value of H here involved is the static modulus, but the difference between it and the kinetic modulus would be too small to affect the calculations. § 22. The results of the experiments on the compound bars are given in the following table. In each case vibrations took place in a horizontal plane, that is, in the plane of fig. 7. The clamped end was very securely bolted to a large lathe-bed in such a manner as to leave no room for doubt as to the applicability of the terminal conditions at that end. Wo! df iii eee ee se Observed: | Galeuiaeeal Experiment. ey % gone we et eG Frequency.| Frequency. a aes eos” | ies | ee aay aa 1143 780 16°5 1°66 1:67 Bitduine. ts ahh 91:5 1604 165 1-78 178 ce eany ei en 91°5 780 16°5 2°40 2°40 Bek. a oe 114°3 1604 6:0 1°26 1:26 Od apoemeess 1143 802 6:0 1-65 1°65 The last column is calculated from equation (20); the values are, however, practically identical with those given Electric Discharge through Gases HCl, HBr, § HI. 465 by (19). It will be seen that the agreement between the observed and calculated frequencies is very satisfactory. I should like to take this opportunity of making a shght correction in my paper “On the Lateral Vibration of Bars subjected to Forces in the Direction of their Axes.” On page 236 of the Philosophical Magazine for September 1906, and on page 227 of the Proceedings of the Physical Society, vol. xx., instead of tanh¢@ I have used its reciprocal. The error makes very little difference to the final equation. the correct expression being = Diego gi 67 yy pol owl? oe KI: Armstrong College. January 1908. LIV. On the Electric Discharge through the Gases HCl, HBr, and HI. By L. Vecarp, Universitets stipendiat of Christiania University *. (Plate XIV. } § 1. [* some recent experiments made by Matthies + on the discharge through the vapours of HgCl, HgBr, Hel, as well as through the elements Cl,, Bro, and I, some very striking results are found regarding the potential gradient in the positive column. When compared for equal currents and pressures the gradients are found to be greatest for Br and smallest in the case of I. This remarkable result led me, at the suggestion of Sir J. J. Thomson, to undertake an investigation of the distribution of potential in the gases HCl, HBr, and HI. As the properties of discharge depend on the form and size of the tube, it is difficult to reduce the numbers to universal units. In order therefore to compare our results with those found for other gases, measurements have been made with the same tube for oxygen. Apparatus and Mode of Procedure. § 2. Fig. 1 gives the general arrangement of the tube- system. The air could be pumped out with a mercury- pump and the vacuum tested with a McLeod gauge. The chemically active gases were removed by blowing a current * Communicated by Sir J. J. Thomson. + W. Matthies, Ann. d. Phys. xvii. p. 675 (1905); id., cb¢d. xviii. p. 473 (1905). 466 Mr. L. Vegard on the Electric Discharge of air through the tube system from e to D (fig. 1). The gas was introduced into the discharge-tube (A) by means of two taps (b) and (c) separated by a capillary tube. The U-tube C containing concentrated sulphuric acid (sp. g. 1°84) served for measuring the pressure. The level difference was read - with a cathetometer ; in that way the pressure could be found with an accuracy of ;},5 mm. He. § 3. The gases were produced in somewhat different ways ; in all cases, however, a method was employed allowing the gases to be formed in an exhausted vessel. The HCl gas was produced from NH,Cl and concentrated H,SO, in the apparatus shown in fig. 1 (H). The somewhat Big: To the gauge To the pump aw ) a glass wool b 4 \ , ite AL _— | & Y ) A ! EO; | | : | f ° wide tube contains the ammonium salt, the small bulb the acid. Before exhausting, the acid was made to fill the boring of the tap. The HBr and HI gases were produced from their Fig. 2. concentrated aqueous solutions in an apparatus shown in fig. 2.. The air from the boring of the tap gy was removed through the Gases HCl, HBr, and HI. A67 by sealing the tube i and evacuating. Then the acid was introduced into the bulb 7. The gas given off by the liquid had to pass through the tube é containing a number of layers of glass wool and phosphorus pentoxide, and finally a plug of phosphorus. Thus water-vapour and traces of bromine and iodine vapours were removed from the gas. The discharge-tube was similar in form to that used by Matthies, the chief difference being that the electrodes con- sisted of elliptical-shaped platinum plates fixed to platinum rods (fig. 3), while he used thick platinum rods. The dis- tribution of potential was measured with fixed explorers of platinum surrounded with narrow glass tubes. The tube had the following dimensions :— Distance betsveen electrodes and Area of | Diam. of the | Area of | explorers. 5 | Anode the tube. Cathode | ” F surface. | SUTACe | =e / ) ) A—l. A—2. A—3. A—4. A—5. A—K. ————————— Oe Oe Oo CO | | mm. mm. | mm, mm. /} mm. | mm. oo cm. | o2em.*| l’3em2| 31 | 253 | 46-1 | 67D | 8i-2 | 91°6 The potential for producing the discharge was taken from a number of storage-cells, the potential of which was measured before and after each series of measurements. The arrangement for current and P.D. measurements is shown in fig. 3. The P.D.’s were measured with a quadrant electrometer (Dolezalek type). This instrument being too sensitive for the purpose, the following way of measuring was used:—The anode and the positive end of the battery being connected through a very small resistance had the same potential. To measure the P.D., say between the anode and the explorer (4), the latter is put in connexion with the terminal leading to the electrometer and the other electrometer terminal is connected to the wire (d) coming from the battery. By taking out a suitable voltage from the battery the P.D. (A—4) can be so balanced that the electrometer gives a suitable deflexion. Wires from the electrodes and explorers were connected to a set of mercury cups cut in a piece of paraffin wax and placed on the periphery of a circle, so that by the key d they can easily be put in connexion with the electrometer. 468 Mr. L. Vegard on the Electric Discharge The current was measured with a d’Arsonval galvanometer (G) put as a shunt to the head circuit. In order to vary the Besliz | d+ Hin, ELUATE current and in order to keep it constant during the discharge, a series of high resistances had to be used. The resistances used consisted of a number of U-shaped glass tubes filled with a solution of cadmium iodide in amy] alcohol (fig. 3, R), and with resistances varying from about 4 to 30 megohm. The large resistances (7), 72) were put into the electro- meter connexions to avoid any short circuit through the electrometer. The whole system was insulated, only at one point the circuit was put to earth through a very big resistance so as to fix the zero point of the potential ; for if the explorers require some time to take up the surrounding potential, fluctuations in the absolute value of the potential in the circuit might cause unsteadiness and faults in the deter- mination of the P.D. through the Gases HCl, HBr, and HI. 469 Results of Measurements. . Measurements were made for a series of pressures ae ing from about 0°25 to 2-4 mm. Hg, and for each pressure the distribution of potential was “measured for a series of currents. In general the same voltage from the cells was used for measurements at the same pressure; the current was changed by changing the resistance. The discharges to be compared for different gases must have the same structure, and for comparison of the po- tential gradients of the positive column the latter must be uniform. It is found that for the greatest part of the current interval that gives a uniform discharge the electric force is very nearly constant all along the positive column. For very small currents it is found (especially for HCl, HBr, and O,) that the P.D. curve is slightly curved, and in such a way that the electric force increases towards the anode. This is in agreement with results found by Matthies for discharge through vapours of HeCl, HgBr, and Hel. Fig. 4 (Pl. XIV.) gives some > P.D. curves for HBr at pressure of 0°55 mm., showing the general character of these curves for varying currents. In the case of this variation in the force we shall for the comparison use the average force, which in our case can be put equal to the potential-difference between the explorers (1) and (4) divided by their distances. Discharge through HCl. § 5. The general character of the discharge aad HCl is the same as for an ordinary gas. hres forms of discharge have been observed, the uniform, the striated, and one form which is got when the positive column is driven into the anode and which we shall call the dark discharge. Some results of the measurements of potential distribution in HCl made with the tube described are given in the following table :— Gm is the mean P.G. (potentiai gradient). U means uniform discharge. S, striated discharge. D, dark discharge. 470 Mr. L. Vegard on the Electric Discharge TaBLe I. Ci. p. |10°I.; Gm. | A—1.| A—2.| A—3.i) A—4. | A—5. |A—K. | Type. mm. | am. | volt/em.!| volt volt ; volt | volt | volt | volt. j 0:30] 35°5 80 | 242 300 | 309 | 243 | 542! U ——— ee ee 27.0) +) 41-6.) 39 || 128 | 175 | 307 | 380i)! “eso O43 Msi Mads) | 86 |) 73. 102+) 127- ase “Gee os | Ott] 408 | 98 | 207 | 285 | 861 | 492 | 755) U |126 | 498 | 56 | 177 | 273 | 877 | 396 | S04] .. | 90). "| 202 | 84 | 104°.| 159. |. 165.) 172.1) eae ie 0-60 —_—-- ——_- P25) 98 ||'45. | 80.) 95.) 105 J 174) ae ee vg | P15] 750. | 129 | 367 | 538 | 618 | 704 | 1024) U 358 | 93:0 \ 63 | 287 | 477 | 666 | 804 | 1171 | ,, | | | For the uniform discharge is given the distribution corre- sponding to the biggest and smallest currents which for each pressure are observed tor this form of discharge. On the Stability of the Different Forms of Discharge. § 6. In order to get the greatest possible current-interval for the uniform discharge we must take care not to begin the discharge with too large a current, but it is advisable to undertake the measurements in the order of increasing currents and begin with the lowest that can be made to pass. When the current becomes somewhat large the uniform type will be unstable. Striations set in generally accom- panied by a rapid increase in the current, which means a fall in the potential-ditference between the electrodes. For very small pressures the change sometimes takes place with diminution of current. This is due to an increase in the cathode fall, which is caused partly by the diminution in pressure that generally accompanies this change at low pressures. Also the striated form becomes unstable for very large currents, the positive column is gradually “ driven into the anode,” leaving the positive column dark behind or rather through the Gases HCl, HBr, and HI. 471 with a feeble green phosphorescent light that seems to radiate from the cathode. The stability of the different forms of discharge depends on pressure and the size of the electrodes. When other circumstances are the same the interval for a uniform dis- charge is greater for a greater pressure. With a tube of exactly the same shape and size, but with electrode-surfaces about 0°4 em.’, it was found that the uniform as well as the striated type for pressures below 1°5 mm. was very unstable. The uniform discharge could be got when fresh gas was introduced or when the tube nad been “ resting” over night ; but if the current was larger than about 2.10—° amp. stria- tions set in, which, however, soon disappeared, and the dark type became stable for nearly all currents ; only for the very smallest currents that could be made to pass was the uniform discharge sometimes obtained. ‘The gradients got with this tube for the different types are given in Table II. TaBLe II. HCl. i | sive eh SPTIG Saulehe Sak p=02. p=0-4. x F6 297-0. P " he = ; ( 2 } | _ | 101 | 026 SM ih gGas, |, ALG. bo R7 1-2 SP BS ; .? | Gm. | 252 04 | 256 | 66 @3 5), 34 23 | ae Gb Olio en ee = 2 U Pe Uy S. D U Be 3 We see from Tables I. and II. that the average P.G. in the positive column is greatest for the uniform and smallest for the dark discharge. Thus when the discharge by applying a large current is made to change type, the change is always accompanied by a fall in the average potential gradient. Reversibility of the Discharge. § 7. As long as the discharge was maintained in the un- striated state the conditions were found to be reversible with regard to current, or the distribution of potential does not depend on the order of operation. Within these limits the tube will possess a certain characteristic curve and the potential gradient is expressible as a function of current. When the discharge in the way described is made to assume the striated or dark type, the cunditions are no longer c < 472 Mr. L. Vegard on the Electric Discharge reversible. In both cases the characteristic curve gets a permanent change and the interval for uniform discharge is reduced to such a degree that generally this type is obtained only for the very smallest currents that can be made to pass. A tube giving a striated or dark column when left to itself has a tendency to recover or to increase the interval of uniform discharge. This will make the characteristic curve change with time. The recovery of a tube brought into the state of dark column was also observed by Skinner for nitrogen. | Fig. 5 (Pl. XIV.) shows how the characteristic curve was changed when the discharge was brought from the uniform to the striated state. The reversibility of the uniform discharge is a very impor- tant point in connexion with the discharge through HCl, for it shows that at least within these limits the conditions for discharge are not altered by the current through it to such an amount as to give any appreciable change in the distribution of potential As a _ possible decomposition necessarily would be accompanied by a change in the character, of discharge the reversibility shows that the medsurel: uniform discharge corresponds to the undecomposed hydrochiorie acid Jas. « geen cece Pisoharge through HBr. § 8. The Inwinosity in the positive column compared for equal currents.was much weaker in HBr than in HCl and showed«« darker blue colour. The discharge could be kept perfectly steady and the interval of stability for the uniform column proved to be much greater than for HCl, and as a matter of fact within the current limits that could be got by using the lowest resistance and largest voltage at hand the striated state was not obtained, and as the measurements in a uniform column were my chief object no further effort was made to obtain possible limits for the uniform discharge. If there was no change of pressure the conditions were found to be reversible with regard to current, which shows that no decomposition took place which was able to cause any appreciable influence on the discharge. In Table III. is given the distribution of potential in HBr for a series of pressures. It contains at each pressure the measurements corresponding to smallest and largest current for which observations are taken. through the Gases HCl, HBr, and HI. 473 TasLe I1].—HBr. pos 101.) Gin. A-1. A—2. A—3. A—+. A—5. A—K. : | mm. am. | volt/em. | ) | | Pep yan!t OBB SO ales || 120 | 202 | 218 | 254} 691 [> 94 | 24 || 53 | 125 | 177 | 208] 236] sa9 pe 066. 40 68 | 175 | 283.| 327| 355 |- 650 whoa ae cee” 45 | 125 | 173 | 229| 248] 845 | ons 985} SL | 126 | 351 | 409 | 457 | 491 | 809 | “re ” 195 52 || 48 | 177 | 275 | 387} 458 | 983 | 193° | 65 | let | 389 | 482 S74) 676) 997 | "1433 | 89 || 80 | 282 | 451 | 655| 771 | 1154 | sez | 12 | 138 200 | 523 | 857 | 1090 | 1273 | 1580 | “~ 592 | 146 || 124 | 486 | 7 S6 | 746 | 1068 1239 | 1591 | Discharge through HI. § 9. For very small currents the discharge through HI could be kept fairly constant, and gave under these conditions an unstriated column with feeble blue light. With decrease of resistance the larger current would not keep constant, but increased gradually, the pressure diminished considerably, and the discharge became striated. The potential distribution for different pressures is given in Table IV. TABLE IV.—H1. mm. | am. volt/em. ‘ 051 | 018 64 141 306 = 431 551 6E3 | 980 ; : ’ 054) 033) 84 | 187 | 357 | 485 680 825 1030 | 065 | 095) 91 176 473 «634 = 762, 880 | 1203 | 109 | 062 136 | 166 | 522 | 813 | 1044 | 1230 | 1520 | | | 1:16 | 062) 154 | 162 581 | 906 1157. 1390 16¢0 | ; The Potential Gradients. § 10. For HCl and HBr, where the conditions within the intervals of uniform discharge were reversible, the potential Phil. Mag. 8. 6. Vol. 18. No. 106. Oct.1909. 2K 474 Mr. L. Vegard on the Electric Discharge gradient for each pressure is a function of current. These relations are represented in figs. 6 and 7, and show that except for very small currents the variation of P.G. obeys | Herz’s law, and especially in such a way that the P.G. is very nearly independent of current. The relation between P.G. and pressure for currents of about 0°8.10-° am. is given in fig. 8. For pressures less than 0:3 mm. there is a peculiar difference between the curves for HCl and HBr. The P.G. for HBr falls rapidly %wik diminution of pressure while for HCl it keeps nearly constant. We see that at least for pressures above 0°25 mm. the potential gradients of HCl, HBr, and HI follow in the same order as the molecular weights of the gases, when compared for equal pressures. The value of the P.G. for oxygen is between that of HCl and HBr and nearest to the latter. Table V. gives the P.G. for the four gases for a series of pressures, Asus V—10°l = eaves: | yp. HCl. HBr. HI. One mm, volt/cem. volt/em. | volt/em. volt‘em. | 0-4 36 415 70 40a 0-7 41 57 98 53 Le EO al 68 130 64 | 14 67 86 182 82 | 18 85 106 he eal 2-2 104 127 The results got with respect to the potential gradients for HCl, HBr, and HI as far as the I compound is concerned is contrary to those found by Matthies for the similarly con- stituted gases. Further measurements with the halogen elements and their mercury compounds would be desirable to find the cause of this discrepancy. In these experiments special attention ought to be paid to the structure of the discharge, for the possibility is not excluded that the small P.G.’s for the iodine compounds may be due to a striated structure, and the fact that the tube had to be surrounded with an electrical oven may have made an examination of the discharge difficult. If the values found by Matthies really correspond to a uniform structure it seems natural to seek the cause for the small P.G. in the case of the iodine compounds in some kind through the Gases HCl, HBr, and HI. A75 of secondary process which is most marked in the iodine vapours. The great diminution in the P.G. with increase of eurrent which is found by Matthies for the iodine compounds would point to a secondary effect, for if it existed it ought to be more marked for larger currents. Then to make the secondary effect the least possible it would be advisable to make the comparison for very small currents, as actually has been done for HCl, HBr, and HI. The Cathode Fall. § 11. The normal cathode fall corresponding to a partly covered cathode is determined in a number of measurements for different pressures and currents. As the mean of the observed values we get : Por BO 4 2: 329°6 volts platinum electrodes. fiat yy ouuso 5, " 3 aso pe ee ato), 3 + Fig. 9 gives the cathode fall above the state of saturation of the cathode for the tube described. We notice the charac- teristic difference between the curves for high and low pressures. The horizontal line gives the normal cathode fall, and where the curves cut this line we have the biggest current that gives the normal cathode fall for the tube and pressure considered. The relation between saturation current and pressure is shown in Pl. XIV. fig. 10. These curves cut the p axis, and for all three gases at the same point. Thus for each gas there is a certain pressure, below which no current that can be made to pass can give the normal cathode fall, and which is the same for the three gases. This result suggests that for the same tube the minimum pressure for a normal cathode fall is independent of the nature of the gas. For the tube used the minimum pressure = 0°25 mm. The Anode Fall. § 12. To get a strict definition of the anode fall we shall let the P.D. curves (see Pl. XIV. fig. 4) continue in their direction past the explorer (1) and their points of intersection with the vertical axis through the anode will give the anode fall. In order to find the influence of current and pressure on the anode fall other conditions must be unaltered. Thus the discharge must be reversible, which in our case requires a uniform structure. Further, the tube must be run for some time in the gas to be tested before any measurements are taken. It is found that the anode fall when a new gas is introduced will begin witha too large value. This is probably due to changes in the surface-conditions of the electrodes, for 2K 2 476 when constant conditions are reached they are not changed by introduction of a new portion of the same gas. The anode fall (A) for HCl and HBr, found under the conditions stated above, is given in Table VI. for a series of different currents and pressures. Mr. L. Vegard on the Electric Discharge TaBLeE VI. HCl. | HBi p=O0 p=03:). p= 1:6. | p=027. |. p=0'50. 1 p=103, pee 10°1.| A. |105I.; A 10°L. AL gO? To) An ROPE aes 101. | vie | 10°T. A. 05|58 | O41) 81 | 1:2) 96 | 0-65) 56 0°85 94 065 125 | 0°88! 169 33/52 115 | 60/13/95, 22/51 | 98 | 64) 22/105! 1:9 | 157 | | 79|36 | 23 | 60 | 4:4 83 GO 48.) 76°99) GOe MEE O 70 4:0 | 120 15:8|30°5| 66 | 50 | 9:8) 62 1156 | 39 |20-2 | 44 |276 58/126] 80 22 |98:512-6 | 41 [358/36 24:0 | 37/95 | 95143 | 51/54 | 71 The anode fall can be expressed by either of the two functions : (1) (2) -K[ Agta,p-4-p(dg—bp)e-™, 1 I a Bo p(% + ae **) Within the pressure limits of my experiments both equations satisfy equally well the observations: it is first for higher pressures that the difference would be significant. The constants of the two functions for HCl and HBr are given in the table. A a Ayt+ Tasue VII. Eguation 1. Equation 2. | | HCl. HED. | . HCl. HBr. | Ay «..| 23° 85 Bia | Ay 23° 85:0 Pa NM 2360 wo loca I 17-3 ae ahbvord, 562 pavvliatey Vy | 2, 61-2 110 | ae 12 28 |g 420 | 250 | Mehl ah 11x10 19x10! |’ 11x 10+ 2:0 x 104 | through the Gases HCl, HBr, and HI. ATT The observations are represented in figs. 11 and 12 (PI. XIV.). The curves are determined from equation (1), and we see that they fit in with the observed values to a degree that is almost astonishing when the character of the pheno- menon is taken into consideration. Among the properties of the anode fall expressed in the two formule we shall notice the following two: 1. By diminution of pressure the anode fall approaches a minimum value (Ao) independent of current. 2. For somewhat large currents (when « is not too small) the anode fall will be nearly independent of current and follow a linear law with regard to pressure. Absorption of Gas during the Discharge. § 13. It is a weil-known phenomenon that gas is absorbed in a vacuum-tube when a discharge is made to pass through it. Itis a common phenomenon in Réntgen tubes where it causes the hardening of the rays with age. Considerable quantities can be absorbed in this way: thus J. J. Thomson* observed that several cubic cm. of gas at atmospheric pressure were absorbed without indication of any diminution of the absorbing-power. The absorption has been studied by Riecke and Skinner, and more systematic experiments made by Willows f. In the course of my experiments I have had the oppor- tunity of examining the absorption for HCl, HBr, and O, under conditions of various pressures and currents, and at the same time been able to make comparisons with the distri- bution of potential. In this way I have met with some characteristic properties of absorption, which I think will throw some light on these phenomena that up to the present have been very little understood. Before describing the observations it is good to make clear the following conceptions :— (1) Velocity of absorption (w) equal to number of cm.’ absorbed per se0.= ah oP (V=volume of tube). For the tube used p=081 Se, ¢ (2) The quantity (q) absorbed when 1 coulomb has passed My Pa |.’ through is equal to l760Ai7 1 * J. J. Thomson, ‘Conduction of Electricity through Gases,’ p. 552. + R.S. Willows, Phil. Mag. [6] i. pp. 503-517 (1901). 478 Mr. L. Vegard on the Electric Discharge Absorption in Oxygen. § 14. As long as the pressure is fairly high the absorption ts extremely small even for very large currents.—A current of 157.10-° am. with a pressure so low as 0°8 mm. gave g=0°006. With a pressure of 0°56 mm. and a current of 116.10-° am. the discharge could no longer be kept constant. Current and pressure decreased rapidly, until after 25 min. the current had fallen to 0°38.10-° and the pressure di- minished to 0°13 mm. The average current in the interval was 42°5 .10-® am., which gives the average value of g=0°21, or more than thirty times as large as the value at the some- what higher pressure. The rapid absorption set in with a cathode fall of about 650 volts... Another experiment was tried with a pressure 0:27 mm., but in this case the discharge was commenced with small currents. In spite of the smaller pressure it was found that jor currents below a certain value the discharge could be kept constant and the absorption was inappreciable. Currents from 0°5.107> to 14.10-'% am. were allowed to pass for about 15 min. each, but no panes in pressure was observ- able ; with a current of 40.10-® the pressure and current began to decrease. The variation of the properties of dis- charge during the “running down” of the tube is given in Table VIII., and the variation of current, pressure, and gq is represented in fig. 13. TasBLe VIII. | Time. 10°I. Dp. Gm. | are L- Pee: 0 40 027 | 140 | 640° | | 25 | 395 | 0-26 i 660 | 46.10-5, 0-10 5 385 | 0-22 |, 800), eet) a ne 8 35 | O16 4s a (onset 12 12) 24] .40u1d BUS dient a 31s) iy ze 18 Sie wOtet | 3. || 12205 eee, eee 23 27 | 0088 | ... | 1260 °| O64,, | O94 29 20 | 0075 | 10 | 1265 | 056, | 0-28 We see that the quantity (7) shows a very simple variation in spite of the rather complicated manner in which current and pressure vary. The value of g increases to a maximum value, after which it keeps constant, and the maximum value is of the order of the electrochemical equivalent. through the Gases HCl, HBr, and HI. 479 Absorption in HBr. § 15. The characteristic abrupt occurrence of the absorp- tion found for oxygen is also observed for HBr. With a pressure of 0°55 mm., currents up to 95.10~° gave very little absorption, the value of q for the largest current being only 0°05. For higher pressure the absorption was still less. For a pressure of 0°27 and currents up to 20. 10-° the absorption was almost inappreciable. A current of 24.10~° gave g=0°015; raising it to 34.10-%, however, a sudden absorption took place. The properties of discharge varied as shown in Table IX. TABLE IX. C WE | ees | ie |p. yar aa | a ere 650 40 | 67 0-158 At 22 0:55 0-148 880 | The mean value of I in the time interval is 4°7.10-5 am.,, which gives for g the average value 0:48, or about double the value found for oxygen. Absorption in HCI. § 16. The absorption effect observed for O, and HBr has also been found for HCl; but in those cases examined the effect has not been so abrupt. With a pressure so low as 0-46 the discharge was maintained with currents of 16 . 10-° and 22 .10-* am. each for about a quarter of an hour without noticeable absorption ; but with a current of 98.10-* the absorption became very marked, the current decreased, and within 14 min. the pressure went down from 0:460 to 0°350 mm., the absorption per coulomb g=0°052. With pressure 0°27 a current of 29.10-° gave considerable ab- sorption. As regards the interpretation of this somewhat smaller absorption effect in HCl we must keep in mind that there is always a possibility for a contra-effect in the evolu- tion of hydrogen from the cathode. Concerning the Cause of the Absorption. § 17. A very important property of this kind of absorp- tion is that it is always found to stop immediately the 480 Mr. L. Vegard on the Electric Discharge discharge is broken. ‘This fact makes it very improbable that the absorption can be due to any secondary effects, but leads us to find the cause in some property of the discharge itself. The peculiar abruptness in the occurrence of the absorption, as well with regard to current as pressure, must show that the absorption is not a necessary accompaniment to the discharge, but sets in when peculiar conditions occur. We have seen that the great absorption is always accom- panied with a large cathode fall, and if we suppose that the absorption per coulomb (qg) is mainly a function of the cathode fall, and suppose further that this function has the character that it increases very abruptly when the cathode fall is raised above a certain value, then the character of the absorption phenomenon will be immediately under- stood. This will be apparent by looking at the curves (fig. 9), giving the variation of the cathode fall. For some- what high pressures the cathode fall after “ saturation ” increases very slowly with increase of current, reaches a maximum value andifalls again. If, now, the cathode fall for which the great absorption sets in is greater than this maximum value, the large absorption cannot be got at all for that pressure even for very large currents. First, when the pressure becomes somewhat low there will be a current for which the cathode fall is big enough to produce the great absorption. Our assumption also explains the fact that even for the same pressure the absorption first sets in for a certain strength of current. The cathode fall, for which the great absorption sets in, we might call the critical cathode fall. The value of this may depend on the quality and form of the electrodes and the quality of the gas, and it may also be somewhat different at different pressures. For O, and HBr with the tube used it is about 650 volts. ; The rapid absorption with diminution of pressure is also observed by Willows for air, nitrogen, and hydrogen ; but he comes to the conclusion that the absorption is due to a chemical combination between the gas and the walls of the tube. Such a chemical combination seems a priori very un- likely ; for it would mean that the discharge in a mysterious way imparted to the walls a chemical activity which should only be possessed by the walls as long as the discharge was running, Another objection to Willows’s explanation, which he also mentions himself, is that the absorption seems not to depend essentially on the chemical character of the gas, but is found even for inert gases. through the Gases HCl, HBr, and HI. 481 The only experiment which in the case of ordinary dis- charge should indicate an influence of the substance of the tube, i is that a tube of lead-glass under equal conditions gave 10 per cent. less absorption than a similar one of soda-glass. But this may equally well be explained by differences in the size of the cathode surfaces. Silvering the inside, but keeping electrodes unaltered, gave no change in absorption. Some of his experiments, for which he has not been able to give any satisfactory explanation, are easily explained by the assumed connexion between cathode fall and absor ption. With a tube where one electrode was a small rod, the other a cylindrical vessel surrounding the first one, the ab- sorption for the current used (108. 10-5) was exceedingly small when the cylinder was made a cathode, but had the usual large value when it was made an anode. This is immediately explained by the difference that must exist between the cathode falls for the two directions. Another experiment (loc. cit. fig. 7), where he also used electrodes of different size, is explained 3 in the same way. In an experi- ment where there was dissymmetry with regard to tube, but symmetry as regards electrodes, a reversion of current pro- duced no change ; in absorption. From this it seems beyond doubt that the cathode fall is the essential property for the absorption. The next question will be in what way the cathode fall is able to produce absorption. The assumption that almost forces itself upon us is that the absorption is carried out by the ions which by the large cathode fall are given such velocities as to be shot as it were into the solid matter. This is in agreement with the fact that the maximum absorption is of the same order as the electrochemical equivalent. From the view we have at present as to the mechanism of the discharge, it is further most likely that the greatest absorption effect is produced by the positive ions falling into the cathode. We must remember that the essential ‘thing is not that the ions acquire a certain velocity, but that they have it the moment they strike the solid matter. Vow the positive ions get their maximum velocity just when they strike the cathode. The negative electricity will within the space of the cathode fall mostly exist as corpuscles. Some of these may pass through the gas without collision, in which case they can produce no absorption, some will stick to molecules and communicate to them their kinetic ener gy acquired at the cathode fall ; but these molecules may now make collisions, and thus gradually lose kinetic energy. Thus it should at least only be a small fraction of the negative 482 Electric Discharye through Gases HCl, HBr, & HI. ions that would meet the walls or anode with the velocity necessary for absorption. ‘This is also in agreement with the experiment that silvering of the inner surface had no effect on absorption. And if the absorption was brought about quite as much by negative as by positive ions, it would be difficult to understand why the potential fall between the electrodes had to be concentrated near the cathode in order to produce absorption. | This hypothesis, that the absorption is caused by the posi- tive ions being shot into the cathode, also explains the rapid increase of absorption when the cathode fall exceeds a certain value, for it only means that a certain velocity is required for ions to be shot into solid matter. | a It is worth noticing that it is in the state of the rapid absorption that the most rapid disintegration of the cathode takes place, which suggests, what from our view seems quite natural, that these two phenomena are closely connected. Summary of Results. (1) The general character of the discharge through HCl, HBr, and HI is the same as for elementary gases. (2) In HCl and HBr the discharge could be kept constant and with a uniform structure within wide current intervals ; the conditions were “‘reversible.” For HI a constant dis- charge could only be got for very small currents. (3) Within the interval of reversibility the decomposition is too small to effect the discharge. (4) The characteristic curve depends on the “ history ” of the tube, and a change in structure caused by current is always accompanied by a fall in the P.G. in the positive column. (5) Under comparable conditions the potential gradients | in HCl, HBr, HI follow the order of the molecular weights. (6) The variations of P.G. with current for HCl and HBr follow Herz’s law except for very small currents. (7) The normal cathode fall is found for HCl and HBr ; the smallest pressure that can give a normal cathode fall is the same for O,, HCl, and HBr. (8) The anode fall in the interval of observation is found to be expressible by either of the two functions : A=Aytaptpae—bpje™, 1 a I BO p(a, +a e—*7) The Decay of Waves in a Canal. 483 (9) The * electric absorption ” of gas is found to be closely connected with the size of the cathode fall, which leads to the assumption that the absorption is chiefly caused by positive ions being shot into the cathode. In conclusion, I wish to thank Sir J. J. Thomson for suggesting the work to me. T “have also much pleasure in thanking Mr. E. Everett for his assistance with some of the glassw ork. Cavendish Laboratory, May Ist, 1909. LV. The Decay of Waves ina Canal. ByW.J. Harrison, B.A., Fellow of Clare College, Isaac Newton Student in the University of Cambridge ™. §1. ‘a a paper published recently Dr. R. A. Houstoun gave the results of some experiments on the damping of long waves inarectangulartrough f. The observed damping is from two to three times as great as that calculated from the formulaobtained by him. In this paper an explanation of the discrepancy is attempted. It has been shown by the present author that under certain circumstances the air exerts a great damping influence on water wavest. It may be as well to emphasize here the cause of this influence, as it might appear strange that a fluid of such slight density as air coald attect the decay of water waves. The modulus of decay 7 of wave-motion at the surface of a single fluid of depth large compared with the wave-length X of the motion depends on d? ; when there is another fluid superposed 7 depends on r ; and thus when 2 is large the difference is considerable, despite the small density of air. Now the waves considered by Dr. Houstoun in his paper are of long wave-length, and it was supposed that the air might have some considerable effect. Butit might have been surmised « priori that this would not be the case, as the effect of the finite depth is itself to produce a first approximation of the order 4.00 obtaining the analytical expression for the damping due to the air, there was found to be not the slightest ground for supposing that we have here the explanation ‘of the discrepancy. Although a consideration of the influence of the air is of no use in our present investigation, the expressions for the ; Communicated by the Author. + Phil. Mag. [6] vol. xvii. pp. 154-164. ¢ Proce. Lond. Math. Sce. ser. 2, vol. vi. p. 396. 484 Mr. W. J. Harrison on the period and modulus of decay will be given below §3, on account of their intrinsic interest, and, also, in order that they may be recorded on account of the possibility of their usefulness in some other problem. It is believed that the real cause of the discrepancy must be looked for along the following lines. Dr. Houstoun in his paper treats of waves of the type sin gv sin ry, the axes of « and y being horizontal, but his analysis is only suitable for waves of the type singa. This is clearly brought into evidence by the fact that he obtains for the period of his waves to a first approximation the expression 2a/{g@h}*, whereas the correct expression is 27/{g(g?+7)h}?, as will be shown later. The same applies to the modulus of decay; he obtains it as a function of g?, whereas it is the same function of (g?+7"). But as will be seen later, this in itself does not wholly explain the discrepancy. It will be shown that we cannot adequately take account of the influence of the sides of the trough in damping the motion. Further discussion will be deferred till the question has been analytically con- sidered. The damping of long waves at the surface of a single liquid. §2. This problem was considered by Hough *, and he phiained an expression for the modulus of decay 7, which is equivalent to rae 2 V2 cosh * ids sinh #kh where v is the kinematical coefficient of viscosity, k=2z/), » being the wave-length, and his the depth of the liquid. The motion under consideration is two-dimensional. The term depending on v in the above expression is not correct ; it should be h? kh + sinh? cAq ie [2 cos | ; ‘ A cosh? kh sinh? kh | This makes an appreciable difference in the case of long waves, since we now have 1 Che ef ae = 42 ote sit J This additional term v/4h? makes a difference of from 6 to 10 per cent. in the theoretical damping of waves such as those * Proc. Lond. Math. Soc. vol. xxvii. p. 276 (1897). = Decay of Waves in a Canal. 485 considered by Dr. Houstoun. This will be seen by comparing the third column in Table II. with the sixth column in the table on page 159 of his paper. } The period equation for this motion is given by Bassett *. For convenience it will be repeated here in the notation of this paper. mecosh mh, — sinh mh, 0. , 2vkma in —m sinh mh, cosh mh, a+ 2k*v, gk —ksinh kh , cosh kh, At eh aie gk keoshkh , —sinhka, ON a) a a eanie where m?=/?+a/v. As regards x and ¢ the motion is of the type et”, In the approximation it is assumed that mA is large, on account of the smallness of v, and with this assumption the equation becomes mi @ cosh kh+gk sinh kh} —k{a? sinh kh + gk cosh kh} + 4)?yma cosh kh = 0. We obtain by successive approximations Cone ca ae fa ge a= +{gktanh kh}Pe- 55, Hees a LIS eh 26/2 cosh? kh sinh? kh Bes See k°v(cosh? £h + sinh? kh) ae 4sinh*? kh ecosh* kh ~ The additional term obtained by this more rigorous method of approximation is negligible compared with 2/2y when the wave-length is small; it has only an appreciable value when the wave-length is large compared with the depth. This is probably the reason why it was omitted from Hough’s approximation. Lhe influence of a superposed fluid on the damping of lon g waves. §3. The results given in this paragraph have little bearing on the problem under consideration for reasons already given, but it may be as well to record the solution of the period equation to a second approximation. * Treatise on Hydrodynamics, vol. ii. p. 314. ASH”. Mr. W. J. Harrison on the The pericd of the motion is 27/(6—y), and the modulus of decay is y~’, where ig.c { gk(p—p') sinh kh i ~ Lp cosh kh+p’ sinh kht ’ fe EO a 2,/2{p cosh kh +p! sinh kh}? sinh? kh(p vv! + p',/v) where Q=p{vv'\? + 20'v cosh? kh + p'(v+v’) sinh kh cosh kh +p! (v'—v) sinh? kh; p and v refer to the lower fluid of depth h; p’ and v' to the superposed fluid. J have calculated the solution to a third approximation, but the result is too complicated to be given here, and the additional effect derived from it is negligible, even when the second approximation gives an appreciable additional ettect. Some idea of the damping due to air can be derived from a comparison of Tables II. and III. Waves in a rectangular canal. §4. There is one difficulty which Dr. Houstoun escapes by his use of long waves ; it is that the lapping at the sides of the box is virtually neglected, since the vertical motion is not considered. If the problem be attacked in the ordinary way, and the usual conditions of no motion at a fixed boundary be written down, it will be found that the equations are only satisfied by a state of no motion everywhere. The same applies to motion in which slipping at the boundary is allowed, but which is resisted by a traction proportional to the velocity. Hence to discuss the problem at all we are forced to adopt the assumption of «a canal with smooth sides. The only alternative is to generalize the method for long waves. Suppose the canal to be of depth h and breadth 6. Take the origin of coordinates in the undisturbed surface at one side, the axis of 2 perpendicular to the side and in the surface, and the axis of y vertically upwards. The equations of motion are Decay of Waves in a Canal. 487 where BL 0 fe fe fe m@ameges oy Oz If we Resell the squares of velocities, these equations are satisfied by 19% , 0H _ 2G Ge oF 02’ _o¢ oF oH hae ave O«: ae: aoe OY’ where ee p = Ot 91> provided vo =0, wl = x Ke and “a Consider 4 NTs. 7. @ = (A, cosh my+ Ag sinh my) cos ares yeah tea ) ace F = (F, cosh m'y-|- F, sinh m'y) sin ae eke + oy = (G, cosh m'y + G, sinh m’y) sin == H = (Hi, cosh m'y + H; sinh m'y) cos" i Te 4 ikztat, where m? = k? + n?7 / i, m?= +n'n?/l? + a/v = m*>+a/v. These are not the most general expressions of the type which might have been written down, but they are the only ones which satisfy the conditions of the problem. 488 Mr. W. J. Harrison on the The conditions are (1) uo w=—0) (y= —A), (2) w=0 je=0, c=)), AO HOU ov Pewee iy) ee (3) 0: are ite: Oz i Oy Ta (<=0, z=b), Ou av Ow Qv = i) ss —_ =0 == ( ) Oy T Oe ? Oy = 2 ( (y 0), fo) Some of these conditions are satisfied identically ; from the remainder we derive the six equations a(a+2vm) Ay+gmA,+9 U+2vm'aV=0, 2ikm Ag +ik U+m! W=0, 2mn1/b Agtn 1/6 U+m' X=0, —m A,sinh mh+m A, cosh mh+U cosh m/h—V sinh m’h=0, ik A, cosh mh—ik Ay sinh mh—W sinh m/h+ Y cosh m’h=09, —nmt/b A, cosh mh+nr/b Ay sinh mk +X sinh mh —Z cosh m'h=0, where U=nmz/b F, —7k Hy, V=enm7/b F,—ik Hy, W =m! H,—nz/b Go, X=m' F,—ik Go, Y=m' H,—n7z/b Gy, L=m! F,—ik G,. Among these six quantities there exist the two relations m U+ikW—n7/b X=0, (7) m V+ik¥— n7/bZ=0. (8) From equations (1) to (8) we eliminate A,, A,, U, V, W, X, Y,"Z, and obtain the period equation. Approximating on the assumption that m/h is large by reason of the smallness of v, we find that, if we replace & by m in the results for waves propagated in one direction, we obtain the corresponding solution for this problem. This (1) (2) (3) (4) (5) (6) Decay of Waves in a Canal. 489 result could doubtless be obtained much more simply by generalizing Dr. Houstoun’s method. But Dr. Houstoun, although he allows no motion over the sides of the box, yet obtains the same period and damping as for waves propagated in one direction. Now, in the case of wave-motion in the alt ore” nner tee rectangular trough which he used, m?= pan Hada for waves of the type sin sin ae, where a=152°4 cms., b=20°3 cms. Hence, for the mode p=1, g=1 which he takes as the fundamental one in his solution, m?=7r°/0?, approximately. This leads to quite different results. The Table below gives the periods of the different modes and for the same depths as given by Dr. Houstoun. TABLE I. Depth Observed | p=1> | p=), pl, p=3, ph. in cms, | period. g=0. | gh g=1 g=1, q=2. | | secs. secs secs. secs secs secs | 1 101 10:25 | 1:328 | 1310 | 1-229 451 | 2 7-12 7-02 938 929 ‘872 345 ; 3 | 580 568 779 771 725 313 ee ae ee 4-39 634 629 596 297 : 7 3°68 371 573 | 569 549 295 | 10 3-12 | 311 | ‘534 | “531 ‘09 294 = | In this table the observed periods are those given on page 159 of Dr. Houstoun’s paper ; it will be noticed that they are slightly different from those on page 161, but the difference is quite immaterial for our purpose. Thus there can be no doubt that in the motion experi- mentally observed by Dr. Houstoun there existed the mode p=1,q=0. The periods of the other modes are so much shorter that they probably passed unnoticed. Now, if there is no slipping at the sides and there are no surfaces of slip in the liquid, this mode cannot enter into the motion. But it is evident from the fact that the water rises * This difference between the quantities in this column and the sum of those in the 3rd and 5th columns on p. 159 of Houstoun’s paper is due partly to the fact that the quantities in the 5th column are sometimes miscalculated. Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 21 490 | The Decay of Waves in a Canal. and falls at the sides that there must be either slipping at the sides, or else there must exist surfaces of slip near the sides in the liquid, most probably both coexist. This fact shows that we have been unable to analyse the motion correctly. The sides must influence the damping of the motion in any actual case, and this has been neglected in the analysis, the sides having been taken as smooth. It will be seen from what has been said above, that-we do not know sufficient about the modes in which the water actually vibrates to say that one predominates to such an extent that the damping calculated for that mode should agree with the observed (cf. page 158 of Dr. Houstoun’s paper). But even if we admit that part of the observed damping may be due to the existence of higher modes of appreciable amplitude, we have only found an explanation in the case of the depths 1, 2, 3cms. The discrepancy is still unexplained for the depths 5, 7, 10 ems., as will be seen from Table IJ. Hence the only rational assumption is that the increase of damping is due to the sides. The existence after a time of a surtace film such as suggested by Dr. Houstoun would only increase the damping over those values tabulated by him (compare data on pages 159 and 160 of his paper). | . Table II. exhibits the reciprocal («) of the modulus of decay for the same cases as Table I. gives the periods. Taste IT. Depth | Observed| p=l, p=0, p=, Do. p=iy in cms. K. GEO th ik g=1. g=1 =e. 1 048 0324 ‘0826 | 0849 0853 1271 2 052 0185 0481 0463 0472 "0521 3 028 0133 0309 0313 "0316 0239 | 5 023 “0090 0165 0168 0163 ‘0075 * 022 0070 "0093 0093 0089 0052 10 ‘O11 0053 0040 0040 0037 0047 With the last row in this table may be compared the values. of « when the damping effect of air is taken into account. These quantities are calculated on the assumption that in the formule in §3, we may replace k by m,as for waves in a single liquid. Some Relations in Capillarity. AQT Tasie Dl. - | 10 | ‘O11 | 0053 | ‘00-42 0042 ‘0039 | 0055 | The quantities in Table Il. seem to exhibit no regular increase or decrease from one column to another, but this is due to the conflict between the decay due to the internal friction and the decay due to the bottom of the trough. Clare College, Cambridge. LVI. Some Relations in Capillarity. By R. D. Kuneman, D.Sc., B.A., Research Student of Emmanuel College, Cambridge, and McKinnon Student of the Royal Society*. Nig potential energy of the surface of a liquid due to the attractions between its molecules has been calculated in general terms by Hinstein. WHinstein’s line of reasoning is as follows. The potential energy of a mass of liquid is first considered. It is assumed that the potential energy of two molecules is given by the expression'P,, —c,co(r) where ar(r) is some function of the distance between the molecules and ¢, and c, are constants depending upon the molecules. For n molecules the second term is replaced by a=? B=n 3 > pa Ca ea W(ra, p)- a=1 B=1 If the molecules are identical this becomes a=n B=n 20% & (ra). oi B=1 It is next assumed that the potential is the same as if the matter were distributed evenly in space. The potential energy may now be written P=P_-4 oN? {| dvdrip (ta, ar) where dz and dr’ are elements of volume occupied by matter and N is the number of molecules in unit volume. If each molecule consists of several atoms, we may put c= Xc, as is * Communicated by the Author. 2L2 a here hs. 4’ ‘ 492 _ Dr. R. D. Kleeman on some usually done in gravitational investigations. ‘hus 2 (ag a lh 2, ek dt, dt! Wr dt; ar’) ? where v denotes the molecular volume. This expression, on transforming the integral to rectangular coordinates, becomes P=P,— ue po ae dx dy dzW(V#+P+2), or, if we denote the integral by « K ee = ie (Sy. Einstein then expresses the potential energy of a liquid of volume V and surfaces 8 as P=P LO v— 5 (Se) 5. . ae where Tj—l ier 0 C= =O =o “= { it { i) (ae. dy, dz dar dy dzwp/ (a—a P+ Ys) + @— =0 Y1=0 271=% I=—-B Y=- BD z=0 The potential energy E per unit surface is the coefficient of S in (1), or I PAG i = (Sica f—— — Ce since v=—, where p is the density and m the molecular weight of the liquid. The potential energy of the surface-film of a liquid is also given by (x- ch **) where 2 is the surface-tension at the tem- perature T. This follows from thermodynamics. When the surface is increased by 1 cm.” the external work done on the film is and the heat absorbed, according to the Helmholtz free-energy equation, to keep the temperature constant, is er and thus the potential energy is increased by | (.-1 Relations zn Capillarity. 493 Consequently, dhs} 1p" r—T or — - (%eq)?. a ee a" pe | . (3) Hinstein then proceeded to find the values of ec, for a number of atoms on the assumption that «’ is a constant, and that (.-T5r) is independent of the temperature. The values of cz for a few atoms were calculated from the physical constants of a large number of compounds involving these atoms. That the values of c. should agree well although the number of compounds whose constants were employed is far larger than the minimum number necessary to obtain c,, would be strong evidence in favour of the validity of the formula and the underlying assumptions. Table I. contains in the third and sixth vertical columns the values of Xe, for a number of substances calculated by means of equation (2). The fourth and seventh vertical columns give the values calculated by substituting the values of ¢, in >¢, from the first column in the table. The values of cq, were obtained from the third and sixth columns by the method of least squares. It will be seen that on the whole the values in the two columns agree fairly well. TaBeE I.* Experi- | Calcu- Hels Experi-| Calcu- Formula a rau | ery ag of liquid. ete cee Q : H=-16/|C,,H,, | 510 524 || C,OHCI, 358 335 C=550 |CO,H, | 140 145 ||C,H;OCl | 462 484 0=468 (C,H,O, 193 1 On 492 495 cl=60 |C,H,O, | 250 249 || Br, 217 304 Br=152 |C,H,O, | 309 301 || C,H,Br 251 254 I=198 | C,H,,0, 365 352 || C,H,Br 311 306 | C,H.0, 350 350 || C,H,Br 311 306 | C,H,,0, 505 501 || C,H;Br 302 309 |C,H,O, | 494 | 520 ||C,H,;Br | 353 | 354 C,H,,0, 553 562 || O.H,,Br 425 410 0,H,,0, 471 454 || O,H.Br 411 474 C,H,O 422 419 || C,H.Br 421 526 O,H,,O | 479 70 || C,H,Br, 345 409 'CsH,,0, | 519 517 ‘|| C,H,Br, 395 461 C;H,0, 345 362 || O,HsI 288 300 C.H,,0 348 305 ‘|| C,H.1 343 352 O,,H,,0 587 574 | O,H1 357 352 C,H.Cl 385 379 || C,H;1 338 355 C,H,Cl 438 434 || 0,H,1 428 403 C,H,Cl 440 434 || O;H,,1 464 455 C,H;OCl | 270 270 * The repetition of a formula indicates an isomeric compound. 494 | ~ Dr. R. D. Kleeman on some The assumption made by Einstein that the potential energy of the surface-film of a liquid is independent of the tempe- rature is, however, not true. The potential energy for different substances over a wide range of temperature has been calculated by Whittaker* from surface-tension values. He finds that the potential energy decreases with increase of: temperature, the decrease being about 20 to 25 per cent. over a range of 100°. If the potential energy E in equation (2) is assumed constant, then x’ cannot be constant, for there is no other quantity in the equation to balance the variations in p as m and cq are from their nature absolute constants. — It is very unlikely then that «' should be a constant. It is now necessary, from the above considerations, to modify Hinstein’s formula. Let us assume that «! in equa- tion (2) is, if not a constant, a function which is the same for all liquids at corresponding states. We shall then com- pare the results of this assumption with experimental results, Integrating the equation, we have ow, SOL (pK A=CT— —, (>0q) y) pe 21, where C is an arbitrary constant. Let us write p=ap, and T= AT, where, as usual, p- and T- denote the critical density and the critical temperature. On substitution we have Ab ih 9 Pe Ae aS A=CT——., (2ea) 7 BF. Making use of the fact that \=0 when T=, we obtain the value of the constant (2a) pe* ae OG tine. Lome where & is another constant. Therefore ne ly T, TR i ae With the aid of p=ap, and T=T,, (Sea)? [d8, 8 ('ae’ 19) _ (Sea? ‘ae eon a 3? ap \ = m2 pre", . (4) where «"” involves only quantities relating to corresponding states. For different liquids at corresponding states x” is therefore the same. The expression for X given by equation (4) is, it will be observed, similar to the expression for E given by equation (2). me (Seq)? TL pet aa es * Proc. Roy. Soc. A. vol. lxxxi. p, 21 (1908). Combining equa Relations in Capillarity. tions (2) and (4) we have | Be ii ! K Ki! od If the assumption that «’, if not a constant, isa function which has the same value for all liquids at corresponding states is true, then = should be the same for liquids at corresponding states. are given in Table II. Hy, Hy... Hs and Ay, A, o BH . . Values of a at various corresponding temperatures ... As are the values of the potential energy and the surface-tension at the corresponding temperatures 2T C7 24 ST soT and 3Ts Table III. gives the values of EH, &c., > &e., and p, Ke. at TABLE II. ; Anh. (SG dale E E E, Name of liquid. a x : wi Tis Xs ES ntact Ce 348 | 403 4°76 6-73 11-45 Methyl formate ............ 3°39 3:90 4:67 6-70 Carbon tetrachloride ...... 345 | 396 | 461 | 651 | 11:35 PRIZE oc) o5 3185 t,o | 341 3°98 4:69 6°53 10°80 : Choro benzene.......c.see+0 | 3:36 | 396 | 466 | 622 TABLE III. / | | Name of hquid. /T-2/3.| Aj. | E,. | Py}. |/Tcl7/24) A,. | Hy. | po EPR ee 311-71 14-19 49°36 6907 | 331-1 | 12-02 48:50) -6633 Methyl formate......... 324-7| 19°80| 67-22) ‘9283 | 3449 | 17:20 67-09) -8937 | Carbon tetrachloride .| 371-0) 16-69) 57-64 1-4385 || 393°9 | 14°23 5633/1-3702 BCR EG cusp uhs..-scbioiee 374-3 17-87) 60-93, °7826 | 397°7 | 15-18 60°42) -7634 Chloro benzene ......... eh 17°78) 59°80 ‘9611 ck | 15:14 60:00) 9289 } | ent | / | | 1.3/4 jae | i Ps |Te59/72 Ais K,. P4: Biter si...0...4-age 3506 9-92 47-27, -6432|| 383-2 | 661/445 | 5938 Methyl formate ..... 365-2) 13:98 65°30 “8598 || 399-1 | 9:38 62:83) °7942 Carbon tetrachloride .| 417-0) 11:82) 54-44.1-3356 | 455°7 | 8:00 | 52:07/1:2395 i: peel tpets 421-1 12:57) 58:88, 7336 | 460°3 | 8-43 | 54:93) -6798 Chloro benzene......... 4147 2-56| 58°51. feceel| 5188 | 8:42 | 52:34| 8263 us | 18/9 As. Es. | 05 ther. ...;., shinee 4155 3°55 40°65 5383 Methyl formate ............ | 43829 5°06 ou, “7139 Carbon tetrachloride ...... =~ 494-2 4°36 49°5 1:1183 EAI on 28. n dice cbse aldara 499°1 4°68 50°52 6139 Chloro benzene...........+00 562°7 4:57 4.96 Dr. R. D. Kleeman on some these temperatures. These values were obtained by linear interpolation from Whittaker’s tables*. Table II. shows that the ratio a at corresponding temperatures is very approxi- mately constant. Hquation (2) affords another test of the validity of the assumption that «’ is the same for all liquids at corre- sponding states. If the assumption is true then ee 21 should be.a constant for liquids at corresponding tempe- ratures. Substituting from Table III. we obtain Table LV. TABLE IV. 2 2 2 2 Name of liquid. = : eae = ae ay MiGler ee oh es ali... +939 906 ‘820 721 Methyl formate ......... 956 “884 842 Carbon tetrachloride ...| ‘928 ‘910 847 ‘703 DEWZAGNC cg.wakn sc 92csbieesee- "959 ‘909 "837 "742 Chloro benzene............ 931 991 845 which shows that the relation is true for several sets of cor- responding temperatures. The ratio is not the same, however, for each set of corresponding temperatures, as would be the case if Hinstein’s assumption of a constant «’ were true. From equation (4) we obtain another test of the assumption. 2 nas — should be a constant for all liquids at corresponding 2h 1 temperatures. The agreement of this with experimental results is shown in Table V. Though the ratio is constant TABLE V. alters Aro? | Aj,2p5" Ai70,” A105" Name of liquid. | pt Xp dap? Wee, MCG i nas ancts ob e-anen ewe oe 1:09 toi 1°59 2°38 Methyl formate ......... een "OF 1:13 1°54 2°31 Carbon tetrachloride ...| 1°06 1s 55). |. 2k (PBHZONB 2.3.5 i. sn agauabonee: 1-12 Ply, iGO 8 roe Chloro benzene............ uy L"10 Las 1:56 | * Loe. cit. Relations in Capillarity. 497 for each set of corresponding temperatures it varies con- siderably from set to set. The relation = = constant for corresponding temperatures which has just been proved, can be deduced from a well- known relation connecting surface-tension with other quan- tities. The deduction will also bring some other important relations to light. Ramsay, following Hétvos, has shown that Se ee Ta), . 2... -.(5) p* where A is a constant whose value is about 2°1 for all liquids, and a is another constant whose value is about 6. Let pp and A denote the density and fictitious surface-tension at absolute zero. Then 3 A 3 a a 2 (T.—a) = a ATe, mM m°* since a is small in comparison with T,.. If po is put equal to bpe we have No= 2% BEAT.. m> For any temperature other than absolute zero equation (5) may be written . (hg A(T, Az). m* We may neglect a except when we are dealing with tempe- ratures quite close to the critical temperature. Omitting a, and combining this equation with the one preceding, we obtain w= —(1—8). peal, Wt oat Ae) For different liquids a and @ are the-same at corresponding states, and since absolute zero is a corresponding state for all liquids % is the same, hence pw is the same for all liquids under the same circumstances. This leads to the conclusion 498 ~ Dr. R. D. Kleeman on some that at corresponding states the surface-tensions of different liquids are equal to the same fraction of their surface-tension at absolute zero. Then the ratio of the surface-tensions of a liquid at two different temperatures is the same for all liquids, if corresponding temperatures are taken. Table VI. bears TABLE VI. m\ nN rv A Name of liquid. 7 : ie : a v (SN GLIIGY Res see ee elbos eas 2°146 3'996 Methyl formate ......... 1152 1421 2111 3°913 Carbon tetrachloride ... 1173 1:412 2:086 — 3'828 Ben ZONE an; odds kes sent 1:150 1:422 2:119 3'818 Chloro benzene............ 1°174 1416 2°112 3°891 this out exceedingly well. The variation of the surface-tension of liquids with the temperature is more simply and intelligibly expressed in this way than by aie (5). The equations an H=\—-Tap N= AG ee when combined yield a ro {ue Bo 1 vate -eie\. a At corresponding temperatures the right-hand side is the same for all liquids, a result which has been shown to be true directly (Table I1.). We can now find an expression for «’ from equations (2) and (7). We have ie ae EK u go 1 af ets po? (Seg)? pe (Sea)? UL We fe seen that «’ is a function which has the same value for different liquids at corresponding temperatures. It This shows that Di is tie Pe Relations in ae 499 follows from this that Sa > must be a constant & for all liquids in order that k dw Poem for Soc = “4 u—P dp which makes x’ assume the same value for all liquids at corresponding states. Similarly the function represented by x’’ can be deter- mined. From equations (4) and (6) and the relation X=pAy we have = 3s TS eX, a a (ene a a, 2 (26,)7 pea) ce Since x” must be a function which has the same value for 2 different liquids at corresponding states, then a must be equal to some constant & which is the same for all liquids. Thus we have 1, 0-8) ab? (8) and this is the same for ali liquids at corresponding states. From equation (2) we see that any, change in x«”’ is due to a change in ty since m and (ca)? are constants which do not vary under any conditions. In Table VII. (p. 500) the values of = are calculated for five liquids at temperatures differing by 10° ae arange of about 140°C. The constancy of oT shows that oO is proportional to T, or the function x’ is proportional, at least approximately so, to the absolute temperature. This is a more convenient expression for the variation of «’ with temperature than that eevee above. The values of («’)ic, fora number of atoms have ech E calculated from the equation x’ (2¢z)?= > , and are given 500 Dr. R. D. Kleeman on some TaBLE VII. Ether. Chlorobenzene. E | E A p- E ot aie p- E. aT | ee: oS ——=|| —————__ ——_ | | eee ese Oe eee sO eee 313 "6894 49:1 330 423 "9599 59°8 153 323 "6764 | 48-9 333 433 "9480 59°9 154 333 "6658 48:4 328 443 "9354 60°0 *155 343 | °6532 47°8 *32 453 "9224 60:0 156 353 6402 47-1 326 463 9091 59°3 155 363 *6250 46:1 326 473 | °8955 58°6 154 373 6105 45°5 327 483 8802 58'1 155 383 0942 44-7 301 493 "8672 574 "155 393 5764 | 43°8 336 503 8518 56:7 "155 403 | _ °5580 426 339 513. 8356 55°9 "156 413 D385 All 343 523 "8196 Dol "157 423 ‘0179 39'3 346 533 "8016 53'8 157 Carbon tetrachloride. Benzene. 403 1:3680 59°6 737 393 7692 60°7 261 413 13450 548 734 403 7568 60-1 260 423 13215 53°9 727 413 7440 59°4 260 483 1°1566 50°3 778 473 6605 54:0 *262 9 ‘266 5 | -267 503 | 6065 | 49:9 | +269 518 | 3851 | 481 | -274 Methyl formate. i | | , E Me p- E. er rr. p- E. or" 303 | *9598 69°4 “249 373 "8452 64:6 "249 313 9447 68°8 *246 383 *8264 63:8 "244 323 9994 68°2 244 393 *8070 62:9 °246 333 "9133 67°5 243 403 ‘7860 61°8 *255 343 "8968 67°3 "244 413 "7638 60:4 “25 Relations in Capillarity. 501 in the fourth column of Table VIII., the values of used being given in the second column. The first four liquids supplied the data for the calculation of («’)?Xca for the four atoms involved. Then ‘the («’)?3ca for chlorobenzene was calculated from the (x’)#cq of its constituent atoms, and is given in the third column of the table, while the actual TasLEe VIII. BE” 2 | 3 Name of liquid. * (e")" Se. | Gye. Cy "2 LLELAS e e (ire ae ee Bee |H= 1971) H=1 Methyl formate ............ Gao |), teed C=109°96| C=5-581 Carbon tetrachloride ...... SO Th Ws. cate O=112°66| O=6:224 MEG aes nih fs einai MSO? \ | fo tiseenes Gl==175'76) Cl=8'919 Chloro benzene ............ 9050 935°6 TaBLE IX. Name of liquid. («')'e,- (ie ex a’ | Hther Of1yO ...--:esnesees--s 4042 | 4042 | H=109 | H=1 | Methyl formate C,H,0, ...... 287°7 287°7 C=59°4 | C=5:45 Carbon tetrachloride CCl, ...| 437°5 437°5 O=57'6 | O=5'284 eugene Ogllg) .i:..-.2 22.2053 421-6 4216 C1l=94:5 | Cl=8'67 Chloro benzene O¢H;Cl ...... 493°7 505°4 Ethyl acetate CsH30, ......... 43571 440-0 Propyl formate C4H;O, ...... 428°0 440-0 | Methyl propionate CyHsO,...| 428°8 440-0 | Propyl acetate C;H10O, ...... 502°5 521°2 _ Ethyl propionate C;H,,0,...| 500°8 521°2 _ Methyl butyrate O5HyO, ...| 500-0 521°2 | Methyl isobutyrate C5H190, | 497°6 521°2 experimental value is given in the second column. The agreement is fairly good. It should be added that this table refers to a temperature of 2T,. The last column of the table gives the values of ¢,, the c, for H being put equal to unity. Since the values of ¢, for different liquids can only be compared if they are calculated from data referring to cor- responding states, we are limited to a few liquids since the 502 Dr. R. D. Kleeman on some surface-tension has been determined over a limited range of temperatures in some cases so that a corresponding tem- perature referring to each liquid cannot be found, and the values of ec, for a number of atoms cannot therefore be obtained under this restriction. A formula involving dc, will be developed at a later stage which is not restricted to the same extent in its application. Similarly, the values of («’')?c, for a number of atoms have been calculated from the equation (k")(Sca)?= = and are given in the fourth column of Table IX. (p. 501). As before, the first four liquids supplied the data which were taken at 2T,. The second column gives the values of oe obtained from experiment, while the third column gives the theoretically equivalent values of (K’”)? Xcq. The two columns agree fairly well. The last column of the table gives the values of ¢,, that for H being put equal to unity. These values agree fairly well with those obtained in Table VIII., except for oxygen. If the values of ca were in both cases determined from a larger number of liquids by a method of least squares the agreement would probably be much better. Kl! 2 The equation (4) » — (2c.)* is further interesting since it can be connected with other investigations in capil- larity. An expression for the surface-tension of a liquid is usually given in text-books on physics deduced from the work necessary to produce a new liquid surface. Consider the work required to separate two portions of a liquid A and B, the resulting surfaces to be plane. Let B be divided up into slices parallel to the interface, then the work done in removing the slice whose thickness is dz, and whose height above the plane is z, is per unit of area equal to pif Hoe where p(x) denotes the attraction due to a mass of liquid of density p bounded by a flat surface on unit mass placed at a distance x above the surface. The work required to remove the whole of the liquid B standing on unit area is ( p’vdz, where v= (a) da. 1 Relations in Capillarity. 503 Integrating by parts we have pee Sg AU [prev], at prea. de. 2e0Q : The term within the brackets vanishes at both limits and dv =H). Therefore the work required is p” ( ep (z) dz. “0 The expenditure of this amount of work has resulted in the production of two surfaces each of unit area. Hence the v work expended per unit area (7. e. the surface-tension) is YS val ovr(z)dz. : 0 Comparing this with equations (4) and (8) we see that 2 I] : joe Sn 4” epee = "(805)" = 2 Ged « 0 abs m? The latter expression may be conveniently divided into two parts :— edn s2 ey aig lt The first part depends only upon the temperature, and is the same for different liquids at corresponding temperatures. The latter part involves only quantities which are funda- mental and do not depend upon temperature or anything else except the nature of the atom. The first part therefore expresses the effect of the change in the geometrical con- figuration of the molecules accompanying rise of temperature on the surface-tension of the liquid. Since the function «' is approximately proportional to the absolute temperature it may be put equal to W®@ where W is an appropriate constant. Hence _ We! 2 a eRe a ite da), a 9 Gul pene) Whittaker has obtained a relation between the potential energy, the internal latent heat of evaporation, and the absolute temperature. He shows that LKT = E, where K is a constant which is different for different liquids, 504 Dr. R. D. Kleeman on some The writer * has shown that the value of the constant K is Ce[to ape NEP 6 ia Wl te Oro X LO Hence Whittaker’s relation becomes Bo ee ay x10“, With the aid of (9) we get 0 Ke Ca)? iS See = mipeo°d1 X 107" pM. -,. .. oa M involves constants only, hence L/p? must be a constant. The agreement of this conclusion with experiment is shown in Table X. The agreement is not very good, the value rising slightly with increase of temperature. TABLE X. Ether. Chloro benzene. _i — a L. Q- M 67°07 | -9836 69°31 x) 273 86:16 | *7362 323 73°01 | 6764 61°46 | -9224 72:24 373 60°33 | °6105 | 55:29 | 8672 73°52 423 44°38 | ‘5179 553 4717 | “7834 76°85 Methyl formate. Carbon tetrachloride. 4 ys L. 0. 273 113:2 1:0082 | 73 48°35 | 16327 | 18:11 323 99°51 "9294 | 373 | 39°68 | 14343 | 19°31 373 82°43 "8452 | 423 3442 | 13215 | 19-70 423 64:03 7403 473 | 38:22 | 1:1888 | 19°95 473 33°18 5658 1 523 19°85 "9980 | 19°93 * Phil, Mag. July 1909. Relations in Capillarity. 505 Benzene. | | 273 100/10 ‘9001 | 123°6 137°9 373 | 81:98 | -7927 130°5 23 | 71°93 | -7310 1346 473. 59:95 | -6605 137°5 | 023 | 43°39 | 5609 The deduction of (11) involves the relation that «' is pro- portional to the absolute temperature or «’=W8 which is only approximately true. Hence a better constancy in the value of M or L/p’ could scarcely be expected. Table XI. contains in the second column the mean value TABLE XI. | | Mintoct Na iquid. | M. ‘ { HER a Name of liquid | I | m p, (Se, ; a —$—$$——_— | | Ge ne | 161-4 74 2604 | 1018 Methyl formate ............ bee leeey 60 3489 1032 Carbon tetrachloride ...... | 19-4 154 ‘D576 989:7 21 ee | 132°8 78 3045 1002 Chloro benzene ............ | BOR 112°5 "8654 980°6 of the values of M for each liquid considered in Table X. A rearrangement of equation (11) yields Lean a (ey eee ae LO where everything is constant. The values of the left-hand side are calculated in Table XI. with the aid of the values of c, obtained from Table VIII. The resulting value is very nearly the same for the five liquids, as should be the case since W approximately is independent of the nature of the liquid. If we take the mean value of the constant as 1004°5 the equation for the internal latent heat becomes T= Pe)" 1004-5, hae 3 MEPe3 This equation may be used to find the approximate internal latent heat of evaporation of a liquid. Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 2M 4 506 Dr. R. D. Kleeman on some Some further results of interest can be deduced from some of the equations given. Thus equation (10) states LT mp2. - 4 per eh Oge ee K, e which may be written pe Gry <1 ce a? since T=@T, and p=p.«. Therefore 2 Limp? _ ot Wee ix LO for liquids at corresponding states. And since H/A=constant at corresponding states, it further follows that = constant = constant Lm*p* r for corresponding states. Table XIT. contains the values of the expressions on the left-hand side of the two last equations for five liquids at TABLE XII. WERE a ak Name of liquid. I. —— : ae ; T1072) eda cee ae he ae 75°44 60°6 17-4 Methyl formate ............ 92°85 59°3 175 Carbon tetrachloride ...... 39°87 56:3 16:3 IBOMZOM Gy, peecaiin vai wae eds | 81°73 56°5 16°6 Chloro benzene ............ 65°88 58°5 174 temperatures corresponding to T,2/3. The data used in the calculations are contained in part in the same table, the remainder being given in Table III. It will be seen that the value of each expression is practically independent of the nature of the liquid to which it refers, as is indicated by the above equations. An equation may also be deduced from the foregoing equations which contains &c, but not E ord. Thus from equations (2) and (10) we have LT m*p 3 Tt 19 5°57 x 10-1 = “F- (Se,)?. e Mm Relations in Capillarity. 507 Substituting for T. and pe from the equations T = AT,, p = 2p., and rearranging the equation we have L2mé Kae 3 at ABST x et op BIG... ie: (12) where B is a function which has the same value for different liquids at corresponding states. This equation is more useful in finding values of Xe, than equation (2) or (4), since it involves data which are available for a larger number of liquids. The agreement of this equation with the facts is shown in Table XIII. The fifth column of the table contains the value Tacha MITT, Limes | Name of liquid. m. Eye + py z Bc ee Se | Pl MLE ¢ ee 74 75°44) 6907) 1686 de. 45-4. Methyl formate C,H4Q, ...... 60 2°85 | 9283, 1202 oe) | C= 2406 Carbon tetrachloride C Ul,...| 142 39°87 1:4885 1766 ars O=269°6 Seavene OH, ........--.---.---- 78 81°73 | -7826! 1716 a F=261-4 Fluor-benzene C,H;F1......... 96:09} 69°71 | -9233; 1932 oe, | Cl]=3RE4 Bromo-benzene O;H;Br ...... 157 48°84 1:2792 2154 ... | Br=483-4 Todo-benzene O;H3I ......... 2039 | 40°79 1°5347, 2372 ... |Sn=666°4 Stannic chloride SnCl,......... 260°8 | 27°11 |1:9597 | 2192 ee I=703°4 | Di-isobutyl CsH;g_........... 114 66:05 | -6333| 2762 | 2742 Chloro-benzene CsH;Cl ...... 112°5 | 65°88 | 9611, 2060 | 2052 7 DLAs eee 72 75°47 | 6057; 1784 | 1748 x: Heptane C.Hi¢ Bee Sno Seteim ale os 100 71°40 / "6247 2494 2170 == Seems Oplig ............-....- 114 66°05 | -6299| 2770 | 2742 | H= 1 Seeeene OGlli, ................-. 86 72°61| -6167| 1941 | 1988 | C= 5:30 Acetic acid C,H,0, ............ 60 86°08 | 9315) 1155 | 1202 = 594 Iso-pentane C;H,, ............ 72°1 | 71:09} 6048; 1734 | 1748 | F= 5-76 Hexamethylene CjH),......... 84 76°25 | -7047| 2128 | 2079 | Cl= 8-40 |} Di-isopropyl CH, ...... ..:.. 76 69°39 | -6237| 1782 | 1625 |Br=10°65 Propyl formate C,H30, ...... 88 | 7835) ‘8304! 1860 | 1865 | Sn=14:68 Ethyl acetate C,H;O,......... 88 78°61 | -8305; 1862 | 1865 | [=15-49 Methyl propionate C,HsO,...| 88 | 79772) 8408) 1861 | 1865 Propyl acetate C;Hi0O, ...... 102 74°30) -8046, 2197 | 2196 Ethyl! propionate C;Hi90, ...|}102 | 74°38) -8071) 2193 | 2196 Methyl butyrate C5H,)0, ...| 102 71:07! °8147| 2130 | 2196 Methyl isobutyrate C;H190,. .| 102 69°74} -8102; 2117 | 2196 | Methyl acetate C;H,O, ...... 74 89°08 -8741, 1565 | 1533 | Ethyl formate C3H,O, ...... 74 86°93 8658, 1556 | 1533 1a Cie gt OG GAIA Sree HAE oh a at 18 |455°4 | 9173 660 360 Methyl alcohol CH,O......... 32 |244°9 | ‘7470; 1082 692 Propyl alcohol C3H30...... .. 60 159° | -7475; 1821 | 1355 of the expression on the right-hand side of the equation calculated from data given in the preceding columns of the table. The values for the first eight liquids in this column 2M2 508 Dr. R. D. Kleeman on seme furnished the data from which the value of Be, for each of the atoms H, C, O, F, Cl, Br, Sn, I, was calculated. The upper half of the seventh column of the table contains the values of Be,, and the lower half the values of c,. The values of Sc, for the remaining liquids were calculated by means of the values of Be,, and are given in the sixth column of the table. They agree very well with the values contained in the fifth column which have been calculated from experi- mental data, except in the case of water, methyl] alcohol, and propyl alcohol, the values for these liquids showing a con- siderable disagreement between calculation and experiment. The reason that these liquids do not fit in with the others is probably due to polymerization of their molecules. The existence of such an effect would modify the various quantities in equation (12) to a certain, though at present unknown, extent. The evidence on the polymerization of liquids founded on the deviations from the laws of osmotic pressure, and of surface-tension, &e., shows that each of the three liquids in question, besides a few others, is polymerized to a certain degree which depends on the nature of the liquid and its temperature. The deviations from equation (12) thus seem to indicate the same thing; and another method is thus furnished for testing whether a liquid is polymerized or not. Hquation (12) may be transformed into one involving T, instead of L,. The internal heat of evaporation of a liquid is given by the well-known thermodynamical relation L,+p(vi— v2) = (wt, 2 ; 1 where v,, v2, denote the volume of one gram of vapour and liquid respectively at the pressure p and temperature T. Consider the temperature taken so low that the vapour obeys approximately Boyle’s law. The equation then becomes 1, 42h _ BY m m aly’ which may be written Lm__p, dp T; p aly Substituting for p and T on the right-hand side of this equation from the equations T=6T,, p=yp., we obtain =—R-- ea =u=constant . . (13) for liquids at corresponding states. (Modified Trouton’s law.) Relations in Capillarity. 509 With the help of equation (13) equation (12) can be written see ETS G5). Fe ilar siica» Yo CA) where H is a function which has the same value for difterent liquids at corresponding states. This equation has been tested for the liquids contained in ‘able XIII., the result being exhibited by Table XIV. The TABLE XIV. 1 2 T,? m3 Name of liquid. 2T c. : =, Hee He,. Pl _i i eee SET, 398°3 =p H= 9-05 Methyl formate ............ | 324-7 290-2 ee C= 60°3 | Carbon tetrachloride ...... 3710 454-2 ree O= 666 TE eT ra he 3743 4159 a == 110-7 Fluor-benzene ............... WARE fe: 497-3 a Cl= 93°47 Bromo-benzene ............ 4467 522°6 fut Br=115'6 Todo-benzene ............... 481 570°9 ae Sn=143 Stannic chloride ............ | 3945 517°6 ae I=163°9 Me inolniyl ....5;..-..0c00: |, 362°5 607°3 645°7 | Chloro-benzene............... | 422 491°5 500°5 “Ee 313°5 498-4 410 RAIS Aa Ce ba caieg 359°9 599-7 506 6 LL ee Se aa 3795 623°6 645°3 Sepeitie esd Oo: | 338-5 495°1 488°5 ETC Ee | 3964 320°0 290 PRG-ORIANG ...........0.0.-<. | 3807-2 425°5 4011 Hexamethylene ............ 368-7 465°4 470-4 Di-isopropyl.................. | 333°6 448°8 398 Propyl formate ............ | 355°9 422-4 4468 Ethyl acetate ............... t S483 417°9 446°8 Methyl propionate ......... 3592°5 4166 4468 Propyl acetate ............... 36671 482-8 525-2 | Ethyl propionate ............ = 8636 480°1 5252 | Methyl butyrate ............ 367°3 4796 525°2 Methyl isobutyrate ......... 360°3 476°7 525°2 Methy] acetate ............... | 38373 354-1 368°4 Ethyl formate ............... baa 355°3 368°4 EME cldecete sa ee 424°9 150 64:7 Methyl alcohol...............| 342 226°4 163 ) Propyl alcohol ............... | 357°8 352-0 319-9 | data used in the calculations involved corresponded to 3T,. The vapour of each of the liquids at that temperature very approximately obeys Boyle’s law. The table will be readily understood without any further explanation, as it resembles 510 Messrs. G. N. Lewis and R. C. Tolman on the in outline Table XIII., of which it may be said to be a econ- tinuation. The values of Sc, calculated by means of the values of He, omitting those referring to water, methyl alcohol, and propyl alcohol, agree approximately with the values contained in the third column which were derived directly from experimental data. The agreement is, however, not so good as that exhibited in Table XIII. From the way equation (14) was obtained it is obvious that this must be due to deviations from the relation expressed by equation (13). Cambridge, June 24, 1909. LYIL Phe Principle of Relativity, and Non-Newtonian Mechanics. By GiLBert N. Lewis and RicHarp C.ToLMAN*. | E Eee a few years ago every known fact about light, electricity, and magnetism was in agreement with the theory of a stationary medium or ether, pervading all space, but offering no resistance to the motion of ponderable matter. This theory of a stagnant ether led to the belief that the absolute velocity of the earth through this medium could be determined by optical and electrical measurements. Thus it was predicted that the time required for a beam of light to pass over a given distance, from a fixed point to a mirror and back, should be different in a path lying in the direction of the earth’s motion and in a path lying at right angles to this line of motion. This prediction was tested in the crucial experiment of Michelson and Morley }, who found, in spite of the extreme precision of their method, not the slightest difference in the different paths. | It was also predicted from the ether theory that a charged condenser suspended by a wire would be subject to a torsional effect due to the earth’s motion. But the absence of this effect was proved experimentally by Trouton and Noble tf. The skill with which these experiments were designed and executed permits no serious doubt as to the accuracy of their results, and we are therefore forced to adopt certain new views of far-reaching importance. It is true that the results of Michelson and Morley might be simply explained by assuming that the velocity of light depends upon the velocity of its source. Perhaps this assumption has formerly been dismissed without sufficient * Communicated by the Authors. t+ Amer. Jour. Sci. xxxiv. p. 333 (1887). ¢ Phil. Trans. Roy. Soc. (A) ccii. p. 165 (1904). Principle of Relativity and Non-Newtonian Mechanics. 511 reason, but recent experimental evidence, to which we shall revert, seems to prove it untenable. This possibility being excluded, the only satisfactory explanation of the Michelson-Morley experiment which has been offered is due to Lorentz *, who assumed that all bodies in motion are shortened in the line of their motion by an amount which is a simple function of the velocity. This shortening would produce a compensation just sufficient to offset the predicted positive effect in the Michelson-Morley experiment, and would also account for the result obtained by Trouton and Noble. It would not, however, prevent the determination of absolute motion by other analogous experi- ments which have not yet been tried. Hinstein t has gone one step farther. Because of the experiments that we have cited, and because of the failure of every other attempt that has ever been made to determine absolute velocity through space, he concludes that further similar attempts will also fail. In fact he states as a law of nature that absolute uniform translatory motion can be neither measured nor detected. The second fundamental generalization made by Hinstein he calls “‘the law of the constancy of light velocity.” It states that the velocity of light in free space appears the same to all observers, regardless of the motion of the source of light or of the observer. These two laws taken together constitute the principle of relativity. They generalize a number of experimental facts, and are inconsistent with none. In so far as these generali- zations go beyond existing facts they require further verifi- cation. To such verification, however, we may look forward with reasonable confidence, for Einstein has deduced from the principle of relativity, together with the electromagnetic theory, a number of striking consequences which are remarkably self-consistent. Moreover the system of mechanics which he obtains is identical with the non- Newtonian mechanics developed from entirely different premises by one of the present authors}. Finally, one of the most important equations of this non-Newtonian mechanics has within the past year been quantitatively verified by the experiments of * Abhandlungen iiber theoretische Physik, Leipzig, 1907, p. 443. + An excellent summary of the conclusions drawn from the principle of relativity, by Einstein, Planck, and others is given by Einstein in the Jahrbuch der Radioaktivitit, iv. p. 411 (1907). An interesting treatment of certain phases of this problem is given by Bumstead, Amer. Jour. Sci. xxvi. p. 493 (1908). t Lewis, Phil. Mag. xvi. p. 705 (1908). 512 . Messrs. G. N. Lewis and R. C. Tolman on the Bucherer * on the mass of a 8 particle, to which we shall refer later. : Therefore, in as far as present knowledge goes, we may consider the principle of relativity established on a pretty firm basis of experimental fact. Accepting this principle, we shall accept the consequences to which it leads, however extraordinary they may be, provided that they are not incon- sistent with one another, nor with known experimental facts. The consequences which one of us has obtained from a simple assumption as to the mass of a beam of light, and the fundamental conservation laws of mass, energy, and momen- tum, Hinstein has derived from the principle of relativity and the electromagnetic theory. We propose in this paper to show that these consequences may also be obtained merely from the conservation laws and the principle of relativity, without any reference to electromagnetics. In dealing with such fundamental questions as we meet here it seems especially desirable to avoid as far as possible all technicalities. We have endeavoured to find for each of the following theorems the simplest and most obvious proof, and have used no mathematics beyond the elements of algebra and geometry. | The Units of Space and Time. The following development will be based solely upon the conservation laws, and the two postulates of the principle of relativity. The first of these postulates is that there can be no method of detecting absolute translatory motion through space, or through any kind of ether which may be assumed to pervade space. The only motion which has physical significance is the motion of one system relative to another. Hence two similar bodies having relative motion in parallel paths form a perfectly symmetrical arrangement. If we are justified in considering the first at rest and the second in motion, we are equally justified in considering the second at rest and the first in motion. The second postulate is that the velocity of light as measured by any observer is independent of relative motion between the observer and the source of light. This idea, that the velocity of light will seem the same to two different observers, even though one may be moving towards and the * Ber. Phys. Ges. vi. p. 688 (1908); Ann. Physik, xxviii. p. 513 (1909). + We will imagine that the observer measures the velocity of light by means of two clocks placed at the ends of a metre stick which is situated lengthwise in the path of the light. Principle of Relativity and Non-Newtonian Mechanics. 513 other away from the source of light, constitutes the really remarkable feature of the principle of relativity, and forces us to the strange conclusions which we are about to deduce. Let us consider two systems, moving past one another, with a constant relative velocity, provided with plane mirrors aa and bb parallel to one another and to the line of motion (fig. 1). An observer A on the first system sends a beam of light across to the opposite mirror, which is reflected back to the starting-point. He measures the time taken by the light in transit. A, assuming that his system is at rest (and the other in motion), considers that the light passes over the path opo, but he believes that if a similar experiment is conducted by an observer B in the moving system, the light must pass over the longer path mnm’, in order to return to the starting-point. For the point m moves to the position m’ while the light is passing ; he therefore predicts that the time required for the return of the reflected beam will be longer than in his own | experiment. A, however, having established communication with B, learns that the time measured is the same as in his own experiment *. The only explanation which A can offer for this surprising state of affairs is that the clock used by B for his measure- ment does not keep time with his own, but runs at a rate which is to the rate of his own clock, as the lengths of the paths, opo to mnm’, B, however, is equally justified in considering his system at rest, and A’s in motion, and by identical reasoning has come to the conclusion that A’s clock is not keeping time. * This is evidently required by the principle of relativity, for contrary to A’s supposition the two systems are in fact entirely symmetrical. Any difference in the cbservations of A and B would be due to a difference in the absolute velocity of the two systems, and would thus offer a means of determining absolute velocity. 514 Messrs. G. N. Lewis and R. C. Tolman on the Thus to each observer it seems that the other’s clock is running too slowly. | This divergence of opinion evidently depends not so much on the fact that the two systems are in relative motion, but on the fact that each observer arbitrarily assumes that his own system is at rest. If, however, they both decide to call A’s system at rest, then both will agree that in the two experiments the light passes over the paths opo and mnm/ respectively, and that B’s clock runs more slowly that A’s. In general, whatever point may be arbitrarily chosen as a point of rest, it will be concluded that any clock in motion relative to this point runs too slowly. Consider fig. 1 again, assuming system a at rest. We have shown that it is necessary to assume that B’s clock runs more slowly than A’s in the ratio of the lengths of the path opo to the path mnm’; in other words, the second of B’s clock is longer than the second of A’s, in the ratio mnm’ to opo. This ratio between the two paths will evidently depend on the relative velocity of the two systems, v, and on the velocity of light, ¢. “Obviously from the figure, (op)? = (in)? = (mn)?— (ml). Dividing by (mn)?, (ope (ia (ml)? (mn)? (mn)? * But the distance ml is to the distance mn as v is to e. Hence Denoting the important ratio 2 by the letter 6, we see c that in general a second measured by a moving clock bears to a second measured by a stationary clock the ratio ib LB Whatever assumption the observers A and B may make as to their motion, it is obvious that their measurements of length, at least in a direction perpendicular to their line of relative motion, will lead to no disagreement. For evidently, if each observer with a measuring-rod determines the distance from his system to the other, the two determinations must Principle of Relativity and Non-Newtonian Mechanics. 515 agree. Otherwise the condition of symmetry required by the principle of relativity would not be fulfilled. But let us now consider distances parallel to the line_of relative motion. | Fig. 2. ———S——_— $< / ; : U/ m m oS n n A system (fig. 2) has a source of light at m and a reflecting mirror at x. If we consider the whole system to be at abso- lute rest, it is evident that a light-signal sent from m to the mirror, and reflected back, passes over the path mnm. If, however, the entire system is considered to be in absolute motion with a velocity v, the light must pass over a different path mn’m’ where nn’ is the distance through which the mirror moves before the light reaches it, and mm’ is the distance traversed by the source before the light returns to it. Obviously then, nn’ ov 7=-, and mn ¢ / mm v mn'm! ¢ Also from the figure, mr’ =mn+nn’, mn'm’ = mam + 2Znn’ —mm'. Combining we have, mn'm' 1 if mam 1 vw 1—p?’ Hence if we call the system in motion, instead of at rest, the calculated path of the light is greater in the ratio I 1—,?" Now the velocity of light must seem the same to the observer, whether he is ai rest or in motion. His measure- ments of velocity depend upon his units of length and time. We have already seen that a second on a moving clock is lengthened in the ratio , and therefore if the path Penwid « » Haves of the beam of light were also greater in this same ratio, we should expect that the moving observer would find no dis- crepancy in his determination of the velocity of light. From 516 Messrs. G. N. Lewis and R. C. Tolman on the the point of view of a person considered at rest, however, we have just seen that the path is increased by the larger ratio = In order to account for this larger difference, we must assume that the unit of length in the moving system vi-# il has been shortened in the ratio We thus see that a metre-stick, which, when held perpen- dicular to its line of motion, has the same length as a metre-stick at rest, will be shortened when turned parallel ae and indeed any to the line of motion in the ratio moving body must be shortened in the direction of its motion in the same ratio *. Let us emphasize once more, that these changes in the units of time and length, as well as the changes in the units of mass, force, and energy which we are about to discuss, possess in a certain sense a purely factitious significance ; * Certain of Einstein’s other deductions from the principle of relativity will not be needed in the development of this paper, but may be directly obtained by the methods here employed. For example, the principle of relativity leads to certain curious conclusions as to the comparative readings of clocks in a system assumed to be in motion. Consider two systems in relative motion. An observer on system a places two care- fully compared clocks, unit distance apart, in the line of motion, and has the time on each clock read when a given point on the other system passes it. An observer on system 6 performs a similar experiment. The difference between the readings of the two clocks in one system must be the same as the difference in the other system, for by the principle of relativity, the relative velocity v of the systems must appear the same to an observer in either. However, the observer A, considering himself at rest, and familiar with the change in the units of length and time in the moving system which we have already deduced, expects that the velocity determined by B will be greater than that which he himself observes if 1—p?? longer, and his unit of length in this direction is shorter, each by a factor involving “1—%. The only possible way in which A can explain this discrepancy is to assume that the clocks which B claims to have set together are not so in reality. In other words he has to conclude that clocks which in a moving system appear to be set together really read differently at any instant (in stationary time), and that a given clock is “ slower’”’ than one immediately to the rear of it by an amount propor- tional to the distance. From what has preceded it can be readily shown that if in a moving system two clocks are situated, one in front of the other by a distance /, in units of this system, the difference in setting will in the ratio since he has concluded that B’s unit of time is lv ‘ ; : hg ; ‘ Bhs be @: From this point Einstein’s equations concerning the addition of velocities also follow directly. 1 Principle of Relativity and Non-Newtonian Mechanics. 517 although, as we shall show, this is equally true of other uni- versally accepted physical conceptions. We are only justified in speaking of a body in motion when we have in mind some definite, though arbitrarily chosen, point as a point of rest. The distortion of a moving body is not a physical change in the body itself, but is a scientific fiction. When Lorentz first advanced the idea that an electron or in fact any moving body is shortened in the line of its motion, he pictured a real distortion of the body in consequence of a real motion through a stationary ether, and his theory has aroused considerable discussion as to the nature of the forces which would be necessary to produce such a deformation. The point of view first advanced by Hinstein, which we have here adopted, is radically different. Absolute motion has no significance. Imagine an electron and a number of observers moving in different directions with respect to it. To each observer, naively considering himself to be at rest, the electron will appear shortened in a different direction and by a different amount ; but the physical condition of the electron obviously does not depend upon the state of mind of the observers. Aithough these changes in the units of space and time appear in a certain sense psychological, we adopt them rather than abandon completely the fundamental conceptions of space, time, and velocity, upon which the science of physics now rests. At present there appears no other alternative. Non-Newtonian Mechanics. Having obtained these relations for the units of space and time, we may turn to some of the other important quantities used in mechanics. Let us again consider two systems,.a and 8, in relative motion with the velocity v. An experimenter A on ‘the first system constructs a ball of some rigid elastic material, with a volume of one cubic centimetre, and sets it in motion, with a velocity of one centimetre per second, towards the system } (in a direction perpendicular to the line of relative motion of the two systems). On the other system, an experimenter } constructs of the same material a similar ball with a volume of one cubic centimetre in his units, and imparts to it, also in his units, a velocity of one centimetre per second towards a. The experiment is so planned that the balls will collide and rebound over their original paths. Since the two systems are entirely symmetrical, it is evident by the principle of relativity, that the (algebraic) change in velocity of the first 518 Messrs. G. N. Lewis and R. C. Tolman on the’ ball, as measured by A, is the same as the change in velocity of the other ball, as measured by B. This being the case, the observer A, considering himself at rest, concludes that the. real change in velocity of the ball } is different from that of | his own, for he remembers that while the unit of length is the same in this transverse direction in both systems, the unit of time is longer in the moving system. Velocity is measured in centimetres per second, and since the second is longer in the moving system, while the centi- metre in the direction which we are considering is the same in both systems, the observer A, always using the units of his own system, concludes that the change in velocity of the ball V1—6 2 b is smaller in the ratio RR ESSE than the change in velocity of the balla. The change in velocity of each ball multiplied by its mass gives its change in momentum. Now, from the law of conservation of momentum, A assumes that each ball experiences the same change in momentum, and therefore since he has already decided that the ball } has expe- rienced a smaller change of velocity in the ratio he must conclude that the mass of the ball in system 6 is greater than that of his own in the ratio In general, /1—8? therefore, we must assume that the mass of a body increases with its velocity. We must bear in mind, however, as in all other cases, that the motion is determined with respect to some point arbitrarily chosen as a point of rest. If mis the mass of a body in motion and mp its mass at rest, we have * m a: —— 7M = Feager . . ° akithe ° (1) The only opportunity of testing experimentally the change of a body’s mass with its velocity has been afforded by the experiments on the mass of a moving electron or 8 particle. The actual measurements were indeed not of the mass of the electron, but of the ratio of charge to mass (=). m * This equation and others developed in this section are identical with those obtained through an entirely different course of reasoning by Lewis (Phil. Mag. xvi. p. 705, 1908). ‘The equations were there obtained for systems in motion with respect to a point at absolute rest. We shall show here, however, that they are true, whatever arbitrary point is selected asa point of rest. Principle of Relativity and Non-.Newtonian Mechanics. 519 Tt has, however, been universally considered that the charge eis constant. In other words, that the force acting upon the electron in a uniform electrostatic field is independent of its velocity relative to the field, Hence the observed change * é * . = e . ' in — is attributed solely to the change in mass. It might be well to subject this view to a more careful analysis than has hitherto been done. At present, however, we will adopt it without further scrutiny. The original experiments of Kaufmann*™ showed only a qualitative agreement with equation(1). Recently, however, Bucherer + by a method of exceptional ingenuity, has made further determinations of the muss of electrons moving with varying velocities, and his results are in remarkable ‘accord with this equation obtained from the principle of relativity. This very satisfactory corroboration of the fundamental equation of non-Newtonian mechanics, must in future be regarded as a very important part of the experimental material which justifies the principle of relativity. By a slight extrapolation we may find with accuracy from the results of Bucherer that limiting velocity at which the mass becomes infinite, in other words, a numerical value of ¢ which in no way depends upon the properties of light. Indeed merely from the first postulate of relativity and ‘these experl- ments of Bucherer we may deduce the second postulate and all the further conclusions obtained in this paper, This fact ean hardly be emphasized too strongly. Leaving now the subject of mass, let us consider whether the unit of force depends upon our choice of a point of rest. An observer in a given system allows such a force to act > . * . Cm. upon unit mass as to give it an acceleration of one ——,, and sec.” calls this force the dyne. If now we assume that the system is in motion, with a velocity v, in a direction perpendicular to the line of application of the force, we conclude that the acceleration is really less than unity, since in a moving ; 1 system the second is longer in the ratio Tia and the centimetre in this transverse direction is the same as at rest. On the other hand, the mass is increased owing to the motion 1 of the system by the factor wie Since the time enters to the second power, the product of mass and acceleration * See Lewis, loc. cit, : + Bucherer, loc. cit, 520) Messrs. G. N. Lewis and R. C. Tolman on the is smaller by the ratio ha than it would be if the system were at rest. And we conclude, therefore, that the unit of force or the dyne in a direction transverse to the line of motion is smaller in a moving system than in one at rest by this same ratio. In order now to obtain a value for the force in a longi- tudinal direction in the moving system, let us consider (fig. 3) a rigid lever abe, whose arms are equal and perpendicular, and equal forces applied at a and e¢ in directions parallel to cand ba. The system is thus in equilibrium. a Now let us assume that the whole system is in motion with velocity v in the direction be. Obviously, merely by making such an assumption we cannot cause the lever to turn, never- theless we must now regard the length be as shortened in V1——? 1 We must therefore conclude that to maintain equilibrium the force at a must be less than the force at ¢ in the same ratio. We thus see that in a moving system unit force in the longi- tudinal direction is smaller than unit transverse force in the the ratio , while ad has the same length as at rest. LONE? ratio eae, and therefore, by the lire paragraph, smaller than unit force at rest in the ratio ai * It is interesting to point out, as Bumstead* has already done, that the repulsion between two like electrons, as calculated from * Bumstead, loc, cit. Principle of Relativity and Non-Newtonian Mechanics. 521 the electromagnetic theory, is diminished in the ratio pe Bae they are moving perpendicular to the line joining them ; and in the ratio 7 the line joining them. From the standpoint of the principle of relativity, one of the most interesting quantities in mechanics is the so-called kinetic energy, which is the increase in energy attributed to a body when it is set in motion with respect to an arbitrarily chosen point of rest. Knowing the change of the mass with velocity as given by equation (1), the general equation for * kinetic energy *, E’, may readily be shown to be, / 2 1 EK = MC (A ~1). ° es ° (2) From equations 1 and 2 we may derive one of the most interesting consequences of the principle of relativity. If E is the total energy (including internal energy) of a body in - motion, and HK, is its energy at rest, the kinetic energy LH’ is equal to E—E, and equation (2) may be written, E-—E, — MgC” — ri ° . ° (3) Moreover, we may write equation (1) in the form m—My = ™( ae =), sec hs nese ee and dividing (3) by (4), No oa Fath bat ae ig VD) In other words when a body is in motion its energy and mass are both increased, and the increase in energy is equal to the increase in mass multiplied by the square of the velocity of light. From the conservation laws we know that when a body is set in motion and thus acquires mass and energy, these must come from the environment. So also when a moving body is brought to rest it must give up mass _as well as energy to the environment. The mass thus acquired by the environment is independent of the particular form if moving parallel to * Consider a body moving with the velocity v subjected to a force f in the line of its motion. Its momentum M and its kinetic energy E’ will be changed by the amounts dM = fdt, dk’ = fdl=fvdt. Hence -d&' = vdM or substituting mv for M, dE’ = mvdv+v*dm. Eliminating m between this equation and equation (1), and integrating, gives at once -the above equation (2). Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 2N 522 Principle of Relativity and Non-Newtonian Mechanics. which the energy may assume and we are thus forced to the important conclusion that when a system acquires energy in any form it acquires mass in proportion, the ratio of the energy to the mass being equal to the square of the velocity of light. We might go further and assume that if a system should lose all its energy it would lose all its mass. If we admit this plausible although unproved assumption, then we may regard ‘the mass of every body as a measure of its total energy according to the equation, Mh yea (6) For a body at rest : E, Mo =. ie Combining this equation with (3) gives ie a Ko V1—,? We thus see that energy changes with the velocity in the same way that mass does, and that the so-called kinetic energy is a ‘‘ second-order eftect ” of the same character as the change of length and the change of mass. The only reason that this effect is easily measured, and has become a familiar concep- tion in mechanics, while the others are obtainable only by the most precise measurements, is that we are in the habit of measuring quantities of energy which are extremely minute in comparison with the total energy of the systems. investigated. Conclusion. We have shown how observers stationed on systems in motion relative to one another have been able to preserve their fundamental principles of mechanics only by adopting certain novel conclusions. These conclusions are self consistent ; in the one case where they have been tested they are in accord with experiment; and they enable us to save all the fundamental physical concepts which have been found useful in the past. We have, however, considered primarily only systems which are initialiy in uniform relative motion. Whether our conclusions can be retained when we consider processes in which the relative motion is being established, in other words, processes in which acceleration takes place, it is not our present purpose to determine. The ideas here presented appear somewhat artificial in character, and we cannot but suspect that this is due to the Moving Force of Terrestrial and Celestial Bodies. 