" E —- = : Se Soe “ps ean = x aie me bs . si —_ rae 845 PE es > —r- os SS Sit Sle 4 DRIORIONT YIP OLIN LILI PIPES YACMAPYIVNLPNNLHLY w) <4) VA ane e> % Sees rr is ae = 3 ears & £0 f= a QD pert Cae Sas ul (S Y% | e— co a) nat ny %& YY ey 6 * = re i % ot, g a i % xy wa a © a 2 . S, O Ls 3 8 : — %* x eB) a) r% Ly} Star ParSPar Far Ka Taso Car Pac Car Fa Lar Lar Mor Pov PIAL HALILILILIN GOVERNMENT PRENTING OFFICE THE LONDON, EDINBURGH, anv DUBLIN PHILOSOPHICAL MAGAZINE AND _JOURNAL OF SCIENCE, CONDUCTED BY LORD KELVIN, LL.D. F.RS. é&c. GEORGE FRANCIS FITZGERALD, M.A. Sc.D. F.R.S8. AND WILLIAM FRANCIS, Pu.D. FL.S. F.R.A.S. F.C.S. “Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not. ——___ VOL. XLIII.—FIFTH SERIES. JANUARY—JUNE 1897, LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. SOLD BY SIMPKIN, MARSIIALL, HAMILTON, KE NT, AND CO., LD.; WHITTAKER AND CO. ; AND BY ADA M AND CHARLES BLACK Sauls ANDY Te CLARK, EDINBURGH ; SMITII AND SON, GLASGOW »--HODGEs, FIGGIS, AND CO., DUBLIN ;— PUTNAM, NEW YORE 5-- VEUVE J. BOYVEAU, PARIS ;— AND ASITER AND CO., BERLIN, “Meditationis est perscrutari occulta; contemplationis est admirari perspicua .... Admiratio generat queestionem, questio investigationem, investigatio inventionem.”—Hugo de S. Victore. “Cur spirent. venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obsura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas, Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tam yario motu.” J. B. Pinelli ad Mazonium. f FLAMMAM. CONTENTS OF VOL XLIII. (FIFTH SERIES). 10637 NUMBER CCLX.—JANUARY 1897. Prof. A. Schuster’s Electrical Notes.—I1I[. On the Magnetic Forces acting on Moving Electrified Spheres............ — Mr. W. Sutherland on Boyle’s Law at Very Low Pressures. . Prof. W. Stroud and Mr. J. B. Henderson on a Satisfactory Method of Measuring Electrolytic Conductivity by means emEMnOnS CUTPENtS. i eben ee eee Sn ee — Miss Dorothy Marshall on the Heats of Vaporization of Maqmdsat ther Boiling-Points ........5..00 20. 0- nee: Dr. Charles Davison on an Error in the Method of Deter- mining the Mean Depth of the Ocean from the Velocity etEmemieisea- Waves 227 jer iat. bee kk Meee ee Prof. Andrew Gray on the Estimation of ‘“‘ Waste Space round mie Needle of a Galvanometer” ..0.....002.6 cca ee eee Dr. E. H. Barton and Mr. Geo. B. Bryan on Absorption of Electric Waves along Wires by a Terminal Bridge .... Prof. J. G. MacGregor on the Relation of the Physical Properties of Aqueous Solutions to their State of Ionization. Prof. J. C. Bose on a complete Apparatus for the Study of Peeeemeperiics-Or Elecite Waves... 2. ets... es Notices respecting New Books :— Dr. F. Bedell’s Principles of the Transformer ........ Geological Survey of Canada: Annual Report, Vol. VII. The Scientific Papers of John Couch Adams. Vol. I... Proceedings of the Geological Society :— Prof. T. G. Bonney on the Sections near the Summit of pce utckawkass (om™ltzerlamd)\ Sos .0e 4 ce 4 go eves Dr. T. L. Walker’s Geological and Petrographical Studies of the Sudbury N ickel District (Canada) . Dr. Charles Davison on the Distribution in Space of the Accessory Shocks of the Great Japanese Earthquake or LUD, "oR a AS lanes ny rire ena On the Action of Rontgen Rays on a Jet of Steam, by Franz LSE 2 2d a ea a ea ae Page iV CONTENTS OF VOL. XLIII.—FIFTH SERIES. NUMBER CCLXI.—FEBRUARY. Page Messrs. John Trowbridge and T. W. Richards on the Spectra of Arvon: .¢ ...4...502) see ee eee fe Mr. W. Sutherland on Two New Pressure-Gauges for the Highest: Vaeua ... «wa sie ese Soe ee oe eee 83 Prof. J. G. MacGregor on the Relation of the Physical Properties of Aqueous Solutions to their State of Ionization. 99 Mr. W. Barlow on the Relation of Circular Polarization, as occurring both in the Amorphous and Crystalline States, to the Symmetry and Partitioning of Homogeneous Structures, 2.¢. of Crystals 2.0.2... dacs met « Vases 2 ee 110 Dr. G. A. Miller on the Transitive Substitution Groups of Order 8p, p being any Prime Number .......-=. eee 117 Lord Rayleigh on the Passage of Electric Waves through Tubes, or the Vibrations of Dielectric Cylinders ........ 125 Angelo Battelli on Photographic Action inside Discharge MBeS she =. m4 woe aa tees oS a A ee Sr 133 Messrs. J. Trowbridge and T. W. Richards on the Multiple DPECiTA OLAGASES 2. oc a dee oy 1 et ee 135 Dr. G. J. Stoney on the Generality of a New Theorem .... 139 Prof. Osborne Reynolds on Thermal Transpiration and adiometer: Motion % .c8 pcs. dna Sele ee: 17, for 2—* or -63 read (3/2)~® or +76. _ iy 18, , for 13 read 15 ” 99 298, in the second table, in the column headed L;, for 80:01 read 88 Ol. 316, line 4 from bottom, for eB read eBra. ae as ~s % a Hs ’ THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. % 6 Ss [FIFTH SERIES.]_-*" gy + iA Pain & se JANUARY 1892, “1 1897 I. Electrical Notes. By AxtHur Scuuster, F.R.S. Ili. On the Magnetic Force acting on Moving Electrified Spheres*. ea IC opinion inclines to the view that electric conduction in gases and liquids is a process of molecular convection, the moving particles being charged with definite quantities of electricity. If we follow out that hypothesis we meet with a number of problems in which it becomes necessary to calculate the effects of magnetic forces on charged and moving electrified particles, and also the mutual magnetic effects of two or more such particles. To some extent the old question of the behaviour of current elements is thus renewed, although the recognition of “displacement currents”? has diminished, if not entirely removed, the ambiguity of the problem. The question of the magnetic field produced by a moving electrified sphere and the magnetic reactions on the sphere was first attacked in an important paper by J. J. Thomson f. \ Some time afterwards it was reopened by Heaviside t, who, | “whilst agreeing with J. J. Thomson in the fundamentals,” was “unable to corroborate some of his details.” J.J.Thom- son returns to the same problem in his ‘ Notes on Recent Researches in Electricity and Magnetism.’ As regards the * Communicated by the Author. t+ Phil. Mag. vol. xi. p. 227 (1881). £ Ibid. vol. xxvii. p. 824 (1889). Phil. Mag. 8. 5. Vol. 43. No. 260. Jan. 1897. B 2 Prof. A. Schuster’s Electrical Notes. magnetic effects of a moving charge all these investigations have led to the same result, but there is a remarkable discrepancy in the expression for the force which acts on the charge if it is moving in a magnetic field. In his first paper J.J. Thomson calculates that force to be 4uepH, where p is the magnetic permeability, e the charge, p the velocity, and H the field, the motion being supposed to take place at right angles to the lines of force. Heaviside omits the factor $. In his later researches J. J. Thomson calculates the force to be 4uepH, and I believe he still takes this expression to be the correct one, applying it to some of his experiments on gas discharges. There are also some other discrepancies between J. J. Thomson’s first paper and Heaviside’s, which are exhibited in a tabular form as follows :— J. J. Thomson, 1881. Heaviside, 1889. J. J. Thomson, 1893. ae 2me*p?/1da pep /3a pe*p?/3a X. 4 epH pepH LuepH M. Jueresprpys——- me (cos e+ cos a cos ) Here T represents the energy of the magnetic field pro- duced by a moving sphere of radius a, and M the mutual energy of a pair of spheres carrying charges ¢, ¢,, and moving with velocities p,, p.. X is the force already referred to which acts in a magnetic field H on the moving particle. 2. In the ‘ Bakerian Lecture” of 1890, I calculated the effects of a magnetic field on kathode rays, and adopted Heaviside’s expression for the force acting on a moving electrified particle. I may here give the simple reasoning which seemed to me to show its correctness. Let A BC (Fig. 1) be a circular ring made up of a large number of rigidly connected but insulated electrified parts. ip. i: Let e be the electric charge of each of these parts, and let their number per unit B length be N. Let this ring be set into A ¢ rotation about its axis MM’, the linear velocity being p, and let the two following assumptions be made :— (1) The magnetic field produced by the convection of the electrified ring is the M” same as that of a current of strength Nep circulating round a conductor coinci- dent with the ring. (2) The magnetic action of the revolving ring on a magnet Prof, A. Schuster’s Electrical Notes. 3 MM’ is equal and opposite to the total reaction of the magnet on the electrified parts of the ring. The first of these assumptions is supported by experiment, for since Rowland showed that electric convection did produce a magnetic field, he and others have proved that the field eannot differ much in intensity from that of an equivalent eurrent, and is probably identical with it. Both J. J. Thomson’s and Heaviside’s investigations agree on this point. As regards the second of the above assumptions, it is tacitly made, I believe, by everyone, although the possibility has been pointed out that part of the reaction may take hold of the “medium ;” but so far we have no ground to doubt the truth of Newton’s third law as applied to matter alone. The current Nep will produce a force on a magnetic pole of strength m, placed at M, which is equal to =: Nep. This will also be the force with which the pole will act on the ring tending to drive it in a direction parallel to its axis; as the magnetic force H at the ring due to this pole is =), and the y) total number of particles is 27Nr, it is seen that each particle must be acted on by a force equal to wHep, which is Heavi- side’s result. To trace the cause of the discrepancy it is necessary to enter somewhat fully into J. J. Thomson’s first paper ; but in criticising the correctness of some of its deductions I wish specially to guard myself against the supposition that I do not appreciate the high value of that paper. Criticism after a lapse of years is an easy task compared with the opening out of a new line of thought, when errors of detail are of compa- ratively little importance. JI begin with an independent calculation of the magnetic forces acting on the sphere, assuming J. J. Thomson’s values for the magnetic forces which are due to the sphere. 3. If the surface charge of the sphere is qg, and the velocity is along the axis of X and equal to w, the components of magnetic force are ry tiem, os 3 5 © (1) where the velocity w is supposed to be small compared to the velocity of light. To obtain the force which acts on the sphere in a magnetic field H, we may imagine that field to be homogeneous and produced by magnetic matter covering a concentric sphere 8 of radius R, with a surface-density o= 3H cos y/47, where uw is the permeability and y the angular distance between P and B2 eee EE ET ee St ie Pe POPF PIE me 4 Prof, A. Schuster’s Electrical Notes. the pole of H. The force which acts on the moving sphere will be equal and opposite to that which acts on S, and there- fore its components are x —lacd8, i —(Bed8, Le The values of a and 6 at the surface S are surface harmonies of the first degree, and the same holds for co. Hence if C and A are the values of a and o at the pole of H, the surface integrals may be written down at once, and we thus obtain _ AR? Ps If the axis of Y is chosen so that the axis of H lies in the plane of YZ, and @ is the angle between it and the direc- tion of motion of the sphere, X=pqwH sin 6, 0 0 This is Heaviside’s result. 4, To bring out clearly the cause of the different result ob- tained by J. J. Thomson it is necessary to form expressions for the mutual energy of the sphere and an outside magnetic system. The potential energy of a magnet placed in a magnetic field is x CA. W=—((\(Aet+ BB+ Cy)dedydz, . . . (2) where A, B, C represent the components of intensity of mag- netization and a, 8, y, those of the magnetic forces acting on the magnet. If for e and 8 we substitute their values we find bak at Ne Ae eee ee aoe — where F; is the z-component of the vector-potential at the centre of the moving sphere. We may also consider the energy as kinetic and use the equation T= NI (aa+Bb+yc)dedydz, . . . (A) a, b, ec being the components of magnetic induction. The expression is deduced under the supposition that the magnetic forces are all due to electric currents. In isotropic media So Prof. A. Schuster’s Electrical Notes. 5 we may therefore write ly Deore s T= \\\( +b? +e jdedydz.. 4. « :(5) This integral may be transformed either in the manner indicated by Heaviside or in that of J. J. Thomson, and it is found that, retaining only that part of the energy which depends both on the outside magnetic force and the moving sphere, the result is T=qwFk. 5. J. J. Thomson’s value differs from this because he wrongly applies equation (4) to the case in which the field is due partly to permanent magnets, substituting for a, 6, ¢ their values a + 47rA, Ke. Kiquation (4) thus becomes a - (\\ (a? +0? +c?) —47(aA +6B+cC) | dea dy dz. . (6) In the subsequent investigation Thomson puts a, b, ¢ equal to px, uw, wy, where pw is apparently the magnetic permeability of the medium in which the charge moves. Ii is easily seen that if under these circumstances (6) 1s compared with (2) and (5), a relation is obtained between Ty, T, and W, viz., T=a(0 + 4W) =$eT =4nquF, This is J. J. Thomson’s value, which differs therefore from that of Heaviside by the factor 3m. It follows that J. J. Thomson’s forces, which are calculated from this value of the energy, only give half the correct results in a medium of unit permeability ; but the appearance of yw in the expression for the energy is alone sufficient to show that there is some- thing wrong with it. 6. It has already been pointed out that in his ‘ Recent Researches in Hlectricity and Magnetism,’ chapter i. J. J. Thomson obtains a value for the magnetic force which is only a third of that deduced by Heaviside and verified above. I con- fess I find it difficult to follow the method of “‘ moving tubes ” employed in that investigation. I speak with diffidence on the subject, but the investigation on page 22 of the work quoted seems to me to be obscure and incomplete. In the equations for U, V’, W the components 7, g, hare taken to represent the polarization of the moving sphere only. Should there not be some additional polarization due to the outside magnetic forces? In the meantime all recognized methods give Heaviside’s value for the force which acts on the sphere, viz. : : 6 Prof. A. Schuster’s Electrical Notes. ewH, and it is the only one really consistent with the third re of motion. . The energy of the magnetic field established by the Lae sphere. can be calculated either as Heaviside has done directly from the volume-integral of the square of the magnetic force, or as J. J. Thomson has done from the vector -potential according to Maxwell’s equation 3\\\(ArCi + A.C, + A;C,)dadydz. . . . (7) A is the vector-potential, C the current-density, and the indices represent the components along the three axes. To calculate the vector-potential for the system of currents which are assumed to take place owing to the varying displacement in the space surrounding the moving sphere, I consider first the simple case ofa sphere of radius a, the surface of which acts like a sink of an incompressible fluid, the total quantity abstracted in unit time being g. ‘The current-density at a distance r from the origin would be g/47?