523 arbitrary way in which we have assumed this point or that point to be at rest, while at the same time we have asserted that a condition of rest in the absolute sense possesses no significance. If our ideas possess a certain degree of artificiality, this is also true of others which have long since been adopted into mechanics. The apparent change in rate of a moving clock, and the apparent change in length and mass of a moving body, are completely analogous to that apparent change in energy of a body in motion which we have long been accustomed to call its kinetic energy. We may with equal reason speak of the kinetic mass found by Kaufmann and Bucherer, or the kinetic length assumed by Lorentz. We say that the heat evolved when a moving body is brought to rest comes from the kinetic energy which it possessed. We thus preserve the law of conservation of energy. Itis in order to maintain such fundamental conservation laws, and to reconcile them with the Principle of Relativity, which rests on the experi- ments of Michelson and Morley and of Bucherer, that we have adopted the principles of non-Newtonian Mechanics. These principles, bizarre as they may appear, offer the only method of preserving the science of mechanics substantially in its present form. If later, when more complex systems are considered, and especially when we deal with acceleration, these views prove untenable, it will then be necessary to revolutionize the whole of mechanics. Research Laboratory of Physical Chemistry, ) f Mass. Inst. of Technology, Boston, ! . May 11th, 1909. LVIII. On the Moving Force of Terrestrial and Celestial Bodies in Relation to the Attraction of Gravitation. By Henry Wixpe, D.Sce., D.C.L., F.RS.* 1. J N ihe course of a lecture which I delivered before the Society in 1902, “On the Evolution of the Mental Faculties in relation to some Fundamental Principles of Motion,’ prominence was given to the historic controversy respecting the measure of moving force of terrestrial bodies which has exercised the minds of distinguished men of science and learning for more than two centuries. * Communicated by the Author. Reprinted from the Memoirs and roceedings of the Manchester Literary and Philosophical Society, vol. liii. pt. ii. (1909). 2N2 524 Dr. H. Wilde on the Moving Force of Terrestrial and 2. The proposition was enunciated by Descartes in his ‘Principia ’*, ‘That when a part of matter is moved with double the quickness of another, and that other is twice the size of the former, there is just precisely as much motion, but no more, in the less body as in the greater.” Forty years later Newton adopted in his ‘Principia’? Descartes’ definition of the quantity of motion in a moving body in substantially the same terms as follows :—‘“‘ The quantity of motion is the measure of the same arising from the velocity and quantity of matter conjointly. The motion of the whole is the sum of the motion of all of its parts; and therefore in a body double in quantity with equal velocity the motion is double ; with twice the velocity it is quadruple.” To make this definition more explicit, Newton states under his second law, “if any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively.” 3. Although Galilei had long before demonstrated that the spaces described by heavy bodies from the beginning of their descent are as the squares of the times and also of the velocities acquired in falling through those spaces, yet the significance of this law in relation to the moving force of bodies was entirely overlooked until Leibnitz made the announcement that the force of a body in motion, by the free action of gravity, is as the square of the velocity. To this measure of moving force Leibnitz applied the term, vis viva, or living force. 4, The controversy which has since gathered round the question of the measure of moving force, and still remains unsettled, forms a remarkable chapter in the history of the physical sciences. As might have been anticipated @ priori, philosophers, mathematicians, metaphysicians, and men of letters, unskilled in experimental methods of interrogating nature, adopted the Cartesian measure of moving force. Of these may be mentioned, Maclaurin, Hutton, and Young; Locke, Kant, Schopenhauer, Voltaire, and other writers of more or less note up to the present epoch. Happily for the progress of science a number of natural philosophers, among whom Smeaton, Wollaston, Ewart, Dalton, Joule, and Fair- bairn stand pre-eminent, have proved conclusively by various methods, that the true measure of the moving force of a body under the free action of gravity is as the square of the * Principia Philosophie, Pars, 2, § XXXV., 1648. Z a Celestial Bodies in relation to Attraction of Gravitation. 525 velocity *. Nevertheless, modern scholasticism has not yet pronounced decidedly in favour of the law, and the traditional error of Descartes and Newton still survives in manuals of elementary and advanced science, under the name of momentum, in contradiction of Newton’s second law which expressly excludes the element of time in the measure of the quantity of motion in a body. 5. In the pretace to his ‘ Principia’ Newton set forth with singular lucidity and ingenuousness, the dependence of the mathematical principles of natural philosophy upon experi- mental mechanics in their application to the motions of celestial bodies. It will therefore be obvious that the question, whether the quantity of motion in a planetary system is simply as the velocity, or as the square of the velocity, is one of fundamental importance. So far as I know, no attempt has yet been made to deal with this probiem, and no explication of astronomical science can be considered complete so long as it remains unsolved. 6. In order to demonstrate that the moving force by which the moon and other celestial bodies are maintained in their orbits is as the square of the velocity, it is postulated as general knowledge in physical astronomy :— (a) That the equatorial circumference of the earth is 24,900 miles. (Lb) That the versed sine of five miles (or more exactly, 4-936 miles) of the earth’s circumference, is 193 inches = 16 feet 1 inch. (c) That a body at rest near the earth’s surface falls perpendicularly through the versed sine of 4°936 miles of are of the earth’s circumference = 16 feet 1 inch during one second of time. (d) That as versed sines are as the squares of their arcs, and the accelerative force of gravity increases in the same proportion, a body projected horizontally near the earth’s surface with a velocity 4°936 miles (26.062 feet) per second, would revolve round the earth continually without touching it. * These results have been abundantly confirmed by my experiments with the gyroscope described in the lecture referred to, wherein it was shown (1) that four times the weight falling from the same height were required to generate a double velocity of the revolving disk ; (2) that one unit of weight falling through four times the height also generates a double velucity of the disk ; (3) that the moving force required to generate a double velocity of the disk is independent of the time of its application and is as the square of the velocity. Manchester Memoirs, vol. 46, 1902. 526 Dr. H. Wilde on the Moving Force of Terrestrial and 24900 miles 50448 ,,. ; : (e) That £936 miles = 60" = 84:07 minutes=the time of revolution of a body round the earth with an angular velocity of 26,062 feet per second (d). 7. The mean distance of the moon according to modern astronomy, is 60°28 semi-diameters of the earth, and the time of its revolution in respect to the fixed stars, 27 days, 7 hours, 43 minutes = 39343 minutes. Now as the times and velocities of rotation are reciprocally equivalents of each ee = 468 as the ratio of the orbital times or velocities of a body revolving round the cireum- ference of the earth and the moon’s orbit respectively. Therefore 468 x 84:07 = 39344™ = 27 days, 7 hours, 44 minutes, for the time of the moon’s orbital revolution. 8. Again, from the square of 468, as a velocity, divided by the moon’s distance in semi-diameters of the earth we have 2 2 = 3634, or reciprocally a the total moving force of a body revolving round the earth’s circumference and the moon’s orbit respectively, the numbers being the same as those deduced from the law of attraction of gravitation for the same distance. 9. As the radius of the moon’s orbit is 60°28 semi- dia- meters of the earth, we have with the earth’s radius in miles, 3964 x 2 x 60°28 x 3°1416=1501370 miles for the circum- ference of the mcon’s orbit. Dividing this by the time of revolution in minutes we have 1501370 miles = 38°160 39344 miles miles per minute =3358 feet per second for the moon’s orbital velocity. other, we have 10. That forces of any kind radiating from every point of a body in free space are inversely proportional to the square of the distance is a proposition requiring but little demonstra- tion seeing that it flows directly from the geometry of space. It will be sufficient if I mention in this connexion the intensity of light which increases and diminishes in this same ratio, as is commonly demonstrated by photometers. Experimental mechanics were not sufficiently advanced in Newton’s time to enable him to determine the ratios of the attractive and moving forces of celestial bodies, as there was apparently no physical connexion between such bodies, and it was chiefly from observation and his geometry that the law of attraction of gravitation as the inverse square of the distance was established. Celestial Bodies in relation to Attraction of Gravitation. 527 11. The application of the law to the moon’s orbit is the subject of the fourth proposition of the third book of the ‘Principia, and is of so much importance in relation to my paper that I have thought it well to give an abstract of the text from Motte’s classical translation. The linear quantities in the original are expressed in Paris feet, but are here given in English measure in accordance with modern usage :— ‘Let us assume the mean distance of the moon to be 60 semi-diameters of the earth, and if we imagine the moon deprived of all motion to be let go, so as to descend towards the earth with the impulse of all that force by which it is retained in its orbit, it will, in the space of one minute of time, describe in its fall 16 feet 1 inch. For the versed sine of that are which the moon, in the space of one minute of time, would by its mean motion describe at the distance of 60 semi-diameters of the earth is nearly 16 feet 1 inch. Wherefore since that force in approaching to the earth in- creases in the reciprocal duplicate proportion of the distance, and, upon that account, at the surface of the earth 60 x 60 times greater than at the moon, a body in our regions falling with that force ought, in the space of one minute of time, to describe 60 x 60 x 16 feet 1 inch. And with this very force we actually find that bodies here upon earth do really descend. And therefore the force by which the moon is retained in its orbit becomes, at the very surface of the earth, equal to the force of gravity which we observe in bodies ‘there. And therefore the force by which the moon is retained in its orbit is that very same force which we commonly call grav ity.” 12. I have already demonstrated that the moon’s orbital velocity is 38°160 miles per minute, and that a body would describe an arc of 4:936 miles of the earth’s circumference in one second, during which time it would fall through the versed sine of that are =193 inches. Now as the versed sines of arcs of the same length are as the radii inversely ee = 3:21 inches as the versed sine of 4°936 miles of the moon’s orbit. Again, as versed sines are as the squares of their arcs, we have | Eedaaay ante 7°73? x 3°21, or nearly 16 feet 1 inch, as the 4-936 miles versed sine of 38°160 miles through which the moon falls towards the earth during one minute of time in accordance with Newton’s demonstration. 13. The assumption by Newton of the whole number 60 as the distance of the moon in semi-diameters of the earth in combination with the same even number in seconds and minutes of time greatly facilitated the demonstration of the from the centre, we have 528 Dr. H. Wilde on the Moving Force of Terrestrial and law of the attraction of gravitation, the truth of which could at once be perceived by a simple mental calculation. Thus 60 x 60=3600 is the attractive force at the earth’s surface, and reciprocally a at the distance of the moon’s orbit. Now this same demonstration is equally applicable to the quantity of moving force of terrestrial bodies as well as at the distance of the moon’s orbit. For as the moving force is as the square of the velocity, a body falling during one minute through a distance of 16 feet 1 inch at the moon’s orbit, that is to say, with a velocity 60 times less than at the earth’s surface, its moving force would be 60 x 60=3600 times less than that of a body falling the same distance during one second of time on the terrestrial globe. Therefore the moving force and the attraction of gravitation are alike inversely proportional to the square of the distance, and are correlated equally in amount to maintain and retain the moon in its orbit during the course of its revolution round the earth. 14. The quantitative relations of the moving and attractive forces of the planetary bodies are set forth in the following new calculus of elements, wherein Mercury is taken as unity instead of the Earth, as in ordinary astronomical tables. 15. The masses of the bodies are taken as equal and require to be multiplied by the specific mass of each planet for the total force. 16. As the moving and attractive forces are correlatively equal they are expressed by the same numbers and their re- ciprocals, Mereury=1:000, and Neptune = a = 000016, as in the similar calculus of moving and attractive forces of the moon during its orbital revolution. 17. The planetary distances in radii of that of Mercury may be taken as astronomically correct, as they are derived from the periodic times; but the numerical expression of them in miles is necessarily only a near approximation, from the fact that the value of the unit of distance has not yet been exactly determined. Accepting, provisionally, the unit distance of Mercury to be 35,860,000 miles, we have for the mean distance of the Harth from the Sun 2°583 x 35,860,000 = 92,626,380 miles, and of Neptune 77:59 x 35,860,000 = 2,782,377,400 miles. In like manner the intermediate planetary distances in miles may also be determined. ad * 29 5 ravitation. ion of G& to Attract ton lal ves tn re Celestial Bod NEW TABLE OF ELEMENTS OF THE LUNAR AND PLANETARY ORBITS. Moving and Attractive Forces. Distances in PeriodicTimes.| | Radii. Days. Radii?. Reciprocals. Mercury .... IO008 ses ee ee Wy OO) 2 000 7-97 87:970 F000 = 1:00000 Wiens ne oi 368) => Nie N O022 Gee 2d 6 OT = 00 3°489 028661 HAUG Gots pe 200) "== aan NV 1 oo == Saeloe x87 0( =~ sobo 200 6°671 014990 OATS sai) ona D000 see ew wns O00G0 cee 2 (CUD 8 Oia \\Oo0 vel 15°492 0:06455 Were geesae) § 7148? =... SGD 200s 19110487 07.= 1681-400 51:094 0:01957 upiter....| 1id4d7* = ,.,. Vv 2426000 = 49°250%87'97 = 4332'580 180°6383 0:00553 Saturn ....| 24640 = .. 714957-000 = 122:300x 87:97 = 10759-000 607°129 0:00165 Uranus ....| 49°550? = .. 7121661:000 = 348:840x87:97 = 30687-000 2455 202 0:00041 Neptune ..| 77°590° = ., 7467142:000 = 683-494 x 87:87 = 60127:000 6020°208 0:00016 Moon......; 60°28° = .. 7219038:000 = 468-000 x 84:07 27°322 3634000 0:00027 \ a a SC a a pao | LIX. Vhe Ultra-violet Absorption, Fluorescence, and Magnetic Rotation of Sodium Vapour. By R. W. Woon, Professor of EHxperimental Physics, Johns Hopkins University * [Plates XV. & XVI.] } d bias present paper deals with the optical properties of sodium vapour in the ultra-violet, and forms a con- tinuation of an extended series of papers already published regarding this remarkable metallic vapour. For a proper understanding of its behaviour in the ultra- violet, a brief review of its properties in the visible region will be necessary. The absorption is of two types. A Balmer series of double lines, beginning with the D lines and extending into the remote ultra-violet. Of these but seven members were known previous to the publication of my last paper on the subject in this journalt. At that time I had succeeded in raising the number to about thirty, since which-time, by employing a larger quartz spectrograph, I have raised the number to forty-eight. The wave-lengths, as measured from the new plates, are given in the following table, and full details of the work will be found in the Astro-physical Journal for March 1909. This forms the most complete Balmer series thus far observed, only 12 lines appearing in terrestrial hydrogen, and 30 in solar. Wave-lengths of Lines in Balmer Series of Sodium Vapour. nd. r. | Nd. r. 0. X. Dap pap 589616 ) z | ST erecinc eat 2433°85 DON ovaededee 2417°38 9019} 2) 19.0... 81°48 y 9)/ BB alae 17-10 EE OA ls ait hs SOUR A BN ZO oes vt 29°42 Pot Cae ene Se 16°80 0947) 8) a1. 2772 | BB cecsecess 16-56 or eene ree 10 Var See 2 26°28 BO aie Se aene 16°33 DRA AR ZOU 4G | AW 2B Secacce ns 25°00 cL) Bearer? 1611 Teas 994-05 JE || 24 ......... 93:68 ll 41. si. 15:89 BS aetna SOO ay RAD. saiess02 22°90 Bre eaaent 15°70 Ry Sire cno nee P2715 PASM UE Re — 22°04 AD hsanatetes 15°52 lI OAs aaa se 240-70 2) a aeeaaeee as) Ae cakeee ee 15:37 Lae aS: 75°60 725 ae aA 20°60 DO 152 iat Gene 20)... |. 20:09" alten cae 15-06 aR Sepa: 56:02 thee) eae ee 19°50 is ceneetep 14:94 helices eee ets bee 49°46 HNO ater chai 19-00 ABs een ase 14:78 et Mien Ne 44-24 a Ga 18-4450) aon aoe 14-64 PAO sles see 40:06 | 2.2) ees 18:09 OO eeate 14:50 Tyee wos 36°70 | ae Vay tea * Communicated by the Author. + “An Extension of the Principal Series of Sodium,” Phil. Mag. Dec. 1908. _ Ultra-violet Absorption &c. of Sodium Vapour. aol As will be seen from the table, the last 22 lines, 2. e. nearly one-half of the whole series thus far observed, fall in a region of the spectrum not wider than the distance between the D lines! Kayser gives on page 521 the constants of the Balmer formula for the sodium series, computed from the seven lines known at the time. These seven lines are well represented by the expression 10°A-1= 41496°34—127040 n-?— 843841 n-4. With the complete series now at our disposal it will be necessary to redetermine the constants. I have calculated the wave-lengths of the 32nd and the 50th line from the formula, finding 2417°5 instead of 2418-44 (observed), and 2415:2 instead of 2414°5; that is, the calcu- lated values are separated from the observed by a distance equal to the distance between four of the lines at this point of the spectrum. _ Photographs of the series are reproduced on PI]. XVI. Fig. 1 is an enlargement showing the lines from n=12 to n=40. The last ten members are too close together to appear. Fig. 2 is reproduced natural size, and shows the series from n=8. ‘The source of light was the cadmium spark, and the iron comparison spectrum was taken on the same plate, the image of the are being projected on the slit just below the point illuminated by the light of the spark after it had traversed the sodium vapour. It is extremely interesting to note thata general absorption begins at the head of the series, which extends down to the end of thespectrum. In other words, the vapour is much more transparent to the light between the lines of the series than in the region below the head. This is in accord with the recorded observation of a faint continuous emission spectrum below the head of the series in the case of solar hydrogen. Pl. XVI. fig. 3 shows a series of spectra taken with pro- gressively increasing vapour density, in which the complete Balmer series appears, with the exception of the first member (n=3), the D lines, the position of which is however indi- cated. As the vapour density increases the higher members of the series appear, and the lower members are drowned out by channelled spectra which accompany them. These channelled spectra are analogous to the one which accompanies the D lines, which is the one previously studied with respect to fluorescence and magnetic rotation. They differ ‘from it in one respect, however. The channelled spectrum in the visible region consists of two parts, as is 5382 Prof. R. W. Wood on the Ultra-violet Absorption, shown in PI. XV. fig. 3. Spectrum d was made with moderate vapour density. The position of the D lines is indicated, though in the present case they have widened into a very broad band. A channelled spectrum appears in the red, orange, and yellow, and another in the green-blue, the yeilow- green region being transmitted freely. The red-orange portion spreads over and below the D lines, as the vapour density increases ; while the blue-green one pushes up in the other direction, the two eventually meeting at wave-length 5500, where a broad hazy band appears, which is just appearing in spectrum 6, and is very distinct in a. This point appears to be the “ centre of gravity” (if we may use the term) between the two channelled spectra which border the D lines. With a spectroscope of low dispersion we see merely a close double green line at the point, and the extreme violet-blue, everything else being cut off. The colour of the transmitted light is as deep as, and about the colour of, the light which gets through the densest cobalt glass. As I have already shown, there is some direct connexion between the mechanism which produces this channelled spectrum and the one which produces the D lines, for ab- sorption of blue-green light, carefully freed from yellow by prismatic analysis and colour screens, causes the vapour to emit yellow light of the wave-length of the D lines, in addition to the more powerful emission (line spectrum) in the blue-green region. I find now that channelled spectra accompany the other lines of the Balmer series, but that they are by no means the ccunterpart of the one around the D lines. They are not made up of two portions, with a comparatively bright region between, but spread out in both directions, both above and | below the lines which they accompany. I have found traces. of them as far down as the line for which n=8. They can be well seen in Pl. XVI. fig. 8, spectra d, e, and 7, while fig. 4 shows the one accompanying the first ultra-violet line (A =3300) on a larger scale; this photograph was made with a concave grating, “5” with rare, “a” with denser vapour. The Balmer line 3303 appears to widen on the side towards. the visible spectrum (see (a)), though this may be due to the presence of a group of heavy lines in the channelled spectrum.. An enlargement of this region is reproduced on Pl. XV. fig. 2 to show the complexity of the spectrum. The spectrum resembles the one in the blue-green region in its general appearance. The question now suggests itself:—Do these ultra-violet. channelled spectra exhibit the fluorescence phenomena shown Fluorescence, and Magnetic Rotation of Sodium Vapour. 533 in the visible region? This question I can answer in the affirmative for the first one (at line 3303). The fluorescence can be powerfully excited by the triplet in the zinc arc at wave-length 3300. The fluorescent light is of course in- visible, which makes its detection difficult. The sodium tube was closed with a large quartz lens,and powerful fluorescence excited with a Heraeus zine are in quartz. The image of the green fluorescent spot was focussed upon the slit of a quartz spectrograph by means of a quartz lens. Under these conditions ultra-violet fluorescent light, if present, should appear in the spectrum. Such was found to be the case, as is shown by Pl. XV. fig. 1; the zine are spectrum is shown above, the fluorescent spectrum below. The banded fluores- cent spectrum is strongest at some distance above the zinc lines (2. e. on the side of longer wave-lengths). The inter- vention of a glass plate between the arc and the sodium tube caused the disappearance of the ultra-violet fluorescent bands, showing that they were due to the absorption of ultra-violet _ and not of visible light. An attempt was next made to see whether any mechanical connexion existed between the mechanisms which produced the D lines and the visible channelled spectra (which have been shown to be connected) and the ultra-violet lines. The zine ultra-violet triplet was isolated by means of a quartz spectrograph and focussed on the aperture of the sodium chamber. The room was absolutely dark, and all extraneous light carefully screened off. No visible fluorescence was observed. The ultra-violet fluorescence was, however, pho- tographed with a second quartz spectrograph. In this case one is working wholly in the dark, and the difficulties attending the adjustment of the two optical trains may be well imagined. This experiment indicates absence of connexion between the two systems. The converse experiment was next tried. Powerful stimu- lation by the entire visible spectrum failed to show any trace of the ultra-violet band in the spectrum of the fluorescent light, even though the visible region was overexposed ten fold. This again indicates absence of connexion. It looks very much as if the different lines of the principal (Balmer) series and their accompanying channelled spectra may be considered as produced by different entities. The enormous increase in vapour density necessary to bring out the higher members of the series may perhaps be ascribed to the possible circumstance that the entities producing them are present in smaller numbers. 534 Ultra-violet Absorption &c. of Sodium Vapour. It appears to me that there are two hypotheses which we may make: First, that the Balmer lines and their accom- panying spectra are caused by atoms which have lost one, two, three, four, &e. electrons. Secondly, that they are pro- duced by aggregates or complexes of one, two, three, or more atoms. In either case it seems probable that the members would be present in continuously decreasing numbers. I feel inclined to favour the first hypothesis, for the reason that the channelled spectrum accompanying the D lines appears to be the most complex, the ultra-violet channelled | spectra decreasing in complexity as we pass down the spectrum. It seems probable that complexes made up of large numbers of atoms would have more available frequencies than the single atom, whereas the loss of a large number of electrons might be expected to decrease the number of dif- ferent frequencies. This, however, is a point which can be handled by mathematical physicists. Of course I have not brought as high dispersion to bear upon the ultra-violet region as has been used in the visible, for this region has been photographed by Mr. Clinkscales, one of my students, in the second order spectrum of the 21 foot grating”. This is owing to the fact that it is difficult to get a sufficiently brilliant source giving a continuous spectrum below wave- length 3300. The crater of the arc can be used for the first band, but we have to rely upon the spark below this point. The crater is comparatively weak, even in the region of -wave-length 3300. Mr. Clinkscales’s photographs of the visible channelled spectrum show that there are, in round numbers, about 6000 absorption-lines, as many as thirty being crowded together in a region not wider than the distance between the D lines. ~ Magnetic Rotation. The study of the magneto-optical properties of the vapour in the ultra-violet is attended with great experimental diffi- culties. The only positive result thus far obtained is that the magnetic rotation at the first two ultra-violet members of the Balmer series is in the same direction as at the D lines. The method employed was the usual one, polarized light being passed in succession through the magnetized vapour, a Fresnel double prism of right- and left-handed quartz, and a second polarizing prism, and the image of the horizontal fringes focussed on the slit of the quartz spectrograph. * Wood, “ Resonance Spectra of Sodium Vapour,” Phil. Mag. [6] xy. p. 581 (May 1908) ; Phys. Zert. ix. no. 14, p. 450. a os Interference Phenomena of Chlorate of Potash Crystals. 535 Nicol prisms cannot be used on account of the absorption of the ultra-violet by the Canada balsam. We may, however, substitute glycerine for the balsam, or employ the Foucault prism with its air-film. Both methods were used.- The curvature of the fringes at the ultra-violet lines was very slight at the 3303 line, and scarcely discernible at the 2852 line, but it was in the same direction on each side of the absorption line, and in the same absolute direction as at the D lines. Nothing has as yet been accomplished with the lines in the ultra-violet channelled spectrum, and I feel very doubtful about getting results in these regions. In the visible spectrum, as I have already shown%*, the rotation is positive at some of the lines and negative at others. More complete data regarding this point will appear in a paper which will appear shortly in the Astro-physical Journal, in which the more recent results obtained by Dr. Hachett and myself on the fluorescence and magnetic rotation of the vapour will be described. July 1908. LX. High Purity Interference Phenomena of Chlorate of Potash Crystals. By R. W. Woop f. | ae [Plate XV. fig. 4.] | Per. years ago I endeavoured to prepare large crystal i lamine of chlorate of potash for the purpose of isolating spectrum lines by reflexion for monochromatic illumination of fluorescent vapvurs. The experiments resulted in only moderate success ; but I obtained a few crystals which I believe showed narrower reflexion maxima than any that have been previously described. One flake, measuring about 6 mm. on a side, exhibited total reflexion at normal incidence of a region of the spectrum only 10 or 12 Angstrém units in width, that is, only double the distance between the D lines. The spectrum of the transmitted light exhibited a very black band at the same point, and of the same width. This band was photographed, after having been brought into the vicinity of the D lines by suitable inclination of the plate, and the D lines themselves impressed on the plate by holding a sodium flame in front of the slit for a few seconds. The photograph is reproduced on Plate XV. fig. 4, spectrum “c.” The position of the D lines * “On the Existence of Positive Electrons in the Sodium Atom,”’ Phil. Mag. Feb. 1908. + Communicated by the Author. 536 Prof. R. W. Wood on High Purity Interference I have marked on the spectrum immediately above this one. (The marks refer to the lower spectrum only.) _ ; By increasing the angle of incidence, the band can be made to move down the spectrum, widening as it moves. When in the green it appears as in spectrum “}” and is accompanied by fainter lateral minima. The narrowness of the reflected region has been shown by Lord Rayleigh to be due to multiple twin planes, sensibly equidistant. From the width of the reflected region we can form an estimate of the number of lamine present in the crystal plate. Hach lamina gives us by reflexion a virtual image of the source, these images being in line, one behind the other, at normal incidence. The action is not unlike that of a diffraction grating when the diffracted ray is at grazing emergence. If weare dealing with a first-order spectrum, 1000 lines are necessary to resolve the D lines. As I have shown in a previous paper (“ Interference-phenomena of Chlorate of Potash crystals ””)* we have in general a number of orders present, and if we photograph those in the ultra-violet, we can determine the order of the one (or more) in the visible. (Hach order is represented by a narrow region of wave-lengths selectively reflected.) In the present case since the visible spectrum shows but a single reflected band (in the yellow) we are clearly dealing with the first order. The second order will be found at wave-length 29 or thereabouts. If our visible band at wave- length » was a second order one we should have a third order band at wave-length 2X or 4000 which would be easily visible. If now we compare the width of the band in the photo- graph with the distance between the D lines, it is clear that the crystal plate is very nearly able to separate or resolve the D lines. In other words, if we incline the plate a little less, causing the band to move up the spectrum, it will reflect D, before it reflects D,;. It was, however, not quite able to do this, but would easily separate lines of twice the separation of the D’s. From this we may infer that the number of twin planes in the crystal is somewhere between 500 and 1000 say roughly 700. If we are dealing with a first-order spec- trum the path difference between rays reflected from two adjacent twin-planes must be equal to the wave-length of the light in the crystal. Assuming no phase-change this makes the thickness of each lamina about 0°0002 mm., and multi- plying this by 700 gives us 0°14 mm. as the thickness of the crystal plate, which was not very far from the truth. * Phil. Mag. [6] xii. p. 67. Phenomena of Chlorate of Potash Crystals. 537 This particular crystal plate was selected froma very large number. I have a en directions for preparing the plate in a former paper ™. Possibly by taking a number of ‘selected plates and immersing them in a solution which is cooling off and throwing down. crystals, we may be able to build up plates with even larger numbers of twin planes. I have not yet tried this method. If somewhat larger plates could be made they would prove superior to the spectroscope for the isolation of spectral lines for monochromatic illumination, for a much wider source of light could be used. It is interesting to compare the crystal described in this note with the best Lippmann photographs, which show colour resulting from the same type of interference. Mr. H. E. Ives has made the best Lippmann photographs with monochromatic light that I know of. The spectrum of the band reflected from his best plate is shown in Pl. XV. fig. 4, “a,” on the same scale of wave-lengths, 7. e. taken with the same spectroscope. It has a width about three times as great as the band reflected from the crystal. If I remember rightly, Mr. Ives sectioned a similar film and counted about 250 silver lamine, built up by the stationary waves. This is in good agreement with our estimate of the number in the chlorate crystal. _ It is most remarkable that the lamin are of such constant thickness in a given plate and yet vary over such a wide range when we consider different; a plate which starts with twin planes ‘0002 mm. apart apparently builds up 700 laminz of the same thickness, while another plate starting with a different “ grating constant” sticks to it to the end. The process of formation of these crystals is well worth a further study. It would be very interesting to see whether a crystal once started could be induced to ‘change its mind about its “ constant ”’ by varying the concentration or tem- perature of the mother liquor in which it was forming. East Hampton, Long Island. July 1909. * “Tnterference-colours of Chlorate of Potash Crystals,” Phil. Mag. [6] xii. p. 67. é Phil. Mag.8. 6. Vol. 18. No. 106. Oct. 1909. 20 [ 538 ] LXI. On Velocity of Molecular and Chemical Reactions in Heterogeneous Systems. By Dr. Meyer WI.pErmMan, Ph,D., Base4O0zon:)*. Parr i [Plates XVII. & XVIII. ] I. On Velocity of Molecular Reactions in Heterogeneous Systems and the so-called Diffusion Theory. §1. Tr} the report of the British Association, 1896, Zeit- schrift fiir physikalische Chemie, 1899, xxx. pp. 348- 368, and Phil. Mag. July 1901, p. 50, and some other publi- cations, 1 showed that the velocity of all molecular reactions between two parts of the heterogeneous system, such as trans- formation of water into ice, ice into water, separation of salt from an oversaturated solution, solution of salt, evaporation of liquids, condensation of vapour, solidification of solutions to solids or to solid solutions, &c., all follow the same law : dt vee (t, a= t)(t—tor) =C&r(to—?), 2. e. the velocity of reaction is at the time 7 directly propor- tional to the remoteness of the system at the time 7 from the point of equilibrium, t,—t, and to the surface of contact of the reacting parts of the heterogeneous system, t—é, which is proportional to =;. Further improvements in the methods employed and the photographing of the reactions showed, however, the necessity of introduction of the constant K, which I called the “ instability constant,” 1. e. dt et C (tp —t)(t— boy + K) (see the above papers in the Zevtsch. fiir physikalische Chemie and Phil. Mag.) =K (t,—t) for constant surface. The above equation was therefore given by me in a most general way, including the solution and separation of salts, as a particular case only, in a series of publications before Noyes and Whitney (Zertsch. phys. Chem. 1897, xxiii. p. 689), before L. Bruner and Tolloczko (Zeitsch. phys. Chem. 1900, xxxv. p. 283), and long before Nernst and H. Brunner (Zeitsch. phys. Chem. 1904, xvii. p. 52), who all use it for the particular case of solutions of salts only. The equation * Communicated by the Author. Velocity of Molecular and Chemical Reactions. 589 used by Noyes and Whitney is « =0 (to—t) (they take the surface to remain constant); Bruner and Tolloczko use my equation CS;(to—t); the equation used by Nernst and Brunner is as (t,—t), where 5 are also constants, 2. e. the equation of the above authors is identical with the first (less accurate one) of mine. As my papers were published also in the very same Zeitsch. fiir. phys. Chem. in which these and other authors * later published their papers, I must clearly uphold here my priority rights, since all these authors do is to give their own interpretation to my constant. All the more so, since Nernst and E. Brunner, L. Bruner and Tolloczko, give us in an arbitrary manner (with their methods, see §2) for a part of the curve what was established by me before, on careful experiments, for the whole curve; my reactions were photographed and carried out by methods of infinitely greater accuracy and reliability than theirs. In my general equation the assumption was made that the volume remains the same during the whole time of the reaction. Mr. Drucker also investigated the effect of the volume upon the speed of solution of solids, and found that the speed is indirectly proportional to the volume of the liquid. I wish to add that, from the standpoint of my general equation, this is, at a constant surface of the solid, a self-understood, un- avoidable necessity. Because, as the reaction goes on at the surface of the solid in contact with the liquid, the amount of substance going into solution is, at a constant surface, at the time t only dependent upon the concentration of the solution, and this amount is according to our conception subsequently distributed by the stirrer, through the whole volume of the liquid. If the volume is, for example, twice as large, the increase in its concentration must be twice as slow, i. e. the speed of solution, as measured from the concentrations of the solution, will be twice as small. This naturally applies to all molecular reactions, of which solution of solids forms only one particular case. But I wish clearly to point out, that this dependence upon the volume is only an apparent one, for the reason that we are able only to measure the concentrations of the solution. The true reaction takes place only at the surface of the solid, and here the phenomenon of solution is independent of the volume of the rest of the solution. Only the surface of contact and the concentration of the solution in contact with the solid are the working factors and come into consideration here. * See Karl Druker (Zeitsch. fiir phys. Chem. 1901, p. 173, and p. 698), who wrongly attributes my equation to Noyes & Whitney. 202 540 Dr. Meyer Wilderman on Velocity of Molecular §2. On the Method of Investigation. (a) On the artificial production of solid blocks suitable for investigation in this region. Also on the solids used by Nernst and E. Brunner and others to prove the Diffusion Theory. The speed of reaction is directly proportional to the surface of the solid, and it is quite evident that no reliable research at a constant surface is possible, and still less are comparative quantitative experiments possible, so long as we cannot procure a solid, with a sufficiently large surface, which is quite uniform throughout its whole thickness, which can be reproduced every timie we want it, which is chemically pure, which is suitable for quick and reliable measurements of concentration, and which represents a reaction free from subsidiary reactions and from other complications. To get all these requirements realized at once is by no means easy. Metals seem to answer the requirements of surface, but, except Pt, Ag, and the liquid mercury, they all cannot be got chemically pure, and insurmountable difficulties are created for correct measurements of the speed of reaction by the interference of local action due to small variations in the impurities. Again, some of the minerals, such as marbles, gypsums, and some other few substances, present the best. material for getting suitable blocks for an investigation, but these minerals are seldom chemically pure, few of them are uniformly the same everywhere, and still fewer of them are substances which are suitable for a rapid and reliable titration. The solid substances, which are most suitable and desirable for research, are for this reason those which are artificially prepared in the laboratory, but the difficulty is that these substances are almost without exception obtainable either in small crystals or powders, &c., while we require for the investi- gation blocks with large surfaces. How Nernst and Brunner try to overcome the difficulties here is best to be seen from the two principal substances of their investigation, upon which they tried to build up experimentally their diffusion theory, namely, benzoic acid and “* magnesium hydroxide.” About the first we read that, to create a block, they “melted the benzoic acid in a test-tube, poured it into a porcelain cover of a crucible, 5 cm. diameter. On cooling the same separated from the cover, and they fixed it in again with shellac; the surface was then rubbed down with a _ knife and sandpaper. ‘The surface still clearly retained its crystalline structure. This cake still contained scratches at the rim, and they filled these now up with paraffin.” With and Chemical Reactions in Heterogeneous Systems. 541 this method we always get air-tubes and spaces enclosed in the acid, and this cannot be avoided even by removing the air from the liquid acid in vacuum or by very slow cooling of the acid in a double-walled air-bath. The substance does not erystalliseas one uniform mass. Photo (1) (Pl. XVII.) gives the surface of the block of benzoic acid as soon as the top thin film is removed during the reaction. There is no need for me to add that such a block cannot possibly be suitable for any comparative quantitative measurements. This process of melting can naturally find only a limited application, cannot e.g. be applied to inorganic substances requisite for the research. From among the last Nernst and Brunner chose for their research “magnesium hydroxide.” We are told that they “took advantage of the property of calcined MgO mixed with water, to dry to a thick mass and to become hard.” As a matter of fact, ordinary analysis shows that the Mg(OH), always contains, under their conditions of work, very much carbonate, and we find that Mg(OH), cannot stick together - without it. I find that if we mix MgO with water and let it dry in an ebonite lid with vertical rims over CaCl, in vacuum, so as to prevent absorption of CO, by the MgO or Mg(OH),, we get the block as in photo (2); if we dry pure Mg(OH), mixed with H,O over CaCl, in vacuum, we get a block as in photo (3) (in which one part of the surface has been polished). Both of them show a great contraction on drying, contain numerous air-holes, before and after their surfaces are cut away with a razor,contain big cracks across, and fall to pieces as soon as they come into contact with water, as is to be seen from photo (4), in which the breaking up of Mg(OH), under water is shown. If we mix MgO with 10 per cent. gum- arabicum, fill with it the ebonite lid and dry over CaCl,, we get a disk, which sticks together as in photo (5), which at the same time shows the enormous contraction of the mixture ; but as soon as we bring this disk in contact with water it breaks up to pieces as is seen from photo (6). There is no possible way of getting a block of pure Mg(OH), which could be brought into contact with water without falling at once to pieces! I lost quite a considerable time in my attempts to produce such a block, but entirely failed, though I was with my method quite successful in a great number of other cases, namely: I compressed the mixture of MgO and H.O directly after they were mixed, and the mixture MgO and HO after standing in a closed up vessel for about two weeks; then I compressed dry Mg(OH),, as well as Mg(OH), mixed with water in moulds, under a pressure of several thousand atmospheres ; and though I succeeded with a conical piston in 542 Dr. Meyer Wilderman on Velocity of Molecular this way in getting beautiful uniform blocks free from air-holes and cracks and the blocks seemed quite excellent, yet when the same were brought into contact with H,O they imme- diately fell to pieces. The solids on coming into contact with H,O expand again to such a degree that they fall in no time to pieces. On the contrary, MgCO; shows no such property, but gives excellent blocks which stand water very well. Photo 7 gives a block of MgCO; compressed under 2500 atmospheres, in which the impression of the piston in the centre is still to be seen, and then allowed to remain under water. Photo 8 shows a block of MgCOs3, which was com- pressed in an ebonite lid in a special arrangement by means of a screw, after it was first mixed with water to a paste, and then allowed to remain under water. Photo 9 shows MgCO; as got in an ebonite lid after the same was mixed with water to a paste and dried, and then the lid and the dry disk were allowed to remain for a long time under a dilute HCl solution ; for they show at the same time that water does not break up the same. Nernst and Brunner give us, on p. 79 of their paper, a series of apparent reasons why their theory does not require to hold good in case of Oxides, Carbonates, &c. which do not agree with their theory, and why this one substance, Mg(OH)p, is to be of all substances the substance to be taken for the test of their theory, and we are invited to accept their theory on the basis of “ Mg(OH), ” alone. Now we find that Nernst and Brunner’s so-called Mg(OH), is nothing but a mixture of oxide, hydroxide, and carbonate of magnesia. Not contented with this, since their ‘“‘ magnesium hydroxide”’ blocks do not hold sufficiently well, they mix it with gum arabicum, which, as known, is the potassium and calcium sali of ‘‘ Arabinsiure” or ‘“‘ Gumisiure,” aud so their mixture contains besides also the Magnesium salt of ““Arabinsiiure.” As the conditions of preparation of their blocks were never identical in respect of time, quantity of gum arabicum used, &c., the composition of their mixture was never the same. And with such mixtures Nernst and Brunner give us their quantitative experiments upon speed of reaction, their comparative experiments, their principal experimental proofs of the diffusion theory ! The method I use for getting from a substance chemically pure and suitable for the research, blocks of any desired thickness, of the same uniformity through the whole of its mass, free from air and cracks, and enabling us to use the same blocks for a series of experiments for comparative experiments and to reproduce the same, consists in their artificial preparation under the very high pressure of several and Chemical Reactions in Heterogeneous Systems. 543 thousand atmospheres. The substance is brought into a steel ring of an internal diameter=51 mm., external diameter =127 mm., placed in the steel base (Pl. XVIII.), and is com- pressed here under several thousand atmospheres with the piston, which is 51°mm. diameter and 12 cm.long. The dia- meter of the piston is 51 mm., or very nearly 2 inches. The diameter of the ram of the hydraulic press is 10 inches, the ram is compressed to 75 or 100 atmospheres on the gauge, thus producing a pressure on the piston and the substance of 75 X 25=1875, or 100 x 25=2500 atmospheres per square inch. The maximum compression of the solid usually takes place much below these pressures, already at about 1000 to 1400 atmospheres, and often below this. The substances are left under the above pressure usually for 16 to 24 hours, when the pressure is generally released ; the base is then removed from the ring containing the compressed block of the substance, and the latter is pushed out from the ring (the pressure usually required is 70 to 350 atmospheres per ' square inch), with the piston, into a steel ring of a larger diameter placed below the ring, it being arranged that the disk should fall on a piece of soft felt below. The ring, base, and piston must be perfectly polished so as to get a perfect uninjured block. The ring itself was a little moditied, made internally a little conical (a fraction of a mm. suffices) from top to bottom, in order that the block of substance shall leave the ring at once, as soon as it is moved by the piston, instead of its requiring to be pressed through the ring through its whole thickness. In such a way we get beautiful disks, with perfect surfaces, free from any air-holes, cracks, &c., requiring no admixtures in order to make the substance stick well together, with perfect uniformity through their whole thickness ; whether the sub- stance is crystalline or amorphous, an organic or inorganic solid, a compound or an element (S, C, metal powders, &c.), it is crushed to a uniform body; one disk 1°5 to 2 cm. thick is quite enough for carrying out a long series of com- parative experiments, and we are able to polish and to rectify over and over again the surface of the same block for the same experiment, because it must be a strict rule to allow the solid to corrode during solution only as little as possible and to repolish the same as often as is practicable. We can keep the dissolving surface of the solid always at nearly the same height in the liquid, by fixing the blocks to ebonite disks of different thicknesses. Photo 10 (Pl. XVII.) shows a disk of benzoic acid before treatment; photo 104 shows the block of benzoic acid after solution in water 544 Dr. Meyer Wilderman on Velocity of Molecular during two hours. The surface is still excellent. JI find, however, that while some of them (such as benzoic acid, most organic substances, MgCO;, &e.) remain on placing the disk into water (under stirring) in perfect condition; others, such as Mg(OH),, Fe.(OH)., & ., break up mecha- nically at once, since when the disks are brought into contact with water they suffer too great an expansion. All the same, the above method now opens the way for a true and reliable investigation in this region, putting at our disposal an exceedingly great number of chemically pure substances, suitable and desirable for this research, while before we practically had none, and we were dependent upon minerals, which are seldom perfectly pure. Care was taken to use only the purest chemicals for this research, and the firm of Merck prepared the same for me with special care and under special instructions ; and where minerals had for special reasons to be used, only the best and purest specimens procurable were employed. (b) On the Arrangement of Constant Speeds of Stirrer. If we have a super-cooled or a super-saturated solution, so that very fine particles of ice or salt separate from the whole of the liquid, and through the whole of the liquid, then, by the use of an effective stirrer creating currents in all directions, a uniforin state of the whole system during the reaction can be obtained, as can be seen from the photo- graphic curves in my paper (Zeitschr. fiir phys. Chemie, 1899) giving the speed of these reactions. When, however, we have a solid piece, salt or ice in a liquid mass, so that the contact between the solid and the liquid is only local, and reduced to a comparatively very small surface of contact, it is extremely difficult to get the liquid uniform through the whole mass, as already mentioned in the above paper. Nernst and Brunner use anair-moter, which is known to be inconstant, and the variations of its speed were, according to Nernst and Brunner, as much as 10, 15, sometimes even 30 per cent. The direct experiments with pieces of rubber, of the same specific gravity as water, showed me, that if we keep the solid fixed at the bottom and move the liquid by the stirrer, the number of revolutions which the liquid makes past the solid is not directly proportional to the number of revolu- tions of the stirrer, but is considerably smaller. The liquid is also never equally moved in all its layers, as is to be seen from the fact, that a cone is formed in it with the apex (smallest speed) on the stem of the stirrer, and the base (biggest speed) above it, which is the higher the quicker the and Chemical Reactions in Heterogeneous Systems. 545 stirring. For this reason I preferred to fix the solid disk, as Drucker did, to the stirrer itself, so as to make the number of revolutions of the same equal to the number of revolu- tions of the stirrer, and I placed the investigated disk, always of nearly the same thickness, between the two stirring plates of the double stirrer (see Pl. XVIII. fig. 1), so that, besides moving the block, the liquid was stirred above and _ below it. The double stirrer is made of ebonite, which is affected neither by acids nor by alkalis. The two stirrers are connected with ebonite rods forming a cage for the block of substance to be investigated. The last is covered with paraffin of a high melting-point at all surfaces except the top, a rubber ring is put on it and prevents it from being damaged after it is fixed between the rods. Though apparently little work had to be done, I found that to get constant speeds I had to use a powerful electromotor (} H.P.) to prevent its heating up, and that constant voltage as wellas a regulation ofthe speed had to be provided for. Both the field and armature were supplied - with a series of resistances and with continuous spiral resis- tance when required. In all experiments I usually employed 200 volts thrown upon the common terminals connecting the field and armature. For the variation of speed within very great limits, I used in the first instance different sets of wheels of different diameter, which could be changed as desired, and the wheels were driven by a flexible steel spiral which could be applied to all of them by means of the arrangements seen in fig. 2(Pl. XVIIL.). To get the varia- tions of speed in still greater limits the volts thrown upon the field and armature were different, use being made of accu- mulators. I was thus able to change the speed of the stirrer from about 1 revolution per minute to about 500 and to keep the speed practically constant. The best results were obtained for speeds of about 100 to 150 revolutions per minute, when the variation after hours did not amount to 1 revolution per minute, and which I adopted for my investigations. As the effective stirring depends more upon the construction of the part of the stirrer in the liquid than upon the number of revolutions, I reduced the last by improvements in the first, and this enabled me to get with an ordinary one-fifth second stop-watch, easy, reliable counting of the number of revolutions of the stirrer, which usually were kept at about 130 per minute. The speed-indicator was used only for speeds above 250 revolutions per minute. I found that no permanent speed could be got for longer periods when ordinary cords are used, because as these stretch under work the speed changesalso. A thin steel wire was for this reason 546 Dr. Meyer Wilderman on Velocity o7 Molecular wound to a spiral on a lathe supplied with small hooks and used instead of cords. This has a wonderful flexibility, gives an excellent grip, and allows good adjustment, if required, by cutting off a few rings or by forcible stretching of a few of them, and gives always the same constant speed. By an arrangement, as seen at C of the photograph (fig. 2), the same spiral can be used for the different pulleys. (c) Further details of the Method (see fig. 1, Pl. XVIIL.). The beaker with 1500 c.c. of the liquid was kept in a bath of a constant temperature, a 1/10 degree thermometer having been immersed in the liquid, with its bulb close to the solid block ; the effect of stirring upon the temperature of the liquid seemed to be but small, but had to be adjusted sometimes by the temperature of the outer bath, which was continuously stirred by the second stirrer driven by a pulley from the first. In case of substances of very small solu- bility, such as the gypsums, which do not admit sensitive titration, especially since very dilute solutions had to be investigated here, the method of electric conductivity after Kohlrausch had to be used. Two platinum electrodes (see fig. 1) were fixed in the ebonite lid of the beaker, for making these measurements, the electrodes coming into the middle between the two stirrers. A series of known concentrations of the same CaSO,+2H,0, which later on had to be in- vestigated as a solid disk, was prepared, and smali intervals of concentrations were investigated with a series of resistances, and so a scale was got for them on the bridge, for the same temperature and speed of stirrer, which subsequently was used when the solution of the disk was investigated. The water used in these experiments was the same. The volume of the solution remained for the whole series the same, namely 1500 c.c. In case of other substances, such as benzoic acid, or of mixtures, the speed of reaction was measured by taking out samples and titrating the same. The samples were drawn off with a 10 c.c. pipette through the glass tube fixed in the ebonite lid of the beaker, always from the same place between the two stirrers ; after the pipette was first twice filled with the solution, and the solution let back into the beaker, the final filling of the pipette for titration was carried through within the last 5 to 10 seconds of the minute. Very great and quite exceptional precautions had to be taken with the titrations of this acid. I titrated the benzoic acid with a ‘088 normal baryta, back titrating the same with a ‘022 normal benzoic acid. The baryta was added from a and Chemical Reactions in Heterogeneous Systems. 547 thin well-running tube, 1 mm. of which indicated °01 c.c., and I read the tube with a lens to about *2 mm. or to 002 c.c., and the excess of baryta had to be titrated with the more dilute ‘022 normal benzoic acid so that the last drop should not affect the result much, and this operation had to be repeated twice to further reduce the reading-error. As 50 c.c. of ordinary distilled water contain already an amount of CO, corresponding to 0°3-0°4 c.c. of a 022 normal solution, and at least 50 c.c. of water are required for washing out the sample bottles and for titration, the CO, of the water alone is enough to cause an error of 10, 20, or 30 per cent. in the total difference measured. Therefore the water in the wash-bottle had to be freed from CO, by boiling and then protected by a tube of soda-lime to prevent its contamination with CO, from the air or through our blowing, the total amount of wash-water used for each titration had to be kept the same in each experiment, and the water itself had to be titrated and the samples freed from CO, before titration by boiling. As rapid stirring mixes energetically the solution with the air containing CO., and the experiment lasts for several hours, the water in the beaker had to be protected against contamination with CQ,, as shown in fig. 1 (Pl. XVIII). The glass cylinder was closed up with a thick ebonite piece and sealed up with Crooks’ cement between glass and ebonite. In the ebonite piece a circle was eccentrically cut out to allow the blades of the stirrer mixing the solution to pass through it into the beaker. A deep circular groove 17 mm. wide was cut out in the remaining ring, concentric with the cut-out circle ; to the stem of the stirrer a circular lid with a deep projecting circular rib 7 mm. thick, cut out of one piece of ebonite, was fixed, and the stirrer was fixed so that the circular rib entered deep into the groove, leaving ) mm. free space all round without touching the circular ring at the bottom; this groove was filled with distilled water sufficient to form a secure seal with the rotating circular rib of the lid of the stirrer, and the stirrer was thus always kept in the same position in the beaker. None of these very necessary precautions in the titration were taken by Nernst and Brunner, Bruner and Tolloczko, and others. All the above precautions in the preparation of the blocks, in the arrangement of constant speeds, in the titration &c., I had to take before I was able to get the constants, as I give them in this paper, which are considerably worse than those supplied by Nernst and Brunner and others. It is true, Nernst and Brunner tell us, that “the greater variations of A were omitted if they differed much from the rest,” but o48 Dr. Meyer Wilderman on Velocity of Molecular this is a very strange thing to do, when we are asked to take their results as quantitative measurements and to give them all the credence we have to give the quantitative results, instead of leaving it to the reader to see for himself what value those A’s really possess. specially is this regrettable when we are invited to accept a theory on the basis of con- clusions which are mostly based upon differences in the values of A, which, it is quite evident, are often smaller than the experimental error of the method itself. § 3. The Theory of Molecular Reaction, including the Solution of Solids in a Solvent. Also on the Diffusion Theory. In the first place let me state again, in somewhat greater detail, the content of my equation as far as it concerns the solution of salts, before I pass to the consideration of its content according to the diffusion theory. I assume that every sub- stance has a solution pressure, which causes the solid to pass into the solvent, whenever brought into contact with the same; that this goes on until the solution becomes saturated, so that the solution pressure of the solid is kept in equilibrium by the counter osmotic pressure of the saturated solution, which (leaving out of consideration galvanic cells where we have to deal with electrostatic forces) at equilibrium are equal ; that in case of an unsaturated solution, before equilibrium is reached, the solution pressure of the solid is: greater than the counter osmotic pressure of the solution, and the substance of the solid is still driven into the solution by a force, which is directly proportional to the difference of the existing solution pressure and the counter osmotic pressure, or to the difference of the osmotic pressure of the solution at equilibrium (which is equal to the solution pressure of the solid) and the osmotic pressure of the solution at the time 7, or also directly proportional to the difference of the concentration of the solution at equilibrium and its concentration at the time 7, since the osmotic pressure is directly proportional to the concentration. Similarly, in case of an over-saturated solution, the solution pressure of the solid is smaller than the counter osmotic pressure of the solution, and the substance in solution is driven into the solid by a force, which is directly proportional to the differ- ence of the existing osmotic pressure of the solution and the solution pressure of the solid (or osmotic pressure of the solution at equilibrium). The speed with which the solid passes into the solution or from the solution into the solid, I therefore take to be directly proportional to the driving force, and the number of molecules passing from the solid and Chemical Reactions in Heterogeneous Systems. 549 into the solution, and vice versa, is evidently the greater, the larger the surface from which they pass into the solution, or the larger the surface of contact of the solid and liquid, because the reaction goes on all along at every point of the solid in contact with the solution. Hence my equation Ge. 2 CSt(t.—f). These extremely simple and clear conceptions about the cause of the shape of my general equation, Noyes and Whitney, Bruner and Tolloczko, Nernst and Brunner tried to replace, singling out a special case of solution of solids from all the rest of the reactions, by other conceptions. Let us now see what these conceptions are, how they simplify matters purely theoretically, and how far they are confirmed by true experiments. Noyes and Whitney, dealing with solubility of salts, write :—"‘ We can imagine that the solid substance is always surrounded with an infinitely thin layer of a saturated solution, and that the process consists in a diffusion from this layer to the rest of the solution, which is kept by stirring homogeneous. Then according to the known laws of diffusion the speed of reaction will be directly proportional to the differences of concentration of the saturated solution fs da ug aS and that of the solution, 1. e., 22 = A’(C'—C).” This view was adopted first by L. Bruner and Tolloczko, who went a step further, and assumed that the velocity constant is nothing else but the digusion constant, and later on they introduce also the idea of a finite layer 6 &c. The views of these investigators were later on fully adopted and followed by Nernst and Brunner, who instead of D use Bruner and Tolloczko’s of and make a step further still, by trying to explain the equations of Boguski, Spring, Haber, and Lorenz, giving speed of chemical reactions in heterogeneous systems, as diffusion equations also. With the last we shall deal in detail later on. In this first publication I shall restrict myself principally to molecular reactions only. Returning to the work of Bruner and Tolloczko, as “ 5 had to be made equal to the velocity constant, they soon got the result thatif the diffusion constants were not to upset the theory, 6 or the layer of Noyes and Whitney cannot be taken to be “infinitely thin,” but must have a measurable thickness. In this, as well as in my identical equation, 550 Dr. Meyer Wilderman on Velocity of Molecular every letter denotes the same thing, but C’ is in my con- ception the concentration of saturation which the system is striving to reach, owing to the solution in contact with the solid being unsaturated, U'—C being directly proportional to the force driving it to the state of equilibrium, while Noyes and Whitney assume that the concentration of saturation is always present near the solid salt, while the concentration of the rest of the solution is entirely another one. To make, however, this assumption of constant saturation at a surface possible, Bruner and Tolloczko had further to introduce the conception of infinite speed of reaction at the surface of the solid, while following them Nernst further introduced also the idea of “‘injinitely great forces acting at the surface,” since without such assumptions the above explanation cannot, evidently, be upheld ; and then to suit the idea of the da second hypothesis had to be made, by Tolloczko and Bruner, also adopted by Nernst and Brunner, that the solution cannot be mixed up to the solid itself, but the moxing stops at a distance from the solid. Since without this mysterious property we get from sak, that if 6 were according to Noyes and Whitney infinitely small, D, or the diffusion constants as calculated from this equation, would only prove the falsity of the theory. This is how the original hypothesis of Noyes and Whitney, which seemed to be very simple, grew up into a conglomerate of assumptions. I shall now test, step by step, what this theory and all its assumptions are really worth. | (a) Let us now first see, how Noyes and Brunner support their hypothesis, following in all essential features the ideas given by Bruner and Tolloczko. About the first Noyes writes : “At the surface of contact of two phases (or parts) of the hetero- geneous system equilibrium is extremely quickly established.” “This,” in Nernst’s opinion, “follows already a prior theoretically as a necessity, because otherwise noticeable difference of the chemical potential would exist at the separating surface, 7. ¢., at infinitely near points, which evidently would lead to infinitely great forces and velocities of reaction. This, however, means nothing else than thatin the immediate vicinity of the two surfaces the equilibrium is established with infinite speed. If we assume what is more nearly true, that the surface of separation is not a mathema- tically sharp plane, we have still to deal with dimensions of the order of the spheres of action of molecular forces, and if we can no longer speak of infinitely great velocities of reaction, still they must be of a very great order, which practically and Chemical Reactions in Heterogeneous Systems. 551 amounts to the same.” This says in so many words what Bruner and Tolloezko told us before (Zeitsch. fiir anorg. Chemie, 1901, p. 328) that “the saturated solution at the surface of the solid is formed instantaneously.” Now, this fundamental assumption of Nernst is quite wrong, as can be seen from the following: when we mix two liquids, say in equal parts, and a reaction goes on between them, we have, in the first instance, a certain difference of chemical potentials acting between the molecules in the system, since otherwise no reaction would go on; secondly, the acting molecules can only be removed from one another by double the distance of the spheres of the molecules themselves. According to Nernst all such reactions, such as solution of anilin in acetic acid, &e. ought to go on with an infinitely great speed in the homogeneous system. Now, avery great number of reactions in organic chemistry are carried out by mixing two liquids together in the above manner, and all organic reactions, with few exceptions, belong to the slow, often to the extremely slow, not to the instantaneous, reactions. On the other hand, many reactions, even in very dilute solutions, go on almost instantaneously, though the reacting molecules in the solution are very considerably removed from one another. This is so well known to every chemist, that I need not dwell upon it any longer to show the utter futility of the above assumption. Nernst’s assumption that ‘‘ infinitely great forces”’ are acting between different parts of the heterogeneous system, when it is not in equilibrium, is therefore absolutely unsupported by daily experience. Here we have to deal with ordinary solution of solid salts, where no electrostatic forces come into play, and consequently where the osmotic pressure of the solution at equilibrium equals the total solution pressure of. the solid. We shall see later on that the forces coming into consideration here for the different kinds of reaction are not “infinitely great,’ but of measurable, and often of very small values indeed. So far I much prefer the less detailed views of Bruner and Tolloczko, who speak of “‘instantaneous reactions,’ without binding themselves to ‘infinitely great forces.” (b) I now turn my attention to Nernst and Brunner’s support of the hypothesis that at the surface of the solid a saturated solution is formed, which is only capable of passing into the region of the action of the stirrer by diffusion. My question is, where is the proof forthe same? What is there to prevent the liquids from passing to the very solid? In my opinion neither their deduction of the equation on p. 63, nor 502. Dr. Meyer Wilderman on Velocity of Molecular their own experiments on p. 62, giving the variation of the constant A with temperature—the only experiments which ought to have brought some support to their assumptions— tend to support their views, but on the contrary disprove thesame. The equations (3) and (4) of Nernst and Brunner are not deduced according to proved conceptions, but are nothing else than a graphical adaptation to the above men- tioned” conceptions, which became unavoidable, to make them artificially fit into a known equation. But as Nernst and Brunner admit, that it is impossible to assume that there should be on the one hand a layer of complete rest, where the equalization takes place only by diffusion, and on the other hand a layer outside the same, where equalization takes place only by convection caused by the stirring,—it follows from this that even if Bruner and Tolloczko’s, Nernst and Brunner’s assumption of two layers be made, a gradual transformation of the second layer into the first under a gradual diminution of convection must take place ; the straight line AB is therefore arbitrary, and must be replaced by a curve, of an unknown equation, in all probability by a logarithmic curve, and the value D is not CB, but.a value which may be considerably greater ; and the whole deduction of equation 4, that is of my equation, from the diffusion con- ceptions is arbitrary: the strict existence of my equation is, in my opinion, for this reason, if anything, a proof that their conceptions are wrong, not that they are right. Moreover, for all we know, there is no reason whatever to assume, that even if 2 saturated solution be formed at the surface of the solid, this should not form only an infinitely thin film, as originally assumed by Noyes and Whitney, that this film should not be of the size of the sphere of a molecule, that is of the dimensions 10-° mm. instead of Nernst’s 0-02 mm., and that the liquid from outside this film should not enter It, i. e. should not reach the very surface of the solid itself diluting the same. Indeed, in case of solidification of water in a U-tube, 7. e. even without stirring, the water reaches the ice or the ice the water to a proximity of about 10—- mm.— why should this not be the case with the liquid in contact with the solid especially when it is stirred? The very value calculated by Nernst and Brunner, by the use of diffusion constants, for “6” as being equal ‘to *02 mm., which seems to them “as very probable,” seems to me on the contrary very improbable, in view of the results obtained for solidi- fication of water. With these much more natural assumptions for 6, &e., their deduction of equation (4) would again cease to hold good, and the actual values of the diffusion and Chemical Reactions in Heteroaeneous Systems. 553 constants would present, in my opinion, a striking proof that the application of the above diffusion conceptions here is entirely out of place. (c) Not only is there no proof for their values of 8, but the assumption of the existence of the layer at all is extremely unnatural, and is evidently wrong. My equation holds good also for evaporation of solids and liquids, where the diffusion of the gas into the whole gaseous space is instantaneous, and where there is nothing to keep the gas saturated at the surface of the solid, and in the rest of the space unsaturated, where there is nothing to prevent the moving molecules from reaching the very solid onits way. If this is so for the gaseous space, where is the need and the force of these most unnatural assumptions as regards the solution ? Note also, that the laws of Boyle and Gay Lussac and the whole kinetic theory were deduced without the assumption of the existence of such a layer and presuppose that the gas can reach the very solid. Note, that vant Hof’s laws of Boyle and Gay Lussae in solutions presuppose that the sub- stance in solution behaves in a similar manner to the substance in the gaseous space. All this is, in my opinion, a solid proof against the above fundamental assumptions of the diffusion theory. (d) I now pass to an important experimental test of the diffusion theory, and this is the znjluence of temperature upon the speed of reaction. If the velocity of reaction is, as we are told, regulated by diffusion, then A must vary with temperature as the diffusion constant F does. This, in my opinion, would bea serious proof for the diffusion. theory if it proved to hold good, since it would have represented a quantitative test of the theory instead of remaining a mere assertion with no proof whatever. Now Nernst and Brunner investigated the speed of solution of benzoic acid at different temperatures. They find A at 20°=2°30, at 30°=1°5 x 2°30, i. €. an Increase of 5 per cent. per degree, while it ought to have been only 2°5 per cent. according to the variation of the diffusion constant. One would say, this is a most decisive proof against their theory ; but there is always, according to Nernst and Brunner, a way out of the difficulty. Itis enough for this to assume that the adhesion and with it the thickness of the layer 6, become smaller with temperature. The sole effect of the introduction of this layer 6 is to prove some- thing without proof. To this 6 all sorts of properties are now “attributed, without, however, the least evidence being produced. The diffusion-constant F isa clear, known physical] Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. zP 554 Dr. Meyer Wilderman on Velocity of Molecular constant and can be tested in an independent manner, while 6 presents no such embarrassing feature, as it cannot be tested in any independent way. It will be shown later on that the apparent proof of “6” consisting in the would-be fact, according to Nernst and Brunner, that the speed of solution of magnesium hydroxide, magnesium metal in benzore acid, is the same as the speed of solution of benzoic acid itself, does not exist and is based only upon quite arbitrary experi- ments. About this 6 we read :—“ This 6 should depend only upon speed of stirring and temperature and not upon the nature of the substance in solution;” but a little further again “this, however, is not the case, because this layer has a resting surface on one side and moving on the other, and the effect of the last becomes the greater the more we are removed in this layer from the resting surface,” “ nor is it independent of the value F itself” (7. e. it depends upon the nature of the substance), “nor is it the same at all places of the surface of the solid,” and lastly, ‘‘ whether 6 depends only upon tem- perature and speed of stirring it is difficult to say in advance.” In short we know absolutely nothing about this very 6, about which we ought to know everything and upon the value and existence of which the whole theory depends. It is quite evident that until some independent way be used to determine the value 6 in each case, so as to show that my velocity-constant A is, in each case, really composed of the two known values F and 6, not an atom of evidence can be brought for the existence of such a relationship. All Nernst and Brunner dois to divide F' by my constant A, so as to get the value which 6 ought to have, in order that J should be equal to A which is found in the experiment, as required by their theory, while what we wish to know, require to know, is, does 6 really possess such a value, and does it exist at all? I now give here a very careful investigation of the influence of temperature upon the velocity-constant, carried through with the same benzoic acid which Nernst and Brunner investigated, and for a series of temperatures between 1° C. and 60° C. and Chemical Reactions in Heterogeneous Systems. 555 In the following table— 6’ gives the number of cc. Baryta requisite for neutralization of 10 ce. of the benzoic acid in solution. : C, gives the concentration of benzoic acid in solution at the time ;, if the concentration of the benzoic acid solution saturated at 17°°5 C. is taken as unit and 10 ce. are put equal to 10. v is the volume of the solution at the time r. C is the concentration of the benzoic acid at the given temperature, expressed in unit concentrations of the benzoic acid saturated at 17°°5 C., which we denote with letter (a). Ais =. In as or the velocity constant of the reaction of solution Tv mo of benzoic acid. TABLE I, Influence of Temperature upon the Velocity Constant of Molecular Reactions at different Temperatures. (Speed of solution of benzoic acid in water at 60° C., 40° C., 31° C., 17°5 C., 1°5 C.) No. b’. | Cx v. | C—C,.| dr. A. | | Speed of solution of benzoic acid in water at 60° C. : ) | p1 ...| 0843 3°338 | 41-862 | May, 1907. 9 1-449 5-738 _ 1490 39-462 10 8-797 se ie j Tih ; 1480 Fi 10 | 9-327 C at equilibrium at 60° C. 3 ...| 2058 8150 | _,_ | 37-050 =1-:2132 gr. in 100 cc. of 4.) a711 | 1073 | 4° | 3447 | 10 | 27829 | water; a. ¢. 10 ce. of the — 1460 | 10 9°487> | saturated solution = 45:2 cc. Bb .... 3259 | 12°90 a 32°30 of (a). 6 3-798 15°04 1450 | 30°16 10 DI47 n=1380 rev. per minute. “4 1440 10 | 10-340 Corr. for water=0°05 cc. mee.) 4025 | 1713 | 28°07 Pipette=10 ce. Average... 9°946 Speed of solution of benzoic acid in water at 40° C. 1...) 0428 | 1:695 18°985 21st May, 1907. . _ | 1470 42 §089 | T=813°. ee) LOTT | 4265 | any | E15 | on | gry | O at equilibrium at 40° C. 8 ..| 1-425 5642 15038 | ~— =0°5551 gr. in 100 ce. of eS 1440 30 5548 | water; 7. e. 10 cc. of the ey F859 | 7282 | 439 | 3% 31 | 5-999. | Sat. sol.=20°68 ce. of (a). 5 ...| 2:244 8-886 11°794 n=130 rev. per minute. | q ‘ 1420 30 §819 | Corr. for water=0°03 cc. 6 ...; 2588 | 10:250 10°430 Pipette=10 ce. ) gq Average | 5:756 | 2P2 OAanNt aout, WO ND 556 it 0°656 0°854 1-048 1-302 1514 1-744 2016 2°322 ‘05 TaBLe I, Vv, C—C,. | dr. (continued). A. Dr. Meyer Wilderman on Velocity of Molecular Speed of solution of benzoic acid in water at 31° O. | 2°598 3°382 4150 5°157 5°996 6:307 7984 2-197 ...| 2°630 | 10-415 | 1500 1490 1480 1470 1460 1450 1440 1430 13°222 19 12-438 20 11°670 30 10663'| _, 25 9°824 33 8913 39 7836 60 6°623' 69 5°403 Average ... 4826 4748 4453 4819 4306 EEN ¢ 4087 4214 4-524 10th May, 1907. T=304°. C at equilibrium at 31° C =0°4247 gr. in 100 cc. of water; z. e. 10 cc. of the sat. sol. =15-82 ce. of (a). n2=130 rev. per minute. Correction for water= 0:045 ce. Pipette=10 ec, Speed of solution of benzoic acid in water at 17-°5° C 2154 9°7846 7th May, 1907. Average .. | 2:6 ite 2 o79 | -3404| 148° | 94596 ean! aa 1465 255 | 2782 | T=2905. Seedy LOD “7971 144% 92029 46-5 | 2-31 C at equilibrium at 17°°5 C. Ach BADE WATS 8'525 =0°2684 gr. in 100 ce. of : 5 g ESO i 39°75| 2568 | water; 2. e. 10 ec. of the i a ane ‘4785 9-062 1420 7°938 315 2-95) sat. sol.—10 ec. of (a). 6 ...} 5685 | 2°449 7-551 “°F | 4=120 rev. per minute. a 663 2-856 1410 7-144 23°5 | 3325 | Volumeof pipette=9'19 ce. 8...) 593 | 2555 7-445 1490 185 | 2-482 Pee TIO i WT 280 | | ne Ree BOP spay | 08 | oon ma 11...| -9175 | 3-953 6047 | ~ ° 1445 59:0 | 2-395 | RB MU RT Aah PARE oan ill aaa 13... £095 | 4718 5282 | 14....| 1078 | 4645 5355 ae 1490 365 | 2-798 15 ...| 1:16 4-999 5-001 1480 380 | 2-351 16 ...; 1-228 | 5-292 4-708 eaten i 6-679 3°321 Pyligar | 1485 ~ {1620 | 3-387 18...) 1-788 | 7705 | a, | 2295 |. | cee 9) ‘Oo ‘DIO 19 ...| 1915 | 8-252 1:748 \ and Chemical Reactions in Heterogeneous Systems. 557 dr. A. | No. | Bi. | C,. v. [o-o, Speed of solution ef benzoic acid in water at 1°°5 C. | : ' 1... on | 0486 62404 : Tia aS Po | 23-75| 1326 | 9th May, 1907. = tj) “O44 1742 | 61188 { E ae 907 1480 | 99 19°25 1558 T=274°'5, Re oles 1470 | oe 30:0 | L881 C at equilibrium at 1°°5 C. ee) 182 | .-5228 5:7702 py | =0'1689 gr. in 100 ce. of |. Se 211 | 8356 1460 54574 | 50°0 L627 water; 2 e. 10 ce. of the . es a 5 1450 58:0 | 1377 | sat. sol.=6'293 ce. of (a). ea, 260 | 1-128 51650 | , n=129 rev. per minute. | 898 | 1-584 1440 4°709 600 | 2218 | Correction for water= SS | s 1430 i 450 | 1:225 | 0:04 ee. 8 445 1-762 i 4531 | aa 1-48? Volume of pipette=10 ce. 3) hg ; . 9 “492 | 1-948 _ £345 | | | Average ...| 1°587 | 2 Variation of the velocity constant of molecular reachons wilh teinperature al a corstant speed of stirrer (130 reviprMin) a. 5 x66 E-452% : | dink A’, E-1587 1 ag ye 5 1 ‘ E-A tin the fhbles) ots ep 2’ — ——— Diagram 1 Influence of Temperature upon the Velocity Constant A of Molecular Reactions. We find ad lm we Can | Ay ae Seay aT and At T_T InK= 1. +const. InKy, —In Ky, =A’ TT =~ 195 17°53 a? 40° 60° T = 274:5 2905 304 313 333 Beco) 12587 2-851 4°524 5°756 9-946 It follows from this : 2 Oot!) Caese ae Sn ' = 2920 ; 5B7 ” aymeeopy ght 8 = 2920: dats dene 2 A' =3020; 2-851 290-5 >: 304 na 5756 A x9 4524 304x313 in 97946 _ A’ x20 5756 333x313 and A’=2550 ; and A’=2850. 558 Dr. Meyer Wilderman on Velocity of Molecular Thus I find that the law regulating the variation of the velo- city-constant with temperature is for molecular reactions similar to the law of van’t Hoff for homogeneous reactions; it has the same thermodynamic explanation, 1. e. is in connexion with the maximum work performed during the reaction in a reversible cycle. I will show in my publication on chemical reaction in heterogeneous systems that the same equation holds good in case of reaction of acids &c. upon little soluble solids and confirm it also upon data taken from the investigations of other reliable scientists. The above is a very strong and reliable proof against the diffusion conceptions of Noyes and Whitney, Bruner and Tolloczko, Nernst and Brunner. As to the percentage increase of A, this gradually drops from 5:1 per cent. per degree between 1°5 C. and 17°5 C. to 3°64 per cent. between 40° C. and 60° C., instead of being 2°5 per cent., as required by the diffusion theory; and this increase of A drops with rise of temperature instead of rising. (e) My further question is, what do we gain by the Bruner- Tolloczko’s, Nernst and Brunner’s hypothesis ? “Nothing either in clearness or in generality of conception. In the first instance, what has become of the speed with which the solid passes into the thin film of the solution, the heterogeneous reaction proper? and which law regulates this reaction ? What do we know of the “ infinite forces at play,” mentioned by Nernst? Are we to be satisfied by mere assertions without proof, or are we going to know anything about this speed and about the forces at play and the mode of their action? In the theory of galvanic cells we are, at any rate, consistent, we calculate and measure the solution-pressures, whether they be only an integration-constant or not. We get solution-pressures of 10! or 19-! atmospheres, to which many a serious scientist objected, but we, from our point of view, adhere to them. These forces are great enough and small enough to show us that if Nernst and Brunner’s theory of the process of the ordinary solution of solids at their surface be true, this theory, as given to us at present, still teaches us nothing about the heterogeneous reactions proper even in the sphere of pure abstraction. I, for one, would object to this method of treating the subject of molecular reactions as a clear and lucid conception of a phenomenon which we wish to know, even if pure abstractions were all that interested us. Our conceptions, instead of becoming simpler, became compli- cated, and we are thrown face to face with new unknown problems which are very difficult and inaccessible to test, while the content and the conceptions contained in the equation, EEE = oe and Chemical Reactions in Heterogeneous Systems. 559 as given by myself, are very clear and simple, are almost axiomatic in their character. I return to the argument I have already given in the Rep. Brit. Assoc. Liverpool, 1896, in connexion with Co. My equation is shown to hold for all molecular reactions, including such reactions as the transformation of ice into water, water into ice, &c., where concentration does not come into con- sideration. tis evident that a law of such a generality cannot find an explanation tn diffusion, which can have only a limited application. This is evident proof that there is no necessity whatever in diffusion conceptions to explain the meaning of my equation, and that to give the correct natural interpre- tation to its meaning, we must take as a basis the general features underlying all of them, as I did in my papers’ and here, and not follow the particular line of diffusion. The analogy between the equation for velocity of solution of salt with the equation for diffusion evidently seemed to Noyes and Whitney, Bruner and Tolloczko, Nernst and Brunner peculiar and led them to try to identify them and to adapt the conceptions accordingly. This coincidence may appeal to some as remarkable, but is of no value so long as the physical constants do not prove this identity, because buoyancy is also regulated by a law of a similar nature, sois the law of Newton for cooling &. Why not identify velocity of molecular reaction with the law of Newton? With many assumptions, plenty of hypothesis, and no experimental proof, a much more fascinating theory could be developed here. But, as already explained in my paper (Phil. Mag. July 1901) in great detail, there is no more and no less analogy between all these phenomena (speed of molecular reaction, diffusion, buoyancy, conduction of heat), they all have in common, that, whenever a kind of energy (chemical, thermal, &c.) is removed from the state of equilibrium, the speed with which it strives to attain the same is directly proportional to its remoteness at the time t from its point of equilibrium. This, nevertheless, does not make all these phenomena zdentical. (7) let us now assume for a moment that the speed of solution is regulated by at ay Now the velocity of evaporation also follows my equation, and the well established thermodynamic analogy between solution and evaporation makes this also self-evident. In case of gases the diffusion constant D is about 10,000 times greater ~3 (C=) or =—(O=6), for >=1. 260 Dr. Meyer Wilderman on Velocity of Molecular than in water ; 6, if it existed at all, is evidently much smaller than in solution (we look away from the fact that it is incon- ceivable that a layer of gas should be formed near the solid the molecules of which cannot move into the rest of the gaseous space, or that the gas from the total volume should not be capable to reach the solid). In view of the above equation for solution, the velocity of evaporation ought to go on with an infinitely greater speed than velocity of solution. We find, however, on the contrary, that the speed of evapo- ration of liquids and solids belongs in comparison to the slow reactions, as is to be seen already from the fact how difficult it is to reach the maximum of vapour-pressure in all the researches. , - This is a further proof against the diffusion conceptions. (g) I shall next deal with the variation of the constant A with the number of revolutions of the stirrer. There is no reason why the ordinary velocity-constant should not change with the speed of the stirrer, considering that it does so enormously change with the solvent, with the size and dimensions of the apparatus and other mechanical conditions, but whatever its cause, I will show, however, that this variation of the velocity-constant with the number of revo- lutions proves, if anything, the amprobability of the diffusion conceptions of Nernst and Brunner. Formerly Tolloezko and Bruner found by the very same method which Nernst and Brunner use, that the speed of solution of the same benzoic acid is directly proportional to the speed of stirrmg—a rate of variation which does not seem probable for the layer 6. Nernst and Brunner seem to have got at first the same results, but they tell us that this was due to some cracks at the rims of the acid, and that as soon as these cracks were filled up with paraffin the value of A changed as the two-thirds power ot the speed of the stirrer. It will, however, be seen from the details of the method used by Nernst and Brunner (dealt with in § 2) and from the photographs of the benzoic acid which I obtained by their method, that their benzoic acid was never free from holes, that the speed of their motor changed too considerably for accurate measurements to be carried out in this region, and that even their titrations were not arranged accurately enough for the very dilute solutions they dealt with. With such a method they nevertheless changed the variations of speed (see pp. 60-61) of their stirrer only from 144 to 202 and from 135 to 180, 7. e. only by 25 to 30 per cent., which is not enough to distinguish between the results calculated after one equation or the other, even when the and Chemical Reactions in Heterogeneous Systems. 561 results are obtained with very much: better oe On page 61 they give us n=200 rev. and A=2°63; n=177 rev. and A=2°16, i.e. a diminution of A with the increase of the speed, showing the lack of sensitiveness of their method. On page 72 they give us the variation of A for their so-called “ Magnesium hydroxide ” in benzoic acid :— grt 155-5 A =e se ieane iO aver: 1-66: a 162 5 .Aj= 2A ee 90... 1°87, 1°59 Saver. 192. m=178; A,=2-14, 2-08=aver. 2-11. If we take the velocity constant to be direcily proportional to the speed of the stirrer, we get— my, 182 pee 4 ei Bienes 2 ane ge -—4qan a 1°348 and mice 1-157, 1.é., a difference of 14°2 per cent. Rg fie 0 eRe ae ae 97- = Las 1°318 and Vast rae i272. i. €., a difference of 3°5 per cent. If we take, with Nernst and Brunner, the velocity constant to be directly proportional to the two-third power of the speed of the stirrer we get: lo 192—lo 166 lg 112—Ilg 135 =-487 instead of 667, 1. é., a difference of —26°98 per cent. ; and re ee pe =°8676 instead of *667, i. €., a difference of +30°08 per cent. Thus Nernst and Brunner’s data, if anything, prove more direct proportionality and not the two-third power of n, and in reality they can neither be used for the proof of one nor for the proof of the other, especially considering the fact that besides general great exper imental errors of their method their ‘ Magnesium hydroxide”? proves also to have been a mixture of Mego, Mg(OH)., MgCOg, &e., &e. I now give here a careful investigation of this point carried out with speeds from about 2 to 400 revolutions per minute and more. (See Table II. and diagram 2.) TaBiEe I.— Variation of the Velocity Constant with the number of 5 ci of the stirrer per minute. O-C, qlogs—Gi =i; K,Xx23026=A,. | Pima ra te | eit ae | Benzoic | Benzoic acid in e. c. S : pans ee acid. of the saturated rS A ® —s Molecuie| solution of benzoic| -= 3 5 e) 1) eae No. See gee Si) tS |, (toy aloe RK’ x 23026 normal acid al ae "Ss =|K. x2°3026 (setae eS ee a. Elect. by > os ras = or ‘conduct. meee = | mes | aio | | Diffusion of benzoic acid in water, when not stirred. 1’...| 000896 “4072 4376 | 9°5928) 9°5624 2nd | 1470 | 1060 ‘09654 | -10130 | May, ” 2’... 002302 ; 1:046 | 11110 | 8-954 | 88890 1907. | | | Nl i Temp. V”. 008560 | 1618 | 1658 8382 8347 16°0-@ | | 1430 | 2500 | -07182 | -07392 | 16°5C. a". pae | 2607 | 2-665 | 7-898 |7-335 | - | 1’ | 006533 | 2-968 | 3'°015 | 7-032 | 6-985 | | 1410 | 1008 | -05584 | -06316 2! | 0071387 | 3243 | 3322 | 6-757 iaeie | . 2. €., the velocity constant of diffusion seems to become smaller, the greater the concentration of the solution. Speed of solution of benzoic acid in water at 2°42 rev. per minute. | . 1 i 005737 | 2:°607 2°665 | 7°393 | 7°335 30th 1420 | 367 | -1937 | +1892 | April, 2 . 005583 | 2°968 3°015 | 7:032 | 6°985 1907. é : se 5 Temp. Speed of solution of benzoic acid in water at 2°86 rev. per minute. 17°-6 C. 1.../000108 00491 , 0:0198 9-9509 9-9802 | | | 490) 115 | +2276 | -1969 2 ...|°000489 | 0°2222 | 01703 | 9°7778 98297 | | | 1480 | 152 "1861 ‘2685 3 | ...| 000896 | 04072 04376 95928 9:5624 Average...| “2068 | -2326 Speed of solution of benzore acid in water at 3°00 rev. per minute. 1...|-002451 | 1114 | 1111 [8-886 | 88890 | | | | | 1460 | 1135} -2811 | -3267? 2... 002873 | 1306 | 1336 | 8-694 | 8-664 | | | | 1450 | 152 | +2376 | -2271 3... 008845 | 1520 | 8-480 | | | 76 | °2208 | | 4... 003560 | 1618 | 1-653 | 8382 oon | | | | Average...| -2464 | -2588 Molecular Reactions in Heterogeneous Systems. 563 TABLE II. (continued). Benzoic ; | : C,. C'. |C—C,. C-C’. acid. Elect. Titra- Elect. Titra-| wv. dr. K, X2°3026, No. ay. Mol. norm. cond. | tion. | cond. | tion. =A). / K’ x 2°3026 = AY, Speed of solution of benzoic acid in water at 53 rev. per minute. ; | ! } f=. | 3364-4292) 9:6636 9:57 oe | 91-92 : | | | 198 | 1383 | 1:443 | May, 2... 001085 | 4931, +6075 9°5069) 9°3925 | 1907 | | 1460 | 265 | 1-326 1-465 (13... 001582 | 7190, 8530] 9:2810 91460 Temp. | 1450 | 28:5 | 1-279 1502 | 17°75 4.... 002089 -9496 1-120 | 9:0504) 8:880 C. 1440 | 29:75] +9097?) 1:041 15... -002573 | 1-1170 1-309 | 88820) 8691 31-75] 1:187 1:385 6... 003068 | 1:3950, 1:572 | 86050) 8-428 | 1420 | 530 | 1464 | 1:047 7...| -003983 | 1:8100 1:895 | 8-1900 8-105 | 1410 | 64:25] 1:294 1:248 8...) 005015 | 2:2790 2:343 | 7°7210 7-657 1400 | 53:25] 1:212 1:538 9.... 005780 | 2°62 70 277 8 | 73730, 7-222 | | | 1390 | 500 | 1-332 1-277 10... "006538 9-970 3-102 | 7:0280 6893 | | | | | | Average...| 1°266 | 1°327 | Speed of solution of benzoic acid in water at 122 rev. per minute (17°5 C.). ! | 1...| -000484 220 | °2154 9°7800, aradel | 15-20 | | 1480 | 60 | 2:397 | 3:168 |March 2...| 000692 | -3145 3404 9:6855 9-6596 | 1907. | 1465 | 25:5 | 2°675 2781 001665 | -7568 -7971 9:2432 9:2029 | Temp. | 1445 | 465 | 2452 | 2:309 |17°8 "003204 (|1°456 1:475 8-544 8-525 C. 3 4 a | ) 1430 | 39°75] 2*381 2:567 5...| 004407 | 2-003 2:062 | 7-997 | 7-938 | ;. | 1420 31:55 | 2:303 2254 7 1410 235 2°212 3°324 005282 2-401 2-449 7-599 | 7-551 w-| (005887 |2:676 2856 7-324 7-144 9 Bat 4 002532 3 4 Di. 6 oO | Benzoic | acid. *}Mol. norm.' a. 008440 009729 ‘010163 Speed of solution of benzoic acid in water at 001022 001607 003515 004338 005471 006664 | 007581 008425 4645 | C’. 7 C—C, .| Titra-.| Elect. : tion. 6521 | 6450. TABLE II. (continued). | |C—C’. Titra- |. tion. V. dr. cond. | | TAT5 | 7-445 1490 7211 | 7-230 1475 1460 6163 | 6°047 5°578 | 5°484 1445 1430 5:881 | 5:282 65550 sas ' 61720) 6:285 5:355 | 5001 .. | 4-708 : Top |. [an | 2 Average.. 95855) _ | 1480 ; 10-0 9°2696 88490 1470 | 15:0 8°955 8503 8205 7598 7176 6°708 1460 84020 1450 80280 . 1440 751380 6°9720 1430 1420 1410 SS ee ee SS eee ) Average... K, X2°3026|K’ x 2 302% ge =A’. bt ee ee OP eae 2°895 2 482. 2°224 2°503 2°703 3°088 2°443 (2:395 2" 099 2°191 2°793 2°351 3387 2°533 C—C,./0-C'. | Benzoic ue C’. 2. | 2. ) acid. Elect. | Titra- | Elect. Titra-| v. | dr. Ke cat K ye ae 4 26 | cond. | tion. | © °* | gee i Rete lemmas de A | Mol. n. a. | cond. | tion. | Speed of solution of benzote acid in water at 365 rev. per minute. 1...| -ooceos lo27s91 ... [oral]... | _ |8 May | ~ |1490]} 4 | 6132 me ) 190% | 2...) 000958 [0-4382) ... | 95668) .. bs 4 5285 Re Temp. 3...| 001251 | 05686) ... | 9°4314 17°°5 | | Co ate NOS Bez02 A C. 4...) 002030 09227] ... 90773)... | | | 2 | 4992 5...| “092163 | 09832) 0:9465 9-0168 9-0535 | '1480| 3 | 4987 ), 6...} 002362 |1:074| ... | 8-926 | | | | | Pa hay) ee NBS | 7...) 002675 |1:216| ... | 8-784 | +| 4:656 | | | » | 5 | bia | 8...| 003032 | 1:378 | 8622 | | | bem tby toes: |) aarp 19...) -003194 “1402 1-323 | 8.548 | 8-677 | 1470 | 105 | 5-188 10...| 003879 [1-763 | ... |8237) ... | 5757 | | | » | #5) 5317 | —|11...) 002172 | 1-896 | 1-818 | 8-104 | 8-182 | se | | 1460 | 155] 4-743 ) 12...) 005048 | 2-294 | 7-706 | | | , | Wipe tt ec en ee) ee 13...| -005534 [2:515| ... | 7-485 ee [ | | | 1450 | 24 | 5216 )| fis.) 006896 | 3134 |3-105 6-866 | 6-895 | | | 1440 | 32 | 4969 | 5345 15...| “008476 | 3852 |3:877 6-148 6-123 | } | | Average... 5°268 | 5222 | Speed of solution of benzoic acid in water at 470 rev. per minute. . | | ‘000597 2718 was | SV2Bi | 7 May | | : 1500 | 2 4°559 1908. | 2...; 000727 | -3304 9-6696 ) bs 3 4°835 outs Temp. | 3...) 000932 | 4235 | 9°5765! 18°C. | ) ) Me 2 4:26 | 4...; 001081 | -4776) | 9°5224) ) | | | e 4 5-043 5...| -001330 6045) | 9°3955) / | | / ‘ 3 4-444 6...| 001513 | -6875) 9-3125 4 | | é "i 5-158 | 7... -001999 | 9085) 90915 4g | | | Se a 1) tgs )) 8...) 002777 (1-262! ... |8-738 | | | | 2 15 | 5-389 | /} 9...) 002879 [1:309| ... 8691 | | | | | | ns 85 | 4974 is }0...! 003413 | 1-551 | 8-449 | Lvl ) | itd 4 | 5504 fil... 003683 | 1674 _ 8326 | ) | | ibe Yew we 4°145 2...| 004428 | 2-013 7-987 | | Average...| 4°835 566 Dr. Meyer Wilderman on Velocity of Molecular olectt lar of the 16) ons (175 K~ 2.215 revoluai f lernperalure th the number ons wi sitrrer, at the constant. Diagram 2 Variation of the velocity constant reactti were ewe @ = oe e@ = = The results found here are therefore the following :— 1. When the liquid is not stirred at all, the only way for the substance, passing into the solution from the surface of the solid, to pass into the rest of the solution is naturally, as known long ago, by diffusion. The amount passing in this manner is, however, in comparison with what passes at the maximum revolutions or even at any ordinary speeds, only and Chemical Reactions in Heterogeneous Systems. 567 a small fraction of a per cent. As the assumption that the stirring should produce such a variation in the diffusion- layer is not at all probable, this certainly is, in my opinion, a proof against the diffusion theory. 2. Up to about 3 revolutions of the stirrer, the increase of Ais greater than in direct proportion to the number of revolutions, as the same follows from the curve between 3 and 180 revolutions; the preponderating effect of stirring over that of diffusion is seen even at these slow speeds ; the speed of solution is here due to stirring and to diffusion, and the last cannot yet be neglected. 3. From about 3 revolutions to about 180 revolutions the value of A is directly proportional to the number of revolu- tions of the stirrer (into this region fall the investigations of Bruner and Tolloczko under their experimental conditions, who found the same result). Thus from about 3 revolutions already the value of transportation due to diffusion no longer interferes with the value of speed of solution, as effected by - stirring only. 4, From about 180 to about 400 revolutions, the increase- in the value of A first gradually becomes smaller, until it becomes independent of the number of revolutions of the stirrer, 7. ¢. the maximum value for A has been reached. Into this region fall the experiments of Lorenz and Siegrist. under their experimental conditions. It is, however, evident that the more soluble a substance is, the less will be the number of revolutions requisite to reach a constant maximum value of A’. Nernst and Brunner’s idea that diffusion is the sole factor in transportation of benzoic acid from the surface of the solid to the rest of the solution is, in my opinion, in no way supported by the character of the above results; quite the contrary. One or two revolutions of the stirrer already trans- ports considerably more than the whole process of diffusion can possibly do alone without stirring ; and I fail to see any reasonable support, any reliable proof, that diffusion alone should be operative and that as such it should be (owing to. variation of 6) accelerated by stirring to such an enormous. extent instead of being more or less destroyed by the same, owing to the destruction of the drop in concentration near the surface of the solid, which is naturally formed when the liquid is not stirred at all. Indeed, as already mentioned, there is nothing to prevent the stirrer from mixing the liquid up. to the very solid, and if the liquid can reach the solid during 568 Dr. Meyer Wilderman on Velocity of Molecular solidification to a proximity of about 10-' mm., when the liquid is not stirred, we have no reason whatever to assume that the liquid does not reach the solid to the same proximity when we stir the same. For the diffusion conceptions to find any application at all it is necessary to prove, not that a satu- rated solution can be formed at the surface of the solid (when not stirred), but that the solution is zncapable of entering the layer near the solid when it is moved into it by the stirrer, diluting the same. The assumption that a saturated solution is formed at the solid which passes into the rest of the solution by diffusion, overlooks also the fact that the solid in contact with its saturated solution ought to be in equilibrium with it, ought not to be able to dissolve any more, and that a reaction of solution of the solid cannot possibly go on, unless the layer in the immediate contact with the solid is unsaturated. In this notion we are confirmed by the behaviour of a solid in contact with its gas, and this forms at present an axiomatic notion, which existed for ever so long in physics and che- mistry, which led to many useful and fruittul results which cannot be given up for the sake of peculiar diffusion con- ceptions, even if they should seem capable of explaining some particular case. (h) I will next consider the “important argument” of Nernst and Brunner “for the conception of the diffusion process.” They tell us :—‘“‘ The true size of the surface is of mo importance; when the originally smooth surface of the ‘solid becomes corroded, the velocity constant A does not change, in spite of the great increase of the surface. Only the quadratic dimensions or contour of the surface and not the microscopic properties of the same are of importance ; the last should be of importance, if the reaction takes place on the surface itself.” Assuming, however, that this is true, which it is not *, it is not to be seen, how this is to be taken as a proof for the diffusion conceptions of Nernst and Brunner ? If the diffusion layer 6 were, in comparison with the depth of -corrosions, very thick, so that the depths of the corrosions could be neglected, such a conclusion would be admissible. But when the diffusion layer 6 is even according to Nernst -and Brunner only 0°02 mm. thick, while the corrosions according to them can be as deep as 1 mm. (without affect- ing the constant), it is quite evident that the diffusion layer or surface will be as large as the corrosive surface of the * In my next publication I shall furnish further experimental proof that reaction does take place at the surface of the solid even in case of substances of no small solubility. and Chemical Reactions in Heterogeneous Systems. 569 solid itself, and the increase of the diffusion surface will be the same as that of the surface of the solid during corrosion, 2. €., we gain nothing whatever here by the assumption of a diffusion layer. The true position of the facts here is, in my opinion, the following :— Surfaces which appear to the naked eye smooth are in reality, on inspection with a lens, corroded surfaces, and such surfaces are not always essentially smaller than the surface of the same solid when its corrosions are perceivable; influences of an opposite kind may often counteract one another: on the other hand, | must assert that very often we find an increase of the velocity constant with the increase of corrosion, when this is still very far below the values mentioned by Nernst and Brunner, and | find that repeated polishing of the surfaces is in this region imperative. Part II, Gi.) I now pass to the most important and most direct test of the diffusion theory. This is given to us by the investi- gation :—(1) of the speed of solution of different modifications of the same substance in the same solvent ; (2) of the speed of solution of the same crystal, cut in different directions to its axis, in the same solvent. Because if the velocity, with which a solid dissolves, depends, as we are told, upon the speed of diffusion of its saturated solution from the solid into the rest of the solution, and if the saturated solution is formed instantaneously at the solid, then all the CaSO,+2H,0 of the different Gypsums giving the same saturated solution* must dissolye with the same speed, and the same crystal Selenite must dissolve in different directions of its axis with the same speed. Jf this is not the case, this is the most decisive and direct proof one can possibly imagine, that these funda- mental assumptions of the diffusion theory do not hold good, and the whole diffusion theory tumbles to the ground. Bruner and Tolloczko found (Zeitsch. fiir anorg. Chemie, 1901, p- 325) for Alabaster, the velocity constant A=0:00230 (V=2000 cc., f=22°91 cm.?, number of revolutions 400) and for Marienglass or Selenite A=0°00079 (V=2400 cc., f=20-9 cm.?, number of revolutions 400), z.e. A Alabaster : A Marienglass = 3°44:1. In Zeitsch. fiir anorg. Chemie, 1903, pp. 29, 30, they try to get over this difficulty. They * See the investigations of Kohlrausch and Rose and others. Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 2Q 570 = Dr. Meyer Wilderman on Velocity of Molecular give us A Alabaster : A Marienglass=2°5:1, but they inform us that the surface of Marienglass is smooth, the surface of Alabaster not, and when we polish Alabaster to a smooth surface the constant A drops to half its value. The impression is thus created, that the constants of both are really the same. Note in the first instance, that this explanation is now brought forward by Bruner and Tolloczko, who were the first to find : “The important argument for the diffusion theory consisting in the fact that corrosion as deep as 1 mm. has no effect on the velocity constant ;” that they no longer accept this state- ment in case of Alabaster, which very easily gives perfect surfaces, much better than marble, while they do not take into account the corrosion of all other substances used by them, which are not able to give such smooth surfaces as Alabaster, but for which they nevertheless furnish us with perfect and impossible constants, under conditions when the substances must have corroded during the reaction very con- siderably! With ‘‘ Platre” Bruner and Tolloczko found A to be twice as big as that of Alabaster, but according to them this is only due to the fact that some substance is coming off from the sclid. As the method of Bruner and Tolloczko seemed to me quite unsuitable for a reliable investigation here, this matter had to be investigated again. The solu- bility of the Gypsums is only about 2 gr. per litre, and some of the solutions and differences investigated by them contained no more than °003 gr. in the 25 cc. which they investigated. Such amounts of gypsums Bruner and Tolloczko wish to measure quantitatively either by evaporation or by the more complicated and unreliable method of precipitation with oxalic acid (collecting, washing the same), the decomposition with SO,H, and titration with permanganate, and yet they supply us by such methods with constants differing in a series only by about 2 per cent.! To remove, however, all possible doubt here about the reason for the difference found between Marienglass and Alabaster and to investigate the same in very dilute solutions, when the surface had no time yet to corrode except but very little, I employed the method of electric conductivity as described in paragraph 2, which enables us to make very much more accurate and instantaneous mea- surements than it is possible to expect from the methods of Bruner and Tolloczko, and very great care was taken to polish the surfaces of the gypsums as perfectly as possible. Table III. gives the speed of solution of the following Gypsums CaSO,+2H,0 :—Selenite or Marienglass from, and Chemical Reactions in Heterogeneous Systems. 571 Italy, Alabaster from Leicester, fibrous Gypsum from Nottingham, all perfect specimens, perfectly polished and washed and dried up well and quickly; their surface is almost the same, about 4 sq. in., all were investigated at the same temperature of very near 17°5 C., with the same speed of stirrer (130 to 132 revolutions per minute) and the same volume (1500 cc.) which remained constant during the whole time of the reaction. The surface of the selenite exposed to solution was the flat large side of the twin-crystal, ‘the surface of the fibrous gypsum was cut along the fibre, quite parallel to the same, while the surface of alabaster could be: taken in any direction. Photos 11, 12, 13 (Pl. XVII.) show Selenite, Alabaster, fibrous Gypsum, their structure and their surfaces after solution. It will be seen from the same that their surfaces were not allowed to corrode. The selenite is transparent like glass, and what we see on the photo is the paraffin below the bottom surface. On the contrary, in case of alabaster and fibrous gypsum, the photos show their - structure, not corrosions, which are extremely small. The velocity constant of Selenite is from ‘48 to about °65, of the fibrous Gypsum is about 2°0, of the Alabaster from 3°1 to about 4°0, the average ratio of the constants of Selenite: fibrous Gypsum : Alabaster at the same surface is about 1:3°5:5°4. Thus Marienglass and Alabaster give, not as Bruner and Tolloczko lead us to think almost equal constants, but very different constants indeed, and all the three above specimens of the same Gypsum give undoubtedly different constants, whether we take extremely dilute solutions given by the first three dilutions in the above tables, where the ratio is 1:4:6, or the more concentrated ones. Therefore, as the solubility of all modifications is the same, it is sufticient that the same monoclinic crystal should configurate itself once into a twin-crystal, another time into a fibrous struc- ture, another time into a granular crystalline form; and this physical modification in the configuration of the very same components is already alone sufficient to cause the solid to acquire some new physical properties, of which the speed of solution is one. All the above three spe- cimens are as we find them in nature, their velocity con- stants undoubtedly increase as the reaction goes on, and this may be due either to corrosion or also to some other influences. It is not likely to be due to the presence cf some more easily soluble substances as impurities, because the velocity constants oughtin such a case to decrease with time, instead of increasing. 2 Q 2 TABLE IIT a. a coe, 18 iis ei 5 > A ees = . (I ita = x =e oe ee S) oloMi esa.|-e o Olos | Sa 4] cs o Eto) 2EO | ¢ |e BS g | a #O & | sn Ola #0 | 8p) i eae rs] S (>) eal : PI =| [®) —4 i Ss A Y = a ~ a = wal & . S als xX eS als x ls B. Fibrous Gypsum (from Notting- ham). 17°55 C.; 131 rev. per minute; v=1500cc.; 2=25°5 cm.” 20th May, 1908. A. Selenite or Marienglass (from Italy). 18°C.; 131 rev. per minute ; 7=1500 cc. ; =26 cm.” 14-15th May, 1908. v=1500 ce. ; 16th May, 1908. 0143670 -0001600 0143000 0001730 0142870 000093 es fe |e a: 101 2-065 3 | : 0002754 0141846}, (0002720) 0141880 | oo. 0001880}, 0142770 0003701 0140899 0003629 0140971 0002802 0141798 "| 6871 6 1:987 mee 0004743 ‘0189857 |. 0004743 0189857 0003730 ‘0140870 i 6638 6 1:823 3 0005360 0139240 0005758 0138842 0004665 0139935 ‘5700 : 6 1883 3 0005890 0138710 0006802 0137798 0005662 0138938 564 6 1-811 1g 0006420 0138180 0007797 0136805 0006654 0137946 6080 6 1-866 Ai 0006980 0137620]. jy [0008815] 5, (0135785! 15, 0007603 | |, |-0136997 ‘0007585 0137015 0012586 |." |-0132014 0008597| , |0136003. ‘6683 19 1-860 ia 3 F 0008499 0136101 0015750 0128850 0009524 0135076 6578 19 2-176 nie 0009392 0135208], |[0019255] , . |(0125845) 0011428], 0183172 0010328 0134272 0021550 0123050 0012320]. _ |0132280 6398 15 | 1:902 3 0011182 0133418] _.,,, |'0028860| |. 0120730) | o, 0013292) , 0131308 0012026 0132574] pnco |'0026030| |. 0118570) 0014278 |, (0180822 0012910 0131690 | ____ _-0028300 ‘ 0116300), 40 Ors Ee "0128504 pe Average, *6137 || ygq749| ~° |-0119860 |——___||'0018540| — |-0126060 ished block again. belo | aisieool Average! 1*923 |/.o999¢40) * |.0128960 15 ‘6407 Polished block again. 19 001375 © 15 0130852 Leapp 0032010 | +6 ‘0112580 ie "0026380 10 0118220 001453 4 0130070) 9.4 |/0084340 |, |0110250| 9. 0029320] |, [0115280 5. olf! 001606) ©. ;0128504) _,,,, |+0036250 | , 0108350] |, |/0087600/ a eee = 001700 012760 |—*|loossseo | *° |-o106240| 7°” __Averaee aa Average| "6378 23 2-235 Polished block again. _ , 0042020 5, |'0102580| 9 9, 0051860, |'0092740| 5 eal Excellent surface, ‘0044490 4 ‘0100110 Soa 0054190 i 0090410; transparent like glass. 0046920 AA ‘0097680 2-094 0057410 15 ‘0087190 F 527 | ui 3 9 e For = = 204 em.2 0052740) |, 0091860) 5 a, ial | agi ey ee 0054780 |, 0089820] 90 0069260 |, [0075340 -40 (in the three 0057120 |, (0087480 0, 0074070, (0070580 greatest dilutions), |/0058870 “" -0085730)———__— 0079040 4 , (0065560 , Average 2°080 0088560 | © |-0061040 Excellent surface. | ele) 80 beeen © 0091830 | (0052770 For > — 20s em -0095880| ~~ |-0048720 i | K' =1°7. Average ‘I Excellent surface. | For 5 = 20°4 cm.2 | t . K' = 2°6 (average) | = 2'4 (in the three | ‘ greatest dilution | | TABLE II] B. a4 eae a ee se Att Ol en = =) 1 O10 ge | © = } S| = Irs ', Selenite or Marienglass (the large, flat surface of the twin erystal). min.; v=1500cc.; ==26 cm.? Df 4 ! ! 01600 | ,. 0143000) Ze) | ; 002754 70141846 | 7 by 20 | +5026 003701 -0140899 po4743 | 7° |Loisges7 | 2°72 Lez i 3) | 10] 6638 ? 1005360 ‘0139240 FS. | 5700 005890 -0138710 | : 10 “5767 006420 0138180 ee 10 | "6080 ‘006980 ‘0137620 4 10 | 6610 007585 | __ 0137015 's 15 | "6683 908499 0136101; in 15 “ 657 009392 0135208 | 2 15 | | 6976 0110328 -0134272 y 1 6398 011182 0133418 4 f | _.| "6365 012026 | ~ 0132574 | asp 4 o - 012910 ‘0131690 A Average 6137 iW a oe olished again. Block polished agai 91291 | __ |-0131690 ee 15 y. 07 91375 ‘0130852 ‘ 15 "| +6002 31453 0130070 ig 30 A 6050 016093 | ‘s po128504 at 2 oO 101700 | ~ 0127600 Al iJ ) | Average| ‘6378 _ se ' | Excellent surface, or >=20°4 cm.” K’=:49 (average). 5, "40 (in the three greatest fi J dilutions), f i if 18° C.; 131 rev. per | 1 re =o eS ae _— H Se ft Ore Ss paraffin). 17°-3.C.; 180 rev. | per min.; v=1500ce.; T= | 24 om.2 25th May, 1908. ; 92! _ |-0143208 ee : — sade Ee aha | 3-018 0002019 0142581 (eee 2:970 0002308, _ 0142292 : eee isiona | oo” ‘apeceeel I lover | °°” Cer or ee epee | 3-376 0003555. ~ |-0141045 0005470 ° -o1g91z0| 27 aie: 3-620 0006472 ° |-0138762 | le Fi 33895 0008964, * -0138128 | Average! 3°376 Excellent surface, For >=20°4 em.” | ; | il | / | | i : dr in minutes. i "87. 2 i: x 2'3026 | B'. Selenite or Martenglass (sur- faces cut vertically to the sur- face of A’ and cemented with Molecule normal, dr in min utes, O-—C, 0-0, AiG log X 2'3026 v dr C’. Selenite or Marienglass (pow- dered and compressed to a disk under 2500 atm. during | 16 hours). 17°-40.; 131 rev, per min.; v=1500ce.; >= / 20°4 cm.? ) eee ae ee eee |-0000680 , 0148920 pee 0000930) 5 0143670 ae |-0001452 0143148 : jd 3240 0002067 | | 0142533 wen 0002611 0141989 | 2 2°7 42 0003130) 5 {0141470 oan 0003674 0140926 7 2 2-900 |-0004220 0140380 | tees F004 |:0004780 ‘0139820 S 4 2-920 0005864 0138736 2 2-728 0006367 g (0188238) 5024 0008514 0136086 | ~ 10 2955 (0011171 15 [0188429] once 0015082 is 0129518) |0020454 ; 0124146 ae |-0023390 0121250 : 11 2-978 [0025910 | 0118690 alate 0031230 0113370 Average} 2907 For >=20°4 cm.? K'=2'9. Very good surface. normal. Os Molecule g Olo' s = a; tee “= . olo & | Leo. oS S bay aun) | ee ste ‘ bs w X A". CaSO,+2H,0 precipitated ; with excess of water dried in open air; 2500 atm. for 16 hrs. 131 rev. per min. compressed under 1820s; ae ho) Gls, ==20°4cm.? 29th May, 1908. 000067 000094 000124 000153 000185 000212 000269 000355 000442 000613 000780 001076 002289 003330 003965 004558 004760 004962 005141 ‘0143930 ‘0143660 ‘0143360 ‘0143070 ‘0142750 0142480 ‘0141910 ‘0141045 ‘0140178 ‘0138471 ‘0186803 ‘0133839 ‘0121710 ‘0111800 ‘0104950 0099020 ‘0097000 ‘0094980 ‘0093190 Average Excellent surface. 2797 3-142 3-039 3-384 2-837 3-004 3-056 8-073 3-068 3-029 2-986 3-166 3-087 3-313 2-908 3-090 3-156 2852 3°054 For 3=20°4 em? K'=3°054. Tapia ire: Molecule — normal. C g ols = | S ls ie} s | ose ape Ss s B”. Anhydride CaSO,, Nova Sco- tia: cut to a disk of 50 mm. diameter; 17°°5 C.; 132 rev. er min. ; v=1500 Ces 19°63. 10th June, 1908. 000050 000094 000141 000165 0002040 0002444 0002889 0008452 0004872 0004743 0005060 0006314 0007217 0008332 ‘0009392 £20 0010642 0144100 8 | *5698 ‘0143660 | 8 6173 ‘0143190 d 6302 0142950 6 6792 ‘0142560 | 7 “6140 ‘0142155 8 “5820 ‘0141711 | 10 ‘5971 ‘0141148 15 6536 ‘0140228 6 "6636 ‘0139857 e ? ‘0139540 20 6754 ‘0138286 15 6557 ‘0137383 18 6782 ‘0136268 17 "6886 0135208 | "6976 0138958) Average; "643 Excellent surface; polishes better than marble. For =>=20-4 em.? K' = "67. a OC". CaSO, Anhydride, pre-| cipitated. Got by heating] — at 310° C. for 4 to 5 hours,| — compressed to a disk at} 2500 atm. ; 2=20°4cem.?} From the top surface, powder comes off, 7.¢. can-} __ not be investigated. It i 4 well known that whil q CaSO, prepared from } : CaSO,+2H:20 at 80° C. in : air current absorbs wate q rapidly forming CaSO,2H,O} © and dissolving in water,| | the CaSO, prepared from) CaSO,2H,O by heating at) about 300° C, (as in our) case) absorbs water onal dissolves in water very) slowly. Thus, again, the speed of solution of tbe same) CaSO,-Anhydride, differ| ‘i ently prepared, is different,| the speed of combination) of the CaSO,’s with water, which is also a heteroge-)_ neous reaction, is different, 1 and the speed of reaptionlle is dependent upon the phy] sical state of the solid, nod} independent of the same. | ‘ Molecular Reactions in Heterogeneous Systems. 575 In Table III.B the same selenite is investigated in two different directions in the crystal: the first one is the large flat surface of the twin-crystal already mentioned before (A Selenite, photo 11); the second is a surface cut vertically to the surface A, as in the annexed figure. I cut the selenite crystal, as in the figure, into several strips and connected the vertical surfaces to one surface, the cut-off strips separating into several thin plates, and [ made up a block connecting the same by means of paraffin (see photo 14). The surface of the erystal without paraffin was 49 mm. in length and 49 mm. in width; through the paraffin it became 49 mm. in length and 52 mm. in width. As in case of all other gypsums, all sides were covered with paraffin, except one which was exposed to the action of the solution. The surface was perfectly polished, as is to be seen also from photo 14; the _ velocity constant obtained for this vertical surface is about 3°376, 7.¢e. about 6 times as large as the velocity constant of solution of the other surface of the same crystal (which is °6378), a difference which is truly enormous, and cannot possibly be attributed either to the difference in the surface or to the method employed. This experiment proves beyond any possible doubt that the same crystal dissolves at dif- ferent rates in different directions to the axis of the crystal, and is at the same time an absolute proof that the funda- mental assumptions of the diffusion theory mentioned above are thoroughly wrong and belong only to the world of pure imagination. This experiment also explains the reason, why the different modifications of gypsum give us different velocity constants. In the fibrous gypsum all the crystals of which the gypsum is formed configurate in one direction and not in the other ; in the selenite the crystals configurate in all directions of the twin-crystal ; while in alabaster, precipitated CaSO,+2H,0, or in powdered selenite they configurate in no direction. Owing to this in the selenite twin-crystal in the large side of the same, always the same surfaces of all the crystals (which are least easily dissolving) are exposed to solution, in the fibrous gypsum the surfaces of the crystals lying in two directions are exposed to solution, but not the surfaces in the third direction, which combine to form the fibre, while in the alabaster the surfaces of the crystal in all three directions are exposed to solution in equal or nearly equal shares. So we find for }=20°4 cm.” the velocity constant of alabaster is about 2°6; the velocity constant of selenite in powder and compressed to a disk is for the same surface=2°9, while the velocity constant of CaSO,2H,O 576 Molecular Reactions in Heterogeneous Systems. precipitated and compressed to a block is for the same sur- face = 3:0, 2. e. is only a little different (photograph 15 shows block of powdered selenite after solution ; the corrosion is visible) ; which seems to prove that when the crystal has no special configuration and all its surfaces are equally exposed to solution, the speed of solution is practically the same. It should be noted at the same time that the powdered and compressed selenite (see Selenite) and the fine precipitated and compressed CaSO,+2H,O seem to give a very good constant from beginning to the end, without any essential increase in the same. (ii.) CaSO,+2H.0 and CaSO, Anhydride.-—Tf a substance forms a saturated solution at the surface of the solid with infinitely great speed, and if it passes from the surface of the solid to the rest of the solution only by diffusion, then CaSO,+2H,O must dissolve with greater speed than an- hydride CaSO, Because the CaSO, must either first form CaSO,+2H,0 in the solution at the surface of the solid, before it diffuses intc the rest of the solution in which we know it only as CaSO,+ 2H,0, not as CaSQ,, or CaSO,+2H,0 must be formed first on the solid CaSQ, itself, as a thin solid layer, under the action of water, and then as such pass into the solution. Whether this reaction of transformation of CaSO, into CaSO,+2H,0 be quick or slow, whether it takes place at the solid or in solution, the passing of CaSO, into the whole of the solution by diffusion can only be longer, but not shorter than in the case of CaSO,+ 2H,0, if the fundamental assumptions of the diffusion theory be true, and a reverse phenomenon should not be possible. Table III.c gives the speed of solution of anhydride CaSO,, Nova Scotia (photo 16 gives Nova Scotia after solution), which was turned to a disk of 50 mm. diameter. The velocity constant of the same is © about °64 for its surface ; on the other hand, we found the Selenite CaSO, + 2H,0 gave for the same _ surface > = 20°4 cm.’, and under all other identical conditions of temperature, stirring, volume of solution, &e., a constant of about °49 ; an inspection of the two blocks Selenite and Nova Scotia after they were dissolving in solution, also show a greater corrosion in the last, which is indicative of a greater speed of solution, than in the case of Selenite. Conclusion. I have thus proved, both theoretically and experimentally, that the explanation of my equation for molecular reactions in case of solution of salts, as a diffusion equation, and all On the Radioactivity of certain Lavas. tT the fundamental assumptions connected with the diffusion conceptions of Nernst, Brunner, and others, have no theoretical and no experimental support whatever. I have traversed in this first publication almost all the experimental material of Bruner and Tolloczko, Nernst and Brunner, so far as it deals with molecular reactions in solution. I have shown step by step, that all their experimental proofs here are nothing but arbitrary experiments, that as soon as they are replaced by accurate reliable results the very same substances furnish us with a solid proof against the diffusion theory. In my next publication I will deal with the speed of chemical reaction in heterogeneous systems, and J shall have then a still wider opportunity to show, traversing again the whole of the experimental material of Nernst and Brunner, that from the beginning to the end there is not one experiment which is not arbitrary, and which, when replaced by correct results, _ does not most decidedly refute the so-called diffusion theory with all its numerous and unnatural assumptions. It is a theory, which is neither theoretically sound, nor is it supported in the least degree by direct experiment. Davy-Faraday Laboratory of the Royal Institution, London, 5 ea ; January 1909. No i LXII. On the Radioactivity of certain Lavas. By J. Jory, F.RS.* ers months ago, when determining the radium content of lavas from various parts of the world, I noticed with surprise the relatively large amount of radium contained in one from Vesuvius. This lava was from the eruption of 1855. The reading was so high that before accepting it I re-determined it upon a second chip taken from the interior of the same hand specimen. I obtained identically the same value. Returning to the subject at a more recent date I examined the series of dated Vesuvian lavas in the Museum of Geology in Trinity College, and found quantities of radium in every case supporting my original determination. But the fact seemed brought out that the earlier lavas of the last three hundred years possessed a lower radium content than the more recently ejected rocks. At this stage Prof. Johnston- Lavis was so kind as to send me some samples of the lava- flow of April 1906. Subsequently he also supplied me with one of the oldest lavas: what he has classifiedas Dyke No. 1 of the ancient volcano of Monte Somma. This last rock is— * Communicated by the Author . 578 Prof. J. Joly on the in common with all the Vesuvian lavas—rich in leucite, and is, apparently, a leucite-tephrite. An examination of these rocks afforded results in harmony with the indications of those already obtained. The recent lava was considerably richer in radium than any of the others and the ancient dyke-rock was much the poorest in radium of any yet examined; in fact, it was rather below the normal of igneous rocks. Among prior observations upon the lavas of Vesuvius, I am acquainted with only one, that made by the Hon. R. J. Strutt, effected in the same manner; that is, by solution of the material and boiling off the emanation*. This obser- vation revealed no abnormality. After what has been said, however, I do not think any contradiction with the present results need be supposed to exist. Thus the oldest leucite- tephrite I examined resembled many feebly radioactive lavas, and it is probable that among the earlier lavas similar rocks abound. Hxperiments have also been made upon the lavas of 1906 by Nasini and Levi (Atte R. Acc. Lincet, ser. 5, Rendic. xv. sem. 2, p. 391, 1906) and on the lava of 1904 by Tommasina (Phys. Zeit. vi. 1905, p. 707). In both cases. the investigation was carried out by the dispersion-method ; the powdered rock being introduced into the electroscope and the increased current observed. With regard to the lava of 1906 Nasini and Levi found the greatest effect from the lapilli and dust; obtaining (under certain conditions) a saturation current of 33°4x10- amp. On the other hand, they concluded that the solidified lavas and scoria were inactive. They examined the ejecta of some other outflows. The lapilli and dust of 1872 gave 19°2x10- amp. under the same conditions, and the lava 13x10-% amp. For ejecta of various years the effects upon the electroscope, to the same order of magnitude as the above results, were :-— GOL ee 17:0 MO ee a Word [oO ania aie 14°7 2010 Ch a OR 23°2 1895-99 ...... 4-9 The authors conclude that a lava inactive immediately after solidification may slowly acquire radioactivity. Tommasina found, respecting the lava of 1904, that while obsidian from Lipari showed no determinable effect upon the electroscope the lava of Vesuvius increased the rate of fall of potential from a normal 10 volts per hour to 20 volts, and again the rate of loss of potential might even be increased rather more than three-fold. * Proc. Roy, Soc. A. vol. Ixxvii. p. 472. Radioactivity of certain Lavas. 579 The method pursued in these experiments, depending upon that variable property, the “emanating power,” is liable to give results lesser or greater according to the ultimate com- pactness or porosity of the material under examination. This renders its indications uncertain. These observations seem, however, to point to an abnormally high radioactivity and there are some indications of the rise in radioactivity of the more recent lavas. On the point of the lavas gaining in radioactivity after solidification, if this gain is supposed to be rapid, my experiments are not relevant; as in every case the materials which I examined were some years old. But if the gain is supposed to take place over centuries my results do not support such a view. In fact, we would expect to find the more anciently erupted lavas the most radioactive, whereas it is the other way according to my experiments. In the course of my work onthe Vesuvian rocks additional security against error was obtained by systemmatically inter- polating experiments on materials from other localities. These were in all respects prepared under like conditions and examined in the same way. Of the lavas listed below the following were so interpolated :—Htna, Pantellaria, Stromboli, Chimborazo, Krakatao ash. In addition to these, specimens of Vesuvian biotite and leucite were examined; and (for other work) Moffat Shale (3:1) and Keuper Sandstone (4°0). It will be seen further on that some of these are abnormal only in the sense of being low. The experiments were in some cases repeated upon fresh material, and in every case interior chips were taken from the specimens. ‘The usual precautions as to purity of chemicals, ete. were observed. The standard of comparison is uraninite of Joachimsthal containing, according to a recent analysis made here, 65 per cent. of uranium. More recently I have determined the thorium content of most of the materials dealt with. In some cases this deter- mination was carried out upon the same solutions used for measuring the radium ; in some a fresh solution was prepared. In the course of these experiments, which were carried out by a method recently described by me (Phil. Mag. May 1909), a test of the reliability of the method was made which may with advantage be referred to. The amount of thorium in the Krakatao pumice listed in the table below was found to be 5°2 x 10-° gram per gram. To 10 grams of the powdered pumice I added 1:2 milligram of a specimen of thorianite kindly given to me by Professor Dunstan (Phil. Mag. July 1909, p. 140). The whole was carefully mixed with the fusion mixture of alkaline carbonates (25 grams) and fused in the usual manner. The melt was leached with distilled water and filtered cold. The residue, 280 Prof. J. Joly on the after being brought into solution by 50 cc. of HCl and diluted with water, was tested for thorium. ‘The filtrate was separately tested. The total quantity of thorium found was 139°5x10-° gram. Of this the alkaline solution held just one-twelfth part. Deducting the natural thorium— 52 x 107° gram—a balance of 87°5 x 10-° gram remains. But 1:2 milligram of thorianite should contain 83°7 x 10-° gram of thorium, according to Dunstan’s analysis. The discrepancy is within the limits of error attending the weighing out of the thorianite. A second experiment of the same character on the same pumice was made, in which 1 milligram of thorianite was taken. The filtration was effected while the solution was hot. ‘The thorium found was 117°5x10-° gram, all of which was in the acid solution. Deducting, as before, the natural thorium, a balance of 65°5x10-> gram remains to account for the inserted thorium—which was, on Dunstan’s analysis, 69°8x10-° gram. The discrepancy is again within the errors of the weighing. These experiments were made with the double object of testing the method of determination and of finding whether ThX was removed in the filtrate; which from the well known experiment of Rutherford and Soddy might, perhaps, have been expected. In a few cases out of many I have found some radioactivity in the alkaline solution, and I have not generally been able to connect its appearance with the temperature at which filtration is effected. The radio- activity observed occasionally in the alkaline solution seems generally to diminish in a few days but never quite to disappear. A little both of thorium and of thorium X are possibly separated in such cases. ‘The testing of both solutions is, therefore, desirable, especially if freshly made up solutions are being dealt with. In dealing with old solutions the error, if this is not done, will generally be small. A good plan is to mix both solutions together after the residue has been brought into solution. The alkaline solution should, in this case, be first acidified. In certain basic rock-solutions this procedure is, however, not admissible; a precipitate forming. : : In the thorium experiments carried out in connexion with the lavas, the velocity of air-current from the flask to the electroscope was about two cubic centimetres per second. With this current the sensibility of the electroscope was 1°55 x 10-° gram thorium per scale-division per hour. This velocity of air-draft is sufficiently slow to secure the results against error from the passage of the short-lived emanation of actinium. Radioactivity of certain Lavas. 581 The table here given embodies the experiments on lavas *. It first deals with materials from the Vesuvian focus of eruption. Lavas ejected from the neighbouring petro- graphical provinces are given next. A few results from widely distributed volcanoes are added for comparison. This last list is, I am aware, too short, the subject being deserving of fuller treatment. Finally, some separated rock minerals from Vesuvius are dealt with. It may at once be pointed out that there is evidently no concentration of radium in these minerals. The radium is apparently distributed throughout the magma. In the table a query after a deter- mination denotes the presence of some precipitate in the acid solution, Radium Thorium alOmice 3ClOm os Monte Somma; very old dyke .......,...sceceeeeeesoeees 2°8 2 Wesuyius, 16513) Grew sees less ice co seb ocidoahes TS ber “6 1794; TLorreidehGrecoy 6.5. oo coc) sce eval. 9°8 06 - LSB yaaa ete Mes aia sbiie cimcieitals oeingouiody 13:0 2:3 #3 1855; Le Novelle; (12°5), (12°5) ............ 12-5 2°5 FS LSGS'3 (UPnP ils deo sds clases 12°6 4:1 - 1895-99; Colle Umberto; slow out-flow ; CESS) eos sac Swesandesacedscances 14:6 21 = 1906; Torre Annunziata; interior of lava stream) qm l42) (2) eek selec cceec ess 16:0 2:6 3 1906 ; Glassy lava; cooled in cistern ....., 13°8 bet a 1906; Flotation bomb, Boscotrecase ...... 10°7 (?) : 1906 ; Ejected old lava block with tachylite pW Ce ee She ae a ae ee 9-2 sae Campi Phlegraei, Monte Olibano; trachyte; (7°8). VS) pee I Betta sin vc acis ods ince waness eas 68 4:2 Ischia; olivine trachysey (2 3)) (7S). .0..0ccsescdcasesess 6:0 2:4 Lipari, Rocchi Rossi; lava; (5°8), (4°6) .........0e006 52 4°5 > Wal di Lachts ameite andesite. £2.65 .9us<-sec00e 16 05 Biromboli, scoria 5 (SO) oe) ics .0.0scociacecasiecsersss 35 5 Wulcano ; bona} (oss eea) oe. .acceccccscsecctacs vedas 50 4°6 Bina; Val del Bovey S8ase lava 2 is). 0c i Seckacenee 6:0 1:2 Pantellaria, La Mantua; lava.......... BE A) Ch USE SS ol 2:2 Wilanesd, crater, POgr mana ee. co is elite le ccdces 39 1-4 Ascension Island} Gpateiate ss 0252.00 bscss-scvdeeecs cc dece 16 2°5 Krakatao, ash; collected about 17 miles N.E. of Wi bearies MR ies Sida ccd ba oh evacciegde oaneg 06 owe * PUNGENT is cascvasactlcaceescedes 4°5 5:2 Chimborazo, near Quito; pumice .............ccecceeeeee 3-2 2°4 Bb) Holona Tava ssa ee eens cedeccbasecoeder. 2°3 (?) 06 Martinique ; bomb, much weathered................000+ 1:3 st Mrpianid: TAVAL eres eee ce sol couceedeelcciscasea ote 1°5 (?) Vesuvius ; cube of halite with purple streaks ......... 0:0 dei Fe Teunethay gh a Berek cavevoreanneresy 1:0 06 DOLLA, oan tain cde ba se au vascoacaes> 2°6 * Some of the results have appeared in “ Radioactivity and Geology,” p. 45. Astherein given they are unfortunately affected by an error which arose in calculating the constant of a recently constructed electroscope. 982 : Prof. J. Joly on the It will be noticed that in every case the readings of Vesuvian lavas from 1631 to the present day are remarkably high ; up to three times the normal for igneous rocks and, | indeed, even higher. The thorium-content, although large in comparison with what generally prevails in the rocks of the St. Gothard series (Phil. Mag. July 1909) are not con- spicuously higher in the Vesuvian rocks than in the rocks from other volcanoes. The highest reading was obtained for the Krakatao pumice. The Vesuvian lavas appear to show a progressive increase of radioactivity acccrding as they are of more recent eruption. The old leucitic rock of Monte Somma is of special interest. According to this one sample of the earlier rocks the radio- activity was at first actually less than normal. ‘The culmin- ating richness in radium is attained in a sample from the interior of the lava-flow of April 1906. (The “ ejected old lava block” in the list is, of course, not truly of this date.) Unless we conclude that the radium is transforming within these lavas after their ejection at a rate much greater than would be expected from the period inferred on experimental grounds, and that the loss is not being made good, we must assume that as time progresses, this volcano is tapping materials richer and richer in radium. There is no impro- bability in this explanation save what is involved in the rather contradictory fact that the lavas of Vesuvius have shown a remarkable constancy in chemical composition from the earliest times. This is noticed by many authorities, but specially by Rosenbusch (‘Elemente der Gesteinslehre,’ p. 344), who remarks that notwithstanding great variations in texture, colour, and the nature of the phenocrysts, their chemical constitution has been extraordinarily constant from the oldest pre-historic eruptions of Monte Somma to the most recent eruptions of Vesuvius. It is therefore surprising to find the radium (or uranium) content varying not less than five-fold. The lavas from the surrounding volcanoes emanate from distinct petrographical provinces and show the most diverse chemical compositions (Bonney, ‘ Volcanoes,’ p. 207). Their failure to show the high radioactivity of the Vesuvian lavas is, therefore, not remarkable. On the whole, the Lipari and Etna lavas stand high among lavas from other parts of the world. But an extension of the number of determinations may reveal many cases of radioactivity quite as high. And, of course, the same remark may be made in reference to the Vesuvian results. | The possibility of a connexion between radioactivity and Radioactivity of certain Lavas. 583 vuleanicity is so natural an association of ideas that even before the general prevalence of radium in rocks had been demonstrated by Strutt, a suggestion to that effect had been made. Major Dutton (Journal of Geology, xiv. May—June 1906, p. 259) in 1906 put forward the view that radioactive materials might give rise to fusion temperatures at points within 3 or 4 miles of the surface: indeed, his appeal to radioactive energy was mainly based on the necessity which, according to Major Dutton’s views, exists of locating volcanic foci at these short distances beneath the surface of the Earth. The repetitive character of the phenomena was also regarded as more readily accounted for on the theory of the accumu- lation of radioactive energy than in any other manner. Major Dutton’s ideas were criticised by G. D. Lauderback (ibid. p. 748) more especially as to the necessity of assuming a position so superficial for volcanic foci and of appealing to radium to explain the repetitive phenomena. Moreover, it _ was pointed out by more than one critic at the time that any theory involving haphazard pockets of radioactive materials was not in accord with the fact that the location of voleanoes was by no means haphazard, but was determined according to certain great surface features of the Globe; the geo- synclines, wherein sediments collect and crust-flexure occurs. When recently dealing with the latter subject—the very probable connexion between radioactive heating and the instability of the sediment-laden part of the crust (Address Sect. C. Brit. Assoc. 1908), it appeared to me that a connexion between vulcanicity and radioactivity was, in point of fact, involved in the conditions determining the rise of the geotherms under a superficial covering of some kilo- metres of radioactive sediments. While we are not entitled +o assume upon our present knowledge the existence of radioactive magmas in pockets close to the surface and possessed of sufficient radioactivity to establish a local volcanic focus, some miles down high temperatures might be ascribed to the great sedimentary accumulations which have been sufficiently long in situ for the accumulation of radioactive heat. The crust buried beneath the covering of sediment is, in fact, heated both from above and from beneath, and the quantities involved, as regards depths of sedimentary deposit and average radioactivity of such materials, are such as to justify the view that in the geo- synclines vulcanicity would be specially favoured. If this hypothesis is correct, not only the flexure and distortion affecting these areas, but the chains of volcanoes breaking out along the great mountain ranges, may be logically 584 | Prof. J. Joly on the regarded as primarily traceable to the effects of radioactive energy. As defining a general connexion between radioactivity and vulcanicity, this view appears to be rather strengthened than otherwise by recent advances in our knowledge of the tidal stability of the earth. For if, as Professor Love con- cludes (Nature, April 29, 1909), we may not postulate the general extension of a fluid substratum, we are evidently driven to connect vulcanicity in the geosynclines with some local source of heat. It may here be observed that there does not seem to be difficulty in reconciling Prof. Love’s conditions with the facts attending mountain elevation. Under the new restrictions we are compelled to assume that temperatures deep down cannot generally amount to those of liquefaction. However, “crust-creep”’ on a large scale must at the same time be possible, or the forces acting in the geosynclines become unaccountable. In the wide range of viscosity of siliceous substances, both condi- tions seem attainable. While generally there cannot prevail a temperature of fusion, conditions of rigidity toward tidal stress do not seem inconsistent with sufficient viscosity to permit yielding under the more prolonged, unidirectional, stress of secular cooling. And not without bearing on the connexion between radioactivity and vuicanicity in its wider aspect is the fact that the case for the shallow, superficial, character of the radioactive surface-materials of the earth seems strengthened by the limitation of temperature-rise downward, It appears that the gradients must ultimately be limited to such a gradual slope as will not overtake the rise under pressure of the melting-points of the rock-forming silicates *. Such a condition is absolutely inconsistent with the downward extension of the radium-richness of the surface- rocks. These remarks apply generally to a probable connexion between radioactivity and volcanic outbreak ; they do not generally deal with the particular case to which I have called attention :—the case of a volcano emitting abnormally radio- active lavas. We might suppose that the circumstances connected with the case of Vesuvius were to a certain extent fortuitous ; the exceptionally radioactive materials having been brought to light by a regional crustal disturbance unconnected with the existence of a local deep-seated radioactive magma. On such a view we may admit that the locally great radio- activity has perhaps contributed to the remarkable persistence * For data see Vost, Tschermak's Min. u. Pet. Mit. xxvii. p. 105. Radioactivity of certain Lavas. 585 of Vesuvius as an active voleano, and even assisted in main- taining the vulcanicity in the surrounding region. There may be other cases of the kind. We have only to assume that here and there in the deeper crust are rock-masses of higher radioactivity than generally prevails, and that while regional vulcanicity may require for its initiation and de- velopment prolonged and deep sedimentation, yet where there is coincidence with strongly radioactive magmas, spe- cially energetic and persistent effects will arise. We are, of course, without guidance as to the downward extension of the radioactive laccolith concerned; or as to whether we have yet attained a true measure of its radium-content. An explanation of the exceptional radioactivity of Vesuvian lavas may, however, also be sought on the hypothesis that the materials ejected from Vesuvius are sedimentary in origin. Such an origin has before now been ascribed to volcanic materials. On this view the richness in radium observed in these lavas is in line with the observed radium-richness of many slow-collecting sediments. There is, indeed, nothing in the general composition of these lavas to negative their sedimentary origin. They might represent certain calcareous clay slates, for instance*. It is remarkable that the percentage of potash much exceeds that of soda. Although certain, rather scarce igneous rocks—the shonkinites and some others—sometimes exhibit a similar excess of potash over soda, this feature is, generally speaking, characteristic of detrital remains which have undergone the impoverishment in sodium attendant upon denudation. The absolute amounts of alkalies present are, however, higher than is commonly found in sedimentary rocks. On the whole this view seems less probable than that which assumes the Vesuvian lavas to be drawn from a deep-seated laccolith. Whichever explanation of the origin of these lavas is deemed most probable, it may fairly be asked if we are indeed entitled to assume that any considerable temperature-rise may be ascribed to their radioactivity. This question discloses the unsatisfactory state of our knowledge upon the subject. All depends of course on the extension of the radioactive materials. If they are laccolithic in origin we may reasonably suppose their downward extension considerable, and in this case, the intensification of volcanic conditions, by cumulative radio- active energy, appears highly probable. If, on the other hand, the lavas are sedimentary in origin, the vertical extension of beds so radioactive can hardly be great. In * For analyses of the Vesuvian lavas, see Rosenbusch, Joc, cit. p. 346. Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 2R 586 Messrs. Cameron and Oettinger on Electromotive this case the contributory thermal effects of the radioactive substances has, probably, been sinall, however long a time we are willing to assign to the genesis of heat. An estimate of the intrinsic heatin g-etfect of the radioactive lavas we have been considering is of interest. The mean radium-content of the lavas ejected since 1631 is 12°3 x 10-¥ gram per gram. Assuming that the presence of one gram of elemental radium in equilibrium involves the generation of 201°6 gram-degrees per hour, the heating-effect in the lava is about 25 x 10-!°calorie per hour. The mean quantity of thorium is 2°3x10-° gram per gram. Pegram and Webb’s result, obtained by a direct thermal measurement applied to thorium oxide, gives the heat per gram of elemental thorium in equilibrium as 2°38x10-° calorie. Hence the thorium present would produce 5:5 x 10-!° calorie per hour. The added results of these quantities of heat works out as giving a rise of temperature of about 150° C. in one million years ; assuming no loss by conduction. Those who look to radioactive heating as affording an explanation of volcanic periodicity would do well to reflect upon the slowness with which heat is supplied, even in exceptionally rich radioactive materials. In the case of the Vesuvian lavas the abnormally large amount of radium present renders the heating-effect of the thorium relatively small. The mean thorium-content of the other lavas examined is 2°6 x10—°, and the mean radium- content of these rocks is 4°0x10- gram per gram. The heating-effects are respectively 6°2x10—'° and 8:1x10-% gram-degree per hour. Here there is nearly equality in the thermal values. Blane (Rend. d. FR. Accad. d. Lincet, xviii. ser. 5, p. 289) has concluded that the thermal effect of thorium in rocks may amount to about double that due to the radium series, but his figures are based on a somewhat larger thorium- and smaller radium-content than has prevailed in the rocks which I have, so far, examined. LXIII. On the Electromotive Forces produced by Acid and Alkaline Solutions streaming through Glass Capillary Tubes. By ALEXANDER T. CAMERON and ERicH OETTINGER*. HE electromotive forces existing between glass or other insulating material and aqueous solutions, and the con- sequences resulting therefrom when these solutions are moving over the insulating surface, as, e. g., when they are * Communicated by the Authors. a al ex: Forces produced by Flowing Solutions. 587 forced through glass tubes, have formed the subject of the theory of Helmholtz*. This is based on the facts that, firstly, when a conducting liquid streams through a channel of insulating material, an electromotive force is produced in the direction of the liquid stream or opposite to it, while, secondly, an electromotive force applied at the ends of the channel, or between two points in it separated by a convenient distance, produces a flow of liquid. Helmholtz assumed that there existed a difference of potential at the boundary between the insulating material of the tube and the conducting liquid, and derived an equation connecting this difference of potential $:— a (where @; is the potential of the liquid, ¢. that of the solid insulator) with the pressure P between two cross- sections of the channel, the electromotive force EK existing between these two cross-sections, the specific conductivity « of the solution, and its coefficient of internal friction 7 : ec), ~ dank The formula applies to tubes for which Poiseuille’s law holds, provided also the potential difference between the two cross-sections is not led into an outside circuit, but only produces an electric current along the tube, and that there is no shifting of the last layer of the liquid adhering to the glass. This last condition may be expressed in the form that the external friction is infinite; for a finite value the term $:— da has to be replaced by bb, 4 2E, where € is the constant of slipping, and N the normal to the tube wall. To this, the “electric moment of the double layer,’ Dorn gave the symbol uw. Lambf has proposed a modification of the Helmholtz theory, which differs only by the assumption that the charge of the liquid is rigidly con- fined to the last layer. In Lamb’s theory the same term takes the form ($:- $a) 5, where d is the thickness of the double layer, z. e. a magnitude of the order 10°, while / is the ratio of internal and external friction, 7. e. of the coefficients of friction and slip. Helmholtz veritied his theory by applying to it the experi- mental results of Quincket, who forced water through two * Wied. Anz. vii. p. 337 (1879). + Phil. Mag. [5] xxv. p. 52 (1898). t Poge. Ann. cvil. . a. ; evill. p. 33 (1860). 588 Messrs. Cameron and Oettinger on Electromotive glass tubes connected by a diaphragm of burnt clay and similar substances. Zéllner * showed that what held fora bundle of capillaries applied with equal force to a single tube, while further experimental work was carried out by Edlund +, Haga}, Clark §, Dorn ||, and Saxén{]. Their results are in general agreement with each other, and, fue those of Dorn, entirely agree with the Helmholtz theory. All these experimental investigations consider the factor di—da, or its expanded form w (Lamb’s (¢;—¢,) a as a constant. Whether this is the case or not has remained unverified, since independent determination of this value is not possible. The figure calculated by Helmholtz and Dorn is about 4 daniell (5:1 volts when corrected for modern units), which seems a rather large value for the potential between glass and water, considering the fact that much smaller potentials, so far as we are aware, always produce development of hydrogen gas**. Much smaller values, strikingly altering with the concentration of the solution, have been derived from the electric endosmose experiments of Wiedemann {T, Quincke ff, and Freund $§, so that one point of the theory still remains unsettled. A way of access to the potential difference between glass and solutions has been opened recently by Haber and Kle- mensiewicz ||||, who have been able to prove that the surface of ordinary glass acts perfectly as a so-called hydrogen electrode of constant hydrogen pressure. The change of potential produced with such an electrode by altering the ~ acidity or alkalinity of the surrounding solution is well known. The difference of potential between two such elec- trodes, one dipping into acid the other into alkali, was made * Poge. Ann. cxlviil. p. 640 (1878). + Wied. Ann. i. p. 161 (1877) ; ix. p. 95 (1880). { Lhd. ii. p. 326 (1877). § Ibid. ii. p. 336 (1877). || ded. v. p. 20 (1878) ; ix. p. 518 (1880); x. p. 71 (1880). q| Ibid. xlvii. p. 46 (1892). ** See table of absolute potentials by Wilsmore and Ostwald, Zeitschr. f. phys. Chemie, xxxvi. p. 92 (1901). Billiter’s absolute zero point (Drude’s Ann. xi. p. 187, 1903), although different, is still near enough to Ostwald’s for the validity of the above consideration. +7 Poge. Ann. Ixxxvii. p. 821 (1852). tt ded. exiii. p. 513 (1861). §§ Wied. Ann. vii. p. 44 (1879). \| || Zeetschr. f. phys. Chem. 1909. Forces produced by Flowing Solutions. 589 by Ostwald a method for determining the dissociation of the water *, The fact that glass acts as a hydrogen electrode enables us to state that at ordinary temperatures an increase of a tenth power in the concentration of the hydrogen ions produces a _ change in the electromotive force of 0:058 volt. A solution normal as regards hydrogen ions and one normal as regards hydroxyl ions show, as is well known, a ratio of 10-™ between their hydrogen-ion concentrations. Consequently, the change in the electromotive force between glass and surrounding liquid, when the latter undergoes this change from normal hydrogen to normal hydroxyl ions, will be 14x 0:058=0°812 volt; where both solutions are one-hun- dredth normal, this value becomes 10 x 0:058=0'580, and with one-thousandth normal solutions, 8 x 0°058=0°464 volt, and so on. The sign of the change is always such that pure water, -arbitrarily taken as neutral against glass, in which the con- centration of both hydrogen and hydroxyl ions is 107‘, becomes positive by increase of hydroxyl ions, negative by increase of hydrogen ions. In light of these facts the potential difference $:—¢u, or its expanded form pw (Lamb’s (¢;—¢,) 4) does not seem quite so inaccessible as before. It is now to be expected that if the Helmholtz theory is tested with acid and alkaline solutions, different valuesot ¢;—¢@, will result, and we may : : ee predict that if the term ¢ ot is zero or constant (or Lamb’s 7 N is constant), the difference between the values will be equal to the electromotive force derived from the acidity and alkalinity of the applied solutions. The irregularity of the values for ¢:—¢@. found by different experimenters leads us to expect that the experimental veri- fication is beset with some difficulties, so that perhaps no more than a qualitative agreement can be expected. More- over, there exists a group of facts which will be discussed at the end of the paper, which make it doubtful whether or not the interference of another effect will not prevent more than qualitative agreement. In view, however, of the fact that the values of the single potentials existing ata phase boundary * Zeitschr. f. phys. Chemie, xi. p. 521 (1898); cp. the correction by Nernst, ibid. xiv. p. 155 (1894), and the recent papers by Lorenz and his eollahorators, zbed. 1x. p. 422 (1907) ; Ixvi. p. 733 (1909). 590 Messrs. Cameron and Oettinger on Electromotive (metal, salt solution, as well as other two-phase systems) has for twenty years formed the subject of unsettled dispute, even ~ such a qualitative result did not seem to lack importance. Moreover, the electromotive force at the boundary of two phase systems such as glass and liquid is of special interest, since Haber has shown that the laws governing this electro- motive force are applicable to interesting electro-physiological phenomena. This paper contains an account of attempts to verify the theory from this point of view, and though our results give only a qualitative confirmation, for the reasons just stated, it seems desirable to publish them, especially since considerable time may elapse before the experimental difficulties are sufficiently overcome to permit of completer verification. Experimental Part : Apparatus. The apparatus differs in a number of essentials from those employed by previous investigators, and as it seems easier to construct and to use than these, it may be described shortly. It consists essentially of four parts, an instrument for measuring potentials, a capillary tube containing electrodes, a stout glass vessel to which it is joined, containing the liquid under examination, and an apparatus for maintaining constant pressure. The apparatus was tested by repeating the ex- periments of Dorn with pure water; in this way a number of errors in it were detected which require to be avoided, and may therefore be mentioned. In all cases a quadrant electrometer was used to measure the potential difference; in this way errors arising from polarization, which occur with galvanometers or with electro- meters of greater capacity, were avoided. Both the Thomson instrument with bifilar suspension and that with a platinum hair-suspension and JDolezalek needle, were employed at different times. The capillaries used were calibrated with a shifting thread of mercury, and selected so that the variation in diameter was slight. Different forms of electrodes were tested. At first side tubes were blown on to the capillary, and completely filled with mercury, so that the mercury was. in contact with the stream of liquid; contact was allowed with the electrometer by platinum wires sealed through the ends of the side tubes. The potentials derived from these electrodes were not proportional to the fall of pressure between them, 7. e. did not agree with the Helmholtz formula; on using the same tubes without mercury worse results were —— ee em Clce”DCUlUc ee Forces produced by Flowing Solutions. o91 obtained; in this case the platinum electrodes in the side tubes were not in contact with flowing but with resting liquid. The results showing closest agreement with theory were obtained with electrodes consisting of thin platinum wires fused directly into the capillary tubes, the alteration in the capillary being made as small as possible. External contact was improved by surrounding the portion of tube containing the electrode with tinfoil, with copper wire as binding material; this was connected to the electro- meter. The vessel used to contain the liquid under examination was a five-litre bottle of Jena glass, closed by a two-holed rubber cork, which was held in position when under pressure by a simple clamp. A short glass tube dipping just below the cork connected the vessel with the pressure apparatus. A second wide tube, reaching to the bottom of the vessel, was joined by pressure tubing with the capillary, which was clamped in a horizontal position. At first the device employed by Haga (loc. cit.) was tried, the capillary tube was connected between two similar flasks, and the liquid forced backwards and forwards between them. However, with this method contradictory results were obtained, probably attributable to the “‘ waterfall electricity” effect observed by Lenard or the similar effect observed by Elster*. It is probable that the curious results obtained by HagaT are attributable to one or other of these causes. For the same reasons it was found necessary to prevent the liquid flowing out of the capillary from impinging on any surface, before it was broken up into drops. The pressure arrangement consisted of an ordinary pressure bomb containing compressed air (freed from carbon dioxide) up to a hundred atmospheres pressure. The adjustment was made with a Le Rossignol t valve, which, since it contains a barrel with the small angle of 4°, allows a very fine adjust- ment, and gives fairly constant pressures even with such slight outflow of gas as was required in these experiments. Between the valve and the five-litre vessel were inserted an open mercury manometer reading to one and a half atmo- sphere, a simple safety-valve consisting of a glass tube dipping below mercury, andan outlet tube, joined to pressure tubing, closed by a screw-clamp. * Wied. Ann. vi. p. 553 (1879). + Loc. cit. p. 328. t Chem. Zeit. no. 69, 1908. 592 Messrs. Cameron and Oettinger on Electromotive The apparatus is shown in the accompanying diagram (fig. 1). The electrometer needle was always charged to a con- venient potential by means of a Zamboni pile. One pair of quadrants was earthed, the other connected with the electrode Fig. 1. Mo MMT , Ww a ui Tt UUpes nearest the free end of the capillary. The other electrode was alsoearthed. It was found that the connexions, reversed, did not lead to such certain results; the reason was probably due to imperfect insulation of the second electrode, since connexion with the flask was allowed by the liquid. This source of error was also observed by Dorn. The sensibility of the electrometer was always determined with a normal cadmium cell. Preliminary Haperiments. If the quantities di— du, y, and « are constant, Helmholtz’s formula simplifies to the form K.P, where E and P are respectively the differences of potential and pressure between two electrodes, and K is a constant. Ordinary distilled water of specific conductivity between 10-5 and 10-® was used to test the formula in this simple form, in order to contro! the working of the apparatus. A thin capillary tube ab of diameter 0°65 and length 270 mm. was taken, and four electrodes «, 8, y, 6, inserted, such that aa=29, o8=62, By=—97, yo=68, ob=14 tum, Forces produced by Flowing Solutions. 593 The tube was rinsed out with chromic acid mixture, the end b joined to the flask, and water forced through at different pressures. Three difficulties prevent an exact agreement between the results obtained and the theory. The first arises from the fact that the introduction of the electrodes disturbs the flow of liquid, both through the electrodes themselves, and from the unavoidable distortion of the glass capillary at the point of insertion. Whether we neglect this disturbing influence, consider the space round the electrodes as a normal capillary, and measure the actual distance from electrode to electrode, or whether we neglect the distorted spaces themselves, assuming that there is no effect within them, and measure the distances between the beginning and end of the undis- torted capillary system, we shallalways make a certain error. It was thought that the error might be less if the second assumption were followed. The second difficulty arises from the fact that, according - to the results found formerly by Dorn and Clark, the effects obtained are dependent on time. Clark found that when a tube was rinsed with concentrated sulphuric acid and then distilled water, and then water forced through it continuously for many hours, a decrease in the electromotive force was obtained invariably, which amounted in some cases to as much as 25 per cent. On recleaning the tube the original value was regained. Dorn’s results were not so regular. He obtained both decreases and increases of voltage with lapse of time; these were connected apparently with the method used to cleanse the tube. The last point of uncertainty comes into the results from the calculation of the actual pressures existing between the electrodes. We know the total pressure applied. This is not entirely used up in the tube. With pressures of half an atmosphere or more the liquid does not escape in drops from the tube, but forms a ray possessing kinetic energy corre- sponding to a certain pressure, so that the drop of pressure in the tube is less than the ditference of applied pressure to atmospheric pressure. Moreover, every exit from and entrance into an electrode space causes the formation of eddies, and in any case a slight drop of pressure exists even in the non-capillary portions of the tube. Being unable to state the amount of these losses, we calculated on the as- sumption that the applied pressure was entirely used up in the five capillary stretches, the dimensions of which have been given*. The amount of pressure used up in each portion * The combined length of the three electrode spaces was 12 mm, 594 Messrs. Cameron and Oettinger on Electromotive is consequently over-estimated, and we are by no means certain that this over-estimation produces merely an error consisting of an approximately constant factor. When these considerations are borne in mind the following figures will not seem unfit to support the formula :—™* A are the observed pressures between the ends of the tube corrected for the water column in the glass containing-vessel, B are the pressures calculated to exist between the two electrodes under consideration, from the law that the fall in pressure is proportional to the length along thetube. During the experiment, which lasted an hour, temperature varied between 18° and 19° C. The sensibility of the electrometer was such that 1 cm. on the reading scale corresponded to 0:05 volt. i uk a) 2 el i ae | A Portion of Beate. mm. Hg. tube taken. | mm. Hg. volt. Ed 380°9 ae 87-6 +0593 | 676% 10-3 3813 ay 294:5 1-400 | 6-23 ss22 |. ad 3213 1914 | 5:96 | 380-7 By | 1368 0815 | 596 | 382 0 po || 288-4 1307. | 5-60 381°6 yo | 96°1 0-490 =| 5-10 . | | | 249-5 ap 57-4 0308 | 6-94 | 249+1 ay 146-7 0-971 | 6-62 | 2483 ad) | 208-7 H LBan ea | 249'8 BY hi |. B68 i amet | 6:38 | 249-6 Bo 1526 | 0959 | 627 | | | 575-0 af 1322 | 0833 | 630 594-4 ay 350-0 2100 | 6:00 | 567-7 By | 2040 1197 | B87 | Since when water is stored in a glass vessel and used con- tinuously in an experiment of some duration, there arises the possibility that small changes may take place in the con- ductivity of the water, to avoid such an error experiments were carried out with very dilute solutions of potassinm chloride. Of these the following are typical :— Experiment 2. To test the effect of different pressures and duration of time.—A new tube was employed, containing two electrodes, 242 mm. apart. The whole length of the tube, ex- cluding the electrode spaces, was 470 mm.f, and its diameter * It may also be pointed out that the diameter of the tube was perhaps a little greater than those which strictly obey Poiseuille’s law. + Each electrode space was 5mm. in length. Forces produced by Flowing Solutions. 595 varied between the limits 0°816 and0:823 mm. The solution employed was N/3000 KCl. The temperature varied between 20° and 20°5 C. One em. on the electrometer scale cor- responded to 0:025 volt. The experiment was commenced at 10.32 am. A and B have the same significance as before. ) | | Time. A. B. EMF. | EME/B. | A.M. mm. mm. volt. | i 1028 368-1 189°5 0-288 | 1:518x10-3 41 3615 186°1 0-282 | 1-514 | | 47 360°5 185°6 0-286 | 1544 | 50 707-9 384-6 0-422 | 1158 | 52 407°5 3642 0-428 176 55 203-0 104°5 0144 = | 1-377 58 208°6 107-4 0-159 | 1-478 59 360-4 1856 0-270 =| 1-458 11.01 366-1 188'5 0-279 ‘| 1-480 11 412+] 212-2 0316 | 1-490 16 | 4224 217-4 0327 | 1-504 is | -li87 92:0 0157 | 1-703 19 172'1 88°6 0-154 | 1-737 21 | 6098 3140 0-471 | 1-500 24+ gUg1 310-0 0-456 | 1-471 26 4722 243-1 0:352 | 1-448 23 | 4633 238°5 0347 | 1-454 38° |.) Sepa 204-8 0:300 | 1-464 39 | 32966 2042 0:297 | 1452 If the figures are re-arranged according to pressure it Is seen that for the extreme values there is a certain progression varying inversely as the pressure, but between the limits of 200 and 600 mm. the influence is small, and the simple form of the Helmholtz theory seems well supported by the ex- periment. The small remaining change within these limits seems unavoidable, and must be regarded as due to changes in the behaviour of the tube with time. Experiment 3. To ascertain the effect of temperature.—A dilute solution of potassium chloride was used as in the previous experiment. It was heated to a convenient tempe- rature before introduction into the glass bottle. There it cooled slowly, and measurements were made during the process. A thermometer was placed in the escaping stream of liquid. As a conceivable precaution against a larger “time-effect ”’ a very slow stream of liquid was caused to flow continuously between the sets of readings. The tube used was the same as that in Experiment 2. One cm. on the electrometer scale corresponded to 0°025 volt. The experiment was commenced at 11.10 a.m. 596 Messrs. Cameron and Oettinger on Electromotive | Time. A. B. Temp. | E.M.F. | E.M.F./B. | Mean. —— ee A.M. ©. volt. 11.15 335'7 | 172: 31:9 Ooll 1°799 x 10-3 18 339°6| 174: 31:9 0-216 1°805 24 341°7 | 176: 31:6 0°318 1:808 ‘| 1:804x10-3 8 9 0 3; 301 0324 1°858 D 3 0 6 35 | 338-4] 174 38 | 348°7| 179 30:1 0:338 1-882 40 | 348:21 1793! 29:8 0:334 1:865 45 | 341-7| 176: 29-7 0-318 1-806 49 | 335:2| 172 29°6 0-207 1:780 1:838 P.M. 3.45 347°6| 179:0| 21°5 0°339 1:895 49 380°7 | 196°0| 21:4 0361 1-840 ol 337°3| 173°'7| 21-4 0319 1°836 1857 The change observed is only 3 per cent., 7. e. is within the limit of experimental error previously found. Experiments were also made to ascertain the change of temperature caused by friction while the liquid was passing through the capillary. A thermometer was introduced into the tube connecting the bottle with the capillary, and a second placed in the stream of liquid issuing. A rise of temperature was observed which never exceeded 1°5. For experiments at ordinary temperatures, therefore, slight temperature changes need not be considered. Haperiments with Dilute Solutions. The question under discussion in this paper would be tested most advantageously if series of measurements could be made with different concentrations for different acids and alkalies. We attempted to make such measurements, but found many difficulties in the attempt to employ a large range of concen- tration. When the concentration is greater than N/1000 the H.M.F. obtained with the pressures employed becomes less than 0'1 volt. In this case there become of great importance the errors which arise from a difference of potential of both elec- trodes when the tube is filled with liquid at rest. We never succeeded in avoiding casual differences between the two elec- trodes, in this condition, of the order of several millivolts. In determining these values before and after the determination of the H.M.F. produced by flow of liquid, we found that often they change both in value and in sign. Devices such as connecting the electrodes before the measurement, insulating as well as possible the glass surface (both tube and flask) &c., proved insufficient remedies. It was therefore necessary Forces produced by Flowing Solutions. 597 to make measurements only with such concentrations that the E.M.F. obtained was of a higher order of magnitude than the error. Hence high concentrations could not be used. On the other hand, concentrations of 1/10000 nor- mality must also be avoided because impurities of the water can then exert too great an influence, and the value in the conductivity becomes too uncertain, so that of the many preliminary experiments those between N/5000 and N/1500 were found best; our final experiments were carried out between these concentrations in the following manner :— The solutions used were prepared synthetically; in each case a definite amount of solution of known strength was added to a definite amount of distilled water in the containing vessel, and the whole mixed thoroughly. By addition of more water or solution a second concentration was obtained. The conductivity of each solution was determined immediately after the measurements of the potential. The experiments with each concentration lasted from one to one and a half hours. The capillary tube was cleaned with chromic acid mixture before each change of solution, and it was assumed that during the time of measurement the time effect was no greater than that previously observed. If the conductivities are compared with those derived from the ionic mobilities of the solutions at these concentrations, it will be seen that differences exist. These are due to the fact that the distilled water was not of such a high degree of purity as that employed in exact conductivity measurements; larger quantities were required than could be obtained con- veniently with water of such purity. The errors introduced from this source, however, were not large. Kohlrausch has shown* that the temperature coefficients of the conductivity and of friction, for very dilute solutions, are very nearly the same, so that as the temperature at which the conductivity was measured was always very little dif- ferent from that of experiment, the actual conductivity and coefficient of friction for that temperature were employed. The coefficient of friction was assumed to be the same as that for water t, and was calculated from O. E. Meyer’s formula t * 1775 ™= 1 +0-03315t + 0:00024378 * Wied. Ann. vi. p. 193 (1879). + This assumption is justifiable, since changes of concentration of one-eighth normality with these solutions only produce a difference of from 0°3-1°7 per cent. in the coefficient of friction. t Wied. Ann. ii. p. 394 (1877). 598 Messrs. Cameron and Oettinger on Electromotive Thus for) 267) )=1°111; 17°, »=1°086.5 18a 197; 1°038; Ga: In every experiment the potential at zero pressure (2. e. with the capillary filled with solution at rest) was first measured, until constant, then that at one or more pressures, and finally that at zero pressure again. In these experiments a new tube was used, with the following constants: total length, 518 mm., length between electrodes 256 mm., diameter 0°720 to 0°728 mm.* The following table shows the results with dilute acids. A and B have the usual significance. Itshould be remembered that the concentrations are only approximate, and that an error of 3 or 4 per cent. is possible. HE, and Hs; are the voltages found at zero pressure before and after the actual measurement (H,) respectively. Hy, is the corrected voltage. In order to obtain ¢;—¢, 1n volts (Helmholtz’s formula is given in absolute electrostatic units), the term Ejog9* + was multiplied by the factor 7 x 0:904 x 10°, calculated from the formula. Cis the equivalent of 1 cm. on the electrometer-scale in volts. Solution. | Concentration.| A. B. C. Temp. Ej. Bre EEL ta, gee bende N/5000 372 184 | 0-033 16° | —0-016 +0°098 73 OBL i comes Fins fil Coe O-191 N/5000 389 194 | 0-050 | 16° | —0-002 +0:105 740 BEG) e)) ab chet Pa ce 0-173 CH,COOH... N/2060 762 377 =|: «0083 15° | +0°053 | +0:275 384 POD) Mev aetees bak Re aa 0-168 | | Solution. E,. E,. ie: Bayon: bi — ba. 155 Oe Sears ? +0:114+ ? 0-1383 x 105 | 4:58x10—5 | 460+ ? | eS 0-2072 ? PPR A pial hs 54 426+ ? 0 +0:107+2 013841 «105 | 409x10-5 | 4:11+2 %, pecaies O175+1 %o ware ieee oma ATE 35241 %/, CH,COOH...! +0052 | +0°222+0°4 %, | 0°1647x105 | 3:°58x10—5 | 3:95+0-4 °/, si bide | 0115+0°8 % Rperrerenres i ihscea (0, 420+0°8 % The errors shown after the + sign are calculated on the assumption that the flow of liquid produces an H.M.F. equal * The total length of electrode spaces was 16 mm. + Ejooo is the voltage calculated for 1000 mm. pressure. Forces produced by Flowing Solutions. 599 to the difference of the found value EK, and a value between E, and E;. This assumption is certainly somewhat arbitrary, since we do not know whether these values HE, and E; come from a disturbance which exists only when the liquid is in a state of rest. Thus the real uncertainty is larger than that given with the + sign. In the case of acetic acid we think that some constant external influence came into play, and that the figures were not subject to a larger error. In both the experiments with hydrochloric acid a more concentrated solution was also measured: in a further expe- riment a still more concentrated solution of N/1250 was employed. ‘The results of these experiments are given in the following table. Solution. | Concentration.| A. et. Ce Temp. E,. ¥,. a | 3/2500 =| 760 | 376 | 0-033 16° | +0012 | +0-084 ; N/2500 | 400 | 198 | 0-050 16° | +0-031 | +0-073 FED ae an i BPN A C-ill N/1250 {| 900 | 445 | 0-050 Lie 0 +0047 ! i { | Solution. | He] E,. 1/«. he cyclones | di— da. mee... | 2: | -OOTeaeee 0-0684 x 105 | 279x 10-5 | 280+? % / +0032 +0:041+1:5%, | 0:0652 | 3:17 B18+1:5 % Rekele OOZI Tee | fecnaue seins. 3-21 32341 9 (—0:015 +0:059+10 % | 0-0314 | 4-20 4-22+10 %/, 5 | | : ’ 7 ; It would certainly be expected that all these values should lie close together, since the differences in concentration are so small that the differences in the E.M.Fs. arising from them are quite negligible. The differences between 2°80 and 4°22 may be taken as a sign of the degree of uncertainty con- nected with this second series. We think we are entitled to lay less stress both on the higher value for the N/1250 solution and on the smaller for the N/2500 solution. In both cases the ratio of E, and E; to the value E, is comparatively large, and the experiments are also in bad agreement with each other. Consequently we may conclude that the values for $i—a in the neighbourhood of 4 volts will not be far from the truth. In any case it seems evident from these results that the values for acids are less than 4°5 volts. 600 iad | eee Messrs. Cameron and Oettinger on Electromotive Tn the next table are given the values found for alkaline solutions. Solution. | Concentration.) A. B. C. Temp. E,. Ee NH,OH .....: N/5000 410 | 203 | 0050 | 17° | +0-018 | +0-496 805) 4)-398)) tare wen... 0:834 N/2500 845 | 418 | 0-050 | 17° | +0-022 | +0:599 N/2500 405 | 200 | 0050 | 17° | +0-027 | +0:308 KOR a N/2000 400 | 198 | 0033 | 16° | +40:003 | +0-283 700. || S76 ae a 0-489 Solution. E, Ki. 1/«. Ehoook- pi — pa. | ‘NH,OH....... —0:005 | +0:485+5°/, | 0-4802x10° 555x10-5 | 54545 9, (eae xe OS28223 5 | Neer ee | 481 472+ 3 % -—0:016 | +0596+6% | 0:2602 5:48 5°37+6 % +0009 | +0:290+6°% | 0:2654 546 53546 %, 1 CLS pa Asn. —0-016 | +0-289+6 %/ | 0:2028 | 7-20 7-23-46 %/, ei 048374540), |) 00s 6-41 64444 %, It is at once apparent that these values are all greater than A-5 volts*; the mean can be taken perhaps in the neighbourhood of 5°5 volts, so that there is a distinct difference between acid and alkali much greater than the error of experiment. In all cases the solutions were tested and the acidity and alkalinity were just perceptible. The values obtained for water by Helmholtz from Quincke’s experiments, and by Dorn, are both given as nearly exactly 4 daniell, which, when corrected to modern units, is equal to 5°07 volts. This value lies between our average values for acids and bases. The exact degree of acidity or alkalinity of such “pure” water, or of neutral solutions is of course uncertain. It is of interest, however, to note that an experi- ment which we carried out with a solution of potassium chloride also gave intermediate values. * To try the influence of concentration, an experiment was carried out with N/50 ammonia which, although the value of E, was so small that little stress could be laid on it, at least supports the contention that the higher value for ¢i—qa is valid. The figures are:—A=920, B=455, C=0'060, temp. 18°; E =+0:035, E,=-+0:087, E,= +0023, E,=+0:057+15 °/o volt; 1/e=0-0218010-5; Ejooowe=5'89xX 10-5, di—da=6'24. Forces produced by Flowing Solutions. 601 | | Solution. | Concentration. A. B. C.; |) Temp: E,. Eg. << —_—-|—_—__|____| —— Se N/2000 482 238 | 0°050 | 19° | +0°001 | +0-360 | 905 Bee WR as | nee | senees 0°684 ) | Solution. | E,. | E,. Ve. ER U omes . ae +0-016 | +0°352+4 % | 03065105 | 482x10-5 | 4:738+4°, | ie she | 067642 [oe 4-93 | 48442 °/, Discussion of Results. The experiments just described lead to the conclusion that Helmholtz’s and Dorn’s value of five volts for the potential difference between glass and water is correct, and that when the liquid is made acid or alkaline the change is of the order - of half a volt to the negative side in the first and to the positive side in the second case, the sign always applying to the liquid. If this change is compared with the theory quoted in the beginning of this paper, and if the smallness of the acidity and alkalinity is borne in mind, it is found that the sign of the change is the expected one, but that the mag- nitude is three times larger than the theory predicts. The supposition is suggested that an influence comes into play which enlarges all the values three times. Such a decrease would bring the value of the glass-water potential, as well as that of the acid-alkali change at the glass, to the magnitudes to be expected. The Helmholtz theory does not allow for such a factor. We are therefore led to look for some inter- fering phenomenon. Knoblauch *, Perrin}, and Freundlich and Makelt have found facts which seem to have an important bearing on this question. Perrin especially, in an electro-osmotic investi- gation with powdered materials, as, for example, chromic chloride, and carborundum, found that the direction of the osmosis and therefore the sign of the charge at the surface of the powdered insulating material, always changed at the neutral point, the liquid becoming positive if alkali and negative if acid. From his results it must be concluded that pure water does not show any potential difference against the most different insulators. This view is in striking contrast * Zeitschr. f. phys. Chem. xxxix. p. 225 (1902). + J. de chim, phys. ii. p. 601 (1904) ; iii. p. 50 (1905). Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 28 602 Messrs. Cameron and Oettinger on Llectromotive with the results of Dorn and of ourselves; but the change produced on making the solution acid or alkaline is, in sign, the same which we have found, and which is to be expected from the theory quoted in the beginning of this paper. The theory of Perrin, also, is very different from that from which we start. It is akin to the views of Knoblauch, who found that when platinum was brought into contact with solid acids or bases, it obtained a positive or negative charge re- spectively. The fundamental point of these theoretical views is that the governing phenomenon is the diffusion of the ions. Knoblauch assumes that the platinum has an infinitely thin layer of water on it ; the solid acid or base is dissolved in this to a certain extent and diffuses onto the platinum ; the ions which diffuse faster first come in contact with the platinum, which accordingly becomes charged positively with acids, negatively with alkalies. Perrin, following some ideas of Langevin, thinks that the faster migrating ions are smaller; they are thus enabled to come nearer to the surface of a solid insulator surrounded by electrolytically dissociated liquid than can the slower moving ions. In the case of such a liquid streaming along an insulator he thinks that the faster ions come within the last layer held in a state of rest by external friction at the surface, while the slower moving and, according to his view, larger ions remain in the moving layers of the liquid. This view is applicable to acids and alkalies because the hydrogen and hydroxyl ions are espe- cially fast ; it is supported by Perrin’s experimental data for these ions. It of course would be expected that it holds also in other cases where differences of the migration velocities exist, but Perrin could not verify this for lithium bromide, although he himself emphasized the fact that the lithium ion has only half the mobility of that of bromine *. Contradictory as Perrin’s results are to those of Dorn and of ourselves, so equally contradictory is his theory to that of Lamb, who thinks that the charge is rigidly confined to the first layer of solid and last layer of liquid. Helmholtz’s theory of the phenomenon is so general that that it may be considered in agreement with either standpoint. The most important point, however, is that the diffusion theory cannot be assimilated up to the present time with the views which * The standpoint of Perrin recalls some results obtained by Rutherford with ionized gases. He was able to show that such a gas when it passed through a narrow metallic tube produces a charge at the surface of the metal the sign of which is determined by that of the ion with higher diffusion coefficient. a ee ee ee ee Forces produced by Flowing Solutions. 603 have proved most successful in the explanation of electro- motive forces, 7. e. with the osmotic views put forward by Nernst *. Perrin’s view leads him to the consequence that the electromotive force does not depend on the nature of the wall. The osmotic theory makes the potential difference always a function of the special nature of the properties of the two phases between which it takes place. Haber’s theo- retical deductions, from which we started, are grounded on the same standpoint. The diffusion theory may account for differences in the phenomena caused by the use of different solids, by help of the assumption that a specific absorbing power for ions exists at solid surfaces, but the explanation becomes in this way still more indefinite, and does not show a clearer connexion with the osmotic theory. Though the diffusion theory has up till the present time been unable to give more than qualitative results, whilst every step of the osmotic theory guides to quantitative results, certain difficulties arising especially in the electric behaviour of colloidal substances when considered from the osmotic standpoint, have led to some support being given to the former theoryf. Finally, the fact that the osmotic theory, according to our experiments, is able to explain qualitatively a result which till now seemed only explicable by the diffusion theory; and, on the other hand, the differences still remaining between the predictions of the osmotic theory and our results, suggest further experimental work in this direction; this will be carried out by one of us in this Institution. This problem was undertaken by us at the suggestion of Professor Haber; and we desire to express our sincere thanks for the interest which he has shown and for the help which he has given throughout, both with the experimental difficulties and with the theory. Phys. Chem. Institut u. Phys. Institut, Technische Hochschule, Karlsruhe. * See Wied. Ann. lviii. Beilage, Heft 8, 1896. + It may be remembered that Billiter (Zeztschr. 7. Electrochemie, xv. p- 160,1909) considers that the diffusion phenomena have only a secondary influence. r 60a 9 LXIV. On the Retardation of Alpha Rays by Metals and Gases. By T.8. Tayior*. Introduction. ‘a a preliminary paper t ‘On the Retardation of Alpha Rays by Metal Foils and its Variation with the Speed of the Alpha Particles,” the writer described some experi- ments which showed clearly that the air-equivalents of metal foils decrease with the range of the alpha-particles entering the foils{. By “air-equivalent” is meant the amount by which the range of the alpha-particles in air is cut down by their passage through the foil. It was shown that the change in the air-equivalents is small for thin foils of the lighter metals when the speed of the alpha-particles entering the sheets is high: but, when the speed of the particles is low for thin sheets or, when the sheets are thicker, the change becomes quite marked. A comparison of the change for sheets of different metals of nearly equal air-equivalents showed the rate of change to be in the order of the atomic weights of the metals. The results obtained in these experiments were not sufficient to furnish an explanation of the phenomenon ; but the continuation of the experiments during the last year under somewhat different conditions has furnished results which do lead to conclusions of some interest. Scattering of the Alpha Rays. In the determination of the variation in the air-equivalents with the speed of the alpha-particle, as described in the paper cited above, the source of rays (polonium) with the metal sheet over it was set at such a distance from the ionization-chamber that some part of the top, or nearly horizontal, portion of the Bragg ionization-curve fell within the ionization-chamber. A slight increase in the range of the particle in this portion of curve corresponds to a con- siderable increase in the ionization. With the polonium set * Communicated by Professor H. A. Bumstead. + American Journal of Science, vol. xxvi. pp. 169-179, Sept. 1908. t+ The phenomenon upon which this work was based was first observed by Mme Curie and has later been investigated by several others. Bragg & Kleeman (Phil. Mag. Sept. 1905, and April 1907) observed that the stopping power of a metal was not independent of the speed. Kucera & Masek (Phys. Zeitschrift, xix. pp. 630-40, 1906) and Meitner (Phys. Zeitschrift, viii. p. 489, 1907) ascribe the effect to a difference in the amount of scattering. McClung (Phil. Mag. Jan. 1906), Rutherford (Phil. Mag. Aug. 1906), and Levin (Phys, Zeitschrift, xv. pp. 519-521, 1906) obtained results which indicate that each successive layer of aluminium foil diminishes the range of the a-particle by the same amount, Retardation of Alpha Rays by Metals and Gases. 605 at a definite distance from the ionization-chamber, it was found that, when the metal sheet was moved away from the polonium towards the ionization-chamber, the ionization increased. This increase in the ionization was attributed to the alpha-particle having a greater velocity (or range) upon entering the chamber when the sheet was near the chamber than it had when the sheet was at a distance from the chamber. Hence the metal sheet did not cut down the range of the particle so much when the sheet was at a distance from the polonium as it did when near the polonium. As a preliminary to more extensive experiments by this method two tests were made to ascertain whether a scattering of the rays could explain the increase in the ionization observed when the metal sheets were moved away from the polonium towards the ionization-chamber. First test—Any marked scattering of the rays by the foils would change the shape of the cone of rays, and especially the form of the top portion of the cone. The slope of the top, or nearly horizontal portion, of the Bragg ionization- curve, as well as the value of the maximum ionization, depends upon the form of the cone of rays arriving at the ionization- chamber. Thus, if scattering of the rays exists to a very marked degree, it might be expected that differences between the slope and form of the two Bragg curves obtained with and without the metal foil over the polonium could be readily detected. With polonium as the source of rays, numerous determinations of the Bragg curves, both with and without the various foils over the polonium, were made. A study of these curves showed them to run parallel to each other and to give the same value of the maximum ionization. The effect of putting the foils over the polonium was merely to diminish all the ordinates of the curves by the same amount. Second test—An iris diaphragm whose circular opening could be adjusted to any desired diameter between 1 and 53 cm., was constructed of thin sheets of brass and placed directly below the ionization-chamber. The centre of the opening of the diaphragm was directly below the centre of the ionization-chamber. With the source of rays (radium C) at such a distance from the ionization-chamber that the chamber cut the top portion of the Bragg curve, the ioniza- tion was measured for various distances of the metal sheets above the source of rays ; first with the diaphragm entirely open and then with the opening in the diaphragm of such diameter as to just limit the geometrical beam of rays, or to cut off the edge of the beam. For any given position of the sheet above the source of rays, the ionization was always 606 Mr. T, 8. Taylor on the Retardation of greater when the diaphragm was completely open than it was when the diaphragm just limited the beam: However, the difference between the ionization in the two cases was a constant value for all positions of the metal sheets above the source of rays. This difference would not be a constant quantity if the scattering of the rays was the occasion of the increase in the ionization produced by moving the metal sheets away from the source of the rays. On the contrary, the difference between the ionizations with and without the diaphragm limiting the geometrical beam of rays would be greater when the sheet is far away from the source of rays than when it is near the source of rays if scattering of the rays by the foils was the cause of the increase in the ioni- zation. The fact that the ionization was greater with the diaphragm open than when it just limited the cone of rays signifies that more alpha-particles get into the. ionization- chamber in the former than in the latter case, and therefore confirms the existence of the scattering of the rays by metal foils as found by Geiger *. These two methods of investigation, although in the case of the latter showing the existence of the scattering of the rays, seem to be sufficient to preclude scattering as an explanation for the so-called decrease in the. air-equivalents of the metal sheets as they are moved away from the polonium. By measuring the ionizations with and without the diaphragms limiting the cone of rays when there was not a metal sheet over the source of rays, it was found that the ionization was greater in the latter than in the former case, which shows that the rays are scattered by air as well as by metals. These methods, however, are not particularly suitable for measuring the amount of the scattering, and hence no comparison as to how much each metal scatters the rays was attempted. The important fact is that the effect under consideration is not influenced by the scattering of the rays. Continuation of the Experiments. In the first experiments polonium had been used as the source of rays, but in order to extend the study to alpha- particles of higher range, radium C has been used in the present experiments. This made it possible to use foils of greater thickness than had been previously used. | 21 OSszZi >... | OSes | a | Li 0°853 | | | ‘ 13 | The aluminium foil over the radium to prevent the escape of the emanation cut down the range of the alpha-particles 0°46 cm. The height of the plug containing the radium was 0°9 cm. above the radium. Therefore the maximum ayail- able range of the alpha-particles entering the sheet is 5-70. The values of the air-equivalents for each of the metal sheets in Table II. represent the average results obtained from a series of from six to ten separate determinations, the details of which have been omitted for the sake of brevity. Alpha Rays by Metals and Gases. 609 Experiments were also made with sheets of paper and celloidin*. Two sheets of paper of about one and two cm. air-equivalents respectively, and three sheets of celloidin of air-equivalents of the order of 0°5, 1:0 and 2:0 cm. respec- tively were used. For these sheets of paper and celloidin, the ionization did not increase as the sheets were moved away from the radium but had the same value for all posi- tions of the sheets and hence their air-equivalents remained constant. The behaviour of the sheets of paper and celloidin, the atomic weights ¢ of which are about the same as that of air, suggested the idea of undertaking to obtain sheets of some substance such as hydrogen, whose atomic weight is less than that of air. For this purpose a ring about one centimetre wide was cut from a brass tube six centimetres in diameter and two small brass tubes were put in the ring diametrically opposite each other. Thin films of celloidin were stretched _ across each side of the ring and held in place by universal wax. This formed a cell which could be filled with hydrogen and then used in the same manner as the metal foils. To be certain that the cell was always full of hydrogen a slight current of the gas was kept flowing through it all the time during an experiment. A current of air was kept circulating through the case surrounding the apparatus in order to prevent the hydrogen that might possibly leak from the cell from entering the ionization-chamber. The air-equivalent of the hydrogen cell, or sheet, when 0°9 cm. from the radium was determined by plotting the ionization-curve first with hydrogen and then with air in the cell. The ordinates of the latter curve were all increased by the thickness of the cell of hydrogen which gave the position of the curve if the cell had been evacuated. The difference between the ordinates of the two curves corresponding to a given abscissa was the air- equivalent of the hydrogen sheet. When the cell containing the hydrogen was moved away from the radium, which was kept at a given position as in the previous cases, it was found that the ionization decreased, which signified that the total range in air of the alpha-particle was less when the hydrogen sheet was far away from the radium than when it was near the radium. Thus the amount by which the range of the alpha-particle was cut down by its passage through the cell was greater when the cell was at a distance from the radium than it was when it was near the radium. Consequently the air-equivalent of the * Celloidin is a specially pure preparation of collodion. T By atomic weight of air, paper, and celloidin is meant the average weight of the constituent atoms. 610 Mr. T. 8. Taylor on the Retardation of hydrogen cell increased as the range of the entering alpha- particle decreased. The particles had to pass through the celloidin sheets but this did not influence the effect because, as we have seen, the amount by which the range was cut down by the celloidin sheets was constant for all positions of the cell. Determinations of the air-equivalents in centi- metres of three hydrogen cells given in ‘lable I. were made for various distances of the cell from the radium and the results obtained are recorded in Table III. TABLE: Lik Range ofthe | | -par ee ie ae A Hydrogen. | B Hydrogen. C Hydrogen. | hydrogen. 5:2 0231 0°428 0°762 ) 4°8 0-235 0434 0-776 | 4°4 0-241 0-442 0-791 4:0 | 0:247 0°451 0807 3°6 0°254 | 0-460 0-831 oi | 0-262 0-470 0-861 2°8 0:271 | 0°483 0-896 2-4 0-283 0-499 0-938 | The reason the maximum range here is 5:2 cm. instead of 5°7 cm. as it was in Table II. is because the air-equivalent of the lower film of celloidin must be subtracted since the alpha-particles must pass through it before entering the hydrogen. The air-equivalent of the lower film was 0°5 cm. Although the air-equivalents of the celloidin sheets remained constant, it seemed probable, from the behaviour of the hydrogen sheets, that if the same experiments were performed in an atmosphere of hydrogen, the hydrogen- equivalent * of the celloidin sheet would not remain constant, but would decrease as the range of the alpha-particles decreased. To investigate this point the apparatus was enclosed in an air-tight sheet-iron case, which by several partial evacuations and refillings could be filled with practi- cally pure hydrogen. With polonium as the source of rays the hydrogen equivalents in cms. of sheets of celloidin, aluminium, tin, and gold were determined for various distances of the sheets from the polonium. Only the results for the celloidin and A gold are given in Table [V. as they are sufficient to illustrate the point in question. * The hydrogen-equivalent is the amount by which the range of the a-particles in hydrogen is cut down by their passage through the sheet. Alpha Rays by Metals and Gases. 611 TasLe LV. Range in H \ | | | + : particle .. a4 / | of entering 13°0 | 16 (iS Ale Ls | 11-0 | 10-6 | 10-2 9°8 9-4 | | 23°08 | 22°96 | 22°80 | 22°64 | 22-48 2232 22°16 | 21°88] 21-60 Celloidir ...... 23°20 — 23°91 | 23°01 97°55| 27-11| 26°67 | 26-23 25°75 | 25:17) 24-49 \ a > s5Q eS [SOP SOAINO OY} SUTUTBIUOD OILS [BAtnbo-a1v oy} erv sozVUIpsO ety Q O UVI OY} OLIV SUSBLIOBCV Ol} O bo-uesoapAy oY} Ol8 SOPLUIPLO OY] PUB sJ00qs -vydje oyy jo uabouphy ut se ul "10 Aoy) uoya sopouand-vydye oyg Jo «vy ur sos *SqQ90YS ol[} JO SPUOTBAIN SuBL OYF GAV sUsBIOSqY oy} {IY UL PlOH y,, pur ,, uecoaps PLOTLD », , WOSoarpATT UE P[OF Vj,— 8B pozwu 612 Mr. T. 8. Taylor on the Retardation of The curves in figure 1 (p. 611) represent the results recorded in Tables II., III., and IV. By noting the slopes of the curves some comparison of the rates at which the air- equivalents of the various sheets change can be obtained. Taking the general slope of each curve and dividing it into the air-equivalent of the corresponding sheet when 0°9 cm. from the radium, it is found that for a given metal the quotient thus obtained is nearly constant for all the sheets of the metal. This is shown in column 4, Table V. Thus for TABLE V, ir- | Mean See Sheets. ag é aes Ratio. VW atomic weight. | patio MV atomic wt. —, ——————— — - — | A+ Aw <2) -0'082 0-719 OE SOE B Au...| 0-051 0-980 1°92 x 10! | C Au ...| 0°064 avo 215 x10" 7 : D Au, 2s (C100 1:900 1:90 x 10! | 14'05 28°80 A Sn ¥..|, (0:032 1011 3:16 x 10! | BSn ...| 0:063 1:995 317 x 10! | 10:91 34°34 A Pb ¢.6 900538 1:104 2:08 x 10! | BED eer 1°396 1:96 x 10! CoP b: 24 70210 2°325 AL SOON SF 14°38 29°38 PAA. Le 0:010 0°597 O07 <0 B Al | 0020 1209 6:04 x 10! | Orth. 0:033 1°8038 B46 SCO es 519 30°41 D Al...) 0-045 2672 593 X10! | AH ~...\—0020 0:231 1:16 x 10! | BH. ..)) 0034 0-428 1:17 S< 10! 4 | CH ... —0-064 0-762 1:19 x 10! J l sheets of the same metal the rate at which the air-equivalent of each sheet changes with a change in the range of the entering alpha-particles, is proportional to its air-equivalent when nearest the radium. The approximately constant numbers in column 6, Table V., show that the percentage rate of change in the air-equivalent for any metal is nearly propor- tional to the square root of the atomic weight. The agreement of the values in columns 4 and 6, Table V., is as good as could be expected since the slopes of the curves in figure 1 could only be determined roughly. The proportionality is indeed only approximate, since the curve for any one sheet does not have a constant slope. For the thin sheet of aluminium the air-equivalent is almost constant for the higher ranges or speeds, but as the speed of the entering alpha-particle decreases the air-equivalent de- creases slowly, and in the lower ranges the decrease becomes quite apparent. For the thicker sheets of aluminium the change is more marked even for the higher ranges. The statements of McClung, Levin, and Rutherford that equal Alpha Rays by Metals and Gases. 613 successive layers of aluminium foil diminish the range of the alpha-particles by equal amounts seem to hold true for thin sheets of foil when the range is high; but when the metal sheet is thicker, or for thin sheets when the range is low, it does not hold. The slight difference, however, in the air- equivalent of the thin foil, when near and far away from the polonium, would scarcely be detected by measuring directly the air-equivalent in the two positions. This is probably the explanation of the above statements by McClung, Levin, and Rutherford. Since the air-equivalent of a metal sheet decreases with the speed of the alpha-particle entering it, the ratio of the air-equivalent to the thickness of a given sheet of metal should be less than the same ratio for a thinner sheet of the same metal. This is shown to be true by the last column of Table I. For the hydrogen sheets on the contrary the same ratio should increase as the thickness of the cell or sheet of hydrogen increases. This is also confirmed by the last column of Table I. While the air-equivalent of the sheet of celloidin remains constant the hydrogen-equivalent of the same does not remain constant but decreases as the range of the alpha-particle in hydrogen decreases. The curve “ Celloidin in Hydrogen,” fig. 1, which was plotted from the results recorded in Table IV., illustrates this point. It is to be noted also from the curve ‘“‘ A Gold in Hydrogen ” (fig. 1) that the rate at which the hydrogen-eguivalent of the A gold decreases is much greater than the rate at which its azr-equivalent decreases. The curve designated “A Goldin Air” (fig. 1) is the portion of the ‘* A Gold” curve in the same figure that lies to the left of the abscissa 3°0. The co-ordinates of that portion of the curve are magnified about 43 times so as to be plotted on the same scale as the curves obtained in the hydrogen atmosphere. 42 is the ratio of the thickness of a hydrogen sheet to its air-equivalent when near the radium. ‘The slope of the curve “ A Gold in Air” is practically the same-as that of “ Celloidin in Hydrogen” as can be seen from the figure. The angle which the curve “A Gold in Hydrogen” makes with the curve * A Gold in Air” is about the same as the angle which the curve “ Celloidin in Hydrogen” makes with the axis of abscissas. The slope of the curve “A Gold in Hydrogen” is nearly 32 times the slope of the curve “Celloidin in Hydrogen.” But 33 is the ratio of the square root of the atomic weight of gold to that of air | 197 7 maa i. 614 Mr. T. 8. Taylor on the Retardution of Hence the rates, at which the hydrogen-equivalents of the Gold and Celloidin sheets decrease with the speed of the alpha-particle entering the sheets, are proportional to the square roots of their respective atomic weights. Moreover the slope of the curve “ Celloidin in Hydrogen” is numeri- cally equal (but of opposite sign) to the slope of the curve “B Hydrogen” in air. The hydrogen-equivalent of the celloidin sheet was somewhat larger than the thickness of the ‘“B Hydrogen ”’ cell, but it seems entirely proper to conclude that the rate, at which the hydrogen-equivalent of the celloidin sheet decreases with the speed of the alpha-particle, is the same as the rate at which the air-equivalent of the “B Hydrogen” increases as the speed of the entering alpha- particle decreases. The possibility that the observed variations in the ioniza- tion, which have been taken to be the measures of the changes in the air-equivalents, may be due to secondary rays is precluded by the fact that numerous direct determinations of the Bragg ionization-curves, with and without the metal sheets near the polonium, and again near the ionization-chamber, showed no irregularities in the curves as would be expected were secondary rays present in any appreciableamount. The behaviour of the air-equivalents of the hydrogen sheets in no way conforms to what might be expected to be produced by secondary rays. The increasing of the air-equivalents of the hydrogen sheets and the decreasing of the hydrogen-equivalents of the celloidin sheets when moved away from the source of rays gave occasion for suspecting that some differences might be found to exist between the Bragg ionization-curves obtained in atmospheres of air and hydrogen respectively. To determine these curves, use was made of an apparatus constructed for Mr. F. E. Wheelock, of this Laboratory, which was similar to the one used thus far in the work, except that the vessel enclosing the main part of the apparatus could be completely exhausted. To make any comparison of the two ionization curves, it was necessary to determine them under similar conditions—1. e., the same source of rays was used in the two cases, and the pressure of the air was so reduced as to make the range of the alpha-particles in air equal to their range in hydrogen at normal pressure. Polonium was used ag the source of rays, and several Bragg curves were obtained in hydrogen at normal pressure and in air at a reduced pressure of about 17 cm. of mercury. Two of the curves are shown in fig. 2. The dotted portion of each curve is assumed to be of Alpha Rays by Metals and Gases. 615 the form it would take were it possible to move the polonium entirely up to the ionization-chamber. At all events these assumed portions of the curves can differ but little from what the actual curves would be. io, 2 Fie, 2. | Be ileonle ne fponfio OT ey eee Oo TO eS NON Tl .o) The ordinates of the curves are the distances in centimetres of the polonium from the ionization-chamber. The abscissas are the deflexions in centimetres of the electrometer-needle per second. Curve I. was obtained in air at a reduced pressure of about 17 centimetres of mercury. Curve II. was obtained in hydrogen at normal pressure. It is to be observed that the two curves in fig. 2 present slight differences in form. ‘The probable interpretation of these differences will now be considered. Any given abscissa 616 Mr. T.S. Taylor on the Retardation of of either curve is a measure of the ionization produced by the particles in the gas in the chamber when the polonium was at a distance from the chamber represented by the ordinate corresponding to the given abscissa. Consequently, the total area enclosed by the two axes of reference and either curve is proportional to the total ionization produced in the gas in which the curve was determined. By mea- suring these areas with a planimeter, it was found they were equal. This confirms the observations by Bragg ™* that the total ionization produced by the alpha-particle in air is the same as that in hydrogen. From the curves of fig. 2 it is seen that when the speed of the alpha-particle is high more ions are produced per centimetre of path in air than in hydrogen, but when the speed is low more ions are produced per centimetre in hydrogen than in air. Let us suppose that for a given speed of the alpha-particle the amount of energy required to produce an ion is the same in all substances. Then for air we would have the relation dla = —f(V) dEu. The corresponding relation in hydrogen is dl, = —/(V) dn. Dividing the former by the latter, we have dU, _ f(V) dB dl, CV) dE’ which for a given speed V in each gas reduces to dla ey da dl,” dE, From this it is seen that for a given speed of the alpha- particle the ratio of the rates of the consumption of the energy in producing ions in air and hydrogen, is equal to the ratio of the rates at which the ionization is produced in the respective gases. On the basis of our hypothesis, let us consider the ratios of the energies consumed in the 4th and 13th centi- metres (fig. 2) of the path of the particle in air and hydrogen. This ratio for the 4th centimetre of the path is proportional. area cd 43 ¢ area ab 43 a’ ionizations produced in the gases. The corresponding ratio area é, f, 13, 12, e Th area g, h, 13, 12, 9 ° former ratio is seen from the figure to be greater than the * Phil, Mag. March 1907, p. 333. since the areas are proportional to the for the 18th centimetre is equal to Alpha Rays by Metals and Gases. 