*, and the current components would be LDF Gt ae A a: = gg | — = == 1 Te fe pr)? tly las 1 d=\4ar Inside the sphere there is no current. Hach component of the vector-potential, say Aj,, has to satisfy the following conditions :— eA ig” foes ea fa! | dzr ro VAY = if r ? dz dz\2n—1 on) =_— _ , wo & ete es A,= 2 san Creer ee fe eae A,=" —;)¥- = + pwV_a a a dy\2n—1 a tT The expressions for the inside space are obiained by writing W,, for V_,_,, and interchanging r and a. In the calculations for the magnetic forces the last term of A; is the only one which produces an effect, and, conse- quently, | ae d a rp Oe ee 1 =0. ig B deprits 7 Let V2 represent the harmonic of degree n and type a, .é. with the usual notation and WV, the corresponding harmonic a ee i age sia co sin?@ = dp? a - iin dat. Thee Go i iii On Boyle’ s Law at Very Low Pressures. 11 Then if z=rsin@cos¢, y=rsin@singd, z=r cos 8G, it may be proved that ria ae pe o Be =(n+o)(n+o—1) nt Wri, dV; Ny r 1 Ss 2 ile =—(n+a)(n fo Wea Vi. These equations hold both for positive and negative values of n, which seems.a somewhat remarkable result*. Hence a =(n+2—a) (n+ 1—o) V2 Vo, ge = —(n+2—c) (n+ 1—c)V,. — Vie. From these equations the values of the magnetic forces are obtained in their normal form. The first terms vanish for the zonal harmonics for which ~=0O ; and the second terms vanish inside the sphere when n ie where 3Am,m./7* is the attraction between a molecule of gas m, and of solid m, at distance 1, py being density of solid and v, velocity of m;. This may be written PIPs = Cie es . : 7 y : - (29) denoting 6Am,7p, by 8, and myv,? by k. When we wish to carry this expression right up to the layer of molecules nearest to the solid wall, to find the the pressure there, we have to take z as having a value gz, such that the attraction on a continuous normal cylinder ending at z, from the surface will equal the attraction on the discontinuous molecules in that cylinder ; thus z, will probably not be much different from half the mean distance of a molecule from its immediate neighbours near the solid surface. Now the domain of a molecule near the surface is (m,/p,) ; so that zs is not much different from (m,/p,)*/2. Then, if Boyle’s law holds, ; p,/P aa ! 22/ (m/p,)° ae Sin Nd | oe SaaS (29a) is an equation specifying the density at the surface when that at any distance z is known; but in most cases p becomes practically constant when z exceeds a certain small value, and when it is determined the whole distribution of density in the transition layer of variable density is specified. To determine the mass of gas in a vessel, take an element of surface dS and erect a normal cylinder of height z starting at z,/2 from the surface and reaching to z+4¢s/2; with these * Phil. Mag. [5] xlii. p. 389. at Very Low Pressures. 13 as limits of integration, the mass of the cylinder is dS \ pdz = dS \ p, (2,/2)8!* = d8S p,(z,/2)¥/*az = ale.) 2 +. CO Now if z is large enough to end in the main body of the gas, where surface-action is negligible, dSpz is dB, where B is an element of volume; so the mass of the cylinder becomes {pdB — dSz,(p, —p)/2}/(1—B/4), and total mass M = {pB—S8z,(p,—p)/2}/A—B/k). « « (31) Here, then, we have the surface condensation effect ex- pressed by a surface-term in the expression for the mass in addition to the pB, which would suffice if the density were uniform; p,is given by (29a). Now, without going into details, we may be satisfied that §/k is small compared to unity ; for if & is expressed in C.4.s. units, 8 is to be the force exerted by a long cylinder of square centimetre base on a molecule of the gas at a centi- metre from the base along the axis, which all experience shows to be small compared to the kinetic energy of a molecule at ordinary temperatures. Ofcourse, if we artificially increase the amount of surface enormously—as, for instance, by partially filling a vessel with a powder or a porous material like char- coal—we must remember that we cannot assume the pressure in the centre of each little interspace or pore to be the same as that in the free gas in communication with the manometer ; but for each little interspace we can write an equation like (31), and for the gas in the whole of the interspaces we can use equation (31) if we change p to p,, the average density at the centre of the interspaces. As 8/k is small, it follows from (31) that the surface-term is always small compared to the volume- term, and therefore the equation for a mass of gas in a vessel which is partially occupied by a powder or porous material will be Ni pp B+ p,B pees aera (oe) where the suffix f connects with the free volume, and e with that in the interspaces. The relation between p, and p - depends on the average size of the interspaces and the attraction of the solid for gas, as we can see if we follow in imagination the course of a surface of constant pressure at the boundary between the free region and the powder: if the pores are @ 14 Mr. W. Sutherland on Boyle’s Law large this surface may pass into the pore and clothe all the interspaces ; whereas if the pores are fine it may show only a slight depression opposite a surface-pore and have no existence in the inner interspaces. Thus it would not be difficult to find the surface of constant pressure which is just prevented from entering an average pore, and so determining p, as a function of p,, size of pore, and molecular force, and so to find the theory of Kayser’s experiments on the compression of gases in contact with powders (Wied. Ann. xiv.). For present purposes it is enough to say that by varying the size of the interspaces and the nature of the powder or fibre he was able to demonstrate distinct variation of the mass of gas adsorbed, namely p,B,, with NH3,CO,, and SOQ... With boxwood char- coal (Wied. Ann. xii.) Kayser, in confirmation of previous investigators, such as Chappuis and Joulin, found a measurable adsorption of both air and hydrogen ; for instanee, 1 c.c. of charcoal, of which about two-thirds is interspace, adsorbs about 3 c.c. of air at a pressure of one atmo and at 0° C. and about 1°5 c.c. of hydrogen at 14° C., but at 50° scarcely a trace of air is adsorbed—a fact which shows that the circumstances in the case of charcoal are quite special, and though interesting can throw no light on the present inquiry as to the general action of solid surfaces on gases. If we return to equation (31) in the form M = pB+MB/k—Sz,(p,—p)/2,. . . . (88) we see that in general the surface-term must be smaller than M@/k—that is to say, than a constant small fraction of the mass for a given gas—and therefore that however much we may rarefy a gas the relative importance of the surface-term can never exceed a certain small limiting amount. This is in direct contradiction to the prevailing impression that surface effect becomes of increasing importance with the rarefaction. We have therefore to consider the origin of the general impression, which is twofold, namely, first, the theoretical belief that the mass of a gas ought to be given by an equation of the form where, in contrast to our equation (33), the surface-term has a positive sign, and there is no obvious reason why the surface-« term ought not to become of increasing importance with rarefaction because of p, diminishing more slowly than p; and secondly, the well-known experimental difficulties of getting rid of the last traces of volatile matter from the walls of glass vessels in preparing vacuum bulbs; but the experiments of eae ee ~~ So - Vessel at Very Low Pressures. 15 Warburg and Ihmori (Wied. Ann. xxvil., xxxi.) and others show that there is a chemical reason for eae of the strong attraction of glass for water, since fresh glass has an alkaline film on its surface which can be dissolved off by water—a fact which explains the power that fresh glass surfaces have of con- densing moisture from air which is far from being saturated. This water is easily got rid of, but there is water attached more firmly which can be driven off a glass surface only by heating at very low pressure. It seems to me that we have to do here with a sort of solution of water in the solid glass, and not with a genuine surface condensation ; but the behaviour of water on a glass surface has been cenerally held to be only an extreme case of the behaviour of any gas ; if, how- ever, there is the great distinction which has just been sug- gested, there is no force in the inference from water. Carbon dioxide also comes freely from a glass surface sometimes, but Krause (Wied. Ann. xxxvi.) seems to have shown that the presence of water-vapour is necessary. Thus there seems to be no genuine evidence that gases condense in amounts hitherto measurable on ordinary solid surfaces. Of course, with an easily liquefiable gas below its critical tempe- rature, we can imagine that if the attraction of the solid for the gas is much greater than the attraction of the gas for itself, a thin layer of gas liquefied on the surface would evaporate with greater difficulty than if it were on the surface of a large mass of itself; but from what we now know of molecular force we should expect such an effect merely to modify somewhat for such a layer the ordinary laws of evaporation, but not to alter them entirely, as the supposition of a retention of a layer of liquid at pressures far below that of saturation would necessitate ; the retention of an appre- ciable amount of volatile substance, as of water, on glass brings us back to causes more of a chemical nature, as we have just seen. Thus, with the law of molecular force as that of the inverse fourth power, we are led to the conclusion that condensation of gases on ordinary solid surfaces at pressures far removed from those of liquefaction does not occur to an extent mea- surable by methods hitherto applied, and that apparent departure from Boyle’s law on account of surface condensation is too small to have been hitherto detected, and does not become relatively any larger in rare than in dense gases. The causes for any apparent “breakdown of Boyle’s law in rarefied gases are therefore to be sought for elsewhere than in surface con- densation caused by molecular force if the law of that force is that of the inverse fourth power. 16 Mr. W. Sutherland on Boyle’s Law We have now to consider the experimental evidence, and will begin with the clearest case—that of oxygen, for which Bohr discovered (Wied. Ann. xxvii.) a decided departure from Boyle’s law, and investigated it between pressures of 15 and ‘1 mm. of mercury. As this departure in the case of oxygen is due to its spontaneous change into ozone at low pressures, it will be investigated in a separate paper. But since air consists of about one volume of oxygen to four of nitrogen, it is to be expected that the departure of the oxygen from Boyle’s law will produce a departure of the air from that law, but at a region of pressures five times as large as those in which the deviations are perceptible for oxygen. The case of air will therefore better be discussed in connexion with that for oxygen. But when once the departure of air from Boyle’s law is assigned to a special cause, the bulk of the experimental evidence in favour of the departure of rarefied gases in general from that law has disappeared, for naturally most of the experimental evidence has related to air. That which has attracted most attention is due to Mendeléeff, who seems to have devoted a large amount of work to the subject, but accessible to non-Russian readers only in two short accounts in the Ann. de Chim. et de Phys. (Mendeléeff and Kirpitscheff [5] ii, and Mendeléeff and Hemilian [5] ix.). The most important result obtained in the first of these papers is that between 600 and 20 mm. of mercury pB for air diminishes with diminishing p, and a series of numbers is given to illustrate the case ; but in the next paper it is mentioned that while diminution of pB with p between these limits of pressure is always found, the determinations of its amount are not always accordant. ‘The reason for this variation in the expe- rimental numbers will be given when we are considering the theory of the departure in oxygen and air. Of course it is to be remembered that the departures of most gases from Boyle’s law at a few atmos pressure are such as make pB increase with diminishing p, but towards the limit for a perfect gas ; if, therefore, any tendency in the opposite direction is to set in it must first neutralise the small residual tendency of pB to increase with diminishing p before it can make itself seen as an actual diminution, and this is why Mendeléeff and his co-workers find a pressure of about 600 mm. as the one at which diminution of pB begins to be apparent with increasing rarefaction. ‘lhe same investigators give data to show that with H,, CO;, and SO, a diminution of pB with p sets in at a certain pressure for each, but the amount of diminution obtained is so slight that it can hardly be relied on. Indeed Amagat, after carrying out a research on Boyle’s law Se ee ee oe at Very Low Pressures. 17 in rarefied gases (Ann. de Chim. et de Phys. [5] xxviii.), maintains that Mendeléeff and his co-workers claim for their measurements of low pressures a degree of accuracy that is beyond present experimental possibility. He claims that his data show that with present appliances one cannot read the position of the top of a mercury column to within less than ‘O01 em., which implies that at 20 mm. pB cannot be free from liability to an error of 5 parts in 10,000, which is of the order of the departure given by Mendeléeff and Hemilian for SOQ, ; and while they obtain slight diminution of pB for H, down to 120 mm., Amagat gets an apparent slight increase at 6 and 8 mm., which, however, he speaks of as being of the order of the unavoidable experimental error. Similarly, in the case of CO, Amagat’s results show that at 4 and 2 mm. a departure from Boyle’s law greater than experimental error could not be found by his measurements. Thus it appears that when oxygen and air are set aside as exceptions traceable to a special cause, there is no satisfactory evidence of a failure of Boyle’s law in rarefied gases. The latest experimental paper on the subject is that of Baly and Ramsay (Phil. Mag. [5] xxxviii.), the chief interest of which lies in some startling experiences which they had with oxygen and air, wherein Boyle’s law appears to be completely wrecked ; for example, air which at 4:1 mm. of mercury gave pB=100, at 8 mm. gave pB=9-4. This will be traced in the separate paper to a liberation of free ions of oxygen, whose electrical charges are responsible for the mischief. But with hydrogen Baly and Ramsay found in a somewhat indirect manner that Boyle’s law holds down to 2°5 mm. of mercury, and probably to 760/10‘, and the law of Charles down to ‘4mm. (©O, behaved differently in two different gauges, showing probably a different state of the glass in them, and indicating that apparent departure of rare CO, in glass vessels from Boyle’s law is due rather to the chemical causes already mentioned than to physical ones. Indeed, some other expe- riments carried out by Baly and Ramsay are suggestive of the existence of a dissociation pressure for the combination between CO, and glass; for they found that when the pressure of CO, was about 1/10° atmo, 188 strokes with a mercury-pump, supposed to reduce the pressure to °55 of its original value at each stroke, failed to lower the pressure at all, just as if the glass gave out and reabsorbed CQ, in the same way as a vessel lined with silver chloride and filled with NH; at a suitable pressure would liberate and absorb NH; if an attempt were made to pump it out with apparatus all lined with AgCl. Phil. Mag. 8. 