617 latter. Moreover it is also seen that the ratio of the energy of the alpha-particle absorbed by any given centimetre of air to the energy absorbed by the corresponding centimetre of hydrogen, is always greater than the corresponding ratio for the centimetre just beyond the given one, This is in agreement with the results obtained for the air-equivalents of the hydrogen cells ; because the increase in their air-equi- valents as the range decreases is due to the fact that the ratio of the energy absorbed by the hydrogen cell to the energy that would be consumed by the air which it displaces, continually increases as the cell is moved away from the source of rays. The thicker the cell the more rapid would be the rate of increase, as could be seen by comparing the areas which represent the ionizations in, say, 2 centimetres of air and hydrogen respectively in fig. 2 in two different positions. The increase in the ratio of the energies consumed in air and hydrogen respectively is in agreement also with the decrease _in the hydrogen equivalent of the celloidin film. Still making use of our hypothesis, the ratio of the energy consumed in the 9th and 10th centimetres of air at reduced pressure, to that consumed in the same centimetres of hydrogen at normal pressure, is expressed by the fraction oe The same ratio for the 13th and 14th centimetres is at These ratios were obtained by measuring with a planimeter the areas in fig. 2. The former ratio divided by the latter gives 1:10. Since the hydrogen equivalent of the colloidin film is but slightly more than 2 centimetres, the ratio of its values at 9 and 13 cm. respectively from the polonium should be the same as the above ratio. The hydrogen equivalents of the film in the two positions (see fig. 1) are 2°320 and 2°120 cm. respectively ; and the ratio ot the former to the latter is 1:09, which differs little from the calculated ratio, 1:10, given above. Hence it is seen that the differences between the curves of fig. 2 are sufficient to account for the change in the hydrogen equivalent of the celloidin film, and consequently for the increase in the air equivalents of the hydrogen sheets when moved away from the source of rays. This agreement between the relative ionizations and the relative losses of energy of the particle in the two gases gives a considerable degree of probability to our hypothesis connecting the relation of the ionization produced to the energy consumed. The experimental results show that the air-equivalents of the metal sheets decrease with the speed of the alpha-particle ; Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 2T 618 Mr. T. 8. Taylor on the Ietardation of and hence the ratio of the energy of the alpha-particle con- sumed by its passage through a sheet of metal, to the energy that would be consumed by, say, 1 centimetre of air at the same point in the path of the particle, decreases as the range of the alpha-particle decreases. The behaviour of the metal sheets relative to the air is entirely analogous to the behaviour of the air, or celloidin relative to hydrogen. Consequently, if it were possible to measure the ionization produced by the alpha-particle at different points in the path of the rays in the metals, and if the ionization-curves were plotted on the same scale as those shown for air and hydrogen (fig. 2), it is probable that the curves for the metals would all present some such differences from the air curve as those existing between the air and hydrogen curves. Moreover, these differences might be expected to be such as to agree with the different rates at which the air-equivalents of the different metal sheets change. In the upper portion the curve for gold would probably le within the air curve about the same amount as the air curve does within the hydrogen curve (fig. 2) ; and in the lower portion the curve for gold would probably lie without the air curve by the same amount as the air curve does without the hydrogen curve. At least some such differences would be in accordance with the square root law, since the square root of the atomic weight of air is a mean proportional between the square roots of the atomic weights of gold and hydrogen. The curves for the other metals would occupy intermediate positions hetween the curves for gold and air. We have seen that for different metal sheets of about the same air-equivalents, the rates at which the air-equivalents decrease with the speed of the alpha-particle are proportional to the square roots of the atomic weights of the respective metals. Consequently, the rates of decrease of the ratios of the quantities of energy used up in the sheets to the energy that would be consumed by a centimetre of air at the same positions in the path of the particle decreases also as the square roots of the atomic weights of the respective metals. On the basis of our hypothesis that for a given speed of the alpha-particle the same amount of energy is required to produce an ion in all substances, and from the results in our experiments, it appears very probable that for the high velocities the alpha-particle loses its energy, in going through a substance, more rapidly the higher the atomic weight of the substance ; but as the speed of the alpha-particle becomes less, this changes until for the low velocities the loss of the energy of the particle is more rapid the lower the atomic weight of the substance. " oo Alpha Rays by Metals and Gases. 619 In conclusion, I wish to express my gratitude to Professor Bumstead, at whose suggestion these experiments were under- taken, for his valuable suggestions and interest in the work ; also to Professor Boltwood, who kindly prepared the polonium and secured the radium bromide for me, and gave me many valuable suggestions. Summary of Results. 1. The air-equivalents of metal foils decrease with the speed of the alpha-particles entering them. The decrease is very small for thin foils of the lighter metals when the speed of the alpha-particle is high ; but when the speed is low for thin sheets, or when the sheets are thicker, the change becomes more marked. For different sheets of the same metal the rates of change are proportional to the air- equivalents of the sheets. For sheets of different metals of equal air-equivalents the rates of change are approximately proportional to the square roots of the respective atomic _ weights. 2. The air-equivalents of hydrogen cells or sheets increase as the speed of the entering particle decreases, while the air- equivalents of sheets of paper and celloidin remain constant. 3. The hydrogen-equivalents of sheets of paper, films of celloidin, and air do not remain constant, but decrease as the speed of the alpha-particle decreases. The rate at which the hydrogen-equivalent of a celloidin film decreases with the speed of the entering alpha-particle is numerically equal to the rate at which the air-equivalent of a hydrogen sheet of corresponding thickness increases. 4, The result obtained by Bragg, that the total ionization produced by the alpha-particle in air is the same as that in hydrogen, is confirmed by a more direct method. 5. It is very probable that for the high ranges the alpha- particle loses its energy, in passing through substances, more rapidly the higher the atomic weight of the substance ; but that this difference decreases slowly, until in the low ranges the loss of energy is the more rapid the lower the atomic weight of the substance. 6. A comparison of the Bragg curves for air and hydrogen indicates that the large ionization at low ranges (knee of the curve) is due at least in part to the fact that the particle loses its energy more rapidly in this part of the range, and not wholly to the higher ionizing efficiency of particles of low speed. Sloane Laboratory, Yale University, New Haven, Conn., U.S.A. re _ _ ae [ 620 ] LXV. The y-Rays of Uranium and Radium*. By FREDERICK Soppy, JZA., and ALEXANDER 8. RussELi, M.A., B.Se.T 1. Introduction. Hees at our disposal 50 kilograms of the purest commercial uranyl nitrate, provided by the generosity of a friend, we have been enabled to study the radioactivity of uranium X on a considerably larger scale than previously attempted. This body, which was discovered by Sir William Crookes (Proc. Roy. Soc. 1900, Ixvi. p. 409), was early re- cognized (Rutherford and Soddy, Phil. Mag. 1903, v. p. 441) as a disintegration product of uranium producing the whole of the B-rays but none of the «-rays of that element. It has a period of average life of about 31 days. The period is long enough to allow of the separation of the greater part of the substance, even from a large quantity of uranium. When the activity of one product has decayed too far to work with, a fresh crop can be obtained by repeating the process. At each separation the uranyl nitrate is rendered purer, any fortuitous impurities present being eliminated, and as it is necessary in certain problems to be sure that no radioactive impurities are present initially, it is intended to carry out periodically a long series of such separations. The present work is concerned with the first three separations, carried out at intervals of about three months, and is devoted to a comparison of the y-radiation of the active preparations separated, with the y-rays of radium. We have found that, as in all other known cases, the y-rays of uranium accompany the 6-rays, both resulting entirely in the disintegration of uranium X. ‘The results here recorded do not, however, bear out either of the rival views of the origin of the y-rays, but rather indicate that the @-rays and y-rays may be entirely distinct in origin. Our knowledge of the y-rays of uranium has previously been practically confined to the work of Eve, who examined the y-rays of uranyl nitrate. LHve found in the first place that uranium only gave out about 7, as much y-radiation as thorium, though its @-radiation is, as is well known, very much more intense. Eve states that while the y-rays of radium and thorium are of similar penetrating power, the y-rays of uranium are much less penetrating, and are prac- tically completely absorbed by 1 cm. of lead. Over a range * A preliminary account of part of this work was published in ‘Nature,’ March 4th, 1909, p. 7, and Phys. Zeit. 1909, x. p. 249. + Communicated by the Authors. The y-Rays of Uranium and Radium. 621 of from 0°26 to 0°94 cm. of lead he found that the absorption proceeded according to an exponential law, the value of the absorption coefficient, \(ecm.)~1, being 1°4. For radium he gives the values from 0°57 to 0°46 over a range of from 0°64cm. to 3:0 cm. of lead. With our intensely active preparations of uranium X we have fully confirmed and extended Eve’s statement with regard to the relative poverty of uranium in y-rays as com- pared with the @-rays, and an accurate comparison of the ratio of the @- to y-rays for uranium X and for radium C is detailed in this paper. We may state the result here that radium gives 50 times more y-rays in proportion to #-rays than is the case with uranium. We have found, however, that the y-rays of uranium are not absorbed exponentially until after about 1 cm. of lead, or an equivalent thickness of other substances, has been penetrated, and then they are similar in character, and only slightly inferior in penetrating power to the y-rays of radium, the absorption coefficient being for most substances about 1:2 times greater over a range equivalent to from 1 to 5 cm. of lead. For thick- nesses less than 1 cm. of lead the absorption curve is not exponential. The average slope of the curve, however, in a set of measurements with lead agreed approximately with Eve’s value over a large part of the range he worked over. It is possible that a soft type of primary y-rays is also present. but so far we have not been able to be sure of this, and this part of the subject is reserved for a future communication. In any case the y-rays of uranium and radium examined over the same range are extremely similar in penetrating power and general character, and if a soft type of y-rays from uranium exists, not represented in the y-rays from radium, it is relatively feeble in character, and its existence is difficult to establish. [The statement we made in preliminary communications that the absorption coefficient of the y-rays of uranium was two and a half times greater than that of radium, which has unfortunately been quoted in abstracts, was based upon a published value for the radium rays which we have since found is altogether in error (Section 8). The ratios we ourselves have found for 13 substances are given in the last column of Table III. (p. 646).] This being the case the great relative poverty in y-rays of uranium compared to radium is a very remarkable fact. The #-rays of uranium are, like the uranium y-rays, only slightly less penetrating than the corresponding radium rays. It is hardly possible to continue to regard the y-ray as an 622 Messrs. F'. Soddy and A. 8. Russell on the X-ray pulse generated by the expulsion of a §-ray electron from the disintegrating atom, a point of view which has been already seriously challenged by the alternative theory advo- cated by Bragg. But it is also difficult to accept the ready mutual convertibility of @- into y-rays, and vice versa, which Bragg’s theory requires, in face of the great similarity in nature and great difference in relative intensity which are shown by the 8- and y-rays of radium and uranium. The most natural conclusion is that the two types are not inter- dependent. The work here described falls under two heads. First, the preparation of the uranium X and the comparison of its 8- and y-activity with that of radium under defined con- ditions will be described. Secondly, an account will be given of the absorption of the y-rays of uranium and radium under comparable conditions, which has been studied in considerable detail. The y-rays are much more difficult to measure ac- curately than the less penetrating types, and there is much that is mysterious and unexplained in the actions they pro- duce. In particular we may mention that the y-ray ioniza- tion itself is not in all cases a constant quantity, but may suffer a regular progressive increase in amount from a minimum to a maximum when consecutive observations with the same disposition are made. This variation, which may give rise to errors as great as ten per cent. in an observation, must be guarded against in all measurements in which the y-rays are concerned. So far we have been concerned mainly to find a method of working which will eliminate these fluctuations, and which will give consistent results. In this we have been successful, but the cause of the variation is still to be worked out. So far as the determinations of the absorp- tion coefficients are concerned they have been done under conditions as nearly alike as possible for uranium.and radium. Not much weight is to be attached to the absolute values of the coefficients, for there is necessarily a certain amount of arbitrariness in the choice of the experimental disposition. We have tried a great variety, and our conclusion is that though many give curves which are practically exponential within the limits of error, it is difficult to repeat ab initio measurements of the absorption coefficient even under any one disposition with a variation of less than 5 per cent., while the actual value of the coefficient may depend considerably on the experimental disposition. y-Rays of Uranium and Radium. 623 2. The Separation of Uranium X. We have found the original methods of Sir William Crookes (Proc. Roy. Soc. 1900, Ixvi. p. 409) the most useful in the separation of uranium X. Without entering in the present paper into any detailed description of the methods employed and of the numerous trials which have led to their selection, it is necessary to give in outline some description of the process of separation which has been found most suitable in dealing with these large quantities of material. Crookes found that when uranyl nitrate was crystallized from water the photographic activity, which is due solely to the uranium X (Soddy, Trans. Chem. Soe. 1902, Ixxxi. p. 860), of the crystals was enfeebled, while that of the mother-liquor was correspondingly enriched. The same observation was made by Godlewski five years Jater (Phil. Mag. 1905, x. p- 91), who stated, without giving any details, that it was possible in one crystallization to obtain $ of the total quantity of uranium X in the mother-liquor. We found that the maximum separation of uranium X was effected when about two-thirds of the total quantity of uranyl nitrate erystallized out from the solution on cooling. The mother- liquor is then concentrated and the operation repeated several times until the amount of uranyl nitrate in the mother-liquor is reduced to about 100 grams. The uranium is then re- moved from this concentrate by adding excess of ammonium carbonate, in which uranium is soluble, leaving behind the uranium X and the impurities as a precipitate. An attempt to use the acetone method of Moore and Schlundt to separate the uranium X from a concentrate in the first series of separations failed owing to the considerable quantities of impurities present, and led to much difficulty and loss of time. Dealing with quantities of material such that j, per cent. of impurity represents an actual weight of 50 grams, Crookes’ erystallization and ammonium carbonate methods are still very effective, but indeed it is doubtful if any of the methods subsequently proposed are any better than these original ones in ordinary circumstances. It may be stated that the known methods of separation take advantages of peculiarities in the properties of uranium rather than of uranium X. The latter does not appear to resemble any element very closely, and it is more difficult to separate it from admixture with other elements than from uranium. The crystallization process employed may be illustrated from the case of the third separation after considerable ex- perience had been acquired. Forty-seven kilograms of uranyl nitrate in four lots were dissolved in one-sixth of their weight 624 Messrs. F’. Soddy and A. 8. Russell on the of water, and the solutions heated over water-baths till a density of 2°02 wasattained. The solutions were then poured into large evaporating basins and allowed to cool over night. When crystallization had set in completely the mother-liquor contained about one-third of the total weight of salt. The mother-liquors from each set of crystals were drained off, concentrated over the water-bath to the same density as before, poured out and allowed to crystallize slowly. The resulting mother-liquor is similarly treated, and so on until the amount of uranyl nitrate in the mother-liquor did not much exceed 100 grams. Usually the whole of the crystals so obtained would again be recrystallized, the mother-liquor from the first batch of crystals being added to the next and so on, while the end fractions from this second recrystalli- zation usually were still sufficiently rich in uranium X to be worth subjecting to a third recrystallization. To test the amount of uranium X remaining in each batch of crystals a sample of about 40 grams is taken after thorough mixing. This is placed at a fixed distance below an electro- scope provided with a base of aluminium foil 0°3 mm. thick, and the leak it produces is compared with that produced by a similar sample of standard urany] nitrate. In a single operation arranged so that about two-thirds of the salt crystallizes it was found that the crystals retained from 15 to 30 per cent. of their initial quantity of uranium X, so that of the total quantity of the latter all but from one- sixth to one-ninth is concentrated in the mother-liquor. One- seventh may be taken as an average fraction. In 7 similar successive crystallizations the quantity of salt in the last mother-liquor is (4)” of the initial quantity, while the uranium X contained therein corresponds to ($)” of the initial quantity. Thus after six successive crystallizations 50 kilograms would yield a final mother-liquor containing about 70 grams of uranyl nitrate together with the uranium X from 20 kilograms of uranyl nitrate. In the second and third series of recrystallizations two further similar fractions would result with the uranium X respectively of perhaps 10 kilograms and 5 kilograms. From the weights and activities of the various quantities of crystals obtained as the result of the process the fraction of the total uranium X separated could be deduced. In the second separation about 80 per cent. and in the third about 72 per cent. of the uranium X was removed by crystallization. The next step in the operation consisted in the removal of uranium from the concentrates by means of ammonium car- bonate. Each concentrate as it was obtained was added to y-Rays of Uranium and Radium. 625 several litres of hot water, and treated with excess of a strong solution of ammonium carbonate containing ammonia. Too great excess is harmful, as uranyl ammonium carbonate is less soluble in ammonium carbonate than in water. Should all the uranium carbonate not redissolve the bulk of the supernatant liquor is drawn off and a further large quantity of hot water added. The liquor is then carefully filtered through an extracted filter on the pump and the precipitate washed with hot water, redissolved in dilute nitric acid and reprecipitated with excess of ammonium carbonate once or twice to ensure complete removal of the uranium. This process of separating uranium X is a very efficient one, and in some cases the separation was extraordinarily perfect. ‘Thus on one occasion to the uranium filtrate from a precipi- tate containing the combined quantities of uranium X from - about 40 kilograms of uranyl nitrate a little iron chloride was added and the original process repeated. The @-activity of this iron precipitate was practically inappreciable. When it is considered that the actual weight of uranium X in equilibrium with 50 kilograms of uranyl nitrate is below ‘0005 mg., the removal from the uranium solution of the whole of this, all except perhaps so} 5) part at most, in a single precipitation is a very remarkable operation. This is an exceptional case, but usually the amount of uranium X in the filtrate was relatively small. In the first separation the combined uranium-X-containing precipitates weighed about 4:8 grams, in the second it was much less, and in the third it was only 0°65 gram. These precipitates, which naturally have considerable chemical interest, have not yet been ex- haustively examined. It was not difficult to recognize two groups of substances (in about equal quantity in the first batch), the one consisting of common earths, largely alumina, and the other consisting of a pale yellow body more closely allied to uranium, and possibly a member of the tungsten family. In the last separation the precipitate consisted mainly of the latter substance. The separation of the two groups was simply effected by solution of the precipitate in nitric acid, and by the cautious addition of ammonia, below the quantity required for neutralization, until a yellow colour made its appearance. On setting aside for a few hours, the yellow body precipitated out, containing nearly all the uranium X, leaving the alumina &c. in the still acid solution. In this way further concentration of the uranium X could be effected, but not much was gained by it. It has recently been noticed that this yellow compound is, like uranium carbonate, soluble in an excess of ammonium carbonate, but to a much 626 Messrs. F. Soddy and A. 8. Russell on the less extent, and this observation suggests a simpler method of Malia it from uranium X than has yet been tried. For other experiments it was necessary to obtain the uranium X as the least possible quantity of material in the form of thin films which could be examined in an intense magnetic field. In the first and second separations this was effected by a long series of chemical operations, in which the uranium X was removed from the solution of the precipitates in acid by successive additions of barium nitrate and sul- phuric acid according to the method employed by Becquerel. The barium sulphate was then fused with alkali carbonates, and the well-washed barium carbonate, which contained the whole of the uranium X, was dissolved in acid. A little iron chloride was added and precipitated with ammonium carbo- nate, the precipitate containing the uranium X. In the second separation the filter-papers and precipitates were ignited, brought on to three strips of micro-cover-glass each 75 mm. long, 13 mm. wide, and 0°12 mm. thick. These were placed on a hot plate, a drop of hydrochloric acid added, and the solution made to cover the whole surface. The films were dried and heated till chlorine was given off, and were so obtained in a stable and tolerably coherent form. The weights of the films were 57, 211, and 11 mg. respectively, and their relative activity as 2:1:0°12. In this work they were kept in platinum trays placed side by side on a wood block. In the third separation the concentration was not pushed further after removing the uranium by ammonium carbonate. The burnt filter-papers were placed directly in the three platinum trays and treated with nitric acid (in one ease hydrofluoric acid also to remove silica), the films formed being finally ignited at a red heat. They weighed 285, 200, and 152 milligrams respectively, with relative activities as 1:1: 0:4. The time absorbed in the second separation from the start to the preparation of the products in the final form was twelve days. In the third separation the first film was produced in 3°3 days, the second in 7 days, and the last in 9 days fromthe start. To settle certain points it was desirable to reduce the loss of material and time of preparation, rather than the weight of the product, to a minimum, and this was done by omitting the long process of further concentration adopted in the first and second separations. The increasing purity of the uranium made this possible. An indefinite loss of active material occurs in the numerous operations required to remove the unidentified yellow body, whereas it was re- quired to deduce for one series the exact percentage of the y-Rays of Uranium and Radium. 627 equilibrium amount of uranium X contained in the prepara- tions on the date of their comparison with radium. | Between the secondand the third separations just described appeared the interesting paper by J. Danne, in Le Radium, 1909, vi. p. 42, on a new product in the uranium series, which he calls radio-uranium, intermediate between uranium and uranium X, and acting as the direct parent of the latter. Mr. J. T. Smith kindly undertook for us at this stage a careful series of measurements over a considerable period of the §8-activities of various products separated in the course of this work, and of the whole of the fractions of uranyl nitrate resulting from the second separation, with the object of ascertaining whether in any of them any concentration or impoverishment of the parent of uranium X had occurred. The results show, up to the present time, that the whole of - the preparations lost or regained their 8-activity perfectly normally, and no alteration in the normal amount of the parent of uranium X had been effected. We may thus con- clude that none of the varied chemical operations used in the work have affected the power of uranium to produce uranium X. 3. Relative Intensity of the y-Rays of Uranium and Radium. The bare uranium X films, the preparation of which has just been described, lit up an X-ray screen brightly in the dark-room, and indeed the glow could still be seen in a fully lighted room when the screen was held in the shadow of the observer. ‘The three bare films from the second separation together produced about the same effect when held under the screen as 6°7 mg. of radium bromide in a sealed thin glass tube, though on account of the difference in the area of the glow, and the absorption that occurred in the glass of the tube in the case of radium, this is merely a very rough comparison. But the y-rays from these films were accurately compared with the y-rays trom 0°47 mg. of radium bromide, eight days after the last crystallization of the uranyl nitrate was started. The substances were placed 7°5 cm. beneath the base of a brass electroscope, to which a thickness of 2°5 cms. of lead was clamped up to form a base. The y- activity of the uranium X was only equal to that of 0°056 mg. of radium bromide. Owing to the loss of active material during the numerous processes of concentration it was not possible to deduce accurately the amount of uranium X in the preparations at the time of experiment, but the experi- ment clearly showed the great relative poverty of uranium in y-rays as compared with @-rays. 628 Messrs. F. Soddy and A. 8. Russell on the In the third separation careful check was kept of the weight and initial activity of each batch of crystals after the operation. From the time of accumulation of uranium X in the crystals between the second and third separations it was deduced that the initial content of uranium X before separa- tion was 98°5 per cent. of the equilibrium quantity. All bnt 28 per cent. of the equilibrium quantity of uranium X was separated initially, but at the date of the comparison of the uranium X with radium this had increased. From a curve of the regeneration of uranium X with time, the initial B-activity of the crystals and their weight, it was deduced that on that date 44°35 per cent. of the equilibrium quantity of uranium X was present in the crystals, The amount in the preparations was therefore 98°5 per cent. —-44°35 per cent., or 54°15 per cent. of the equilibrium quantity of 47 kilograms of uranyl nitrate. This is equal to the uranium X in 12°13 kilograms of metallic uranium in equilibrium. Ona particular day, 8 days after the commencement of the last recrystallization, and 2 days after the finish of the separation, the y-activity of the preparations was equivalent to the y-activity of 0°094 mg. of radium bromide, measured through a thickness of 2°52 cm. of lead. Now it will be shown later that the absorption coefficient for lead, for a range of from 1 to 5 cm. of lead, for the radium y-rays is 0°495, and for the uranium y-rays is 0°725 (cm.)—1. It is true that for thicknesses below 1 cm. of lead the absorption coefficients of the y-rays, both of uranium and radium, appear to be greater than those given, but for present purposes no great error is likely to be introduced if we calculate the ratio of the initial intensities of the y-rays of uranium and radium from the observed intensities by means of these coefficients. Thus the initial y-activity of the uranium X in equilibrium with 12°13 kilograms of metallic uranium is equal to the initial y-activity of 0°17 mg. of radium bromide, or that from 1 kilogram of uranium is equivalent to ‘0138 mg. It must be mentioned that the ultimate standard of com- parison of radium in this case and throughout was a sealed tube containing 6'7 mg. of Giesel’s radium bromide. The weight was taken with great care before sealing, but it is probable, since the compound was fairly old when weighed, that decomposition had occurred, and that the weight of radium therein was considerably greater than the formula- weight. Thus if the conversion into carbonate by the air had been complete the percentage of radium in the standard would be 79, instead of 53:5 as initially. Taking provisionally a mean value of 66°6 per cent. of radium in the sample the y-Rays of Uranium and Radium. 629 y-activity of 1 kilogram of uranium is equal to that of "009 mg. of radium, or radium gives about 10* times more y-rays than uranium. 4, The Relative Value of the Ratio of y- to B-Rays jor Uranium X and Radium C, It appeared very desirable to carry out an accurate deter- mination of the relative value of the ratio of y- to B-rays for uranium and radium under strictly comparable conditions. Two electroscopes were used, one for the measurement of 8-rays and the other for the y-rays. The former had a base of very thin aluminium foil, 0°095 mm. thick, and was set up so that the active preparations could be placed on the floor 119°5 cm. below the base. The y-ray electroscope was the lead cylindrical electroscope with a base of lead ~ *975 em. thick described under section 10, and the prepara- tions were placed 13:1 cm. beneath the base. As the source of the @- and y-rays of radium was employed a film of radium C, prepared by exposing one side of a negatively charged copper disk to the radium emanation for 12°5 hours. After the exposure the disk was placed in a brass cell and a piece of 0°095 mm. thick aluminium foil was cemented over the cell to prevent any possible escape of adhering emanation. A similar sheet of aluminium covered the uranium X pre- paration. This consisted of one of the three preparations of the third separation, possessing 0°408 of the total activity. The date of these measurements was one week after those described in the last section. Half an hour after the preparation of the film of radium C alternative measurements of the @- and y-rays were taken over several hours, and from the decay curve obtained from the measurements the §- and y-activity at any time could be readily deduced. Other similar measurements were also made of the §-rays when the base of the electroscope con- sisted of a sheet of aluminium foil 0°9 mm. thick, and of the y-rays when the base of the electroscope consisted of plates of aluminium 4 and 6 mm. thick. The latter thickness is sufficient to reduce the #-radiation of both elements to an inappreciable amount. The former, however, was found to allow a little of the 8-radiation of radium only to get through. For all dispositions measurements were also taken with the uranium X. In this way the relative ratio of the y- to B- activity of uranium and radium under comparable conditions was ascertained. It may be assumed that 07195 mm. of aluminium cuts down the @-rays of uranium and radium to practically the same extent, since the absorption is but small, 630 Messrs. F. Soddy and A. 8. Russell on the The initial values for the y-rays before penetrating the 0°975 em. of lead were deduced by means of the absorption coefficients referred to in the last section. It was found that under the conditions described the ratio of 8-rays to y-rays (corrected for absorption in ‘975 cm. lead) was for radium OC (283 and for uranium X 14:05. The relative value of the ratio of B- to y-rays for uranium X in terms of this ratio for radium C as unity is thus 49:7. Uncorrected for ahsorption this ratio is 62. It therefore appears that the initial y-radia- tion of uranium as compared with its -radiation is fifty times less than for the case of radium. When the 8-rays were measured through 0995 mm, of aluminium instead of 0-195 mm. the ratio was 0°58 times 49:7, which is to be expected, since the §-rays of uranium are rather less pene- trating than those of radium. When the y-rays through 6 mm. of aluminium were compared with the 8-rays through 0:19 mm. of aluminium the result was 3°5 times more favour- able to the y-rays of uranium than through 0:975 em. of lead. Under these conditions the y-radiation as compared with the 8-radiation is for uranium about 18 times less than for radium. ‘This appears to be evidence that uranium gives a soft y-radiation not given by radium, but the point will be discussed in more detail in a subsequent communication. _ The y-activity of a sealed tube containing 0°47 mg. of radium bromide was taken at the same time and with the same instrument as the other measurements. This gave an entirely independent estimate of the relative y-activity of the uranium X preparations in terms of radium bromide through a much smaller thickness of lead than was used in the measurement a week previously. Nevertheless the result was nearly the same. The uranium X in equilibrium with 1 kilogram of uranium corresponded in initial y-acti- vity to 0°0150 mg. radium bromide, as compared with 0:01388 mg. found previously. The former value is probably the nearer to the truth. 5. The Connewion between the B- and y-Rays of Uranium X. On account of this great relative poverty of uranium in y-radiation it was decided to test more closely the view that the y-radiation accompanied the @-radiation in the disinte- gration of uranium X. In the first place the y-activity of a kilogram of uranyl nitrate, the 8-activity of which had been enfeebled to a known extent by crystallization, was compared with the y-activity of another kilogram of uranyl nitrate in equilibrium with uranium X. For this purpose the sub- stances were placed immediately below an electroscope, the y-Rays of Uranium and Radium. 631 base of which consisted of a sheet of iron sufficient to absorb the 8-radiation completely. The crystals just filled a cylin- drical jar of about the diameter of the electroscope. It was found that the y-radiation in the two substances was propor- tional to the $-radiation, indicating that the whole of the y-radiation is derived from the uranium X. The effects measured were small, and naturally no great accuracy was attained. The next step was to determine the rate of decay of the y-radiation of uranium X as accurately as possible. Pre- liminary experiments with the preparations of the second separation had shown that the period of the decay was at any rate approximately the same as that of the @-rays. Measurements of each of the three preparations of the third separation have shown that the decay of the y-radiation is exponential from the date of separation up to the present date (30 days). The value of the coefficient of decay was ~ found to be 0°029 (day)-1, which agrees as closely as is to be expected with the value found for the @-rays 0°031 (Rutherford & Soddy, Phil. Mag. 1903, v. p. 444). Although these results, so far as they go, confirm the view that the y-radiation accompanies the 8-radiation in the disinte- gration of uranium X, there seems no escape from the con- clusion that the y-rays are a primary radiation due to the disintegration of the atom, and not a secondary radiation accompanying the expulsion of the 8-particle. Since for two elements the 8- and y-radiations of which, although similar, each to each, in general character, yet differ in relative in- tensity in the ratio of 50 to 1, there seems no incongruity in contemplating the possibility of a 8-radiation wholly un- accompanied by y-radiation. One may even hazard the suggestion that possibly 8-rays will be found to accompany the change of uranium X into radium while y-rays accompany the change of uranium X into actinium. Although there is no evidence at present in favour of this there is equally nothing to be urged against it. DA. (Later results for the decay of the y-rays over a period of 80 days are now available. For the last 49 days the prepa- rations have not been used in other experiments, or disturbed between the measurements. The value of X (day)! over this period has been found to be 0:028. This is about 10 per cent. smaller than the original value found for the decay of the B-rays, but it is possible that the discrepancy is due to an error in the determination of this latter constant. We are now investigating this point. | 632 Messrs. F. Soddy and A. S. Russell on the 6. Absorption of Uranium y-Rays by Matter. (First Series.) After preliminary trials with the uranium X of the first separation, a careful series of measurements was carried out with the preparations of the second separation on the absorp- tion of the y-rays by various substances. The selection of the particular experimental disposition employed involves necessarily a certain amount of arbitrariness, for as is well- known the ionization produced by y-rays results largely from the secondary radiations it sets up in the walls of the measuring instrument. Again, one may, while keeping the distance between the active material and the electroscope constant, place the absorbing screens either directly over the active material, or directly under the electroscope, or at any intermediate position. Or, one may have the active material near to the electroscope and include a large cone of rays, or far away, and work with practically a parallel beam. It is curious that in all the published measurements of the absorp- tion of y-rays, only Wigger (Jahr. Radioakt. 1905, ii. p. 430) has given full and precise information on these important points. The electroscope employed was a cylindrical brass one of internal height 12-8 cm., internal diameter 10°52 cm., and of wall thickness 0°'145 em. It was supported by four brass pillars 15°8 cm. above a permanent base-board. Most of the absorbing plates used were 11 cm. square, but lead and brass were in the form of circular disks, 11 and 12°7 cm. diameter respectively. They were clamped up tightly to the bottom of the electroscope forming its base. When the absorbers were insulators the upper surface was covered with aluminium foil, 0°0035 mm. thick. For light substances, with a density below 2, a plate of lead 1:26 cm. thick formed the base of the electroscope. The uranium X mounted on one of two wooden stands, of heights 1°2 and 7°55 cm. respectively, according to the nature and amount of the absorbing material under investigation, was placed underneath the electroscope. The following table gives the results. The first column gives the number of the experiment, the second the distance of the preparation from the base of the electroscope, the third the absorbing material, the fourth its density d, the fifth the range over which the absorption is exponential, the sixth the value of the absorption coefficient X%(cm.)—1, and the seventh the mean value of the ratio A/dx100. Some of these results are plotted as curves in fig. 1. The ordinates represent logarithms of the ionization leak, in divisions per minute corrected for natural leak, and the abscisse are thicknesses in cm. To separate the curves in the figure from y-Rays of Uranium and Radium. 633 one another an arbitrary constant has been added. to the logarithm of the ionization leak in some cases. The numbers on the curves refer to the numbers in the first column of the table. For mercury a different arrangement had necessarily to be adopted. A circular hole 11°5 cm. in diameter was cut in a block of wood 4 cm. thick, and to the bottom was fixed a circular plate of glass about 3mm.thick. This was provided with levelling screws, and placed close over the preparations. It was levelled and sufficient mercury placed in it completely to cover the surface, and then weighed amounts of mercury were added or withdrawn. In experiments Nos. 1 and 2 the base of the electroscope was a plate of lead 1°2 cm. thick. In experiment No.3 it was two sheets of tinfoil. The results in the latter case lie on a continuous curve convex to the origin, and no one value can be assigned to 2X. TasLe I.—Uranium X. y-Rays. Brass Electroscope, absorbing plates forming base. No. Pitanne| Material. Density. | Range (em.).| \(em.)—1. | A/d x 100. 1 | 33 to 2:55| -687 5-05 2‘) 825 | Mercury. 13:59 | 33 to 2:60| -760 5:59 z - Not ex|ponentiai. 1:26 to 5:00} 634 556 Bt) —— 1140" 11-9 to 5-00| 620 544 ee FO to BO)" “413 4-69 | " Copper. S81 119 to 68 | -430 4-88 me) | 13) to 60 |. 410 4-9] 9} " nee 639 111 to 58 | > -443 5°30 i} : Iron. 762 |252t0 757) 3a) aie 12 ? Tin. 7245 |1:90to 551| 351 4-84 13 Z Zine. 707 |19 to 60 | -873 5:27 15 | 1463 | Slate. 235 |60 to126 | 158 5:54 14 » | Aluminium. | 277 50 tolld | 148 5:34 16 » | Glas. 2°52 |52 tol03 | 165 6-54 Below this the base consisted of 1-26 cm. of Lead. | | | 18 » | MagnesiaBrick., 1-92 | 27 to 11:8 | 1029 5:36 17 u | Sulphur. 179 | 2:2 to 116 1046 5°84 19 P Paraffin Wax. | 0:862 | 3°8 to 11°4 ‘0576 6°68 20 | ; Clemo 0386 20tolld | 0214 5:4 Mean value of \/d=:0536. Phil. Mag. 8. 6. Vol. 18. No. 106. Oct. 1909. 2U 634 Messrs. I’. Soddy and A. 8S. Russell on the It will be seen from the other curves that after a certain initial thickness of matter has been penetrated, corresponding Fig. 1, 6 THICANESS (C20) ae to 1 em. of lead, or an equivalent thickness of other sub- stances, the absorption follows an exponential law represented by the equation where ¢, and ¢, refer to thicknesses in centimetres, I.) and I...) to the corresponding ionizations, and X is a constant, which is usually termed “ the absorption coefficient.” Owing to the obliquity of part of the beam this absorption coefficient departs slightly from the true absorption coefficient corre- sponding to the » of the theoretical equation a 1 ae which represents the exponential absorption of a parallel homegeneous radiation passing through the absorbing plate normally to its surface. It can be shown, for example, to be | —AlI, y-Rays of Uranium and Radium. 635 about 2°5 per cent. greater over the whole range for the dispo- sition described in detail in section 10. For thicknesses less than 1 cm. of lead the curves are no longer exponential, and the value of \ apparently increases. The study of this part of the range forms the subject of a separate communication. It will be seen that as a general result the experimental values of X/d are nearly the same for all substances, the mean value being 00536, The departures of the values of )/d from this mean are, however, greater than should be the case if they were due merely to errors of observation. Indeed the varia- tions seemed not to be due so much to differences in the metals, as different results were obtained for different series of observations on the same metals, as to other unexplained causes. ‘The extreme values for \/d vary between °0668 and *0440, a difference of about 20 per cent. on either side of the mean value. | Beyond a thickness of 5 cm. of lead, or an equivalent thickness of mercury, the absorption appeared to be less than the normal. At this range, however, the effects produced are of the same order of magnitude as the natural leak of the instrument, and are too small to be measured with any certainty. Subsequent experiments with the more active preparations of the third separation failed to establish beyond doubt any alteration in the value of the absorption coefficient. The disposition employed in this series is a troublesome one to work with in practice, but in our opinion the general results obtained are, from a theoretical point of view, of equal value to those obtained with another disposition detailed in section 11. 7. Variation of the Lonization produced by y-Rays. In order to compare directly the y-rays of uranium with those of radium and to obtain further light on the variations referred to, experiments were now undertaken with radium. It was found, in the first place, that the errors of observation were reduced by removing the source of light a considerable distance from the electroscope, and interposing a sheet of ground glass between it and the electroscope. A thin cardboard cover also was placed over the electroscope which was re- moved only when the leaf system was being charged. This hood had the effect of maintaining a constant temperature around the wall of the electrossope while its presence did not affect the leak ofthe instrument. In the second place, a very curious effect was noticed, first in working with the more powerful y-rays from radium. Ifthe time for the leaf to cross the scale was taken and the experiment repeated a number 2U 2 636 Messrs. F'. Soddy and A. 8. Russell on the of times, the rate of leak gradually increased, considerably at first and then less rapidly, until a maximum rate was reached. This phenomenon was got with different electro- scopes, different absorbing plates, and with both radium and uranium X. The sign of the charge on the leaf did not seem to produce any effect. The maximum rate of leak was found in all cases to be about 12 per cent. greater than the minimum. The cause of the steady increase in the rate of leak to a maximum remains unknown. We cannot at present give any explanation of it. In certain new forms of lonization- vessels we are now working with it is not shown. In this connexion may be recalled an experiment by G. Jaffé (Ann. Phys. 1908, xxv. p. 271), who found it to be impossible to obtain complete saturation in air at atmospheric pressure ionized by the y-rays of radium, even with a potential gradient of 5000 volts per cm. Kleeman (Phil. Mag. 1907, xiv. . 622) also called attention to gradual fluctuations in mag- nitude of 5 to 10 per cent. in the values of the leaks obtained by using a differential method with two ionization-chambers and a steady sonrce of y-rays. He suggested that the ema- nation might be coming off from the radium salt inter- mittently, causing alterations in the centre of origin of the y-rays. This certainly does not apply to our case, for the effect is shown also by the y-rays.of uranium X, and the irregu- larities moreover are quite definite. The effect depends on the maintenance during successive observations of the charge on the leaf system; for if with everything in place the whole be left undisturbed for a quarter of an hour, and then a series of consecutive observations are taken without pause, the minimum leak is first obtained, and this gradually increases tothe maximum. Thus in one experiment 6-7 mg. of radium bromide in a sealed tuhe was placed below a brass electro- scope, the base of which consisted of 6°28 cm. of lead, and everything was left for ten minutes. Consecutive observa- tions, then taken over 100 divisions of the eyepiece scale, were, in divisions per minute, 111, 114, 118, 120, 120, 122, 123°5, 124, 124°2, 125,125, 125. If now the radium were held up to the side of the instrument for a minute without recharging, and the observations repeated, the minimum leak was again obtained, and this again increased to the maximum. In practice it is easier and quicker thus to obtain the minimum leak than the maximum leak, and we have so far been concerned to employ a method of working which shall avoid these errors and give consistent results. This is achieved in the following manner. After each observation, the leaf being still partially charged, 6°7 mg, of radium bromide in a sealed tube is placed near y-Rays of Uranium and Radium. 637 a window of the electroscope and the air within thoroughly ionized for about 40 seconds. The radium is then removed and the leaf charged up but slightly more than is necessary to get it onto the scale. The leak so obtained is the minimum leak, and seems t be, if not the true, at least a consistent measure of the ioni- zation of the y-rays from the source used. The leak with the new electroscope of lead described later is quite constant for a particular disposition over any one day, leaks of 12 minutes duration rarely varying by more than three or four seconds. Also the values of X obtained by this method for any one substance on different days do not usually differ by more than one or two per cent. After this method of working was found, the measurement of ionization leaks due to y-rays became almost as simple as in the case of the other radiations, whereas before they were very uncertain and variable. Without some such precautions being employed y-ray measurements can hardly be depended upon to 10 per cent. 8. Absorption of y-Rays of Radium under Various Conditions. The published values of X for the y-rays of radium show considerable differences among themselves, and we have carried out a large number of experiments to determine whether this value depends on the conditions. McClelland (Phil. Mag. 1904, viii. p. 70) and Eve (Phys. Zezt. 1907, viii. p- 183) agree fairly closely. The latter gives the value of Xas varying from 0°56 to 0°46 over a range of from ‘64 to 3 cm. of lead. Wigger, who worked over the range from 2°8 to 5 cm. of lead with a peculiar apparatus, found the value 0°241. Kleeman (Phil. Mag. 1907, xiv. p. 643) came to the con- clusion, from experiments on the secondary cathode rays generated by y-rays, that the latter must consist of three groups of rays. Madsen recently (Phil. Mag. 1909, xvii. p- 447) concluded that the y-rays consisted of two homo- geneous radiations possessing values for A/d, independent of the nature of the absorbing substance, 0°028 and 0°12 respectively. Thus, for lead X has the values 0°32 and 1:36. Since the present work was done Y. Tuomikoski has published (Phys. Zeit. 1909, x. p. 372) a determination of X for y-rays of radium over a range up to 18 em. of lead. He gives the following values :— | } | 5° (em.) | to 10 2 te 22 | 5:4 12: 15°8 180 OO Thickness ffrom| 4 | 10 | 22 | | | *50 4 | 12:0 158 0 | | X(om.)—} vee She 58. || 52 / 638 Messrs. F. Soddy and A. 8. Russell on the From the paper, which is merely a preliminary account, no conclusion can be formed, in view of the results to be given in this section, as to whether the convexity of the absorption curve to the origin, which these numbers disclose, is due to a real change in the value of the absorption coefficient. 7 We obtained for several dispositions results similar to those given by Eve and McClelland, and in no case near Wigger’s lower value, so we repeated the latter’s work as closely as possible. The apparatus consisted of a vertical brass cylinder 105 em. long, 4°5 cm. inside diameter, 0°5 mm. wall thickness provided with a central electrode 95 cm. long passing through an insulator and directly connecting with a leaf system inside an ordinary brass electroscope. The lead plates were placed over the open top end of the cylinder and the radium was fixed at a definite height above. The capacity of the arrange- ment was 3() times greater than that of an ordinary leaf system. Inan experiment with the radium 56 mm. from the top of the cylinder, as used by Wigger, the absorption pro- ceeded exponentially from a range of 2°8 to 47 cm. of lead, the value of the absorption coefficient \ being 0°479, instead of 0°241 as stated by him. Wigger, however, appears to have calculated his results wrongly. He does not state the natural leak of his instrument ; but neglecting this and recalculating from his own observations gave a value similar to what we obtained experimentally. The effect of increasing the distance of the radium from the end of the cylinder to 78 mm. and 100 mm. was then tried. The leak fell off with great rapidity as the distance of the radium was increased, showing that only a few cm. ot the top end of the long cylinder could be effective in con- tributing to the ionization. The curves obtained over the same range as before were quite exponential, but the values of X were now different, being 0°438 at 78 mm. and 0°393 at 100mm. This effect of the variation of X with the distance of the source of radiation from the ionization-chamber was then investigated with a common form of apparatus. The brass electroscope, used in the measurements of section 6, was mounted on brass pillars on a wooden plank one end of which was supported on the slate bench while the other was supported by.two long legs standing on the floor. A large hole was cut in the plank so as to allow free passage of radiations from beneath the table into the electroscope. The base of the electroscope was of lead 2°840 cm. thick clamped up as before. It was found that with 5 cm. of lead over the radium placed on the floor and 2°84 cm. as base the leak was y-Rays of Uranium and Radium, 639 considerably less than if all the metal was clamped up to the base and the radium tube left bare. The difference in the leaks due to the two dispositions it would seem natural to ascribe to the generation of secondary rays in the slate bench and elsewhere sufficiently penetrating to get through the walls of the electroscope, which are produced in greater intensity in the first case than in the second. In consequence the lead, all except the 2°84 cm. forming the base, was placed directly Fig. 2. ye ia THICKNESS OF ies ee 3 0-7 ro PA AT) a n= a o y-Rays. Variation of Absorption with Distance of Radium from the Electroscope. over the radium. The radium was placed below the electro- scope at distances varying from 15°1 cm. to 114°6 cm. The absorption-curves obtained are shown in fig. 2. For the 640 Messrs. F. Soddy and A. 8S. Russell on the smallest distance the curve is exponential (\="465) ; but as the radium is removed further and further away the curves become more and more convex to the origin. From 16:4 cm. to 114°6 em. the preparation is below the level of the slate bench. Although at the time it was deemed impos- sible for any @-radiation, secondary or primary, to penetrate the walls or windows of the brass electroscope, we very pro- bably, owing to our experience having been mainly with the 8-rays of uranium, underestimated the penetrating power of the secondary @-rays of radium. From a mature consideration of the whole of the effects obtained during the work we thought the effect may have been due to secondary §-radiation, as in no other experiments had we been able to obtain any definite evidence of secondary y-radiation, generated by y-rays, more penetrating than the §-rays (compare Sections 8 a and 9). When the electroscope, on the other hand, has a base thin enough to allow secondary 8-radiations to penetrate it, and the radium is placed a few centimetres beneath, it was noticed that the leak was always greater with the absorbing screens directly over the radium than when they were clamped up to the electroscope. This is to be ascribed to lateral y-radiation generating secondary #-radiation at the point when it can enter through the electroscope base. 8 A. [Since the paper was printed we have examined more closely the question as to whether secondary @-radiation caused the effect discussed in Section 8. The wall of the brass electroscope was thickened in places by external sheets of various metals. It was found that whereas the addition of brass up to a thickness of 3 mm. did not affect the actual value of the leak for a fixed disposition, even thin lead-foil cut it down appreciably. Beyond 2:2 mm. of lead no further reduction was noticed. At this stage for the particular dis- position used the difference amounted to a third of the total effect. The leaks at the end of the lowest curve in fig. 2 were only one-half as great as in this case. These results taken in conjunction with those recorded in Section 10 show that the departure of the absorption-curves (fig. 2) from the straight line is to be ascribed to external secondary radiation more penetrating than the @-rays, so far as brass is con- cerned, but readily absorbed by lead. The choice of a thick lead electroscope in the final series of measurements described in section 10 was made from quite other considerations, but it now appears that secondary radiation effects were thus probably avoided, which might not have been the case if an y-Rays of Uranium and Radium. 641 equally thick electrcscope of another metal had been em- ployed. The work of Eve just published (Phil. Mag. 1909, Xvill. p. 175), taken into conjunction with that of Kleeman, Bragg and Madsen, led him to the view that lead is peculiar in that it absorbs secondary y-radiation and generates little or none (compare concluding paragraph of section 10).j 9. The Effect of Secondary Penetrating Radiation. The absorption of y-rays by matter may be conveniently expressed with fair accuracy by an exponential law though small departures from this law are probably always present. We think that in an unsuitable form of apparatus secondary penetrating rays play a large part in causing these deviations. We have not been able by any theory of secondary radiation to predict beforehand what variation is likely to be obtained in any ordinary case. It suffices in the first instance to suppose that the y-rays generate at each point in passage through matter a secondary radiation proportional in intensity to the primary, but with a different coefficient of absorption. If we assume that the rays, both primary and secondary, traverse the plate normally, the mathematical proposition is, reading thickness instead of time, formally identical to that of the theory of successive chemical changes, such, for example, as has been thoroughly worked out by Rutherford for suc- cessive radioactive changes. If Q, indicates the initial energy of the primary beam, Q; the energy of the combined primary and secondary emerging from a plate of thickness ¢, , and A, the absorption coefficients of the primary and secondary respectively, and « is a coefficient of transformation, repre- senting the fraction of the absorbed primary transformed into secondary, it can be at once shown that DOF je! W(e=20, Qo where ee KAy Ae y As the ionizations, not the energies, are measured, and these are directly proportional to the absorption coefficients, this must be allowed for, and we obtain a = (1+ B)e-*’—B(e~*“), 0 where B= é Ag—Ay and I,, I, refer to the ionizations. 642 Messrs. F. Soddy and A. S. Russell on the We may merely state here that we have not yet been able to obtain any verification apart from the effects recorded in Section 8 a of the existence of secondary or reflected pene- trating rays generated by the passage of y-rays through matter in any of the dispositions employed. The above equations apply, of course, equally to the secondary §-radia- tion which is known to be generated ; but the effect of this on the absorption-curve is only apparent over the same range as that of the primary §-rays, which is usually not directly investigable. Beyond this range the second term of the equation disappears, the absorption is exponential, and merely the absolute value of the ionization leak is multiplied by a constant factor. This state, by analogy to radioactive equi- librium, might be called “ radiation equilibrium.” 10. Zhe Form of Apparatus finally adopted. As the y-radiation from uranium X is comparatively feeble, it was important to construct the electroscope of metal which for a given volume would give the largest effect. Lead was found to be easily the best for this purpose. This is curious as precisely the opposite effect was expected. For when the absorbing plates form the base of the electroscope the leak in the instrument for equivalent thicknesses (7. e. thickness X density) isleast for lead. We have probably here an example of the difference discovered by Bragg and Madsen (Phil. Mag. 1908, xv. p. 663) between the incidence and emergence secondary radiation. The emergence radiation of lead is not greatly different from that of light metals like aluminium, whereas the incidence radiation is much greater than that from aluminium. Hlectroscopes of lead and brass with circular cross-section and electroscopes of lead, aluminium, zinc, and cardboard with square cross-section all of the same height were compared under identical conditions of experiment. It was found that in the two lead electroscopes the ionization produced by the y-rays was proportional to the volume of the electroscope. Lead was easily the best, then came zinc and brass which gave about equal ionization. Cardboard lined with tinfoil came next, and lastly aluminium. The electro- scopes were of varying thicknesses, but in no case was the ionization increased by increasing the thickness of the walls. The relative values of the ionization in the electroscopes were approximately :—Lead. 100, zine 75, brass 75, cardboard 68, aluminium, 57. To eliminate the possible effect of secondary rays and to secure the maximum ionization by y-rays a cylin- drical lead electroscope with small glass windows was con- structed with the following dimensions :—Inside height y-lays of Uranium and Radium. 643 12°8 cm., inside diameter 9°0 cm., wall thickness 0°65 cm., thickness of top 1°18 em., thickness of base 2°84 cm. The electroscope was completely surrounded by two circular screens of lead of height 12°6 cm. and of thickness 0:244 cm., provided with small windows cut in them. The whole was fitted with a wooden stand and mounted on four brass pillars above the wooden table. With this new instrument the effect of varying the distance of the radium was again investigated in amanner precisely similar to that already described for the brass electroscope. In every case the exponential law of absorption now held even up to distances of over a metre. In contrast to the similar experiments with Wigger’s apparatus, the value of X also only varied slightly, if at all, with the distance. The value of A(cm.)~1from 2°8 to 8-9 cm. of lead in this series was 0°483 with the radium 1371 cm. and 0°480 with the radium 113 cm. below the base of the electroscope. _ At intermediate distances \ was intermediate. The base was too thick for work with the feeble y-rays of uranium X, and it was replaced by a permanent base consisting of a plate of lead 0°975 cm. thick. With this alteration the instrument formed the standard one in all subsequent mea- surements. All the active preparations were placed at the uniform distance of 13 em. from the under surface of the base, the absorbing plates were placed directly over the active material, and the air in the electroscope was thoroughly ionized between each observation. Before giving the final results, it is of interest to refer to some observations which show that even in this method of work a certain amount of arbitrariness is introduced into the results by the particular disposition adopted. The effect on the absolute value of the leak in the electroscope of alternately placing the same plates over the active material and against the under side of the base of the instrument was examined. For the radium y-rays the leak was slightly less both with copper and lead when the plates were clamped up to the base. For uranium X the same held true except for great thicknesses of lead when the converse held. Thus for uranium X the absorption curves for.lead with the two dispositions actually cut one another. The effects so introduced, however, are not large, and the advantages in ease and quickness of working in placing the plates directly over the active material are very great as compared with the first method emploved. At the same time we do not think that there is much to choose between the two methods from a theoretical point of view. Each is open to some objection. 644 Messrs. F'. Soddy and A. 8. Russell on the 10. Comparison of the Absorption Coefficients of the y-Rays of Uranium and Radium. With the method described in last section a series of com- parable measurements of the absorption coefficients of the y-rays of uranium X and radium were finally carried out. The only difference between them is that the uranium X was in the form of a surface of about 30 cm.? area, while the radium constituted practically a point source. The uranium X preparations employed were those of the third separation. The results with radium are given in Table II. and fig. 3. They bear out the values of McClelland and Eve. TaBLE [J.—Radium y-Rays. Lead Electroscope, base :975 em. thick. Absorbing Plates laid directly over Radium, which was 13:0 em. below under surface of base. 0°47 mg. of RaBr, used. No. Material. Density. | Range (cm.). | \(em.)—1. | 100xA/d. } 1. | Mercury. 13°59 34 to 3°32 642 4:72 2. | Lead. 11-40 0 to 791 "495 4:34 3. | Copper. 8°81 0 to 7-60 351 3°98 4. | Brass. 8°35 0 to 586 325 3°89 5. | Iron. 7°62 0 to 7:57 "304 3°99 62) Lin: 7245 Oto 551 "281 3°88 7. | Zine. 7:07 0 to 6:00 ‘278 3°93 8. | Slate. 2°854 Oto 9-44 118 4:14 9. | Aluminium. 277 0 to 11°19 111 4:01 10. | Glass. 2°52 0 to 11:26 "105 4:16 11. | Magnesia Brick. 1-92 O to 11°86 076 3°96 12. | Sulphur. 1-785 0 to 11°59 0782 4°38 13. | Paraffin-wax. 0°862 0 to 11°39 040 4°64 Mean value of A/d (Nos. 3 to 11)=:0399. The results with uranium X are given in Table III. and fig. 4 (pp. 646, 647). From the curves (figs. 3 and 4) it can be seen how nearly the exponential law is followed in the case of all substances. Only the first points on the curve, with zero thickness, show slight irregularities. There is no evidence of the existence of the second negative exponential term, showing that if secondary rays are generated by the y-rays of either uranium or radium, they are unable to penetrate 1 cm. of lead. Moreover the value of the absorption coefficient is for all sub- stances of average density independent of the nature of the substance. . y-Rays of Uranium and Radium. 645 Fig. 3. | | | eT smal 0-6 Y Be 0-4 7S 0-2 Be \ 1-2 2-4 3 4 5 6 48 6-0 re 8: 6 10-8 le-0 y-Rays of Radium. All through 1 em. of Lead, The mean value of X/d for all substances having a density between the range of from 2°6 to 8°8 is for radium -040, and for uranium X ‘047. It may be noted that the deviations from the mean value are, considering the nature of the expe- riment, very small indeed. This is largely due to the pre- cautions taken each time to secure the minimum leak referred to before. Thus /d for uranium X for zine gave a value of -0465 twice on different occasions. Repeating the experiment under exactly similar conditions, on the same day as one of the measurements, except that the leak was taken without thorough ionization of the air in the electroscope before each 646 Messrs. F. Soddy and A. 8. Russell on the Taste II[.—Uranium X y-Rays. Disposition as in Table II. except that the Uranium X occupied a surface of about 30 sq. cm. No. Material. Density. | Range (cm.). | A(em.)—1. | 100xA;d. — = ) a 1. | Mercury. 13°59 343 to 3°535 832 6:12 1:297 2. | Lead. 11°40 0 to 4:5 "725 6°36 1:465 3. | Copper. 881 0 to 76 ‘416 4:72 1:186 4. | Brass. 8°35 0 to 586 392 4:70 1:208 5. | Iron. 7:62 0. to “7-57 *360 4:72 1°183 6. | Tin 7°245 0 to 551 341 4:7 1:212 7. | Zine LOT 0 to 6:00 *329 4°65 1:1838 8. | Slate 2354 | 0 to 9°44 | 134 4:69 1-133 9. | Aluminium. 2°77 0 to1119 130 4:69 1:169 10. | Glass. 2-52 0 to 11:26 +122 4-84 1:160 11. | Magnesia Brick. 1:92 0 to 11:86 ‘0917 4°78 1-207 12. | Sulphur. 1:785 0 to 11°59 0921 5:16 | LOS 13. | Paraffin-wax. 0-862 0 to 11:39 0435 5:02 | 1-082 14, | Pine-wood. 0°386 O to 12°51 *02926 1:58.60 ee Mean value of A/d (Nos. 3 to 9) *0470. A UrX r Ra x observation, gave the value 0:0441 for X/d, a value 5 per cent. less than the former value. Hqually good experiments with the same metals in Table I. gave values for X/d differing by 8 per cent. Now for uranium X the extreme values of A/d for bodies within the density range specified are ‘0465 and °0472, which is only a variation of about 2 per cent. For radium the extremes are 0387 and ‘0414. For substances-of density beyond the limits 2°6 to 8°8 on either side the values of X/d are considerably larger, the departures being more apparent for the case of uranium X than for radium. These departures seem to be genuine, for all the results showing them have been repeated, and the same or very similar results obtained. They probably have their origin in the disposition used. Thus in the original work with uranium X (Table I.), when the absorbing materials were clamped up, A/d was, on the whole, fairly constant over the entire range from mercury to pine-wood, with a mean of ‘0536, while in the later work both with radium and uranium X, in which the materials are laid directly on the source of radiation, differences appear. The general arrangement of the experiment and the method of working in the former case, however, were much less accurate L165, ¥-Rays of Uranium and Radium. 647 than in the latter. A determination of X for lead with uranium X with the new disposition and method of working Fig. 4. { : ae = : | | N ae Ss < oi o Ne, os “4 gon ~ | ‘ ay ! i] 0 BE Si - . : i 2 3 6 5 6 A er? 8 9 19 a le 13. y-Rays of Uranium. All through 1 cm. of Lead. except that the metal was all clamped to the base of the electroscope gave a value 0°66, which is much nearer to the value given in Table I. than to that in Table ITI. Considering now the ratio of the absorption coefficients for uranium and radium shown in the last column of Table III., it will be seen that, excluding the two heaviest substances, mercury and lead, and the two lightest, sulphur and paraftin- wax, the mean ratio is 1°182, and the actual values are wonderfully close to this mean. If we exclude also slate, which is an indefinite sort of material, the extreme variation from the mean value is only 2 or 3 per cent. [It is very interesting to note that the division of the sub. stances in Tables II. and III. into three groups, according to the values obtained for X/d, is practically the same as the division made by Kleeman for totally distinct reasons in his study of the secondary radiations generated by y-rays. (Compare Phil. Mag. 1908, xv. p. 644, Tables J. and IT.) ] 648 ea i. y-Rays of Uranium and Radium. Lead is entirely anomalous with the value of the ratio 1:465, and this no doubt, as explained, is to be attributed partly to the disposition employed, and possibly also to the fact that the measurements were done in a lead electroscope. It is rather curious that lead, of all metals, seems in many ways to be the most unsuited for accurate measurements of the absorption of y-rays, and yet it is the one which we, in common with previous investigators, have worked with most. We have noticed repeatedly that it is more difficult to obtain consistent results with lead as the absorber than with any other material. This is partially perhaps, but not wholly, due to its own high natural radioactivity, necessitating frequent redetermination of the natural leak. If we were repeating the work we should use by preference another metal in many of the measurements described in the first part ot the paper. Summary of Results. 1. The y-radiation of uranium X, separated from 50 kilograms of uranyl nitrate, has been compared with the y-radiation of radium, and it is concluded that the B- and y-radiations are probably not, as hitherto assumed, inter- dependent. 2. The initial y-radiation of the uranium X in equilibriuin with 1 kilogram of uranium (element) is equal to that of 0-015 milligram of a particular sample of a radium compound, which may be provisionally regarded as containing 66°6 er cent. of radium. 3. The ratio of the @- to the y-rays of uranium X is 62 when the same ratio for radium C is taken as unity, the y-rays being measured through 1 em. of lead. Correcting for the absorption in the lead, and assuming the rays to be homogeneous in each case, the value of the ratio for uranium is 50. When the y-rays are measured through 0°6 cm. of aluminium, so as to admit any soft y-radiation if present, the ratio for uranium is 18, not correcting for absorption. It is not yet decided whether a soft primary y-radiation of uranium exists. 4, The y-radiation accompanies the #-radiation of ura- nium X, and decays at approximately the same rate. [4 a. Later results give 0°028 (day)-1! for the value of X -determined from the decay of the y-rays. This is about 10 per cent. less than the known value derived from the decay of the §-rays. | 5. For thicknesses less than 1 em. of lead, or its equivalent, the absorption of the uranium y-rays does not follow any Kinetic Energy of Positive Ions. 649 simple law. For greater thickness the absorption is quite exponential, and nearly or wholly independent of the nature of the substance traversed, being proportional to its density. In one series the absorbing plates themselves formed the base of the electroscope, and the mean value of A/d was 0°0536. 6. In a thick-walled lead electroscope with a base 1 cm. thick, the absorbing plates being placed directly over the preparation, the absorption both for uranium and radium was strictly exponential. The value of A/d for all but the heaviest and lightest substances was 0°047 for uranium and 0°040 for radium, the ratio being 1:18. Lead appears exceptional under these conditions, and the value of A/d is 0:0636 for uranium y-rays, and 0:0434 for radium y-rays, the ratio being 1:465. In the first disposition lead appears quite normal. 7. Some evidence of the existence of a secondary radiation more penetrating than 8-rays, generated by the y-rays, has ~ been obtained, but almost certainly none exists able to affect measurements taken through 1 em. of lead. 8. The y-ray ionization is not in all cases constant, but suffers a progressive increase with certain dispositions, from a minimum to a maximum about 12 per cent. greater, when consecutive observations are made without pause. The effect depends upon the presence or absence of a charge on the leaf system; for if the charge and the ionization are maintained, the rate of leak tends towards a maximum: while if the ionization is maintained for a sufficient period after the charge has been dissipated the rate of leak becomesa minimum again. Physical Chemistry Laboratory, University of Glasgow. June 1909. [ Additions made August 1909. ] \ LXVI. The Kinetic Energy of the Positive Ions emitted from various Hot Bodies. By F. C. Brown, Ph.D.; Porter Ogden Jacobus Fellow, Princeton University *. HIS paper describes an investigation of the kinetic energy of the positive ions from gold, silver, palladium, tantalum, nickel, platinum, aluminium phosphate, osmium, tungsten. and iron. It was shown in a paper by Richardson and Brown fF that if the kinetic energy of the ions is due solely to thermal * Communicated by Prof. O. W. Richardson. + Phil. Mag. [6] vol. xvi. p. 353 (1908). Phil. Mag.8. 6. Vol. 18. No. 106. Oct. 1909. aX 650 Dr. F. C. Brown on the Kinetic Energy of the agitation and is distributed among the different ions in accordance with Maxwell’s law, then the current carried by those ions escaping from a hot portion of an infinite plane to a neighbouring parallel plane can be expressed by the formula 1) = toe where V is the difference of potential between the planes, ne is the quantity of electricity carried by half a cubic centimetre of hydrogen in electrolysis, 2 is the value of the current when the difference of potential is V, 2 1s the value tor a potential-difference V=0, @ is the absolute temperature, and R is the ordinary gas constant in the equation pu= R@, taken for a unit volume of gas under standard conditions of pressure and temperature. This formula was tested experimentally for the negative ions from ‘platinum, carbon, and sodium-potassium alloy. The verification was quite satisfactory for platinum, but it was not so for carbon or the alloy. At that time it was considered that the failure of the experimental results to comply with the theory in the instances mentioned, was due to the disagreement between the experimental conditions and those required by the theory. Ina more recent paper * the author showed that the above formula was satisfactory for the positive ions from hot platinum. In that paper the hot platinum strip described was constricted slightly in the middle, so that only a small portion of it was heated by the electric current. It was estimated that no portion of the emitting surface differed from zero potential by more than +0:04 volt. Recently, while investigating the kinetic energy of the ions from tungsten and tantalum filaments, results were obtained which were not in agreement with those previously ob- tained with a platinum strip. It was not clear if the disagreement were mainly due to the hot body not having a plane surface or to the fall of potential over the conducting surface. It will be seen later in this paper that the errors arising from a small fall of potential over the strip can be neglected in comparison with errors arising when the emitting surface is not a plane, and parallel to the receiving surface. * Phil, Mag. [6] vol. xvii. p. 355 (1909). Positive lons emitted from various Hot Bodies. 651 Theory of the Method. Stated briefly the underlying theory of the method used in these investigations is the same as that presented in the paper by Richardson and Brown [loc. cit.]. The hot body, or thermionic radiator, comprised a plane of from 0:2 to 0°3 mm.? area, located in the centre of a disk of 13 mm. diameter. The ions emitted impinged on a parallel disk less than 1 mm. distant, which for reference we may call the upper disk. On the view outlined above, the thermionic current * to the upper disk is expressed by the equation, ; which is equivalent to ee ne(V.— V;) (2) O(log, 2;—log,t) ° The working method consisted in applying different potentials to the upper plate and then measuring the rate of charging up. There are several advantages of this method over the one given in previous papers, which always required merely the recording of the potential to which the upper plate changed in a given time. The chief advantages of the present method are, that time is saved in the taking of the observations, the calculations are shortened and simpli- fied, and inaccuracies due to any changes in the electrometer constant are avoided. From the data, curves were made showing the thermionic current for different potentials and also curves showing the logarithms of the current for these same potentials. In general the curves permitted a quicker and more accurate verification of formula (2) than was obtained without them. From the curves the value of the kinetic energy of the ions due to the velocity components normal to the surface of the thermionic radiator was readily determined, by making use of the methods previously given. E«perimental Arrangements. The special part of the apparatus used in these investigations is shown in fig. 1. It was put together in three parts, a glass tube of 20 mm. diameter and two well-ground glass stoppers. Into the upper stopper were fitted a brass rod KH, and a brass tube H,. The tube and the rod were separated and insulated from each other by glasstubing g. These parts were fixed and * For justification for this and similar new terminology used in this paper, see paper by O. W. Richardson, Phil. Mag. June 1909, 2X 2 Se 652 Dr. F. C. Brown on the Kinetic Energy of the made air-tight by sealing-wax covered over on the outside by soft wax. On the bottom of the rod was threaded a brass disk, 6, to which was soldered a platinum disk of the same diameter. The guard-ring G was fastened to the bottom of the brass tubing, as shown in the diagram. It was an easy matter to clean the platinum disk on this upper plate before any series of observations, and thereby avoid any complica- tions that might be due to the high potential effect. The nature of this effect will be explained further on in the paper. Fig. 1. The guard-ring arrangement made it impossible for any collected charges on the glass to leak to the upper plate or its electrical connexions. The hot body H and the surrounding disk, c, were held in Positive Ions emitted from various Hot Bodies. 653 place by the stopper at the bottom. The disk ¢ was of thin copper or platinum. It was adjusted to its place after the adjustment of the thermionic radiator H. This radiator in the experiments with gold, silver, palladium, aluminium phosphate, and iron, was in the form of a disk of approxi- mately 3 mm.” area. In the other experiments the form was a strip or a wire. The radiator was attached directly or indirectly to two copper wires shown in the figure. The gold disk was welded to the uppermost point of a platinum- wire loop, in order that the temperature measurements might be checked by the measurement of the resistance of the platinum-wire loop. The apparatus just described, together with the electro- meter and its connexions, were placed inside a galvanized iron box 24x24x18 inches, in order to be free from moisture effects which are so aggravating in our climate during the summer months. The top of the box was in four parts. Hach part turned down at the edge into a trough, so that when melted paraffin was poured into the trough, the top of the box became air-tight. This box arrangement was found quite satisfactory. Wires inside such a box do not need any additional shielding in order to be free from electrical disturbances. The electrical connexions are shown in fig. 2 (p. 654). The surface of the thermionic radiator was placed at H and was in the same plane as the surface of the lower disk L and from 0-5 to 1:0 mm. below the upper disk U. It was attempted to have the two disks so near each other that only a com- paratively small number of ions would escape to the guard- ring G. The upper disk was connected to one pair of quadrants of a Dolezalek electrometer and the condenser C through the keys k, and &,. The other pair of quadrants are seen to connect electrically to the following: the key hk, the guard-ring G, one terminal of the batteries which charged the electrometer needle, and to a variable point 2 in the resistance Rv. The last was a resistance of about 90 ohms across which there was a fall of potential of 2 volts. It was earthed at one end, as shown in the diagram. By adjusting the point « various potentials could be applied to the plate U, the values of which could. be read on a voltmeter placed at V. By separating the quadrants by the key &,, the rate of charging up of the electrometer indicated the current to the upper disk against the given potential. Usually about 24() divisions on the electrometer scale represented one volt. However, the method does not require that the sensibility be known accurately. The capacity of the electrometer system 654 Dr. F.C. Brown on the Kinetic Energy of the was varied by inserting in parallel a standard condenser. This was carried out by a key manipulated from outside the air-tight box. Fig. 2. ey : Lee LARTH EARTH IIIS The thermionic radiator was heated, indirectly most often, by an electric current. The heater was merely a single loop of platinum wire or a loop of metal foil, a rough cross- sectional view of which is shown in the diagrams. The loop supported the radiator and the heat produced by the electric current flowed into the radiator by conduction. This device enabled the emitting surface to be kept at the same potential. It was quite essential that this potential should be zero. This was accomplished by shunting the heater with the resistance A, of about 20 ohms. The shunt resistance was earthed at such a point that the magnitude of the thermionic Positwwe Ions emitted from various Hot Bodies. 6355 current was unchanged when the direction of the heating current was reversed. The heating current was regulated by a large and a small resistance r, in parallel. The heating coil and shunt together formed one arm of a Wheatstone- bridge mesh. In some instances the temperature of the thermionic radiator was checked by the resistance of the platinum heater, and in others the resistance merely indicated whether or not conditions were unchanging during the observations. The temperature was ordinarily determined by an optical method which within the working limits was perhaps subject to a possible error of 10 per cent. A standardized platinum wire of 271 cm. length was placed in a vacuum-tube. This wire was in one arm of a Wheatstone-bridge mesh (see fig. 2). The temperature of this wire was adjusted until it appeared to the eye to be at the same temperature as the - thermionic radiator studied. Then the two bodies were taken to be at the same temperature, and this temperature was read from a temperature-resistance chart for the standardized temperature wire. In the calibration, the fiducial points were taken at the temperature of the room, at the temperature of the melting of potassium sulphate, 1066° C., and at the temperature of melting platinum, 1745° C. [see paper by Richardson and Brown, loc. cit.]. Results of the Experiments. After the thermionic body had been properly adjusted in position, there was usually not much difficulty in obtaining the necessary observations in order to arrive at the value of the Kinetic energy. In no instance was there any trouble arising from a mixture of negative ions with the positive, such as was noted in the previous papers. This was mainly because the observations were taken at low temperatures and before the heating had been continued much over one hour. The heating never extended over more than five hours. All the materials studied showed a perceptible decay in the magnitude of the thermionic current after about 30 minutes’ heating. Of course this rate of decay was a function of the temperature. No attempt was made to determine just how it decayed at different temperatures. The pressure in the different experiments varied between 0°0001 and 0°1 mm. In a previous paper [loc. cit.] the author showed that within quite a large range the kinetic energy of the positive ions from platinum was practically independent of the pressure. Consequently, very little 656 Dr. F. C. Brown on the Kinetic Energy of the attention was given to adjusting the vacuum to any par- ticular degree, except when working with bodies that oxidized readily. Air was the only gas let into the vacuum system previous to taking observations. The amount of absorbed gas given out by the different thermionic radiators varied considerably. As this was only secondary to the investigation, the amounts of gas were not observed carefully. However, it was noted that silver and tantalum especially gave out much less gas than platinum or palladium. In carrying out the experiments a potential was applied to the upper disk, and the electrometer was allowed to charge up until there was a readable deflexion. The deflexion was noted and the current was taken as ae In case AV covered several divisions it was necessary to make a small correction, in order to allow for the variation in the potential that the ions went against. Often there was a difference in the magnitude of the thermionic current with the heating current direct and the heating current reversed. Pre- sumably, this was because the thermionic radiator was not at zero potential, but slightly above zero in one instance and below in the other. However, it is evident that the ther- mionic current for zero potential should be between the values found with the heating current direct and the heating current reversed,.and if the difference is not too large, the mean value cannot be far from the one desired. Gold. The gold used was in the form of a disk of about 3 mm.? area and 0°005 cm. thickness. It was welded to the top of a platinum-wire loop. The contact between the platinum and the gold probably extended over a length of 0°5 mm. If there was any fall of potential over the radiating surface of the gold, it was certainly less than 0:01 volt. In this particular experiment there was a natural charging up of the electrometer amounting to 1°5 mm. in 30 seconds, when the heating current was off. This was not noticeable after completing this one set of observations. The correction for this is made in the accompanying table. The temperature was first measured by the optical method previously mentioned. It was afterwards checked by measuring the resistance of the platinum-wire loop. The resistance at which the gold disk melted (1064° C.) was taken as a fiducial point. The table shows two sets of observations. For the lower temperature the optical method Positive Ions emitted from various Hot Bodies. 657 gave 1030 degrees absolute and the resistance method gave 973 degrees. For the higher temperature the optical-method gave 1190 degrees and the resistance method gave 1163 degrees absolute. In each case the mean of the values by the two methods was used in the calculation of the gas constant R. These determinations of the temperature are probably subject to less percentage error than that which might be expected to arise from the plane of the thermionic radiator not being in the plane of the disk. SCALE OF L0G, t 3 4 “2 . POTENTIAL - VOLTS. From the data given in the table were plotted curves 1 and 2 (fig. 3) showing the values of the current for different © 4 a a o 4 Electrometer Deflexions, = = 5 = s F 5 = mm, Oo | > a3) e one pies 2 eS fire oO @ H Io Sl! 2 a Laos © ef )asq Sji8fic|s 5 =e al et Heating current. = |e a ee sa | #@ | g2\|e¢ S |ha4 8 | 2 es a o oo : 5 3 ene ro ee | es Direct. Reversed. | S 15 SC] S 1 a | £973 S5sec. 11,9,9,105 9,9,11,10| 99) 96-02 0001 | 007 111030; 9 14, 17 17,15 | 58] 55-05 01 |10sec. 64,65,68 60,70,62] 33] 30/113| S 02 | 30sec. 80,78,85 80,62,68) 13] 10/216] 4 0:3 | 30sec. 5,38,60,40 43,40,50] 8] 5/31 | ~ 0-4 | 30sec. 3:5, 3°7, 3:1 2:5, 3:0,20]} 5] 21-40 OL | 01 [{ 37991 9 | See. 6.6% 70,55 | 126|126}-013 O1 | 10sec. 5:0 57 63) 538i01 || 0-2 |10sec. 22 2-4 23| 23|-2- I 03 | 30sec. 32 27 96/96/3 | oa 0-4 | 30sec. 1:0 15 40 | 40/4 | ~ 0°55 | 30sec. 06 0-9 2:0 | 20\5 658 Dr. F. C. Brown on the Kinetic Energy of the potentials on the upper disk. Curve 1 applies to the lower temperature of i000° absolute and curve 2 applies to the observations at 1177° absolute, and is plotted on a scale 50 times smaller than is the other curve. That is, the absolute magnitude of the current is about 80 times smaller Positive Ionization from Gold. at 1000° than it is at 1177°. Mean gas constant 4:0 x 103. This is not made clear in the table. The curves 1b and 20 show the corresponding logarithms of the current at the different potentials. From these curves and the other data the value of the gas constant R is easily calculated from the equation R= neV 7 log, 2 10 For 6=1000° ab. R= 4°2x 10° and for 6=1177° ab. R=3°9x 108. More reliance is placed upon the latter value, because the current was 80 times larger and was therefore capable of more accurate measurement. Positive Ions emitted from various Hot Bodies. 659 Tantalum. Tantalum was investigated under varying conditions. At first the thermionic current was measured from a filament of circular section 0°05 mm. diameter. This filament was taken from an incandescent lamp. The logarithm of the current when plotted against the potential was approximately a straight line which led to the value R = 9°6x10* for the gas constant. The mean kinetic energy was therefore apparently larger than the predicted value. A second filament was rolled into a strip with a thickness of 0-01 mm. and a width of 0°04mm. This strip was bent over a form with square edges, so that it had the form | The lower disk surrounded the upper surface, leaving an area of about 0°2 mm.’ free to emit ions to the upper plate. There was a fall of potential over this surface of probably 0:03 volt. The heating current was of the order of 0:05 ampere. The results are shown in the accompanying table. The curve 3 (fig. 4) is for the absolute temperature 1050 degrees and curve 4 is for the temperature 1273 degrees absolute. Tantalum. a : x 1 Gl | a 3| 2/2 |3 2 E E bs ; | Sai = = os s = | | eel ee la |! 8 =z 5 2 See ea Sey | ae SRE ° ea | 2 | Se eee | BB of Bele a | Ss (aoe | lek = ee ee: | 66 | 198x10 "| 0-014 | 0001 | -001 sae ee Mota | al es a a 0-11 | | 02; 29 | 145, | 0-205 | Come 1713.) abs, 0:30 04) 06 | 17, | 0-40 30108 0-01 002 |1270| 0 | 46 | 230x107"! 001 een 21, 0S», > | 0-108 Ree) i032") ly O18 Za 2a Ny 42. 0-21 | O3id. 2:3 | 19» 0-31 | 04) 380 | 67, 0-40 | } a a0 |) 8.4) oh 0 3°6 x 103 660 Dr. F. C. Brown on the Kinetic Energy of the The logarithmic curves are 3b and 4b. Most of the points are seen to lie close to a straight line. The resulting values of R (3:0 x 10° and 3°6 x 103) are not very concordant. As in the case of gold more reliance is to be placed on the value 3°6 x 10° obtained with the larger current. Fig. 4. 120 100 CURRENT. 80 60 SCALE OF LOG, 2 apres ~ =D : FOTENTIAL - VOLTS. Nickel. The thermionic current from nickel was investigated under essentially the same conditions as those last mentioned in connexion with tantalum. The ions were emitted from a nickel strip 0-004 cm. in thickness. The area of the emitting ty Positive Ions emitted from various Hot Bodies. 661 surface was about 0°6 mm.” The fall of potential across this surface was approximately 0°05 volt, and no portion of it probably differed from zero potential by more than 0°025 volt. The effect of the fall of potential along the strip was investigated by shifting the potential of the centre of the strip from zero to +°02 volt. Thereby the thermionic eurrent was increased by 10 per cent. This does not necessarily indicate that there would be an error as large as this in the value of R, because R depends on the way in which the current falls off as the upper plate acquires a potential. It is not easy to say how a small fall of potential would influence the distribution of energy. = ae aH Ss AIS aS yee | SCALE OF £06). U NL 0 | “2 : 7 pia POTENTIAL - VOLTS. From observations taken in the same way that the previous ones were, the current-potential and the logarithm of the current-potential curves were plotted. These are respectively 5 and 56 in fig. 5. The temperature was 1120 degrees 662 Dr. F. C. Brown on the Kinetic Energy of the absolute. The value of the gas constant is calculated to be 3°6 x 10°. Tungsten and Osmium. Because of the difficulty of gettiny many of the materials in the form of a strip, it was thought advisable to try a round emitting surface, such as the surface of a wire or a filament. A platinum wire and tungsten, tantalum, and osmium fila- ments were substituted for the strip or the disk. At 1650 degrees absolute a platinum wire ‘11 mm. diameter gave the observations represented by curve 6 (fig. 5). Fora tungsten filament similar observations at 1260° absolute gave the points marked [-], which are also shown roughly by curve 6. The corresponding logarithms of the current are shown in curve 6 0. ' The value of the gas constant for the platinum wire was 62x10? and for the tungsten filament was 8°0x10% We might readily ascribe the results to the form of the emitting surtace were it not for the results from osmium, which show the value of the gas constant to be R=2°5x 10%. The ob- servations in the case of osmium are shown by curve 8 and the corresponding logarithms in curve 8 0. Silver. The form of the thermionic radiator in the investigations with silver, palladium, aluminium phosphate, and iron was that of a disk. The silver disk was of the same dimensions as the gold disk previously described. It was welded to a palladium strip similar to the way the gold disk was welded to the platinum. Two series of observations were taken, using the same disk at different temperatures, in which the magnitude of the ionic current was 44 times as large in the one case as it was in the other. The mean energy was deduced from the curves in the ordinary way. It is given by R=3:0x 10% and 2°9 x 10°. There is no evident reason why these results should not be fairly accurate. The mechanical adjustment seemed perfect. Palladium. Palladium gave quite a large ionization at first. One series of observations were taken from a palladium disk at a temperature of 1170 degrees absolute. The value of R was 3:410%. The amount of gas emitted was also large. Positive Ions emitted from various Hot Bodies. 663 Silver. . | tes | Mean | eile ’|Pressure, Temperature, aia | Current seers oe Gas | farads, | ™™- | absolute. volts, |, volte. Serre 0001 | 002 | — 1020 0 | 163 | 017 | t ; 1 « 4 > ol 4-5 106 — | 0-2 12 2 | | 03 oe 3 3:0x108 art Ses Mie Fare Pee een ee ) | ‘01 | 00s | 1150 0 680 014 | ) | 01 | 216 ‘112 ae | -/93 2 | / | 03 25 3 | | 7 4 29103. | 0-4 an 0 1660 018 b SES 620 ll 0-2 290 20 ) 03 180 :30 : 0-4 | 125 -40 3-9 x 103 01 0-006 1190 | os ae 2 . 5 . 0-2 250 21 0-3 94 -30 0-4 35 -40 0°5 4 “50 34x 10° Aluminium Phosphate. After the palladium was heated for somewhat more than an hour, the thermionic current at zero potential decreased to about 20 per cent. of its initial value. Then a water paste of aluminium phosphate was placed on the disk and the thermionic current was measured as noted in the table. 664 Dr, F, C. Brown on the Kinetic Energy of the A second series of observations were made after a second coating of the phosphate had been put on by a slightly different treatment. The water was allowed to evaporate from the paste at room temperature, thus leaving an even white coating on the disk. The current was somewhat larger than it was in the first trial. The kinetic energy of the ions arising from the velocity components perpendicular to the surface of the disk, was, within the limits of error, the same as it was for the ions from the metals. That aluminium phosphate gives a larger positive ionization than do the metals was first observed by J. J. Thomson. Tron. chose, SACRO Cepesity pressure) Temperetre| Apia, Phermionil Moen | Vatu farads, ij ees: volts, | Arbitrary | volts. ? Units. 0001 — 1100 0 21:0 02 0-1 97 12 0:2 55 21 03 2:1 ‘31 0-4 ‘9 “4 4-6 x 10° 0001 0:005 1100 ‘ : 16°5 017 ; 8°6 12 0-2 51 21 0-3 2-4 3) 0-4 1s], "4 5'2< 108 01 01 1240 ) 1400 01 0-1 810 10 0:2 360 20 03 170 30 0-4 63 “40 4°3 x 10° | Iron. The positive ionization from iron was studied in essentially the same way as it was from the other elements. A silver disk was welded to a platinum heater and the iron disk was welded to the silver disk. This device was used mainly for convenience. The behaviour was somewhat irregular, but in every case the kinetic energy is seen to be larger than the normal value 3°7 x 10°. oe, 'y Positive Ions emitted from various Hot Bodies. 665 Summary of Results. | f Temper- Se ke Gas , ‘ Form o at zero | Vacuum | Radiator material. Radiator) 2t¥re poten Bail reser sea acidl 7, x 1022, /10 AEGIS tcl. N disk |{ 10231) 10 | 007 | 42 ; ae J Ee ee disk { 1163 60-0 | “Ol | 39 aver (1), 2.805) tae disk 1020 ‘8 “002 3:0 | Sue C4 anor rae? disk 1150 35-0 008 2-9 feed betcipainn J. ..3, Sede scetee disk 1170 25:0 "04 34 Aluminium phosphate(1)} disk 1230 100-0 iat 39 | Aluminium phosphate(2)} disk 1170 120-0 006 34 a nice vine sates strip 1120 2-5 093 36 Meret h) 2.08. st ee disk 1100 1-0 oe 4-6 Rese) 2 otc. .0danodeeneee disk 1100 & 005 52 UE es es disk 1240 ‘01 4:4 PEMANGM ..n.c60<- 000 srsar- wire 1695 ae “a 51 PORteGMrSUEM «223.0020 Scenes filament} 1150 10 0003 5:1 LT ES a enero filament | 1050 ed. "0005 9-6 PP RIELTIT oen sege Diaries strip 1050 10 002 30 (bc ea ae filament} 1120 30 nae 25 Discussion of Results. In interpreting the results of the measurements it is necessary to consider to what extent they are reliable. In our discussion we have a right to discard the values obtained with tungsten, osmium, and with tantalum and platinum wires, because the form of the thermionic radiator is quite different from that required by the theory. There is, how- ever, no obvious reason why the results with filaments should show such wide variations in the values of R. The obser- vations with osmium were taken after several hours’ heating, and negative ions may have been emitted simultaneously with the positive ions. This might account for the much lower value of R than those obtained with the other filaments. The other wires all gave values distinctly higher ‘than those obtained with plane surfaces of metal, and it seems reasonable to attribute the discrepancy to the curvature of the surface used. In the calculations of the mean energy certain hypotheses are assumed, and strictly speaking we are justified in these hypotheses and calculations only by virtue of the result. The theoretical value of the gas constant is taken from the equations R@=4nmvr? and RO= pv, and is easily calculated to be 3°7 x 10° for a unit volume of gas under standard con- ditions of pressure andtemperature. The lowest experimental Phil. Mag. 8.6. Vol. 18. No. 106. Oct. 1909. ZY. 666 Dr. F.C. Brown on the Kinetic Energy of the determination is R=2°9x 10? which is for silver, and the highest value is given for iron, which is R=5:2x 10%. The mean of all the experimental values is R=3°8 x 10°. This last fact is not inconsistent with the view that all the variations between the experimental and theoretical values are due to experimental errors. These errors may be largely due to the inherent structure of the thermionic radiator, such, for example, as might obtain in a very irregular crystalline surface. Considering the close agreement between the mean experimental value and the theoretical value of R, and that the disagreement is not very bad in any instance, we may state the following law to be true as a first approximation : The mean kinetic energy of the positive thermions emitted. from hot bodies is independent of the material from which the thermions radiate and varies directly as its absolute temperature. By referring to the summary it is noted that the varia- tion in the values of R for any one material is decidedly less than the variation in the values when different materials. are considered. for example, the mean variation of the values of R for each radiator separately is 5 per cent. from the mean value obtained, while the mean variation of the values of R for all the radiators together is about 16 per cent. from the value 3°8x10?. From these facts we may obviously make two deductions. First, the errors in the temperature determinations cannot be great enough to explain all the variations in the values of R. Second, there is no such change in the material with the time of heating or the intensity of beating as would warrant the variations obtained. Changes in the form or the size of the metallic’ crystals would be included in this. Of course these state- ments would not necessarily be true outside the limits of temperature and time prevailing in the experiments. We must look elsewhere then for an explanation of the variation of our values of R. If the temperature were not uniform over the surface, the conditions would be such as. the theory does not provide for. But as the area of the thermionic radiator was only 3 mm.’, and set up as it was, there should have been very little difference of temperature at any instant. To the eye the surface appeared to be at the same temperature all over. Such errors as would arise from the edge of the disk being at slightly lower temperature than the middle would tend to give relatively too many ions with small kinetic energy. The author is quite certain that the errors arising from unequal distribution of temperature would not be sufficient to explain the variations obtained. oe b i! a“ Positive Ions emitted from various Hot Bodies. 667 Without going into any further discussion here it is also improbable that the lack of uniformity in the electric potential of the disk could explain the variations. After removing the silver disk it was noted that a spot of some impurity covered about one-fifth of the area of the disk. The thermions that penetrated this layer would probably have had their total energy diminished. Thus the relative number of low-energy ions over the whole surface would have been too great and the value of R would have been too low. ‘This is the most plausible explanation for the low values given by silver. In some instances at least some ions escaped to the upper disk from the heater by going between the radiating disk and the lower disk, or by going between the lower disk and the guard-ring. But the number was probably small. It is difficult to say just what correction should be applied for such conditions. It was considered possible that the high values of R obtained in some instances might be accounted for in the fact that the disks do not fulfil the conditions of infinite planes which is required of them in order to apply the formula Particularly in the experiments with iron, which were the last performed, there was the most probability of a large number of ions escaping to the guard-ring, because of the large distance existing between the thermionic radiator and the upper disk. Therefore the error that should accrue if the distance of the radiator to the upper disk were 2 mm. was calculated. In equation (8), as given in the paper by Richardson and Brown (loc. cit.), the current to the upper disk is expressed as >. ayia (oon N95) i=ne( _ Fu) dug ( , F'(W)dW, where pg is the radius of the upper disk and a is the distance between the upper disk and the thermionic radiator. By substituting kmv?=2 and y=/«m, after putting in the values of F(u)duy and F’(W)dW, the above equation may be put in the form Po A Sts joke M4 (27+ Vz+2keV) = —= A eVdy. 2 > 2xeV 0 2Y¥ 2 668 Dr. F. C. Brown on the Kinetic Energy of the For different values of V and = curves were plotted 0 showing the relation between 2 and w. The area of any curve gave the total value of the current to the upper disk for the given potential on this disk. Such procedure showed that between 2 and 3 per cent. error should obtain in the value of the current at V=‘01, when the distance was jp=2 mm., and that the error for the same or less distance with a potential of 0-1 volt on the upper disk should be less than 1 per cent. Hyrrors arising from ions striking the guard-ring then should give an experimental value of R too large, but such errors could not account for values of R as large as were obtained with iron. In addition to the sources of error which we have men- tioned there are probably errors of a second order due to the photo-electric effect, to the electric and magnetic fields of the heating current, and to the high potential effect. In the photo-electric effect negative electrons should be given off from the upper disk of platinum. Ladenburg and Markau*, in their investigations, obtained currents from a small platinum disk of the order of 10—* ampere, by the use of intense ultra-violet light from a mercury-vapour lamp. They also showed that the current was larger with the shorter wave-lengths of ultra-violet light. As the positive thermions were obtained at very low temperatures it is quite improbable that the number of photo-electrons emitted could have furnished a current as large as 10-'° ampere, which should lead us to expect errors of a very small order in our results owing to this cause. Eigh Potential Effect. In the paper by Richardson and Brown (loc. ct.) mention was made of a peculiar effect, for which at that time there seemed to be no reasonable explanation. It was named the high potential effect, because of the way in which it first appeared. When a potential of 200 volts was applied to the upper plate, thereby drawing off thermions, the sign of which depended on the sign of the potential, there was, after the removal of the high potential, a thermionic current seemingly of the opposite sign, and this current would seemingly go against a potential as high as 75 volts. Often the imposed effect would remain 24 hours practically undiminished, pro- viding the thermionic radiator were not heated, but when ions were being given off from it the effect decayed rapidly, * Verh. der deutschen Phys. Gesell. x. no, 14, p. 562 (1908). Positive Ions emitted from various Hot Bodies. 