5. Vol. 43. No. 260. Jan, 1897. C 18 On Boyle's Law at Very Low Pressures. Baly and Ramsay consider the coefficient of expansion of hydrogen is proved by their experiments to remain at 1/273 down to a pressure of ‘4 mm., below which there are the three observations of 1/276 at ‘25 mm., 1/297 at ‘096 mm., and 1/300 at ‘077 mm., which they consider to prove a diminution of the coefficient with diminution of pressure ; but it seems to me that the sudden onset of the diminution is suggestive of some unrecognized source of experimental error, such, for instance, as electrification of the glass of one of the gauges with alteration of the capillary correction for the meniscus of mercury in the capillary volume-tube which amounts to 7mm. of mercury. An error due to such a cause would, of course, produce more effect-in altering the apparent coefficient of expansion the lower the pressure. For nitrogen Baly and Ramsay found the following reciprocals of the coefficients of expansion :— SP Saas ae 53mm, 4:97 3 al 8 6 304 309 302 304 331 = from 301 to 377 Mean 3438 Although these values all mean coefficients smaller than 1/273, it seems to me that the sudden change from 304 at 1-1 mm. to 331 at *8mm., so analogous to the sudden change with hydrogen near the same region of pressure, 1s suggestive of a hidden source of error such as that already indicated, and casting doubt on the measurements even at 5mm. _ Baly and Ramsay mention that at pressures below ‘6 mm. some un- ascertained cause of irregularity came in and caused their method to give worthless results—a fact which is again suggestive of the irregular operation of a source of error such as variable electrification. With oxygen, Baly and Ramsay found coefficients of expansion larger than 1/273 at pressures from 5 to ‘07 mm., which in the special paper on oxygen will be accounted for by dissociation of ozone at the higher tem- perature. If the coefficient for nitrogen is really smaller than 1/273 at low pressures, this would be most readily accounted for by association of the nitrogen molecules at the higher temperature with possible production of an allotropic form of nitrogen ; therefore, on all accounts, a continuation of Baly and Ramsay’s research is desirable. The contentions of the present paper may be summarized thus :— Departures from Boyle’s law found experimentally in rarefied gases may be due either to a true failure of Boyle’s law in the highest sense, that is to say, to a change in the kinetics of all molecules, or to only an apparent failure, which may be due to actions at the walls of the containing vessel or Method of Measuring Electrolytic Conductivity. 19 dissociation of the molecules. According to the law of the inverse fourth power, apparent departures from Boyle’s law on account of pure moleculer attraction of solid walls for the gas cannot be of amount at present detectable in ordinary vessels, but are possible in small interspaces between solids, as in powders or porous bodies, if the interspaces are small enough. As the kinetic theory gives no hint that the kinetics of molecules should alter with rarefaction of gases, except towards stricter and stricter rigorousness of Boyle’s law, and as the theory of molecular force requires a very small effect for the walls of ordinary vessels, we may say that theoretically there is no cause to expect real or apparent departures from Boyle’s law at low pressures on general grounds, and that when such are obtained experimentally they are due to special causes, such as a chemical or quasi-chemical attraction of glass for water or moist CO,, or dissociation or combination, as in the case of oxygen (to be proved in a separate paper), and therefore in that of air. The case of hydrogen may be regarded as the typical one hitherto investigated that is free from special con- ditions, and the whole tenour of the experimental evidence relating to it is to justify the laws of Boyle and Charles for it when rarefied. The direction which further experimental inquiry should take is obviously that of varying the conditions more widely than hitherto. Although the amount of direct experimental evidence in favour of Boyle’s law in rare gases has been shown to be small, it seems to be cogent; and in my next paper, on ‘Two New Pressure-Gauges,” I shall show that it is well supported by indirect evidence obtainable from Crookes’s experiments on High Vacua. Melbourne, Aug. 1896. Ill. A Satisfactory Method of Measuring Electrolytic Conduc- ivity by means of Continuous Currents. By Prof. W. SrrouD, D.Sc., M.A., and J. B. Henperson, B.Sc.* HE devices for eliminating or reducing the disturbing effects of polarization in the measurement of the con- ductivity of electrolytes are very numerous. Wheatstone, Horsford, Wiedemann, Beetz, Paalzow, Ewing and Mac- gregor, Bouty, and others have all experimented on this subject. It will, however, be universally conceded that * Communicated by the Physical Society: read Oct. 30, 1896, C2 20 Messrs. Stroud and Henderson on the Kohlrausch’s method of measuring the conductivity of elec- trolytes by the use of alternating currents and a telephone is superior to any method at present in use in which con- tinuous currents are employed. That there are difficulties in the use of this method, arising from self-induction, capacity, &e., is admitted by Kohlrausch himself. Ever since the intro- duction of this method in 1875 physicists have not ceased to try to improve the continuous current methods, with the desire unquestionably of employing a galvanometer instead of a telephone as the indicating apparatus. In the method used by Fitzpatrick*, where the alternating currents are confined to the four arms of the bridge, we have an example of a suc- cessful attempt to utilize the advantages of alternating currents _ while dispensing with the telephone in favour of the more satisfactory galvanometer. In the face of all the experimental work done in the past it may seem a bold thing to say that if the proper conditions. are only satisfied, continuous currents are preferable in every way to alternating currents for the measurement of electro- lytic conductivity, but such we believe to be the fact. The idea underlying the method to be described struck one of us some six months ago. This idea was to obviate the detrimental effects of polarization in the electrolytic cell by inserting a second cell with the same size of plates &e., but with a very different length of electrolytic conductor in the corresponding arm of a Wheatstone bridge circuit. The notion of employing such a balancing cel] we subse- quently found was suggested in 1877 by Kohlrausch and employed by Tollinger 7. The method used by Tollinger consisted in having an electrolytic cell in each arm of the bridge, but the method of finding the resistance was to obtain a balance for a particular position of the electrodes in one cell, then to diminish the | distance between them by a measured amount and increase the resistance in that arm so as to restore the balance. A conceivable source of error arises in consequence of the motion of the electrode through the liquid producing a possible alteration in its polarization. The results of Tollinger’s work show that resistances measured by his continuous current method were 0°6 per cent. lower on the average than the same resistances measured by the alternating current method. Hlsast has also employed the balancing cell method. He * Brit. Assoc. Rep. 1886, p. 328. + Wied. Anz. vol. i. 1877, p. 510. t Wied. Ann. xliv. p. 666. Measurement of Electrolytic Conductivity. Oy used a long trough of known section with two fixed non- polarizable electrodes at the ends (Cu electrodes in CuSQ,) and one movable electrode between them. A resistance in series with the shorter column of liquid was adjusted to balance the bridge. The resistances so measured were of the order of 12 ohms or less. For many purposes the use of non- polarizable electrodes is impossible or inconvenient. The method to be described is in many respects similar to those of Tollinger and EJsas, but it differs from them in the form of electrolytic cell employed, and especially in a very material point, viz.:—the employment of high voltages and high resistances so as to effectually drown any residual error arising from differential polarization. | Fig. 1 wiil make the arrangement clear, rv are equal re- sistances, Cc are two similar electrolytic cells equal in all Fig. 1. respects, except that in C the electrolytic conductor is very long, inc very short. ‘The resistance-box RB is adjusted till there is a balance, when, of course, the resistance in the box is equal to the difference in the resistances between the two cells C and c. Since the resistances rv are equal it will be clear that when approximate balance has been obtained equal currents will be traversing both electrolytic cells, and therefore there should be the same polarization in each cell, and these polarizations are clearly opposed and are in theory eliminated. Instead of the arrangement shown in fig. 1, in which the cells are arranged in parallel, we have also tried the effect of interchanging the battery and galvanometer so as to arrange the cells in series. In the first case the polarization of one cell is opposed to that of the second, so that the polarization of each cell is much more persistent ; in the other case the cells are joined in series, so that the polarization falls as soon OOS] 22 Messrs. Stroud and Henderson on the as the battery circuit is broken. Experiment shows that the arrangement shown in the figure is much the better of the two. In practice, however, it is found that the polarization in the two cells is not always exactly the same; generally speak- ing at least 99 per cent. of the polarization may be balanced in this manner, but ordinarily the balance is much more perfect than this. The next point then is to drown the residual differential polarization by working with high re- sistances and high voltages, and in this way the detrimental effects of polarization are reduced to insignificance. With electrolytic cells having a difference in resistance of about 20,000 ohms, the remaining arms being 1000 ohms each, and with a D’Argonval galvanometer of about 300 ohms, when the voltage on the bridge is 30 the measurements are very like measurements of metallic resistances. | To get the specific resistance immediately in ohms, without reference to any other electrolyte, the cells C and ¢ are con- structed as shown in the figure. Kach ce!l consists of three parts, twe being small, thick- walled test-tubes with necks half-way up their sides. Into these necks fit the well-ground ends of a tube of nearly uni- Fig, 2. form bore. In the case of the cell C this tube is 30 centim. or more in length, while in the case of ¢ it is only a few centim. long. In every other respect the two cells are as nearly as possible alike. The vertical limbs of the H cells were about 1-2 centim. in diameter, and about 6 centim. high, and the horizontal tubes about 0°6 centim. external diameter, the diameter of the bore being chosen to give a convenient resistance with the Measiiement of Electrolytic Conductivity. 23 electrolyte used. The lengths of the tubes were about 30 centim. in the one case and 5 centim.in the other. The tubes were calibrated by measuring their lengths and weighing in a watch-glass the mercury required to fill them. In this way a constant can be obtained for a particular pair of tubes such that on multiplying by the observed resistance of the electrolyte its specific resistance is at once obtained. In determining the weight of mercury required to fill the tubes we found tliat the results were most concordant when the finely ground ends of the tube were stopped by means of a small piece of thin cover-glass backed with cork about # inch thick, the diameter of the cover-glass and cork being about the same as the external diameter of the tube, so that the pressure of one finger might suffice to keep the cover- glass firmly against the end of the tube. In this way any tilting of the cover-glass relatively to the end of the tube was avoided. The following weighings of mercury and watch-glass for one pair of tubes were made: 29°836, 29°837, and 29°835 grms. for the long tube, and 11°482, 11°481, and 11°481 for the short one. The lengths of the tubes were 29°70 and 4°39 centims. From these data, assuming the density of mercury to be 13°558 at the temperature of the experiment, the constant for this particular pair of tubes was 775. If we were making fresh cells we should make them with the cross-tube near the foot instead of in the middle of the tubes. This would much facilitate mixing when a portion of the electrolyte is removed and replaced by water so as to alter the concentration. All that would then be necessary would be to tilt the cell two or three times to ensure effective mixing. ‘The electrodes were pieces of platinum foil bent into cylindrical form to fit the vertical tubes of the cells. A platinum wire was welded on to each electrode and electrical connexion established with the arms of the bridge by the intervention of a mercury cup. By this means the electrodes were easily removable from the cells. The cells and mercury cups were mounted on a wooden stand placed in an oil bath, oil being used as it was found that with a water bath the apparent resistance of the electrolyte depended on the direction of the current. The explanation of this was traced to leakage over the glass surface and through the water, and was entirely obviated by the substitu- tion of an insulating liquid for the fluid in the bath. The following tables give the results of some experiments made with a solution of potassium chloride, the strength being 94 Messrs. Stroud and Henderson on the 1 molecular equivalent per litre. The arms rr of the bridge were each 1000 ohms, 30 volts were used, and the balancing resistance R was of the order of 20,000 ohms. Between each two measurements of resistance the electrodes were washed, heated to redness, replaced, and the current reversed. The method of making an experiment was as follows :—The current was made for about half a minute to polarize the plates, and then broken ; two minutes were allowed to elapse to enable the electrolyte to assume the temperature of the bath, which was constantly stirred, and then the balance was obtained by momentarily making the current and adjusting the resistance. Solution I.—The solution was made from KCl twice re- crystallized from water and dried in the air between filter- paper. With Kohlrausch’s notation we found Binet. be We give no details of the experiment with this solution because the atomic weights used in making up the solution were only approximate, viz.:—K=39 and Cl=35°5. Cor- recting for this error the result would come about 0:1 per cent. higher. The salt, too, was dried in air, and it is pro- bable that all the moisture was not removed, and any error resulting from this would cause the value obtained to be too low. Solution II. (prepared for us with great care by Dr. Hwan). —The salt was prepared by fusing KClO; ina platinum crucible until no more gas was evolved. It was then recrystallized from dilute hydrochloric acid and dried by heating over a bunsen. The molecular weights used were K=39°13 and Cl=35°45. The strength was as before } molecular equi- valent per litre. 21121 TABLE I, Direction of . Resistance reduced | ee Temp. | Resistance. to 18° C. 5 er SSE 18°26 21085 | 21149 eae Sb ain: 18-19 -21045 21129 SSE ere 18907 21045 21119 a fck see tats 18°11 21065 211138 ASE eae one 18-08 21085 21120 eieeler ss: 18:06 | 21095 25 The temperature coefficient used in the reduction was taken as 2°1 per cent. per 1° C. The galvanometer gave a clear indication for a variation of 10 ohms. Specific Resistance = Measurement of Electrolytic Conductivity. 21125 454-6 Specific Conductivity in ¢.¢.s. units=2151°9 x 10-14, Conductivity compared with mereury=2024'4 x 107°. is se N74 SDSS be = 46:47 ohm-centim. units. Solutzon III. (prepared by Dr. Ewan).—The details of preparation of this solution were similar to those employed in the previous case, except that the salt was not recrystallized from dilute hydrochloric acid, so that it is possible that a trace of chlorate or perchlorate might have been present, and this would tend to diminish the conductivity. TasueE II. Directi fe | E Resist d 1 mee : Temp. | Resistance. SE saice C. ug? 5 eee ee 18:11 21155 21204 Ser estates Lz, p has a positive value; . . . (7) hence this curve is, broadly speaking, an inversion of that just considered, the maxima occurring for those values of the abscissee at which the minima of the curve for R=0 occurred, and vice versd. This is exemplified in the dotted curve, H, on the diagram, restilting from the experiment with the bridge whose resistance was of the order 1350 ohms. Finally, we have for R= Lv, p=0. . |, 2 ee In this case, sin'ce no waves are reflected, no stationary waves can obtain, and consequently no waxing and waning of the electrometer-throws can occur. Thus theory predicts a straight line as the outcome of an experiment with a bridge of this critical resistance. This is approximately the case with the full-line curve, G, on the diagram, obtained with the bridge whose resistance was of the order 560 ohms, the theo- retical value of the critical resistance for the line used. Of course an absolutely straight line cannot be expected, since the sparks in the oscillator vary slightly. For this reason, throughout the experiments hitherto considered the ‘throws with the bridge under examination at any desired distance beyond the electrometer were alternated with those obtained with a no-resistance bridge at the standard distance of a quarter-wave-length beyond. And the ordinates of the curves on the diagram represent, not the actual electrometer- throws with the bridge and distance in question, but the ratio of these to those obtained under the standard conditions just described. Thus the maximum ordinate in the diagram is unity, all the curves are reduced to the same scale, and the errors due to variations of the sparking at the oscillator are in great measure eliminated. In the above experiments the electrometer was used as a single-needle instrument, and the throws obtained varied up to 100 scale-divisions. Electric Waves along Wires by a Terminal Bridge. 45 As a further test of the non-reflexion of waves by the bridge G, the electrometer was afterwards used differentially, the upper and lower needles having their disks attached to points on the line a quarter-wave-length apart. The bridges were placed at the end of the line 0°25 m. beyond the second needle. With a no-resistance bridge the throws were positive and of the order 50 scale-divisions ; with a simple discon- nexion (“infinity bridge”) the throws were of the same order but negative. The bridges F and H gave smaller throws, positive and negative respectively. The bridge G also appeared to yield a small throw ; but this was no larger than might be due to a creep of the zero or an imperfection in the adjust- ment of the electrometer-needles. The use of the differential electrometer is thus seen to confirm the results of the expe- riments conducted with a single needle. 3 It should be noted that this paper deals only with the absorption of waves by terminal bridges; no intermediate - resistance-bridge will absorb all the waves arriving there. The reflexion and transmission coefficients p’ and 7 for an intermediate bridge of resistance R are given by* —Lv 2R = OP lon and WSR Le o el he (9) the notation being the same as that previously used. Thus the condition for non-reflexion is R=, in which case all is transmitted. Hence complete absorption is impossible. If, therefore, we wish to pass electric waves along wires through any layer of dielectric, or through any other arrange- ment which affects them, and are desirous of avoiding the annoying disturbance due to return of the transmitted portion after reflexion at the end of the line, the following method will suffice. 1. Place at the end of the line a bridge of the form herein described, whose resistance has the value given by the theory for plane waves. 2. Test experimentally the absorbing-power of the bridge, and, if necessary, adjust its resistance until no reflexion can be detected. University College, Nottingham, September 1896. * Oliver Heaviside’s ‘ Electrical Papers,’ vol. ii. pp. 141-142. * [od VILL. On the Relation of the Physical Properties of Aqueous Solutions to their state of Ionization. By Prof. J. G. Mac- Greoor, Dalhousie College, Halifax, N.S.* i has often been pointed out that, according to the dis- sociation or ionization conception of the constitution of a solution of an electrolyte, the difference between the phy- sical properties of one in which ionization is complete and those of the solvent must be compounded additively of the differences produced by the two ions. It would seem to be equally obvious that, in the case of solutions in which the ionization is not complete, the differences referred to must be similarly compounded of those produced by the undisso- ciated molecules and by the free ions; and if so, it should be possible to express the numerical values of the various pro- perties in terms of the state of ionization. Such an expression would take its simplest form in the case of solutions so dilute that the molecules, dissociated or undissociated, might be regarded as sufficiently far apart to render mutual action between them impossible, and in these circumstances the change produced in the properties of the solvent by the un- dissociated-and the dissociated molecules respectively might be expected to be simply proportional to their respective numbers per unit of volume. It is the object of this paper to test the applicability to sufficiently dilute solutions of such an expression, V1z., P=P,+h(l—a)n+tlan, . . . . (1) where P is the numerical value of any property (density &c.), P,, that of the same property for water under the same phy- sical conditions, n the molecular concentration of the solution, 2. e., the number of gramme-equivalents of the dissolved substance per unit volume of the solution, @ the ionization- coefficient, an and (1—a)n consequently the numbers of dis- sociated and undissociated gramme-equivalents per unit of volume respectively, and & and / constants, which may be spoken of as ionization-constants, which will vary with the solvent, the substance dissolved, the property to which they apply, the temperature, and the pressure, but not with the concentration of the solution. The formula can obviously apply only to properties for which P,, has a finite value. Thus it is inapplicable to elec- trical resistance, for which P,, would have a practically infinite value. * Abstract of a paper read before the Nova Scotian Institute of Science. Communicated by the Author. 4 Se _-s. On the Physical Properties of Aqueous Solutions. . 47 Simple Solutions. In order to test the applicability of the above expression I have determined the ionization-constants for the density, thermal expansion, viscosity, surface-tension, and refractive index of solutions of Sodium and Potassium Chlorides, by the aid of observations made by Bender*, Briickner f, and Rothert. I selected these observations as a first instalment not because of their precision (for in one or two cases more exact obser- vations are available), but because these observers, in all cases but one, determined the values of the above properties for mixtures of solutions as well as for simple solutions. I selected the above chlorides partly because I thought it well to begin with salts of simple molecular structure, but largely also because, for the purpose of calculating the conductivity of mixtures of them (as described in my paper on this sub- ject§), I had already obtained interpolation formule and curves which, judged by the results of that paper, gave with considerable accuracy the ionization-coefficients of the simple solutions of these salts in terms of their molecular concentra- tion. ‘To save space I may tabulate here the values of the ionization-coefficients used in the calculations for simple solutions. They are as follows :— Sodium Chloride. Potassium Chloride. Tonization- Tonization- Grm.-mols. 3 Grm.-mols. : per litre. ee zh per litre. Saoaaeee at 25 "792 1875 8267 3) 736 °3402 811 "8928 6866 315 “796 1:0 676 °5 "788 ro” 633 6856 “769 1°8353 601 “75 "768 220 "0866 1:0 "756 2°5 5504 1-0467 "755 2°8373 °5255 1:4292 "731 30 514 1:5 "731 3°93875 4516 2:0 “712 27185 "7048 2°5 *695 2°986 “681 3:0 “680 _* Wied. Ann. vol. xxii. (1884) p. 184, and vol. xxxix. (1890) p. 89. T bid. vol. xlii. (1891) p. 293. t bid. vol. xxi. (1884) p. 576, § Phil. Mag. [5] xli. p. 276 (1896); and Trans. N.S. Inst. Sci. ix. (1896) p. 101. 48 Prof. J. G. MacGregor on the Relation of the Physical These coefficients were obtained from Kohlrausch and Grotrian’s and Kohlrausch’s observations of conductivity at 18° C.* In obtaining them I took the specific molecular con- ductivity (referred to mercury) at infinite dilution to be 1216 x 10—° for KCl, and 1028 x 10-8 for NaCl, not being aware at the time that Kohlrausch had given 1220 and 1030 respec- tively as more exact values. Nevertheless, to save labour I have used the above values of « in the calculations of this paper, having satisfied myself by a re-calculation in one case that no appreciable difference in the results would be pro- duced by the employment of more exact values. It will be noticed that in one or two cases the above values of @ are obviously a little out; but they would seem to be sufficiently accurate for my purpose. I did not foresee the extent of the calculations, or I should have determined all the values of «. required at the outset, and checked them by comparison with one another. I have determined the ionization-constants (& and /) in all cases in which more than two observations of a property on solutions of sufficient dilution were available by the method of least squares. The constants thus determined and used in the calculations are tabulated below. In all cases the ayail- able observations had been made on solutions of such great concentration that the values of the constants obtained cannot be regarded as exact; but the calculations may serve as a test of the general applicability of the expression referred to above. The only available observations, so far as I know, on solutions of sufficient dilution for the determination of the ionization-constants and the limits of concentration within which the above expression is applicable, are those by Kohl- rausch and Hallwachst on the specific gravity of dilute solutions, from which two of my students have undertaken to determine the density-constants for the salts and acids exa- mined. With regard to the observations which I used in deter- mining the various ionization-constants, the following state- ments should be made :— Bender’s determinations of density (7. e. specific gravity referred to water at 4° C.) were made at 15° C., but were readily reduced to 18° by the aid of his observations on the thermal expansion between 15° and 20° of the same solutions. According to his statement, the fourth place of decimals in his values may be in error by +2 or +3. The density of water was taken to be 0°99863. * Wied. Ann. vi. (1879) p. 37, and xxvi. (1885) p. 195. + Wied. Ann. lili. (1894) p. 14. —— ee ee ee ee ee Properties of Aqueous Solutions to their State of Ionization. 