669 the rate depending chiefly on the temperature of the radiator and the potential on the upper plate. It was found later that the quantity of electricity in this effect was not only of the opposite sign to that drawn from the radiator, but that it was also equal in amount. Many other exper iments were undertaken which seemed to lead to the unreasonable view that the ions drawn off by the high potential acquired additional energy from the high potential and held it in a potential form on the upper plate, and when the high potential was removed and the radiator was ghee this energy became kinetic. The effect was ultimately fonnd to be due to the presence of an insulating layer which had developed on the upper disk. The special parts of the apparatus were enclosed in a glass tube fitted on to a brass plate. It was made air-tight by sealing-wax covered over by soft wax. No doubt after a time some of the soft wax condensed on the upper plate, forming an insulating layer thereby, thus making a condenser with the conducting layer on one side missing. The high potential pulled the ions on to this insulating layer and held them, and then when the high potential was removed, these held the ions on the opposite side of the insulating layer. This left a difference of potential between the one side of the condenser and the hot radiator. Thus ions of the opposite sign were pulled across from the hot body until the bound ions on the condenser were neutralized, 7. e. until the so-called high potential effect had decayed. In one instance the quantity of electricity collected on this condenser in this way was sufficient to charge up a capacity of :2 microfarad to a potential of 1 volt. This required the thickness of the insulating layer to be about that of 20 hydrogen molecules. The capacity of this condenser was measured directly by the method of mixtures by bringing up to the surface of the upper plate a globule of mercury on the end of a copper wire. The mean of several determinations showed the capacity to be 2'1 x 10* £.s.U. per sq. em. of surface. To establish that the insulating layer was something condensed on the upper plate and not due to an oxide or impurity emitted from the platinum itself, several other experiments were carried out. Entirely new apparatus showed the effect after continued heating. When the upper plate was cleaned it would disappear for a time, but would always reappear in time, even when the purest resistance platinum was used as a thermionic radiator. Also when the surrounding atmosphere was hydrogen there was no essential 670 Dr. F.C. Brown on the Kinetic Energy of the difference in the results. The apparatus mentioned here was encased entirely in glass with ground joints. The joints were made air-tight by vaseline. The vaseline is no doubt what formed the insulating layer. For when an entirely new apparatus was made of platinum and glass and the whole was boiled in nitric acid, it was impossible to obtain the effect, even after several days’ intermittent heating. In the work described in our former paper there was probably a greater chance for errors arising from the high potential effect than there was in this work. In some of the series of observations we noted that the current fell off more rapidly than the theory warranted. This would have resulted had the condenser been charged almost to its capacity. Had the capacity been much smaller the errors might have proved serious. . The Charge carried by the Thermions. It is interesting to note that we can determine from the experimental curves the charge carried by the thermions. To do this, however, we must assume that the transiational kinetic energy of the ions has the same mean value as would the molecules of a gas at the same temperature. In curve 2, to which we have already referred, is given a current-potential curve for the thermions from gold. The area of this curve gives the total energy of all the ions which are emitted at zero potential. By dividing this value by the number of ions, the mean kinetic energy is obtained in the form eV=e IV> V iL = Phil. Mag. Ser. 6, Vol. 18, Pl. XIV. YucanD. | Phil. Mag. Ser. 6, Vol. 18, Pl, XIV. t Hie. 7, a Fie, 5. Fig. 6. 8 8 = ju = 0.26 itt f = 0.50 —+ Wo= 2-35 80 M »= O75 . 2 hee : a v= I. — : 60 73 100 ‘e H s Vv > i eo 80 0: ia 4 is 9 Ww 3B 2s Za —_—— a 3 i g i S =3\ Ne I a ag b= T i" Ay 20 A uniform 20 B striatet “Ke 10 20 30 ld anv I 20 30 40 50 io'am Current. Current, Fie. 8. & Ourrent ca. 0'8 10-° am, ey Fie. 9. 3 : & HBr HCl 700 Fie, 10, 120 600} 500} Z 100 : = 400 Jer p ; g / E 80 3 = Z © 300) | a 60 2.00 Cc ft Fsmean | Seman 40 Saturation current, 20 40 60 80 100 20 40 60 *80 joan. 20 Current. 04 08 12 16 20. mm / s Fia,!12. Fra, 13 1p =2.35 Fie. 11. 2 See 1.03 j 16 ii) = 0.55 = 6mm = f i ie 08 » 4 = 0.26 3 »= O05 » f _ Anode-fall. Woop. “aay zai NEGTD “ANTE Phil. Mag. Ser. 6, Vol. 18. Pl. XV. ‘P ‘OI Phil. Mag. Ser. 6, Vol. 18. Pl. XVI. WooD. Fia. 3. oF ul ‘ PL XVI 18, Phil. Mas. Sey. 6, Vol WILDERMAN,. Beste cy. Phil. Mag. Ser. 6, Vol. 18, Pl. XVIII. Rares 1 THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCLENCE. c () [SIXTH SERIES.] / : ; t A f fy NOVEMBER 1909. LXX. The Kinetic Energy of the Ions emitted by Hot Bodies. —Il. By O.W. Ricwarpson, W.A., D.Se., Professor of Physics, Princeton University*. ey the first part of this paper? the writer showed how valuable information concerning the initial kinetic energy of the thermions could be obtained from observations of the way in which they spread out in a uniform electric field. The method employed was to apply the electric field between two parallel conducting planes. In one of these lay a narrow straight platinum strip which could be heated by means of an electric current. The opposite plane was movable by small measurable amounts in a direction perpendicular to the length of the strip. It contained a narrow slit whose edges were parallel to those of the strip, and thus perpendicular to the direction of motion. The proportion, which passed through the slit, of the total number of ions received by the plane was measured for a series of positions of the former. It was pointed out that the apparatus used in the above investigation had been designed for another purpose, and was far from fulfilling several of the geometrical conditions laid down by the theory. The results obtained could, there- fore, only be regarded as approximate. The present experi- ments have been carried out with a new apparatus involving the same principles, but made larger and constructed so as to satisfy accurately the geometrical conditions. Itis believed * Communicated by the Author. + Phil. Mag. [6] xvi. p. 890 (1908). Phil. Mag. 8. 6. Vol. 18. No. 107. Nov. 1909. 2Z 682 Prof. O. W. Richardson on the Kinetic that difficulties of that character have been overcome, and the theory has been subjected to a much more exact test than before. The following experiments form a very satis- factory confirmation of the theory, but only under certain rather restricted conditions. It will be seen that under certain other conditions, which will be considered later, the curves obtained are not at all what was expected. The dis- crepancy, however, is probably due to causes lying outside of the present theory. The Apparatus used. The apparatus previously used has already been fully described*, so that it will only be necessary to specify the changes which have been made. The essential parts are shown in detail in figs. 1 and 2, in which the same parts are Hig ds A B NO HRS | F (Ss ERS Sioa / ee 3 F777, JEALLLS SS) MY “lhe i iL Z ’ NAYANNT om Ul Dsl LL acts TP ATL SFL SPT ISITE / Vf ff [Mt SLIM LEILA LL LALT LL LEMS VL denoted by common letters. These figures are drawn to scale, natural size, and represent respectively sections by vertical and horizontal planes perpendicular to the conducting planes A and B. The latter were the surfaces of brass plates of the thickness shown ; their length, which is not shown by the figures, was about 20 cm., and they were insulated trom each other by hard rubber blocks, into which they were * Phil. Mag. [6] xvi. p. 740 (1908). Energy of the Ions emitted by Hot Bodies. 683 screwed, at the ends. The platinum strips C (fig. 2) were cut by means of a dividing engine, so that their edges were accurately parallel. They were 0°02 cm. broad in some experiments and 0:04 em. in others. In order to cut the thin platinum-foil it was cemented on to plate-glass with shellac and afterwards loosened with alcohol. ‘The strips were welded to stout platinum plates about 2 mm. square, and subsequently boiled in nitric acid and distilled water. The plates were then soldered to the screws D, E. As the plates were of substantial thickness compared with that of the strip it was believed that this method would prevent the solder from diffusing into the hot strip during the experi- ments. When thus mounted the strip lay in the front of a narrow slit in the plate A of the shape shown by the trans- verse section in fig. 1. The narrowest part of this slit was about 0-05 cm. wide, and was a little behind the plane surface (about 0°01 cm.) as the edges were cut away, so as to give a very slight taper for about 0:1 cm. distance. The strip was set so as to be exactly parallel to the plane A, but the least bit behind it, probably about 6°005 cm. The object of these precautions was to prevent the ions emitted by the sides and back of the strip from straying into the field between the plates A and B. To the same end the slit was backed by an insulated plate F, which could be connected by the wire shown with the plate B. This ensured that whenever there was a field between A and B there was a field of the same sign and of somewhat greater magnitude tending to drag back the ions from the back of the strip. Trouble was experienced at first in keeping the strip C in 22Z 2 | 684 -Prof. O. W. Richardson on the Kinetic the plane in which it was supposed to lie, on account of the thermal expansion of the platinum. This was ultimately quite overcome by the device shown (chiefly) in fig. 2. One end of the strip was held by the fixed screw D insulated from the plate A by vulcanized fibre shown black in the figures. The screw E which held the other end was rigidly fixed in a bit of vulcanized fibre driven into the brass cylinder G, from which it was insulated as shown by the figure. This cylinder slid with a pin and slot guide in the outer brass cylinder H which just fitted it. It was pulled ~ back by a light indiarubber band which passed over the pin J. This passed through the cylinder and also over a hook (not shown) attached to the back of the plate A. The cylinder could be pulled forward by a thread passing over the brass rod shown in section at K. The whole of this part of the apparatus was enclosed in a wide vertical glass tube L and the thread passed down a horizonta! side tube M. ‘The rod K passed up another vertical tube N, which carried a mereury sealed ground stopper to which the rod K was rigidly attached. By turning the stopper the string could be wound or unw ound round the rod, and so the strip C could be kept just tight from outside the apparatus. Whenever the heating current was reduced it was of course necessary to unwind some of the string, otherwise the strip would snap in cooling. The opposite plane consisted of a fixed plate B, which contained a rectangular opening P (fig. 2). This extended the whole length of the plate B in a direction perpendicular to the section in fig. 2. The opening contained two plates O, O (fig. 1) which were accurately in the same plane and flush with the fixed plate B. They were almost as wide as the opening, but not in contact with it at any point. The part of them which is shown in fig. 1 is distinguished from the plate B by shading. They were rigidly and metallically connected together and insulated from the plate B. They were supported by the rigid brass carriage Q (both figures) which was pushed by the screw S along the ways R (fig. 2) which were attached to the fixed plate. The edges of the slit between the plates O, O were cut away as shown, so that all the ions which passed through the slit should pass into the copper box T. The number of ions reaching the plates and reaching T were measured simultaneously in the manner previously described*. It will be observed that only the ions reaching the middle centimetre of the plate B were received by either the testing plates or the slit, so that the error arising from the finite length of the hot strip weuld be * Phil. Mag. [6] xvi. p. 740 (1908). Energy of the Lons emitted by Hot Bodies. 685 small. The ions received by the testing system also were emitted by the hottest and most uniformly heated part of the strip, and irregularities in the electrostatic field due to the mounting of the ends of the strip were eliminated. The strip was shunted by a high resistance, and the potentials were applied at a sliding contact near the mid-point of this. The adjustment could be tested by the change in the ther- mioni¢ current under zero potential when the heating current was reversed”. ; The glass tube L was closed at each end by brass plates cemented with sealing-wax. The necessary connexions to the exterior were made in an obvious kind of way and pre- sented no novel features. To exhaust the apparatus a Gaede mereury-pump was used and worked continuously. This enabled the screw 8 to be connected to the head outside by an axis passing through a mercury-sealed rubber and brass joint, in which it turned freely. The air leakage was always small compared with the gas evolved when the strip was heated. The connexions to the pump and McLeod gauge were made with short wide tubes. Even at the highest temperature the pressure could always be kept below -004 mm., and in some of the experiments at lower temperatures the pressure registered on the McLeod gauge did not exceed ‘0004 mm. The evolution of gas when the strip was heated soon reached a steady condition, when further heating seemed to produce little or no diminution in the rate at which it was given off. The screw head, which was below the main ap- paratus, was provided with a toothed wheel device for regis- tering the whole number of turns, and was also divided into tenths so that fractions could be measured. One complete turn was equal as before to ‘0635 cm. Zero Electric Field. It was pointed out in the first part of this paperf that in the particular case when the plates A and B are at the same potential, so that there is no electric field between them, the~ value of the ratio of the current through the~slit to ‘that which reaches the plates is given by the very simple relation Wb=(sen) > ++ @ where I is the ratio when the slit is in any position distant z from the central symmetrical position, for which I has the maximum value I, and z is the distance between the strip * See Richardson and ee, ae wi [6] xvi. p. 353 (1908) Tt Loc. cit. Equation (14), p. 686 Prof. O. W. Richardson on the Kinetic and the slit and plates. I) is thus the value of I when «=0. This formula presumes that the widths of the strip and slit respectively are negligibly small, a condition which was satisfied in the experiments. For the deduction of formula (1) it will be sufficient to refer to the former paper. It follows directly from the assumption that the electrons leaving the metal, do so with a distribution of velocity, which is identical with that given by Maxwell’s law for the particles of a gas of equal molecular weight leaving the same surface at the same temperature. The fact that the normal component of the velocity of the escaping electrons is that required by Maxwell’s law has already been proved by Richardson and Brown*. If the present experiments confirm formula (1) it will be legitimate to conclude that the velocity components parallel to the emitting surface also obey Maxwell’s law, and the observed disagree- ment will set a superior limit to the amount of deviation from the requirements of the theoretical law. The apparatus used in this part of the investigation was not quite the same as that shown in figs. 1 and 2. The slit D was not cut in the plate A. Instead of lying in the slit the strip C was 1 mm. in front of the conducting plane A, and it was, therefore, only 4 mm. distant from the plane B. Otherwise the arrangements were the same as those described above. It was intended at first to have the strip mounted in front of the plane in this way throughout the investigation, but it was found that when a difference of potential was applied between A and B the experimental curves instead of having only one maximum had wings on each side of it. These were clearly due to ions from the back of the strip being drawn out by the electric field. The arrangement with the slit D was adepted to avoid this effect and was found to be successful. In the case where no electric field was applied there could be no objection to the strip being in front of the plane. The results of the experi- ments with the apparatus arranged in this way, which were made with great care, have been retained, and are those which are described in detail below. In order to be quite sure, however, fresh experiments were made after the slit had been constructed, and the position of the strip changed. These were found to agree satisfactorily with the results obtained with the first arrangement. The temperature of the strip was regulated by keeping its resistance constant. The observed resistances also served to measure the temperature, the resistance corresponding to * Phil. Mag. [6] xvi. p. 358 (1908). Energy of the Ions emitted by Hot Bodies. 687 the melting-point of potassium sulphate being subsequently observed and used as a fiducial point. It was not possible to vary the range of temperature over which observations were taken much; since at lower temperatures complications were caused by the presence of positive ionization in amounts comparable with that of the negative, whilst at temperatures slighly higher than those used the negative ionization became too big to be measured en the electrometer when all the available capacity was inserted. In addition to this the theoretical conditions are vitiated in the case of large currents as the theory neglects the dynamical action of the electrons on each other after they have left the metal. The writer never succeeded in getting the conditions so that the proportion of the thermionic current which passed through the slit was independent of the direction of the primary heating current. No matter how the earthing-point in the shunt was adjusted the ratios were all invariably from ten to twenty per cent. greater with the heating current in one direction than in the other. There are two effects de- pending on the direction of the heating current which are not altogether eliminated in the apparatus used. These are the effects of the electrostatic force parallel to the length of the strip arising from the fall of potential required to drive the heating current and the magnetic force in a perpendicular direction arising from the same current. Both of these will give the ions a drift parallel to the slit which will reverse in direction with the current. This ought not to make any difference provided the slit, the plates, the box-shaped elec- trode, and the strip are perfectly symmetrical about a vertical plane down the centre of the apparatus. These conditions were satisfied, so far as was possible with an apparatus of this kind in a reasonable time, but there was always a small amount of asymmetry arising from defective mechanical construction. There is no doubt that this explanation is correct, as there was no disagreement within the limits set by the errors of observation in the relative values of the ratios for different positions of the slit in the different experiments. This will be brought out quite clearly when the actual ex- perimental data are tabulated (see fig. 3, p. 688). Formula (1) in fact only involves the relative values of the ratios, so that it will hold whether asymmetry of this kind occurs or not. For this reason the further refinement of the mechanical structure of the apparatus was not proceeded with, as it was felt that it would involve an amount of labour and time which would be quite incommensurate with the benefit to be ex- pected. The point is that this asymmetry, after all, is not 688 Prof. O. W. Richardson on the Kinetic very big, and there are many other points of a much more pressing character which can be satisfactorily investigated with the apparatus in-its present state of development. Hie, 3s ‘ ce Led H : | : = a bo . [ ease a Sy a sae a S: | Le | N fee) (fo), {@) Sie Sees Hee ee = asks a2 alae Pree Na PASSING THROUGH SLIT ARBITRARY SCALE) FROPORTION & nt R : | | ON CLEGS MemaS ioe) MET i6 Ia 20 en Mea coliean Sonlise oa SomONnenE DISPLACEMENT OF SLIT (/=*0635 cm) The results of a typical experiment will now be given:— The electrometer suspension was a quartz fibre, and the needle was charged to a potential of 80 volts. The instru- ment then gave a deflexion of 437 divs. for a volt, and the spot was a fine line about one-fifth of a millimetre wide, so that tenths of a division were read. It is necessary to use a sensitive electrometer, otherwise the back electromotive force due to the charging up of the plates vitiates the results. The capacity attached to the slit-electrode was 0°01 microfarad, that attached to the plates 0°3 microfarad, and the electro- meter and its connexions had a capacity of 180 cm. The capacity for the slit-readings was therefore 9 x 10?+ 180 cm., and that for the plates and slit together 27 x 10*+9 x 10 +180 cm. The temperature when the readings were taken with the current direct was 1034° C., and the pressure about °009 mm. of mercury. When the current was reversed the temperature was 1069° C., and the pressure varied from ‘003 to°005 mm., the average pressure being about ‘004 mm. The temperature estimations are probably only accurate to within about 20°. The values found are given in the subjoined table. 689 vés. y of the lons emitted by Hot Bod Enera x ql. Position of Screw. Turns. OG A ne: LO Suse Baths MS scseoee rie Osea 1G ae. | LCR ate eae y 1 ee ey ae are, | I ae ee 4 1) ae nite ie. Oo Re cai ae, LD gee, nen SO eC aah A) eee avi ihn os Current Direct. eS yee ee —_-- +) Aa 2. ob 4, 5, | s | Deflexion ; OT ce | ‘or es | Seal pias ASOT Sith ands elatese oS oe a ee | ae | 10:7 100 075 86} | 11:0 99 11 126 236 98 241 19'1 . 40-0 | 96 ‘416 | 30-0 | 73:4 94-9 ‘779 53:0 | 105 94-4 1114 83:5 | 119°5 92°8 1:288 | 85°3 | 126°2 91:8 1:377 | 86°4 | 125 | 91-6 1365 84:5 | 1142 91 1:258 | 78:8 | 98 | 89:4 1095 | ard | 68°5 89 ‘770 | 39°4 41-0 886 ‘468 245 Poy OO¢ te } 88:8 { oun 16-2 140 86.5 162 | 86 66 87°6 ‘O75 | 45 | = ae 6. 7. e Ratio of Slit Means of hondeat to Total. (4) and (6). | sstedihigde 144 | , 145 } é | x ‘178 AD S|: Sea ORe 302 27 22 509 -46 | "425 ‘064 ‘87 ) 86 1446 1:28 | 1-27 1-635 1-46 |= ae 1-719 1°55 Pee 1389 baa S| 1-154 1125 | 122 ‘176 ‘773 | ‘827 478 47 | ey 313 296 ) ‘21 ‘177 ‘17 | ‘O97 099 Lin bea 045 690 Prof. O. W. Richardson on the Kinetic Columns 1 to 4 refer to a set of readings with the current — in one direction, called direct, and columns 5 and 6 to a set in the opposite direction. Column 1 indicates the relative displacement of the slit as measured on the screw-head. Columns 2 and 5 give the readings in scale-divisions due to » the thermionic current through the slit in 380 seconds. Column 3 gives the deflexion of the electrometer after the condenser attached to the plates has been connected with the electrometer. The numbers are therefore proportional to the charge received by both the slit and the plates in the same time-interval. The numbers in column 4 are obtained by dividing the numbers in 2 by the corresponding numbers in 3. Column 6 gives the corresponding quantities for the experiment with the current reversed. These ratios are therefore proportional to the fraction of the total current to the plates which passes through the slit; they are not identical with this on account of the capacities being different. To get the actual fractions it is necessary to multiply the values given by the ratio of the two capacities used in the two cases. In these experiments this multiplier was 102/3102. It will be observed that the values in column 6 are throughout somewhat greater than those in column 4. The causes of this want of symmetry have already been discussed. To eliminate it as far as possible the mean of the two series of values are given in column 7, whilst column 8 contains the values of I/Ip calculated from formula (1) for the particular value, <="04 cm., of the distance between the strip and the plates which occurred in these experiments. It will be ob-. served that the formula does not involve any arbitrary con- stant except in so far as Io, the value of the ratio of the two currents at the central maximum, may be regarded as such. Thus all the other points are determined as soon as the height of the central maximum is given. The agreement between columns 7 and 8 is very satisfactory near the middle of the table when the values of the ratio are considerable ; but it is not so good further away from the centre where the ratios are small. The extent of the agreement can be gauged better when the results are exhibited graphically; and it is con- venient to postpone further discussion of theresults until that has been done. In order to exhibit the results graphically it is convenient to multiply each series of ratios by a common factor, so that they all have the same maximum point. This enables us to test the assertion made above that the differences which arise when the current is reversed disappear when relative values only areconsidered. For in that case if each series is brought Energy of the Ions emitted by Hot Bodies. 691 to the same maximum by multiplying all the terms in it bya common factor, then all the points of all the different series should lie on a common curve which should be identical with that predicted theoretically. To test this the results of the experiments recorded in the foregoing table have been plotted in fig. 3. The method adopted has been to first plot the numbers in column 4 against those in column 1. The points x thus obtained are found to lie on a smooth curve witha maximum ordinate of 1°39 at 204 turns. The theoretical curve i ee oy, Be acres * | which passed through this point was then constructed, the distance z during the experiments being 0'4cm. This is the continuous curve shown in fig. 3. In addition to the set of observations corresponding to the current direct, those with the current reversed are also shown in fig. 3. The values in column 6, however, have not been taken as they stand, but have all been multiplied by a common factor so as to reduce the maximum to 1°39. They can thus be compared with the current direct at the same time. They are shown by the points marked thus © in fig.3. ‘The series of points marked thus A correspond to another set of observations also with the current reversed, in which a somewhat higher temperature and larger capacities were used than in the preceding. These again have all been multiplied by an appropriate factor to bring the maximum to the value 1°39 corresponding to the first set of numbers. The exact data corresponding to fig. 3 are :— (1) Full curve represents the theoretical curve 2X 3 I=1- ( id ® 39 ue (2) x Current Direct. Temperature=1034° C. Capa- cities used =*3 microfarad and ‘01 microfarad. Mean deflexion for plates and slit 93 divs. in 30 secs. (3) © Current Reversed. Temperature =1069° C. Ca- pacities *3 and ‘01. Mean deflexion 53 divs. in 30 secs. (4) A Current Reversed. Temperature =1098° C. Ca- pacities 1 microfarad and ‘04 microfarad. Mean deflexion for slit and plates 68 divs. in 30 sees. The mean deflexions have been given so that an estimate may be made of the total thermionic current to the slit and the plates. 692 Prof. O. W. Richardson on the Kinetie Reverting to fig. 3, we see that the points A and © are identical within the limits of experimental error. This justifies the reduction to a common scale by multiplying each series of observations by a suitable factor. We also notice that a smooth curve drawn through the points © and A would also include the points x within the limits of experimental error. This proves that the percentage change in the ratios produced by reversing the heating current is independent of the position of the slit ; or, in other words, the ratios I/I, of the thermionic current I through the slit in any position to its value I, in the central position is independent of the direction of the heating current. This fact has already been stated ina rather different manner. It will be observed that the different observations shown not only agree with one another, but they also agree fairly well with the theoretical curve. In fact, in the central part of this figure from «=12 to e=26 turns the agreement is within the limit of the errors of observation. Outside these limits the deviation is too great to be explained in this way, and it is found that in this case the obsarved current through the slit is invariably greater than the calculated. There are several ways in which the current at some distance from the centre might become too big. The normal thermionic current is much greater near the centre, and scattering of the ions by the small quantity of gas present would have the effect of making the current through the slit too big at points further off. However, a comparison of the experimental results failed to reveal any connexion between — the divergence of the curves and the gas pressure, which varied considerably in the different experiments. It is im- portant to notice also that after the platinum strips have been heated for a little while their surfaces are no longer plane, owing to a recrystallization of the metal. Under the micro- scope the originally smooth rolled foil is found to have developed a well-defined crystalline structure, which begins to make its appearance after the foil has been heated a very short time. It is difficult to decide how much ought to be allowed for this; it will evidently become much more im- portant when there is a normal electrostatic field between the two planes. The writer is inclined to the view that the effect arises from the scattering of the electrons by the plates rather than the gas. It seems quite possible that a much more marked effect when a normal electric field is present arises in the same way, and the question will be reconsidered later on in that connexion. Our general conclusion, then, from the results exhibited in Energy of the lons emitted by Hot Bodies. 693 fig. 3 is that the agreement between the observed results and those predicted theoretically * is a satisfactory one. We may therefore infer that the electrons emitted by hot platinum have the distribution of velocity required by Maxwell’s law to a very considerable degree of accuracy. Tt has already been stated that similar results were obtained after the slit had been cut in the plate A and the strip arranged so that it was a little behind but almost flush with the surface of A. Under these circumstances the value of z, the distance between the strip and the plates, was increased to 0'5cem. The mean of two series of observations taken with the heating current in opposite directions at an average temperature of very nearly 1100° C. (measured as 1102°C.) gave the following values of the ratio of the charge passing through the slit to the total at the distances, expressed in turns of the screw, stated :— Fesiawee os oss: 0 5 10 13 15 V7 18 Observed Ratio ... ‘12 17 Db 5d ‘88 1:16 less: Calculated Ratio... ‘07 NGF “*B4 ‘61 -90 1:23 1:44 BARNES Sons 19 20 DA 2D 23 a! 40 Observed Ratio ... 1:59 1-68 E66. kor) S86 08 03 Calculated Ratio... 158 1:64 164 1°36 140 861-22 ‘09 It will be seen that the results exhibit a satisfactory agreement with the new calculated values corresponding to z=0°5 cm. ‘The pressure recorded in these experiments only varied between ‘0021 and 0027 mm. If we refer to the previous paper we see that formula (13) (loc. cit.) may be written Lym= £. . dye acest Fad besarte | C2) In this formula zis the distance of the strip from the plates, & is the width of the slit in the Jatter, and n, is the total current received by the plates and slit. If the slit extended the whole way across the plates and the box behind were set so as to catch every ion which passed through the latter, then I, would be the current through the slit. In the present experiments the width of the plates was ‘854 cm. and that of the box only ‘60cm. This would indicate that the experi- mental vaiues of I, ought to be multiplied by °854/°6 before being substituted in the above formula. The correction will, however, be somewhat less than this, as some of the ions which passed through the slit beyond the outer edge of the * Phil. Mag. [6] vol. xvi. p. 909 (1908). 694 Kinetic Energy of Ions emitted by Hot Bodies. box would probably reach the outside of it. As the exact amount of this correction is somewhat uncertain, it will be most satisfactory to see first what is obtained when it is dis- regarded altogether. Let us calculate the values of I)/n, for each of the three sets of experiments recorded in fig. 3. For the observations with the current direct marked x the capacities were ‘(1 microfarad for the slit and *3 microfarad for the plates. The ratio of the deflexions at the centre of the scale was 1:39. The value of I)/n, is therefore heen ee gees Ueny sy ics mo OTR 104 9x Se With the current reversed and the same capacities, points marked ©, the maximum was 1°39/°81, so that I,/n, = "0564. With the current reversed and the capacities ‘04 microfarad and 1 microfarad respectively points marked A the maximum was 1°30, so that I,/my="0502. The mean of the two values of I,/n, with reversed current is ‘0534, and of this with the value with the current in the opposite direction *0496. The value of £/2z in this experiment was °04/2 x -4=°050. Thus without allowing for the correction considered above, there is complete agreement between the two sides of the equation. As the correction will probably amount to 20 per cent. and possibly somewhat more than that, it seems clear that for some reason or other the slit is receiving more than its share of the thermions as compared with the plates. This result is readily explained on the supposition, that some of these electrons are reflected when they strike the plates, which was made to explain the divergence between the expe- rimental values and the calculated curve in fig. 3. These results would suggest that from 20 to 40 per cent. of these low-speed electrons are reflected when they strike the plates, but the arrangement used was not suitable for obtaining an exact numerical estimate. Finite Electric Meld. A great many experiments have been made with this appa- ratus with a difference of potential applied between the plates A and B. As regards agreement with theory, the results obtained do not show any improvement over those recorded in the previous paper. In fact, with the improved apparatus On the Kinetic Theory of Matter. 695 the negative electrons show a very definite spreading out in excess of what is required by the theory. This was indeed shown by the older experiments ; but one could not be so certain of it, owing to the limitations of the apparatus then used. The matter is being investigated further on the view that it is due to reflexion of the electrons from the plates, and it would be unprofitable to discuss it further until more expe- riments have been made. The experiments in this direction have not been confined to platinum, but have included an infusible alloy called nichrome as well. Conclusions. The chief point of this paper is to be found in fig. 3, which exhibits a very close agreement between the distribution of the electrons from a hot platinum strip, in the absence of an external electric field, as found experimentally, and that which was predicted in the former paper on the hypothesis that the electrons emitted from the strip left it with a distribution of velocity equivalent to that required by Maxweli’s law. In conclusion I wish to thank my assistant Mr. Cornelius Bol for his assistance in carrying out these experiments and for drawing the diagrams of the apparatus used. | f& ay. ie LXXI. Notes on the Kinetic Theory of Matter. By O. W. RicuarpDson, /.A., D.Se., Professor of Physics, Princeton University *. | eae present communication is a brief discussion of the expression for the probability F(w)du that a molecule leaving any surface in a gas should havea velocity component perpendicular to that surface which lies between u and w+du. The value of this probability is By ee Be Pw bye, ie, nl . es 3 . where m is the mass of the molecules and Tk their mean translational kinetic energy. This result was stated ina paper by Richardson and Brown + on the Kinetic Energy of the Negative Electrons emitted by Hot Bodies. It was given there without deduction as the writers were under the impression that it was a familiar result. A number of persons, however, who have taken an interest in the paper * Communicated by the Author. + Phil. Mag. [6] xvi. p. 357 (1908). 696 Prof. O. W. Richardson on the have had difficulties with it, so that it may not be out of place to give the deduction here. It is important to remember that the above expression does not represent the probability that the velocity of a molecule selected from a given volume at any instant should lie within given limits. The selection has to be made from among those molecules which leave a given surface in a given time. It will probably conduce to clearness to get rid of the notion. of probability altogether and to use instead the number N(w)du which leave unit of surface with a velocity component perpendicular to the surface between u and u+du. If formula (1) is true it is clear that N(ujdu=2hmuNe du. > where N is the number of all sorts which leave unit area in unit time. It is necessary therefore to prove formula (2). It is proved in practically every text-book of the Kinetic Theory of Gases that if n is the total number of molecules of any gas per cubic centimetre at any instant, the number which leave unit area of surface in unit time with components of velocity perpendicular to that surface between wu and Wee ATA ES NQvdu=n() uerbmedn . aetna Whence oP, * a n N= i Nau = gee Substituting for n in (3) in terms of N we get N(u)du = 2khmuNe-*™du, whence (1) follows. It is interesting to observe that this expression is un- changed when the geometrical surface to which we have so far confined our attention is replaced by a physical boundary in escaping through which the molecules have to do work. The author has shown* that the velocity component wp normal to the surface after escape is related to the correspond- ing quantity wu, impinging on the surface by the equation ; D ur=uze— — where m is the mass of the molecule and @ is the change in the work function in passing through the surface. The * Phil. Trans. A. vol. 201, p. 501 (1908). Kinetic Theory of Matter. 697 number of particles escaping per second for which w lies between wp and w+duy will be the same as the number of those striking the surface per second inside for which w lies between zw and uw -+du,, where 2 < ad Up? = Uy? — ae and = updup=uduj. ? This is, from (3), = km\2 aK No (eo) dup =n = u,duye—#mn* ~*~ 2 =n ( —) wdue-eruer+—*), | (4 _ 0 0 mv ( ) where x is the number of molecules per c.c. inside the boundary. The total number N, which escape per second will be those for which wy is greater than zero, i. e. km (” 2 No=n i ) i, i datge emiucrt | ®) ee Substituting for n in (4) we therefore have N (uo) det = 2kmugN pe—*”™"" dug, (9) whence F (up)duy= Nato == Dkmuge dup.» (6) No It follows that the distribution, among the particles leaving any surface, of the component of velocity normal to the surface, is independent of the amount of work done by the particles in crossing the surface, including the usual case where the work has the particular value zero. The application of this result to the evaporation of electricity, or thermionics, has been considered in numerous previous papers. It is, however, equally applicable to ordinary molecular evaporation. If we suppose, as in the theory of surface tension, that the molecules of a liquid, in order to escape into the vapour, have to get through a skin in which they are acted on by forces which on the average are directed along the inward normal: then it follows from the above calculations that the proportion of the molecules escaping in a given time, for which wu lies between wu and u+du, is Zkmue~*"*du. Itis therefore independent of the Phil. Mag. 8. 6.. Vol. 18. No. 107. Nov. 1909. 3A 698 On the Kinetic Theory of Matter. forces in the surface layer which determine the latent heat of evaporation, and is the same for the molecules leaving the liquid as for any other surface drawn in the vapour at the temperature of the liquid. The distribution of the components of velocity parallel to the surface will be unaltered by the passage of the particles through it. This is clear even if, as is presumably the case, the component ®, of the work function parallel to the surface deviates, in individual instances, from its average value zero. For, for each class of paths for which ®, has a given positive value, there will be an equal number for which it has a negative value, so that the change introduced by those which are accelerated parallel to the surface will just be com- pensated for by others which are retarded. The distribution of velocity among the particles leaving any surface will therefore be completely independent of the work done in passing through the surface. As a particular case it follows that the distribution of velocity among the molecules escaping from a liquid by evaporation will be just what is proper to a gas of the same molecular weight at the temperature of the liquid (or its vapour). The escaping molecules will be in complete statistical equilibrium with those in the surrounding vapour. It is necessary to lay stress on this point as there is a wide- spread heresy to the effect that, since the molecules have to do work in escaping from the liquid, their average kinetic energy in the vapour will be less than in the liquid ; so that the surface layer, with its force directed towards the interior, will act in some sort like Maxwell’s Demon, letting only the quicker molecules through. When this argument is kept to the qualitative plane it may be used to demonstrate a violation of the second law of thermodynamics. The © preceding considerations show that there is nothing in this. It may be permissible to add that both the case of a liquid and the surrounding vapour and that of a conductor and the escaped thermions which are in equilibrium with it are particular examples of a general theorem in the kinetic theory of matter which states that the mode of distribution of kinetic energy among the ultimate particles of a system is independent of the potential. energy of the part of the system in which they occur (Jeans’ Dynamical Theory of Gases, p. 78). The potential energy only affects the con- centration of the ultimate particles in the different parts of the system, the average value and mode of distribution of the kinetic energy being unaffected. [ 699 ] LXXIT. Alternating-Current Spark Potentials and their Rela- tion to the Radius of the Curvature of the Electrodes. By JOSEPH DE Kowatuskr, Ph.D., Professor of Experimental Physics at the University of Fribourg, Switzerland, and Utrico J. Rapper, Ph.D., Assistant in Physics at said University *. [Plate XIX.] Introduction. HE phenomena of the disruptive discharge, and the measurement of the respective spark potentials, have long occupied the attention of physicists. In an excellent work by J. J. Thomson+, we find an extensive enumeration of the principal works on this subject. A series of accurate measurements have been made by Lord Kelvin, Paschen, Baille, Heydweiller, Orgler, de Kowalski, Voigt, Algermissen, and C. Mueller, all with direct current. The measurements carried out up to the present time with alternating current were more or less of a technical character, with the possiple exception of Steinmetz{. But with our present improved methods these can to-day be carried out more accurately, and this has furnished the motive for the following work. We have endeavoured to find a method of the greatest accuracy. It seemed to us that a method should give results of a higher degree of accuracy than those carried out up to the present (1 per cent. to 2 per cent.), in order to justify theoretical deductions. In the first part of the work, the methods applied for obtaining this accuracy are set forth, with the results of the direct measurements. In the second part, these figures are utilized in examining more closely the theory of the relation of spark potentials to the radius of curvature of the electrode, as expounded by the leading physicists. * Communicated by the Authors. Paper presented on the 8rd of May at the Imperial Academy of Sciences, at Cracow. + J. J, Thomson, ‘Conduction of Electricity through Gases,’ p. 366 (1906). t C. Steinmetz, Trans. of Amer. Inst. of Elec. Eng. vol. xv. p. 281 (1898). 700 ~~ Prof. J. de Kowalski and Dr. U. J. Rappel on Parr I. Method and Apparatus. The circuit was set up in accordance with the diagram presented herewith (fig. 1). B represents a storage-battery, - en capable of giving from 110 to 130 volts. M is a direct current motor. Suitable rheostats are inserted in the circuit of the armature and fields. Coupled directly with the motor is a 3°5 K.w. monophase generator G, which was specially constructed for these measurements by the Comp. éi. de Geneve. Its voltage curve very nearly approaches a sine- wave, as is evident from the oscillogram reproduced in fig. 2. Fig. 2. The current from the generator is fed through a rheostat to a step-up transformer T, constructed by the firm Brown, Boverie & Co., of Baden, Switzerland. The indicated ratio of transformation is from 70 to 50,000 volts. V and A indicate respectively a voltmeter and an ampere- meter, which were simply used for orientation purposes, and not for the measurements. Alternating-Current Spark Potentials. 701 The high-voltage terminals are connected with the dis- charger, represented on Plate XIX. This piece of apparatus was specially constructed for this series of experiments by the Société Génevoise pour la Construction d’Instruments de Physique, according to the plans furnished by us. Uf the two marble columns carrying the electrodes one is attached to a block of ebonite, which in turn is firmly bolted to a cast-iron frame; the other is similarly constructed, but is bolted to a rider, capable of being displaced horizontally by means of a threaded screw. This screw was constructed by the Société Génevoise with their customary care, and its pitch guaranteed to be exact to the hundredth part of a millimetre. Parallel to the screw is a metre-scale along which slides a little brass plate attached to the rider. This little brass plate carries a fine scratch, enabling one to read off on the metre red the number of entire millimetres. Attached to the outer end of the screw is a circular disk of brass, having its circumference divided into 100 equal parts, enabling one to read exactly to the hundredth part of a millimetre. Joined to the screw of the discharger, by means of a ball and socket joint, is a cylinder of ebonite, having a diameter of 4.cm. anda length of 85cm. The other end of this ebonite rod is furnished with a disk for measuring exactly to the hundredth part of a millimetre, and also with an ebonite crank for turning the screw. This appliance enables one to move the screw and take the exact measure- ments, without danger to the operator from the high potential of the discharger. The marble columns contain two metallic cylinders carefully centred: these are furnished with screws, upon which the various spherical electrodes are to be screwed. Most of the previous determinations of spark potentials were made by setting the electrodes a given distance apart, and then raising the voltage slowly until the spark jumped. This method of procedure rendered the exact reading of the difference of potential very difficult because of the failure of the instruments in responding quickly enough to the change of potential; thus the individual readings differed greatly. To eliminate this source of error we proceeded in the follow- ing manner. The ends of the wires leading to the spherical electrodes were joined to a precision-milliamperemeter of Siemens and Halske by means of suitable resistances. One of the electrodes was kept grounded. When the milliampere- meter readings were definite and constant the electrodes were brought closer by moving the one that was grounded. In this way we were enabled to obtain results whose maximum 702.“ Prof. J. de Kowalski and Dr. U. J. Rappel on difference for the same reading of the milliamperemeter was Q°2 per cent. The phenomena of dilatation, observed by Warburg* and others, was eliminated by the use of an arc-lamp. The alternating current milliamperemeter was carefully calibrated. It was capable of indicating directly to 30 milli- amperes, but the region of the scale between 10 and 27 was exclusively used, because the readings here could be more exactly taken to the hundredth of a milliampere. The resistances used were of manganese wire and free from self-induction. Measurements undertaken previously with the pendulum of Helmholtz proved that the self-induction and capacity of these resistances were so small that they could practically be neglected. The resistances were re- peatedly calibrated by comparison with normal resistances, the latter having been calibrated by the Phys.-Technische Reichsanstalt. The total value of the resistances at our dis- posal was 1298800 ohms, and was capable of carrying a current of 30 milliamperes for a length of time without being appreciably heated. The spheres employed as electrodes were most carefully made by the Société Génevoise. There were 6 pairs of spheres with the following diameters:—2, 3°85, 10, 15, 20, and 30 cm. Measurements taken with the cathetometer showed that the irregularities in the construction did not exceed 0-2 mm. We make use of this opportunity to thank the Société Génevoise for the splendid execution of this difficult task. At each series of experiments the zero for the distance of the spheres from each other was determined, likewise the barometer and thermometer readings. Evidently the number of amperes in the high-tension circuit, multiplied by the number of ohms, gives the value of the effective voltage, whereas to determine the maximum voltage one must know exactly the curve of tension. For this purpose an oscillograph, constructed on the principle of Blondel, by the firm Siemens and Halske, was utilized. The high periodicity of the galvanometers (frequency to 6000 per second) permits an exact reproduction of the curve with an alternating current whose frequency is 33. In spite of the grounding of one of the poles, the greatest care must be exercised because of the extreme danger connected with the work, which must of necessity be performed in the dark. From the oscillograms and the milliampere readings the maximum voltage is deduced according to the method in common use. | In the following table are found the values determined for the ratio of the effective to the maximum voltage :— * Warburg, Ann. d. Phys. v. p. 811 (1901). Alternating-Current Spark Potentials. Diameter of spheres in em. No. of Resistance- Boxes. 703 | Average Ratio. bo On oS Oo iG — CODFR Onocw OO HH Ww AOoww W-~Io ce | | 30 | | 1-433 1-44 1-44 1°43 1°43 / | In the following section are given the tables of the striking- distances, with the corresponding voltages, both effective and maximum :— TaBLE I].—Diameter of spheres 2 cm. Frequency of alternating 715 mm. Explosive Distance in cm, [ito pay | 0-0850 ) 01364 / 01767 0-2200 } | / : : 03163 03723 04936 05370 0°6724 0°8752 0°9533 1:0689 1:3536 1°5316 1:7473 2°2151 —_——. current 33. Ratio 1°44. Barometric height “Temperature 20° C. Effective oS ee Maximum 31207 44938 ae Volts. | Volts. 2730 3931 36884 | 5593 4733 ~=«|| «S816 ae 8764 12620 11094 15975 11876 17101 | 14349 20663 | 17802 | 25635 19028 27400 20830 29995 24383 | 35112 26332 | 37918 28047 | 40388 704 Prof. J. de Kowalski and Dr. U. J. Rappel on Tapue LiL Diameter of spheres 3°85 cm. Ratio 1:44. Frequency of alternating current 33. Barometric height 720 mm. Temperature 19° C. Explosive Distance| Effective Maximum in cm. Volts. Volts. 0:1030 3106 4472 071452 4026 5797 01812 4779 6882 02379 5982 8614 0°3110 7442 10716 0°3871 8992 12948 0:5070 11291 16259 0:6903 14674 21130 0°8425 ) BLG4OZ 25188 09293 19055 27439 10416 20966 30191 1:2526 (24555 35399 1°3703 26482 38134 14735 28194 40599 16597 31032 44686 TaBLe IV. Diameter of spheres 10 cm. Ratio 1°43. Frequency of alternating current 33. Barometric height 716 mm. _ Temperature 19° C. Explosive Distance | Effective Maximum in em, Voltage: Voltage. 071119 3279 4689 0°1549 4180 5977 0:1981 5094 7284 0:2475 6140 8780 0°3057 7295 104382 0:4030 9220 © 13185 0°5185 11454 16379 06425 13722 19622 0°8632 17761 25398 0°8848 18161 25970 0:9902 20050 28674 1°2365 24259 84692 1:3404 26071 37280 1:4360 27805 39761 1°5932 30368 43429 1°7800 33450 47834 Alternating-Current Spark Potentials. 705: TABLE V. Diameter of spheres 15 cm. Ratio 1°43. Frequency of alternating current 33. Barometric height 714 mm. Temperature 20° C. pet Bice | Effective Maximum | in cm. | Volts. Volts. | 0-1154 3318 A744 0-1534 4118 5888 0:1900 4868 6961 | 0:2365 §823 8326 | 0:2927 6940 9924 | 0:3766 8600 12298 0:4627 10231 14630 0:5426 11755 16809 0:6560 13882 19851 0:8172 16737 93933 0-9410 18995 27162 1:0109 20306 29037 | 1-2380 24201 34607 1:3546 26245 37530 | / 1:4793 28268 | 40423. | ) 1:6514 31085 44451 | 1:8730 34683 49597 TABLE VI. Diameter of spheres 20 cm. Ratio 1:43. Frequency of alternating current 33. Barometric height 716°4 mm. Temperature 21° C, Explosive Distance | Effective Maximum in em. Volts. | Volts. 0-1148 | 8290 | 4704 0-1504 | 4063 5810 ar rt). Beas 8358 0:2883 6896 9861 0:3817 (4 S731 12485 0°4717 | 10436 14923 0-544 | 11822 16905 | 0°6546 es ige8e 8 | n9ge. ty 0:8123 | 16684 23858 0-9961 | 19993 28582 1:1088 eager | 81419 1:2419 | 24252 | 34680 13540 | 26202 | 37468 1-4430 | 27756 | 39691 16310 | 30969 | = 44285 706 Prof. J. de Kowalski and Dr. U. J. Rappel on ‘TasBLE VII. Diameter of the spheres 30 cm. Ratio 1°43. Alternating current frequency 33. Barometric pressure 716°9 mm. ‘Temperature 19° C. Explosive Distance | Effective Maximum in cm. Voltage. | Voltage. O-1144 3273 4680 0-1493 4029 | 5761 02311 5198 | 8233 0-2846 GBOT NS oO kB O-3777 8644 12360 0°4666 10335 14779 0°5380 11700 | 16731 OO485 13783 io oe Oo 0-8040 16540 23652 1:0360 20618 | 29483 1-1166 22100 _ 31600 12470 24324 | 34783 138595 26311 | «pose 14606 28023 | 40072 | A direct comparison of our figures with the measurements undertaken by other physicists is hardly possible. Spark potentials for alternating current have seldom been deter- mined under well-defined conditions. The researches of Steinmetz, which up to the present were the most reliable, do not make allowance for tardiness or dilatation, which is apt to give values that are too high, as has been sufficiently proved by Warburg* and Starkef. Consequently, our figures are smaller than those found by Steinmetz. As Steinmetz tf, in his series of researches, allows a divergence of from 4 per cent. to 6 per cent., it seems clear that these differences are traceable to this source. Weare able, however, to make an indirect comparison with the values found by other physicists, who employed the direct current. Ac- cording to M. Toepler§ the following holds true :—Taking as unity the spark potential corresponding to S=1, where a=the explosive distance and d the diameter of the spheres, the spark potentials corresponding for the same distances are independent of the values of d. * Warburg, Ann. d. Phys. v. p. 811 (1901). + Starke, Wied. Ann. lxvi. p. 1009 (1898). 7 Russell, Phil. Mag. vol. xi. [6] p. 265 (1906). § M. Toepler, Elektr. Zetésch. p. 998 (1907). Alternating-Current Spark Potentials. 707 In the following table is set forth the comparison of our determinations with those of other physicists: | Freyberg. | Heydweiller. | Kowalski & Rappel. din cm. 10 20 10 62-0 20 385 | zx:d=01 | O18 0-19 .. 018 018 O-18x 02 | 037 032} 032 O=2 0:32 0°82 ) 03 | 045 0:44 . 0°45 044 0-44 04 | 0:54 0°55! 0:53 0°58 0-55 0:53 05) | O65 O65 |... 069 0:66 | 06 | O75 O74 | 0:74 0:79 0:75 | CO ad aco keene pete ee 0:83 | / 0-8 | 0-90 SO OSOF th .... 0-90 0-9 | 0-98 | St rats 0:96 * 0-18 was taken as the basis in these calculations. The table shows that the general results obtained agree very well with those found by other physicists. Nevertheless the absolute values are from 4 to 6 per cent. smaller than those which the direct current yields (application of the law of Paschen). Whether the cause lies in the elimination of dilatation or in the nature of determinations with alternating current is difficult to determine. Researches in this direction are now in progress. Parr IJ, Relation of the Spark Potential to the Radius of Curvature of the Electrodes. Recently A. Russell tT has endeavoured to establish a theory on the relation of the spark potential to the curvature of the electrodes. Previously it was commonly accepted that the spark would jump when the maximum electric intensity between the electrodes had passed certain definite limits. Since this theory failed to explain all observed facts A. Russell has added an hypothesis of his own. He assumes that for explosive distances greater than 0:1 cm. a certain value & is to be deducted, in the determination of the maximum stress, which he terms lost volts. For air he takes this value to be 800 volts. The following reflexions are to serve as a test for the proposed theory of Russell. f A, Russell, Phil. Mag. vol. xi. [6] p. 237 (1906). 708 Prof. J. de Kowalski and Dr. U. J. Rappel on Formule for the Electrical Intensity between Spherical Electrodes. The formule for the electrical intensity between two spheres of the same radius have been given already by Kirchhoff*, and have been lately brought into a more elegant form by Russell. , If the two spheres have respectively a potential of V, and V, the following formula applies :— Peet)! S Ea ee max. a l—g fi (14+ 9-3)? EAE (1+9) 20 1—¢"-) ail @ a Cael gh where a is the radius of the sphere, and g defined by the following equation A /A?—4a? 2qg= — — ——_—__, a a where A represents the distance between the centres of the spheres. In case Vj;=—V,= A we have , V Omax.— rt ay where Mee AAO San a ito.” 1—g iG (+g? -~ when « represents the shortest distance betweeri the centres of the spheres. When V,=V and V,=0, as is the case in our problem, we have where * Kirchhoff, Crelle’s Journal, p. 89 (1860'. Alternating-Current Spark Potentials. 709 To determine f, we have made use of the following formule which possess a degree of exactness greater than 0:001:— sane d, ‘Blame or e ° ° . . . . ° (1) v Bere aaah aia 2 Ki Lise tea a2 piss fv ene: 3) Uo: = le ia ist ae a ° pl = ee ate! | 53760 ab (3) & | 03<=<07, f=ft+d y where | peta yh at 184 at =!" 3a 45 att 53760-a° | * and zx atda ki Ke | A= — ‘ > iene 1” Here &, k’, and K are determined from the following : L (4) 2K Sn? a/R a142 B pta14 gt ate't -) [2K < 2 a a ee) oo I = pe | = Ne ee eee eens where 710 ~~—- Prof. J. de Kowalski and Dr. U. J. Rappel on and has the same value as in formula (4), ay ie v a ~ + 1 Uv afr = SE a (E+1)(5 +2). a a e (6) In the following tables we have collected the results of these calculations for testing the theory of Russell. Diameter of spheres: 2 cm. Explosive Distance in em. 0:085 01364 0°1767 0:2200 0°3163 0°3723 0:4936 05370 0-67.24 0:8752 0°9533 10689 1°3536 15316 - 17473 2°2151 47568 Maximum Intensity volt PT gansess cm. 42871 40856 39944 38549 38549 38696 38801 39827 41853 42645 44028 46425 47918 48960 51332 Explosive a Distance = in cm. fe 01030 0:0535 0:1452 0:0754 071812 0:0941 0:2379 071236 0°3110 0°1615 0:3871 0°2011 0:5070 0:2634 06908 0°3586 0°8425 0°4377 0°9293 0:4827 1:0416 0:5411 1°2526 06507 1:3703 0°7118 1°4735 07654 1:6597 0°&622 According to Russell volt 37888 36739 36063} 56038 35689 36106 36759 36986 38285 40547 © 41400 42854 45366_ 46907 47991 50418 Diameter of spheres: 3°85 cm. | | | f. 1:0178 | 1:0251 1:0314 10415 1:0541 1:0679 10898 1:1810 UGTG 64 11900 | 1°2206.° 4 12742 | 13216 1:3567 1-4201 Maxiinum Intensity volt According to Russell volt Alternating-Current Spark Potentials. Diameter of spheres: 10 cm. c | | Maximum | According Explosive | x | Intensity to Russell Distance / Pk: Sis iia geal } . volt ayer / 7 eta 7 ™ om. - 01119 | 0:0223 | 1:0075 | 42226 35021 01549 | 0:0309 | 1-0103 38986 33769 01981 | 0:0396 | 1:0132 37154 33063 02475 | 00495 | 1:0165 35038 31753 03057 | 00611 | 1°0204 34820 32150 0:4030 00806 | 1:6269 33596 31558 05185 | 0:1037 | 1:0348 32689 31093 06425 | 01285 | 10432 31860 30562 03632 | 01726 | 1-0582 31151 30171 0:8848 | 01769 | 1:0597 31101 30143 0:9902 | 0-1980 | 1-0669 30892 30030 12365 | 0:2473 | 1-0888 30683 29982 13404 | 0-2680 | 10937 | 30419 29767 1-4360 | 02872 | 11012 | 30380 29867 15932 | 0:3186 | 11343 30919 30349 1-7800 | 03560 | 11553 31046 30527 Diameter of spheres: 15 em. ) | Maximum | According | Explosive _ P Intensity to Russell | Distance | 2. | Were _ volt volt in cm, ret in en bd in cm id : 01154 | 0-0153 | 1-0051 41335 34366 0:1534 | 00204 | 1-0068 38649 33399 01900 | 0:0253 | 10068 36945 32700 02365 | 0:0315 | 1:0105 35578 32160 02927 | 00390 | 1:0130 34339 31571 03766 | 00502 | 1-0167 33200 31041 04627 | 00617 | 1-0205 32661 30897 05426 | 00723 | 10241 31725 30216 06565 | 00874 | 1-0291 31144 29889 08172 | 01089 | 1-0365 30358 99344 | 09410 | 01254 | 1-0421 30082 29197 10109 | 01347 | 1-0453 30025 29198 12380 | 01650 | 1-0556 29507 28825 | 13550 | 01806 | 1-0609 29393 28697 | 14793 | 01972 | 1-0665 99144 28568 | 16514 | 0-2202 | 1-074 28921 28401 | 18730 | 0:2497 | 1:0846 28722 28259 ED RT pi PR ER | 711 712 Alternating-Current Spark Potentials. Diameter of spheres: 20 cm. ; Maximum | According Explosive c Intensity to Russell Distance at ie volt volt in em, in — - in . em. em 0°1148 0:0115 1:00388 41118 34126 071504 0:0150 10050 387705 32361 0:2357 0:0236 1:0078 35733 o2ola 0:2883 | 00288 | 1-0096 34526 31725 0°3875 0:0387 1:0127 33120 30998 04717 | 0:0472 1:0157 52133 30411 05444 | 0:0544 10181 31615 30119 0°6516 0:0655 1:0218 30999 29751 0°8123 0:0812 1:0270 30167 29156 09961 0:0996 1:0332 29653 28823 1°1088 0°1109 1:0372 29384 28636 1:2419 0:1242 1:0417 29089 28428 1-3540 071354 1:0455- 28982 28315 1°44380 0°1443 1:0486 28842 28261 1°6310 0°1631 1:0549 28645 28128 Diameter of spheres: 30 cm. ; Maximum According Explosive x Intensity to Russell Distance =a Si. volt _ volt in cm, 74) === oe in —* cm. cm. 0°1144 0:0076 10025 41012 34002 01493 0:0099 1:0083 38707 | 33331 0°:2311 0:0154 1:0051 30802 32324 0°2846 00189 1:0063 34387 | 31559 0:3777 0:0252 1:0084 338000 30865 04666 0:0311 1:0104 32000 30268 0°5380 0:0358 1/0119 31468 29964 06485 00432 1:0144 30831 29580 0°8040 0:0536 1:0178 29944. 28932 1:0360 0:0690 1:0230 29115 28325 1:1160 0:0744 1°0248 29049 28315 1:2470 00831 1:0277 22666 | 28007 1:3595 0:0906 1:03802 28511 27905 1:4606 0:0973 1:0324 28328 | 27763 These tables show that the claims of Russell are not justified regarding the constancy of this maximum stress, We see rather a certain regularity in the results, and for a definite explosive distance a minimum seems to exist. The theory of Russell is, therefore, no satisfactory explanation of the question. a : ; oope713, J LXXITT. Musical Are Oscillation in Coupled Circuits. By EK. Taytor Jones, D.Sc., Professor of Physics in the University College of North Wales, and Morris Owen, B.Sc., Isaac Roberts Student of the University College of North Wales, Bangor*. [Plate XX.] 5 at a recent communication f one of us has shown that if the primary of a pair of coupled circuits, in series with a condenser, forms the shunt to a Duddell musical arc; and if the secondary coil is connected to another condenser, either of two notes may under certain circumstances be heard. It was also shown that the frequencies of the electrical oscil- lations in the circuits corresponding to the two notes are generally much lower than those calculated for the circuits from the inductances of the coils and the capacities of the condensers, the resistances being neglected. In the present paper the influence of the resistances of the circuits isconsidered. Itis shown that the difference between the observed and and calculated frequencies cannot be mainly attributed to the resistances, and a different explanation is suggested. One of the chief difficulties attending experiments on this subject is that of obtaining really simultaneous values of the two frequencies. It is of little use to sound the two notes one after the other and determine their frequencies. The conditions in the are can change so rapidly that the constants of the circuits cannot be regarded as identical on two occasions, even if separated by only a short interval of time. A number of cases are considered in the present paper in which the two oscillations were recorded simultaneously. The method consists usually in arranging matters so that one oscillation corresponds to the octave or a higher harmonic of the other. Some cases are also considered in which, in addition to the two ordinary arc notes, a third note is pro- duced ; and the view is put forward that this is a difference-tone of the other two, arising, however, from an electrical oscil- lation of the same frequency in the circuits. The oscillations were studied by means of the short-period electrometer, or electrostatic oscillograph, described by one * Communicated by the Authors, + E. T. Jones, Phil. Mag. p. 42, January 1909, This paper will be referred to as “J. c.” Phil. Mag. 8. 6. Vol. 18. No. 107. Nov. 1909. 3B 714 ~=Prof. HE. Taylor Jones and Mr. Morris Owen on of us*, This was connected to the terminals of the condenser in the secondary circuit ; the photographs obtained therefore represent the waves of potential at the plates of this condenser. In most of the experiments the secondary condenser was of the parallel-plate type and of variable capacity, with heavy paraffin-oil as the dielectric. The primary capacity consisted of a paraffin-paper condenser, or a number of these in parallel. In all cases the primary coil was of self-inductance 004619 henry, and resistance 1:038 ohms: the secondary coil had self- inductance L,=70°15 henry, and resistance R,= 14022 ohms. The mutual inductance M of the two coils was *2192 henry. The carbons used for the arc were solid and 9 mm. in diameter. The total capacity C, in the secondary circuit includes the © capacity of the secondary condenser, of the oscillograph, and of the secondary coil. The capacities of all the condensers were determined by measuring the periods of their electrical oscillations when connected in series with coils of known self-inductance. Full details as to the methods employed in the determi-~ nation of periods of oscillation and of the constants of the circuits were given in the previous papers, referred to above. (1) Resonance of the Octave. Case I. C,=primary capacity =9°55 microfarad. @,=secondary + 4; +=O002To tae, This case was referred to in the previous paper {, where it was pointed out’ that the octave, which is generally present when the lower arc note is sounding, becomes in this case very much intensified. ‘The photograph showing this was also given in the paper referred to§. The frequency determined from the photograph was 613. The frequencies calculated from the inductances of the coils, and the capacities of the condensers, the resistances being neglected, were 1301°2 and 723°1, which do not satisfy the octave relation or agree with the observed frequency. In order to find the influence of the resistances of the circuits the frequencies m,, 2, were calculated for the above value of R, and for various values of R,, the resistance of the * E. T. Jones, Phil. Mag. ser. 6, vol. xiv. p. 238, August 1907. + In the previous paper the Value of this capacity was given as “about” ‘000275 microfarad. Subsequent measurements chowed that this Hee: is aig to within one part in 800. sae Oe § ZL. ce. Plate roma Musical Arc Oscillation in Coupled Circuits. 715 primary circuit. In these calculations the following formule, given by Drude *, were employed :— T?+T?-26=T,?+T,? —4(0,— 0)’, 28(1?—T”?) = —(6,—@,)(T? —T,”), Gi ed jay pet 88?(T? cE T) — (i —T,’) —9(T,? + T.”)(0,— 62)? +4 MPC, Co, J | y bay DD where 6,=iR,G,, T?+02=L,C,, #,=$ RC, T,? + 0,?=L,Co2, T— ade. T= 1 Qi ny aT Ns and 8 is a constant which vanishes when the resistances of the circuits are neglected. The elimination of ‘T and T’ between these equations leads _to a cubic for 8”. In each of the cases examined the cubic had only one positive root (giving real values for 8), and 8? being thus determined the above equations allow T and,1", and hence the frequencies 7, and 7g, to be calculated. Table I. contains the values of 8?, n,, and n., calculated in this way for various values of Ry, the other constants having the values given above, and L, being taken as the self- inductance of the primary coil. TABLE I, R, in ohms. Peete ORME RNG em fee Se | 2 | Toy ey Ca Pa | 0 0005 721°8 1309 3 | 002112 725°1 1300°5 | | 5 | 006669 729 1296-7 | 10 =| ~— 02964 | TAT | 1285-4 | 15 | 071804 7318 | 12649 | 32995 | -472159 1187°8 11873 | | 38 | 665507 16436 | 11781 | iit or SO: ney | ee OI LESS | le. Lama | 41 | 795478 2596°6 M722 50 1250994 Imaginary 1163°2 L * Drude, Ann. der Physik, xiii. p. 534 (1904). 3B2 (16 Prof. EH. Taylor Jones and Mr. Morris Owen on From the last two columns it will be seen that as the value of R, is increased the frequency of the slower oscillation ancreases, and that the ratio of the two frequencies at first deviates more and more from the octave relation. It is clear, therefore, that the observed frequency 613 of the musical are note and the intensification of the octave of this note cannot be accounted for by merely assuming that the are has any constant resistance during the oscillations and including this in our calculations. It seems desirable to examine next the hypothesis that the arc behaves as if it had self-inductance. This supposition is not anew one. It has been employed * to account for the well-known fact that the alternate-current arc has a power- factor different from unity. It has also been pointed out by M. La Rosa f that oscillations may be produced by the musical are even when the shunt circuit connected to it has ne natural period of oscillation. Very intense high notes may in fact be produced by connecting the carbons to a paraffin-paper condenser by well-twisted insulated wires, no coil being included in the circuit. Assuming, therefore, that the arc has self-inductance which is to be added to that of the circuit connected to it, the problem in the present case is to find what value of L, will make the frequency of one oscillation of the system twice that of the other. Neglecting the resistances of the circuits, the frequencies of the system are given by Oberbeck’s formula 4M? ie if 1 1 Lee 25 LAs St eo Gorn _ aM sdb 1 ae be - LC, 4/5 LC; Lf ) v LL ne hy Substituting the above values of L,, C,, C., M, and putting NM,=2n,, we have a quadratic equation for Ly, the roots of which are ‘003811.10° and °0066795.10°. The former value is less than the self-inductance of the primary coil (004619 . 10°), andis therefore discarded. Taking, therefore, L, ='0066795.109 cm., and substituting in (2) we find for the frequencies of the system 617 and 1234. It was pointed out in the previous paper that at the time when the photograph was taken, the amplitude of the wave was not quite at its maximum; so that the frequency corre- sponding to the exact octave relation is slightly different from the measured value 613. It is in fact very difficult to obtain a photograph during strong resonance, since the * Cf. Ayrton and Sumpner, Proc. Roy. Soe. vol. xlix. p, 424 (1891). t Science Abstracts, p. 697 (1907). Musical Are Oscillation in Coupled Circuits. 717 oscillations are easily stopped by “ brushing ” or sparking at the terminals of the secondary circuit. Further, in arriving at the above calculated values the resistances of the circuits are not taken into account. These considerations are probably sufficient to account for the small difference between the observed and calculated values of the frequency, while the close agreement between these values gives support to the views that during these oscillations the are may be regarded as having a constant self-inductance, and that when the two frequencies of the system are nearly an octave apart, and when the lower note is sounding, the octave of this note produces forced oscillations of “creat amplitude in the system. Case II.—This ease is similar to the last.. The coils were the same, and the capacities were C,;=11°63, C,=-0003911 microfarad. The lower note only * was heard, and at a certain length of the are the octave resonance occurs. Several photographs were taken of the curve of secondary potential, but in none of them was the amplitude quite atits maximum. Two curves showing the intensified octave were measured, the observed frequencies being 490 and 546. Assuming as before that ny=2n, the values of L, deduced from (2) are °0019362 . 10° and ‘0080879 . 10° em., the former of which isinadmissible. Taking, theretore L,=" 0080879. 10°, (2) gives for n, the value 510°5, ‘which does not differ greatly from either of the observed values. Case [11.—Another example of the same kind is given by C,=16°98, -C,=-0004771 microfarad. Several photographs were taken showing the intensified octave, and the curve having the greatest amplitude was found to havea frequency of 452°9. With no=2n,, equation (2) gives L,=:006471 .10°, and N,=469°9. The difference between the observed and calculated values is here again probably within the limits of error explained under Case I. Case 1V.—This case differs in one respect from the others. The capacities were C,=14°62, C,=:0002898 microfarad. If the condition n,=2n, is inserted in (2), the two values of L, obtained are less than the self-inductance of the primary coil, and are therefore inadmissible. For all possible values of L, ; is greater than 2n,. The question therefore arises whether the octave relation may not be satisfied by the two frequencies if the resistances of the circuits are taken into account. A few trials showed * Cf. lc. p. Al. 718 Prof. H. Taylor Jones and Mr. Morris Owen on that this was the casé. If L, is taken as ‘006.10° em., equation (2) gives ny=528°7, n»=1205°'4. With R,=14000 ohms, R,=15 ohms (2. e. nearly 14 ohms being assumed fer the arc), equations (1) give m=572, n,=1194: while R,=25 ohms makes nz, less than 27}. The observed frequency in this case was 573; and it is clear that this condition and the octave relation are satisfied by assuming L, to be slightly greater than °006. 10°, and R, rather greater than 15 ohms. The length of the arc during the octave resonance was about 1°5 mm., the current in the are about 1:7 ampere. From the results given by Duddell * it seems probable that an are of this length conveying so small a current might have a resistance of over 14 ohms. The photographs for Cases II.-IV. are similar in character to that given in the previous paper for Case I., and are not reproduced here. (2) Resonance of Higher Harmonics. Case V.—With a large capacity in the primary circuit and a small secondary capacity, other notes, lower than that which gives the octave resonance, become prominent, and are accompanied by high potentials at the terminals of the secondary condenser. ‘hese appear to be due to reso- nance of the third and higher harmonics of the are note. Thus with C,=14°62, Cs;=-0002895 microfarad (as in Case IV.), if the arc-length is made slightly greater than the value which gives the octave resonance, the note falls gradually in pitch, but becomes fairly stable and prominent when about a fifth below the value given in Case LV. The photograph showing the curve of secondary potential for this ease is given in Plate XX. fig. 1. The curve appears to consist chiefly of a prominent third harmonic superposed upon the fundamental. The frequency of the latter, deter- mined by comparison with the curve given by a 768 tuning- fork photographed simultaneously, was found to be 359-4. If we insert the relation n.=3n, in equation (2), we find L,=°011589 .10° cm., and hence, by (2), ;=385. The difference between the observed and calculated values is within the limits that may be expected from the considerations explained above. Case V1.— With C,;=19:03, C.="00029 microtarad, reso- nance uf the fourth harmonic of the are note may be obtained. * Duddell, Phil. Trans. vol, cciii. (A) pp. 323, 326 (1904). Musical Arc Oscillation in Coupled Circuits. 719 The curve of secondary potential is shown in Plate XX. fig. 2. The frequency determined from the photograph is 285:2. If we assume n.=4n, in equation (2), we find} L,=-016289 . 10° cm., hence n,=285°4. Case VII.—Using a still larger capacity in the primary circuit, C;=21°32 microfarad, and the same secondary con- denser, a photograph was obtained showing a prominent fifth harmonic. This is shown in Plate XX. fig. 3. The observed frequency is 224°5. With ny=5n, equation (2) gives L,=*023088.10° cm. Hence 2, = 2267. Case VIII.— With the same capacities as in Case VII. and a slightly longer arc, a still deeper note, about a minor third below the last, can be recognized as producing resonance. We did not succeed in obtaining a photograph of the curve for this case. If, however, the relation n,=6n, is inserted in equation (2), we find L,;=:03361.10° cm., giving n,=188, which is very nearly a minor third below the note of Case VII. (3) “Difference Tones” produced in Coupled Circuits by the Musical Are. Case IX.—It was pointed out in the previous paper * that if a certain relation exists between the primary and secondary capacities the two notes of the arc are equally stable. This is the case with C;=16°98, C,=:001098 micro- farad, and the two notes are separated by an interval of about a fifth. If, with these two condensers, the lower note is sounding and the arc-length is gradually diminished (the pitch gradually rising), at a certain stage the note suddenly drops by an octave. This deep note is fairly rich in quality, and it differs from the ordinary arc notes im that it is perfectly definite in pitch. Any alteration in the arc-length made when the deep note is sounding either causes the sound to stop altogether, or changes it into one of the two primary notes. The deep note was not very stable in this case, and several exposures had to be made before a photograph was obtained showing the curve of secondary potential while this note was sounding. The photograph is shown in Plate XX. fig. 4. The photograph in fig. 5 happened to be taken just as the note was changing from the lower primary into the deep note an octave below, and covers the whole period of Adie Gs Da 41, 720 Prof. EH. Taylor Jones and Mr. Morris Owen on this change. The photographs show that the deep note corre- sponds to an electrical oscillation of the same frequency in the circuits, and is not merely produced in the air, or in the ear, as is sometimes the case when the difference-tone of two musical notes sounding simultaneously is heard. The deep note appears to be the difference-tone of the two primary notes, and is due to an electrical oscillation in the system which is only produced when the two primaries are equally stable and (in the present case) when the ratio of their frequencies is exactly 3/2. If we assume = Sm in equation (2) we obtain the two values *004633.10° and -007586.10° for L,. Taking the smaller value (since the arc was very short when the differ- ence-tone was sounding), and substituting in (2) we find N= 484°73, ng=727:09. Hence no—n,=242°36. The frequency of the difference-tone measured from the photograph was 237:5. The observed frequency of the deep note therefore agrees closely with the difference of the. frequencies of the two primes calculated on the assumption that the interval between them is a perfect fifth. Case X.—C,=14°62, C;='0008722 microfarad. In this case also the two primary notes are equally stable, and the deep note, an octave below the lower primary, is produced at a certain arc-length. ; ny in (2), the values 004734. 10° and °006540.10° cm. are obtained for L,. Taking the former value as being more appropriate for a short are and inserting it in (2), we find ,=529°7, n,.=7194°5. Hence Ng — Ny == 264'8. _ This agrees closely with the frequency of the deep note determined from the photoyraph, which was 263°8. Case XI.—C,=5°64, C.='0002886 microfarad. In this case the difference-tone was exceptionally stable and powerful, quite as loud, in fact, as either of the two primary notes, and more easily produced and maintained than in the two previous © cases. The lower primary note was often heard simultaneously with the difference-tone, but we are not sure that the upper primary could be distinguished when the latter was sounding. The length of the are when the difference-tone was sounding was about 0°75 mm., the current in the are generally about 2°5 amperes. Several photopraphs were taken with the difference-tone sounding. These (as well as those of Case X.) are very similar in character to the curve shown in Plate XX. fig. 4, and are not reproduced here. Assuming as before no= ~ “a Musical Are Oscillation in Coupled Circuits. Tat The frequency of the difference-tone determined from the photographs was 438-6. With regard to the calculated frequency the assumption Ng = in in equation (2) leads to no real values of L, in this case. The resistances must therefore be taken into account. After a number of trials Table LI. was drawn up showing the values of the two frequencies, calculated from equations (1), for various values of the resistance, R,, of the primary circuit, the self-inductance of the primary circuit being taken as ‘0049 . 10° cm. TABLE II. | R | R | n | ohms | ohms. / er | 7: | a to ee BO Oh 0. 8 e692 | ees ho 4528, |) 4597 ‘Shae | 14000 | 8734 | 18257 | 1-517 452:3 Be td ier) |. BBO U 18225), 1508 24. | Mihi Pit sisee fst BERT LAG Ys TH6) |, | ABBR a d+ 9608 | 1238'1 | 1-277 2683 It is clear, therefore, that if the primary circuit has a resistance of slightly over 8 ohms (7. e. ifthe resistance of the are is about 7 ohms), and a self-inductance of the above value, the ratio of the two frequencies will be exactly 3/2, and their difference will agree closely with the observed frequency of the deep note. From the measurements given by Duddell* it appears that 7 ohms is not an impossible value for the resistance of” the are under the circumstances of this experiment. (4) Conelusions. From the above results it may be concluded :— (1) That tbe great differences between the observed fre- quencies of the electrical oscillations in coupled circuits produced by the musical arc and the values calculated trom the inductances of the coils and the capacities of the condensers, cannot be accounted for merely by allowing for the resistances of the circuits. * W. Duddell, Phil. Trans. vol. eciii. (A) pp. 323, 326 (1904). 722 Mr. G. Green on Flexural (2) That the principal cause of the difference is the fact that the are behaves as if it has self-inductance, which is constant during any particular train of oscillations (though different under different circumstances), and which must be taken into account in calculating the frequencies. (3) That any one of the harmonies of the arc-note up to the sixth can be strongly reinforced by suitably adjusting the ratio of the two frequencies of the system. (4) That if the two notes of the are are equally stable, and if the interval between them is a perfect fifth, a third note may be heard, which corresponds to an electrical oscillation of frequency equal to ius difference of the frequencies of the two primes Bangor, July 1909. . ig —_ LXXIV. Flexural Vibrations ae Thin Rods. By GEORGE GREEN, M.A., B.Sc., Assistant to the Professor of — Philosophy y in ‘the University of Glasgow™. yuk fl ins main object of this paper is to point out a method of applying hydrodynamic solutions already obtained to the solution of problems relating to flexural vibrations of thin elastic rods. The results found apply to rods not subjected to permanent tension, and vibrating so that one principal axis of each transverse section lies in the plane of vibration. The central line of the rod is assumed to remain unaltered in length ; and particles lying in a plane transverse section, when un- disturbed, remain always in a plane normal to the central line. For convenience in what follows we may here derive the equation of motion of a rod subject to these conditions. Taking » as the area of each section, x’w its moment of inertia, q as Young’s modulus, dz as the length of the central line of a small portion, R its radius of curvature, and N as the total tangential force acting on the cross-section at 4, we obtain the equation of angular motion of the element ony where y is the vertical displacement of the element and p is its density. The equation of vertical motion is ON ory aa Pe a2 gE Oe * Reprinted from Proc. Roy. Soc. Edin. vol. xxix. 1909, hone ae copy communicated by the author. qo oO EB + N=pk? Vibrations of Thin Rods. 723 As pointed out by Lord Rayleigh*, whose notation we have adopted, terms depending on the angular motions of the sections of the bar may be neglected in the above equations; accordingly, by eliminating N from (1) and (2) we obtain finally the equation Z 4 Oy +e S40, Scone e emer I os 9 2, in which we have put oe for - and b? for : : § 2. Consider now frictionless liquid in a straight canal with vertical sides. Take the origin of coordinates at point O, at a distance h above the undisturbed level, and draw OX parallel to the canal and OZ vertically downwards. Let the motion be infinitesimal and let &, ¢, be the displacement components at any time ¢ of any particle of water whose undisturbed position is z, z. If the motion of the water be started primarily from rest by pressure applied to the free surface, the hydrodynamical equations of motion take the well-known form aes ae tie B= 57 Pl, % 85 aaa aes ony eas (4) from which we obtain by integration ROO) oem wl Dinan y E= ae <9 t)5 c= 5 0 <5 t). We (5) In virtue of the incompressibility of the fluid we have also the equation Pokae 2 D2’ + of = 0, . e e s . (6) which shows that if @ be known at all points of the free surface, and if it be zero at points infinitely distant, its value can be determined at all points throughout the fluid. The equation to be fulfilled at the free surface, according to a result given by Cauchy and Poisson, is oe see a a ee where g denotes gravity. § 3. Remembering now that every function derived from ¢ by differentiations or integrations with respect to 4, z, ¢, * ‘Theory of Sound,’ vol. i. 724 Mr. G. Green on Fleaural satisfies all the equations satisfied by the function ¢, we see that we have oo _ lod | O22 — g oe . . e . . e (8) at a free, or level, liquid surface. Equations (6) and (8) combined give us the relation od __1 O'¢. So oT giae) and when we put y in place of ¢, xb in place of oN and interchange « and ¢, this equation may be written in the form OY . 20 | apo tk? ae J. which is the equation already found for flexural vibrations of an elastic bar, when terms depending upon the angular motions of the sections of the bar may be neglected. Ac- cordingly, equation (9) proves that every hydrodynamical potential function, with # and ¢ interchanged, is a solution of equation (3) above. (The converse is not always true.) In relation to the flexural-waves problems z is in general to be treated as a constant. § 4. It may be of some interest to note that, in all solutions for elastic bars obtained by applying the above result, the displacement y at each point of the bar may be regarded as derived from a single function V(t, <, x) such that =f ee Further, it follows from the relationship established between such a function V and the hydrodynamic potentiai function, that every function derived from V by differentiations or integrations with respect to ¢, z, 2, is a solution of the dif- ferential equation (3). Thus any solution of (3) may be a displacement potential, or a displacement, or a velocity. If the function V represents displacement, we readily find from equation (7) that the curvature at each point # of the bar can be obtained by a single differentiation with respect to <¢, being given by the equation 1 1 OY; Bigiuchbe? olRY, aie Hate Ra ao ale (11) from which the potential energy can easily be obtained. Vibrations of Thin Rods. 725 § 5. Solutions for vibrations of a rod of finite length / are derived directly from the hydrodynamic solutions for waves in a canal of length / by simple interchange of x and ¢; and they are applicable to all cases, whether the rod has its ends free, or clamped, or “‘supported.” In particular, the normal functions are easily obtained in this way. In the case of an infinite rod, all mathematical results relating to surface waves in a canal infinitely long and in- finitely deep become immediately useful ; space-curves in the hydrodynamical waves problems becoming time-curves for the flexural waves, and vice versa. § 6. In this connexion it may be useful at a later time to examine some of the numerous hydrodynamical solutions relating to surface waves and groups of waves. A number of curves are shown in papers on Water-Waves* by the late Lord Kelvin, illustrating results derived from particular hydrodynamic solutions comprehended in the following general expression, given in his last Waves paper :— Outer i gt 5 aioe Oz a € ~ &(z+iz) ° t Oz / (2+i2) +12) In this, {RS} denotes a realization by taking half the sum of what follows it with +72; {RD} denotes a realization by taking the difference of what follows it with +7 divided by 2:1. As an example of fiexural waves in an infinite elastic rod, arising from a given initial displacement, we may take the solution {RS} or {RD} —— 5 z2 € 4Kb(z+7it) RB 1 vt By dy eee : =a/7 cos (po —57)e 4KUT2 ) , tabs (12) t where Day (eS 2A) and c= tan—(" ) In what follows, z is taken as 1 and kb as 3 in order to allow us to use Lord Kelvin’s hydrodynamical results in our present problem. § 7. Taking the origin of coordinates at the middle of the bar, the initial configuration j is given by ye ~ 4Kb ; ae ed «Ee ohne (13) Almost immediately after the commencement of motion an * Proc. Roy. Soc. Edin. vol. xxv. Feb. and June 1904; vol. xxvi, Oct. 1906. 726 Mr. G. Green on Flexural infinite number of waves are formed along the bar, with a2 amplitudes diminishing according to the law e 41? and with the distances from zero to zero becoming shorter and shorter as we pass from the middle toward the ends of the bar. The zeros come into existence at the ends of the bar, and begin travelling inwards to the middle. The first zero formed comes almost instantaneously to the middle region, and the others follow it in their order of formation. The inward progress of the zeros soon ceases, the first zero never quite reaching the centre; in a short time they begin to move in the opposite direction and continue to do so for ever, and the amplitudes at any point # ultimately fall off according to : . The middle point of the rod subsides to its undisturbed position nonvibrationally, while the distance from it to the first zero on either side continually increases after a certain time, being given by the equation w?=3kbzt. § 8. The seven curves given by Lord Kelvin, as space curves for water-waves, on page 191 of his paper (Proc. Roy. Soc. Edin. vol. xxv. Feb. 1904), show the condition of things in our present problem at seven different points near the middle of the bar, as ¢ increases from 0 to ©, provided the curves be continued to meet the axis of t asymptotically at infinity (see fig. 1 and §9 below). These curves show Fig, ae Abscissas represent space for water-waves, time for flexural-waves. that points very near the origin never pass through their initial positions, but fall back nonvibrationally to them ; points farther from the middle rise slightly and then behave in the same way. At points along the bar more and more Vibrations of Thin Reds. oe distant from its middle point the disturbance consists of a larger and larger number of waves which travel inwards past the point considered, before t=1, and after that recross the point in the opposite direction one by one. When the first zero recrosses the point it subsides gradually to its original place of rest, only reaching it, however, after an infinite time. The successive maxima of displacement in- erease very slowly at first, then more quickly, and then diminish finally according to 74 2S already stated. §9. The diagrams of figs. 1 and 2 are taken from Lord Fig. 2. Abscissas represent time for water-waves, space for flexural-waves. Kelvin’s paper referred to in § 8, and they are reproduced without change of the lettering applicable to them as water- wave diagrams. To make them correspond exactly to the flexural-waves problem solved by equation (12), we must reduce the ordinates in both figures in the ratio ,/2:1; then in fig. 1 replace ¢ by wz on each of the seven curves, and take ordinates as representing displacement and abscissas as representing time. As a water-wayves diagram fig. 2 repre- sents the vertical displacement of the water at point r=2, from t=0 to t=~ ; asa flexural-waves diagram it represents the shape of the right-hand half of the rod, z=0 tow=nH, at time ¢=2, corresponding to the initial configuration given by equation (13). ; , These curves are useful chiefly as illustrations of the pro- pagation of waves in dispersive media from a given initial disturbance confined in the main to the neighbourhood of the origin. They show clearly the distinctive features of wave- propagation in the two cases where the wave-velocity varies 728 Flexural Vibrations of Thin Rods. directly as the square root of the wave-length and inversely as the wave-length respectively, for an infinite succession of regular sinusoidal waves. It is interesting to observe that in both cases the wave-disturbance is ultimately spread throughout the entire medium, but that in the case of water- waves the wave-length of the disturbance at any time increases continuously, and in the case of flexural-waves it diminishes continuously, as we pass outwards from the middle point of the initial disturbance. In the case of water-waves also, Lord Kelvin’s investigations show that each individual wave lengthens and increases in speed as it advances, while in the case of flexural-waves each wave lengthens and diminishes in speed, as we shall see by equations (15) and (16) below for the solution we have chosen for illustration. § 10. At a moderate time after the motion has commenced tT may be put equal to 2 in equation (12), and the argument 2 of the cosine varies then only with TehT2’ °° that it is easy for us to trace the outward progress of any particular maximum or zero of displacement along the bar. Thus the position of any zero is determined by an equation of the form xt 4n+3 Ete, 2 7 ae 02 and the velocity of the zero is given by dz 8xbet—a? | 2kbe 45 a og ae When ¢ is large, so that we may put a , equation (14) enables us to write (15) in the following approximate form, de. & oa It can easily be verified that when ¢ is very small and & great the velocity of any zero is given by ae is) iste der Ose In each case, what we obtain in these equations is also the wave-velocity for an infinite train of waves of wave-length equal to that maintaining in the immediate neighbourhood of the point x at time ¢. (16) Problem of the Amagnetic Mariner's Compass. - 729 § 11. To obtain the veiozity of the group of waves of wave- lengths approximately equal to A—that maintaining in the neighbourhood of x at time t—we put Ces ae AKbT? —_— ‘Dh T2 = 2a, He hie 2 which enables us to write down the group-velocity thus:— de 87Kbt—rx 3 dey eum ce When ¢ is very small and « great, the right-hand side of (18) is approximately equal to os ) If in (17) we take the wave-length X as small compared with x, we can obtain the following approximate expression for \ when ¢ is great:— . Anxbt Tae wins (19) With this value for 2, the right-hand side of (18) becomes x (*). ; Equations (15)-(19) show that in the two cases, when ¢ is small and # great, and when ¢ is great, the group-velocity i is twice the wave-velocity; which is in accordance with the theory of group-velocity given by Osborne Reynold and extended by Lord Ray leigh. mM LXXV. A Gyrodynamical Solution of the Problem of the Amagnetic Mariner's Compass. By J. J. TAUDIN CHABOT™. [Plate XXI.] HERE is an ever-increasing desire to replace the geo- magnetic ship’s-compass by an instrument, which would be independent of the earth’s magnetism, as it seems possible to do, in particular at the self-rotating planet’s surface, by the use of rotating masses, whose axes of rotation move only in a plane, unalterable relatively to the rotating planet itself. The precursor of all constructions, ever to be executed for this purpose, is Bohnenberger’s machine, dating from 1817, in Tiibingen. It enabled us, for the first time, to show approximately by experiment some results of the works published over half a century before by d’Alembert, Euler, and especially by Lagrange, on rotation round axes with * (Sergi by the Author. Phil. Mag. 8. 6. Vol. 18. No. 107. Nov. 1909. aw 730) Mr. Taudin Chabot: Gyrodynamical Solution of the only one point fixed, so that since then we distinguish apart from a theoretical dynamics of rotation still a kinematics of rotation of a more experimental kind, and treatises by Ampere, Poinsot, Thomson (Lord Kelvin), &c. on the one side, as well as such by Sang, Foucault, Sire, &c. on the other. We must throughout take note as to whether the axis of rotation is fixed at one point only, viz., the centre of mass of the rotating system, so that it can take up any position in space, or is fixed in one plane, wherein, it is true, it may take up any azimuth, but which it does not leave. The first case indicates the way to obtain an axis of rotation of unchangeable direction in absolute space, like a finger (so to speak) of the great clock, that is Harth. Here, however, we are not able to succeed on account of the unavoidable friction on the pivot—in default of a directing force to overcome this. — But there is fortunately a directing force to hand on the earth’s surface, where it is of value in practical arrangements made according to the second mode, whereby to overcome the bearing-friction ; and a definite direction can be secured of the axis of rotation, which is no longer unvariable in relation to absolute space,, but in relation to the earth alone. Accordingly the conditions appear to be given, by which we may succeed in setting up an amagnetic compass, as one has endeavoured to do in very many ways by gyro- scopic * contrivances for nautical use, trying to determine the meridian on board ship by means of the axis of rotation of a gyrostat *, held horizontally in Cardani suspensions, The whole group of previous investigators have endeavoured to succeed in this manner, but evidence is forthcoming, that no experimentalist has given a general and rigorous account of the actual behaviour and the necessary conditions. And yet for this it is only necessary to analyse the system of forces, which enters into the performance of a gyrostat mounted on board ship in the manner described. It appears then, first of all, that the vertical axis, round which the turning into the meridian should take place, is only an imaginary one. In practice we have to deal with an axis, which moves over the surface of a cone; and the axis of this cone only is the ideal vertical axis, round which constructors have hitherto considered their gyrostats to rotate. Now we can make the apex of the cone small, very small indeed, but never zero, a certain amount of * A gyroscope means the whole of the arrangement including the device for observation (hand, microscope, or the like), whilst gyrostat is the rotating mass in its frame alone. So the gyrostat can be called a gyroscope (as is generally done by French and German authors) with no more sense than, for instance, a spectrum can be called a spectroscope, Problem of the Amagnetic Mariner’s Compass. 731 play in the upper (or, in the cases of suspensions, in the lower) bearing, and therefore a tilting of the horizontal axis of the gyrostat, so soon as forces arise, which turn the upper (or, in the case of suspensions, the lower) end of the vertical axis ever so little in its bearing, being unavoidable. The smallest forced nutation of a gyrostat’s axis, namely, is enough, as Fessel and Pliicker showed with their so-called precession apparatus *, and as one could demonstrate with Bohnenberger’s machine f, to excite a force-component, which constrains the whole system to rotate round a third axis, perpendicular to both that of the gyrostat and that of nutation. This last axis, in the case of a ship’s gyrostat, is unfortunately exactly the vertical axis, round which it should turn for indicating the course. Therefore, every acceleration of the ship’s motion—whether it be rectilinear or curvilinear—acts so as to deflect the gyrostat ; and we are not, in general, in a position to separate this deflecting effect from-the visible deviations, by which a change in the ship’s course should be revealed. The greater the gyrostatic moment of inertia, the smaller will be the influence of the disturbances, but the greater will be the time-period of the oscillation of the amagnetic compass,—far above the limit permitting one to distinguish at every instant between oscil- lations of the compass-card and rotations of the ship. So some years ago (1904) I entered upon a completely new mode of treating the problem, after it appeared to me, that above everything the instrument itself should indicate con- tinually, whether its action is to be depended upon,—and this in the simplest manner, so that it should indicate either with unfailing correctness or not indicate at all; consequently the fact that it is in operation might at the same time be a guarantee, that it operates correctly, and that, further, it is to be recommended, that the would-be vertical axis should, if feasible, be altogether done away with. This consideration led me to a principle of arrangement, which up till now had been most carefully avoided: a dis- turbance of the position, but one, which is periodic, with a fresh adjustment always following it. The playing forces arising trom a complexity of rotations, which must be given a priori, the nature of the new total configuration is charac- terized as of a higher order, of which the gyrostat constitutes but an organic member: in distinction from previous * Fessel’s precession apparatus, described by Plucker and by Poggen- dorft, see Annalen der Phys. u. Chem. vol. xc., 1853. See my communication, “Simple Diagram connecting the various motions in the so-called Bohnenberger’s machine,” Phil. Mag. ser. 6, vol. ix., 1905. 3C 2 732 Mr. Taudin Chabot: Gyrodynamical Solution of the forms tried, it is gyrodynamic ; I might therefore call the instrument, in distinction from the gyrostatic compass, a gyrodynamic compass. | | The development of the idea obviously transforms the ill-fated vertical axis into a horizontal axis, which expe- riences no complete rotation as before, but only periodic oscillations of extremely small amplitude. Further details are afforded by the following explanation, with the help of the description of a model. Fig. 1. The principal axis T of the model (see fig. 1) cuts at an angle (90—@)°>0° the axis of rotation, w, of the forked- Problem of the Amagnetic Mariner’s Compass. 733 bearing of a gyrostat, perfectly balanced about an axis y, normal to the axis x, and having an axis of rotation y, perpendicular to y. Rotations can take place round the axis I’, the axis x, and the axis y ; and that too in this order, in general, with increasing angular velocity: wo,@, >, ~—will here remain undescribed. By observations is obtained the state of equilibrium of the gyrostat, 2. e. of the system round the axis y, while none, one, or more of the rotations round the axis I’, round 2, or round yare excited. Thereby we distinguish between 8 principal cases, partially subdivided, according to the given azimuth of ¥ or ¥: will be the system Aecording as the system and the angle round round ; round between between round Axis Axis z | Axis y | Axisy & Planer Axes y& OP Axis y rests rests _ rests : | astatic | turns | = | ” 5 rests turns ,, | a turns 33 | 3) | 3? rests rests | turns | ” tine calipry : iene ‘ ble | (syntropic motiors) ere turns a ae Sn | =909 | 0° &4180° | negatively stable —11272? i iigcis sa unstable (antitropic motions) ) =(90—¢)° stable | | a apeaean : | | #(90—9)° & 7 rests | turns ‘ | F negatively stable brs | | unstable turns 9 ae oscillating 734 Mr. Taudin Chabot: Gyrodynanucal Solution of the Of these cases Sire specially dealt with No. 66, Gilbert with Nos. 6a and 6 6, without, however, the gyrostat in the state of rest being an astatic system. Sire arrived at the stability of his gyroscopic pendulum ™* in the state of rest merely in that he laid the axis y a good deal lower, than the axis y, Gilbert, in his barogyroscope f, in that he kept both axes in one plane, balanced the system most carefully about the axis y and then added an adjustable weight. Gilbert studied the special case of identity of the axis I’ with the axis of rotation of his planet (Harth)—getting, therefore, w, as the angular velocity of the planet’s rotation,—with the con- sequence, that his model scarcely showed more than a gyrostat. with a permanently horizontal axis y in a forked-bearing, rotative in a foot; whereas Sire kept the axis I as the principal axis of his model, which, according to the relative direction of rotation round the axis y, was approximated (even in opposition to the so-called centrifugal force) or fled by the gyrostatic pendulum. Instead of giving the unbalanced gyrostat a position of rest by means of a gravitational moment, we can make the balanced gyrostat stable in any chosen position by means of an elastic force (acting about the axis y), and then observe the deflexion, brought about as a consequence of rotation at the same time round I’. The cases Nos. 6 and 7 are identical, as is evident, if d= 90°, viz. the axes x and I coincide. In case No. 8, being here of special interest, the pendulum- motion of the gyrostat round the axis y results, as ordinarily, from the intermittent action of a deflecting force against a directing one, which every time brings back the pendulum system into its position of stable equilibrium. The directing force arises from the simultaneous rotation (which also might be considered as a rotary oscillation) round the axis 2, or by means of a control-spring ; whilst, in an altogether similar manner, a force acting around the axis y arises from the rotation round the axis I, which, purely a directive force, in this case means a deflecting one, every time then (and thus intermittently) growing to a maximum, when the y-axis passes the azimuth normal to the Tz plane. The y-axis describes in consequence a conoid-surface round w with about the spiral-ellipse (similar to the Lissajou-figure for oscillation-ratios of 1 to 2 for 0° and 180° or 90° and 270° phase-difference) as generating-line and its apex in the intersection of the axes 2 and y. Moreover, the chief * Sire, Pendule gyroscopique, Archives des Sciences physiques et naturelles, vol. i. 1858. + Gilbert, Barogyroscope, Comptes rendus, vol. xciv., 1882. Problem of the Amagnetic Mariner's Compass. — 739. conditions to be realised here are: exact balancing about the axis y, by adjusting the centre of the rotating mass (and not by an additional weight, as Gilbert did in his baro- gyroscope *), and practically no slack-motion of the axis y in its bearings. Let us now identify the principal axis of rotation, I’, of our model with the axis of rotation of the planet, so that as tangible of the whole merely remain the gyrostat, lying in its bearings, with the clockwork, C, which imparts the angular velocity @,, syntropic with w,; and let this apparatus be mounted with the z-axis in suitable Cardani- suspensions on board a ship, where it, when in the geo- graphical latitude ¢, takes up the position, indicated in the figure relative to the earth’s axis I, whenever the y-axis passes through the meridian. At this moment the gyrostat behaves astatically with respect to the simultaneous rotation round T' (cf. above, No. 6a), and responds exclusively to the directing force, due to the rotation round «, or else to an elastic device, which tends to turn the y-axis into the vertical, i. é. into the extension of the axis of rotation «. But at the next instant the y-axis has passed through the meridian, ex- periences again the deflecting force of the rotation round I, which comes into play, and increases with the sine of the angle of rotation up to a maximum for 90° rotation of the axis y round « (cf. above, No. 60). Were the just-named directing force not available, so would the deflexion of the y-axis from the vertical reach the value (90—¢@)°, 7. e. the y-axis would set itself parallel to the planet’s axis, but as the directing force continues, ‘the deviation remains in general less than (90—@)°, with the exception of the case (treated further later on) of a resonance between the oscillations round y and the rotation round x. After a further 90° rotation of the y-axis round z the elongation will be again zero, and the y-axis again stand vertical in the extension of the axis of rotation 2 A model allowing to observe these movements most beautifully according to the theory—built by Messrs. Hartmann & Braun—is shown in fig. 2, Pl. XXI. Of special importance, as already emphasized in the introduction, is now an analysis of the system of forces, acting in our gyrostat. Besides the practically constant gravitational force, the remaining inconstant forces may be classified as translatory- and rotatory-ones. All translatory forces, resulting from the inertia-reaction, can be separated into vertical and horizontal components, in consequence * Rarissima avis! I saw one only once, and of average workmanship, at the Collége de France in Paris. 