49 Bender’s determinations of thermal expansion are for the interval between 15° and 20° ©.; and will therefore be suffi- ciently nearly proportional to the coefficients of expansion at 18° for my purpose. He considers that they may be in error by +2 in the sixth place of decimals. On plotting his obser- vations, however, it becomes obvious that they do not all attain this degree of accuracy. The expansion of water was taken, according to his observations, to be 0°0;878 for the same interval. Briickner’s observations of viscosity were made at 15° C.; but he gives an interpolation formula, applicable between 15° and 20°, by means of which at least approximate values for 18° were obtained. His values for water at 15° and 20° do not agree well with those given by Landolt and Bornstein. I have therefore taken 0:010613 as the viscosity at 18° of the water used by him, a value which has to his value at 15° the same ratio as Landolt and Bérnstein’s for the same tempe- ratures. The actual concentrations of Briickner’s solutions differed from those given in the tables below by about 0-1 per cent.; but so small a difference could produce no appre- ciable error in the result. He gives as his “ mean probable error of observation,’ +2°4 in the fifth place of decimals for sodium-chloride solutions, and +1°8 for those of potassium chloride. Rother’s observations of surface-tension were made at 15°, and are therefore not precisely comparable with calculated values based on the values of ionization-coefficients for 18°. From Kohlrausch’s data*, however, it would appear that between 15° and 18° in the case of potassium-chloride solu- tions containing 0'5 and 3 gramme-molecules per litre, the - lonization-coefficient changes only by about 0°13 and 1°3 per cent. respectively ; and in the case of sodium-chloride solu- tions of the same concentrations only by about 0°4 and 0°6 per cent. respectively. For the more dilute solutions, there- fore, my calculations will be practically comparable with Rother’s observations. He seems to regard his determina- tions as possibly in error by + 5 to 8 in the third place of decimals. The surface-tension of the water he used he found _ to be 7°357. Bender’s observations of refractive index were made at 15° C., but were reduced to 18° by means of data provided in his paper, based on observations made by Fouquét. The refractive index of the water he used he found to be 1:33310 * Wied. Ann. xxvi. (1885) p. 228. + Compt. Rend. \xiv. (1867) p. 121. Phil, Mag. 8. 5. Vol, 43. No. 260. Jan. 1897. 1D 50 Prof. J. G. Macgregor on the Relation of the Physical Sodium Chloride Potassium Chloride Solutions. Solutions. Grm.-mols. Observed Cale. ‘Differ |Grm. mols. Observed} Calc. per litre. | value. | value. ene? | per litre. | value. | value. Density (Bender’s observations). . 0-25 | 100898 1:00916, +0-0,18 01875 | 100752 1-ca731 | 0-5 | 101930, 1:01929, — Ol 0-379 101567 101586 1-0 — 1:03925 1:03910 — 15 0-75 | 1:03317 | 1:05278 15 1°05834 1:05842) + 08 1-0 | 104562 10401 >0 107772, 1-07701 71 15 1-06630 1-06621 aa 109635 1-09552 ~00, 101 2-0 108767 | 1-08823 | 2-5 | 110755 1-11008 | 3°0 | 1:18057 -1-13177 | Thermal Expansion (Bender's observations) 0°25 | 001013 -001022, +0:0,9 0-1875 000963 000966 05 | €61141 , 001141; + 0 0-375 001037 ‘001040 1-0 001357 | 001849) — 8 0-75 001183 -001173. 15 | (001522 -001526) + 4 1-0 001249 -001255 20 | 001663 -001657| — 6 15 | 0013895 -001395 2-5 | 001776 | -001769| — 7 2-0 001500 -001517 | 3 001876 -001848| —0-0,2 -2°5 001580 -001621 | | ' Viscosity (Briickner’s observations). 0-5 010988 -010978 —00,10 05 010457 -010451 | 10 011480 011475 — 05 140 010395 -010379 | 15 012048 012047 — 01 1-5 010351 ‘010366 | / 20 012707 «0127380 + 23 2-0 ‘010394 -010393 | 25 013472 -015458 — 14 2-5 “O10H4 “O10S57 | | 30 014573 «014267 —0-0,106 2-0 ‘010566 -010555 : | Surface-tension (Rother’s observations) 08928 7482 | 7482 +0000 03402 | 7411 7-408 0°8353 7629 7629 == 0 0°68556 7460 | 7-462 2-8373 7780 | 77798 + 18 10467 =| 7518 | 7319 39375 | 7954 7-997 + 4 14292 | 7584 | 7583 | | 21851 | 7-705 | 7-709 | | 29859 | 7844 ee 7846 bo hohe OS C1 Go or ——_ | 133824) 133824 134307 | 134306 1 | 13477 | 135213 | 1°35673 1 35632 bo by RR © nO wd cr Difference. —0°0,21 -- 19 _ 39 + 39 = 09 56 +0°0,285 + 120 +0-0,05 + 03 _ 10 + 06 35 co +} «Af + 41 —00,06 ~ 16 + 15 oe ol — 13 = ll — 0-003 + 2 _ 1 = | + 4 + 2 133808 133806 +0-0,03 134278 134274, — “O4 134721 | 134722) a 135179 1-35158 21 135623 1'35682| — — Properties of Aqueous Solutions to their State of Ionization. 51 at 18° for the D line. He seems to regard his observations as possibly in error by +1 in the fourth decimal place. The Tables on page 50 contain the results of the calculations of the values of the physical properties mentioned, with both the observed values on which the determination of the con- stants was based, and a few additional observed values for stronger solutions. The following comments may be made on the above tables: — Density.—NaCl. The first four observations were used in determining the constants ; and up to a concentration of 1°53 the differences are within the limits of experimental error, and show a satisfactory alternation of sign.—KCl. The first five observations were used. The differences are large, but the alternation of sign shows that the expression is applicable. On plotting Bender’s values they are readily seen not to lie on a smooth curve. Thermal Expansion.—NaCl. The first four observations were used. The differences up to a concentration of 2°5 are probably within the limits of experimental error, and their alternation of sign is satisfactory.—KCl. The first five ob- servations were used. ‘he differences are not so satisfactory as in the case of the sodium salt either as to magnitude or sion; but on plotting the observations the third is seen to be ‘somewhat out; and it is obviously to this observation that the defective agreement is due. Viscosity.—NaCl. The first five observations were used. The differences are within the limits of error, but the signs are not satisfactory. The fourth observation, however, appears to be defective. Miitzel™, in applying a formula for viscosity in terms of density and concentration to these observations, found also that this observation was out. It is worth noting, also, that Miitzel found his formula, which expressed the in- crease of viscosity due to the salt in solution on the assump- tion that the only action occurring was between salt and water, was applicable to only the first five of the above ob- servations. To represent the viscosity of stronger solutions he had to introduce a term expressing the effect due to the mutual action of the molecules of salt—KCl. All six obser- vations were used. The agreement in this case is quite satisfactory. Surface-Tension.—NaCl. Only two observations on suf- ficiently dilute solutions were available, and the applicability of the formula cannot therefore be tested. The constants were found, for use in the calculation of the surface-tension of mixtures—KCl. The first four observations were used, * Wied. Ann. xliii. (1891) p. 35, K 2 52 Prof. J. G. MacGregor on the Relation of the Physical and the agreement is quite satisfactory up to a concentration of 8 grm.-mols. per litre. ; Refractive Index.—In the case of both salts the first three observations were used, and in both the agreement is quite satisfactory up to a concentration of about 2 grm.-mols. per litre. The above tables seem to be at any rate quite consistent with the possibility of expressing the values of at least five of the physical properties of moderately dilute solutions in terms of their state of ionization. I hope to find leisure at an early date to extend the investigation to solutions of salts and acids of a more complex character and to other properties. The following are the ionization-constants used in the above calculations :— Sodium Chloride. - Potassium Chloride. | k. l, ye l. i ES | —— a Density 1 !sst22, <5 | +°030841 +:045079 +°035438 +°048591 | | Thermal Expansion —-0001445| +-0007658 — “000614 + 0006965 | IP WASEOSILY 22% cc2se2<5 | + 002347 + 0001504 |} +-001904 — 0009247 | Surface-Tension .... +°20574 + 11001 +°24949 +:126806 | | Refractive Index.... +-006318 | +-011713 || 4-0027853 | +-011853 | i ) \ These constants are obtained from solutions of too great concentration to be regarded as exact values. Nevertheless it may be admissible so far as these two salts are concerned to draw the following conclusions :—Undissociated and dis- sociated molecules are nearly equally effective in increasing the density, those dissociated, however, heing somewhat the more effective of the two. (%) Undissociated molecules diminish the thermal expansion, those dissociated increasing it to a greater extent. (3) In the case of viscosity it is the undissociated molecules which have the preponderating influence, those dissociated having but a slight effect, which may be an increasing ora diminishing effect. Thus Arrhenius’s expectation that all dissociated ions would be found to diminish viscosity seems to be only partially realized, though possibly from observations on more dilute solutions, both l’s might be found to be negative. (4) In the increase of surface-tension the undissociated molecules have about twice as great an influence as the dissociated. (5) In increasing the refractive index it is the dissociated molecules which have the pre- Properties of Aqueous Solutions to their State of Ionization. 53 ponderating influence ; and their superiority is greater in increasing the refractive power than in increasing the density. Mixtures of Solutions. For a solution containing several salts, 1, 2, &c., the value of a property, according to the conception under considera- tion, will be :— | P=P,+h,(L—a) ny + Ley + hy (1L eg) ng + lyctgngt+ &e., . (2) the n’s being numbers of gramme-equivalents per unit volume of the solution. If the solution have been formed by the mixture of the volumes x, and v, of two simple solutions of salts, having one ion in common, for which, before the mixing, the property had the values :— i Py+ k,(1l—a,)ny + ae, (3) then, since, on mixing, the state of ionization will, in general, change, we shall have as the value of the property for the mixture, assuming no change of volume on mixing, UV} P= Pe. — (A,(1 = ay’) ny + L,ce;/ny) + (ke (1 = 0t,') No ++ [,c¢9/Ng) Opa ¥2 the n’s being numbers of gramme-equivalents per unit volume of the original simple solutions, and a,’ and a,’ being the ionization-coefficients in the mixture. As the values of the k’s and U’s have been determined above for sodium and potassium chloride for a number of properties, and as I have shown in my paper on the “ Conductivity of Mixtures,”’ cited above, how the ionization-coefficients after mixing may be determined, it should be possible to predict the values of these properties for mixtures of solutions of these salts. The following tables show that this can be done. The ionization-coefficients were determined in the way described in the paper referred to. The constants & and / employed in the calculations were those determined above. ‘The observa- tions were made by the authors whose determinations for simple solutions were used above ; in fact in most cases it was the solutions of the tables given above which were mixed. The limits of experimental error are thus of about the magni- tudes mentioned above in each case. All remarks made above with regard to the reduction of observations to 18°C., the values of the property for water, &c., apply also to the mix- tures. Inall cases, except that of surface-tension, the solutions mixed were mixed in equal volumes. Unfortunately, Bender made no observations on the refracting power of mixtures. 54 . On the Physical Properties of Aqueous Solutions. Constituent Solu- Ionization tions (grm.-mols. Coefficients in per litre). Mixture. Observed | Calculated | 7. : Value. Value. EES 122 NaCl. | KCl. NaCl. | KCl. Density (Bender’s observations). 10 01875 ‘7268 “7720 1:02358 1-02350 —0:0,08 55 0:375 “14 “7625 | 1:02785 102766 — 19 % 0-7 "688 7629 103641 103600 —- 41 i 10 ‘6728 "7632 104139 104158 19 Fe 15 "6494 “7478 105293 1:05263 — 0:0,30 5 30 61438 7283 1:08580 108595 + — ts Thermal Expansion (Bender’s observations). 10 0°1875 “7268 “7720 001174 | -001174 +0°0,00 5 0375 714 "7625 ‘001208 0012035 — 05 Ms 0°75 688 "7629 001275 001264 — tll Es 1:0 6728 "7632 ‘001297 001305 4° “08 bs 15 "6494 ‘TA78 001376 001376 ae #8 3 6143 ‘7283 "001543 001596 + 53 Viscosity (Briickner’s observations). 10 | 05 | -7os9 | -7635 | -o1o9s0 | -o10947 | +00,07 Ms 1:0 6728 7632 ‘010918 ‘010920 “02 a 15 6494 ‘7478 010876 010915 Fe 20 7283 010890 010956 a 86 Surface Tension (Rother’s observations). | 6143 Constituent Solutions. Concentration (grm.-mols. per litre). NaCl. KCl. 08862 1-8109 0°8824 2°38406 18155 1-411 21822 0°6862 2°9887 0-6836 Tonization Coeflicients in Caleu- Volume Mixture. pees lated (litres). Mes) Walne: NaCl. KCl. NaCl. KCl. 0:14487 | 0°14545) 0-6906 | 0°7682 | 7477 | 7-472 0:13993 | 0°14096 | 0°6087 | 0°7279 7607 7-602 014489 | 0°138659 | 0°6123 | 0°7311 7600 7591 0:13511 | 0:14544| 06027 | 07298 7622 7616 0:13996 | 0°18241/ 05185 | 0°7125 7734 7°810° Diffe- rence. i . 4 " F 4 4 : i 4 3 On the Properties of Electric Waves. 55. It will be noticed that in the case of the third mixture of the density and thermal expansion series (the same mixture) the differences are comparatively large, but it is obvious from the data of the fourth column in these series that the ionization-coefficients have not been accurately determined for mixtures of about the concentration of the one referred to. With these exceptions the agreement between observed and calculated values is satisfactory, the differences being either well within or at worst on the limit of observational error, up to mean concentrations of about 1°5. The determi- nation of the ionization-coefficients was especially difficult in the case of the surface-tension observations, because Rother mixed equal weights of his simple solutions, not equal volumes. Nevertheless, in all except the strongest of these mixtures, the differences are probably not beyond the limits of experimental error. Obviously, alternation of sign is not to be expected in these calculations. [To be continued. | IX. On a complete Apparatus for the Study of the Properties of Electric Waves. By JAGADIS CHUNDER Boss, JA. (Cantab.), D.Sc. (Lond.), Professor of Physical Science, Presidency College, Culcutta*. f§\HE work of Hertz and his eminent successors, both here Tf and on the Continent, has opened out for study a new region of ethereal vibration, bridging over the gap that hitherto existed between the comparatively slow ether vibra- tions and the quick oscillations which give rise to radiant heat. In the vast range of possible ether vibrations we recognize only a few octaves by our senses; the rest are beyond our perception. Many unexpected properties of * Read before the British Association at Liverpool, 21st Sept., 1896. Communicated by Lord Kelvin, F.R.S. [Tke apparatus described in this communication is founded on Prof. Oliver Lodge’s and M. Branly’s discovery of the “coherer”’ for detecting electric waves. The general design of the apparatus, both in respect to generator ard receiver, was given originally by Prof. Lodge, and described in his book ‘The Work of Hertz and some of his Successors, published by the Electrician Co. in 1894.—Ebrrors. ] + By “here” is meant not only England, but Professor Lodge’s laboratory especially, where the paper was read, and where, as is well known, some of the most important investigations on electric radiation have been carried out. For my interest in the subject I owe greatly to Prof. Lodge. 56 Prof. J. ©. Bose on a Complete Apparatus for these little-known ether waves are now being gradually dis- covered. Confining our attention to the electric waves, we find that there are many important problems which may perhaps be better attacked with these comparatively slow vibrations ; among which may be mentioned the determina- tion of the indices of refraction of various substances which are opaque to visible light, but are transparent to the electric ray ; the relation between the dielectric constant and the refractive index when the rates of oscillation are made com- parable in the two determinations ; the variation of the index with the frequencies of vibration. Then there are the phe- nomena of double refraction, polarization, and the magnetic rotation of the electric ray ; the determination of the wave- length, and other problems of a similar nature. The fascination of the subject drew me to its study, though the investigations were rendered exceedingly difficult in India from want of facility for making the necessary appa- ratus. I ultimately succeeded in constructing a few instru- ments with which I was able to obtain the values of the indices of refraction of varicus substances for electric waves, the wave-length of electric radiation, to demonstrate the phenomena of double refraction and polarization of the electric rays, and to find out certain substances which act as electric tourmalines. The simplified apparatus with which many of the properties of electromagnetic radiation may be studied is here exhibited. This is a duplicate made by Messrs. Elliott, Brothers, of the apparatus which I brought from India. I also take this opportunity of thanking Mr. Bolton, F.R.A.S8., of the Mathematical Instrument Depart- ment, Calcutta, for the divided circle in my apparatus. The following are the experiments which may be carried out with this apparatus :— A. Verification of the laws of reflexion. 1. Plane mirrors. 2. Curved mirrors. B, Phenomena of refraction. 1. Prisms. 2. Total reflexion. 3. Opacity caused by multiple refraction and reflexion. 4, Determination of the indices of refraction. C. Selective absorption. 1, Hlectrically-coloured media. bene re ee eee the Study of the Properties of Electric Waves. 57 D. Phenomena of interference. 1. Determination of the wave-length by curved gratings. 2. Bi-prism experiments. E. Double refraction and polarization. . Polarizing gratings. : 3 crystals. . Double refraction produced by crystals. 3 3 other substances. i és - by strain. . Circular polarization. . Magnetic rotation. . Electro-polariscope and polarimeter. DAIS OTH Oo NS In the list of experiments above-mentioned, the determina- tion of the wave-length by curved gratings has been carried out with a larger apparatus (vide Proc. Roy. Soe. vol. lx., “On the Determination of the Wave-length of Hlectric Radiation”). Hxperiments with circular polarization and magnetic rotation and with the bi-prism are still in progress. All the others have been repeated with the apparatus to be described below. The complete apparatus consists of :—(1) A radiating apparatus emitting electric waves of short length; (2) A receiver used as a detector of electric radiation; and (3) Various accessories for the study of the different phe- nomena. I used various méthods for the production of oscillatory discharge. One method was to imbed a row of metallic beads, with small spark spaces, in solid paraffin, the end beads being in connexion with the electric generator. Another method was to have the two sparking-balls immersed in kero- sene ; thisis effective, but troublesome. The simplest method, however, is Prof. Lodge’s arrangement of two side balls and an interposed sphere. Electric oscillation is produced by sparking between two beads of platinum and an interposed sphere of the same metal. The discharge ceases to be oscillatory when the ball is roughened, and a platinum ball resists, to a great extent, the disintegrating action of the sparks. Two jointed electrodes carry the two beads at their’ ends. The distance between the beads and the interposed sphere can thus be adjusted. ‘This is a matter of importance, as the receiver does not properly respond if the spark length is too large. It is more convenient to use short electric waves, and these are 58 Prof, J. C. Bose on a Complete Apparatus for obtained by making the radiating spheres very small. The shortest wave-length produced is about 6 mm., and the corre- sponding number of oscillations is about 50,000 millions in a second. The frequency of vibration in this case will be seen to be about thirteen octaves lower than that which produces visible radiation. ‘The intensity of radiation in the above case is rather feeble, and I use in general electric waves of about half an inch in length. The jointed electrodes carrying the beads are in connexion with a small modified Ruhmkortt’s coil, actuated by a small storage cell. The usual vibrating interrupter is generally a source of trouble ; the contact points get worn out, and the break becomes irregular. The great objection (as Hertz found) to the continuous production of secondary sparks is the roughening of the surface of the radiating ball, by which the spark ceases to be oscillatory. It is very troublesome, in the middle of an experiment, to be obliged to take out the radiator for polishing. The flash of radiation produced by a single break is enough for an experiment, and it is a mere waste to have a series of useless oscillations. In my apparatus for quantitative measurements I have therefore discarded the vibrating interrupter in favour of a simple break- key. To econ- omize space, I wind the condenser (a long stiip of paraffined paper with tin foils on opposite sides) round the secondary of the coil, appropriate connexions being made with the interrupting key. The coil and a small storage cell are enclosed in a metal box, in accordance with the precautions which Prof. Lodge had found to be necessary. I used tinned iron in order to screen the space outside from magnetic disturbances due to the making or breaking of the primary circuit of the coil. A sudden magnetic variation disturbs the receiver. The iron box is placed inside a second box of thick brass or copper. These precautions are taken to prevent straying of electric radiation. Through a small opening in the back or side of the box the stud of the press-key projects. In front of the box is the radiator- tube, which may be square or cylindrical. Inside this tube is mounted the radiating originator. A flash of electric radiation is produced by a proper manipulation of the interrupting a ee Yr 4 : | the Study of the Properties of Electric Waves. 5Y key. The radiating apparatus may thus be made very small and portable, and requires very little attention. After the Fig. 2.—The Radiating Box. storage cell is once charged, experiments may be carried on for days, a flash of radiation being produced at any time by merely manipulating the key. Spiral Spring Receiver. For a detector of radiation I used a form of Prof. Lodge’s coherer. At first I used one made of metallic filings, origi- nally discovered by M. Branly; but great difficulty was experienced in making the receiver respond to different vibrations, and in the capriciousness of its response. The difficulty was still further enhanced when the radiator and the receiver had to be enclosed in narrow tubes to enable angular measurements to be made with any accuracy. It seemed to me that the frequent loss of sensibility might be due to the particles getting jammed together, and the fatigued condition of contact surfaces. In order to avoid this I used a layer of narrow spirals of steel, lying side by side, and rolling on a smooth surface. The points of contact are numerous, and fresh surfaces can be brought into action by a slight rolling of the spirals. By this spiral-spring arrange- ment the pressure exerted on contiguous spirals is also made fairly uniform. From a series of experiments carried out to determine the other causes which may be instrumental in producing loss of sensibility, I found that the sensibility of the receiver to a given radiation depends (1) on the pressure to which the spirals are subjected, and (2) on the H.M.F. acting in the circuit. The pressure on the spirals may be adjusted, as will be described later on, by means of a fine screw. The E.M.F. is varied by 60 Prof. J. C. Bose on a Complete Apparatus for a potentiometer-slide arrangement. This is a matter of great importance, as 1 often found a receiver, otherwise in good condition, failing to respond when the H.M.F. varied slightly from the proper value. The receiver, when subjected to radiation, undergoes exhaustion. The sensibility can, how- ever, be maintained fairly uniform by slightly varying the E.M.F. to keep pace with the fatigue produced. The receiving circuit thus consists of a spiral-spring coherer, in series with a voltaic cell and a dead-beat galvanometer. The receiver is made by cutting a narrow groove in a rect- angular piece of ebonite, and filling the groove with bits of coiled steel springs arranged side by side in a single Jayer. The spirals are prevented from falling by a glass slide in front. The spirals are placed between two pieces of brass, of which the upper one is sliding and the lower one fixed. Fig. 3.—The Spiral Spring Receiver. These two pieces are in connexion with two projecting metallic rods, which serve as electrodes. An electric current enters along the breadth of the top spiral and leaves by the lowest spiral, having to traverse the intermediate spirals along the numerous points of contact. The resistance of the receiving circuit is thus almost entirely concentrated at the sensitive contact-surface, there being little useless short-cireuiting by the mass of the conducting layer. When electric radiation is absorbed by the sensitive surface, there is a sudden dimi- nution of the resistance and the galvanometer spot is violently deflected. By means of a very fine screw the upper sliding-piece can be gently pushed in or out. In this way the spirals may be very gradually compressed, and the resistance of the receiver diminished. The galvanometer spot can thus easily be brought to any convenient position on the scale. When ee ee ee a the Study of the Properties of Electric Waves. 61 electric radiation falls on the sensitive surface the spot is deflected. By a slight unscrewing the resistance is in- creased, and the spot made to return to its old position. The receiver is thus re-sensitized for the next experiment. The sensitiveness of the receiver may be increased by a proper adjustment of the H.M.F. acting on the receiving eireult. The receiver at each particular adjustment responds best to a definite range of vibration lying within about an octave. The same receiver could, however, be made to respond to a different range by an appropriate change of the H.M.F.; very careful adjustment of this is necessary to make the receiver respond at its best to a particular range of electric vibration. or simple experiments the adjustment of the receiver is not difficult; but for delicate experiments eareful manipulation is necessary. The proper adjustment of the H.M.F. is effected by taking a derived current from a circular potentiometer-slide, fixed at the base of the galvanometer. ae oe It may be, therefore, that an estimate of the resistance in the tube can be obtained by measuring the self-induction which is required to change from the blue dis- charge to the red. When the tube containing argon at a suitable pressure is brought near a Hertz oscillator giving a rate of about 115,000,000 oscillations per second, it immediately shows the blue colour. In this case the oscillator consisted of two zine plates about 40 centim. square with a spark-gap between them. The capacity and impedance of the circuit were ex- tremely small. The extreme sensitiveness of an argon tube to oscillatory discharges leads us to believe that it w vill be of great use in the study of wave-motions of electricity. As we have seen, it is competent to show when the Hertz oscillator is w orking properly, that is, sending forth electrical oscillations and not unidirectional discharges. The change of colour in the tube from red to blue is so marked that an argon tube reveals what is not shown in a conspicuous manner by other gases. We have thought this remarkable property of an argon tube worthy of being distinguished by a name which might describe it, and we have therefore called an argon tube fitted for the study of electrical waves a Talantoscope (raAdvTwors). In an oscillatory discharge the molecules receive powerful electrical impulses of opposite sign. These impulses are separated, it may be, by one millionth of a second. It is significant that the shorter wav e-lengths of light accompany these electrical oscillations. It is our purpose to extend our study of the effect of electrical oscillations through more highly rarefied media in which arise the Rontgen rays. These rays are probably highly modified by the oscillatory discharge. A battery of a iarge number of cells now at our command will afford the best means of studying this subject ; Two New Pressure-Gauges for the Highest Vacua. 83 for its discharges, as we have pointed out, are free from the fluctuating effects produced by induction- coils, transformers, and Hecirieal machines. Our present paper is therefore only preliminary to a more exhaustive study of the discharges of electricity through rarefied gases by means of a stor age battery of ten thousand cells, which will give an electromotive force of about twenty thousand volts. Harvard University, Cambridge, Mass., U.S.A., December Ist, 1898. XIV. Two New Pressure-Gauges for the Hig Vet Vacua. \ By WitL1AM SUTHERLAND * ITHERTO the M‘Leod gauge has been poets as the most accurate instrument for the measurement of pressures in vacua, although there has been a good deal of misgiving as to the limit up to which its indications are fairly reliable, with an impression that near a millionth of an atmo its measurements become illusory. Baly and Ramsay, in their experiments on rare gases (Phil. Mag. [5 | xxxviii.), after working with two M‘Leod gauges of very high sen- sitiveness, pronounced the type of gauge worthless “for air and CQO, though reliable for hydrogen; but the failure of their gauges with air was due to a most interesting and very special phenomenon, to be considered in my next paper, liable to occur only under special circumstances and not affecting the principle of the gauge or its application to air with avoidance of the perturbing conditions. In the case of CO, the M‘Leod gauge is less reliable than with other ases on account of some action between glass and CQ,, especially if moisture be present ; but this does not necessitate that the gauge should be worthless for CO,, but that there should be a limit to its application, this limit probably depending on the nature of the glass and its treatment. To- wards the end of this paper it will be shown that Crookes’s M‘Leod gauge begins to fail decidedly at 5/i0® atmo, with increasing unreliability at lower pressures, the cause of which will be proved to be probably a small residue of water-vapour dissolved, so to speak, in the glass ot the gauge. ‘Thus, if the theoretical reasoning of “ Boyle’s Law ‘at very Low Pres- . sures” + is sound, the principle of the M‘Leod gauge ought to be applicable up to any degree of rarefaction, if we can only make it of such a material or so manipulate it as to free it from this trouble with moisture. * Communicated by the Author. + Supra, p. 11. 