736 = Mr. Taudin Chabot: Gyrodynamical Solution of the either of the rolling and pitching of the ship (see Poggen-: dorff’s falling machine * , of date 1854), or else horizontal as. a result of rectilinear accelerations on her way and their variations; they have no influence on the position for the time being of the balanced gyrostat. Translatory forces along an are (or circular translatory forces) in consequence of the rotation of y round «, which tend to give the bearings of the gyrostat a rotation——w,, exist only whilst the gyrostat is started and soon vanish; they are of no further importance. Rotary forces enter in two ways into the phenomena; the in- termittently acting deflecting force, already considered, arising in consequence of the rotation round the planet’s axis I’, and the permanent directing force, likewise referred to, resulting from spring tension or from rotation round z. In the last is also merged any disturbance, arising from an alteration of the ship’s way, which, taking place in a horizontal plane, has.the same character as a rotation about a vertical axis, that is round 2, or, what means the same thing, round an axis parallel to w ; therefore, an increase of w, only can influence the directing force dependent on and proportional to it—viz. to a vanishingly small extent—what solely means a variation (of practically unassignable value) of the maximum elongation of the gyrostatic oscillation and in no w ay will disturb the frequency of the pendulum-motion. And this frequency only is of importance to us;,-1t is equal to that of the rotary motion of the forked-bearing, and necessarily goes through a to-and-fro motion round y during each’ rotation round wz. If now the rotations on board ship are counted by reading a mark, fixed rigidly to the ship, it will happen, that apparently. less or more, than a compiete pendulum oscillation about y corresponds to a single rotation round 2 This phenomenon is easily ex- plained: the ship altering her course, she alters her angular position to the same extent as the phase-change between the oscillation and the rotation of the gyrostat. Indications of this phase-change imply then indications of the variation of the ship’s way, or rather of the way in general, in so far as only the passing of the y-axis through definite azimuths at the planet’s surface affects the oscillation, and these indi- cations can easily be obtained by any stroboscopic method, with the help of electromagnetic sending- or contact- contrivances, which would be controlled by the rotation or by the oscillation. The last one is allowed to arise not with the largest _ * Poggendorff’s Falling Machine, Annalen der Phys. u. Chem. vol. xcii., 1854. ; Problem of the Amagnetic Mariner's Compass. 737 possible amplitudes, but playing only with an arm of the pendulum-system between two stops placed near to- gether, and the breaking of an electric circuit. is brought about by the motion of the y-axis through the vertieal in (so to speak) statu nascenti. If we keep then, for example, a vacuum-tube lighted whilst it rotates round an axis normal to its own axis, synchronously with the axis of the fork 2 (thus at the same time with angular velocity w,), so will the ship’s way and its variations @n, lest wz, in general, in relation to the surface of the planet, might become = zero. The rotating-velocity wz, and the oscillating-one ty, must be such as to suit one another, that is, such, that they synchronize (a to-and-fro motion round y corresponding to a complete rotation round «), whence the amplitude of this oscillation may be small. One recalls further the fact, that the time- period of an oscillation, 27I?7F—*, will be determined by the magnitude of the moment of inertia, I, and the directing force I’, this one as shown previously, the other built up by the factor I,, and a gyrostatic term, which is a quadratic function essentially of I, and wy. The described arrangement with horizontal bearings for the gyrostat introduces the important advantage over all those with vertical gyrostatic axes, that a construction is possible, which permits this axis to be regarded as very nearly indeed rigidly fixed, and at the same time to content with a very small directing force, viz. inertia; the small angular motion, instead of complete rotation, allows one the use of the finest cut bearings obtainable, or possibly of magnetic setting or adjustment of the pressure on the bearings, so that in consequence the directing forces to be chosen (or the impulses Iy wy) can be smaller than is usual with gyrostats, this meaning right away a shortening of the time-period of the oscillations. ‘And for a completely rigid axis the period of oscillation would be simply inversely proportional to the square-root of the restoring force in the actual model, subject then to a small correction for the non-absolute rigidity of the material of which it is made. Valuable is a comparison of the formule given formerly at Montreal, however in another connexion, by Lord Kelvin*, who saw still the principal contents of the present communi- cation. The synchronism being obtained between the rotation round z and the oscillations about y, we generally get forced oscillations, that is, oscillations, which are differently possible between the limits, determined by the selected values of * Reports of the British Association, liv., 1884. Multiple Atomic Disintegration. 139 the separate factors, and thus can be forced into synchronous motion. This oscillation-region involves also the so-called free oscillation-period ; if we determine wz correspondingly, resonance will arise between the rotation and the oscillation, and thereby result the strongest tendency to oscillate. This shows us the manner, in which, even when large gyrostatic moments exist, short periods of oscillation may be obtained, namely, by compensating the inertia by simple stiffening of the control-spring (F,), because in the case of resonance the greatest possible amplitude of oscillation is the resultant of the directing and deflecting forces’ combined action ; the ratio wz/w, is here to be taken accordingly large. By means of suitable transformations (electromagnetic syn- chronous motors or the like) the ratio w,/#:, may then be forced to an equally constant magnitude as that of the once- for-all determined magnitudes of mass and moment of inertia of the regarding parts of the constructed instrument. For practical needs we might employ two or more gyrostats of smaller construction, oscillating in one frame together round a common axis y, rather than a single larger gyrostat, so as to combine two or more such systems with axes y, shifted round through equivalent angles with respect to one another, their bearings either over one another in a single framework, rotating about the vertical x, or again each in a forked bearing rotating individually, the synchronous motions of all the bearings maintained with a constant phase-difference between them in the same manner as in the contro] of electrical clocks, equally at distant points of the ship, where- ever these synchronously-acting instruments may be instailed, —whilst their paths of connexion count amongst the numerous nervous fibres of that gigantic creature, the modern ocean- runner. Hohenwaldau, near Stuttgart.. . February 13, 1908. i LXXVI. Multiple Atomic Disintegration. A Suggestion in Radioactive Theory. By Freprrick Soppy, M.A.* akc: cause of atomic disintegration remains unknown. It is difficult to construct any model of the disintegrating mechanism, chiefly on account of certain features in connexion with the process. In particular may be mentioned the fact that the period of average life of the atoms disintegrating is the same whether newly formed atoms or those which have * Communicated by the Author. 740 Mr. F. Soddy on already survived many times the average period are con- sidered. What may be termed the inevitableness -of the process, and its entire independence of all known conditions, suggests that the cause of disintegration is apart from the atom. It is difficult to believe that the cause is resident in space external to the atom. It seems more probable that it exists within the atom and at the same time is uninfluenced by it. The question about to be discussed is whether necessarily only one mode of instability can exist within the atom at the same time. In certain’ problems in radioactivity it is becoming necessary to take into account that the same element, for example uranium, may give rise to two different series of disintegration products, represented for example by actinium and radium. Rutherford has suggested in order to account for the small quantity of actinium, relatively to radium, in minerals that actinium may be formed from uranium as a side or branch chain, not in the main line of descent. The suggestion in this paper is that multiple modes of disinte- gration may be vroceeding simultaneously and independently within the same atom. There is nothing in this idea opposed to all that is known of the character of atomic disintegration. On the other hand it will be shown that such disinte- grations would simulate closely in many respects simple disintegration. It has been established that the law of simple disintegration really expresses the operation of the law of probability for a process selecting the particular individual atoms dis- integrating without reference to the character of the individuals, but solely according to the total number in existence. That is to say, the period of actual life of the individual remains indefinite up to the moment of disinte- eration, and no process of sorting a collection of atoms into long-lived and short-lived varieties is even conceivable. Similarly for multiple disintegration the view advocated is that the law of simple disintegation applies to each mode of disintegration exactly as if it were the only one in operation. It follows that the question by which particular mode any individual atom will disintegrate remains indefinite up to the moment of disintegration and no process is conceivable which would sort a collection of atoms according to the mode by which eventually they will disintegrate and to the product which eventually they will produce. If for the same atom two modes of disintegration can occur independently, the constant of the first mode being represented by A, and that of the second by Ax, the quantity Multiple Atomic Disintegration. TAL Q of the substance will diminish according to the differential equation dQ _ Ge = — MuQ—AKQ Qe _ —(a+Ax) or a : Q where Q; is the quantity remaining at time ¢ and Q, the initial quantity. That is to say, for a radio-element underg going a dual disintegration the quantity would diminish exponentially with the time as in a simple disintegration. The radioactive constant of the multiple change would be the sum of the separate constants. If, for example, a-rays were given out in one of the modes of disintegration, and 6-rays in the other, each type of radiation would decay at the same period, namely, the sum of the two separate periods. The same holds trie whatever the number of modes of disintegration. So that multiple disintegration would not be easy to detect so far as ordinary criteriago. But with regard to the products formed in the various modes there will be constancy of pro- portionality between them. To suggest a concrete case, let us suppose the disintegration of uranium X is dual, one mode producing ultimately radium, the other ultimately actinium, and let the constant A, apply to the radium mode and Ax to the actinium mode of disintegration. ‘Then the ratio between the number of uranium atoms forming radium and the number forming actinium is given b Ma If the further disinte- g g y' ee grations of both these elements are simple the same ratio will express the relation between the quantities of the final inactive products of the two series. This suggests at once a method of obtaining evidence of the process < and at the same time of determining the nature of the final products. baie constant ratio were found between any two inactive elements present In uranium minerals it would be very strong evidence from the present point of view. According to the researches of Boltwood (Am. Journ. Sci. 1908, p. 296) on the proportionate a-radiation contributed by the separate constituents in equilibrium in uranium minerals, it is possible to deduce (Phil. Mag. Oct. 1908, p. 517) that of eight atoms of uranium seven go to form radium and one to form actinium. ‘The ratio _ is therefore equal to 7. VX 742 Mr. F. Soddy on This is also the ratio between the quantities of the end- products of the two series in minerals on the assumption stated. _Proceeding with the idea that the disintegration of uranium X is dual, it makes no difference whether we regard the @- and y-rays as derived from one only or from both of the modes of disintegration. Or, we may even suppose that the 8-rays come from the radium mode, while y-rays come from the actinium mode of disintegration, which appears to have something to recommend it as it would explain the relative poverty of uranium in y-rays (Soddy and Russell, Phil. Mag, Oct. 1909, p. 631). Both types of rays would decay atthe same rate. The apparent value of the radioactive constant of uranium X (about ‘03i (day)—! ) would be the sum of the two separate constants, one of which is seven times the other. The radium mode would thus have the constant °027 and the actinium mode of disintegration, *004. This point of view explains perfectly the known relations between uranium, actinium, and. radium, preserving the inevitableness of the phenomenon, without the necessity of supposing, as on Rutherford’s theory of a side-chain, that actinium is not a lineal descendant of uranium in the same sense as radium is (‘ Radioactive Transformations,’ p. 177). Considering the long series of successive disintegrations passed through by the radioactive atoms it would be rather re- markable from one point of view if multiple disintegration did not sometimes occur. The relations between thorium and uranium in minerals would receive perhaps a_ better explanation on the view that thorium is one product of a multiple disintegration in the uranium series. The evidence has been discussed by Boltwood (Am. Jour. Sci., 1905, xx. p- 256) who concluded that it was most probable that thorium was a disintegration product of uranium. The period of thorium is probably five times as long as that of uranium, and hence thorium cannot be intermediate between uranium and radium as in this-case. there should be a-constant ratio between thorium and radium in equilibrium and not between uranium and radium, On the present idea the ratio of thorium to uranium and to the end-products of radium can be calculated but the expressions involve the age of the mineral. These expressions are i As (Aa+Ax—Az)t a SPN y i U ec ya i ) T Aa(Ag + Ax) (_— Fh, pene Aa). ee ee where ¢ is the age of a mineral, assumed to contain no thorium Multiple Atomie Disintegration. 743 or end-product initially; T, U, and EH, the existing quantities of thorium, uranium, and end-product of radium ; Aa, Ax the con- stants of the thorium and radium modes in the multiple dis- integration of uranium ;_ Az the constant.of thorium itself, and kis the fraction of the number of uranium atoms undergoing the radium mode of disintegration which eventually become atoms of the end-product in question. Were all subsequent disintegrations simple & of course would be unity. The effect of the intermediate bodies between uranium and the end- product has been neglected. So far asis known this would be small. Unfortunately on account of the long period of thorium and the isomorphism of uranium and thorium oxides it is doubtful if much evidence can be derived from the composition of minerals. Thorianite is regarded as an extremely old mineral geologically yet it contains so great a percentage of thorium that from the point of view of radio- activity it must be a recent formation. As Boltwood has pointed out (loc. cit. p. 262), Hillebrand’s analyses of uranium minerals show generally that the percentage of total rare earths (less perfectly of the thorium) increases as the lead increases but there are numerous exceptions. It is probable that geological time is all too short to enable the necessary evidence to be obtained from the composition of minerals, Before concluding a special case may be referred to which has some points of interest and might very probably occur. If one of the modes of disintegration were a relatively mild form of rearrangement, rather than an explosive disintegration, it is conceivable that the ray-producing change might occur with the same period independently of whether the rayless change had or had not occurred, expelling the same character of ray ineachcase. On this viewactinium would proceed from re- arranged but undisintegrated uranium X, radium from uranium X disintegrating directly, or vice versa. If, represents the constant of the rayless and Ax that of the ray-producing mode of disintegration, it can be shown for this case that the rays will now follow the exponential changes with their own true period, Xx, rather than with the A,+)x period. This holds true whether the rearranged uranium X is present or absent initially. The calculation which gives this simple result is lengthy and may be omitted. If y-rays accompanied the B-rays in the direct mode of change of the uranium X, and not in the change of rearranged uranium X, the y-rays would decay with the A,+Ax period, the 8-rays according to the Ax period. The difference in period would be small and might well be overlooked. 744 Mr. W. T. Kennedy on the Active Deposit At present there is no experimental evidence either for or against the view that the disintegration of uranium X is multiple, although such evidence has been sought for in this laboratory for some time past. It must be understood that this particular case has been taken for purposes of illustration only. | Physical Chemistry Laboratory, University of Glasgow, Sept. 13th, 1909. LXXVII. On the Active Deposit from Actinium in Uniform Electric Fields. By W.T. Kexnepy, 6.A.* [Plate XXIT.] I. Introduction. N a number of experiments which have been carried on with the emanations and the emanation products from the radioactive substances, it has been shown by Rutherford f that with thorium emanation the amount of activity imparted to a rod charged negatively was independent of the pressure until a pressure of 10 mm. was reached, and that below this pressure it decreased as the pressure in the containing vessel was lowered. At 1/10 mm. pressure it was only a small fraction of its maximum amount. Makowert has also ob- tained similar effects with the excited activity from radium emanation. Further, Rutherford § experimenting with yadium emanation, found that at atmospheric pressure the greater part of the active deposit went to the cathode, while only about 5 per cent. went to the anode. From these results he has drawn the conclusion that while most of the active deposit particles of radium are positively charged, some at least must carry a negative charge, inasmuch as they are drawn to the anode in electric fields. More recently Russ || showed that when positively and negatively charged electrodes were placed in a vessel containing either air, sulphur dioxide, or hydrogen charged with the ema- nation from radium, the relative amounts of the active deposits obtained on the two electrodes varied with the pressure at which the exposures were made. With all three gases the * Communicated by Professor J. C. McLennan, and read before the Royal Society of Canada on May 26, 1909. + Rutherford, Phil. Mag. Feb. 1900. + Makower, Phil. Mag. Nov. 1905. § Rutherford, Phil. Mag. Jan. 1903. || Russ, Phil. Mag. May 1908. from Actinium in Uniform Electric Fields. 745, active deposit on the negative electrode gradually decreased as the pressure was lowered, while that obtained on the positive electrode showed a corresponding increase, until ultimately at the lowest pressure investigated, the amounts of the active deposit obtained on the two electrodes were approximately equal. In a second paper Russ * gives an account of a similar set of observations made with the emanation from actinium. In these experiments positively and negatively charged elec- trodes were again exposed in a vessel filled with air and containing a quantity of actinium. In this case as the pressure of the air was lowered the amount of the active deposit obtained on the negative electrode gradually in- creased, passed through a maximum value at a certain critical pressure, and ultimately fell away again at the lowest pressure inv estigated. On the other hand, in these experi- ments Russ found that the active deposit obtained on the positive electrode steadily decreased as the pressure of the air was lowered. In his second paper Russ also describes a series of experi- ments in which exposures were made in air when the distance between the actinium and the electrodes was gradually in- creased. The results which he gives show that with the air at 760 mm. the amount of the deposit obtained on the cathode steadily decreased as the salt was placed at distances varying from 2 to 50 mm. from the electrodes. Under similar cir- cumstances the amount obtained on the anode at first increased as the salt was removed, and finally, after passing through a maximum value, fell away again at the longer distances. With the air at 2 mm. pressure, however, the amount obtained on the cathode steadily increased as the distance of the salt from the electrode was varied from 2 to 42 mm., but the active deposit obtained on the anode with the same variation of distances gradually decreased. In discussing his results Russ points out that Debierne had found that the amount of emanation obtained at atmo- spheric pressure from a uniform layer of actinium fell to half value in going °55 cm. from the layer, and that con- sequently one would expect to find a decrease in the activity of the electrodes as the salt was removed, and possibly, too, a continuance in the ratio of the activities of the deposits obtained on the two exposed terminals. The results given by him, however, show that this was far from being the case. * Russ, Phil. Mag. June 1908. Phil. Mag.8. 6. Vol. 18. No. 107. Nov. 1909. 3D 746 Mr. W. T. Kennedy on the Active Deposit In the various experiments referred to above on the active. deposits from radium, thorium, and actinium, the different. investigators—with the exception of Debierne—do not appear to have taken any precaution to study the behaviour of the active deposits with uniform electric fields, and as it was thought that some points which are more or less obscure in connexion with these active deposits might be cleared up if they were studied in this manner, it was decided to apply this method to the investigation of the active deposits from actinium, which on account of the short life of its emanation is peculiarly suitable for the purpose. Il. Apparatus. The apparatus consisted of a metallic cylinder about 5:5 cm. in diameter, which was supported horizontally in an air-tight. chamber. Into this cylinder (as shown in fig. 1) there were Fig. 1. Ci) OR) 3 129 We SYA OWANAM IPTC LARLO MIMO TN ie ELectTRODe., Wee ees sft Barrery. Harti. fitted two electrodes provided with guard-rings. The salt was carried in a small tray which could move freely up and down in a vertical tube (1°5 cm. in diameter), which led into the cylinder. The tray could be clamped in position at. any desired distance from the electrodes, and the latter, which were capable of easy motion, could readily be placed in the exposing cylinder at any selected distance apart. The air-tight chamber was also provided with tubes for the. from Actinium in Uniform Electrie Fields. 747 admission and removal of the different gases used, and through its base wires suitably secured were led, for the purpose of charging the electrodes. The electrodes, which were circular, were 2°5 cm. in diameter, and the guard-plates. which surrounded them were each °5 em. in width. III. Measurements. In the various experiments which are to be described later, the sample of actinium used was obtained from the Chininfabrik, Braunschweig. In making the exposures the electrodes were exposed in every case to the action of the emanation for two hours before being removed from the ex- posing vessel for measurement. The activities of the elec- trodes were tested by an ordinary «-ray gold-leaf electroscope, and all the values which are quoted in the paper represent the activities of the electrodes 10 minutes after the exposures ceased. In making the measurements of the activities of the two electrodes, observations were continued for a period of forty or fifty minutes. From these observations, of which fig. 10 (Pl. XXII.) is illustrative, the rates of decay of the deposits on both anode and cathode were found to be the same, and to be approximately about 39 minutes. In making all the exposures the electrodes were charged to a potential of approximately 250 volts. IV. Active Deposits and Distance between the Electrodes. In commencing the study of the active deposits from actinium a set of measurements was made on the active deposits obtained on the two electrodes when the salt was placed in the vertical tube at a constant distance from the cylinder, and the electrodes were gradually separated. Ina particular set of observations the plates were placed vertically 1 mm. apart, and the salt was brought as close to them as the construction of the apparatus would permit. With this arrangement the salt, which was always covered with a layer of thin filter-paper, was at a distance of 11 mm. from the lower edge of the plate electrode. Observations were made at atmospheric pressure on the active deposits obtained on both electrodes for distances 1, 2, 3, 4, 5,6, and 8 mm., and the results are all recorded in Table I. A curve illustrating them is shown in fig. 2 (Pl. XXII.). From these results it will be seen that as as the electrodes were separated the activity obtained on both plates steadily decreased. With distances apart greater than 3 mm. no measurable activity was obtained on the anode, but with the greater distances, viz. 8 aie the active deposit obtained 3 D2 NG Pa ’ 748 Mr. W. T. Kennedy on the Active Deposit TasLE I.—Atmospheric pressure. Separation of Activity on the Activity on the Electrodes. Cathode. Anode. 1 mm. 17:0 15 Be iss 13:7 : 3 + * 1 11°5 0 » 10°3 0 5 9°0 ae) Git; 8-7 0 AES 86 0 on the cathode was still about one-half that obtained for a separation of only 1 mm. on the same terminal. V. Active Deposits and Distance of Salts from the Electrodes. Measurements were also made on the active deposits obtained on the electrodes at pressures of 760, 120, 25, and 5 mm., when the distance between the electrodes was maintained at 2 mm., and the salt placed at a series of distances from the electrodes varying from 1-1 cm. to 5 em. These results are recorded in Table II., and curves illustrating TABLE If. Pp Distance of Salt | Activity on the | Activity on the oo from Electrodes. Cathode. Anode. Atmospheric 10 cm 39°5 8 39 1:3 ” 26°5 3 ‘ 208 « 8:5 “ij - Sen TD 0 ee 40 ” 1:0 0 °? 5-0 ” D 0) 120 mm 1-1 em. 730 5D ” 2°0 ” 36'8 32 | : 35), 16:5 1-7 | ” 40 ” 6:3 “t | 25 mm 1-1 cm. 63°5 27°0 | oa AO), 41:0 17°5 ¥ 3D is:, 25'3 11'8 | ¥ DOr 5. Lae 67 5 mm 1-1 cm 32°83 28:5 "4 ZO 27:0 23°7 ” he Ao ar 16:0 BO 13°5 Ils | from Actinium in Uniform Electric Fields. 749 them are drawn in figs. 3, 4,5,and6 (Pl. XXII.). From the numbers given and from the form of the curves it will be seen that for all pressures the activity obtained on both electrodes steadily decreased as the distance between the salt and the electrodes was increased. This result, it will be seen, is somewhat different from that obtained by Russ with his apparatus, for, as stated above, he found at certain pressures that the active deposits slightly increased as the salt was removed, attained maximum values at certain distances, and finally fell away as the salt was still further removed. VI. Activity of Deposits in Air dependent upon Pressure. The next variation made in the experiments was to keep the electrodes at a constant distance apart, 2 mm., and the salt at a fixed distance 11 mm. from them, while the pres- sure of the air was gradually lowered, and the activity of the deposits corresponding to different pressures was measured. The range of pressures investigated was from 750 to ‘5 mm. of mercury. Table III. gives the results for air, and TABLE ITI. é Activity on the Activity onthe | ate. Cathode. eas ‘*5) mm in Er ¢ its >. 14:5 140 at) 18°5 17:0 cok 375 29°0 or. 49-0 33:0 ro | ee 62°5 28°5 420 ,, 82°3 17-7 720)? 92:0 10-0 220, 91°0 TD 1904)... ¢, 76:0 . 55 te 73:0 5:0 | iGO .. 68:0 4:0 2) 66°5 30 / 320'0 ,, 43:0 iS ) MOO, 31:0 ‘70 1500 ., 20°5 45 | figs. 7, 8, and 9 (Pl. XXII.) were drawn from them, and illustrate the manner in which the deposits occurred at the various pressures. The curves for both electrodes, it will be seen, follow similar laws. The activities on both elec- trodes steadily rose as the pressure fell, both passed through maximum values, and both fell away again and approached equality at the lowest pressure. 750 Mr. W. T. Kennedy on the Active Deposit The maximum activity for the cathode was obtained at a pressure of 80 mm., while that on the anode was not obtained until a pressure of 17 mm. was reached. The maximum cathodic deposit, it will be seen, too, was only about 2°75 times that obtained on the anode. From time to time decay curves were drawn for the active deposits obtained on the two electrodes, and it was always found that these deposits decreased in activity to half value in about 39 minutes, irrespective of the electrodes upon which they were obtained. This fact, combined with the similarity of form in the activity curves for the two electrodes, goes to show that with both electrodes the deposit always consisted of the same transmutation product or products, and that the difference in the amounts obtained on the two terminals must be traceable either to differences in the charge acquired by the deposit particles in their passage, by diffusion or otherwise, through the air, or to the phenomenon of recoil recently noted by Otto Hahn *. VIL. Activity of Deposits obtained in Carbon Dioxide at different Pressures. In order to study how the deposits might be affected by a modification in the conditions of: their diffusion a set of measurements, similar to those carried out with air, was made with carbon dioxide at pressures varying from 750 mm. to 1 mm. of mercury, and the values of the active deposits obtained are recorded in Table IV. From these results TABLE IV. J Activity on the Activity on the | Pressure. Cathode. ends 1:0 mm 15°6 14:7 * 37°5 28°5 180s), 60°5 20°5 300. 75'5 19°6 400 _,, SRD 16:0 (isi! eae 81'6 9:0 L050 Oy, 72:0 70 1230) 5, 66°5 58 235:0_ ,, 46:7 30 480°0_., 22:0 29 T7500 s, War, ‘75 curves in figs. 11 and 12 (Pl. XXII.) have been drawn. It will be seen that these curves also follow laws similar to those * Deut. Phys. Ges. xi. Jahr. no. 3. from Actinium in Uniform Electric Fields. 751 obtained with air, and that the deposits on the two electrodes gradually increased as the pressure was lowered. Both passed through a maximum, and for still lower pressures the active deposit. on both plates decreased and approached equality for the lowest pressures investigated. The maximum activity on the negative electrode was obtained at a pressure of 60mm., while the maximum active deposit on the positive terminal was not obtained until the pressure was 14 mm. The maximum active deposit on the cathode was about 2°68 times the maximum deposit on the anode, and this, it will be seen, is not very different from the ratio which was found for the maximum activities obtained in the case of air. Care was taken in the experiments with carbon dioxide and air to repeat all the observations a number of times, and the curves indicated in figs. 7 and 11 (Pl. XXII.) were uniformly obtained for the two gases under the conditions described. VIII. Activity of Deposits obtained in Hydrogen at different Pressures. Another series of measurements was made with hydrogen, under conditions similar to those already described with air and carbon dioxide, and the active deposits obtained at the varlous pressures are given in Table V., and a curve repre- senting them in fig. 13 (Pl. XXII.). From these observations TABLE V. | i Activity onthe | Aetivity on the | Pressure. Cathode. } Anode. 6 mm. 21-0 20:0 | 46 ,, 52:0 43:0 | UN Game 83:0 43°7 Zea 3: 106:0 27°7 a7 «4, 873 15:0. | 760 ,, 783 | 83 it will be seen again, that as the pressure was lowered, the active deposits on both electrodes steadily increased, passed through maximum values, decreased, and on the de- crease approached equality at the lowest pressures examined. In hydrogen the maximum active deposit on the cathode was obtained at about 250 mm., but the maximum active deposit on the anode was not obtained until about 80 mm. pressure was reached, The maximum active deposit on the negative 752 Mr. W. T. Kennedy on the Active Deposit electrode was about 2°3 times the maximum active deposit on the positive terminal. Repeated measurements have not been made to confirm these results, but the same precautions were taken with hydrogen as with air and carbon dioxide. It will be seen from the values given, that the ratio of the maximum activities for the two terminals in the case of hydrogen is. only slightly less than the corresponding ratios for air and carbon dioxide. IX. Comparison of the Active Deposits in Air, Carbon Dioxide, and Hydrogen. For purposes of comparison the active deposits obtained under the various circumstances are collected in Table VI. From this Table it will be seen that the pressures at which TABLE VI. Gua Active Deposit Pee Active Deposit ae on the Cathode. Seka on the Anode. Air. ‘| 205 750 mm. “45 i 92:0 (maximum) SOT GS ST. UES eee ee iy Ca PUM NS Mai atic ay. 33°0 (maximum)| - 117 . Carbon Dioxide.| 11°7 750 mm. “Wo F 82:0 (maximum) GO a3 ch Siena BR TMP IS a ase siaecc ones 4 ,, 31:0 (maximum) Nah 15°6 ~ 4:7 Hydrogen. 78°'3 760 mm. 8:3 108°0 (maximum) 250) eh) ee a ee Se Ri iberay ARQ ints celia iale eye 80. ;, 46 (maximum) | %9 21:0 4 20 the maximum cathode deposits were obtained for the different. gases are—carbon dioxide 60 mm., air 80 mm., hydrogen 250 mm. These pressures are approximately in the ratio 1:1:33:4:2. Now, since the coefficient of diffusion of a gas isinversely proportional to the molecular weight of a gas into which it is diffused; and since, further, the coefficient of diffusion is inversely proportional to the total pressure of the two diffusing gases, it follows, since in this case the diffusing transmutation product must be exceedingly minute, that the coefficient of diffusion for the product will be inversely pro- portional to the pressure of the gas into which it is passing. Further, since the maximum activities on the cathode for the different gases are approximately the same, 7. e. 82, 93, and 108, we may look upon the results as due to the diffusion from Actinium in Uniform Electric Fields. 753 of a maximum effect in the three gases, and consequently for the critical pressures given above, deduce an approximate estimate of the ratios of the coefficient of diffusion of the active product or products into the three gases at atmospheric pressure. These follow directly from the argument just presented, and are given in Table VII. Tasie VII. / Calculated Ratios of / the Coefficient of Gas. Pressure for maximum Diffusion of the Active | Active Deposit on Product into the | the Cathode. different Gases at | Atmospheric Pressure. Carbon Dioxide......... 60 | 1 a J | 80 | 13 SAVHEMSER 2.25 .6.2.5.: | 250 | 4:2 Following the same line of argument in case of the anode deposits, since the maximum effects were obtained at pressures 14 mm., 17 mm., and 80 mm., for carbon dioxide, air, and hydrogen respectively, it follows that the ratios of the co- efficients of diffusion of the active products concerned were as 1: 1°21: 5:7, 2. e. the relative coefficient for air was slightly lower and that for hydrogen slightly higher than the values deduced from the behaviour of the cathode deposits. The ratios of the coefficients of diffusion of the active pro- duct concerned, as deduced from the cathode deposits, are practically the same as some values given in a paper by Russ *; and this agreement goes to show that it is a diffusion phenomenon which is the paramount one in the present investigation. The interpretation of the maximum effect obtained on each electrode with the three gases, however, presents some difficulty. Oneshould have expected, with the active deposits in the experiments in which the salt was placed at different distances from the electrodes, that in the case of the lowest pressures a maximum value would have been obtained for a certain critical distance of the salt from the plates. But, as the curves in figs. 5 and 6 (PI. XXII.) show, no such maximum values appeared. * Russ, Phil. Mag. Mareh 1909. {54 Mr. W. T. Kennedy on the Active Deposit X. Active Deposits in the Absence of Electric Fields. In the experiments described up to the present the active deposits were all obtained with a potential-difference of approximately 250 volts between the electrodes ; with these conditions, however, it was impossible to draw any definite conclusion as to the relative quantities of charged and uncharged deposit particles involved in any particular measurements. With the object of throwing some light on this point an additional set of observations was made on the deposits obtained in air at different pressures with the elec- trodes uncharged, and at a distance of 2 mm. apart. The activities obtained on the two electrodes in these expe- riments were added together, and the numbers representing them are given in Table VIII. For purposes of comparison the total activities obtained with air at different pressures under a field of 250 volts are also inserted in the Table, and curves re- presenting both sets of values are shown in fig. 14 (Pl. XXII.) TABLE VIII. Pransupe Total Deposit with Field Total Deposit. ‘ of 250 volts. No Field. 9 mm. 461 216 ae 64-0 | 52-0 ee 653 | b4-4 127 2? 50°5 F 50-4 422 ,, 23:0 24-9 155 5; 13:4 - 108 From an inspection of the two curves it will be seen that the total active deposit was practically the same with and without the field at all pressures above the critical one. At and below this pressure the deposits obtained with the electric field applied, as the figure shows, were somewhat in excess. From this experiment it would seem that the deposit particles in very great measure go to the walls of the vessel in which they are produced whether an electric field be applied or not. The manner in which they are carried there, however, is not evident. It is possible that a certain proportion of the deposit particles are uncharged, and that these reach the walls by ordinary diffusion. | | Then again these deposit particles may be electrically charged, some of them being of one sign, and some of the from Actinium in Unijorm Electric Fields. 755 opposite, and diffusion again may be the chief factor in pro- ducing the deposit ; or further, if the disintegration recoil phenomenon is the determining factor, it is possible that, with the plates close together, the deposits are made by reason of the velocity of expulsion alone. If this latter be the explanation, the sign of the charge carried by the deposit particle would not then exert any considerable influence except in the most intense fields. , In all the measurements made the cathode deposit was, except at the very lowest pressures, considerably in excess of that obtained on the positive terminal. This goes to show that part at least of the deposit particles carry a positive charge and reach the electrode under the influence of the field. The manner in which these particles gain their positive charge, however, is not clear. From experiments by Logeman* and others it is known that a plate of copper on which polonium is deposited emits a copious stream of delta particles. These, it is also known, are beta particles of low velocity, which are very probably ejected either from the copper or from the polonium or its transmutation product under the bombardment of the alpha particles. Itis possible too that the delta radiation may be caused by and accompany the a particle in its expulsion from the parent atom. Such a plate of copper as that mentioned above is known to acquire a positive charge when placed in a very high vacuum, which shows that an excess of negative electricity leaves it as a result of the action of the various radiations. It is possible then that some of the deposit particles from actinium or other active emanations may gain a positive charge under the action of the alpha radiations present in much the same way as the copper plate in the polonium experiments. This would then account for the positive charge on the particles, and consequently for their removal under the field to the negative terminal. On the other hand, some experiments recently made by H. W. Schmidt + have brought out a parallelism between the amount of active deposit obtained in air under different electric fields and the intensity of the ordinary conduction current through the air under the same fields. This would seem to show that the charges are acquired by the deposit particles as a result of collision with the gaseous ions present in the same vessel. * Logeman, Proc. Roy. Soc. A, lxxviii. p. 212 (1907). + Phys. Zeit. ix. pp. 184-187, March 1908. 756 Mr. W. T. Kennedy on the Active Deposit Many of the results obtained in the present investigation go to support this view, and one in particular is of special interest. In this experiment the electrodes were 2 mm. apart, the salt was placed 1°3 mm. below the electrodes in the exposing vessel, and the exposures were made under different voltages in air at a pressure of 9mm. The exposures were made first with the two electrodes at the same potential, and then with them at different potentials ranging in extent up to 1150 volts. The results of the various activity measurements are given in Table [X., and curves drawn f10m these numbers are shown in fig. 15 (Pl. XXII). TABLE LX. Pressure 9 mm.; Electrodes 20 mm. apart ; Distance of Salt 13 cm. Ne Activity on Activity on Voltage. Negative WlesHode Positive Electrode. Ue | 11:0 10°6 83 . 1271 10-0 242 14:9 10°2 | 467 155 10°83 523 lips 11:2 545 | 18°6 14:2 | 605 17-4 13:0 | 641 39°8 25:0 | 683 eho”, 13:1 794 30°7 19-2 928 20:7 25-0 955 38°7 21°6 1149 29:4 ; | 19-2 Note.—Sparking potential for pressure 9 mm. and distance 2 mm. ==460 volts, (Carr, Phil. Trans. Roy. Soc. vol. cci. pp. 403-433.) From these results it will be seen that when the potentials. of the two plates were the same the activities of both were alike ; but that for all potential-differences the activity of the negative terminal was greater than that of the positive. For potential-differences from 200 to 450 volts the activities were practically independent of the potential-difference applied, From 460 volts upward; however, the activities of both electrodes increased, and finally at about 800 volts again became independent of the applied potential. 5 i f ‘ ; ~ See Cele ee J eee ee ots from Actinium in Uniform Electric Fields. 757 From Carr’s results * it is known that 460 volts is the spark potential for a pressure of 9 mm. with the plates 2mm. apart. Consequently for all voltages above 450 the exposures were made with a current passing between the plates. This would mean that a large number of ions were present between the terminals during the exposure; and it is interesting to note that the presence of these ions resulted in a considerable increase in the activity of the two plates. But just how this result is brought about is difficult to explain as the exact relation which exists between the number of ions present in a gas and the active deposit particles is still obscure, and it will be necessary to make additional experiments before the question can be cleared up. One of the main questions left open in the present investi- gation is the cause of the decrease in activity of the electrodes in the three different gases at the low pressures. It seems fair to conclude from the results that in the region of low pressures there was a gradual decrease both in the excess of positively charged deposit particles, and also in the total number of the particles present in the space between the electrodes. The experiments, however, do not show whether this de- crease was due to a falling off in the amount of emanation coming into this space or in the amount of emanation and deposit particles passing directly through it into the outer chamber of the apparatus. From the fact that at the low pressures as well as the high ones the activity fell away as the distance of the salt from the electrodes was increased, it would seem that the decrease mentioned above was due to decrease in the amount of emanation entering the space between the electrodes. The matter, however, is not clear, and consequently the explanation of the decrease must be deferred until the scope of the investigation can be extended. In conclusion I desire to thank Professor McLennar for the selection of the subject, and for the very helpful sugges- tions he has offered from time to time during the investigation. Physical Laboratory, University of Toronto. May 26th, 1909. * Phil. Trans. cci. pp. 403-483. age LXXVIII. Talbot’s Fringes and the Echelon Grating. By R. W. Woop, Professor of Experimental Physics, Johns Hopkins University *. oat f 7 | [Plate XXIII] ‘ash i 4 er O much has been written in explanation of Talbot’s fringes and the curious circumstance that they appear only when the retarding plate is introduced from the side upon which the red of the spectrum appears (in the case where the plate is in front of the objective of the spectroscope) that it may appear at first sight that anything further must be superfluous. Personally I never felt satisfied that I fully understood the physical explanation of this circumstance until Schuster’s explanation appeared, which is quite satisfying and very easily grasped. On looking into the matter a little more fully, and subjecting some of the conclusions drawn fr m theoretical considerations to the test of experiment, it has seemed to me that this explanation does not account for the failure of the fringes to appear when the plate is introduced from the wrong side. I have accordingly been forced to work out another explanation, which I believe to be more complete and to present less difficulty than the previous ones. The conclusions arrived at are doubtless contained in the elaborate mathematical treatments which have been given by Airy and Stokes, but there seems to bea good deal of difficulty in forming a definite idea of just what happens in each case from an inspection of these equations. Incidentally we shall find that the echelon grating is a special case of Talbot’s plate, the aperture with its retarding plate being simply an echelon grating of two elements. The treatment given by Walker (Phil. Mag. April 1906), while correct as far as it goes, makes no mention of the splitting of certain monochromatic elements of the continuous spectrum into double lines, which I pointed out in my ‘ Physical Optics,’ and is in addition a little difficult to follow. An explanation to be perfectly satisfactory should enable us to form a clear picture of exactly what happens to each monochromatic element of the continuous spectrum, and how these elements are re-arranged so as to give us a spectrum traversed by black bands. The following brief treatment enables us to understand the action of the echelon grating and all of the peculiarities of the Talbot fringes. Assume plane waves of monochro- matic light incident upon a rectangular aperture, brought to * Communicated by the Author. Talbot's Fringes and the Echelon Grating. 759 a focus by a lens. The first diffraction minima to the right and left of the central maximum will lie in directions such that the path difference between the disturbances coming from the edges of the aperture is a whole wave-length. If the right-hand half of the aperture is covered with a trans- parent plate which retards the wave-train one half wave- length, we shall have zero illumination at the centre, and two bright maxima of equal intensity in the position pre- viously occupied by the first minima. It is clear that the path difference for the left-hand maximum is one wave-length, and for the right-hand one zero. We may therefore call the former the spectrum of the first order, and the latter the spectrum of zero order, considering the aperture as a grating of two elements. If we consider the change as taking place progressively, starting with a transparent lamina of intinite thinness which gradually thickens, it is clear that the central maximum moves to the right, decreasing in intensity, while its neighbouring maximum to the left increases in brightness moving in the same direction. When the thickness cor- responds to a half-wave retardation these two maxima are of equal intensity, and occupy the positions previously occupied by the minima to the right and left of the central maximum. If we increase further the thickness of the plate the maxima drift further to the right, the left-hand one increasing in brilliancy, the right-hand one decreasing. When the re- tardation becomes one whole wave-length we again have a single bright maximum at the centre, as with the uncovered aperture. In this case, however, it is the spectrum of the first order which is at the centre. As we go on increasing the thickness of the plate the march of the fringes continues, new ones coming into view on the left and disappearing on the right, and the order of spectrum increasing. The con- dition when we have a pair of bright maxima will be recog- nized as the condition which obtains when an echelon grating is set for the position of double order, the single order position corresponding to the case when we have a single bright maximum at the centre. Suppose now that we have a thick retarding plate and gradually decrease the wave-length of the light which illuminates the slit from which the plane waves are coming. We shall have the same march of the fringes as before, the gradual increase in retardation resulting from the decrease in wave-length. If our source emits two wave-trains of different wave-length, and the retardation for one of the trains is an odd, and for the other an even number of half wave-lengths, it is clear that the single and double maxima 760 Prof. R. W. Wood on Talbot’s Fringes exist simultaneously, and all trace of the maxima and minima will disappear owing to the form of the intensity curve ; in other words, the lines are not resolved. If, however, we increase the number of retarding plates, placing them so as to divide the aperture into a number of vertical strips of equal width, the width of the maxima decreases in proportion to the distance between them, as in the case of the ordinary diffraction-grating when we increase the number of lines, and we have resolution of the lines. Our aperture is now acting as an echelon grating, set in position of single order for one train of waves and double order for the other. With very thick plates, as in the case of echelons such as are actually used, it is evident that a very minute change in wave-length will be sufficient to change the retardation by the amount necessary for resolution. We are now in a position to discuss the effect of the thickness of the plates, their number, and the width of the steps. De- creasing the width of the steps increases the width of the space between the spectra, in other words, forms the system of maxima and minima on a larger scale. Increasing the thickness decreases the change in wave-length necessary in passing from the condition of single order to that of double order, in other words the greater the thickness the greater will be the shift of a maximum for a very minute change in 2, and in consequence the greater the resolving power. An increase in the number of plates merely reduces the width of the maxima, without affecting the distance between them, or the amount of shift produced by a given change of 2X. This then is the whole theory of the echelon in a nutshell (a coco-nut perhaps). Personally I have found that a class can be made to understand the echelon much more clearly by this method than by prolonged study of the mathematical treatment. I have already viven a very simple treatment of the decrease in the width of the principal maxima, and the increase in the number of the secondary maxima in the case of the ordinary diffraction-grating as the number of lines is increased (Phil. Mag. vol. xiv. p. 477 (1907)). We are now ready for the Talbot fringes. Consider the slit of a spectrometer illuminated with mono- chromatic light, the prism, aperture, and retarding plate arranged as shown in fig. 1. If the plate retards the stream an even number of half wave-lengths, we shall see in the instrument a single bright line with accompanying faint maxima and minima. If we now decrease the wave-length a trifle the line will move a little to the right, if we disregard the action of the prism. We can verify this experimentally las | and the Echelon Grating. 761 by removing the prism and viewing the slit directly with the telescope. The slit can be illuminated with a monochro- matic illuminator (spectroscope with narrow slit in place of the eyepiece), the slit of the instrument being substituted for the slit of the first spectroscope. Fig. 1. — | N ‘ As we gradually decrease the wave-length by turning the prisms of the illuminator we shall see the line become double and single in succession, the doubling being accomplished by the march of the fringes to the right and their fluctuating intensity in the manner already described. It is a little difficult to put into words the changes which accompany the alteration of wave-length. The appearance is much like that presented by a picket fence in motion viewed through a narrow vertical aperture, 7. e. the pickets are only visible as they pass across a narrow vertical region. If we imagine the visibility of the pickets to be a maximum as they cross the centre of the aperture and least when at the edges, we shall have a fairly accurate conception of the appearance of the moving maxima. Suppose that a change of 100 Angstrém units in the wave-length is sufficient to change the single line to the double line. The changes which take place in the focal plane of the telescope (prism removed) as we decrease the wave-length over this range are indicated in | fig. la. To avoid confusion I have represented each suc- cessive appearance a little lower down in the figure. Now consider the prism in place, turning the telescope so as to view the deviated image. As we decrease the wave- _ length there will be a shift to the right as before resulting from the retardation of the plate, and a shift to the left due: Phil. Mag. 8. 6. Vol. 18. No. 107. Nov. 1909. 3H 762 Prof. R. W. Wood on Talbot’s Fringes to the increasing deviation produced by the prism. If the compensation is perfect the prismatic dispersion will shut up the picket-fence arrangement of lines in the diagram into single lines ; in other words, if we illuminate the slit simul- taneously with all of the wave-lengths in the given range of 100 A.E. we shall not see a short continuous spectrum, but single bright lines, to the intensity of which all the waves contribute. These lines are of course much narrower than the corresponding range of the continuous spectrum which would be formed in the absence of the plate. We thus see that the retardation has the effect of compressing a narrow region of the spectrum into a much narrower one which con- stitutes one of the bright Talbot bands. If we consider what happens to the entire spectrum, we can perhaps obtain a still clearer idea of how the bands are formed. Consider a large number of equidistant monochromatic constituents of the spectrum: call these the lines A. Mid- way between them is another set of lines B. The distance from a line A to B is such that the difference in the retarda- tion for the two lines is half a wave-length. If the retar- dation for the A lines is an even number of half waves, they will remain single and fixed in position. The lines B will, however, double and fall upon the neighbouring lines A. The regions previously occupied by the lines B are the dark Talbot fringes. It may at first sight appear as if the same result would be obtained regardless of the side on which the retarding plate was introduced. It obviously would for the wave-lengths A and B; but if we consider the elements of the spectrum between the A and B lines, we shall see that in one case they are shifted so as to fall upon the stationary lines A, while in the other they are moved into the region between. In the latter case we have a continuous spectrum if we consider the widths of the regions A and B infinitely narrow. In the foregoing treatment we have considered the condition as that of the ‘best thickness ” which obtains when shifts due to retardation and prismatic dispersion exactly compensate. It is clear also that to obtain the bands the aperture must be somewhat restricted so as to obtain an appreciable doubling of the lines for which the retardation is an odd number of half waves. I have verified all of these points experimentally to make sure that no slip had been made. To show that the different monochromatic constituents were differently affected by the retarding plate, three spectra were photographed in coinci- dence. The first (No. 3) shows the Talbot bands with white light illuminating the slit, the second (No. 2) with the iron and the Echelon Grating. 763 are spectrum under the same conditions, and the third (No. 1) the iron are without the retarding plate. These spectra are reproduced as negatives on Pl. XXIII. fig.1. At some points in the spectra the iron lines appear the same, in other points they appear doubled. These latter points are indicated by arrows. We thus see that the Talbot bands can be fully accounted for without in any way making use of the idea utilized by Schuster, that a stream of waves which is already behind another stream cannot interfere with the latter, if it is put still further bebind by retardation. The advanced portion of the train must be retarded if interference is to take place. While this explanation is not open to criticism, if it is true that the grating constructs the monochromatic elements of the spectrum from the assumed irregular pulses which are supposed to constitute white light, it appears to me that we ean account for the fringes without making this supposition. In other words, Talbot’s fringes would be formed even if the two streams could interfere regardless of which one was retarded, and this being the case it does not seem as if Schuster’s explanation can be accepted as the correct one. We can, in fact, form Talbot’s fringes under conditions which preclude the factor considered by Schuster, and we find that they fail to appear when the retarding plate is on the wrong side, though interference is still taking place. We find that if we take highly homogeneous light to start with, such as the iron spectrum, the lines are doubled as before even when the plate is introduced from the wrong side. This is what we should expect, for we now have much longer trains of consecutive disturbances, and one train can interfere with the other regardless of whether it is advanced or retarded. The same will hold true if we take a band spectrum of very narrow and close lines which appears. con- tinuous in our spectroscope. Talbot’s bands can be seen in the nitrogen band spectrum only when the plate is intro- duced from the proper side, though we must consider interference as still taking place when the plate is put on the wrong side. Supplementary Note. The interference in this case is not to be considered as introducing dark regions in the spectrum, but as redistri- buting the wave-lengths; in other words, decreasing its purity. Let us calculate what happens to the continuous spectrum for the two cases involving the correct and incorrect placing 3 E 2 764 Prof. R. W. Wood on Talbot's Fringes of the plate. This may be done by taking the limited region of the spectrum DE (fig. 2). Fig D B A Cc E (i a MN WRLC D A c placed. eS A oy ee D € 2 Plate on wrong side. D B ey CO amare Assume it to be of infinite purity, and consider that the narrow regions at D, A, and E remain single when the re- tarding plate is introduced, while those at B and C become double, in the manner previously described. Furthermore, consider that they also become double when the plate is introduced on the wrong side, as is the case when we use - homogeneous light. I have made the calculation for the wave-leneths D, B, A, C, E, and also a number of inter- mediate values, by drawing the spectrum on coordinate paper, and calculating what happens to each element, as a result of the retardation. The lines between those which are lettered become double, the components, however, are of unequal intensity and are un isymmetr ically placed with respect to the original position of the line. With the retarding plate in the right position we find that the elements of the spectrum are pushed together into the position of the lines D, A, and Hj, forming the bright Talbot fringes (see fig. 2). In the case of the incorrect position, the regions of the spectrum between AB, AC, &c., instead of being squeezed together are pulled out, the intensity distribution being as shown in fig. 2 (superposition of 3 lower figures). It is clear that no dark bands appear in this case, and yet at any point in the spectrum we shall find in general a number of different wave-lengths, as a result of the interference which we have assumed to take place. It seems to me, therefore, that we can account for the failure of the bands to appear, ie and the Kehelon Grating. 765 even if we assume interference between the retarded and unretarded portions of the wave-train. The question now suggests itself ‘‘ Does interference take place, in the manner supposed, in the case of the continuous spectrum formed from white light?” I have attempted to test this matter in the following way :—The Talbot fringes were focussed upon the slit of a second spectroscope. If the slit fell upon a bright band, the band appeared much drawn out, owing to the presence in it of a number of different wave-lengths. If it fell upon a dark band the image in the eyepiece appeared much fainter. If the slit of the second spectroscope was opened wide the bands appeared, but they were very faint, owing to the widening of the bright bands by the dispersion, which caused them to overlap the dark regions. The slit was now narrowed again, and the retarding plate introduced from the wrong side. If interference took place in the manner assumed we should expect three or more wave-lengths (lines separated by dark spaces) to appear in the eyepiece. In other words, if we put the slit at the point A in the spectrum we should expect A to appear very bright, and C and B as well, with about half the intensity of A. This was found to be the ease. Three bright lines, separated by very black regions, appeared in the eyepiece. I next removed the mica plate from the aperture. In the eyepiece there now appeared in monochromatic light the diffraction maxima and minima of the Ist class, a central one very bright bordered by others much fainter. On introducing the mica plate, again on the wrong side, the central maximum became furrowed by black minima, breaking up into the three bright lines previously alluded to. This seems to show that interference takes place even when we retard the wrong half of the train. Very likely I have fallen into some pit- fall, and I am sure that I hope that Prof. Schuster will discover it. The subject seems to me to be a tricky one to deal with, so many factors have to be taken into account, such as the decrease of purity resulting from the limited aperture, the presence of the second spectroscope, &c. It is probable that the second spectroscope can be shown to be responsible for the interference, as when showing fringes of high order in the case of the so-called direct interference of white light. There seems at first sight to be no escape from the conclusion, that if a spectroscope shows three bright lines when placed at a given point in the spectrum, these three wave-lengths must be present. We must remember, however, that spectroscopic analysis of white light, interfering 766 Talbot's Fringes and the Echelon Grating. with large path-difference, might be erroneously interpreted, as indicating the presence of long trains of monochromatic radiation in the white light, whereas the thing is in reality produced in the spectroscope. This paper must not be considered in any way as an attack upon the impulse theory of white light. The only point which I wish to question is this: If we can account for the presence and absence of the Talbot bands in the two cases, by the rearrangement of the wave-lengths, assuming interference as taking place in each case, are we justified in saying that their absence in one case can be ex- plained by the inability of the retarded portion to interfere with the unretarded? Would they not be absent just the same even if interference did take place? I am not to be understood as claiming that interference does take place in the case when we start with white light, in spite of the experiment which appears to show that it does, for I cannot imagine how a wave-train, already behind another train, could be made to interfere with it by further retardation, unless perhaps we explain it in the same way (by resonance) as Schuster explains the formation of interference fringes with white light when no spectroscope is employed. The object of the present paper has been merely to “visualize”? the manner in which the fringes are formed. I have attempted to carry the thing a point further, for it has occurred to me that even with a source giving what appears to be a continuous spectrum in a spectroscope of low power (e.g. the band spectrum of nitrogen), the line constituents of which are highly monochromatic, and hence capable of interfering regardless of which half of the beam is retarded, an infinitely narrow linear (vertical) element of the spectrum is made up of more than one wave-length, on account of the limited resolving power. I have not, however, been able to see just how ‘this will affect the case just considered. Very likely Professor Schuster will be able to defend his position, and I am sure that I hope he will, for his explana- tion is a very neat one, and I dislike to feel that we must abandon it. Talbot’s Fringes produced by an Echelon. If, instead of covering the aperture with a single thin plate, we cover it with a pile of thin plates arranged in steps, we find that Talbot’s fringes appear as before. Their appearance is however quite different, for the minima are now very broad and the maxima very narrow and bright. Prof. A. Schuster: What is Interference ? 767 Our pile of plates forms an echelon grating, and the dif- fraction maxima are much narrower, consequently the light of the continuous spectrum is squeezed into regions which are narrow in comparison to the width of the dark regions. The mica echelon, which I described in a previous paper (Phil. Mag. vol. i. 1901, p. 627), answers admirably for the production of these fringes, a photograph of which is repro- duced on Pl. XXIII. fig. 2. | Fainter secondary maxima appear in the dark regions, their number, position, and the distribution of the intensity among them depending upon the angle at which the echelon is set. We find very unsymmetrical distribution of intensity when the echelon is quite oblique, a circumstance which is of interest in connexion with the recent work of Raman on the diffraction by oblique apertures (Phil. Mag. Nov. 1906). LXXIX. What is Interference? A Rejoinder to Professor Wood. Sy ArtHuRr ScHusterR, F.BR.S.* S| PF co the courtesy of Professor Wood I am enabled to add a few words of comment to the foregoing paper. The question at issue is the explanation of the observed fact that when a spectrum is viewed with the pupil partly covered with a thin transparent plate, it is found to be crossed by dark bands only when the plate is introduced on that side on which the violet end appears. In the complete theory of these bands which has been given by Airy and Stokes, the characteristic feature, that the bands do not appear when the plate is introduced from the red end, requires a compli- cated mathematical analysis, which I have shown to become unnecessary when white light is treated as a collection of impulses. It is then at once seen to be obvious that in order to bring two series of impulses to interference, we must retard the front one or accelerate the one that is in the rear. The explanation, which I have based on this principle, throws a new light on the phenomenon, but was not intended to invalidate the correctness of the older theory. The two representations of white light (by homogeneous waves or by impulses) are not mutually exclusive; they represent two points of view, and we may adopt either one or the other in different problems according to convenience. Professor Wood in his experimental investigation of Talbot’s bands approaches the subject by building up his * Communicated by the Author. 768 Prof. A. Schuster : What is Interference ? continuous spectrum from a discontinuous one, and the treatment of Stokes becomes therefore to him the more natural one. With his usual skill, he devises instructive experiments illustrating the intermediate steps; and those who prefer to adhere to the older view of white light may find in these experiments sufficient excuse to skip Stokes’s rigorous mathematical treatment without too great a strain on their conscience. My own investigation, so far as I ae see, remains untouched, as I dealt with white light alone. Professor Wood now. throws doubt on my treatment of the subject by an argument which may be summarized as follows :—(1) Schuster’s explanation of the absence of the bands when the plate is introduced on the wrong side is based on the principle that there cannot be interference when there is no overlapping. (It is admitted that the principle is correct.) (2) Interference effects can be observed with homogeneous light even though the plate is introduced on the wrong side. (It is admitted that there is overlapping in this case.) (3) White light can be built up with homo- geneous light ; and if this is done, the plate still being on the wrong side, the bands disappear, while interference persists. (4) The absence of interference cannot therefore be made the criterion for the disappearance of the bands ; and hence “it does not seem as if Schuster’s explanation can be accepted as the correct one.” The fallacy here lies at the end of the third step where it is asserted that interference persists even though the effects of interference have disappeared. Matters of definition should be kept clear of arguments on the validity of a certain reasoning, and if two discussions which both explain observed facts satistactorily, lead to different results as to whether there is “interference” or not, the only deduction that can correctly be made is, that there is disagreement in the use of the word. What indeed is “‘interference” ? Every writer on Optics uses the expression, and yet we may search the literature of the subject without finding a definition which can be applied to test whether in any particular case we can say that there has been interference or not. As long as one is satisfied to use the term generally and somewhat vaguely to classify a certain group of phenomena, no harm is done, and it is sometimes useful to retain a word which by common consent has a plastic meaning. But ifit is to be made the test by whichan explanatiom is to be judged, then we must have recourse to some adequate definition. In Mascart’s treatise on Optics it Prof. A. Schuster: What is Interference ? 769 is stated that the principle of interference is identical with the principle of superposition. This is clear and definite, but it would force us to abandon the word altogether, because every optical phenomenon would become a phenomenon of interference, and we should have to admit that rays from independent sources of light could and always would interfere with each other. In order to retain a meaning which shall be definite and concordant with the present usage, I have introduced a definition into the second edition of my ‘ Optics,’ which I think specifies what I believe to represent the consensus of opinion on the subject. [If the observed illumination of a surface by two or more pencils of light is not equal to the sum of the illuminations of the separate pencils, we say that the pencils have interfered with each other and class the phenomenon as one of interference. Stress should be laid on the adjective “ observed.” It means that the effect must be observable in the actual case considered and not only be capable of being made visible by some additional appliance. Adopting this definition, the only way in which it can be decided experimentally whether inter- ference takes place when the plate in Talbot’s experiment is introduced on the wrong side, would be to observe each part of the aperture separately, and see whether the combined effect is equal to the sum of the separate effects. There is no indication in Professor Wood’s paper that he has found any changes of illumination which would indicate that there is interference when the bands are not visible. Professor Wood’s difficulty can be brought to an issue by means of a much simpler case than the one treated by him. Consider the formation of a spectrum by a grating. I assume it to be generally known how an “impulse” of white light is converted into a succession of impulses by the grating, and how at each point of the spectrum more or less homogeneous light is formed by such a succession. Shall we say in this case that a grating acts by interference? My answer is “ No,” if the impulses are sufficiently short not to overlap. If instead of white light we use homogeneous light, there is undoubtedly interference because the illumination of the whole grating is not equal to the sum of the illuminations due to each line separately. Let now white light be formed by a large number of homogeneous waves spread all over the spectrum. If we argue that the interference of the homogeneous waves is preserved when they are sufficiently crowded together to form a continuous spectrum, we should have to draw a distinction between two kinds of white light, one of which is 770 Prof. A. Schuster: What is Interference ? white ab initio and the other white through the overlapping of homogeneous waves. Though the distinction would only be a verbal one, it is obviously inconvenient. If we adopt the above definition of interference the matter becomes definite. We should have to interpret the result of expe- riment by saying that interference has disappeared during the process of forming white light. In effect interference is not like a substance which, if present in the several con- stituents of a mixture, must also be present in the mixture itself. It may be destroyed as well as produced by over- lapping. If this be accepted difficulties such as those raised by Professor Wood will cease to trouble us. The case of Talbot’s bands with the retarding plate intro- duced on the wrong side is best represented by a grating ruled in two parts which are separated by an opaque portion. With white light we should then have at each point of the spectrum a succession of impulses followed first by a quiet interval and then by another succession of impulses. There cannot be a question of interference here; but if we apply a second grating to investigate the spectrum formed by the first, then if the resolving power be sufficient, we can make the second group of impulses overlap the first and interference would result. For this reason Professor Wood’s second spectroscope complicates the phenomenon by introducing the conditions necessary for interference and the observations made with it have no bearing on the question whether there has been interference in the original spectrum or not. These questions were fully considered and settled during the dis- cussion on the nature of white light which it is not necessary to revive now. The manner in which Professor Wood tries to prove that there is interference with the plate in Talbot's experiment on the wrong side, is identical with that by which the regularity of vibration in white light used to be thought capable of being proved by means of experiments with spec- troscopes, which themselves manufactured the regularity they were supposed to disclose. 1 have entered into these elementary matters because I think that under present circumstances a more scientific use of the word interference would help students over difficulties. At any rate, the point at issue between Professor Wood and myself can only resolve itself into a question of the proper use of words, so long as he cannot point to some experi- mental and observable distinction between light which is white ab initio and light which is made white by mixing homogeneous waves. ore 4] LXXX. On the Formation of Strive ina Dust-Tube by an Elec- tric Discharge. By TuHos. Jas. Ricumonp, B.Sc. (Lond. ‘S Research Student at University College, Nottingham. [Plates XXIV.-XXVIL] i 1898 H. V. Gill, S.J., in a paper in the ‘ American Journal of Science,’ propounded a theory to account for the striation of the electric discharge in vacuum-tubes. In this paper the author draws attention to the fact that, under suitable conditions, lycopodium powder placed in a glass tube arranges itself in well-marked strize under the influence of an electric discharge. This suggested the following experiments on the various factors involved in the formation of the strie, the special object being to ascertain whether the frequency of the electrical oscillations could be obtained from observation of the striation of the powder under their influence. The nature of the striation might conceivably depend on the nature of the powder used ; that is on the size and form of the grains; on the electrical conditions; and on the dimensions of the tube containing the powder. It might also depend, perhaps, on whether the further end of the tube were open or stopped. All these questions have been considered in the following, and quantitative experiments were made in which the frequency and wave-length of the electrical oscil- lations were measured by means of Fleming’s Cymometer, and the striation in each case observed ; and although no definite relation between the frequency of the electrical oscillations producing a certain striation and the distance between the stris was detected, some results were obtained which appear of interest and worth recording. As regards the effect of the structure of the powder, it is to be observed that an aggregation of spherical particles tends, under the influence of fluid motion, to arrange itself as striz across the direction of the motion. An example of this effect is afforded by the well-known method due to Kundt for the determination of the velocity of sound. When the note is first elicited from the sounding rod, the lycopodium forms itself into a series of fine close lines along which a series of nodes and antinodes is more or less clearly discernible, but these nodes are not at first sufficiently clearly defined to allow an accurate value of the half-wavelength to be obtained, and it requires more or less continued stroking of the rod to cause the lycopodium to assume that very distinct pattern from * Communicated by Prof. E. H. Barton. 7720) Mr. T. J. Richmond on the Formation of Strie which the value of the half-wavelength can be satisfactorily obtained. A similar phenomenon was observed in the following experiments especially in the wide tubes. Preliminary Experiments. Variation of figures with diameter of the tubes. The first experiments were made with a large Wimshurst machine giving an intense spark about two centimetres long. A length of glass tubing was taken and carefully cleaned by means of a cotton-wool plug, and dried. A small quantity of carefully dried lycopodium was then poured into the tube, the latter being shaken in order to get the particles of powder as evenly distributed in the tube in the form of a cloud as possible. The powder was then allowed to settle, and by gently tapping the tube when horizontal the powder was obtained as a practically uniform line along the tube, which was now placed on supports with one end near the spark-gap of the machine and perpendicular to the discharging-rods. The tube was then rotated very carefully about its axis until the line of powder was just on the point of slipping down the side of the tube. Under these conditions, one or two sparks usually sufficed to give the pattern to the lycopodium, but continued sparking usually added to the distinctness of the striation. It was noticed that at the passage of each spark the powder jumped and fell again at the cessation of each spark. _In the case of the first tube, which was 1°5 centimetres radius, the figure consisted of very distinct close parallel lines filling the whole length, about 60 centimetres, of the tube. It was also noticed that the strize were curiously bifurcated at places. This bifurcation was found to be removed almost completely by continued sparking. In this and other wide tubes, the first effect of the discharge was to produce a series of very fine interlacing lines which by further sparking gave the tinal system of parallel lines more or less bifurcated. A second tube was now taken about one centimetre in diameter, and using the same spark as before the striation of lycopodium was obtained. The pattern formed in this case differed in several respects from that of the previous one. In the first place the distance between successive strize was greater than in the case of the larger tube; also the lines were of the nature of irregular heaps compared with the remarkably clear regular lines obtained in the first case. Another difference consisted in the lack of bifurcation of the lines in the narrower tube. This freedom of the lines from bifur- cation in the narrower tube was found to render the use of such tubes more suitable for quantitative experiments than in a Dust-Tube by an Electric Discharge. 173 wider ones on account of the greater certainty as to the number of lines contained in a certain length of the tube. The difference in the distances between the lines in the above two cases suggested thé investigation of the relation between the strize-distance—2. ¢., distance between successive strize— and the diameter of the tube in which the pattern was formed. A set of five tubes ranging in diameter from 1 centimetre to 4-6 centimetres was taken, and using the same spark in all cases the figure assumed by the lycopodium was observed and measured, care having been taken to ensure the cleanness and dryness of the tubes. This somewhat rough set of readings indicated a turning value in the variation under investigation, as shown in figures given in Table I. and graphically in Curve I. fig. 1 (p. 775). Taste [.—Variation of figures with diameter of tube. Diameter of tube. | Strix-distance. ) | | | ‘9 em. ‘77 mm. | LG | ee ee £6 3 POO ) : = ) 2-6 ; sé 2 3 ae ‘DO From these figures it appears that the strize-distance has a maximum value, viz. 1°00 mm. in the 1°6 cm. tube. In con- firmation of the existence of this turning value a second set of readings was taken. The tubes having been carefully cleaned and dried and the pattern in each case obtained as clear as possible, a vernier microscope was used to measure the intervals. The tubes were in turn laid on the stage of the micro- scope, a piece of black paper being placed underneath to facilitate the reading of the microscope. By this means the figure as viewed through the microscope appeared very distinct and the separate lines could be counted with ease. The striz-distance was obtained by observing the distance through which the microscope travelled in order that say 10 lines should pass across the intersection of the cross-wires of the eyepiece. It was noticed that some uncertainty existed in some cases as to whether one or two lines had passed across the intersection of the cross-wires owing to the bifurcation of the lines as previously mentioned. This most probably explains the several high values obtained in the figures for the 4°4 centimetres tube shown in Table II. There were 774) ~“Mr. T. J. Richmond on the Formation of Strie important differences in the character of the striation in the various tubes. Thus in some tubes, particularly in one about 3 cms. in diameter, as many as 50 to 150 lines were clearly formed and measured, while in others only about 20 were formed at all and some of these indistinctly. The readings of this set of experiments are shown in Table II. and graphi- eally in Curve II. fig. 1. A further set of readings is given in Table III. and graphically in Curve III. fig. 1. TABLE II, Diameters of tubes (mm.). 0 3:5. Qi oak meee UAL Maal o | = Eevee naa Seer 5 ‘72mm. | 1°93 mm "75 mm, 52 mm 2 80 99 “94 99 99 9)9) 99 i S204; “Qo ites phi take 2 oO) ss casi. EU Re OO gs Z Or Gs ‘09, = ‘Dd ” P 59, % 4 5 ‘64, S ‘DT ” a "Gai as #515 Means ...| ‘77 mm. 94 mm. ‘76 mm. *56 mm. TAB rEALEE. Diameters of tubes (mm.). So: 8. 10. 22. oo. Ree a 3 2. 2: . ae x 23'6. 98 | 93'1 10 122 10 2.10 158-4 = 72'8 83'5 18:5 59 : S Pas) we LO | 150°3 hs 25 U6 ll 10 156-8" 29 2 32°79 17°4 -10 <—) ie ---10 : -10 | 160°6 83'°5 41'1 23°4 8 mo 6 BO ---10 10 2 82°2 47°38. 109 23°9° 10 160°0, 59 Z) 54-7 33'8 | 128°7 ze Payee) Lang © 70-0 122 ys | DM 1158.39 e 109° 30 z | 717.40 "969°" 10 a=} 79:2. -100 147°7 78°49 26:2 Means 50 mm. | ‘99 mm. ‘71 mm. ‘57 mm. ‘64 mm. — in a Dust-Tube by an Electric Discharge. 775 From these figures we observe that the distance between successive strie for a given spark varies with the diameter of the tube in which the pattern is obtained; and while the strie in wider tubes are distinctly more crowded than in narrow tube, there is a particular diameter for which the strie-distance isa maximum. This maximum for different sparks is found to occur in tubes of different diameters (see fig. 1). This variation of strie-distance with diameter of tube is shown in ig. I. (PI. XXIV.). The figures given in Table II. refer to sparks obtained from the Wimshurst having a battery of condensers in parallel with its condensers: those in Table III. to sparks from the machine without the battery, 7. ¢., for an oscillation of higher frequency. The figures formed in the latter case were remarkably well-defined and regular. Fig. 1.—Variation of strie-distance with diameter of tubes. - Ss STRIAE) DISTANCES =) - al ae = ns , Z (ao if / © (9) e =. 7 al Oy | / Tl;—e ‘O™o DIAMETERS OF TEs ‘ Very wide tubes were now taken—about 8 to 15 cms. in diameter. In these, the final striations did not differ much from each other or from those obtained with the wider tubes used above. The first stage of the striation was a system of curiously bifurcated fine close lines. Repeated sparking caused the striation to change somewhat in appearance, the tinal effect being a set of lines about ‘5 millimetre apart. Using tubes of the same diameter but of various lengths, it was found that change of length had no observable effect on the striee-distance for a given spark. Tubes having the end remote from the spark-gap stopped by a cotton-wool plug were also used. In these cases, the striation obtained did not differ from that obtained with open tubes. Also a tube was taken, and the striation for a given spark was obtained. The powder was observed to jump quite a millimetre high at each spark as previously pointed out. The end near to the spark-gap was then stopped by a plug of cotton-wool. The passage of sparks now left the Bah. “he LA: M4 j 776 = Mr. T. J. Richmond on the Formation of Strie powder absolutely unmoved. The pattern was then destroyed by knocking the tube and no amount of sparking would cause the striation of the powder. ‘This shows that the formation of the striation is due to aerial motions. Variation of figures with nature of powder. The effect of the nature of the powder was now looked for. Using the same electrical arrangements as above in all the cases strize were obtained in tubes about 1 cm. in diameter with various powders, the figures in Table IV. were obtained. TasLe LV.—Variation of striation with powder. | Name of Powder used. | Striz-distance. | Nature of Powder: form and size. | daycopaeinims &:;. = e . T | Se ; the efficiency z ie Thus it is necessary to obtain a record of the area of the shutter opening at every instant of the exposure. For the determination of the efficiency the method employed is essentially that proposed by Sir William Abney, who uses a siren to measure the time. We proceed as follows:—The Fig. 4. shutter is removed from the vibrating beam of light (see fig. 4) so that a continuous sine curve is recorded over the * Proc, Roy. Soc. A. vol. Ixxviii. p. 208 (1906); 786 Method of Testing Photographic Shutters, whole length of the plate, and this curve serves now simply as atime record. A line source of light B is focussed by a lens L; on to a narrow horizontal slit } 6’ placed in a diametral plane of the shutter as close as possible to the shutter-leaves. An image 8 §’ of this slit is formed by the concave mirror C on the photographie plate by the side of the vibrating beam of light. As the plate falls the shutter is opened as before, and a record is obtained giving at every instant of time the length of slit through which light was passed by the shutter leaves (fig. 5). Measurements are then taken of — _— “< aN. (es Fig. 5. —_— = ra = SS es a ee a: = the area of shutter aperture corresponding to a number of lengths of the slit opening. Fig. 6 shows some stages in the opening of a particular type of shutter, the white line representing the position of the slit. From a pair of records such as shown in figs. 5 and 6 a curve is drawn showing at every instant of the exposure the area of the shutter aperture through which light can pass to the plate. It is now evidently a simple matter to find the amount of light cut off owing to the finite length of time taken by the shutter leaves to open and close, and hence to calculate the efficiency. Form of Pulses constituting Full Radiation. 187 IV. Examples of Records. A number of shutters of different types have been tested with the apparatus. Figs. 7 and 8 (PI. XXVII.) are examples of the records obtained, the former at 50 and the latter at 500~ per second. Figs. 5 and 6 are copies of records obtained in testing the efficiency. vv For general use the most convenient frequencies to work with are 50 and 500~ per second, with possibly 2000 for special work ; or perhaps 100 and 1000~ per second would be suitable. The full advantages that the method offers can only be secured by the use of round numbers, such as the above, for the frequencies of the oscillations. In conclusion, we wish to thank Dr. Glazebrook for the kind interest he has taken in the working out of the method. LXXXII. On the Form of the Pulses constituting Full Radia- tion or White Light. By Ausert Eacunz, B.Sc., A.R.C.S., Imperial College of Science and Technology”. a -. cet to the modern theory of White Light founded by Gouy, and subsequently developed by Lord Rayleigh, Schuster, and others, White Light does not consist of periodic wave-trains of all wave-lengths, which are simply separated or “dispersed” when it is drawn out into its spectrum, but consists essentially of a succession of non-periodic pulses emitted independently of one another. It is out of such pulses that the spectro- scope builds up the periodic wave-trains we observe in the spectrum, If these pulses are all similar and follow one another * Communicated by the Physical Society: read June 11, 1909. 788 Mr. A. Eagle on the Form of the Pulses quite at random, it follows that the distribution of energy in each pulse must be the same as the distribution of energy in the total succession of pulses. The distribution of energy in the spectrum obviously depends on the shape or form of the pulses making it. Lord Rayleigh has shown how * the distribution of energy in a pulse of any given form could be calculated, and calculates the distribution of energy for a pulse of the form f(t)=e—**. Other sug- gestions as to the form of the pulse have been made by other writers, and the distribution of energy which would be obtained from them has been calculated. In no case, however, has a form been hit upon which gave a distribution in accordance with fact. The inverse problem—viz., from the distribution of energy, to find the form of pulse which would give rise to it—has not, as far as I know, been published, and its solution is the object of the present paper. We ought, however, to state that the problem is not one which admits of a definite solution, as the distribution of energy in the spectrum is independent of the relative phases of the infinitesimal harmonic components out of which the pulse may be con- sidered to be built up; whereas its form must obviously depend as much on the relative phases of the components as upon their relative amplitudes. Let y= f(x) denote the form of the pulse in space. Lord Rayleigh has given f the now well-known relation ( (oy? de = a ( (A? +B?) day. ...4 0. —o T /0 where A=] /() cos am du, 12.9) and B= /(u)sinapdp. The left-hand side of (1) is clearly proportional to the whole energy of the pulse, and the equation is to be interpreted as implying that the energy belonging to the waves comprised between @ and a+dze is proportional to (A?+B?) da. The wave-length » is of course aD Hence, ie Phil. Mag. vol. xxvii. p. 465 (1889), or Collected Works, vol. iii, p. 268. constituting Full Radiation or White Light. 789 if we are given that the energy between « and a+dza is proportional to F(a) dz, we have ae) = [| COS am a] ee [rw sin au ap). ce) This equation solved for 7 will be the solution of the problem. Two particular solutions may very easily be obtained, first when the pulse is an even function, and second when it is an odd function. In the first case (2) reduces to (i cosawdu = F(a)*, . . . . (3) and in the second case to (hw sinaudu=F(a)?, . . . . (4) Now, in Fourier’s Theorem | (2) = = [a 40) cos a(A—w) dn, let d(z) be equal to zero if <0, and be equal to f(x) if «z>Q0. Then we have {| 7) GOS Ra AN 4), 5) nia tnD) T is equal to f(x) for positive values of # and equal to zero for negative values of +. Hence = {| 40) cosa(A+xr)dry . . . . (6) is equal to zero for positive values of a. Adding and subtracting (5) and (6), we obtain Ke) = = | 0: ad da 70) COP AN EA o/s GD 9 ioe) 70 a | sin av da | Fs) sin adn! 65h) BY 7 Jo “0 for positive values of z. In much of what follows we shall frequently have an equation involving a cosine with a similar one involving a sine. 790 Mr. A. Hagle on the Form of the Pulses In order to prevent os to duplicate such equations, we will write them with ° a in which either the upper or the lower may be taken; but in one equation upper must be taken with upper and lower with lower. Kquations (7) and (8) may very conveniently be expressed in the form of the theorem : lf lg {(v) ae madx = p(m), | vs cos cu a ir Aj P#) sin MAE = 2 Mies | In this form the equations are useful for finding certain definite integrals ; for instance, from the result then @ = art a é cos mz dz = ——, 0 m* + a we can at once deduce “ cos max ra ties 2 2 Ax = ——€ ° me ae 2a Further examples will not be given here, as the author hopes to discuss some results which may be obtained from equations (9) in another paper. Hgquations (7) and (8) enable us to solve at once (3) and (4). Multiplying each side of (3) by cosawda, and integrating from 0 to «, we obtain by (7) a) = 2 | Fe! cos av da, (3 > which gives the form of the even pulse; similarly, the odd one is given by ee = = |. F(a)tsinegde . . . - We will now determine the form of the pulses for some of the different formule that have been proposed for representing the distribution of energy in full radiation. Both Lord Rayleigh’s and Wien’s formule are included under K, dA = CO" ems the former being obtained by putting »=1 and the latter by constituting Full Radiation or White Light. 791 putting n=0. Transforming this so as to obtain the energy 2a between « and 2+da where a= ~, we get F(a) da = A@” aa eee, C where 2b=5-4: 7 | Hence, dropping factors outside the integral sign, the forms of the pulses are given by So Rp fay [ere anda... (12) /0 5—n\ cos {[o—n, -1% r( 2 | ee Te ee ee 5—n (Pat) Putting n=1 for Lord Ra yleigh’s formula, the expressions reduce to 6? — x? 2bx (paye 4 Orypaty Taking Planck’s formula for the distribution of energy, —5 H,dx = ss i ere—] this transforms into Adcdz ¢ F(a) da = ES BET: where 2 =9-9 38 before. Extracting the square root of this expression by expanding the denominator in ascending powers of e—, substituting the result in (10) and (11), and integrating term by term, we get for the form of the pulses eon 5" zh Gost or) tes a si a 2 tan DS 1 sin | 5} tan 3), 7 Hs ad at ae Ste PS pe +-= 5 i ( v) (b? + x”)* 2 (37L? + x?)* cos | 5 xv , oO 3, sin ' 2 a an ae SPER ¢ + | ee a 13 8 (57? + x?)* ( ) To the eye these pulses have much the same formias the simple ones obtained from Lord Rayleigh’s formula. 792 Mr. A. Eagle on the Form of the Pulses It is interesting to observe that all the pulses we have found satisfy the condition f Aa)de=0. This is obvious for the odd pulses; for the ee ones, we have only to show that { f(w)da=0. 0 Now /(z) consists of one or more terms of the form io.2) | ae cos ar da. 0 This integrated with respect to # gives v P(p) sin |p tae = p (14) (q?+.2*)2 fe 8) Bea cesta S { ee ™ sin avda = 0 which vanishes when taken between 0 and o if p be positive. On the electron theory these pulses are due to the radiation from moving electrons, and the function giving the form of the pulse as a function of ¢ is the same as the function giving the acceration of the electron at time ¢. Hence, to find the displacement at any time, we must integrate the function giving the form of the pulse twice. By integrating the left- hand side of (14) twice with respect to 2, we observe that we merely change p into p—2. Hence, to integrate the right- hand side twice we have only to change p into p—2. Applying this to equations (12) and (13), we get the motion of an electron which will give rise to these pulses. b?— x? 2bx B+ x) yee (P+ a2)” Lord Rayleigh’s formula, the motion of the electron is given by For the pulses obtained from y =Alog(a’+é) and y= Btant/a, where a= a Hquations (10) and (11) show that the pulses may be regarded as resulting from a superposition of a series of sine curves of all wave-lengths, each with a suitable amplitude so as to give the required energy distribution. This being so, we may. expect that we shall be able to obtain a more general form of pulse by assigning an arbitrary phase to the constituting Full Radiation or White Light. 793 component sine curves, without thereby altering the dis- tribution of energy in any manner. That is, we may expect i 2 | Fe! cos {ax—d(a)}da. . . (15) to be a more general solution of (2) than (10) or (11). This in fact is so, as may be verified by splitting up (2) into the two equations F(a) cos d(a) = TW) cos au du and F(a)? sin ¢(2) = { (pH) sin ap dp, and trying to find a solution of these—in the same manner in which (3) and (4) were solved—which at the same time satisfies both of them. Equation (15) will be the result. It is no longer, of course, believed that white light consists -of a succession of pulses all of exactly the same form. It consists rather of a succession of pulses capable of being represented by an equation with one or more arbitrary parameters, the number of pulses emitted per second which have their parameters lying within definite limits being given by some law analogous to the Maxwellian distribution law. But the form we have obtained may probably be looked upon as some mean or average form of the pulses, and may perhaps be of some value in determining, to a first approximation at least, by what intermolecular forces the free electrons in a substance must be acted upon in order to give the observed distribution of energy in the spectrum. Although, as we have seen, the problem does not admit of a definite solution, yet it is not impossible that physically all the pulses in white light may be (say) even ones. For instance, if an electron moves in a straight line against an opposing force which is a function of the distance, and which is insensible at the beginning of the motion but becomes sufficiently powerful to bring it to rest and reverse its motion, the pulse produced will obviously be an even one, under which conditions the form of the pulse for a given distribution of energy is unique. Phil. Mag. 8. 6. Vol. 18. No. 107. Nov. 1905. 3G RAR Gy | ’ nd , 7 Bee LXXXIII. On the Measurement of Wave Length for High | Frequency Electrical Oscillations. By ALBERT CAMPBELL, BAL » (From the National Physical Laboratory.) [Plate XXVIII. | § 1. Introduction. | all work with high frequency electrical oscillations, such as for example in wave telegraphy, it is of the utmost importance to be able to determine with accuracy the wave-length actually employed, and for this purpose several types of wavemeter are now in common use. In order to ensure accuracy in such measurements, it was suggested some time ago by the Post Office Authorities that arrangements should be made for the calibration of wavemeters at the National Physical Laboratory. As the results of our first series of investigations in the matter appeared to be of general interest, we publish them here by the kind permission of Major O’Meara, C.M.G., Engineer-in- Chief to the Post Office. Our experiments comprised the construction and testing of a standard wavemeter, and the verification of an ordinary commercial wavemeter sent to us by the Post Office. I shall designate this instrument (A) and our standard wavemeter (B) respectively. While it is unnecessary here to go into the history of the subject, I should like to give one or two references to earlier work by other observers which gave us much assistance, namely the experiments of Pierce f and those of Gehrcket. While our work was in progress an important paper by Diesselhorst § appeared, and the results there published were in ample confirmation of those we were obtaining, as also were the earlier results of Pierce. | § 2. Description of Wavemeter (A). Wavemeter (A) is of the Donitz type and consists of a variable air condenser, with a range from about 100 to 1070 mmfd. (micromicrofarads), a thermo-junction and galvanometer, and a series of coils (A1, A2,....to A 10) of self inductances ranging from 0°76 to 2313 microhenries. * Communicated by the Physical Society: read June 25, 1909. tT Phys. Review, vol. xxiv. p. 152, 1907. t Elektrotech. Zettschr. (26), p. 697, 1905. § Jahrbuch der drahtlosen Telegr. u. Teleph. vol. i. (1908). High Frequency Electrical Oscillations. 795 The combination is capable of measuring oscillation fre- quencies over arange extending from about 20,000,000 down to 100,000 ~ per sec., or wave-lengths from 7=15 metres up to A=3000 metres. It must be kept in mind, however, that the accuracy obtainable depends on the part of the condenser scale at which the reading is taken. For example, at a reading of 20 the frequency can barely be read to 0°5 per cent. As the coils (Al, A2,...... ) of (A) are of solid (not stranded) wire of diameters from 0°32 up to 3:2 mm., the values of their self inductances at the high frequencies are, for most of the coils, considerably lower than those obtained at ordinary frequencies of 0 to 1000 ~ per sec. With a view to checking the results of the direct experi- ments by calculation from the measured inductance and capacity of a wavemeter in which the inductances would be much less affected by frequency, and thus to obtain a standard instrument for future use, we constructed a wavemeter (B) in which the coils are all of highly stranded wire. § 3. Description of Standard Wavemeter (B). The general arrangement of (B) was similar to that of (A). The variable condenser (from 100 to 900 mmfd.) was of special design, with amberite washers to give very high insulation. It was kindly presented to the Laboratory by Dr. Alexander Muirhead, F.R.S. We added to it a direct reading scale, which can be read to 1 in 2000 at the upper end and to 1 in 200 at the lower. The scale was constructed by a very careful series of tests by Maxwell’s Commutator Method and was found to be very uniform. For the inductances, three coils (Q 6, Q1, and Q 2) were used. They were all wound on ebonite tubes with stranded wire (7/36°), 2. e. containing seven insulated strands, each of diameter 0°19 mm. In each coil the terminals were brought to a considerable distance (18°5 cm.) from the centre of the coil by fixed leads run parallel to one another 1 cm. apart. In this way too close proximity between the coil and the condenser plates was avoided. A Duddell thermo-ammeter of 1-5 ohms resistance was used to complete the circuit of the coil and the condenser, and by observing its maximum deflexion the point of resonance was obtained. The sensi- tivity of course varies with the coil used and with the nature of the oscillatory circuit ; it was found to be sufficient for the purpose in the experiments described below. Fig. 1 (Pl. XXVIII.) shows a photograph of the wavemeter and of one of the coils separately. G 2 796 Mr. A. Campbell on Measurement of Wave Length § 4. Measurement of the Self Inductances of the Coils. The self inductances of all the coils were measured at ordinary frequencies (0 to 1000 ~ per sec.) by a method specially designed for the accurate measurement of such low values (A. Campbell, Phil. Mag. Jan. 1908). The com- parisons were made against a standard variable mutual inductance with ranges of 0 to 200 and 0 to 2000 micro- henries, the lower range being readable to 0:01 microhenry. The absolute value of this was measured in terms of the new Laboratory Standard of mutual inductance, whose value has been calculated to a very high degree of accuracy (see Proc. Roy. Soc. A. vol. 79, 1907). The subdivision of the scale of the variable mutual inductance was effected by the help of Maxwell’s method of comparing two mutual inductances, Its accuracy was verified by an independent method as follows. A mutual inductance coil was constructed with the primary and secondary circuits both of well stranded wire (10 and 20 strands respectively), and, with all the strands in each circuit in series, the value was adjusted to be equal to the 10 microhenry reading on the scale. Then, by taking p strands of the primary and gq strands of the secondary, the value would be aa x 10, and thus inductances of 5) 5, 326, ao, --- of the full scale reading were obtained. On testing these against the actual scale, the subdivision was found to be perfectly satisfactory. | The details of winding and values of the self inductance of the coils of Wavemeter (B) are given in Table I... In actual working these values had to be increased by the addition of the measured self inductance of the rest of the circuit, consisting of the leads, ammeter, and condenser ; the total addition was about 0°5 microhenry, of which 0:1 micro- henry was due to the condenser. TaBeE I. | Coil | Axial | Self Coil. | Diameter. Length. Turns. | Inductance. | em. Sym. Microhenries. |__| e a QB Ey lang 36 | 40 360°3 Qs ikke sa. tanecee: TA 3°9 48 1707 OD heaceemiuest emis 76 | se ae 23 578, for High Frequency Electrical Oscillations. 1gt § 5. Tests of Standard Wavemeter (B) by Photographing Sparks. In order to obtain an absolute calibration of the standard wavemeter, the frequencies of the oscillations with which it was tested were determined by including a spark gap in the main oscillation circuit to which the wavemeter was loosely coupled and photographing the spark trains by help of a rotating mirror. The apparatus was arranged as follows :— The source of current was a small alternator whose fre- quency could be varied from 50 to 200 ~ per second ; this was connected through a small high voltage transformer to a spark gap with cadmium electrodes shunted by a glass plate condenser and a bare wire inductance in oil. A large variable air condenser consisting of six aluminium disks, each 100 ems. in diameter, could be put in parallel with the glass plate condenser, and, by suitable variation of the capacity and inductance in circuit, oscillations of frequencies from 300,000 to 1,200,000 ~ per sec. could be obtained. A special camera (fig. 2) was constructed and mounted for rigidity on a long slab of sandstone. At one end of the camera was the rotating mirror, which was concave and of 200 ems. radius of curvature. It turned on a vertical axis and was driven by a small motor, the speed being kept constant by an arrangement described below. The other end of the camera had two branches which carried respectively the spark electrodes and a pair of guides allowing the plate carrier to be smoothly raised or lowered while the rotating mirror threw the images of the spark trains as streaks upon the plate. The distance from the mirror to the plate was 200 cms. The speed of rotation of the mirror was kept constant (usually at about 60 revs. per second) as follows. On the axis was mounted a commutator and this was connected with a condenser, a bridge, battery, and galvanometer, for Maxwell’s Commutator method of measuring capacity. By applying a slight variable brake to the rotating axis, the galvanometer light-spot could be kept at zero. When this was the case the speed was steady, and could be measured with a counter or deduced from the value of the condenser and the resistance in the bridge. From measurements of a number of the spark train photographs on each plate, the average displacement from spark to spark was found; and the frequency was calculated from this displacement, the distance from the mirror to the plate, and the speed of rotation of the mirror. 798 Mr. A. Campbell on Measurement of Wave Length While each photograph was being taken the reading of the standard wavemeter was also observed, care being taken to keep the coupling to the spark circuit very loose. The value (n) of the frequency obtained from the spark photographs was in each case compared with the values (7) calculated from the measured values K and L of the capacity and inductance in the wavemeter circuit. Since the wave- meter coils have a certain amount of distributed capacity, it was necessary to take account of this. The required correc- tion was made by Glazebrook and Lodge’s formula (Cambridge ‘Phil. Trans. p. 171, vol. xviii. 1899), 2D iff PLR — op where p=2an, N=number of turns in coil, 4=capacity from turn to turn, and the capacities and inductances are in absolute measure. ‘The value of k was found by testing the capacities of coils with bifilar windings of wire similar to that in the coils used. The correction is small, being in no case more than 1 part in ]000. ‘The results are given in Table II. TABLE II. n | ny By Sparks | From K & L of ee —~persec. | Standard Wavemeter. j | —~- per sec. 61 & 62 290,300 | 290,500 Aq 516,800 516,800 Lh ke BS 818,300 821,200 | 5D 1,042,000 1,039,000 We may remark that the small differences between n and my, are quite within the limits of probable experimental error. On the same plate the value of n deduced trom the various spark trains sometimes showed an extreme variation of 12 per cent. from the mean; in the best experiments the variation was about 0°5 per cent. from the mean. In general the mean of 5 to 10 spark trains was used and the average variation from the mean was from 0:2 to 0°6 per cent. in the value of n. for High Frequency Electrical Oscillations. 799 § 6. Comparison of Wavemeter (A) with Standard (B). The condenser of (A) was tested throughout its range by Maxwell’s Commutator Method and gave the results shown in Table III. which shows the scale readings to be very nearly proportional to the capacity. At the higher readings the accuracy of measurement of K is here of the order of 2 or 3 parts in 1000. TABLE "ERI | Reading. Kk K/Readi Degrees. mmfd. (eeatiae: 20 126 6-1 40 DAS 6-0, 60 367 6.1, 30 486 60, 100 607 6:0, 120 724 6-0, 140 Salus 1) G05 160 966 6-0, 180 1075 59, Phe coils (A4,°A5) |... to AQ) were tested for self inductance (Lo) at ordinary frequencies. In Table IV. are given the values found (including the working circuit in each case). Approximate dimensions of the winding are also given. In the last column are given the values of L,, (2. e. the value of the self inductance for infinite frequency, TABLE LY. 2a | Z d N Self inductance, Coil Coil Axial Wire T ae microhenries. ‘| Diameter. Length. | Diameter. anh em. cm, | cm. Lo. be ee 52 10°7 | 0°32 | 32 21°6, 19°5, 5... 80 ive 0°32 oo 44°9, 42:0 / 1: GRY AW | 56 | 0°09; 55 100°5 97°5 7) ene 571 96 0°09; 95 195°0 189°8 AB Loy: 76 53 O05,°. 1 °..30 5381°8 524 os 7-6 89 0-05, | 150 | 1039 1025 800 Mr. A. Campbell on Measurement of Wave Length assuming that the current in that case is practically confined to the skin of the wire). These values have been calculated by the approximate formula (due to Heaviside) :* : 2ZONad . : . L,—-L,= To00r 2 microhenries, where N=number of turns, a =radius of coil, 1 =axial length of coil, d = diameter of wire, all the dimensions being in centimetres. The application of the formula to such short coils is not quite appropriate, however, as it has been deduced on the assumption that the solenoid is long. The two wavemeters were then loosely coupled to the same oscillation circuit and simultaneous readings taken at various frequencies. From the calibration of (B) already established and the results in Table IIT. the effective values of the self inductances of the coils of (A) were deduced ; they are given in Table V.. TABLE V. Comparison Effective L = Coil. Frequency, | (deduced). : —~ per sec. | Microhenries. Ce 2 ae Ls eee oo eee ees, ete Ses ale yy eee 1,125,000 20°1 19:9 1,338,000 19°8 AD ebsites 837,400 42°6 42'5,, 975,500 42°5 AG Kescenceaatas. 665,100 99°1 99°1 ATT pad hsbetinee 366,700 190°5 | 394,800 190°5 466,800 1911 191-2 473,400 192°0 665,100 191°8 . WAS ',cceasbadevees 284,500 530 . 290,300 530 53, 322,800 532°5 IND ehavatere duets 290,300 104, 104, * Collected Papers, vol. i., p. 356. for High Frequency Electrical Oscillations. 801 From Table VI. it will be seen that the observed effective values of L (to be used in working the instrument) lie between L, and L,, in all cases but the last. The discrepancy here may be due to an error of 0°5 per cent. in determining n which might occur in consequence of the reduced sensi- tivity when using a coil of such high resistance as A 9. The column headed L, gives the values of L calculated from L,, for the actual values of n by means of Cohen’s formula *. It will be noticed that this brings the observed and the calculated values of the inductances (at the high frequencies) considerably closer. Tape VI. Coil. Effective L. Lp. eet NG ol ha Ae iat tes) | 199 19:6 216, | 195, aa 42-5. 21 449, | 42:0 PING ee. hee 994 Bane 1 O05: 4) 95. BOAT Pees, | 1912 1908 | 1950 | 1898 | i eee | 531 | 526 5318 54 PAS pes..,!... | 104, 1029 1039 1025 | § 7. Conclusion. Thus it appears that within the limits of wave-length used, the wavemeter with coils of well stranded wire gave results in close agreement with theory, while in the case of the instrument with coils of solid wire the agreement was as close as could be expected, as the correcting formulas are only strictly applicable to long solenoids. In conclusion I would express my best thanks for kind assistance to Major O’Meara and his staff; to Prof. R. Ll. Jones, Messrs. H. C. Booth and T. L. Eckersley, who skilfully aided in the experiments ; and to Dr. Glazebrook for valued help and advice throughout the work. * Bulletin, Bureau of Standards, vol. iv., no. 1, p. 177 (1907). e028 a LXXXIV. An Electromagnetic Method of Studying the Theory of and Solving Algebraical Equations of any Degree. By ALEXANDER Rousset, 1.A., ee and J.N. Aury, A.ELE., Faraday House! Doudon CONTENTS. . Introduction. . The Electromagnetic Method. . Quadratic Equations. The Equation to Curves passing through the Neutral Points. . Cubic Equations. . Finding the Roots of an Equation. Description of Apparatus. NID OV COND 1. Introduction. Tee electrical device recently invented by Mr. Arthur Wright enables us to find approximate values of the real roots of an equation at once by simple mechanical and electrical operations. In order, however, to find-approximate values of the imaginary roots it is necessary to perform certain analytical operations, and then apply the device to find the roots of an equation of a higher degree. The method described in this paper has the great merit of giving approxi- mate values of all the imaginary roots as well as all the real roots. It is not capable of such high accuracy as the Arthur Wright device, and it cannot be directly applied when the indices of the powers of the unknown quantity are fractional. On the other hand, it is exceedingly instructive, as it shows how the numerical values of both the real and imaginary roots vary as the coefficient of any power of the unknown quantity in the equation is varied. The apparatus required is exceedingly simple, and is to be found in practically every physical laboratory. We have found it quite a suitable experiment to include in a laboratory course for first year students. The method suggested itself to one of the authors when ~ studying a series of papers by Mr. F. Lucas which are pub- lished in the Comptes Rendus, t- 106 (1888). The final electrical method (p. 1072) devised by Mr. Lucas is a practical one. A sheet of tinfoil is spread over a large flat plate of glass or other insulating material. If the equation is of the nth degree n+2 sources and sinks for electrical current are provided. These are arranged on a line at equal distances apart. The currents in n+2 wires touching at the sources and sinks are adjusted so that they have certain definite values. The method of calculating these values is practically * Communicated by the Physical Society : read June 25, 1909. Electromagnetic Method of Solving Algebraical Equations. 803 the same as in the method described below. The equi- potential lines are then traced out either by an electro- chemical method or by the Kirchhoff and Carey Foster method. If the line of sources and sinks be taken as the axis of x, and the origin be chosen midway between the outer wires, the coordinates of the nodal points, that is, the points where an equipotential line intersects itself, enable us to write down all the roots, real or imaginary, of the given equation at once. If (2, y,) be the coordinates of a nodal point, we can see from the symmetry of the arrange- ment that (2, —y,) will be the coordinates of another nodal point. It follows from the method of adjusting the currents that 2,-+y,¥ —1 gives a pair of conjugate roots of the given equation. The real roots, therefore, are all given by the abscissee of the nodal points lying on the axis of X. The method is not rigorous, as Mr. Lucas has not considered the magnitude of the error introduced owing to the finite size of the conducting sheet. It would be very laborious to apply in practice. In solving a biquadratic, for instance, the currents in five wires would have to be adjusted to given values before the equipotential lines could be mapped out. We shall now describe an electromagnetic method, in which the horizontal field due to the earth’s magnetism is used in an analogous manner to the conducting sheet in Mr. Lucas’s method. A drawing-board with a slit cut in it, a few pieces of bell-wire, any form of “charm”? compass, ordinary ammeters and rheostats or lamp-resistance boards such as are found in every physical laboratory can be utilized at once for the experiment (see § 7). 2. The Electromagnetic Method. Let us suppose that we have to find the roots for the equation T= 6p Bay ye ag 00), AY) We first, by the ordinary methods given in books on algebra, resolve the expression f(#) (w—b;)(@—b,) ... (a@— bn) into partial fractions. The numbers 0, 0,,...bn are any convenient numbers so chosen, however, that by +bo+ as +b, = =" ly —1/Ans ~\ 4% . . (2) For example, if the second term of f(#) be missing we must choose b;, bo, ... so that 2b=0. 804 Dr. Russell and Mr. Alty: Electromagnetic Method We thus obtain 7, (x) | Ay As An Go GEEN elk) tos too where, by (2), an Aj + Ath ded Ae 0). 05 ney and f f(b) a al (b; — be) (b) —b3) ... Pain (bg —b1) (0g— bs) ... } (5) BOL Let us now consider the magnetic field round a long vertical wire carrying a current of C amperes, and let us suppose that the earth’s horizontal field in the neighbourhood is uniform, and that its horizontal intensity in C.G.s. units is H. The magnetic force at any point P at a perpendicular distance of 7 centimetres from the axis of the wire will be the resultant of a force C/5r acting at right angles to the plane containing r and the axis of the wire and a force H directed to the magnetic pole. There is always a neutral point* on the line through the axis of the wire perpen- dicular to the magnetic meridian. If « be the distance of this point from the axis #2 C/E). ik? es eae This formula is utilized in a well-known rough laboratory method of measuring H when C is known or vice versd. Let us now suppose that we have n vertical wires arranged in a plane perpendicular to the magnetic meridian, and let Fig. 1. Y them cut the plane of the paper perpendicularly at {B,, B,, ... B, (fig. 1) which are at distances )j, b.,...b» from O. * A. Russell, ‘The Electrician,’ vol. xxxi. p. 282 (1893). of Solving Algebraical Equations. 805 If C,, Cy, ... Cn be the values in amperes of the currents in the wires and H the horizontal intensity of the earth’s magnetic field, the components X and Y of the resultant magnetic force at P(2,, y1) will be given by yi iC ta) ts pant and y= Hci m eats on it Crean Vy Ya 9 Jags where 7,?=(@1—bn)? +y 12. Hence multiplying X by « and subtracting we get Y+X.=H+ Le ee t) + oe (%y—bo— Ye) + ... Ory BY C,/5 a C,/5 Lytyy—b, ~ ajtyyt—b, =H+ Ata neutral point the resultant magnetic force is zero, and therefore both X and Y are zero. Hence, if «, and y; are the coordinates of a neutral point, x,+y 4 is a root of the equation 0=H+ oe +e Ho) kul ont hs sae Comparing this with equation (3) we see that if we adjust the values of the currents so that C,H ° Aj/an, C= SE, Ay/an; eee C, =o .A,/a;, then a +y0 is a root of the equation f(x) =0, and therefore ?;—Yy,t 1s also a root. It follows from (4) that }C=0, and therefore only n—1 ammeters and only n—1 rheostats are required. As an introduction to the method let us consider the theory of quadratic equations. 3. Quadratic Equtions. Let us suppose that the equation is v’+be+c=0. In3this case it is convenient to write v’+bhete ss: c/b cfb a(a+tb) a «e+b? 806 Dr. Russell and Mr. Alty: Electromagnetic Method and, therefore, H a’ +be+e pee (5He/b) (5He/b) (e+) bo (ee) | In fig. 2 let us suppose that the plane of the paper repre- sents a horizontal plane, and that H is the direction of the earth’s magnetic force. Let us also suppose that two long Fig, 2. L= N | t | | | | | $ | NC vertical wires cut the plane of the paper perpendicularly at O and B respectively, the length of BO being 4 centimetres and the magnitude of the current C, in amperes, in the O wire being 5Hc/b, and the B wire carrying the return current —5Hce/b. If the direction of the current C be into the paper at B and out of it at O, the circular lines of force due to the currents in each wire will act in the directions of the curved arrow-heads shown in the figure. We shall now consider how the numerical values of the roots of the quadratic equation alter as c, and therefore also C, increases from zero to infinity, b which we suppose to be positive remaining constant. : We have already shown that the coordinates of the points at which the resultant magnetic force is zero, that is, the neutral points, determine completely the numerical values of both the real and imaginary roots of the equation. When ¢ is very small and positive the neutral points lie between B and O. For a particular value of c, for instance, they are at N, and N, on the axis of X. We see at once from symmetry that ON,=N,.B. If the length of ON, on the same scale that BO is.b be — a, the roots of the equation for this value of ¢ are both real and equal to —a, and —b+z, of Solving Algebraical Equations. 807 respectively. As we increase the value of c, and therefore of the current in the wires, the neutral points N, and N, approach one another and coincide at P. In this case the roots are each equal to —b/2. For greater values of ¢ the neutral points cannot possibly lie on BO as the resultant magnetic force due to the currents at all points of this line is greater than H. From symmetry the neutral points lie on the line N,PN, bisecting OB at right angles. For a particular value of the current they are at the points N, and N, on this line. [f PN,=y, then PN,=—y, and the cor- responding roots of the equation are —b/2+yy/—1 and —b/2—y./—1. The real part of the imaginary roots is therefore independent of c, but the coefficient of ./—1 increases as ¢ increases. When ¢ is negative the curved arrow-heads in fig. 2 must be drawn in the opposite directions. N, will now be at a distance x, from O along OX, and N, will be at a distance —b—.wz, from O along OX’. The roots in this case, there- fore, are always real and of opposite sign, and continually increase numerically as ¢ increases. When 0 is negative the point B in fig. 2 will be to the right of OY, and the discussion of the roots in this case is, equally simple. 4. The Equation to Curves passing through the Neutral Points. From the preceding discussion it will be seen that the locus of the real roots of an equation determined in this way is the axis of z. Fig. 2 shows that for a quadratic equation when 6 is positive the locus of the points giving the imagi- nary roots is the straight line N,'N,’. Similarly when 0 is negative it is the parallel line given by equation x=b/2. It is important to know the equations to curves on which the neutral points must lie in the general case. Let us suppose that x+ye is a root of the equation *(€)=0. In this case we have f(at+y)=0, and, therefore, by Taylor’s theorem, KO, (+i f(a)... +wf/'(@)- Bf” (a) +... b =0. 808 Dr. Russell and Mr. Alty: Electromagnetic Method This equation can be satisfied either by f(#)=0, and y=0).. 2). (on or by f(a) Sy" (a) +4 fe (xv) — PES 2G : (10) d wy ca | ae fe) 4 @) +5 fe)... =0 an The equations (9) obviously give the real roots of the equation which must all lie on the line y=0, that is, on the axis of X. The points of intersection of the equations (10) and (11) determine the imaginary roots. As equation (11) does not contain the constant term of the equation f(£)=0, it follows that it gives the curve locus of a series of imaginary roots of the equations formed by varying c. Where the curve represented by equation (11) cuts the axis of w we have f'(z)=0. At these points there are at least two equal roots. | For the quadratic equation 2?+bxe+c=0, (11) becomes 2c+b=0, and this is the equation to the line of neutral points N,'/PN,! shown in fig. 2. 5. Cubic Equation. Let us suppose that the equation has been reduced to the form a — ba +oe=0s% 5. 5 a> We easily find that - x — b?a + ¢ C yd C H RMT ay Ss 5a +6)” ra en where C=5Hc/20’. In this case (fig. 3) three long vertical wires are used. Let them cut the plane of the paper at right angles at B,, O, and Bg respectively, and let B}O=OB,;=0. The currents in the wires passing through B, and B,; must each be made equal to C, and the current in the wire passing through O should be the return current 2C. The arrow-heads indicate that the direction of the current flow is out of the paper at B, and B, and into it at O. H denotes the direction of the earth’s magnetic field. : Let us now suppose that ¢ increases uniformly from zero to infinity. When cis small, and therefore the currents are 10; PERI. — ©: = es A (ab) (op) oie mai = I a Hitt | fa Ay es jomt 33 — =| ‘ DM: i a DE KOW. es typed e yin , yer : yer « tg MggoP « @ pe ‘GOL 16 Osa & MORRIS OWEN. Tel TAYLOR JONES Phil. Mag. Ser. 6, Vol. 18, Pl. XX. ‘91107 eoUedoyIp 0} Arvvatid TaMoy WOT ooURTO CUTMOYG -o ‘'G ‘OI 2 = "4 — %U Ty & = ca TEAC a ies ‘9U0} SOUALOY I(T > + » 4 45% ¢% Pe ,* a * ed 3? ’ ‘a’ ‘at \? W M “ W bai my “., Wis * j i j ; ’ ‘Pp OT ‘ CHABOT. Phil. Mag. Ser. 6, Vol. 18, Pl, XXT. 18, Pl. XXII. 6, Vol. . ser. Lag 1 Sa SeESe SISee i. 4 aoe sieeestreate £ ae eG eee fl 3 HH aia Pate . Te 2 Ce aoe ne atte - eat le et HE: ee pth He set SER tHe ee aie eee {tie ial ate iE Hii _ HEE ps ebolel. fe oO i wo oO + te] x = Se ete REET OTT HH ana arate Ea Saetiea ao Se ae i Sree ainsi eMeaeE pL ae ee LSet a Ee cooee _—————_———— = ass a KENNEDY XXII, Phil, Mag, Ser, 6, Vol. 18, Pl Ct Eig. Tro. § =) Siaio alc wei a CeO “aims areny’'GanSOdx] BILIY “NID = S Bae “QL ALIA Loy 40, 60, & 100. = «120 Pressure nM MS 20. Fra, 14. Fie, 138, 14,16, 1 iA xo 500 600 00 G00. Pressure tr mm. foo 200 500 400 z = 8 & 3 = . a 2 2= = S su g as I) Saiex 3a Soe (-5 3 Soe DE FSS ieasdss a settee 8 HEE tg z Ep 5 sees: 3 S [= ww To oe =| 5 csscs o =| E E 5 <= Ww i 5 g , iS 2 o 2 ni 3 S = = a fax) 3 pasuvuiey gun S0dX7] Baldy * NI aes) # a 8 = = 5 fin 3 s Esp] ca i 5 - e =} « 52) & SELES 2 Fistsstsse| U2 re fetal > é a A 5 2 I are =| EEE 3 Eetet = Sonnet & Fe a Ss Ss = = Ss r=) 2 = R = ns mnuiny GUNSOAXF UILIY “NI|A “| ALIAI LOY 6 wi f HE aaa fii 8 ie zi ae = 4 S = se SEER ES HEE a =| Se: fessasey 4 peestien {Cos # Sonee F Hstinza Fa 5 { Hae fe ca Hi = E fet fatet einai iat S Se 2 (2) i af siirites el a AS # EB , =e : = ; Xa = Ae : + 2 = rf < si za! aaa 5 F pasza tes] vii ci ir enn aazt nian faz f 2 za seeles = Eel) = a Ht ieee 2: i as e = = S s & 3 = aes sermany JUN sodXy “ELI NIA) “gy ssiatuay ‘5 ata ist 4 Fig. 3. 2 Ss Ss Disrance.in.Cms. of.aut. From. EvecrRopes: < 3 S av2S) Se AEN OAK ? ualdyy “NI W c 01 ‘ ALIAL 5 EPARATION. IN Mns. or. EvectR ODES. r=) WO) Atta ry rs ON DBNSOAX F . Yaa “NI ILO Fa. 12. Fig. 11. Fie. 10, Fia. 9. vos Mveuaayra UNSOAXT] ULI” = = } Pals = 20 2 Janeeise & | ++ le E =e = Soe =) ae Ss =" == = = eee =p esi isos =e 500 600. 700. Pressure wn Mus. 400. 300 3 a = s — uh pes : s= HE 2 H ts iF = ssa (i fata i aH Sf i ne Beis 3 = a Banal eed eatitefest a # esd feees eats aeS| 8 |psEseievtaes Sal fereitrtl ist eal a 3 EfS|° aE et ese ase EE : He eae Se See is all tt Hel False] dniitisy b Sees a vustuea ceeetanest toad et + ist ae: i = HH th +H 5 Eoaee aS E tt = =] Fa] = eG 8 es cee MY DANSOAXT] USWA NI OQ] ALIA LOY 2 3 io s = ee 3 Aa Hic 56= I z HE = ge § a ae On =s s cosst SP Se Eeestesteretes| . SeeCOeTm trie a a SO Tores wveveny Un SOdX] AIL Y NIN QT ALIAILO VY H Fr SST EpCairest a = Se eee este | Sete His SHEE Hass beicay/ dessa fae 3 fr ft isa FE : HH sey if t Sze frsad tay aon ets + aa > = fies i SRE 4 Betas Eeaes eisi? = aise te Sa ESE = Balin ieee ueedteee ott fi faa) ss zs f $e a & San = Hl at al fits ae Pratice HESS a = 3 Ea yatta ah Henin ey la = 3s 7, : Heats [= ae : it é pe Ree ee syed inj (sees pstad ns Hf: tS aaa ETS bse seers} iz Hs EE EEEE 3 Tt fe H sre ii tnt rte = Ss HO he AST SS Fg iB | Cape ee oo RR a sys mrminy “LIs0dd "40" ALIAILOVY Fi 7] c) | seed fe: Sf BS HEE ii eS sss He : Feees esezy FEestEE +t io) nore 2 saytt A 2 = S ui 2 2 i ppvasanreninny #5 UN BOd. x7 ‘° - cy Mada yy ‘ iia i s Nuh QP Aunts yy Woon. Phil. Mag. Ser. 6, Vol. 18, Pl. XXIII. 11G, ily RICHMOND. Fie. I.—Showing the variation of the striation with diameter of tube. 3mm. -67 mm. 6 mm. 5g mm. 9 mm. *82 mm. 12 mm. ‘59 mm. 22 mm. °63 mm. 33 mm, ‘47 mm. 44 mm. ‘57 mm. The diameters of the tubes are written on the left and the stris-distances on the right. "Phil. Mag, Ser. 6, Vol. 18, Pl. XXIV. Fie. II.—Variation of the striation for the same spark with various powders. @), hy copodium: 2: .2:.c.00.5. sscdseees | SO HM, (OV LES 1 01D oo Ro ROP te cere Ae ‘76 mm. A) STARE Siuseateattevcs ceales weenie ‘58 mm. The strise-distances are given along with the name of the powder. RICHMOND, Fie. I11].—Variation of the striation with variation ot electrical conditions. (a) ‘68 mm. (2) ‘61 mm. (c) -84 mm. (d) ‘80 mm. (¢) 1:1 mm. Figures (a) to (e) were obtained from circuits the frequencies of the oscillations from which are in descending order of magnitude, The mean strix-distances are written on the right, Phil. Mag. Ser. 6, Vol. 18, Pl. XXYV. Fre, [V.—Variation of the striation with electrical conditions. (2) (2) (¢) (d) (e) Figs. (a) to (e) refer to circuits giving oscillations in descending order of frequency. Figs. (/) to (4) refer to a series of circuits for which the frequencies were measured, These are shown to the right of the corresponding figures. ‘46 mm. (7) 58 X 106. “38 mm. (9) ‘79 X 108, “40 mm. (/) 14 x 106, 33 mm, (/) 2:1 x 106, The strige-distances are shown on the left, RICHMOND the same tube. o fo) Fie. V a.—Variation of the striz-distance alon Phil. Mag. Ser. 6, Vol. 18, Pl. XXVI. ‘ATWO ouLyoVU oy} ULOIZ yavds OYY OJ VOTZeIAVA OYY SMoYs ATAE[TIULIS @ 4, Sig ‘savl Jo serroqqQuq snoreA pur OUTYOVUL UOT SBA yieds ong, ‘yareds oy} tvou puo oy} VY 4B Suruutseq UMOYs SI ‘MULIp ‘UO [ puB SuCT ‘suo CF Oqnq v Jo Yue] opoyM oy} v A “SI UT ‘oqny oUlvs OY SUOTL OOULASIP-KII4S OY JO MOIYVIUVA—-"g A “YTYT ” CampPBELL & SMITH. MINIVAN LAANAAWAA AA AAR AAA AAA AAAAAARAA VVVV VEN YS é ‘an . Vw ww YM . ” AAR EA AAA AAA A A Se ee eere nan & ‘¥NN VV ¥ . Phil. Mag. Ser. 6, Vol. 18, Pl. XXVII. SGP RSEECeRG ESA ES ERAS SARRS Ys PEPER SEITE + Yt eA : Wy rey Seeeteces Beaten ae * A #24 8S eeases ARSE E SERRE SS | "AS * es eepepanet + tte ¥ ve SFE eee *" @ ®Rwaeeaeeae? PEP SSESCES SPSS SSSR PPR RRS eee eee es ee PECTS TETEPeF eeec ee eee ee & vu Pv eee eee >Re Cee eaeees $e Ff &ePsteeseeepede Fig. 7 a. Fig, 9. CAMPBELL. Phil. Mag. Ser. 6, Vol. 18, Pl. XXVIIT. of Solving Algebraical Equations. 809 small, two neutral points N, and N, obviously lie between O and B; anda neutral point N, lies along B,X’. Fie. 3. Asthe current increases the neutral points N, and N; approach one another and the neutral point Nj’ moves along B,X’. For a particular value of c, N. and N; coincide at P, and we have two equal roots. [or greater values of c the neutral points N, and Nz move uniformly along the curve N,'PN,', one being as much above the line XX! as the other is below it. But the neutral point N, always moves along the axis of X. The equation (12), therefore, has always three roots. When ¢ is small thev are all real, two of them being positive and one negative. For a certain value of ¢ the two positive roots become equal, and for greater values of c¢ we have two conjugate imaginary roots and one real negative root. Both the real and imaginary parts of the conjugate roots continually increase as c increases. The equation to the curve N,'PN;' in fig. 3 can be found at once from (11) ; it is ee as ws | Sha) tee Bier Glee) The negative branch of this hyperbola indicated by the dotted curve in fig. 3 gives the locus of the neutral points when ¢c is negative. In this case there is obviously always one real positive root. Increasing the value of b in (12) is equivalent to putting the wires B, and B; further apart. This obviously increases the limits of the values of the Phil. Mag. 8. 6. Vol. 18. No. 107. Nov. 1909. 3H $810 Dr. Russell and Mr. Alty: Electromagnetic Method positive real roots. When 0 is negligibly small we see by (14) that the locus of the neutral points is the two straight lines represented by (y—2 ¥3)\(y+e ¥3)=0. Hence the imaginary roots are of the form #,+2,,4/3,/ —1 where — 2.2, is the value of the real negative root. Similarly we can discuss the roots of the equation et+hPe+tec=0. In this case it will be found that the currents in the wires through B, and B, are unequal, and that the equation has always two imaginary roots, the neutral points lying on the hyperbola y?—3a2?=0", which is conjugate to the hyperbola shown in fig. 3. Equations of the fourth and higher degrees can be dis- cussed in like manner. To get the most instructive results care has to be taken to choose the distances between the wires so that the analytical expressions for the required currents may be as simple as possible. If this be not done analytical difficulties will often be encountered in interpreting the results. 6. Finding the Roots of an Equation. The great and so far as we know the unique advantage of this method is that it enables us to find the imaginary as well as the real roots of an equation almost at once. In equations occurring in many physical problems it is the latter roots which we desire to find, and this method enables the physicist to find quickly approximate values of these roots. If due precautions are taken the maximum inaccuracy of this method need not exceed one per cent. This is the accuracy obtainable by careful students, who need have no previous experimental training, in findmg H by measuring the distance of the neutral point from a long vertical wire carrying a known current. 7. Description of Apparatus. We shall now describe the simple apparatus we use for teaching purposes. In fig. 4 the arrangement of the apparatus for solving a cubic equation is shown. 8,8 represent springs of Solving Algebraical Equations. 811 attached to insulators. These are necessary in order to keep the wires tight. The wires are No. 16 single cotton-covered wire, and pass through a long slit cut in a drawing-board BB. The ammeters A are any of the ordinary ammeters used in the laboratory reading up to 10 amperes, and are in series with lamp-boards and rheostats. The currents are adjusted to the required values, and a sheet of sectional paper with a slit in it is put on the board. By means of an ordinary charm-compass the neutral points can then be readily found. It is advisable to make a little sketch of the lines of force near the neutral points, as this is a help in indicating their true position. The coordinates of these points read off from the sectional paper give the real and imaginary roots of the equation. [ sl2 J LXXXV. On the Radium Content of certain Igneous Rocks from the Sub-Antarctic Islands of New Zealand. By C. CoLeripek Farr, D.Se., and D, C. H. Fiorance, ie Se UTHERFORD (‘ Radioactive Transformations’) has cal- culated that 4°6x10-™“ gramme of radium per unit mass of the Harth would generate an amount of heat equal to that lost by the Earth by conduction through its crust. Strutt (Proc. Roy. Soc. 1907) has examined the radium content of a number of igneous and sedimentary rocks, and his results, corrected by Eve and McIntosh for an error of standardization, give for mean values Toneous rocks.....,... 1:7 x 10-” gramme radium Sedimentary rocks... 1:1x10-¥ 99 13) a result which is about 28 times as large as the theoretical quantity. Hve and McIntosh (Phil. Mag. Aug. 1907) find a mean for Igneous and Sedimentary rocks of 1:1 x 10— per gramme of rock. Joly (‘ Nature,’ Sept. 1908) finds values much higher than these, his mean for igneous rocks being 6'1 x 10-!*, whilst the mean content of the Basalts examined by him was 5:°0X10-¥, which is much higher than the value found by other investigators for similar rocks. Method of Testeng—The rocks examined by us were ground to a very fine powder, and 20 grammes were fused in a platinum crucible with ordinary fusion mixture, one gramme of the powdered rock being mixed with six grammes of the mixed carbonates which had been previously tested for radium. The fused mass was dissolved partly in distilled water and partly in HCl, both of which were separately examined. The acid and alkaline solutions were then sepa- rately corked with glass tubes and clipped rubber connexions in position, and the cork coated with sealing-wax to prevent possible leakage of the emanation, and the flasks were then set aside for three weeks to mature. The apparatus was similar to that described by Strutt (loc. cit.). The solution was boiled for one hour, the steam being condensed in a Liebig condenser and the gases evolved being collected over fresh distilled water. Before the boiling was stopped, the water in the jacket of the condenser was run off and steam was passed through as far as the collecting vessel to drive over the last traces of emanation. The electroscope was similar to that used by Boltwood (Amer. Journal of Science, * Communicated by Professor HE. Rutherford, F.R.S. Radium Content of Rocks from Sub-Antaretic Islands. 813 1904), and it was exhausted to half an atmosphere by means of an oil-pump before any of the collected gases were passed in. These gases were allowed to enter very slowly through CaCl, and H,SO, drying-tubes, and the pressure was then brought up to atmospheric by the admission of air, the time occupied over this..transference through the drying-tubes from the stoppage of the boiling to the commencement of observations in the electroscope being in every case 15 minutes. Readings of the position of the leaf were taken every two minutes for half an hour, and the instrument was then re-charged and the leak for the next half hour similarly determined. This was sufficient indication that the effect was that due to the radium emanation. In some cases, how- ever, the gas was studied for three or four hours, but although the presence of radium was shown clearly by the increase of the rate of leak, yet, owing to the active deposit, so much time was lost in bringing the electroscope back to a normal condition of natural leak, that it was decided to pump the gases out after an hour. The electroscope was charged to a potential of 220 velts and the movement of the leaf was read by a microscope and a micrometer eyepiece, so that the large scale-divisions could be subdivided into hundredths. For the means of its stan- dardization we are indebted to Professor Rutherford, who kindly sent us.a solution containing 3:14x10-* gramme of radium. ‘Two separate eighths of this, each containing 3°925x 10-'° gramme of radium, were used as_ standards. Hither of these treated in the same way as the rock solutions produced an initial leak of 64 micrometer divisions per minute, hence one micrometer division per minute corresponded to 6°13 x 10-” gramme of radium. “ Natural” Leak.—The determination of this is an im- portant matter in an attempt to evaluate with accuracy the amount of radium contained in a rock. In our case the electroscope was always charged over night—the insulation was sufficiently good for it to retain a considerable portion of its charge for forty-eight hours—and the leak found. In general it decreased from the time of its initial charging the night before to the introduction of the rock gases. Froma value of 1°5 micrometer divisions per minute the night before, it became about 0:8 per minute at the time of intro- duction of the emanation. We consider that this latter number cannot be more than ‘2 from the actual value during the examination of any of the rocks. Such an error would lead to a wrong estimation of the amount of radium in 20 grammes of rock of 1:23 x 10-, or an error of 0°10 x 10- 814 Dr. Coleridge Farr and Mr. Florance on the Radium per gr amme of rock. We therefore consider that for the specimens we have examined the results may be relied upon to about this extent. Results. Granite. Bouthhy, 183): :/0'6 taal oes Trachyte. | Auckland Is., Musgrave Penin. Granite. Auckland Is., Musgrave Penin. Pitchstone. Auckland Is., Musgrave Penin. Basic Por- Auckland Is., Adams Island. phyrite. Basalt. Auckland Is., Adams Is. (sea- level). Dolerite. Auckland Is.. Adams Is. (top). Diabase. Auckland Is., Musgrave Penin. Gabbro. Auckland Is., McClure Head, Carnley. Campbell Island Rocks :-— Porphyry. Perseverance Harbour ......... Trachyte. Waligk Pointy jas cstslee seid se su cpt Trachyte. Whoa hive x. Lid venaiabene neers Melilite lomant Taye: cil ive paenaetane Basalt. Dolerite. Mowing dehemey ». 2) ond fouviddetie: Limegtoné.:!' ‘Garden: Gave, 4:2). ose aes Gabbro. INO Wis Boctyg: acts iat pda ata tee Marble. Ni Wie. Beeutiet) ins i aaloan bee eee The three following rocks are of special interest :— (1) Andesite from the latest flow of Ngauruhoe, about sixty years old. Radium content °41. 2°50 % Line 2°10 (2) A lava from the lip of the crater of Mount Erebus. This is fairly recent, and was given us by Mr. D. Mawson, of the Nimrod Expedition. fem 2 ate Radium con- This rock has had to be tested rather hurriedly, and is perhaps under true value. (3) The Meteorite is a stony meteorite which fell at Mokoia in New Zealand, on November 26th, 1908, and was sent to us by Mr. G. R. Marriner, Curator of the Wanganui Museum. It contains 37 per cent. of iron oxide, and 37°5 per cent. of silica. Radium content °52. This value is nearly equal to that obtained by Strutt for a stony meteorite. Conclusions.—Since all but two of the rocks examined are derived from islands to the south of New Zealand which lie at eee a Content 0j Igneous Rocks from Sub-Antarctic Islands. 815 are mostly igneous in character, the indication appears to be that the distribution of radium in the rocks of this region is in excess of that required to maintain the constancy of the heat of the Earth; and the necessity of an examination of rocks from all places and of all ages is emphasized. The mean radium content of these rocks approximates very closely to that found for others by Strutt and by Eve and McIntosh, but differs considerably from Joly’s values. Further inves- tigations are being made on the rocks of these regions ; and it is hoped to examine the distribution of radium in the material encountered in piercing the Lyttleton Tunnel, which will give a range of time from the earliest sedimentary rocks to the last flow of the volcano, through the wall of whose crater the tunnel is bored. The following notes on the geological properties of these rocks by Mr. R. Speight, F.G.S., may be of interest. The two granites are both biotite granites of ordinary type and of uncertain age. The other plutonic rocks—the gabbros though coming from widely separated localities of the same region, exhibit marked similarities: both are olivine gabbros, but that from Auckland Island is very coarse-grained at times. The coincidence of their radium content is very striking. The porphyry from Campbell Island contains large numbers of zircon phenocrysts. The trachytes are all of highly alkaline type. Those from Auckland Island contain a very high percentage of soda and a very iow percentage of alumina (11 per cent.) and a small quantity of free quartz; they are decidedly acid. Anorthoclase is a common constituent as well as an alkaline hornblende. The pitchstone belongs to the same group but is somewhat more basic in composition, and contains abundant eegerine-augite microlites. The Campbell Island trachytes, according to Dr. Marshall, are slightly more alkaline and contain less iron. They are all augite trachyte with anor- thoclase and occasional riebeckite and cossyrite. These rocks together with the melilite basalt all appear to have similar amounts of radium present. The other rocks from Auckland Island are basic in character and include flows and dykes. They are generaily marked by a high percentage of titaniferous magnetite. No. 8 isa diabase of greater age than the rest, and No. 5 a porphyrite approaching an augite-camptonite in character and basic composition, found penetrating the more recent basalts. The age of these basalts is probably from middle to late Tertiary. There is no marked difference between the earlier 816 Mr. J. A. Gray on the Ultimate Product of and later basaltic flows, but the one from sea-level at Adams Island is fine-grained and contains hornblende, while the other is very coarse-grained with large phenocrysts of olivine and augite, The Campbell Island limestone is of Tertiary age and markedly foraminiferal; the marble is derived from it as a result of basic intrusion. A general conspectus of these results shows that the radium content corresponds roughly with the basicity, and not with the age of the rocks. Canterbury College, New Zealand, May 12, 1909. LXXXVI. The Ultimate Product of the Uranium Disintegration Series. By J. A. Gray, B.Se.* JN Amer. Journ. Se. (vol. xx. p. 253, 1905, and vol. xxii. p. 77, 1907) Boltwood gives considerable evidence which goes towards proving lead the ultimate product of this series. He finds, e. g., that in primary uranium minerals the ratio of the lead to the uranium is practically the same for minerals of the same age, and greater the greater the age of the mineral. These are conditions that the ultimate or any inactive product must fulfil, and lead was found to be the only substance fulfilling them, except perhaps helium, which has been definitely proved to come from the «@ particles (Rutherford and Royds, Phil. Mag. vol. xvii. p. 281, 1909). However, in all the minerals of which analyses were obtained, there was a great deal of contamination from other sub- stances; so that it is not unlikely that the lead was deposited in some other way than as a product of the uranium series. Certain mineral substances exist which do not appear to’ be open to this objection. These are the hydrated phosphates of uranium with (1) calcium, (2) copper. These substances exist in characteristic crystals having somewhat the appear- ance of artificially purified substances, and are undoubtedly derived from the comparatively recent recrystallization from water of the salts derived from pitchblende lodes. A spectro- scopic examination was made of these salts, to see what light they would throw on the question. A spectroscopic analysis was first made of mineral autunite, {Ca(UO,)2P,03+8H,0} from Portugal. This contains ap- proximately 50 per cent. of uranium. If old enough the mineral would contain the products of uranium and enough of the ‘final product to be detectable by spectroscopic analysis. * Communicated by Prof. R. J. Strutt, F.R.S, the Uranium Disintegration Series. 817 Therefore any line in the spectrum obtained, other than those due to calcium or uranium, might possibly belong to a final product. To simplify the examination, a comparison was made with a carefully purified specimen of uranium oxide. To obtain wave-lengths, an iron reference-spectrum was used. The are with carbon poles was used to burn the substances. As the mineral did not burn very well, calcium chloride was used asa flux. The three spectra were obtained on the photographic plate, one above the other, that of the mineral being in the centre. In this way we could see what lines were in the mineral spectrum and not in the uranium, and by means of the iron spectrum find the wave-lengths of such lines. In this way it was found that the only lines in the spectrum of the mineral not belonging to calcium or uranium belonged to iron, lead, barium, and strontium. Barium and strontium may certainly be discarded as most calcium salts contain a little of them. Iron is an almost universal constituent of minerals, being present even in clear white salt and Iceland spar: thus not much weight can be laid on its appearance. Other analyses carried out on (1) another specimen of autunite, locality not known, (2) torbernite from Cornwall, the double phosphate of copper and uranium {Cu (UO) sk4Q, aa 8 H,O}. Except that in the first of these there was more barium and in the second that the calcium was replaced by copper, the analyses give the same result. We see, therefore, by the analyses of three minerals from different localities, that lead is the only substance not accounted for. We all know that if the final product is metallic and the mineral old enough, lines belonging to that product ought to appear in the spectrum. The spectroscopic analysis of these minerals therefore strongly points to lead being the ultimate product of the uranium series. Certain phosphatized bones have been shown by Strutt (Proc. Roy. Soc. Aug. 1908) to be moderately rich in radioactive con- stituents. It was thought worth while to test these for lead. The result was positive. No connexion could, however, be traced between the geological age of the specimens and the quantity of lead. It must be supposed that here the lead is not wholly of radioactive origin. Summing up, we find that lead is the only substance which by spectroscopic analysis can be considered as the ultimate product of the uranium series. It has often been pointed out on theoretic grounds that lead was probably the ultimate product. Boltwood’s experiments lead to the same conclusion. A rough estimate was made of the amount of lead in the Phil. Mag. 8. 6. Vol. 18. No. 107. Nov. 1909. Ag 818 Notices respecting New Books. first specimen of autunite, and from that a determination of its age. A tenth of a gramme of autunite was burnt in the are with a little calcium chloride, the image of the are being exposed on the slit for two minutes, which was practically sufficient to burn the lead out. The same thing was done for similar amounts of two specimens of calcium chloride, the first Feneainaing apDp gramme of lead per gramme, the second $5:999 gramme of lead. ‘There was less lead in the mineral than in the first specimen of calcium chloride and more than in the second. It was judged that the mineral contained s0-p00 Zramme of lead per gramme. As it contains 50 per cent. uranium, this means that for one gramme of uranium the autunite contains 455 8 of lead. In radioactive equilibrium, in one gramme of uranium there is 3°8 x10‘ gramme of radium. ‘Taking the period of radium as 2500 years, the fraction of radium under- going transformation per year is 2°8x10-*. This means 9) that 3°8 x 10-7 x 2°8 x 10-4 x a gramme of lead or 9x 10-° would be formed per year for one gramme of uranium in radio- active equilibrium. Therefore the time taken for 10-* gramme —4 of lead to form would be 9x 1025 Ye years *. In conelusion, I wish to record my thanks to Professor Strutt, who suggested these experiments, for his interest and help throughout, and also to Professor Fowler for his help in overcoming the difficulties of spectrum analysis. . ars, or about a million LXXXVII. Notices respecting New Books. Report of a Magnetic Survey of South Africa. By J.C. BEattin, D.Sc. Published for the Royal Society and Sold by the Cambridge University Press. Liondon, 1909. 20s. net. 4to., pp. x+126, with six Appendices, pp. 1-235, and nine Charts at the end. TIXHIS volume deals with observations made at fully 400 places in 8S. Africa, ranging from the extreme South of Cape Colony to Victoria Falls in the North. The stations are mostly in British territory, but a few are in Portuguese Hast Africa. The observations were made by Prof. Beattie with the assistance of some friends, especially Prof. J. T. Morrison, between 1898 and 1906. The * On p. 204 of his book, ‘The Interpretation of Radium,’ Soddy mentions that autunite contains no detectable quantity of lead. This is probably due to the small amount of lead, which would be very hard to detect by ordinary chemical methods, and which would also depend on the age of the mineral. Geological Society. 819 results are reduced to July 1, 1903, by means of secular change data derived from the repetition of the observations at a selected number of the stations. Details as to the geographical position of the stations and the observed values of the magnetic elements are reserved for Appendix E (215 pages). In the body of the work are a number of tables showing the values of the magnetic elements for July 1, 1903, as observed and as calculated by methods intended to eliminate local disturbances. Deductions are made as to the disturbances, “ridge” and “valley ” lines, &c., after the method of Riicker and Thorpe, and these are illustrated by a number of small maps in the text. The large charts at the end of the volume show the position of the stations, isogonal lines, isoclinal lines, and iso- magnetics for the total intensity and a variety of its components. They also include a geological map prepared by Mr. A. W. Rogers. LXXXVIIL. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. {Continued from p. 680.] March 24th, 1909.—Prof. W. J. Sollas, LL.D., Sc.D., F.R.S., President, in the Chair. See following communication was read :— ‘Glacial Erosion in North Wales.’ By Prof. William Morris. Davis, For.Corr.G.8. An excursion around Snowdon in September 1907, followed by a further visit in 1908, led the author to the conclusion that a large-featured, round-shouldered, full-bodied mountain of pre-Glacial time, had been converted by erosion during the Glacial Period— and chiefly by glacial erosion—into the sharp-featured, hollow- chested, narrow-spurred mountain of to-day. The peculiar in- difference of topographic form to the trend of formation-boundaries and the insequent stream-arrangement, are what might be expected as the result of prolonged erosion upon a mass of complicated and resistant structure. ‘The author discusses Ramsay’s theory of a plain of marine denudation, and is of opinion that the upland seems to deserve classification rather with peneplains ; he suggests for it a Tertiary date, which would not be inconsistent with the erosion of open valleys in the uplifted peneplain after its elevation, and argues that Snowdon and its high neighbours had a relief ot some 2000 fect above the plain. As the result of a comparison with the non-glaciated regions of Devon, it is considered that the dissection of North Wales must have been somewhat less developed in pre-Glacial times than in Devon to-day. On this assumption it is possible to make a tentative restoration of the pre-Glacial form of Snowdon: subdued mountains, with dome-like summits and rounded spurs, drained by prevailingly graded streams of accordant levels at their junctions. In fact, the characters were 820 Geological Society. those of ‘moels’ such as Moel Tryfaen, or like the well-worn Appalachian Mountains of North Carolina, or the Cévennes. The chief abnormal features of Snowdon are the following :— Alongside the graded summit and slopes of a ‘ moel’ stand the head-cliffs of a rock-walled cwm, in the floor of which talus is now accumulating. The cwm-floors are generally stepped, sometimes more than once, and the streams cascade down into the valleys. The cross-profile of the valleys is often a fine catenary curve, down the sides of which streams fall from hanging valleys. The slepe of the main valleys occasionally decreases even to the point of reversal, as where lakes occur; and in the immediate neighbourhood of smoothly-graded, waste-covered slopes knobby or craggy ledges and bars of rock often appear. After pointing out that such features are generally associated with glaciation, the author pro- ceeds to discuss two out of four possible hypotheses put forward: ‘that glaciers are essentially protective agencies,’ or that they ‘ are active destructive agencies.” The consequences deduced from the hypotheses are confronted with the actual facts, and it is found that these, and especially those relating to rock-steps, cannot be explained on the protection-theory, while the theory of a destructive agency seems to explain most of the facts. These facts are dealt with under the following heads :— Valley- head curves; valley-floors, lakes ; valley-floors, rock-steps ; valley- sides; hanging lateral valleys; and glacial overflows. With regard to the first, it is shown that there is no systematic relationship between the height of the cwm-cliffs and the distance of the front rock-step ; the serration of ‘ cribs’ or arétes cannot be explained by pre-Glacial or post-Glacial weathering according to the protection- theory.. It is suggested that it might be possible on the erosion- theory to work out and classify cwms according to their age and growth, and as a contribution to this enquiry the cwms of Mynydd Mawr are dealt with. The valley-lakes are likely to be only a small part of the glacial erosion. No consistent explanation of the valley-steps can be found under the theory of ice-protection, whereas they are explicable on the assumption of glacial erosion. They may have originated in resistant beds, and have then retreated up the valleys. The catenary curve of the cross-section of such valleys as those containing Llyn Gwynant and Llyn Cwellin might be expected to result from long-continued ice-erosion ; and the occurrence of great cliffs on the sides of these valleys is not incon- sistent with such an origin. Several good examples of hanging vaileys occur, and they seem to show that the deepening of the main valleys by glacial erosion may be from 200 to 400 feet, and in some cases aS much as 500 or 600 feet. The lateral erosion may easily amount to 1000 or 1500 feet. The most striking case of a glacial overflow is that at the head of the Nantlle valley, which appears to have carried much of the West Snowdon ice. The head of the pass would seem to have been farther westward and higher in pre-Glacial times. sume THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. | [SIXTH SERIES.] DECEMBER 1909. LXXXIX. Positive Electricity. By Sir J. J. THomson, Professor of Experimental Physics, Cambridge *. . eo most important questions to be settled as to the nature of positive electricity are :—(1) Does a definite unit of positive electricity exist? (2) If so, what is the size of the unit ? Question (1) may perhaps be made clearer by considering a definite case. Suppose we could get a pure gas, say oxygen or nitrogen, would it be possible to get in such a gas, positively charged particles smaller than the residue left, when a cor- puscle is removed from an atom of oxygen or nitrogen ? Again, we know that we can get negative particles of the same kind whether we extract them from oxygen, hydrogen, or nitrogen. Is there anything analogous to this in the case of positive electricity? Can we in short get positively electrified particles of the same kind from different gases ? Our knowledge of charged positive particles (other than a particles) has been derived from two sources: (1) the study of positive particles in systems of positive rays found in vacuum-tubes ; (2) the study of the velocity of the positive ions in ionized gas. To begin with the first method. The two sets of positive rays which have been most closely studied are, firstly, the Canalstrahlen which are found passing through a perforated * A paper introducing a discussion on this subject read on August 30, 1909, at the Winnipeg meeting of the British Association. Communicated by the Author. Phil. Mag. 8. 6. Vol. 18. No. 108. Dec. 1909. 3K 822 Sir J. J. Thciasan on cathode, and, secondly, the rays shot out from the cathode in the same direction as the cathode rays but which are deflected much less than those rays by magnetic forces, and which instead of carrying a negative charge are some of them positively charged while others are electrically neutral. To take the Canalstrahlen first. These can be studied by an apparatus like that represented by fig. 1. It consists of a Pager i. . VY] Y Y AVION vacuum-tube: with a perforated cathode through which a beam of Canalstrahlen is streaming. The rays strike against. a willemite screen at the end of the discharge-tube and produce phosphorescence when they reach the screen. In their path to the screen the rays pass between the poles of an electromagnet which deflects them in a vertical direction and simultaneously between two parallel metal plates con- nected with the terminals of a large number of storage-cells ; the electrostatic field deflects the spot horizontally. The magnetic deflexion is equal to Be/mv, where e, m, v are respectively the charge, mass, and velocity of the particles, and B a constant depending upon the strength of the magnetic field and the distance of the screen from the cathode. The electrostatic deflexion is equal to Ae/mv’, where A depends. on the strength of the electric field and the size of the apparatus. When both these fields are in activity, the appearance pre- sented by the willemite screen when the rays strike against it is, when the pressure is not very low, somewhat like fig. 2.. The small spot which marks the place of incidence of the pencil when the magnetic and electrostatic fields are not on, is drawn out into a ribbon the edges of which are often very approximately straight. In some cases the original position ot the spot, even when the magnet is on, is more brightly Positive Electricity. 823 illuminated than any other part of the ribbon ; in others the illumination is fairly uniform throughout. Fig. 2. Fig. 3. On the other side of the undeflected position there is a luminous tail, formed, as the direction of the deflexions shows, of negatively electrified particles. The brightness of this in comparison with the positive part changes very con- siderably : in some cases it is too faint to be easily perceived, in others it is sometimes almost as bright as the positive part of the ribbon ; in general, however, it is much feebler and there is distinct discontinuity in the brightness of. the light in the tail and in the other portions. | If y is the vertical, « the horizontal deflexion of the rays, ve y/x elm «x y?/ax. Thus when the ribbon is straight, the values of y/xv and there- fore the velocity of the particles are approximately constant, while y?/z ranges from zero up to a maximum value at the end of the strip. This maximum value, in all the cases I have tried, gives a value of e/m equal to 10*. When the pressure of the gas is reduced, the luminosity of the band concentrates into a spot or spots and presents the appearance shown in fig. 3. There is a bright spot at the end and a faint band which at low pressures becomes almost invisible connecting this spot with the position of the undeflected spot; at this place there is not infrequently a considerable amount of luminosity even when the magnet is on. This luminosity is often indistinct and sometimes vanishes. When it is present it indicates the presence of a considerable number of rays which are not deflected in passing through the magnetic and electric fields, and which are therefore not charged when they pass through these fields. Neglecting for a moment the faint luminosity connecting the spots, the bundle of rays in this case consists of a mixture of positively electrified particles and electrically neutral systems, uncharged rays we may call them ; these uncharged rays, however, in their course through the gas my gradually get broken up amg $24 Sir J. J. Thomson on and become positively charged rays. The breaking up of these uncharged rays may be shown and the rate at which they break up measured by the following method. A tube (fig. 4) in which the distance between the perforated cathode Fig, 4, and the willemite screen was considerably greater than in the tube fig. 1, was made, and two electromagnets arranged, one close to the cathode, and the other much nearer the screen. The magnets were arranged so that the magnetic force in the first was horizontal, and the deflexion of the spot due to the field vertical, while in the second magnet the magnetic force was vertical and the deflexion horizontal. ‘The deflexions due to each magnet were thus separated and could be measured independently. The effects observed when the magnets were applied in succession and then simultaneously are interesting; and a typical case is represented in figs.5 & 6. Fig. 5 represents the appearance of the screen when only the electromagnet next the cathode is in action; fig. 6 the appearance when both magnets are on. In fig. 6 the undeflected spot is much fainter than in fig. 5; part of itis deflected to another spot a’, while the spot b is deflected to 0’. 6! is vertically under a’, so that the deflexion produced by the second electromagnet on the rays which were uncharged when they went through the first electro- magnet is the same as that produced by the second magnet on the rays which were charged when they went through the first one. It is evident that the latter have for the most part kept their charge from the cathode right through the second magnet; the formation of the spot a’ shows that some of the neutral rays have in their journey from the first magnet to the second split up into a positive and negative part (the negative part being deflected far out of the field and not Positive Electricity. 825 reaching the screen), while the positive has been affected by the magnet to just the same extent as those which were positively electrified in the field of the first magnet; this shows that the rays which break up in the journey move with the same velocity and possess the same charge as those which break up at an earlier stage. Fig. 5. Fig. 6. Sa ANMNER Ron ia Said A ey tet rb b sa eter Sarcyanas Cue O ee qin, ete PON EMM, ee bY The relative brightness of the spots a and b varies a good deal with the pressure. I have found that when the pressure is reduced the spot a gets fainter than }, though at higher pressures it might have been brighter. This is what we should expect, since at the lower pressure the neutral doublets make fewer collisions in their course between the two magnets, and so fewer of these are broken up into ions. Again, as the pressure increases, the spots become less well- defined, there is more luminosity between the original and the displaced positions of the spots; for example, there may be considerable luminosity between the position of b when the vertical magnetic field is off and 0’, the luminosity stretching right up to 0’. This shows that at this pressure some of the particles which were positively charged when they were passing through the first electromagnet have got neutralized before reaching the second and so are not deflected by it. The breaking up and re-formation of the doublets become more 826. Sir J. J. Thomson on frequent as the pressure increases, and more and more particles are positively charged for only part of the time they are in the magnetic field. Since: they are only deflected when charged, the deflexion will vary with the time they have been uncharged while passing through the magnetic field ; and if this time varies continuously the spot will be drawn out by the magnet into a continuous band such as is represented in fig. 2, and which is always observed when the pressure is not too low. An important point as to the determination of e/m occurs in connexion with this effect: the values of e/m got from. the magnetic and electric deflexions are the average values of e/m whilst the system is in the magnetic and electric fields. Since some of the systems are at times electrically neutral, the average value of e/m cannot be greater than the true value, and it may be considerably less. It may be asked, have we any security when we deduce the value of e/m for the positive ions from the measurement of the tip of a drawn out band such as that in fig. 2, that the particle under consideration has been charged the whole time it was passing tnrough the field ; if this is not the case, the true value of e/m may be much greater than the value calculated. This consideration does not apply to the case when the bright spot is deflected as a spot and not as a band; buta great many determinations of e¢/m have been made when the pressure was too high to give spots, and the ends of the bands have been used for this purpose. I have made some experiments to see if in my measure- ments any errors have been made from this cause. The principle of these experiments was as follows. If the particle at the tip of the beam has not been charged the whole time, 2. e. if it has united with a corpuscle before leaving the magnetic field, then the value of e/m determined by this method will increase as the length of the path travelled in the magnetic field is reduced until it is comparable with the length of the path described by the particle whilst it is positively charged ; and when the magnetic field is so short that the particle can retain its charge for the whole of the distance between the poles of the magnet, the value of e/m given by this method would rise to a maximum. Now take two magnetic fields, one short but strong, the other long but weak, and adjust the strengths of the fields so that if the positive particle retained its charge the whole of the time it was in either field, the deflexion of the particle would be the same in both cases. If the particles whose a 5: Positive Electricity. 827 deflexion we are measuring become neuiralized in passing through the longer field, the deflexion produced by the short field will be greater than that by the long, provided the length of path of the particle when uncharged is comparable with the length of the shorter field. For this experiment, chisel-shaped pole-pieces whose ends were rectangular were used, the longer side of the rectangle was 4°5 cm., the shorter side *7 cm. ‘The distance between the pole-pieces was 6mm. ‘The poles were arranged (1) so that the longer side of the rectangle was parallel to the path of the positive particle, so that this was exposed to a magnetic field for about 5 cms. of path, and (2) with the shorter side parallel to the path so that the particle was exposed to the magnetic field for less than a centimetre of path. The currents through the electromagnets were adjusted so that the deflexion would be the same for a particle which retained its charge the whole of the time it remained in either field. It was found under these circumstances that when the pressure was too high to give well-defined spots the deviations of the tips of the luminous bands into which the phosphores- cence was drawn out were the same in both cases ; showing that the maximum value of e/m got by this method is the ratio of the charge on the particle to its mass, and not the average extending over a time during part of which it is uncharged. Though the maximum deflexion is the same with the two fields, there are minor differences in the appearance of the phosphorescent patch ; with the short field the portion of the band which is not deflected at all is noticeably brighter than in the longer field. This is what we should expect if the rays contain large quantities of neutral doublets which break up into positively and negatively electrified parts as they pass through the tube and collide against the molecules of the residual gas. The behaviour of the portion of the luminosity due to negatively charged portions of the Canalstrahien is interest- ing and throws light on their origin ; the determination of e/m for these shows that they are not corpuscles but that their mass is much the same as that of the positive particles, they are in fact neutral doublets which have acquired a negative charge. ‘he brightness of the negative part of the phosphorescence depends very much on the intensity of the magnetic field; as the intensity of the field increases these negative rays at a certain stage increase so quickly in brightness as to give the impression that they suddenly spring into existence.. Again, 828 Sir J. J. Thomson on with a constant magnetic field the negative rays are much brighter when the magnetic force is at some distance away from the cathode and towards the screen than when it is applied nearer to the cathode. The action of the magnetic field in increasing the number of these negatively electrified particles is easily understood, for in a strong field the negative corpuscles can only move along the lines of force and thus get concentrated into a cloud ; an unelectrified doublet passing through this would be very liable to get electrified. There is in general an abrupt falling off in the intensity of the luminosity under electric and magnetic forces as we pass from the position of the spot corresponding to uncharged rays into the position corresponding to negatively charged rays, — This shows that the uncharged rays are not rays which start by being positively electrified, then take up a corpuscle and get neutralized, then another corpuscle and become negatively electrified, then lose a corpuscle and so on, repeating this process so that on the average the charge is as often positive as negative ; for if this were the case, the number of these would be very nearly the same as that of those which had slightly overshot the mark and become on the average just a little more negative than positive, and these would be found amongst the negative rays, and the transition from the one to the other would be gradual. | Hverything points, | think, to the conclusion that even at the start from the cathode the Canalstrahlen include a large number of neutral doublets, if indeed they do not wholly consist of them. | These neutral doublets are found not only in Canalstrahlen, the rays at the back of the cathode which have passed through it, they are also found in front of the cathode travelling away from it, mixed up with rays which carry a positive charge of electricity and which are thus travelling against the electric field. The values of e/m for these positively charged rays in front of the cathode are, as I have shown (see Phil. Mag. Oct. 1908), the same as for the Canalstrahlen ; it is convenient to call the positively charged rays which travel away from the cathode in the same direction as the cathode rays, “‘ Retro- grade rays.” The presence of neutral doublets is even more marked among the retrograde rays than among the Canal- strahlen. | These neutral doublets are very interesting, as they form an intermediate stage between the ion and the neutral molecule. They are found not only in these high tension Positive Electricity. 829 discharges, but also when the electric field is much less intense than when the discharge is produced by the induction- coil. This can be shown with an apparatus like that shown in fig. 7, where W isa hot Wehnelt cathode, connected up with a battery of small storage-cells, causing it to emit slow cathode rays which ionize the gas in the tube C, a and 0 are two carefully insulated Faraday cylinders; there is a very small hole, in some cases Jess than } mm. in diameter, in the plate d which separates the Faraday cylinders from the ionized gas ; through this hole the ions produced in C can diffuse and charge up the Faraday cylinders. We can, however, by suitable means prevent the ions passing through the hole: the negative ones which are mainly corpuscles, and easily deflected by a magnet, are prevented by applying a strong magnetic field which bends them back before they reach the cylinder ; the positive ions, which are not easily deflected by a magnet, can be stopped by a strong electric field between the wire gauze f and the top of the cylinder d, the gauze being negative to the cylinder. When the ions are stopped by these means we find that though no perceptible electric charge reaches either cylinder, the gas between them is a conductor of electricity, and if either cylinder is charged up the other wili slowly acquire the same potential, whether that potential be positive or negative. That the conductivity of the gas is not due to ultra-violet light coming from the luminous discharge in the upper tube is shown by the fact that itis destroyed by putting a thin quartz plate over the hole in d ; and since it is also destroyed when a piece of the thinnest aluminium foil obtainable is placed $30 Sir J. J. Thomson on over the hole, it cannot be due to any ordinary form of Rontgen radiation. The conductivity can easily be explained if we suppose that there are neutral doublets in the ionized gas in the discharge- tube, and that since these are not deflected by either electric or magnetic forces they can pass through the hole though the ions are stopped. Then by collision with the molecules of the gas in the Faraday cylinder, they break up into ions is and thus make the gas a conductor. The velocity of the neutral doublets in the discharge pro- duced by an induction-coil is approximately the same as that of the positively charged particles which accompany them. This follows from the fact that the deflexion of the spot b (fig. 6) is the same as that of spot a, though the former spot is produced by positively charged particles which have been detached from the neutral doublets after passing the first magnetic field, and the second by positively electrified particles which were free before the first field was reached. The doublets seem to travel in directions approximately normal to the surface of the cathode. Hxperiments described in my paper on ‘ Positive Rays” (Phil. Mag. Oct. 1908) show that the retrograde rays travel in this direction, and it is well known that Canalstrahlen are not obtained unless the aperture in the cathode is approximately normal to the face of the cathode facing the anode. ‘The direction of the doublet is in short approximately that of the lines of force close to the cathode; they may move in either direction along the lines. ~The doublets seem to start from beyond the dark space next the cathode, for if a vertical obstacle such as a thin glass rod or a metal wire be placed inside the discharge-tube in such a position that its projection on the plane of the cathode passes across the hole in the cathode through which the Canalstrahlen pass, then when the pressure is so low that the dark space extends beyond the obstacle, the dark shadow of the obstacle is apparent on the willemite screen, stretching across the phosphorescent patch even when this is spread out by the electric and magnetic fields. If the pressure is increased so that the obstacle is outside the dark space and in the negative glow, no shadow can be perceived. In this form of the experiment the shadows cast by an obstacle are much more easily perceived and much more definite than in the original form in which it was tried by Schuster and Wehnelt. ‘i have got quite sharp shadows with a fine wire placed several centimetr es away from the cathode. Some very interesting questions arise in connexion with. Positive Electricity. 831 these doublets. Is the doublet the thing set free from the atom when it is ionized? and are the ions produced by the splitting up of the doublets, or are the ions first produced and the doublet produced by a combination of the positive and negative ions ? There are arguments to be urged in favour of either view. The fact that the direction of pr rojection of these doublets is parallel to the direction of the lines of forve at the cathode, points to the projection being due to electrical forces. We can easily understand how these might set the doublets in rapid motion. Thus doublets which accompany the retrograde rays may have had a corpuscle attached to them when they were in the neighbourhood of the cathode, and before losing this corpuscle have been projected away from the cathode in the same direction as the cathode rays; thus these doublets acquire their velocity when they are doublets. The doublets which accompany the Canalstrahlen and which move in the opposite direction to the preceding, may be supposed to have acquired their velocity when they were in a dissociated state ; t. @., We may suppose that a positive ion in front of the cathode acquires in its fall to the cathode a high velocity, and then after passing through the cathode unites with a corpuscle and becomes a doublet retaining the velocity acquired by its positive constituent. We have already had examples of the formation of doublets in the Canalstrahlen group. ‘Thus, for example, in the case represented in fig. 6, we saw that when the pressure was not very low, some of the positive ions which had retained their charge whilst passing through the first magnetic field, and which form the spot 6, had lost their charge, 7. e. had become doublets before entering the second field and were not deflected by it, so that instead of the spot being entirely removed when the second magnetic field was put on, some of it was left behind. Though we can har aly doubt that there must be positively charged particles passing through the hole in the cathode which owe their velocity to this cause, yet, as the experi- ments I shall now proceed to describe show, Canalstrahlen such as those used when their electric and magnetic deflexions are measured in the way I have described and which travel perhaps 15 cms. before they reach the screen, seem to owe their velocity to a different cause, for I have found that the velocity of these is but slightly affected by the potential- difference between the electrodes of the discharge-tube or the pressure of the gas. 832 Sir J. J. Thomson on I have made many determinations of the velocity of Canalstrahlen at different pressures using tubes of very different shapes, and the results were so nearly constant in spite of the wide variations in the conditions, that I was led to suspect that the velocity of the positive rays was not influenced to any great extent by the strength of the electric field in the tube. To test this matter in as direct a way as possible I used the following method. Fig. 8. This discharge was produced by a large induction-coil ; the discharge-tube, fig. 8, had a perforated cathode faced with calcium, so that the discharge would pass at very low pressures without sparking through the glass walls of the tube and breaking the apparatus. The anode A was an aluminium cylinder perforated with a very small hole. When the discharge was passing through the tube a pencil of cathode rays passed through the hole and produced a small well-defined spot on the fluorescent willemite screen 8, placed at the anode end of the tube. During their path up to the screen after leaving the anode they could be exposed to a known magnetic field produced by an electromagnet, and the distance through which the spot moved when the magnet was put on enabled us to calculate the velocity of the cathode rays. The Canalstrahlen after passing through the aperture in the cathode pass along a metal tube of very fine bore (one of the perforated needles used for hypodermic injections) and emerge between two parallel vertical metallic plates. (4 mm. apart in one set of experiments, 3 mm. in another) which can be connected with the terminals of a kattery of small storage-cells ; the rays are thus exposed to a strong electric field and are deflected horizontally. | Two poles (about the same length as these plates) of a powerful electromagnet of the Du Bois pattern, are placed on either side of the tube, and the horizontal magnetic field due to this magnet deflects the rays in a vertical direction. The deflexion of the rays is measured by the deflexion of the Positive Electricity. 833 phosphorescent patch they produce on the willemite screen T; from the magnetic and electric deflexions the values of e/m and v can be deduced in the usual way. Observations were made simultaneously of the deflexions of the spots on the screens S and T when the pressure was varied from the largest value at which both rays produced phosphorescence on the screen toa very high vacuum. The deflexion of the cathode rays under a constant magnetic field was 8 mm. at the highest pressure and 2 mm. at the lowest; thus the velocity of the cathode rays was 4 times greater at the lower pressure than at the higher, but in spite of this large change in the cathode rays, there was no appreciable change in the deflexion of the Canalstrahlen over the whole range of pressure. The results of two sets of experiments with different tubes are shown in the following table. By equivalent spark-gap is meant the distance between two large electrodes placed in parallel with the tube and adjusted so that the sparks passed about equally readily through the tube or across the air-gap. Defiexion of Canalstrahlen. / Defiexion of | Equivalent ) Cathode Rays.| Spark-Gap. Magnetic. | Electrostatic. | mm. | mm, mm, | cm. 6 6 6 / zs) | 6 6 4°5 | 55 | 65 25 | | 65 6 2 3°8 | mn. | mm. mm. | 6 | 4 65 | 6 4:5 5 / 6 4 3 | | 55 35 2 The numbers in one horizontal line were observed simulta- neously, one observer reading the deflexion of the cathode rays, another those of the Canalstrahlen. At the very highest pressures at which Canalstrahlen appear their deflexions seem greater than those at lower pressures, though the difference is on quite another scale to that of the cathode 834 Sir J. J. Thomson iy rays. The phosphorescence at these pressures is very diffuse and faint and the rays are evidently much scattered in their journey to the screen. I think the increased deflexion is due more to this and their loss of velocity during the journey, than to any considerable falling off in their initial velocity of projection. | Though the equivalent spark-length has changed in the ratio of nearly 8:1 and the deflexion of the cathode rays as 3:1, there has been hardly any change in the deflexions of the Canalstrahlen. This makes it very improbable that they owe any considerable part of their velocity to the action of the electric field upon them whilst they approach the cathode. We must remember that the bundle of Canalstrahlen when it passes through the hole is a mixture of rays of different kinds. With such an apparatus as that just described the only rays investigated are those which can traverse the very considerable distance between the cathode and the screen and yet retain their power of producing phosphorescence. Coming through the hole there may be, in fact in certain cases we know there are, positive particles which have been set in motion by the electric field, with velocities depending on those of the molecules of the gas in the tube. These, in the experiment Iam describing, have disappeared before travelling as far as the screen, their “range,” to use an expression familiar to those who study the @ particles, is less than the distance between the screen and cathode. , The existence of this range in the case of the a particles may be explained by supposing that when the velocity of the particle falls below a certain value, the particle is no longer able to escape from the negative corpuscles which it has to: pass through on its travels. The same argument will apply to Canalstrahlen ; if they move with less than a certain speed they may not be able to escape from corpuscies near which they pass. Since the « particle has twice the charge of a particle in the Canalstrahlen, the velocity, other circumstances being the same, required for the escape of an a particle will be greater than for one in the Canalstrahlen. The velocity of the latter, in round numbers 2x 10° cm. per sec., is about that required for a particle of unit charge and 10-8 em. in radius to escape from a corpuscle. In the preceding experiments the velocity of the cathode rays at the lowest pressure was 6x10° cm./sec., taking e/m=1'7x10". The velocity of the Canalstrahlen particle is thus considerably less than that of a cathode ray particle ; the energy of a cathode particle is, however, less than that of a particle in the Canalstrahlen. | Positive Electricity. 835 Experiments were also made with the retrograde rays, and it was found that the velocity of these was also practically independent of the strength of the field and very nearly the same as that of the Canalstrahlen. The small range of velocities in the Canalstrahlen is explicable if we suppose that the rays we are measuring exist originally as neutral doublets which are formed by the combination of a positive unit and a negative corpuscle ; these doublets moving towards or away from the cathode, the direction of motion being approximately at right angles. to the cathode. These doublets could not have more than a certain amount of energy ; for if the relative velocity of the carriers of the positive and negative charges when uncombined exceeded a certain value, the charges would fly past each other without entering into combination and they would remain dissociated : it is only when the kinetic energy of the two falls below a certain value that combination will take place ; thus there will be a superior limit to the energy of the doublets. The doublets which we investigate when we measure the velocity of the cathode rays are those which dissociate again into positive and negative charges. Now, as the kinetic energy of the doublet decreases it gets more and more stable and less likely to dissociate, and when it ceases to dissociate we cannot measure the velocity. Thus doublets are not formed possessing energy greater than a certain value ; on the other hand, they are not split up if the energy is less than a certain value. ‘Thus the doublets whose velocity we can determine will have velocities between definite limits which are independent of the strength of the electric tield. The case is analogous to that of a gas which dissociates as the temperature is raised: there is a certain range of temperature in which there is appreciable, but not complete dissociation ; beyond the upper limit of this range of temperature the undissociated molecules are too few to be detected ; beneath the lower limit the products of dissociation are not numerous enough to be appreciable. The properties both of the Canalstrahlen and the retrograde rays could also be explained on the view that neutral doublets moving with high velocities are given out by the molecules of the gas in the discharge-tube, that these break up into the Canalstrahlen and the retrograde rays; these doublets are supposed to be of the same character from whatever kind of gas they may originate. We should, however, expect that these doublets shot out from the molecules by explosions would be found moving in other directions than just along the lines of force in the tube, which seems to 836 Sir J. J. Thomson on be the only direction in which an appreciable number of Canalstrahlen or retrograde rays move. If doublets form an intermediate stage between the ions and the atoms, the doublets being the systems formed from the molecules of the gas by the ionizing agent, say Réntgen rays, then the number of doublets liberated may be enor- mously greater than the number of ions set free, so that this number may give no indication of the percentage of molecules affected by the rays. Thus, suppose g doublets are liberated per second per cubic centimetre in a gas at a pressure p, let D be the number of doublets per cubic centimetre, let BpD of these reunite with the molecules per sec., and ypD split up into ions, let m be the number of positive or negative ions per cc., a the coefficient of recombination ; then we have dD Pe ge q—BDp—yDp, din: ty DR on =yDp—am’, When things are in a steady state eR n= —_—- —— 190 A a By The saturation current is proportional to the value of dm/dt when m is zero; hence, when things have settled into a steady state, the saturation current is proportional to Y ata? Thus, if y is very small compared with @, the number of ions taken from the gas per second may be very small compared with the number of molecules affected by the rays. This point isan important one in connexion with the structure of the Rontgen rays, the small percentage of the molecules decomposed has always been difficult to understand. If we suppose that the ions are the first product of the Roéntgen rays on the molecules, this difficulty disappears on the assumption that there is a stage intermediate between the molecules and the ions. The values of e/m for the Canalstrahlen and for the retro- grade rays are the same when the pressure is low whatever be the gas in the tube. In a former paper I described experiments which showed that if a vessel was exhausted until the pressure was so low that the discharge would not pass, and small quantities of hydrogen, helium, air, oxygen, a Positive Electricity. 837 carbonic acid, or argon, were introduced so as to raise the pressure sufficiently to produce the discharge, the values of e/m and the velocity of the particles were the same for all gases. Since then I have repeated the experiments and have tried in addition to the gases I have mentioned, sulphur dioxide, methyl iodide, carbon tetrachloride, and also the vapour of a radioactive substance UrCl, With all these gases the values of e/m for the Canalstrahlen were the same and equal to 10*. This seems strong evidence that there is a definite unit of positive electricity as well as of negative, the carrier of the positive unit being much larger than the negative. This view seems to me to be very much strength- ened by some results recently obtained by Mr. Wellisch at the Cavendish Laboratory. The experiments were on the mobility of the positive and negative ions in mixtures of different gases. If we take the view that the positive ion is but the residue left after a corpuscle has been abstracted from the molecule, then it would seem probable that in the ease of positive ions there would, in a mixture of two gases A and B, be two different types of positive ions moving with different velocities. In one type the positive ion would be the molecules of A minus a corpuscle, or an aggregate formed round it ; in the other the nucleus would be the molecule B. Mr. Wellisch found, however, as M. Blanc had previously found for a mixture of air and carbonic acid, that in the mixture all the positive ions moved with the same velocity. We might, however, without assuming an independent unit of positive electricity, explain this result by supposing that the ions were aggregates continually breaking up and reforming, and that the velocity measured is the velocity of the average aggregate. This explanation is, however, refuted by some of the cases examined by Mr. Wellisch. The ionization under Réntgen rays of methyl iodide, mercury methyl, or carbon tetrachloride, is so vastly greater than that of hydrogen, that in mixtures of these gases with hydrogen, even when there is only one or two per cent. of these gases in the mixture, practically the whole of. the ionization is due to the methyl iodide. Wellisch found that in these mixtures the velocity of the positive ion is nearly the same as in pure hydrogen, although practically all the ions came from the heavy gases. If the positive ion was merely the residue left when the corpuscle was taken out, the positive ion would be at least as large as a molecule of methyl iodide. We can show, however, that. the velocity with which the charged molecule would move through the Phil. Mag. 8. 6. Vol. 18. No. 108. Dec. 1909. 3 L = he ie? 838 Sir J. J. Thomson on mixture, would be less than the observed velocity of the positive ion, which was about that of a charged hydrogen atom. It is clear, then, that the positive ion is not the molecule of methyliodide. Thus the ionization of the methyl iodide has produced positive ions which are not molecules of — methyl] iodide. It might perhaps be urged that the molecules of methyl iodide which were positively charged to begin with, have, by the electric force they exert, pulled a corpuscle out of the neighbouring hydrogen molecule, and that this corpuscle neutralizes the methy! iodide molecule and leaves the hydrogen molecule, from which it has escaped, with the positive charge. ‘There are several objections to this view of which I will only mention one. The result of this process is, by the electrical forces between the molecules of methyl iodide and hydrogen, to transfer the charge from the larger system (the methyl iodide molecule) to the smaller (the hydrogen molecule). Since the potential energy of a given charge is greater when the charge is on a small system than when it is on a large one, the change under consideration would involve an increase in the potential energy, and would therefore not be brought about by the action of the electrical forces. The results obtained by Wellisch are exactly what we should expect if there were a definite positive unit of electricity which could, like the corpuscle, be detached from the molecule of the gas. I have elsewhere suggested that the process of ionization consists in the detachment of a neutral doublet from the molecule, the doublet consisting of a positive unit and a corpuscle, and that this breaks up into its components, which subsequently attach themselves to the molecules by which they are surrounded. Slowly moving Positive Rays and the Size of the Carriers. The slowly moving rays were studied in the following way :—The gas at a very low pressure was ionized by the cathode rays emitted from a Wehnelt cathode W (fig. 7, p. 829). By means of a feeble eleciric field between the plate D, called the collector, and a piece of wire gauze /, the positive ions were then driven through this gauze, which was distant about -5 mm. from the top of the plate d. Between this gauze and the top of the plate was the potential relied upon to give the positive ions their velocity. The difference of potential between the collector plate and the gauze was 10 volts, that between the gauze and d varied from 40 to 200 volts. There was a very small hole in the Positive Electricity. 839 plate d, and the positive ions, after passing through the hole, travelled through the strong magnetic field produced by a Du Bois magnet. The magnetic deflexion of the rays was measured by the ratio between the charges received by the disk 6 and the cylinder a: these were connected with Wilson tilted electroscopes, and the ratio of the charges measured in the way described in my paper on the Positive Rays (Phil Mag. Oct. 1908). If V is the tall of potential between the gauze and the top of the plate, eV = tmv’, while the magnetic deflexion gave the value of mv/e. Thus from these results m/e and v can be determined. We find that for these slowly moving positive rays the velocity depends upon the strength of the electric field. The point that I wish to dwell upon here is, that in some eases the method seemed to give values of e/m for the positive ions much greater than 10*. I think these high values are not genuine, but I will first describe the effects which seem to indicate them. We may get, perhaps, the clearest idea of these by describing what happens when the arrangement is altered so as to send negative ions and not positive through the same hole in the top plate. In this case the corpuscles and negative ions pass through the plate. If we compare the charges on the disk and the cylinder when there is no magnetic field on, we find that in general there is more negative charge on the cylinder than on the disk, and the effect of a small magnetic field, say 200 units, is greatly to diminish the proportion of the negative charge on the cylinder to that on the disk: when the magnetic force is greatly increased this proportion again increases, due to the deflexion by the magnet of the heavy negative ions from the disk to the cylinder. It will be noticed that the effect of putting on the small magnetic field is to diminish the scattering. This is what we should expect if these were negative corpuscles getting through the hole when there was no magnetic field. If these rays were rather diffuse they would reach the sides of the cylinder. Now when a magnetic field of say 100 units is put on, it twists up the path of the particles into very small circles, so that they are prevented by it from even getting as far as either of the Faraday cylinders. The magnetic field is not raga to affect appreciably 3L2 ; 840 Sir J. J. Thomson on the heavy negative ions which move on to the disk, and are not deflected until the magnetic force is strong enough to deflect ions whose mass is comparable with that of atoms. | I have occasionally observed a similar effect when the positive instead of the negative ions were sent through the cylinder. This effect has only been observed when the potential- difference between the gauze and the top of the plate exceeded about 120 volts, and then only occasionally ; still, on several occasions it was found that the amount of positive electricity going to the cylinder when there there was no magnetic field on, was a larger multiple of that going to the disk than when the magnetic field was increased to about 100 units : this effect is similar to that observed with negative electricity and which could be explained, as we saw, by supposing that there were particles of exceedingly small mass along with the others. Are we to conclude that there are similar small positive particles, particles whose mass is very small compared with that of the atom? I do not think that the effect I am describing is due to this. In the first place, while the effect is invariably observed with negative electricity, it is quite exceptional with positive. I had worked with the apparatus described for months, making observations almost daily, before I found an example of it. I think that it arises from the presence among the stream of positive ions which pass through the hole in the plate, of some ions which are moving with much smaller velocity than that which they would acquire by a fall through a potential-difference equal to that between the gauze and the plate. : We have seen that these positive ions are continually getting neutralized in their journey through the gas, and that some of them are hardly deflected at all, that is, do not acquire an appreciable velocity whilst they are passing through the electric field. | Thus we might expect that some of the ions would be neutralized for part of their journey between the gauze and the plate, and would thus only acquire a small fraction of the velocity due to a fall through the whole potential-difference between the plates. . ‘These slowly moving ions would be easily deflected, and a comparatively weak magnetic field will be sufficient to prevent them entering the Faraday cylinders. If the effect T am describing is due to the slowly moving ions, it ought Positive Electricity. 841 to disappear if the Faraday cylinders are insulated and maintained at a potential a few volts above the plate A. The ions, which have acquired an energy due to the fall through the whole potential-difference of say 160 volts, will be but little affected by having to go against the difference of say 20 volts, but those ions which have acquired only a fraction of this velocity may be wholly stopped by it. On raising the potential of the cylinders to about 20 volts, I found that the effect in nearly every case disappears. There were, however, one or two cases in which it still remained ; if the slow moving particles remain neutralized for part of their journey between the plate and the cylinder, they could not be much affected by the field, and the positive particles might still force their way in. As the question of the existence of small positive ions is a very vital one, I have made some other investigations with other cases of easily deflected positive ions with the object of seeing if the deflexions were in these cases also due to the smallness of the velocity rather than to that of the mass. The appearance of the discharge in the neighbourhood of the hole in a cathode offers several features of interest ; on some of these, light is thrown by the consideration of the distribution of the lines of force near the hole before the discharge starts. Let A and B be two parallel metallic plates, B having a small hole in it. Let us suppose that A is at a higher potential than B, then the negative electricity is not uniformly distributed over B but is very much concentrated near the edge of the hole, the density being infinite at the boundary of the hole if the edge is sharp. The electric force is proportional to the density, so that up to a distance from the hole comparable with the radius of the hole the electric intensity is far in excess of its average value. Again, this accumulation of electricity is not confined to the part of the plate facing A. If the plate B is thin in comparison with the radius of the hole there will, close to the hole, be practically as much electricity on the face of B turned away from A as on the side next to A: in fact the field of force in the neighbourhood of the hole is much as if a fine ring of the same radius as the hole were highly electrified and placed by itself in the field. The appearance of the discharge through the hole when the pressure is not very low illustrates this very well. One of the stages of the discharge is shown in fig. 9, and it will be seen that this is 842 Sir J. J. Thomson on symmetrical on the two sides of the hole. If a strong magnetic field is applied to the neighbourhood of the hole, - the lines of force being parallel to the surface of the cathode, some very interesting effects are observed. Those in the Fig. 9. Fig. 10. Cen RS RNa most deve oped form are represented in fig. 10; unless the pressure is within certain limits one or other of these parts may be absent. a and a’ are two streamers coming from the hole and following the directions of the lines of magnetic force. In this respect they resemble the magneto-cathodic rays of Villard and Righi, but whatever may be the nature of the magneto-cathodic rays in front of the cathode, there can be no doubt, I think, that the rays we are describing consist of slowly moving corpuscles describing spirals of very small radius around the lines of force: for, as the magnetic force is very gradually reduced, we reach the stage when the widening of the radii of these spirals becomes so large that the spiral nature of their path becomes quite obvious. That they are carriers of negative electricity can easily be shown by sending them into a carefully insulated Faraday cylinder surrounded by another cylinder with a hole in it. The outer cylinder was put to earth, the inner one was connected with a sensitive galvanometer (the one I used gave a deflexion of 1 mm. at one metre for 3x10~-?° ampere). When one of the streams passed through the hole in the outer cylinder there was a deflexion of 70 or 80 scale- divisions in the direction corresponding to a flow of negative electricity into the Faraday cylinder. The other two luminous portions ¢ and d are bent at right angles to the direction of the magnetic forces, just Positive Electricity. 843 as they would be if c were a stream of negative and d of easily deflected positive particles. That there were streams of particles of this kind was proved by again directing the streamers into Faraday cylinders connected with a galvano- meter. This showed that when the stream c entered the cylinder it carried with it a negative charge, while d carried a positive. cis in most cases much more developed than d. As the pressure is reduced and the dark cathode space gets well developed, the appearances presented by the rays through the hole are very interesting ; they are represented in fig. 11. Fig. 11. Fig. 12. The rays in front of the hole may be traced as a fine well- defined pencil passing through the dark space and often visible for some distance from the negative glow ; while it ean be traced backwards through the hole for considerable distances, producing, when it strikes the glass walls, the phosphorescence characteristic of cathode rays. Under the action of the magnet the two parts of the pencil are bent in opposite directions, and their appearance shows that they consist of pencils of cathode rays travelling in both directions from the hole (fig. 12), those between the anode and the cathode travelling in the directions of the ordinary cathode rays, whilst those going through the hole travel in the > opposite direction, the hole acting as if it sent out cathode rays backwards as well as well as forwards. When the pressure falls below a certain value this pencil disappears, the two portions vanishing simultaneously, and we are left with Canalstrahlen passing through the hole and without any of the other rays. These other rays can also be made to disappear by the action of a transverse magnetic force, even 844 Sir J. J. Thomson on though the pressure is such that they are well developed when the magnetic force is absent. The value of the magnetic force required to get rid of these rays is very well defined, a change of a few per cent. in the value of this force will entirely alter the appearance of the discharge. It will be seen that when the Canalstrahlen are accom- panied by the other portions of the discharge, there are two sets of positive rays present which suffer very different deflexions in the magnetic field, the Canalstrahlen being very little deflected, while the portion d is very largely deflected. The comparison with the behaviour of the negatively electri- fied particles shows I think, however, that this difference is due to a difference in the velocity of the particles and not to a change in their mass, for we have seen that there are two streams of negatively electrified particles which are very differently deflected, viz., the rays which constitute the pencil ¢ and those forming the pencils a, a’ which are bent up into small spirals following the lines of magnetic force. In the case of the two sets of negative rays, we have clearly to do with rays moving with very different velocities; we may regard the more rapidly moving ones as primary rays, the slower ones as secondary rays arising from the ionization of the gas by the primary in weaker parts of the electric field, so that these secondary rays never acquire the velocity of the primary, and are therefore more easily deflected. A similar explanation applies to the two sets of positive rays, the more easily deflected ones arising from the ionization of the gas in the weaker parts of the electric field, where they have no opportunities of acquiring large velocities. ee Note on a Method of Measuring the Effective Magnetic Field in the Magnetic Deflexion of the Canalstrahlen. lf O represents the mouth of the tube from which the Canalstrahlen emerge, B the screen supposed to be at right angles to the undeflected path of the rays which we take as the axis of z, H the magnetic force at any point parallel ti z, y the deflexion of the rays due to the magnetic field, then if + is the initial velocity of the rays. As the deflexion is EQ | Positive Electricity. 845 small this equation is approximately so that if J is the distance of the screen from O, H the value of the magnetic force at a distance x from O, l x : = ( Hae dz ea e 1 = ( (l—z) Hdz. vA) Mv Hence the quantity we have to determine is l i} (l—x) Hdz; 0 let us call it M. m P @) F E Now suppose we have a coil of triangular section DEF (DF=EF) placed with its vertex at the screen and its base ED at the hole through which the rays emerge, the plane of the coil being at right angles to the magnetic field. The magnetic induction through the coil age _ DE? U1 ZN A =|, 2H PN, al HEN d= On| (l~x) Hde DE = OF Hence if we measure the magnetic induction through the coil, which can be done in a few minutes by a Grassot fluxmeter, we can at once determine M. This method takes into account the stray field and is applicable whether the field is uniform or variable. M. I have much pleasure in thanking Mr. Kaye and Mr. Everett for the help they have given me in this investigation. /’ oS [) BSBS XC. The Relation between Uranium and Radium.