84 Mr. W. Sutherland on two New But it is very desirable to have an independent method and instrument for controlling the indications of the M‘Leod gauge, reaching to higher vacua and simpler in its prac- tical working ; and one outcome of the paper on ‘‘ Thermal Transpiration and Radiometer Motion” * is the furnishing of two instruments capable of independently measuring the pressure in high vacua. These two instruments were in a manner united into a single one in Crookes’s torsion radio- meter briefly described but rather fully discussed in that paper; and though for some purposes there might be advantage in uniting the two forms, each would be capable of its best performance when separate. The two instruments are a disk viscosity-meter and a torsional radiometer of special design to be discussed in this paper. Crookes used his torsion radiometer as a viscosity-meter by forcing it to vibrate and determining the decrement of the logarithm of the angular amplitude of successive vibrations. At pres- sures near one atmo the vertical plate of the radiometer in oscillating round a vertical axis in the bulb sweeps air bodily in front of it and draws air behind it in a very complex manner, so that its motion is conditioned partly by the mass motion of the gas, as well as by viscosity of gas and viscosity of suspending fibre ; but as Crookes’s experiments showed, in a manner brought out by Stokes’s theoretical discussion (Phil. Trans. clxxii.), the effect of the mass motion of the gas on the log. dec. disappears rapidly, and the log. dec. is practically constant for a considerable range of pressure, proving that viscosity alone is effective in retarding the motion of the vibrating vertical plate. The following values of 10* times the log. dec. in air are taken from Crookes’s results (Phil. Trans. clxxii.) :-— p(mm.).. 760 550 3801 155 47 12 4 3 1 1124 1073 1022 1006 1001 1000 1000 994 988 These show that from 47 mm. to 4mm., the latter being only 1/12 of the former, the log. dec. is constant ; so that at this range of pressure the mass motion of the gas is negligible, and the viscosity is independent of pressure, as it ought to be according to Maxwell’s discovery, so long as slipping of the gas on the solid surfaces of the edge of the plate and the walls of the bulb is negligible ; but then at 3 mm. and 1 mm. the log. dec. diminishes decidedly in a manner more fully illus- trated by the following further data from Crookes, the unit of pressure being now 1/10° atmo :— (De Peepers 1000. 495 ~~ 300. +100 53 24 13 8 G88" 529009052 816 774 ~620 ~~ 500 390 * Phil. Mag. for November and December 1896. SS eee ee ee ee — a a Pressure-Gauges for the Highest Vacua. 85 Now, as was first shown by Kundt and Warburg, and as has been shown in “Thermal Transpiration and Radiometer Motion,” the effect of slipping of gas on the influence of viscosity is to replace the viscosity » by /(1+26/D), where ¢is the coefficient of slipping and equal to ad,, where a is a fraction which is probably nearly the same for most gases, and X, is the mean free path of a molecule of the gas near the solid surface, D being distance between moving and resting solid surfaces ; for a given gas, d, is nearly proportional to a, the mean free path of a molecule far from the surface, and as X is inversely proportional to the density, we have the result that ¢ varies inversely as the density of the gas. Thus a mea- surement of slipping furnishes a means of measuring density, and therefore, if the law connecting density and pressure is” known, of measuring pressure. If Boyle’s law holds, then X=) p/p, where Xp is the mean free path at some standard pressure pp ; thus 7 is replaced by n/(L+2arp/Dp). When p is large enough, this is indis- tineuishable from 7, as we saw to be the case in Crookes’s experiments with air from 47 mm. to 4 mm., through which range the log. dec. retained a constant value which we may denote by L. Then, if / is the log. dec. at lower pressures, L/l gives 1 + 2ar po/Dp, whence we can get values of 2a 9p/D which ought to be all the same. But there is first one little correction to make, namely that for the viscosity of the torsion fibre, because a small constant portion of the log. dec. is due to its small viscosity ; it is the value of the log. dec. for the apparatus if an absolute vacuum were attained in it. Call this part of the log. dec. w, then jot-1)p = ele ten ee mee.) At the higher values of p we can neglect w and obtain at once a mean value of the constant 2ad)p,/D, and then with this as a known quantity solve for ~ at the lower pressures. In this way, from the data already given for air, 2aX9p)/D appears to be 15 and w to be 004. With these values and that for L, namely °1000, the last equation becomes one for obtaining p by a measurement of /; and to show how it works, we give the values of p obtained by it from Crookes’s values of l already given :— p by gauge ..........0 1000) 49555300) (100) 53), 245018 8 p from log. dec....... 11538 406 288 101 49 28 188 8&6 Now it is obvious that the new method of finding the 86 Mr. W. Sutherland on two New pressure in a vacuum becomes less delicate when / becomes nearly equal to L, for then the value of p is liable to be greatly affected by only a small error in J. Thus, for exampie, a diminution of / in the first case from :0988 to °0986 would reduce the calculated pressure to 1000 ; thus the first two or three values of the calculated pressures belong to a range where this particular torsion radiometer is not sensitive as a pressure-gauge. Of course we are at present assuming that the pressures as given by Crookes’s M‘Leod gauge are correct ; it must be remembered that what the indications of the M‘Leod gauge really amount to is a sort of a measure of the density of the gas, with an inference as to its pressure by means of Boyle’s law, and I have already pointed out that the measurement deduced from slipping is strictly only a measurement of density with a pressure inferred by means of Boyle’s law ; the fact, therefore, that the pressures as found by the log. dec. and by the M‘Leod gauge in the last table are on the whole so consistent furnishes no proof of the validity of Boyle’s law at low pressures, but this, however, has been fairly established on other grounds in “ Boyle’s Law at very Low Pressures,” and therefore the consistency of the two sets of pressures is a proof of the relative correctness of the pressures obtained by Crookes with his M’Leod gauge. The great advantage about the new viscosity-meter gauge is that its sensitiveness tends to increase with diminution of the pressure which it has to measure. Let us therefore proceed to compare the pressures of air as found by Crookes’s M‘Leod gauge at still lower pressures, and as calculated by (34) from his measurements of the log. dec. pubygeauge ..aeses- 72 59 ° 41 34 26 19 1:3 10 paicom loss dete.) C0 6:7 5:0 ana 3°6 30 2°5 2°2 LO Plog sdeciese. aes: ofa 6807. 281, 256 | 225 198) ial p by gauge”... 5)<.. 05 “46 “22 “14 ‘06 02 ‘» fromlog. dec. =. “1:82 1°65 1°33 1:25 95 ‘53 HOsoe deer s.; in hydrogen is altered in its relation to X simply by a factor such as (1—ph/A,po) with a limit 1 and not any other number; but if from the last table we take 10 as the value of (2¢/D+°03) p, and compare it with the value 15 for (2¢/D)p in air, which stands for 2ad p)/D, and remember that at any standard pressure py the values of A) for hydrogen and air are as those of »/m?, that is nearly as 2 to 1, we find that (2¢/D+:03)p for hydrogen would have to become 380 to give this theoretical relation of 2 to 1 if the alteration of ‘03 were all that is required; this then indicates that with hydrogen, in addition to a factor (1—ph/Appo) in the relation of 2, to X, there is a factor 1/3 whose occurrence here, and not in deflecting force, has to be explained. The explanation probably lies in the presence of a trace of water-vapour, for notwithstanding the very thorough mea- sures which Crookes took to get rid of the water-vapour after it had given him considerable trouble, I am still in- Pressure-Gauges for the Highest Vacua. 95 clined to think that a trace had been left in the hydrogen which both the Viscometer Gauge and the Transpiration Gauge have succeeded in detecting. The first question that naturally arises is, why should we not have similar evidence of the presence of water-vapour in the case of other gases? the answer to which is that, just as Graham showed experimentally in his study of the viscosity of mixed gases that the viscosity of hydrogen is specially sensitive to the presence of other gases, a partial theory of the phenomenon being given in “The Viscosity of Mixed Gases” (Phil. Mag. | 5] xl.), so it is probable that a small amount of impurity largely affects the slipping of hydrogen while only slightly affecting that of the other gases, the difference between the case of hydrogen and those of the other gases being due to two causes, first, the small attraction of the solid for the hydrogen molecules, whereby they are less condensed at the surface than mole- cules of other gases, so that a given amount of vapour of water in the gas makes a larger impurity in the surface hydrogen than in the surface layers of other gases, and, secondly, the small mass of the hydrogen molecule. Thus we ean give the following general sketch of the effect of the presence of water-vapour in a gas on the surface phenomena which we are treating of at present. Water-vapour appears almost to dissolve in solid glass, forming a union which also retains some free water-vapour at the surface; thus a vibra- ting solid surface would practically carry such a layer of water-vapour as part of itself, and thus the layer would in- troduce error into the slipping of the gas, the amount of which for the ordinary gases is small, but becomes important with hydrogen for the reasons already stated. Now if the water-vapour is mostly gathered at the surface it cannot affect the general viscosity of the gas, but only the slipping and the deflecting force. In the case of hydrogen the effect of the water-vapour seems to be to shorten the mean free path by an amount which is nearly constant, and, moreover, in the case of slipping alters the constant a in the relation ¢=aX to 1/3 of its usual value, so efficient is the layer of massive water molecules in sweeping the light hydrogen molecules with it. The curious result that the shortening of _ the free path of hydrogen near a solid surface by the water- vapour should be independent or nearly independent of the pressure invites inquiry, but we can hardly delay any longer here on this hydrogen episode. Resuming the study of the pressure-gauges, we will now calculate the pressures in Crookes’s highest hydrogen vacua T2 96 Mr. W. Sutherland on two New according to the equations p( fae -14-03)=2aropy/D, . es with L=:0499, w="004, and 2aryp)/D=10°5, and deflecting foree=c//{A”p/(1—ap) +B’ +1/p}, . (86) with of = ANG. A= 0006, w—-0016) 1377-0 104 log. dec. ... 824 304 270 253 232 214 191 172 169 157 130 118 detfor sos 497.45. 337. 3129), 26° =15 240° 39 eee p by gauge ...145 12 8 65.5 94 — 26-18 1:5- dO ea aaeais ptrom log. dec. 163 136102 89 74°63 51 42 41 26525028 mirom def, for. 15-2 133 103 83 77 68 93:8 Zo 22° 17s 1 10° 1:0 fas 1:0 93 7 9” eo eons The numbers in the last row are the ratios of the pressures given by Crookes’s radiometer when used as a viscometer gauge and as a transpiration gauge, and they show that they agree with one another down to a pressure of about 5/10® atmo as given by the viscometer gauge, although at that pressure they have become 50 per cent. larger than the pressure given by M‘Leod’s gauge. Then, just as in the case of air, we find the value of the ratio rise suddenly to be nearly 2 instead of 1, and the same explanation holds for the fact here as for air, namely that the mean free path is getting to be about as large as the radius of the bulb. Nowas the mean free path in hydrogen is about double that in air, the pressure at which the change in the ratio occurs with hydrogen ought to be about double that with air, and as the change occurs at pressures about 5/10° atmo and 2°5/10° as measured by the viscometer gauge, the theoretical condition is realized in the experimental results. According to the viscometer gauge. the lowest pressure is 13 times as great as that given by the M‘Leod gauge, a result - which shows how useful the control of the different gauges by one another will be in measurements of the highest vacua, The change in ratio which we have found both with hydrogen and air seems at first sight to disqualify the transpiration gauge, but it is to be remembered that the magnitude of the change is the result of the unsuitableness of Crookes’s torsion radiometer to serve as a type of the ideal transpiration gauge, which, if designed on the lines explained a few pages back, would be liable to only a trifling change of ratio, which could be reduced to zero if steps were taken to bring the whole eee 7 ics — Prone j ; ; \. ‘ | Pressure- Gauges for the Highest Vacua. 97 inner surface of each of the two chambers connected by the annular space to a uniform temperature. We will now briefly discuss the performances of the two gauges with CO,, CO, and N, by means of Crookes’s measure- ments of log. dec. and deflecting force, for using the latter of which the appropriate values of c’, A’, and B’/” are given in “Thermal Transpiration and Radiometer Motion ;” for using Crookes’s values of the log. dec. we have the following:— CO, CO. Ne: RS Wes 3 chs 822 968 970 Daag Ds: an 15 17 16-6 CO.,,. Co. ts Be ae — Re See 10? Noe. dee......... 424 347) 825. 28 474 448 305 SeORS Pos. oc. canes 16 11 10 8 14 13 7 p by gauge ......... 15 10 9 76 18 12 6:5 p from log. dec.... 14:4 OT. 8:6 Ge 14-9 134 68 p from def, for.... 14:5 9300 Cio a Oo 13:1 TAS) BF N;: CE a a —___—_——— FCs ou Gee EO oe dec......5.+: 420 351 318 257 207 178 BON faeces co. 17 14 13 9 3 1 PDy CAULC 5....0- 13 9°6 83 58 33 2°8 p from log. dec. .... 11° 8:3 TA Sell 3°6 29 p from def. for. ... 