—IlV.* By Freperick Soppy, Jf.A.T HE measurements of the amount of radium in the uranium solutions purified and prepared by Mr. T. D. Mackenzie have now been in progress for nearly four years, and during the past year have all begun to yield certain evidence of the growth of radium. It may be recalled that the quantity of radium in the oldest preparation, which con-- tained 255 grams of uranium, remained almost constant within the error of measurement for the first two years, while in the next year a very slight increase was noticed. It was deduced from this result that the period of average life of the intermediate parent of radium (ionium) must not be less than 16,500 years, on the assumption that, neglecting uranium X, it was the only intermediate body in the dis- integration series. During the fourth year, now nearly passed, the measurements have been taken to a higher degree of accuracy than formerly, various improvements having been effected, and these have established that the production of radium within this period has been going on at a rate proportional to the square of the time, within the error of measurement. As the methods employed are the outcome. . of considerable experience, and as the details are of im- portance in securing accuracy, it may be useful to give a short account of them as they are now carried out, though they do not involve anything new in general principle.. Throughout the term “ unit leak” will be used to denote a leak of 1 division a minute in the electroscope, and the term. “unit of radium” the quantity 10-" gram. One division. of the eyepiece-scale of the microscope equals ‘023 mm. Il. Method of Testing for Radium. The uranium preparations at the commencement of the fourth year were removed from the mercury-pump, to which. | * T, Phil, Mag. June 1905, p. 768; II. (an conjunction with T. D. Mackenzie, B.Sc.), tbd. Aug. 1907, p. 272; III. bed. Oct. 1908, p. 634 A preliminary account of some of the results in this paper appeared in a letter to ‘Nature,’ May 13th, 1909, p. 808, and the Phystkalsche- Zeitschrift, 1909, p. 396. The paper was read on Oct. 22nd, 1909, before: the Physical Society of London, under the title “The Production of Radium from Uranium.” * Communicated by the Author. Relation between Uranium and Radium. 847 they had previously been connected, and transferred to large flasks, as shown at A, fig. 1. Ro B H DS LL EYE “i, YU, —_—_ (| + PUMP Wel ea <= = , —AS =< j Yf Yj Aa Ven Be i um inti SSS f F IY — A ay " ita Se SSE In the new method of testing the principle is the same as was first employed by Boltwood. After each measurement the flask A is sealed at B and ©, after being exhausted through C, and is left for at least a month for the equilibrium amount of emanation toaccumulate. The apparatus as shown in fig. 1 does not need detailed description. Before the measurement it is exhausted through D, and then water in the flask E is admitted through F, by opening the clamp. This is repeated several times to remove any emanation in the water. The flask A is heated gradually by steam on the water-bath for a short time before the seal is broken to avoid percussive boiling. Violent irregular boiling is necessary thoroughly to agitate the liquid and to remove the emanation. If the flask is immersed in warm water boiling tends to be confined to the upper layer, and the extraction of emanation is imperfect. The seals of the flask are broken under thick rubber tubing, a little fresh air being allowed to enter occa- sionally as required through the thermometer-tube K. After half an hour of vigorous boiling, the clamp C is closed and F opened, admitting water until all but a smail definite volume of G is filled. H is then disconnected, and some air thus allowed to enter, removing nitric oxide if present. The tube F is then connected to G at H, andthe arrangement is ready for the transference of the emanation into the electroscope. The latter is shown in fig. 2 (p. 848). It consists of a glass 848 Mr. F. Soddy on the globe A of about half a litre capacity, provided with a circular plane parallel plate W to serve as a window, and silvered Fig, 2. internally except opposite the window. ‘The window greatly improves the sharpness of the image in the microscope, and the accuracy of the readings. C, D are circles of aluminium- foil to act as baffle-plates, which are pasted over the inside at the inlet and outlet taps Band G. The fine thermometer- tube E also assists in moderating the disturbance of the leaf by the entering air. The electroscope is kept exhausted and charged when not in use during any series of successive measurements. Its normal natural leak has been constant within 10 per cent. at 1:1 units since it was constructed. This is first determined accurately. Several small quantities of air are admitted and pumped out, before finally filling the instrument with air. The natural leak is then taken over several hours, prior to the admission of the emanation. When this has been done the instrument is exhausted and the calcium-chloride tube K connected to the tube D of fig. 1. When the whole of the gas in G has been drawn in, D is disconnected and fresh air allowed to enter to atmo- spheric pressure. No trace of emanation is thus lost. The leak is taken over the period from 8 to 16 minutes after the admission of the emanation, and again after the lapse of three hours. The leaf is kept continuously charged (nega- tively) with the charging-rod earthed over the whole interval. This is important, as otherwise a considerable error is intro- duced, which does not appear to have been previously pointed out. The error just referred to applies particularly to the calibration of the electroscope. With the minute quantities of radium present in the uranium solutions, the leaf if fully charged initially remains charged over the three-hour interval, and the practice throughout since this method of measurement was adopted has been to keep it charged during the whole interval. With the radium standards, however, rec error Orr a i i ee ii Relation between Uranium and Radium. 849 the charge has to be renewed every few minutes. At first this was not done, and the active deposit, instead of being concentrated on the leaf system in the most favourable position to produce ionization, is distributed over the surface of the globe. ‘The leak under these circumstances after the three-hour interval is from ten to twenty per cent. too low, and rises gradually with successive measurements for a further period of three hours. III. Calibration of the Electroscope. The two standards used in previous work had been made by directly weighing 2°9 and 3°5 milligrams of pitchblende of 53 per cent. uranium content, and differed from each other by about ten per cent., due no doubt to the error of weighing directly such small quantities on an ordinary balance. For the present electroscope an entirely new set of six standards were prepared with the utmost care, from a different sample of pitchblende. Three separate quantities weighing 59°45, 133°7, and 58°32 milligrams were separately dissolved in nitric acid which had recently been distilled over barium nitrate to remove any sulphuric acid, and diluted in 100 c.c. graduated flasks. Out of each of the three solutions two standards were made, by taking a known fraction of the liquid, determined by weighing, and sealing it up after dilution in a flask similar to A (fig. i) of about 100 c.c. capacity. These six new standards agree extremely well among themselves. On the remainders of the solutions used in preparing the standards three analyses of uranium were performed, which agreed in showing that the proportion of uranium in the pitchblende used was 49 per cent. The results are shown in Table I. 7 TABLE I. = | E E ea, BE III. | v. S| Pircusienpe. ‘Urantu. RavDiuM. | CoNSTANT. = | (Milligrams).| | (Milli- |(x 10-12 gram.), iene: | ) GET Y SY, a | grams). | pee minute). ....| 0628 | 0308 104°6 | ete thea be i. 3040 | 1-490 506°4 | 865 | B85 = | SS ET SS | a = re IT... 1-420 | 0696 236-6 41:6 Zz 5°69 IV....| 13°59 6660 22266 (370) Marcy (6 02) V....} 0°305 0149 50'8 2 Betta 591 VI....| 1-510 | 0-740 2516 | 566° Mzan (omitting LY): 9. 48 850 Mr. F. Soddy on the The factor used to calculate the quantity of radinm from the quantity of uranium is 3°4 x 107‘, instead of 3°8 x 10-7, as previously used. It will be seen that the standards differ among themselves in content of radium in the ratio of over 40 to 1, but the constant of the instrument as determined by the individual standards does not vary from the main value more than two per cent. It must be mentioned that the value for standards IV. is not comparable with the others. The quantity of radium was too high to permit of the charge on the leaf being maintained as it leaked away, so the leaf was kept permanently connected through the charging rod to the negative pole of the 250 volts mains. Under these conditions the charging-rod as well as the leaf-system would attract the active deposit, and the part deposited near the cork in the neck of the flask would not contribute its full effect. For this reason the constant, as is to be expected, is too high, and the value has been omitted in caleulating the mean. The latter is 5°78, that is 5°78 x 10—” g. of radium produces a leak of 1 divisiona minute. The two old standards gave a mean value of 7-3 for the constant, the leaf not being kept charged during the three-hours interval. This difference is not much, if any, greater than can be accounted for by the effect of keeping the leaf charged. IV. Results. The results are shown in Table II. for the three uranium preparations described under Experiments I., II., and IV. (II. pp. 285-289 and 290). The later tests in each prepara- tion have been performed with the electroscope in its existing condition, for which the constant has been accurately deter- mined as described. The first tests were done with another leaf-system, which was destroyed after one test owing to nitric oxide having been present in the gases boiled out of the solution. The factor necessary to reduce the readings with this system to the same value as those with the present system was found to be 0°96. In the initial test shown both for Experiments I. and II., to which not much weight can be attached, the charging-rod was left after charging close to the system as in all previous measurements, whereas the present practice is to turn it as far as possible away, which was found to increase the sensitiveness 1°15 times. The three tests indicated by a * in the last column of the table were done by the mercury-pump before the solutions had been transferred to the sealed flasks they are now kept in. The table shows that in all three preparations the quantity Relation between Uranium and Radium. Sol TABLE II, | Reduced Radium | Leak. (X10-12 gram). Observed Reduction Leak. | Factor. | Time : 2 Date. \(years) (Time)?. Experiment I, 255 grams Uranium purified, 24/10/00. 9/6/08 | 262 | 686 | 289 x-96x1:15] 32 age —_—_—_—_ ———————- =a — —— gee |278 | 770 | 338. | x96 | 817 18-4* 25/9/08 | 295 | 857 | 3538 | x96 | 339 | 19-6 20/11/08 | 308 949 | 3-44 a Sag Ags 59/09 | 3531246) 390 |... 3-90 22:5 14/6/09 | 3-64 | 1324 | 420 |... 420 | 943 97/8/09 | 3:85 1480 | 428 a 428 247 29/9/09 3-93 | 15438 | 416 ns 4-16 | 94-1 | Experiment IVY. 278 grams Uranium purified, 14/8/06. | | et | 30/5/08 | 1:80 | 3°24 273 |x :96X115| 3:02 | is 7/509 | 273 | 745 | 368 |... 3:68 213 Baio |. 287 | S22 |. 372..) 3°72 21°5 4/10/09 | 315 | 990 | 400 | _ .., 4:00 23-1 I } Exrerment I]. 408 grams Uranium purified, 13/12/06. | 8/8/08 | 1°66 | 275 |. 0°70 x96 | 067 3°87* 19/11/08 | 193 | 373 , 0:80 x96 | O77 4-45 6/5/09 | 240 | 5°76 | 1:25 wee 1:25 7:20 15/6/09 | 250 625 | 1:26 3) 1-26 7°30 Have | 280) 783° |, BT |. 1:37 7-90 | | of radium has increased with time. The measurements are plotted against the square of the time in fig. 3 (p. 852). It will be seen that all the points lie close to straight lines. The maximum departure is in the case of the last test performed in Experiment I., which lies about 2 units too low. The ordinary error is not more than 1 unit, or 10-” gram. Con- sidering the nature of the measurement the agreement is perhaps closer than might have been expected, as it is doubtful if any previous measurements of these small quantities of radium have been made to anything approaching this degree of accuracy. 852 _Mr. F. Soddy on the Fig. 3. ae V. Period of the Direct Parent of Radium. As detailed. in the last communication (III. p. 635) the growth of radium from uranium should proceed according to the same power of the time as there are products in the series (counting radium itself) between the two elements, provided all these products have periods long compared with the time of observation. Rutherford, assuming only one intermediate product—the direct parent of radium—to exist, first showed that the production of radium should proceed according to the formula mara i 1/2 Aerg Rot? or 1/2 MA, U2, where R represents the quantity of radium, U that of uranium, R, the quantity of radium in radioactive equilibrium with the uranium, )j, XA», A3 the constants of uranium, the direct parent of radium, and radium respectively, and ¢ is the time. This may be written R=6 x 10-°A,2?, where R represents the radium formed per kilogram of uranium and A, and ¢ are expressed in years. It is of interest to calculate the value of A, from this equation, although, as will be shown later, the calculation is seriously in error if other intermediate bodies of period comparable with the time of observation exist in the series. From the Relation between Uranium and Radium. 853 eurve (fig. 3) representing Experiment ‘I. the growth in 4 years (#?=16) is about 13°3 units, or 52 units per kilogram of uranium. The value of A, is therefore 5:4 x 10-°, and the value of 1/A., the period of average life, is 18,500 years. The lower value (10,000 years) given in the preliminary communications is solely due to a value having been used for the constant of the instrument, which is subject to three corrections all operating in the same direction: (1) the effect of keeping the leaf charged, (2) the effect of altering the position of the charging rod, and (3) the alteration in the value of the ratio between U and Ra in pitchblende. In Experiment IV. the value depends entirely on the initial observation to which, as already mentioned, not much weight can be attached. The experiment shows for the first three years a growth of 7°65 units, or 27°5 units per kilogram of uranium. This gives for A, a value 5:1 x 10-°, and for 1/r, 19,600 years. ' Experiment III. is very interesting on account of the very small total amount of radium present, though the quantity of uranium is considerably greater than in the other two. It has not been in progress long enough to give the slope of the curve very accurately. As drawn in fig. 3 the growth in ,/8 years is 7°5 units, or 18:4 units per kilogram, The calculated value of A, is 3°3x10-%, and of 1/A, 26,000 years. : The experiment is of interest in this way. If the growth of radium had been proceeding at the same rate as in Experi- ment I., in ,/8 years 10°6 units of radium should have been produced, whereas the total amount of radium now present is less than this, being so far as the measurements indicate only 8’5 units. Even if it is assumed that this difference is due to errors of experiment, it is difficult to believe that the solution as initially prepared contained absolutely no radium, The results of the three experiments taken together thus indicate that the rate of growth of radium in terms of the square of the time is less for the first three years than for the subsequent year. This points to the existence of one or more intermediate bodies of relatively short period in the series, which would retard the rate of production of radium initially. The actual measurements of the initial quantity of radium in Experiment I. bear this view out, although it must be remembered that the errors of measurement initially were very much greater than now, and this evidence thus only has a doubtful value. For Experiment II, the initial measurements may be rejected, as the quantity of radium Phil, Mag. 8. 6. Vol. 18. No. 108. Dec. 1909. 23M 854 Mr. F. Soddy on the was almost too small to be within the range of the older methods. In Experiment IV. no initial measurements were taken. In the older tests a brass electroscope had been used, and this was calibrated at every test with reference to a y-ray radium standard. As was pointed out (II. p. 286) the measurements so corrected were not nearly so regular as the actual observations. In light of recent results on the un- certainty attaching to y-ray measurements, it is best to reject these calibration tests altogether and to assume that the sensitiveness of the electroscope did not vary. Recalculating trom the table (II. p. 282) gives, according to present data, the value 12 for the constant of, the instrument. The mean of the first nine tests over the first 309 days given in the table (II. p. 286) recalculated gives the initial quantity of radium as 15°8 units. The initial quantity indicated by the curve on the assumption that the rate of production in terms of the square of the time has been constant from the start, is about 12°5 units. This evidence so far as it goes thus bears out the view that new short-lived intermediate bodies. exist. VI. The Hiects of Short-lived Intermediate Products. The general effects of short-lived intermediate bodies may now be considered. Let A, B, C, D, E... and Ay, Ag, As, Ay, As... denote the quantities and radioactive constants respectively of a parent element and its successive products. It is assumed that initially the products are absent, and that the change of the parent is so slow that its quantity may be considered constant. The ditferential equations connecting the terms are aB dC \ i) — . =A.b— I ee =r,0—[a,D]; o =2,D—[r,E]. d If we assume that the periods of the first two products, B and CG, are short and those of the others long the terms in square brackets may be neglected. The case then corresponds to the disintegration series Uranium -—> Uranium X — “ Uranium A”? —> Parent of Radium -~ Radium, where B denotes uranium X, for which ), is about 11:4 (year)~, C the suspected new intermediate body “uranium A,” for which the period is probably of the order of unity, D the direct parent of radium, and H radium. Relation between Uranium and Radium. 855 Solving the equations, the growth of radium is given by 2 2 2 Baan yi athe), Mat + Aaha + As 2 AvAz3 Aes? Xe —Agt As. ) —Acgt \ . conn) g (eam i ah The last term is always very small, and may be neglected at once. The penultimate term approaches to zero as ¢ increases. After a period several times that of uranium A it nay be neglected. The expression then becomes i Ag +r 2 +AA 2 Banna — (Saree eh Tf instead of reckoning the time from the start we reckon it from a date iater by the sum of the periods of average life of the two short-lived bodies, that is, for ¢ in the equation we substitute IT; where ie a nae Oi then 2 1 K=1/2 MrA4 ee ved l = 1/2 X,A,AT? + constant. ‘ A As J That is to say, when the short-lived intermediate bodies come into equilibrium the production of radium proceeds strictly according to the square of the time reckoned, not from the start, but from a date later by the sum of the periods of the intermediate bodies. To show the effect of the intermediate bodies initially the graphs of equation (I.) have been plotted against the square of the time, for the following values of X3 :—4, 2, 1, °66, °5, 33, and °25 (fig. 4, p. 856). The curves therefore show the production of radium according as the hypothetical body uranium A has the period of three months, six months, 1, 1:5, 2,3, and 4 years. The straight line uppermost on the diagram shows the production of radium on the same scale if no short-lived intermediate products intervened. It will be seen at once from these curves that if the portion between the third and fourth years, that is between ?=9 and t?=16, is examined, even for the lowest curve corre- sponding to the four-year period, the curve departs but little 3M 2 856 Mr. F. Soddy on the from the straight line. It is doubtful whether the departure would be experimentally detectable over this period. This shows that the straightness of the experimental curve over the period available is no argument against the existence of Fig. 4. TTT TT 4 Se is 2 ees eS de intermediate bodies. On the other hand, the figure at once reveals the serious error introduced into the calculated period of the parent of radium by the formula used in Section V. if intermediate bodies exist. The true period of this body is obtained from the slope of the straight line uppermost in the diagram, which represents the rate of production of radium if no intermediate bodies intervened. If an intermediate body with a period of 1 year intervened, the period of the parent of radium instead of being 18,500 years as calculated in Section V. would really be only 0:72 times this or 13,300 years. If the period of the intermediate body were 4 years, ~ the true period of the parent of radium would be only 0°32 of the apparent period, or 6000 years. Yet even a four-year period body might exist without producing in the curve a departure trom the straight line enough to be detected experimentally with certainty as far as the measurements have yet gone. ! 265.14 15 16 7 18 oeoe Relation between Uranium and Radium. 857 VIl. New Experiments. Two new experiments are being commenced which it is hoped will yield in the course of time further evidence on the existence or otherwise of short-lived intermediate bodies in the series. In the first the purest fraction of the 50 kilograms of uranyl nitrate which has been repeatedly crystallized frum fresh water in the work on the y-rays of uranium (Soddy and Russell, Phil. Mag. Oct. 1909, p. 620) has been withdrawn from the fractionation and sealed up in a flask. It contains 3 kilograms of uranium (element), which is 12 times the quantity in the oldest preparation. It is being tested at monthly intervals for growth of radium. The initial quantity present has been determined in two agreeing consecutive experiments to be 42 units. Considering the mass of the material this is gratifyingly low. In the course of a year or two the growth of radium from this solution should settle the question whether new intermediate products exist in the series. Secondly, now that the rest of the 50 kilograms of uranyl nitrate has been repeatedly purified, it is proposed to seal up one of the preparations of uranium X to be separated from it, as in the work with Mr. Russell, and to measure from it the rate of production of radium. Unless intermediate bodies exist this would hardly be worth while, as it would be prac- tically impossible to distinguish the parent of radium formed from uranium X—if it is so formed—from that initially sepa- rated with the uranium X. Keetmann (Inaug.-Dissert. d. Verf., Berlin, 1969) has stated that uranium X and the parent of radium both have the same chemical properties as thorium and cannot be separated from this element or from one another. But if an intermediate body exists of period of the order of a year it should be easy to distinguish between the parent of radium initially present with the uranium X and that subsequently produced from it. If U represents the quantity of uranium initially in equilibrium with the uranium X separated from it, and R represents the quantity of radium formed from the uranium X, it can be shown that i ae Aids _As As ear ie {Hes a We w (1 N+ a0 S75 aie a dfs assuming the same disintegration series as before. Whereas if all the parent of radium were present initially, the pro- duction of radium would of course proceed proportionally to the time. 858 Mr. EF’. Soddy on the VIII. Conclusions. The measurements on the growth of radium in the three uranium solutions purified by Mr. T. D. Mackenzie between three and four years ago, have shown that in all of them the growth of radium is proceeding according to the square of the time within the error of measurement. The period of the direct parent of radium calculated from these results, on the assumption that no other intermediate bodies intervene, is 18,500 years in the case of the oldest solution for which the most complete data are available. But in the solution prepared last, the total quantity of radium now present is less than what would have been produced from the radium, assuming the rate of production to have been the same as in the first solution. This suggests the existence of at least one new product “uranium A” intermediate between uranium X and the parent of radium, with the period of the order of one year. From a mathematical investigation of the effect of such a body on the growth of radium it is concluded that it would not, if it existed, appreciably alter the production of radium according to the square of the time over the period observations have been made, but it would vitiate the calculations of the period of the average life of the parent of radium according to. Rutherford’s formula. In conclusion, it may be mentioned that a good deal of additional evidence bearing directly on this question of the existence of new intermediate products has been accumulated in an investigation on the rays and product of uranium X, with which it is convenient to deal in a separate communi- cation. ' Physical Chemistry Laboratory, University of Glasgow, October 1909. XCI. The Rays and Product of Uranium X. By Frepericx Soppy, M.A.* haar preceding paper has dealt with the evidence from the rate of production of radium from uranium, which suggests the possibility of the existence of at least one new intermediate product in the disintegration series. Although the experiments are not yet complete, it is advisable also to publish a short account of the results obtained in a different * Preliminary accounts of part of this work appeared in two letters to ‘Nature,’ Jan. 28th, 1909, 79, p. 866, and March 11th, 1909, 80, p. 37. The paper was communicated to the Physical Society of London on Oct. 22nd, 1909. Rays and Product of Uranium X. 859 field of investigation which bear also upon the same problem. Attempts have been made to determine whether, during the decay of the 8-radiation of the intensely active preparations of uranium X, separated with the help of Mr. Russell (Phil. Mag. Oct. 1909, p. 620) from 50 kilograms of pure uranyl nitrate, there occurred the growth of a feeble a«-radiation increasing concomitantly as the other decayed. This is to be expected from the work of Boltwood, Keetmann and others, who have shown that the direct parent of radium gives an a-radiation, provided that it is the direct product of uranium X. The work was started in the hope that inter- mediate bodies intervened, and that the growth of a-ravs would occur long enough after the @-rays of the uranium X had decayed to be detectable by ordinary measurements. But through the generosity of the friend who provided the uranium a powerful electromagnet of the Du Bois type was acquired, and with this it was attempted to deviate the B-rays of the uranium X, so that measurements of the a-rays of the preparations could be taken from the start. The problem proved a difficult one, but gradually the experi- mental methods have been perfected, so that now it is claimed that they are sutiiciently delicate to detect such a growth of a-rays if it occurred in the intensely active uranium X preparations investigated to the extent to be expected from theory. Much remains unaccountable in connexion with these experiments, but they appear to have definitely answered the main question in the negative. No production of «-rays, such as is to be expected from theory, has occurred, and therefore it does not seem possible that the direct parent of radium can be the direct product of uranium X. The experiments indeed raise the further question whether the parent of radium can be a product of uranium X at all, but are not yet far enough advanced to be conclusive. Were the parent of radium a product of uranium X the number of a-particles it emits should either be equal to, or one-half of, the number emitted by the uranium in equilibrium with it, according as one or two z-particles are given off from uranium. The latter assumption will be made as it gives the smaller growth of a-rays theoretically to be expected from uranium X. Assuming that the a-activity is proportional also to the ranges of the respective a-particles, which are 2°7 and 3°5 cm., the a-activity of the parent of radium will be 2°7+3°5 x 0: 5, or 38 of that of the uranium. The period of the parent of radium as deduced in the last paper on the assumption that no new intermediate bodies exist in the series, is 18,500 years, while that of uranium X 860 Mr. F. Soddy on the is about 32 days, or 5x 10-° in terms of the other as unity. The amount of uranium X in equilibrium with a definite amount of uranium should produce therefore upon complete disintegration about 5 x 10-° of the amount of the parent of tadium in equilibrium with the same quantity of uranium. The asactivity of this product would therefore be about 2x10-° of that of the uranium. In other words, the uranium X in equilibrium with 1 kilogram of uranium should thus produce in its complete disintegration a product having the a-activity of 2 milligrams of uranium. The uranium X, after concentration to the greatest possible extent, was finally prepared in the form of films in rect- angular trays having an area of 10 sq. cm., which could be slipped between the poles of the electromagnet. The undeviated radiation entered an electroscope placed above the poles provided with an opening in its base covered with very thin aluminium-foil. The first attempts were frustrated and the first preparations decayed without result, owing to the totally unexpected difficulty in deviating the #-rays. The latter previously had been supposed to consist of homo- geneous rays having a value for Hp=2000. But it was found that a field twice as strong as was necessary completely to deviate such rays failed to deviate about 5 per cent. of the total @-radiation. In the later dispositions the width of the gap was reduced to one-half the former width, and the field was sufficient to deviate completely all rays with a value for Hp below 8640; but the leak due to the still undeviated @-radiation, although now proportionately very small, was stiJl several times that due to the y-radiation. It was still too great in the earlier measurements for the small growth of e#-radiation, theoretically to be expected, to be within the range of certain detection. In the later experi- ments the electroscope was filled with hydrogen instead of with air, and this constituted an enormous advance. Not only is the ionization due to the @- and y-radiation greatly reduced and that due to the a-radiation greatly increased, but the convection-currents generated in the electroscope by the warming up of the magnet are also enormously reduced. The readings are far more regular and can be continued for a longer time before the leaf begins to be disturbed. In air, after half-an-hour’s work or less, the leaf commences to wave like a flag, and nothing can then be done for eight hours. A preparation which gave (in divisions per minute) a leak of 370 divisions bare, and 351 covered with thin mica (a-rays therefore 19) when the electroscope was filled with air, gave in the same apparatus filled with hydrogen, bare 1052, Rays and Product of Uranium X. sol covered 66:2 (a-rays therefore 39). As the subsequent history of the preparations showed, a large proportion of the radiation reckoned as “a-” in air is due to the slight absorption of the B-rays in the mica, whereas in hydrogen this absorption is nearly negligible. So that in air, even if the theoretical growth of «-radiation occurred, it would probably be largely, if not entirely, masked by the diminution in the. difference between the two leaks, covered and un- covered, due to the diminution in the absorption of the 8-rays as these decayed. In hydrogen the effect is still present to a slight extent but not enough to prevent the observation of the growth of a-rays, if it occurred at the theoretical rate. Subsequent work has thrown doubt on the earlier measure- ments in air, and on the conclusion drawn from them in the second communication to ‘ Nature,’ that in one preparation a rapid growth of a-rays occurred which reached a maximum in 2°5 days from the start. This observation has not been repeated either in air or in hydrogen with more perfect methods. This is not itself conclusive against it, for it has been impossible to prepare two sets of uranium X preparations in the same way. The chemical methods, of separation from uranium and of concentration from unidentified impurities, employed have varied widely, being dictated by circumstances from moment to moment during the process, owing to the perpetually changing character and amount of impurities and the totally different chemical behaviour of the uranium X accordingly. In fact the methods adopted in the last separation were often the converse of those formerly most relied upon, the uranium-free, uranium X -containing substances being dissolved in excess of ammonium carbonate and fractionally precipitated by boiling. Sometimes the uranium X came down in the last minute fraction almost entirely, and in other cases in one of the middle fractions. This new method proved an extremely valuable one in the last separation. Unfortunately it was not discovered before the whole of the uranium X had been first separated by the tedious barium sulphate process. The earlier observations and the conclusion referred to may be rejected at least for the present. The difficultly deviable rays behave in an anomalous manner which was at first not suspected, in that they do not seem to be a constant quantity. In the case of the most recent preparation, which, as already explained, differed in the manner of its separation from the earlier ones, two successive measurements of the difficultly deviable radiation from the covered preparation in air, the first immediately after preparation, and the second 862 Mr. F. Soddy on the 9 hours later, showed a diminution in the interval in the ratio of 4 to 3. The y-rays of the preparation, measured in the usual way in a lead electroscope at the same times, showed no perceptible variation. It was later found that the value of the leak due to the difficultly deviable radiation varied in a completely unaccountable way. The variation is far more marked in air than in hydrogen. The behaviour suggested strongly in certain cases that the preparation was giving off a radioactive emanation, and from the manner of its preparation thorium was suspected. But this was completely disproved by special experiments. But the most striking proof that the behaviour was not in any way due to this cause or to defects in the method of measurement is that the a-radiation as measured by the difference between the leaks with the preparation covered and uncovered remained from the start perfectly constant. ‘This shows that all the numerous errors to be guarded against in experiments where the gas in the instrument is changed have been avoided. A good many rapidly improvised experiments, done with the first batch of preparations before their activity decayed, had indicated that the difficultly deviable radiation was entirely similar in general character, both in the direction of their deviation and in the value of their absorption coefficient, to the ordinary 8-rays. The absorption coefficient for aluminium, determined by placing strips of foil directly over the preparation, placed in the magnetic field, had been found to be about 24 (cm.)-1. This is much less than the usual value (14), given for the ordinary 6-rays, and is about equal to the value after 2-5 mm. of aluminium have been traversed. The field would cause the trajectories of the rays in the metal to be lengthened, but owing to the complete scattering suffered by these rays by even thin films of metal, it is difficult to state precisely what the effect of the field on the absorption coefficient would be. If these rays are really B-rays, the value of Hp shows that they must possess a velocity practically that of light, and a kinetic energy many times that of the ordinary $-rays. In view of the great decrease in penetrating power which a very slight diminution of velocity appears to produce in this type of radiation, it might be expected that the difficultly deviable rays would have a very great penetrating power, whereas the value found was actually less than the normal value. Similar difficultly deviable radiation is given out also by radium, although here the value of Hp is even higher, and the upper Rays and Product of Uranium X. 863 limit does not appear to be reached at 9000 to 11,000. Further study may show that they are to be connected with the scattering of the B-rays, though the experiments done rather point ‘to the view that they may be a new kind of radiation. So far attention has been concentrated rather upon the main problem. The electroscope used for hydrogen had a very thin mica sereen, thick enough to absorb a-rays, hinged inside, which could be turned up or down from the outside, without opening the instrument, to uncover or cover the preparation at will. The first measurements, with the third set of preparations, were interfered with somewhat by difficulties encountered in making and keeping the electroscope perfectly gas-tight. Later a new instrument with properly soldered j ints throughout was constructed and is now used entirely. There were three preparations in the third set, two practically identical in every particular, containing initially the uranium X in equilibrium with 5:1 kilograms of uranium, and a third containing that of 2 kilograms, as measured by means of the y-radiation. They all showed the same behaviour, and cne only of the two stronger preparations need be considered here. It weighed 200 milligrams. Measurements were done in hydrogen only. No evidence of a growth of a-rays either initially or at any subsequent time was obtained. The mean of the first five observations over the first 28 days gave 14 for the a-rays, which, corrected for the difference between the two instruments, gives 16 for the leak in terms of the present instrument. The actual observations varied a few per cent. from the mean for the reason stated. Sub- sequent measurements with the new electroscope 76, 99, and 137 days from the start, gave for the a-radiation 17, 17-2, and 16°6 respectively. In the fourth separation there was one preparation only, weighing 77°6 milligrams, and containing initially the uranium X in equilibrium with 5°05 kilograms of uranium. The measurements of the a-radiation were done at first both in hydrogen and air. Those in hydrogen, at different times from preparation, are given in the following table. They are the most accurate so far done and are all comparable with one another. Sas nahh Sea B= Slat MANS eB DOR GA CC OE 20 s0| 40) 6 6 | 9 | 18 | | 38 | 38-9 9990802 sr ar seas . | 864 Mr. F. Soddy on the The initial value of the leak due to the penetrating rays was 75. It will be seen that from the start over a period of 33 days—about the period of average life of uranium X, in which 0°632 of the total disintegrates—the a-radiation has been practically constant. To obtain an idea of the growth of a-rays theoretically to be expected, the «-radiation of a film containing 24 mg. of uranyl nitrate (=12 mg. uranium) was measured in hydrogen under precisely similar conditions. It gave an a-ray leak of 17°8. The growth of a-rays to be expected in the last experiment in 33 days, if the change of uranium X into the parent of radium occurred directly, is equal to that of 0°632 x 5°05 x 2=6°5 mg. of uranium, or about 9°6 divisions. Hven if a considerable reduction is made for the fact that the weight of the uranium-X film was about three times the weight of the uranyl nitrate film, it is difficult to believe that the growth would not easily have been detected in the experiment if it had occurred. In the preceding experiment with the preparations of the third separation, the initial a-activity was less than half the value in the last experiment. Any rise could therefore have been still more easily detected. But up to the period of 137 days from preparation, when less than 2 per cent. of the original uranium X remains undisintegrated, not the slightest growth has been recorded. The most active preparation of the second separation tested recently in the new hydrogen electroscope in hydrogen on two occasions 200 days and 227 days from preparation, gave the same a-ray leak (about 80). The best preparation of the first separation—the best one ever prepared from the point of view of smallness of mass—tested in air (in a much weaker field than now used) has latterly, now that the (-radiation has nearly decayed, shown no change in the considerable «-radiation present. In the last tests 264 and 291 days from preparation, the e-leak has been constant at 35 (in air). This and a still earlier preparation now 16 months old, prepared from 3 kilograms of urany] nitrate in preliminary work, have now decayed so far that their a-radiation can be examined without the aid of a magnet in an ordinary electroscope against suitable standards. Since these tests were started the e-radiation has remained constant. A still older preparation, dating from 1903/4, prepared from probably not more than 50 grams of uranyl nitrate, has also quite an appreciable a-radiation. This has been kept under careful observation for over a year and no change has been ~ recorded. Rays and Product of Uranium X. 865 These tests, therefore, although still incomplete, cover for different preparations the period from the start up to nearly a year in the case of the main preparations, and for con- siderably longer for weaker preparations. They have given no evidence of the growth of an a-radiation at any time during this period. ‘They all show a considerable constant a-radiation, but in all it appears to be due to a body present from the start, unconnected genetically with uranium X. The statement of Keetmann, that uranium X and the parent of radium are identical in chemical behaviour and are always separated together, would explain the presence of the a-ray body in all the preparations so far kept under observation. The conclusion seems to be justified that the parent of radium is not the direct product of uranium X, and the question now arises whether it can be considered a product of uranium X atall. Even if there was a new intermediate product in the series “uranium A,” with a period of a many years, provided there was but one, some indication of growth of a-rays should before now have been obtained in these experiments. For it must be remembered that its existence would greatly reduce, as explained in the last paper, the period of the parent of radium, as calculated from the measurements of the rate of growth of radium, and so would increase correspondingly the growth of a-rays ulti- mately to be expected. The subsequent history of the preparations may be expected to throw further light on this question. The results so far obtained are difficult to reconcile with the experiments on the rate of production of radium from uranium, on the assumption that the parent of radium is a product of uranium X. There is no proof of this, though on uccount of the intense character of the @-rays of uranium, it seems natural to suppose that uranium X, the @-ray-pro- ducing body, is in the main radium series rather than in that of actinium, Physical Chemistry Laboratory, University of Glasgow. October 1909, B66. XCIL. Effect of Temperature on the Hysteresis Lose tn Fa wn a Rotating Field. By W. P. Fuuurr, B.Eng., and H. Gracr, B.Eng.* T was shown by Professor Baily ¢ that the hysteresis losses due to a rotating field in iron reached a maximum value with an induction density (B) of about 16,000 C.G.S. units. With a value of B equal to 20,000 the hysteresis was ap- proximately 1, of the value. These results were confirmed by Messrs. Beattie & Clinker}. ‘The experiments described below were undertaken in order to determine to what extent the results attained by Professor Baily were modified by variation in temperature. , In these experiments, the rotating field was produced by means of two phase-currents. Fig. 1 shows the arrangement, the two magnetizing coils carrying the two phase-currents being marked E, D. A is a slab of plaster 2 ems. thick and 22 ems. square, having a circular hole 84 cms. diameter in the centre. At the top and bottom of the hole the heaters B are placed, and in the chamber so formed the iron specimen is suspended. Hach heater was made by winding No. 40 s.w.G. nickel wire zigzag fashion over the surface of a circular piece of mica. Its resistance cold was 13 ohms, but increased rapidly with temperature. With the two in series a current of 1°6 amps. at 180 volts produced a maximum temperature of 500° C. ata point close to the iron disk. The specimen used was a circular disk of iron 4 cms. diameter, 027 thick: it was attached by nuts to a brass spindle CU, which had a weight attached to one end, and a concave mirror at the other for indicating the motion of the specimen. The whole was supported by a bifilar suspension, the sensitiveness of which could be varied by altering the weight or by varying the distance apart of the supporting wires. The weight of the whole moving part was 285 grams. The two magnetizing-coils D D, belonging to one phase, are each made by winding 14 turns of 7/14 asbestos-covered cable. The two coils are arranged to slide over the plaster slab to within a short distance of each other, at the centre. The coils for the second phase, E EH, are placed so as to produce a field at right angles to that of DD. ‘They are of the same shape as DD, so that the two together produce a close ap- proximation to a uniform rotating field at the centre of the coils where the specimen is placed. ‘The large coil was found x Communicated by the Physical Society: read May 14, 1909. + Phil. Trans. 1896. t ‘ Electrician,’ 1896. Hysteresis Loss in Iron in a Rotating Field. 867 to produce a field 10 per cent. greater than that of the smaller tor the same current, but with 25 amps in one and 27°95 in the other, the maximum values of the two fields were equal, Fig. 1. ina General arrangement of the magnetizing coils and specimen. each being about 250 c.c.s. units, and the two together pro- ducing a uniform rotating field of this magnitude. Ata distance of 2 cms. from the centre of the coil the field produced was 14 per cent. less. The phase relationship of the currents in the two phases was indicated by means of a wattmeter, the thick coil oeing in one circuit and the thin coil connected between the ends of a non-inductive resistance in the circuit of the other phase. A phase-difference of 90° between the currents in the two circuits was shown by a zero reading on the wait- meter. The phase-difference was kept within °3 per cent. of 868 Messrs. Fuller and Grace: Hffect of Temperature 90° by using a variable choking-coil in the primary of one of the transtormers supplying current. The numerous adjustments which have to be made are @ disadvantage of the alternating current method compared with the rotating magnet method used by Baily and others ; but the absence of rotating parts is a distinct advantage, and this fact would render the method very suitable for high- frequency experiments. To measure the flux in the iron, a coil of 8 turns of bare wire was wound round it and insulated therefrom with mica. As the H.M.F. induced in the coil is alternating and of the order of ‘04 volt, a suitable galvanometer had to be con- structed in order to measure it. The instrument constructed for the purpose is shown in fig. 2. ABCD are four coils of conical shape and wound with no. 28 wire. A and B were connected in series through a resistance to one phase, C and D to the other phase, of the machine supplying current to the magnetizing-coils of the test apparatus DE, Witha on the Hysteresis Loss in Iron in a Rotating Field. 869 current of ‘31 amp. a rotating field of about 20 C.G.S. units was produced at the point O. A small coil, made up with 200 turns of no. 46 wire (140 ohms resistance) 5 cms. long and 1 cm. broad, is suspended in the central space between the coils, and is connected to the search-coil on the iron specimen. In the galvanometer-coil there are two E.M.F.’s, one, E cos pé (say) due to the flux in the iron specimen, and one due to the rotating field of the galvanometer itself. Referring to fig. 2, let H H’ be the direction of the rotating field of maximum value H when E cos pt is a maximum. The angle between it and the coil at a time ¢ will be 0+ pt, and the component along the coil H cospt+6@. The flux normal to the coil is Hsin pt+ 0, and the E.M.F. induced is proportional to ‘i H p cos pt +0 = EH, cos pt+é. If R be the resistance of the coil and the self-induction is negligible, the resultant current is equal to te cos pt + HE, cos pt+ 6). The torque at a time ¢ will be proportional to = R Hence the mean torque acting on the coil is proportional to H cos pit | (E cos pt+ E, cos pt +8) * 7 {E cos6+H;}. This deflecting torque therefore consists of two parts, one constant and one which depends on the position of the four magnetizing-coils A BCD. In the apparatus used these coils were fixed to a turntable, which could be rotated until the deflexion was a maximum. The deflecting torque would then be proportional to 4 (E+E). Another way of using the instrument is to get E and H, in opposition, in which case the minimum deflexion is proportional to (HE, —E) ; and this is the better method because the total deflexion is smaller, and greater sensitiveness is obtained. The instrument was calibrated by putting a resistance of 4000 ohms in series with the coil and applying a measured pressure of 1°95 R.M.S. volts to it. The detlexion, after deducting that obtained by shortcircuiting the coil through the 4000 ohms, equalled 22°4 centimetres, consequently one Phil. Mag. 8. 6. Vol. 18. No. 108. Dec. 1909. 3N 870 Messrs. Fuller and Grace: Effect of Temperature centimetre corresponds toa voltage of maximum value -00416 — applied to the moving coil. The induction density in the iron disk was readily calcu- lated from the maximum voltage measured as above, the dimensions of the search-coil on the iron being known. The disadvantage of this type of instrument is that the constant part of the deflexion depends on the cube of the frequency, so that the speed of the machine must be very exactly regulated for a constant value. The E.M.F. induced in the coil on the iron varies approximately as the frequency, and so the torque on the galvanometer due to this current depends on the square of the speed. It was found better in practice to have the two voltages E and E, in opposition, as mentioned above, so getting a deflexion proportionate to H,—E. One other measurement required to be made, namely, that of temperature. This was effected by means of a Platinum-Platinum-Rhodium junction (placed close to the ppc connected to a suitable galvanometer. Fig. 3. ee Zi pees Sceeeeeaee 13 le UI wl : &5 = s, CPE CCE qeseresees-ocdeeer es i ee a oe SCLIGeL Tieton Oe Le one | sa UA al es . OP 2053 he Se By 7B OG WO the 2) PS) eS ee (yDuUCcTION CGS UNITS. Curves showing relation between Hysteresis Loss and Induction at different Temperatures in a sample of armature iron from Messrs. Sankey. The results obtained are shown in figs. 3 and 4. The temperature of 107° C. was the lowest at which it was found possible to make any measurements, on account of the heating on the Hysteresis Loss in Iron in a Rotating Field. 871 effect of the magnetizing-coils. The results in fig. 4 were obtained after the iron had been heated to 580° and cooled slowly. These experiments show that the effect of increasing the temperature of iron is to greatly reduce the hysteresis Fig. 4. SN a i a PMR si 9 a ao © Lea) ERGS PER CoM PER CYCLE. an > /wOUCTION CGS UNITS loss at a given induction, and to cause the maximum to occur at a lower value of B. At a temperature of 580° C. the maximum hysteresis loss occurs at an induction density of 11,000 C.G.S. units instead of 16,000, while the maximum hysteresis loss is only 2600 as compared with a maximum of over 15,000 per c.c. per cycle at ordinary temperatures. The effect of heating to 580°, as shown in fig. 4, is most marked ; although the actual maximum hysteresis loss is not greatly altered at the higher temperature, the reduction in the hyste- resis loss at the lower temperature is considerable. The shape of the curve between ergs per cycle and B is quite different, the hysteresis loss falling off much more rapidly from the maximum. The permeability of the iron is not greatly affected by changes in temperature within the limits of the experiment, as was shown by Morris *. The above experiments were carried out at the Applied Electricity Laboratories of the University of Liverpool, and the authors thank Professor Marchant for his valuable advice and assistance. * Phil. Mag. Sept, 1897. 3N 2 aN om XCIII. The Apparent Dispersion of Light in Space, and the Minuteness of Structure of the dither. By C. V. Burton, JI ASG , : 3 | i | Oe observations by Nordmannf and by Tikhoffft have been held by these authors to establish a dispersion of light in interstellar space: the velocity of pro- pagation appearing to be a direct function of the wave- length. On the other hand, the reality of the phenomenon has been denied by Lebedew§, who attributes the effects recorded to peculiarities of the star-systems observed. It is not the purpose of this note to discuss questions of astro- physics on which the views of specialists are so widely different, but rather to direct attention to a theoretical point regarding the possible scale of structure of the ether, and the relation which might be expected to obtain between that scale of structure and differences of velocity corresponding to radiations of given wave-length. 2. Amongst the considerations advanced by Lebedew, there is one concerned with the inevitabie connexion between dis- persion and absorption of light in material media. He points out that any known substance (hydrogen at low pressure, for example), if present in sufficient amount to give rise to the dispersion which has been inferred, would absorb so much light that the sun and the stars would be invisible to us. This appears to be undeniable, and accordingly it would seem that any definitely proved dispersion of light in inter- stellar space would have to be attributed to properties of the sether itself. Pe 3. In any homogeneous isotropic || elastic medium, which can be adequately treated as a continuum—that is to say, in which the specific properties of the medium in bulk exist unimpaired in any volume thereof, however small—any dis- * Communicated by the Author. + C. Nordmann, Comptes Rendus, cxlvi. pp. 266 & 3883 (1908) ; exlvii. pp. 24 & 620 (1908). : . + G. A. Tikhoff, Comptes Rendus, cxlvi. p. 570 (1908) ; exlvii. p. 170 1908). § P. Lebedew, Astrophys. Journ. xxix. no. 2, p. 101 (March 1909). || Though isotropy is not a necessary condition for ensuring that (in any given direction) the velocity of propagation is independent of the wave-length, the statement in the text is limited to isotropic media for the sake of simplicity of expression. The term elastic is used in its most. extended sense, denoting merely that it is possible to increase the potential. energy of the medium by doing work upon it, and that the medium is capable of doing an equivalent amount of work in reverting to its normal. state. . The Apparent Dispersion of Light in Space. 873 turbance of given type and of sufficiently small amplitude will be propagated with a velocity entirely independent of the wave-lengths involved. This is readily proved from general considerations, and familiar examples immediately present themselves. There is no better instance than the elementary form of electromagnetic theory, according to which an isotropic nonconducting medium is characterized simply by a definite dielectric capacity together with a definite magnetic permeability ; and the failure of any such simple theory to account for dispersion, 4. But although the dispersive and other optical properties of material substances compel our attention to their structure, there are as yet no well-established facts of observation which forbid us to regard the free ether as an absolutely homo- geneous medium, ideally divisible to any extent ; in a word, structureless. It is interesting to attempt to form some idea as to how far this elementary conception would have to be modified if the velocity of light ix vacuo were actually found to be a function of the wave-length. 5. Not knowing what kind of structure should be provi- sionally assumed for the ether, we are driven back on the consideration of mechanical models and analogies; these may perhaps furnish a hint as to the order of magnitude of the quantities involved ; as to the sort of relation which must hold between wave-lengths and the scale of structure of the ether if certain specified dispersion effects are to be accounted for. Essentially we must aim at representing a structure which will produce dispersion without absorption; or at least in which the absorption is far less than in any material medium of comparable dispersive power. 6. In the first place, consider waves of transverse dis- turbance which are being propagated along a loaded string of indefinite length. Suppose the string itself to be without appreciable inertia, while the loads, each equal to m, are concentrated at points which succeed one another at regular intervals (b) along the string. The transverse vibrations of a limited length of such a loaded string are fully investigated in Lord Rayleigh’s ‘Theory of Sound’*, and the results there obtained could be adapted to the problem now proposed. But the required relations can in this case be more simply deduced from first principles. We may confine our attention to vibrations taking place in a single plane which passes through the string in its undisturbed state. 7. Calling S the tension of the string, let y, denote the * Vol. i. § 120. 874 Dr. C. V. Burton on the Apparent (lateral) displacement of the rth load. The force on thie load is (S/d) (Yr-1 + Yrti— 2Yr), _ which is therefore equal to md?y,/dt?. Assume now that the motion is periodic, with period ae and let the motion of the 7th load be given by emp ehs's ills 2 Solutions can be obtained corresponding to the further assumptions that the motion of each of the remaining loads is periodic, and is represented by an equation of the same form as (1), while Ain /A,SAVAp,a= 1. =k) Then, if for brevity we write a = pbm/ 8). 4.) Se (e?—2)k+1i+tP?=05. . 9. ee it follows that whence | k=1—4e?+ia(1—de? 2. 8) 8. It is here supposed that the wave-length of the dis- turbance in question is sufficiently great to make pbm/S less than 4. If, then, we put k=B(cos8+7sin8) . ... J. as equivalent to (5), B and @ being real; we obtain on equating real and imaginary parts B=1 and tan@=+a(1—ie’)/(1—4a7); . (7 so that sin $8= +4e= +4 p,/(bm/S)...) . | ee 9. Rejecting now the imaginary terms in (1) and in the solution, there remain the given motion yr Ap Cospe 60 0 and the solutions Uri grm Ag Cos (pt gi) 5 iit) et where g is any integer positive or negative, and 8 is an acute angle given by (8). The lower sign corresponds to a wave-train propagated in the direction of g-increasing, the upper sign to a train in the contrary direction. In either case the amplitude is invariable throughout the train ; that is to say, there is no absorption. On the other hand (as Dispersion of Light in Space. 875 below), the velocity of propagation is a function of the frequency p/27, or in other words, it is a function of the wave-length. | 10. If x is the distance from the rth mass to the (7+ 4)th, then g=./b and (10) may be written y=A cos (pi+B/b.x); . . . . CI) the suffixes being suppressed. The velocity of propagation is thus | PY cre PA RE Sa werlh apy’: oxy Pv noes lacs) LEE MD = pb/2 sin-! {4,/(bm/S) =,/(bS/m) 1—-sk p*bm/S ...). . . (18) 11. For infinitely great wave-lengths (when p=0) (13) reduces to seh I a TUN: ances ion, Oi pens pe ee Gee Bite 9 Cast av pen fees t= —~—,t—{— 28, eel C7 —v cé—v This transformation reduces to the ‘one considered by Voigt *, Lorentz t, and Hinstein t, if we change the sign of a! and put Since 2a —y2 Dera 3%, : =a s(a—vt), t=t—->z (e—nt), —v ¢ it is clear that at any time every point of the moving mirror (w=vi) is transformed into itself. The image of a point moving with the same velocity as the mirror is another point moving with the same velocity, for if dots denote differentiations with regard to t The image of a stationary point, on the other hand, is a point moving with the uniform velocity 2ce7v C2 aE yy? . * Gottinger Nachrichten, 1887, p. 41. + Amsterdam Proceedings, 1904. { Ann. d. Phys, xvii. (1905). Tight at an Ideal Plane Mirror. 893 Further, since e+ 2c?v Y r= — stim = are pee he we have for a given value of ¢ c2 +? , 1 — tg= — a (1 ma )s The image of a stationary object, therefore, suffers a contraction proportional to c?—y? e+y =/1-% times its length in a direction parallel to the axis of 2. This is the proper contraction for velocity U according to the hypothesis put forward by FitzGerald* and LorentzT to explain the negative result of the famous experiment made by Michelson and Morley. To show that this transformation gives the correct laws of reflexion of a plane wave we introduce dashed letters into the argument of the periodic function of the reflected wave and make the necessary substitutions. The argument y/ fy x’ cos d!--y' sin ey 3 is then transformed into r k +v° — 2cv cos $', rea PG: +4sing'|, oa Cc? —v and if we compare this with ; [e+ z COS a sin 1, we obtain the relations (1). The transformation can evidently be applied to waves of any form. The formule connecting the components of the electric * Public Lectures in Trinity College, Dublin. t ‘Versuch einer Theorie der Elektrischen Korpern’ (1895). See also Larmor’s ‘ Aither and Matter.’ 894 Reflexion of Light at an Ideal Plane Mirror. and magnetic force in the incident and reflected waves are obtained by putting * [ + Ez’ dy'dz’ + E,! dzda' +H, da'dy! —cHz' dx'dt! —cH,/ dy'dt'— cH? dz'dt! | = Hidydz+ Hydzda + E.dady + cHidedi + cHydydt + cHedzdt, where (E,, Ey, Hz) (Hz, Hy, Hz) are the components of the electric and magnetic force respectively. Calculating E,’, Hz’... by means of the formule _p Oy, 2) O(Z, «) 0(#, ¥) 0 (2, t) E/=E, H i Hoy, a) crn Oy’; oye anit ae oe ae ee OL) Oz, 4 Hrs iy, 2) aG@aee we have / E, => + E,, avy nt a ee 2 Dp, 2 2 : +4 2cv F C+v 2cv A av, C2 vw Ky co 5 He, Hy — Te ee ae H,— go ple ce 2 , 2 2 ge ee OL Cali 2 aay Lk © 2cv E 2 EE These give Be + uh (E,+vH,), H,’—vH,'= — (E,— vHy,), Hy — oh,’ =— (H, —vEz), H,'+vEy’= —(Hz+ Ey). Relative to an observer moving with velocity v the com- ponents of the electric and magnetic force are Ex, Ey+ vHz K,— vHy ’ ‘ ® 15 By ee Reena IN se 2) Hence the above equations indicate that the sum of the tangential components of the two vectors in the incident and reflected waves is zero at the surface of the mirror. * See a paper by the author, Proc. London Math. Soc. 1909. Doppler Effect in Positive Rays in Hydrogen. 895 The formule of transformation for the convection currents and volume density of electricity are obtained from the equation * p'we’ dy'dz'dt! + p!w,! de'da'dt! + p!w da'dy'dt! — p'dx'dy'dz! = pw, dydzdt + pw,dzdedt + pwzdadydt — pdadydz, where (pwz, pwvy, pwz) are the components of the convection currents, p the volume density of electricity. Thus 2Qv @+v? = o We — ~o 5 ° nS micas, / sem Since (w,) (Xea) ? where X is the surface tension, and x”’ a constant which is the same for all liquids at corresponding states. Both of these formule are shown to agree well with the experimental facts. By means of the above and certain other relations given in the previous paper the following relations were deduced :— Lims wane ah: a ene ogee er eel T2mz 2 3 =i 5 ENG RRA) He 9 L denotes the internal heat of evaporation, and B and H are constants which are the same for all liquids at corre- sponding states. Another relation similar in form to (1) and (2) will be deduced in this paper. M*c, will be expressed as a function of p, m, and p, where M is a constant similar to B and H. The internal latent heat of evaporation of a liquid is given * Communicated by the Author. + Phil. Mag. Oct. 1909. t¢ Annalen der Physik, iv. p. 513 (1901). Phil. Mag. 8. 6. Vol. 18. No. 108. Dee. 1909. 3 P 902 Dr. Kleeman: Relations between Critical Constants. by the well-known thermodynamical relation, di L+p(m—%)=T(—r) aps where v, and v, are the volumes of one gram of the substance in the gaseous and the liquid states respectively, p and T denoting the pressure and temperature. Tor all liquids at corresponding states, v, and v, are both the same fraction of the critical density, or Vj=Ay/pc, y= Ae Pe» and therefore Y= ; where a is the same constant for all liquids at corresponding states. Thus | a a dp Wiel am ‘ Combining this with (1) we get ENS Gl eae ms p Pe pedi or peB? (2ca)ip? _—p , ap La Wie ie oe Dee pene each side of the equation by T and integrating, we obtain a (PB? (Zea)?pt om _ P 0+ |i ms regia dh Iixpressing the density and temperature in terms of the critical density and temperature, p=ap. and T= T,, the integral becomes —* pes(Zc,)? T (Bai mes. Pee) Ta Be ars $ (Xe,)? Bat _ p® (Ca) at = apt. ans VE ak \ a8? The part within the brackets is the same for all liquids at corresponding states, it may be denoted by N. The integrated equation becomes TC+ (2) (Se,)7 iN =p. and certain Quantities connected with Capillarity. 903 To determine C put p, p, and T equal to their critical values. The equation may then bé written e 1 (pe\5 ps 2{ P_ 5 ws Na or W (2ca) = Paha 8 - e (3) where W is the same for all liquids at corresponding states. Putting p=¢p-, which is approximately true, we have H-s)-wear() If we denote by M the quantities which are the same for all liquids at corresponding temperatures, we have (2) =o Se. Piet ata (4) At the critical state M is an indeterminate fraction, but its limiting value must be finite, because all the other quantities in the equation have perfectly definite values at the critical temperature. This equation will now be applied to a number of liquids at their critical state. The values of m, p,, and p, are given in Table I. (p. 904). The values of ¢, for the eight elements involved are obtained from the application of equation (1) * to the eight liquids, ether, methyl formate, carbon tetrachloride, benzene, fluor-benzene, bromo-benzene, iodo-benzene, and stannic chloride. It will be seen that M is approximately a constant for all liquids at their critical states. This shows that equation (4) is approximately true. The mean value of M is 116°8. From the physical behaviour of the liquids, water, methyl alcohol, propyl! alcohol, and acetic acid, it has been deduced that they are polymerized at ordinary temperatures. The surface-tension formule, in particular that of Hotvos, Ramsay and Shields, have not been found to apply to these liquids as the extent of polymerization, and therefore the molecular weight, is not known. In fact, the departure of the surface tension from that given by the formula of Hétvos, Ramsay and Shields, is regarded as evidence of polymerization, and the extent of it has been calculated by means of this formula. * See previous paper, Phil. Mag. Oct. 1909. 2P 2 904 Dr. Kleeman: Relations between Critical Constants TABLE I, Values of ¢g:— H=1, C=5:299, O=5:939, Fl=5757, Cl=8401, Br=10-60, 2 — 14°68, T=15-49, | Critical Name and formula pressure | Critical | Molecular p ‘oe 3 A ‘ & ° ° 6 of liquid. in atmo- | density. | weight. = (=) : spheres. | Panes Isopentane «.........+65 C;H,. 32°92 "2343 72°10 Lig Pentaile (2. ts snteros ese C5H,. 33°03 2323 72°10 120°5 Ag (25.012) Gia ae se etl 29°62 2344 | 8611 116°9 Me pianes pires-ecnssacee C,H, 26°86 "2341 100:13 127°3 Octane) ie deccceksaas As ee 24°64 2327 11414 113:2 Di-isopropyl .........+.. aang 30°72 2411 76:0 127°4 Di-isobutyl............... C,H,, 24°55 2366 11414 1108 Fluor-benzene ......... C,H;Fl| 44-62 3541 96:09 108°4 Bromo-benzene ......... C,H;Br} 44°62 4853 157 1193 Todo-benzene ............ 0,H;1 44°62 5814 | 203-9 1190 Chloro-benzene ......... C,H;Cl; 44-62 8654 | 1125 1s Hexamethylene ......... OMe 39°8 °2735 84:09 1150 Stannic chloride......... SnCl, 36°95 “7419 260°8 1176 Benzene a. o..2..sceee coe wae 47°89 "3045 78 118°2 2,0 alae Ge ae Me oy | C,H,,0| 36-28 “2604 74 1181 Propy! formate ......... O,0,)| 242-7 “805 88 118-0 Ethyl! acetate..,......... C,H,O,| 39°65 2993 88 1162 Methyl propionate ... CyH,O, 39°88 ‘300 88 1142 Propyl acetate ...... C31,,0,| 33:17 "2957 102 108°7 Ethyl propionate ...... C.H,.0,| 3464 "286 102 115°7 Methyl butyrate ...... C;H,,O.| 36:02 “291 102 115-4 Methyl isobutyrate ... C;H,,O,| 33°88 3012 | 102 107-6 Isobutyl formate ...... C5H,,0,| 38°29 2879 102 120°6 Carbon tetrachloride CCl, 44-97 5576 154 121-4 Hydrochloric acid ... HCl 86°00 ‘610 36°5 116°8 Carbon dioxide ......... CO, (re) 464 44 100°7 Ethyl butyrate ...... C,;H,,0O,) 30°24 ‘276 116 113-6 Ethyl] isobutyrate...... CHO) 3048 ‘276 116 113°4 Isobutyl acetate ...... Ca Oph aeelee "281 116 113°3 Methy! valerate ...... 0,H,,0,| 31-5 279 116 114°5 Amy] formate re C,H,,0,| 34:12 "282 116 Vt a Monochlorinated chloride ot be i . BLIGE, fo scenzsind > ere OFC), \ 53°0 4516 99 1247 Chloraldehyde ......... C,H,Cl,' 50:0 “419 99 132-2 | Methyl acetate ......... C,H,O2 47°54 320 74 1170 | Ethyl formate ......... C,H,O, 48:7 "315 74 120°6 fautasd formate,.!...... C,H,0, 56°62 3489 60 115-4 Rak CTT Stee ea ean { Mean ... 116'8 ‘ Wanker 45/14 pieicuuleree HO | 1946 | 2086 | 18 3186 | Methyl alcohol ......... C H,O 78°63 2722 32 145°9 ; Propyl alcohol ......... C,H,O 50°16 “2734 60 127°9 , INCOUG MOI) ia vases toate C,H Oo) cork 3506 60 | ij q A and certain Quantities connected with Capillarity. 905 The writer found that formula (1), first given in the previous paper, did not apply to the first three of the above- mentioned liquids, and the discrepancy was explained in the same way. The four liquids have, therefore, been placed separate in Table I. It will be seen that the constants for water and methyl alcohol differ considerably from those obtained for the liquids in the first part of the table. The values of the constants for propyl alcohol and acetic acid . are, however, approximately normal. Since polymerization decreases with increasing temperature it is probably small at the critical temperature, or perhaps zero. However, the polymerization at lower temperatures may modify the value of the critical constants, and thus produce a departure from the above formula. The formula (2) was tested in the previous paper for different liquids at 3 of their critical temperatures. In Table II. the same formula is tested for the critical tem- peratures. H appears to be approximately constant for all the liquids, and its mean value is 24°88. The polymerized liquids are placed separately in the table. As before, they show considerable deviations from the law, and probably for the same reasons. The equations (2) and (4) when referring to the critical state may be written —_ yy2( Pe 3 2 = iE ( *(Se,)”. nr Combining these two we obtain pe = MP p, 1 Hea’ or Bile =) i fe ie Hy? ne’ which is the well-known empirical law of Young and Thomas, which states that the critical temperature, pressure, and volume are connected in the same way as are the temperature, pressure, and density for a perfect gas. Young and Thomas expressed their results in the form _ RT~. ery A 10 : where R is the usual gas constant and A a numerical quantity 906 Dr. Kleeman: Relations between Critical Constants equal to 3°70. Comparing this with the theoretical form of the equation, we see that On putting R equal to 82°6 x 10° and the mean values for M and H from Tables I. and IJ., A is found to be equal to 3°66, which agrees well with the value given by Young and Thomas. Taste IT. Rea = | Absolute} H= ab fa critical | [3 /m\2 ‘e ae critical z 2 Name of liquid. tempe- | > (=)*. Name of liquid Lean Be (=)°. retune. rue rature, | ~°% \Pe Jsopentane | ....4.)-.0..... 460:8 25°41 : Isobutyl formate ...... .. 551° 24°31 Pentane.. «278 seas nes 470°3 25 25 Carbon tetrachloride ...| 5561 25°48 Hlexane: cP .ci ese 507°8 24-82 Hydrochloric acid ...... 325°3 29°41 Heptane ..... 6c EN 539°9 25°25 Carbon dioxide ......... 3043 21:13 Gatane . skies sn 569-2 24°56 | Ethyl butyrate............ 565'8 | 23°97 Di-isopropyl............... 500-4 28:95 Ethyl isobutyrate........ | 553°4 23°72 Di-isobutyl ...........-... 543-8 9373 |; Isobutyl acetate ........ 561°3 23°59 Fluor-benzene ............ 559-5 23:23 || Methyl valerate ......... 566°7 23°82 Bromo-benzene ......... 670-0 25°72 Amyl formate ..... ...... 5756 23°83 lodo-benzene ............ 721-0 25:58. Monochlorinated chlo- Chloro-benzene ......... 633:0 25:20 | ride Gfethiyl 2.2 a.cee 561°4 ' 27°43 Hexamethylene ......... 553-0 23°36 || Chloraldehyde............ 523-0 27°83 Stannic chloride ......... 591°7 25:03 || Methyl acetate ............ 505-9 23°82 IBSNZGNO Weesagaasenteceee b61°5 25-29 Ethyl formate ............ 503°0 25°38 CULES: AE GR GSK MMe 467-4 25:04 || Methyl formate ......... 487°0 2b'1t Propyl formate ......... 533°8 24:56 || = Fithyl acetate ........... 5225 | 24-60 | Mean ...| 2488 Methy! propionate ...... 28°7 24°68 | | Propyl acetate ............ 549-2 23°83 Waker | Vs oes 637°3, | Gaia Ethyl! propionate ......... 545-4 24-28 Methyl alcohol............ 513-0 34:37 Methyl! butyrate ......... 551-0 94-13 |) Peopyl aleqhol 02. 227-3. 5367 28°25 Methyl isobutyrate ...... 540°5 93°35. .\'\Acetie acidh)..csccce aaake 5946 28°40 If we apply equation (4) to liquids below their critiacl temperatures the agreement obtained is not so good. The reason appears to be that pressures at corresponding tempe- ratures are only roughly equal to the same fraction of their critical values which was supposed to hold exactly in deducing equation (4) from equation (3). That the agreement is best at the critical state would then indicate that the pressures for corresponding temperatures become more nearly corre- sponding pressures as we approach the critical point. The equation (3) should therefore apply better to a liquid in the form in which it stands. When the temperature is sufficiently below the critical Se Pe — = ed ol ene id and certain Quantities connected with Capillarity. 907 point, the value of p in equation (3) may be neglected in comparison with p,. Omitting p and combining equation (3) . with equation (1), we obtain | ny CeO Lg) Pe where U is a constant which is the same for all liquids at corresponding states. The value of a for values of L and p at temperatures equal to $T is calculated for a number of liquids (Table III.). The constancy of : —2°39 ,, , TaBLE VII. Remarks. | Time. | Pressure. Difference. | Added 75:52 c.c. (corr.) ...... 0-1 minute. — — | 3 minutes. 310 mm. —_ | | [ore Res 97. | es | Took out 5°69 c.c. (corr.)...... 4421 =~; oe _— | 54, 25:18 mm, _— (cae 25°05, —0'13 mm, | 9 Ns 24-61 ,, —O57 ,, | 13 hi 24774 —101 ,, 182 ,, 23°76 ., —142 ,, 33k, 22°84 , | —2°34 ,, 73 ay LANES 2h —366_,, 117 20°74 | 5 —444 ,, 4 hours. 20°56, —462 ,, ig os, 19°93); —i25 Sy, 1920). —598 ,, a ” 19-09 ” —6-09 ” 103 ,, Mig%er —6:20 ,, 123, 19°01 ,, —617 ,, 282, 20°43. ,, —475 ,, 45 99 24:01 ” —117 ” | | The importance of these pressure changes may now be discussed, for at first sight their magnitude appears to be: insignificant. Thus in Table VII. the highest pressure re- corded is that at 5} minutes, namely 25°2 mm., and the lowest at 113 hours, 19°0 mm. The high pressure indicated that out of the total 69°83 c.c. (corr.) of hydrogen in the apparatus 66°97 c.c. (corr.) was taken up by the carbon, and Adsorption of Hydrogen by Carbon. 923 at the lowest pressure 67°70 c.c. (corr.); that is a difference of 0°73 c.c., or just over 1 per cent. But attention must be drawn to the one feature of great significance, viz. that the higher pressure at 54 minutes was even less than corresponded to the gas condensed on the surface of the carbon, and yet after a dozen hours had elapsed a much lower pressure was attained, a pressure which then actually did correspond to the condensed gas in equilibrium with it. Thus a considerable body of hydrogen © has been transferred from the surface to the interior of the carbon. The extent of this transfer can be at least approximately calculated. The calculation may be based upon the assump- tion that at the beginning all the gas is on the surface, and that only after many hours does the interior solid solution reach its normal concentration. The pressure at 5} minutes (e. g. Table VII.) is certainly too low to correspond to the surface condensation alone (although it must be taken for the calculation), for there is considerable opportunity for diffusion to take place, even under the best circumstances. The approach to the value it would have were all the gas condensed in the surface and none in the interior, is clearly greater the sooner the pressure reading is taken after the removal of the gas, and the less amount removed from the apparatus and the shorter the initial exposure of the carbon to the gas at high pressure. The minimum pressure observed later on in the experiment requires two corrections. In the first place the value is higher than it would have been had no new gas passed into the carbon out of the bulb and manometer. This can be allowed for by using the equilibrium formula found by Travers *, 4/p=kz, where p is the pressure, and a constant, and «x the percentage of hydrogen sorbed by the carbon. In the second place the liquid air of the thermostat has been evaporating, its composition varying, and consequently the temperature slowly rising; a correction for this was made by blank experiments. If the calculation be carried out for the experiment re- corded in Table VII. an observed minimum pressure of 19:0 mm, is found. The temperature correction leaves ap- proximately 17°9 mm. The total amount of sorbed gas is | 67°70 c.c. (corr.), of which 0°73 c.c. passed into the carbon from the bulb and manometer spaces while the diffusion was taking place. Hence the true minimum pressure should * Travers, loc. cit. 924 Dr. J. W. McBain on the Mechanism of the 67°70\3 have been 17 9&5 33 was 25°2 mm. If the (equilibrium !) formula .°/p=ka be employed a value is obtained for the ratio of the amount of gas on the surface at the end of the exponent to that on the surface at the beginning Ry a 86°5 per cent. approximately. =16'°3 mm. The maximum pressure Hence 13°5 per cent. of the final sorbed gas is in a state of solid solution. 13°5 per’ cent. x.67°70 c.c. (corr.)=9'1 Cel (corr.) for 2°293 g. carbon. That is, the solubility of hydrogen in coconut carbon is roughly 4:0 c.c. (corr.) per gram at a pressure of 19 mm. and at the temperature of liquid air. These values are certainly too small, for the maximum pressure is not entirely due to surface-gas, and the minimum pressure would have still further decreased with time ata truly constant temperature. Table VI. gives the total amount of gas sorbed by the carbon at 7 and 275 minutes respectively, as 56°70 c.c. (corr. ) and 57:02 ¢.c. (corr.). The minimum pressure is 15‘7 mm., and after temperature corrections 15°5 mm., and this cor- rected for the new gas taken up becomes 15°2 mm. The ratio between the amounts of surface hydrogen at the end and the beginning is therefore 93°7 percent. Since 2°293 g. carbon was used the dissolved hydrogen is 1°6 c.c. (corr.) per gram under a pressure of 15°5 mm. If the dissolved hydrogen be proportional to the square root of the pressure (see later) the value calculated for 19 mm. from the above results amounts to 1°8 c.c. (corr.). From the conditions of the experiments the result obtained from Table VII. must be very much nearer the true value. Consequently, it appears that the order of magnitude of the solubility of hydrogen at 19 mm. at the temperature of liquid air is 4 e.c. (corr.) per gram of coconut carbon. Supersaturated Interior. Bare Surface. It appeared to the author that the best check upon the explanation of the qualitative phenomena studied above would be to attempt to produce the pressure changes in the inverse sense. This is possible if the carbon by long contact is allowed to become saturated with hydrogen. Now when this carbon is quickly exposed to a much lower pressure the surface at once gives up its hydrogen, while the diffusion of the dissolved gas requires time. Thus we have carbon with empty surface and supersabineel Adsorption of Hydrogen by Carbon. J25 interior. If a small amount of gas be then quickly intro- duced before this very unstable condition has disappeared, the interior is still surcharged with respect even to the new (intermediate) pressure, and it will continue to give off gas. Bui this effect is masked for a few moments because the surface is not saturated with gas at the new pressure, and consequently the hydrogen very rapidly condenses to make up the deficiency. It is clear that the cycle of changes must be rapidly carried through, and the following experiment shows how well the predictions are confirmed. The carbon had previously stood in liquid air, and exposed to 62°84 c.c. (corr.) of hydrogen, for twenty-four hours. After this the liquid-air vessel was filled up to the top once more, about an hour before the experiment began. TaBLE VIII. | Time. Pressure. Difference. | | Remarks. | | | 26 head aa | Pumped out 14°72 c.c. (corr.).| O minute. 22:0 mm. — | Added 4°70 c.c. (corr.)., O-43 minutes. — == al — . Gey; 14°59 mm. —_ | | 8 . | 14:54 ,, —0:05 mm.' ) | Ov Wve R ive, h, LAGS. 0:08 ) 12 ? 14°63 ,. +004 ,, | 14 be | 1466_,, +007 ,, | ) 25 a 14°78 ,, +019 ,, | 47 “3 14°87 __,, +028 ,, | | 2 hours. LOS... +044 ,, | ) ea | 15°42 ,, +083 ,, | 20 ” 16°51 2” +192 2 | ! ee = Poa: 4 ah. i Sm > BR The characteristic phenomena of the previous experiments have here been reversed (in the most thoroughgoing manner), and yet the results are entirely in accordance with the hypothesis that has been advanced. Blank Experiment. The complexity of the pressure changes described in the foregoing paragraphs makes it desirable to be certain that these complications do not occur where not predicted by the theory of the process which I have advanced. In the follow- ing experiment a portion of the gas was removed from the apparatus after the carbon had been standing for a day in contact with it at the temperature of liquid air. The total 926 Dr. J. W. McBain on the Mechanism of the amount of hydrogen was 71 ¢.c. (corr.) of which 19 ¢.c. (corr.) was removed. TABLE [X. Remarks. Time. Pressure.. | Difference. Removed gas ......secsseeseeee 0-73 minutes. — _— bs 8:43 mm. | — 1Ginitey $51 ,, | 4008 mm | 12 4 BD ie +012 ,, ee 53 860 _,, +017 ,, Pls ” 8°68 ” =f 0°25 ” | 26 2? 8°76 ” at 0°33 ” | | 50 ” 8:88 ” aia 0°45 ” | 5 hours. DDN sy +079 ,, | pemeail a aN 10°96." ,; +13 | ! As expected, the sign of the pressure-change is constant. Surface Equilibrium. It is clear that adsorption does not take much time, for in one experiment quoted later (Table XV.) carbon was ex- posed to gas at a pressure of 1200 mm. at room temperature. Tt took only 65 seconds to plunge the whole of the carbon bulb into liquid air, but meanwhile the pressure had fallen to 35 mm. But while the initial stages of the surface condensation may consequently be enormously rapid, it does not follow that the final equilibrium value is fully attained in such a short time. The following experiment was carried out in order to test this point. The carbon bulb was allowed to stand for a day in liquid air with 59 ¢.c. (corr.) hydrogen. Then a measured amount of gas was added and almost im- mediately removed again. TABLE X. | Remarks. . Time. | Pressure. Difference. Put in 12°49 e.c. (corr.) «..... | 0 minute. _ | = 1 ‘. 35°6 mm. | — 23 minutes.| 3405 ,, — Removed 13:14 c.c. (corr.) ...) 3-5 ,, — = oD Sha tae 20°26 mm. | — ne 2035 ,, | +009 mm 13 a 2040 ,, | +014 ,, 19 4 20°47 ,, +021 ,, 47 i 20°47 ,, +021 ,, 88 Hy 20°49 ,, + 0°23 =, Adsorption of Hydrogen by Carbon. 927 The effects of this considerable disturbance had vanished in less than 14 minutes, which observation affords a maximum value for the time required for surface equilibrium and for thermal effects. Indeed even this must be mainly attributed to the diffusion simultaneously involved. Part of the diffu- sion is further due to the fact that rather more gas was taken out than was added. Surface Action at Higher Pressure. Since the amount of solid solution is proportional to the square root of the pressure (see later), whereas the amount ot adsorption varies only with the cube root of the pressure, diffusion must be much more prominent at higher pressure. For this reason the isolation of the time required for surface action is much more difficult. No attempt was made in the following experiment to minimise this disturbing diffusion factor. The procedure was as before, except that the hydrogen was removed by quickly opening the connexion to the Toepler pump and then the same amount of gas was replaced a few minutes later. TABLE XI. Remarks. Time. | Pressure. | Difference. | | | O minute. 161°3 mm. — | Removed gas .......... ates 0 a — — | 3 minutes. 120 mm. — | Put gas in again ..............: 3 a -— ~~ 4 - | 175°3 mm. — ) 6 - he ASG soe — 9-6 ram. | He eat 1688, | ee 24 i | IG2 0. —128 , | | ZO oP 609. | 4 hours. ORs se oy ae —147 , | Solubility at Higher Pressure. As would be expected from the relatively great import- ance of diffusion at higher pressure no alternation was’ here observed in the sign of the pressure changes when carrying out experiments of the type of those in Table VII. 928 Dr. J. W. McBain on the Mechanism of the TABLE XII. Remarks. | Time. | Pressure. Difference. | q Soh | | Added 35°39 c. c. (corr.) ...... 0°10 second. — a | L minute. 380 mmm. —_ | minutes. ABO 2; — 100 mn. MA POD", jay — 125 ,, | Took out 5°60 c. c. (corr.) ... 3 cn — — heat’ 5 “s 139°1 mm. — | 6 ” 1348 _,, — 43 mm. 9 be 1279 —112 ,, 39 of 108°5 ,, — 306 ,, | a! ss oo ae Gk — 434 ,, | hours. 89:0 ,, — 501 ,, | 9 oF) 88:0 +B) ay 51°] a 10 ae Oe OP isy —514 ,, 19 . 894), —49°7 ,, 23 A 90°8_,, —483 ,, | TABLE XIII. | Remarks. Time. Pressure. ) Difference. | Put in 42717 ¢.\c¢. Xcorr:)'..:... 0 minute. _- | — se — 495 mm. | — 3 minutes, 405 35, | — Took out 6°34 c. c. (corr.) ...| 34-3% ,, — — | 5 a 231°0 mm. — ge 2203S, — 105 mm 12 o 2006 ,, — 304 ,, 32 ns 7S — 52:3 ,, 100 ne 1659.5. —651 , | 2 hours i6is 2 G05 ae LOE e053 LeO-5) 3: —70°5 ,, l i LOO Ties = "FOR nee 23 fs 1650" ,, °° || = GG Less than ever can these experiments realize the full value of the diffusion effect. Table XII. yields the following computation :—Volume of bulb 7°40 c.c. Total gas taken up by the carbon at 5 minutes and 10 hours, 25:10 e.c. (corr.) and 26°84 c.¢. (corr.). Minimum pressure 87°7 mm.; corrected for temperature drift 84°2 mm., and for extra gas. sorbed 68°9 mm. The ratio between the final and initial surface hydrogen is therefore 79 per cent. The carbon weighed 0°626 g. The dissolved hydrogen ata pressure of 88 mm. is therefore 8°9 ¢.c. (corr.) per gram of carbon. The corresponding calculation for ‘Table XIII. :—Bulb Adsorption of Hydrogen by Carbon. 929 7-40 c.c. ; gas in carbon at 5 minutes and 10 hours, 28°04 c.c. (corr.) and 30°40 c.c. (corr.).. Minimum pressure 160°5 mm., corrected for temperature drift 155°5 mm., and for extra was 12270 mm. Therefore the ratio between final and initial surface condensation is 81 percent. The dissolved hydrogen under a pressure of 160 mm. is thus 9°3 ¢.c. (corr.) per gram of carbon. Inaccurate as the absolute values must be, yet the mathe- matical treatment has shown that all the values (apart from experimental error) are affected by a relative error of the same order of magnitude for each case. Thus the relative values may be subsequently trustworthy to give an insight into the variation of the solubility with the pressure, and hence to furnish information with regard to the molecular weight of the hydrogen dissolved in the carbon. A large part of the inaccuracy must be ascribed to the inconstancy of the temperature of the thermostat and to the difference of 3 to 4 degrees in absolute temperature depending upon the liquid air employed in different experiments. Again, the formula here employed is not the true absorption formula but the total sorption formula v ee The hypotheses between which it is necessary to discriminate are that the dissolved hydrogen : (a) is polymerized, (6) has the same molecular weight as in the gaseous state, or (¢) is dissociated into atoms. In the first case the solubility will be proportional to the square (or higher power) of the pressure, in the second directly proportional, and in the third proportional to the square root of the pressure. In the following Table a comparison is made between these assumptions. TABLE XIV. : Pressure. | Solubility observed. Calculated for H. He. Hy. 19 mm. | 4:0 c. ¢. 4lee 19c. ce, 04 ec. 88 mm. | 89 c. ¢c. 89eae 89c.c. 89 c.c. 160 mm. | 9°3 c. c. 120c.c. 162¢.c. 29°4c.c¢. The results thus lead to the deduction that dissolved hydrogen is split up into atoms, and it further follows that 930 Dr. J. W. McBain on the Mechanism of the the ratio between the absorbed and adsorbed hydrogen is proportional to the pressure. It is very important to point out that these experiments at a high pressure constitute a direct disproof of the funda- mental assumption of the clogged diffusion column hypothesis. For they show that just the same length of time is taken for hydrogen to diffuse at 160 mm. pressure as is taken at 20 mm. ; whereas Zacharias’s hypothesis had predicted that it would take sixty-four times as long. Solubility at Room Tenperature. There is no reason why the methods presented in the previous section should not be applied in the demonstration and measurement of the solubility of hydrogen in carbon at room temperature (compare also page 919). Instead of this, carbon was exposed to hydrogen for a day at a pressure between one or two atmospheres at room temperature. The carbon bulb was then quickly plunged into liquid air, and experiments of the type of Table VII. were carried out with it. The apparatus contained for the first day 58:06 ce. c. {corr.) hydrogen. TABLE XV. Remarks. Time. Pressure. Difference. O minute. 1200 mm. — | Cooled in liquid air............ Q-1 Ms 35 A Ss 12 31 A — 4 mm. 5 minutes, Bend fuss —11°3 ,, 29 ” 217 ” —13°3 ” | Removed 4°68 c.c. (corr.) .../31-32 __,, — caus 34 5 18°32 mm. — 36 My 18°39)... +0:°07 mm. 38 i 13385) 45 +006 ,, i 56 Hs 18:24 ,, —008 ,, 142 Ms Leal ce —091 ,, 4 hours. 16°54 _,, —178 ,, ane 16°35 __,, —1:97 ,, TO as 1659; —1-73 ,, The amount of gas which had passed into solution subse- quent to the slight removal at 31-32 minutes is therefore 3°5 ¢.c. (corr.). From this the solubility at 19 mm. would be 3:9 c.c. (corr.). But it was shown (page 924) that the Adsorption of Hydrogen by Carbon. 931 total solubility at 19 mm. was 4:0 c.c. (corr.). The differ- ence between the two numbers (which in these particular experiments were merely semiquantitative) indicates the excess of solubility of hydrogen in carbon at the tempera- ture of liquid air (at 19 mm.), over its solubility at room temperature (under 1200 mm. pressure). It follows that the solubility of hydrogen in carbon at room temperature is nothing like as great as that at the temperature of liqud air, even though the gas pressure be 60-fold greater in the former case. Ofcourse the pressure difference may be allowed for on the assumption that the solubility at room temperature also varies as the square root of the pressure, and the two solubilities may then be compared directly. Here we get the result that the solubility is at least a hundredfold greater at the temperature of liquid air. For accurate work a thermostat of fixed and constant tempera- ture (e. g. liquid oxygen) would be required, and compara- tive experiments would have to be carried out under strictly comparable conditions. Probably the most accurate method of all, which was not investigated, would consist in exposing the carbon at room temperature to greater and greater pressures of hydrogen, until on plunging the carbon bulb into into liquid air, the pressure becomes quite constant within say fifteen minutes (time for the carbon to assume the temperature of the liquid air). It is easily seen that this phenomenon will only be observed when the actual amount of dissolved hydrogen at _ room temperature under very high pressure is the same as it is at very low temperature and pressure. Thus, the relation- ship between solubility and pressure at ordinary temperature might be studied. It is interesting to note that this method measures directly the difference in the amount of surface condensation at the two temperatures. This follows from the fact that owing to the conditions of the experiment, the solid solution is constant in amount. Sorption at Room Temperature. The diffusion of hydrogen into carbon is not quite instan- taneous even at ordinary temperatures, as shown by the following experiment (among others) :— 932 Dr. J. W. McBain on the Mechanism of the TABLE XVI. Remarks. Time. | Pressure. | Difference. Added hydrogen ............... 0 minute. = = 2 minutes, 142°9 mm. — 9 Mi 142°5 ,, —0-4 mm. 14 ve 1423'S" —0O6 ,, 8 M4 14271 ,, —08 ,, 45 =e 141°9 ,, —- 1 ee 4 hours. ih iS ates -1l0 ,, Further investigation of sorption phenomena at room temperature was not undertaken. The question as to whether the smallness of the effect measured here is due to the rapidity of diffusion at this temperature or to the relative unimportance of the absorption factor was left untouched. Discussion of the Results. The main thesis of the present paper is the demonstra- tion that the so-called adsorption of hydrogen by carbon is dual in its nature. The striking fact upon which this is based is that hydrogen is temporarily evolved from unsaturated carbon, and that such gas is taken up by carbon, which is known to be already supersaturated. It is considered that the experiments disprove the simple surface action theory. Their weakness consists in the fact that they do not in the same way exclude a clogged diffusion hypothesis *. The only refutation of the latter that it seems possible to bring forward appears to be, first, that it is irreconcilable with the known laws of diffusion, and secondly that the fundamental assumption of the clogged diffusion hypothesis has admitted of direct experimental disproof (page 930), for this assumption was that diffusion would be more difficult and slower the higher the pressure or concentration. In Davis’s paper t the method adopted for showing the co-existence of surface action and solid solution, when iodine solutions are exposed to carbon, was as follows :— It was first demonstrated that an equilibrium of some type * See, for example, Zacharias, Zeetschr. physikal. Chem. xxxix. p. 468 (1902); Travers, loc. cct.; compare Zeitschr. physikal. Chem. \xi. p. 241 (1907). Tt Davis, loc. cit. - Adsorption of Hydrogen by Carbon. ie could be attained in a short time ; for the amount of sorption after a day was the same when approached from both directions (supersaturation and unsaturation), a phenomenon which is characteristic for all equilibria, This equilibrium point lay, however, appreciably below the final saturation value attained after several weeks. Hence the first equilibrium value was referred to surface condensation, and the after increase was ascribed to diffusion. It should be mentioned that in these experiments with iodine as in those with hydrogen the diffusion effect is greater than it at first seems ; for it is partly masked by the necessary simul- taneous transfer of some of the surface accumulation into the interior, as the concentration of the liquid iodine solution falls off. This method was not employed in the experiments with hydrogen, for it would demand a thermostat of accurately reproducible and sensibly constant temperature, such as furnished by liquid oxygen. The weak point in Davis's proof lay in the fact that the after diffusion etfect could be ascribed to pores and fine cavities in the carbon employed. Consider a tiny cavern in the carbon, having a relatively very small entrance. As soon as the carbon was wetted, the cavern would prebably become filled with solution. Practically at once the walls of this cavity would become permeated with surface condensa- tion of iodine. But the amount of carbon surface which would have to be supplied with iodine from the small amount of enclosed solution might easily be relatively much greater than the total carbon surface which was supplied from the total iodine solution in the vessel. Thus the minute amount of solution in the enclosure would become very much weaker than the main bulk of the solution. Since the only commu- nication with the body of the liquid outside would be through the small opening of the pore or cavity it follows that a slow diffusion would take place, but it would be diffusion through the liquid enclosed in the pores. But the whole purpose of the method is to ascribe this after diffusion effect to diffusion in the solid carbon phase. Conse- quently the existence of this possible objection must be taken into account. It is true that experiments might be carried out on finely pulverised carbon, and where the pores were excessively small (molecular dimensions) the objection would fall to the ground, as diffusion would then become nearly instantaneous. It is, however, satisfactory that such objection cannot be Phil. Mag.§S. 6. Vol. 18. No. 108. Dec. 1909. 38 934 Adsorption of Hydrogen by Carbon. urged against the experiments with hydrogen, nor against the methods employed in the present paper. | No mention has been made in the preceding pages of the large evolution of heat which accompanies sorption. I¢ will certainly influence some of the methods employed, as sorption is very sensitive to temperature changes. Fortunately, however, the experimental results cannot be ascribed to such effects. Most probably the effects of these heat changes would be in the very opposite direction to those observed in each case ; this is practically certain in Table VIII. where the manipulation was very rapid. However, Table IL. may be discussed ; immediately after the final removal of gas the carbon must be either warmer or colder than the liquid-air bath. In the first case the above sentence holds good, the temperature influence would be opposed to the observed pressure changes. The second case is obscure unless it is clearly kept in mind that throughout the whole period from “14 minutes” toa couple of hours later the carbon is not saturated with hydrogen even at the higher final temperature; hence if sorption be simple and not dual in its nature the observed intermediate rise of pressure is a priori impossible. A division of the total surface condensation into more accessible and less accessible regions does not suffice to meet this difficulty, for it ultimately leads to the untenable alternative explanation of my experimental results—that a considerable fraction of the surface of coconut carbon, at the very lowest estimate one-seventh, is so inaccessible that a dozen hours are necessary for hydrogen to come fully into contact with it. Similar reasoning holds for Table VIII. Finally there remains but one objection to be discussed. The apparent after diffusion effect cannot be caused by slow chemical action ; for it always ceased after some hours, and further no difference could be detected in the amount of hydrogen before and after the experiment. Summary. 1. It is considered that the “adsorption” of hydrogen by carbon has been definitely proven to consist of a surface condensation and a ditfusion (solid solution) into the interior of the carbon. 2. The surface condensation is nearly instantaneous at the temperature of liquid air, requiring only a few minutes zv maximo ; whereas the diffusion requires about twelve hours. 8. Various experimental methods have been elaborated for the isolation and study of these phenomena. Geological Society. 935 4, An approximate measurement was made of the true solubility (as distinguished from the surface condensation) of hydrogen in the coconut carbon. At the temperature of liquid air it varies with the square root of the pressure. Hence hydrogen dissolved in carbon is split up into simple atoms. The solubility amounted to 4 cc. (corr.) hydrogen per gram of carbon at a pressure of 19 mm., equivalent to one seventh of the total gas taken up by the carbon. The true solubility at room temperature is less than one hundredth as great. 5. Since “adsorption ” in the only cases hitherto investi- gated has been shown to be of a dual nature, the general non-hypothetical term sorption is proposed to embrace ail adsorption and occlusion phenomena. University of Bristol. July 27, 1908. C. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. | Continued from p. 820. ] April 7th, 1909.—Prof. W. J. Sollas. LL.D., Sc.D., F.R.S., President, and afterwards H. W. Monckton, Treas.L.8., Vice-President, in the Chair. a following communications were read :— 1. ‘On Overthrusts at Tintagel (North Cornwall)’ By Henry Dewey, F.G.S. In this paper the author deals with the geological structure of the Tintagel area. After brief reference to the stratigraphy north of Bodmin Moor, mention is made of the apparent difference in order of superposition of the beds near Tintagel. The several types into which the Upper Devonian rocks are divided are next described. The beds in descending order are :— (6) Tredorn Phyllites. (5) Trambley Cove Gritty Slates. (4) Volcanic Series. (3) Barras Nose Beds. (2) Woolgarden Phyllites. (1) Delabule Slates. The above order is preserved for many miles, between the Boscastle coust and Lewannick on the eastern side of Bodmin Moor. A change of strike at Tintagel reveals the anticlinal structure of the district. To the south of the nose of this great fold, minor folds eross the strike. These folds increase westwards, until they are $36 Geological Society. replaced by overthrusts. Four sections from east to west show the increased folding and overthrusting towards the northern part of the area. The paper concludes with a reference to the age of the folding. 2. ‘The Lahat “ Pipe”: A Description of a Tin-Ore Deposit in Perak (Federated Malay States).’ By John Brooke Scrivenor, M.A., F.G.8. (Geologist to the Federated Malay States Government). Large quantities of tin-ore have been obtained during recent years in the Kinta district of Perak, principally from detrital deposits, but also in some cases from the limestone which forms the floor of the Kinta Valley. From 1903 till 1907 the Société des Etains de Kinta secured over 1000 tons of dressed tin-ore from a peculiar deposit which had the form of a pipe in the limestone, measuring only 7 feet by 2 at the surface, but widening when followed downwards. It was worked to a depth of 314 feet. The veinstone was a deep red mixture of calcite and iron-oxide with some quartz, chalybite and chalcopyrite, but no tourmaline was found in it. In this the cassiterite occurred in irregular pieces and broken fragments, some of which consisted of radiating needles. In Kinta the tin-ores occur in the limestone in two different ways :—(1) As lodes or veins with fresh sulphides but not iron-oxides. ‘The tin-oxide crystals have a definite arrangement. (2) As transformed masses, deposited in fissures. The cassiterite is in rounded grains, and quartz, tourmaline, and other minerals, also well rounded, accompany it. For a long time, it has been doubtful to which of these classes the Lahat pipe should be assigned, as it presents some features of each class. Recently, however, specimens have been obtained showing veins of arsenopyrite and cassiterite in limestone, and from these the author concludes that the Lahat pipe was originally a vein or lode-deposit in the limestone, which sub- sequently afforded a course for surface-waters ; these dissolved away the calcite and oxidized the sulphides, caves being formed ‘into which the insoluble ores were carried by the water. Finally, the brecciated mass was recemented. Some foreign material has been introduced, but the bulk of the contents of the pipe is of local origin and consequently not rounded by transport. In other words, the Lahat pipe is a lode-deposit which has been converted intoa detrital deposit an situ. 3. ‘On the Sculptures of the Chalk Downs in Kent, Surrey, and Sussex.’ By George Clinch, F.G.S., F.S.A. Scot. The author classifies the various forms of sculpture of the Chalk Downs under three heads, namely, (1) dry valleys of simple form, (2) dry valleys of complex form, and (3) wet valleys. He draws attention to the relatively small catchment-areas of the dry valleys, and to the large number of tributary valleys found in some districts, two points which he considers have not received hitherto entirely satisfactory explanation. : | i Se . ~ METCALFE. Phil. Mag. Ser. 6, Vol. 18, Pl. XXTX. Fig. 2. a SaaS 80 ie) Zee CMS. OF 14, SO; TEN, ae) A . 130 ‘ a id at Lo¥ q 1. 2 . > Se ea “ isteres) a a ey ee RY a ee ED a he le ae a ree oe a 4 id ny eee ee ee a ae eer ee eames Ape en eae eee Peden aye weeony © H ee en eee ae UE ee ene Pee $ i ; } ; ; Ne i ! Zi barton 2 ; { j j i ¢ po tetawe eee = y : i } \/ ; i ~ ‘ ; t neem ener Deere ttn ream erceDeS ye a regen ane dene She TIS Sets erjreme enn emi nsw : t ery as ree ern, Chore Py SRN He re Neaenticnonpee se TEI Esa af Pane nent ri si ee oie oh emygttn shea enc Serer See ae “bite soembmticency aetna ct has. 2 ana SNE ested ts Get Teel eniatet aie See AD aah IME ASS, Seo ver wet * “es oe Cras i i) AP AAT ENO ED PR (A PAROS STI PNET Me ee =o a TR NR > re SE Ze ae ‘ , a Sa <- = 2 ve o Pak~ . é . y ~ MADSEN. Fie. 4. Rt Bens See SS eee ee TS eT as sa eS jel te a (A al ei (a Ga cl Eee be zc Ses + AEs ee ee [ fe Lt ee Ee l 200} CURRENT 70 ARBITRARY SCALE. -004 008 OF 06 -02 “04 : ; GRAMMES PER SQ. CM. WIS YId SINWYY! 10: G0: seer |. naval | | | Hel So cee ee WC a | > aa Eta owe Bato nae 0 BaaMenaees Phil. Mag. Ser. 6, Vol. 18, Pl. XXX. CURRENT 70 ARBITRARY SCALE. & = oOo Ss = &) = a Ss Sa SS [ESSha SS eRaei memes __ JERR Saee Sy =e a m ® t | aa0 |_ Lets z ; : Bry || y || _ -USEERE. | « Snr aean Zee cape +H SESS [aky Be Se @ meh | meee | alt Bemh |_| al. | || SEES oe “OTT r) ’ “¢ ~] Intelligence and Miscellaneous Articles. 93 While accepting the view that frozen conditions in former times altered the drainage-system of the Chalk, he argues that the most potent excavating force was the frost itself acting on Chalk saturated or highly charged with water. He propounds a theory to account for (1) the great size and breadth of the valleys in relation to their eatchment-basins ; (2) the ramifications of some of the valley- _ Systems ; and (3) the remarkable fact that many dry valleys die out just before the crest of the Chalk Downs is reached. CI. Intelligence and Miscellaneous Articles. INDUCTANCE AND RESISTANCE IN TELEPHONE AND OTHER CIRCUITS. the paper published by me, under this title, in the Phil. Mag. for September last, there is an error to which I desire to call attention. ‘The magnitude A in the investigation should be replaced by /?c, so that, in the results, p stands not for log. hu, but for log, A7ac. Trinity College, Cambridge, J. W. NIcHOLSoN. November 17, 1909. THE ULTIMATE PRODUCT OF THE URANIUM DISINTEGRATION SERIES. To the Editors of the Philosophical Magazine. GENTLEMEN,— Manchester, Nov. 24, 1909. I would like to correct a mistake which occurred in a paper of mine, published in this month’s Philosophical Magazine. Taking lead as the final product of the uranium series, I find the age of —4 some autunite to be dx 1079 Years, or nearly 10,000 years, not a million years, as appears in the paper. As in the calculation no account was made of the fact that radium takes some time to reach equilibrium with the uranium, a greater age must be given to the mineral. I am, Yours faithfully, J. A, Gray. [ 938 J INDEX vo VOL. XVIII.