10°5 81 73 4:9 15 az) In the case of N, the pressure from the log. dec. and that from deflecting force agree down to about 5/10° atmo, although systematically less than those by the M‘Leod gauge and Boyle’s law; butat the two lowest pressures a great difference appears, which is too large for the same explanation as applied to the change of ratio with air and H,; in comparison with the deflecting force in air that in N, dies away in a very sudden manner—for example, while at 3/10° atmo the de- flecting force in air is about 10, in Ny, it is only 1, a very remarkable difference, calling for further experimental inquiry. Crookes’s measurements for oxygen, being of special im- portance, will be discussed separately in my next paper. The fairly good agreement which we have found between the in- dications of the M‘Leod gauge at low densities and those of the viscometer gauge and the transpiration gauge furnish an indirect proof that there can be no surface condensation which suffices with the gases discussed to produce any appre- 98 Ontwo New Pressure-Gauges for the Highest Vacua. ciable departure from Boyle’s law; for if there were, there could not be a constant relation between density as found by the M‘Leod gauge and by the other two; but as to departure from Boyle’s law due to other causes than surface condensa- tion the agreement telis nothing, as it simply means an agree- ment in three measurements of density. But it is of some importance to learn that surface condensation produces no appreciable effect, even by way of an apparent departure from Boyie’s law in rare gases (see “ Boyle’s Law at very Low Pressures’’) ; of course it is not implied that there is no sur- face condensation, for, on the contrary, its nature and amount kave been calculated in “‘ Boyle’s Law at very Low Pressures,” but in ordinary vessels the mass condensed is a small constant fraction (for a given gas) of the total mass in the vessel, and produces no effect on Boyle’s law to the degree of accuracy of measurement hitherto attained. The trace of water-vapour which was the probable cause of the abnormalities discussed in connexion with hydrogen is also the probable cause of the failure of Crookes’s M‘Leod gauge at pressures near and below 1/10° atmo both with hydrogen and air. As at the lowest pressure in air the M‘Leod gauge gave a measurement of the pressure only 1/26 of that of the viscometer gauge, it follows that 25/26 of the gas in the highest vacuum would appear to have been H,O, which, when the gas is compressed into the volume-tube of the M‘Leod gauge, simply recombines with the glass again ; if this is so, then the pressures calculated from the log. dec. and from the deflecting force both for air and hydrogen are inaccurate, as they ought to be calculated with the values of the parameters for H,O instead of those for air and H,. In fact, if at the highest vacua in both air and H, water-vapour is the main constituent, then /, the log. dec., ought to have the same value both for air and H, at the same erroneous values of the pressure given by the M‘Leod gauge. ‘The following little table furnishes a comparison of the log. decs.:— apparent p... 1°3 1:0 SM eee lip 1O-itor am..5. 175 Lo! 126 115 10*/ for Hy... 164 157 130 118 This shows that our supposition as to water’s forming the chief ingredient of Crookes’s highest vacua is probably true, and therefore the pressures which we previously’ obtained from the viscometer and transpiration gauges at the highest vacua are erroneous, being calculated for air and Hg instead of for H,O, but obviously the amount of their error cannot | On the Physical Properties of Aqueous Solutions. 99 attain to that of the indications of the M‘Leod gauge. Thus there is strong evidence that in the investigations of highly rarefied gases in glass vessels there is always an unremoved trace of water which exercises a perturbing influence in- creasing with the rarefaction, and becoming serious in Crookes’s experiments at about a millionth of an atmo. In investigating the highest vacua it would seem to be desirable to dispense with glass or to ascertain if glass can be obtained which does not exercise a special “dissolving ’”’ action on water-vapour. Melbourne, August 1896. XV. On the Relation of the Physical Properties of Aqueous Solutions to their state of Ionization. By Prof. J. G. Mac- Grecor, Dalhousie College, Halifax, N.S.* [Concluded from p. 55. | Relative Values of a Property for a Mixture and for its Constituents. “ Corresponding” Solutions. WA” change of ionization in general occurs on mixing two solutions, it follows from (3) and (4) that the value of a property for a mixture of two solutions having one common ion will differ from the volume-mean, (v, eeu P,)/(uy + v2), of its values for the constituents by the amount (4-4) (aq — ay) ab ie (5) The name of “corresponding” solutions has been given to solutions for which this quantity vanishes. In general it will obviously have a value, though that value may be small. In most cases this conclusion is borne out by experience. But Rother has concluded from his observations that, in the case of surface-tension, throughout a wide range of concen- tration, solutions of all concentrations are “ corresponding.” Were this the case it would throw serious doubt on the pos- sibility of expressing surface-tension in terms of state of ionization. If, however, with the aid of the constants for NgV9 “IL (ay! —a) + (—h v1 +05 (ay a) all 2 a) V1 + v; surface-tension determined above, we compute, in the case of Sodium and Potassium Chlorides, the difference between the value for a mixture and the volume-mean of the values for its constituents, we find it to be beyond the limit of Rother’s ower of observation. Thus, in the case of his first mixture calculated above, the difference amounts to only 0°0315. His * Communicated by the Author. 100 Prof. J. G. MacGregor on the Relation of the Physical conclusion should thus have been that the difference, if any, between the surface-tension of a mixture and the volume-mean of those of its constituents was within the limits of his experi- mental error. He might even have concluded, however, that there was probably such a difference in the case of Sodium and Potassium Chlorides ; for in all the mixtures of solutions of these salts which he examined, the volume-means of the values for the constituent solutions were found to be less than the values for the mixtures. The above expression (5) will vanish if the constituents of the mixture are isohydric, z. ¢., have states of ionization which do not change in the mixing ; and it will vanish in that case, whatever the values of the other quantities involved in the expression may be. When the constituents are not isohydric the condition of its vanishing will be My (ly — ky) (a! — a )¥2 (6) My, (ly—ky) (ay — ay’) vy SOS Se It is obviously improbable that in any case in which this con- dition may be fulfilled the numbers of gramme-equivalents per litre in the constituent solutions will have a simple relation, suchas 2) 4 = 3. dc. The conclusions drawn by Bender and Briickner from their observations on density, thermal expansion, electrical conductivity, and viscosity, viz. that there is such a simple relation in the case of all ‘‘corresponding’”’ solutions, so far as the properties mentioned are concerned, 1s thus inconsistent with the possibility of expressing the values of these properties in terms of the state cf ionization. Both Bender* and Briicknerf obtained their results from numerous series of observations, in each of which a solution of given concentration of one salt was mixed in succession, in equal volumes, with a number of solutions of different con- centrations of a second salt. having one ion in common with the first. The values of the property under consideration were determined both for the simple solutions and for the mixtures and the arithmetic means of the values for the con- stituents of the several mixtures were found. Curves were then plotted with molecular concentrations of the simple solu- tions of the second salt as abscissae, and the observed values for the mixtures and the arithmetic means of the values for the constituents, respectively, as ordinates. The “ corre- sponding” solutions were indicated by the points of intersec- tion or contact of these curves. In all cases the curves for * Wied. Ann. xxii. (1884) p. 184, and xxxix, (1890) p. 89. + Ibid. xlii. (1891) p. 298. Properties of Aqueous Solutions to their State of Ionization. 101 each series are found to run very close together, so close that it is impossible to determine exactly at what points they touch or cross ; and when the observational errors admitted by the authors are taken into account, they must be considered to be within touching or crossing distance at considerable distances on each side of the points at which Bender and Briickner assumed them to be in contact or to intersect. It is probably needless to give details ; but I may say that I have plotted a number of these curves so as-to indicate accurately all signi- ficant figures, and have found, on taking possible errors of | observation into account, that in no case can a more definite conclusion be drawn than that “corresponding ”’ solutions have pretty nearly the simple relations as to concentration claimed by the authors. i have found also that in most cases the limits of the concentration of the second salt within which the curves must be considered to be possibly in contact, include the isohydric concentration. It would thus appear that both Bender and Briickner drew too definite conclusions from their observations, and that the observations themselves are not inconsistent with the applicability of expression (1) to the physical property of solutions. | Applications of the Assumed Law of Ionization- Constants.— Variation of Temperature and other Coefficients with Con- centration. If the expression under consideration is applicable to solu- tions of moderate dilution it should give by deduction the laws which have been found to hold for particular properties of such solutions, and might be expected to be of use in show- ing their relation to one another. I need not refer here to the more obvious of such deductions, as, for example, the properties of non-electrolytes, or of electrolytes at extreme dilution, but may restrict myself to cases in which both con- stants & and / play a part. The temperature-coetticient for any property of a solution of given concentration will be Ob OF -=|.(0l OF Oa Lee oy, +5-"+(5,—5; Jan t —Bcon riot Py tkn+(l—k)an : The pressure-coefficient will have the same form, p being written for t. The concentration-coefficient will be Fy (7) LaP_ b+ (II (a+ oe P On Pytkn+(l—k)an ~ oh Geena? 102 Prof. J. G. MacGregor on the Relation of the Physical In the case of a solution of a given salt of given concentration, temperature, and pressure, «, n, and @’s rates of change have definite values the same for all properties. For moderately dilute solutions, 02/dt, 0a/dp*, and Q42/dn are all small, and Q«/dt and Qa/dn at least have the same sign. Also the k’s and l’s for the different properties all depend upon the mutual action between molecules and solvent, and may thus be expected to have more or less closely related values. We may therefore expect not only that the coefficients of one kind for the various properties of solutions of a given salt will vary with concentration in a somewhat similar manner, but also that the variation with concentration of all the coeffi- cients, but especially the temperature and pressure-coefticients, will exhibit a certain family likeness. It is obviously not to be expected that the variation will be exactly similar in any case. This family likeness has been observed in the case of the temperature-coefficients for electrical conductivity and fluidity by Grotrian +, who found that, in general, with increasing concentration both of these temperature-coeflficients undergo changes in the same sense. Grossmann{ claimed to have proved these coefficients to be equal; but afterwards withdrew the claim as based onanerror §. Kohlrausch and Hallwachs also have noticed for very dilute solutions a close similarity between the curves representing the density and the con- ductivity respectively of the same salt as functions of the concentration. The following tables show that this family likeness extends, to a greater or less extent, to all the coefficients for at any rate a considerable number of the properties of solutions. The tables include some of Grotrian’s coefficients with others calculated from the observations of Kohlrausch, Bender, Briickner, Rother, Roéntgen and Schneider ||, Fink, and Timberg**. ‘Tlie coefficients are in almost all cases mean values, the ranges of temperature &c. to which they apply, though the smallest for which data are available, being not in * T have not seen Rontgen’s paper, on which the statement that 9a/Qp is small is based. The Fortschritte der Physik reports Tammann as quoting him to that effect. +t Wied. Ann. viii. (1879) p. 552. t Ibid. xviii. (1883) p. 119. § See Kohlrausch, Wied. Ann. xxvi. (1885) p. 224. || Wied. Ann. xxix. (1886) p. 194. q| Ibid. xxvi. (1885) p. 505. ** Ibid. xxx. (1887) p. 545. to their Slate of Ionizatzon. 103 tons re > of Aqueous Solut lé8 O P ropert Sodium (Chloride Solutions. Temperature-coefficients for ~ Pressure-coefficients for Concentration-coefficients for Surface- Conductivity.| Fluidity. Density. Conductivity. Density. Conductivity. Fluidity. Density. awk m, | Coett.| 7 | Coeff. 7. Coeff. 1. Coeff. m. |Ooeff.| ”. | Coeff. | x. Coeff. nm. |Coeff.| m. | Coeff. 0°883 | 0218 10 |—-0,271 | 0:170 0,801 | 0°712 |:0,429 0°5 1:67 0°5 | —:0895 0°5 |:°0394 | 0-895 | -0209 1°828 | °0215} 1°441| 0245; 15 |—-0,304 0°882 0,600 | 1:496 |-0,394 10 | 06389) 1:5 | —:1081 15 | -0868 | 1°835 |-0198 2839 | -0213| 2°694| 0243) 2:0 |—-0,333 | 1:828 0,491 | 2°651 |-0,852 a0) | OPP BO) olla, 3°0 | :0314 | 2°837 | -0203 3'918| 0217 | 4655 | 0252) 2°5 |—-0,855 | 2°806 0,381 3941 ‘0,313 3'°937 | 0243 5078 | -0228 3:0 |—0,375 | 3:885| -0,083 | 5-420|-0,277 5:059 | —-0, 110 5-421 |—-0,142 Barium Chloride Solutions. Calcium Chloride Solutions. Concentration-coefli- : Temperature-coefficients cients for Temperature-coefiicients for for Surface-tension. Conductivity. Fluidity. Density. Conductivity. N. Coeff. nN. Coeff. . Coeff. N. Coeff, N. Coeff. a | a ——o ee ea es About 6'4 —'0,154 0501 ‘O2Q15 0-781 0240 1:0 — 0,258 0:5 1629 1051 0207 1°704 0226 15 — ‘0,290 1:0 0610 ,, 10:0 — 0,179 1:652 ‘0201 2945 0222 2:0 —'0,318 2°314 0196 2°5 — 0,341 2°895 0193 3'0 — 0,361 104 Prof. J. G@. MacGregor on the Relation of the Physical all cases the same. As I wish to show only a general simi- larity, it is not necessary to specify the ranges. The tempe- ratures &. of the lower limits of the ranges are also not in general exactly the same. The data of the tables are thus not exactly comparable ; but they are sufficiently so for my purpose. The heading n stands for gramme-equivalents per litre. A glance at these tables shows that, if regard be had to sign, Grotrian’s conclusion as to the temperature-coefficients for conductivity and fluidity applies to all the coefficients for all the properties tested. A given change of concentration produces a change in the coefficients in the same sense. Too much importance, however, must not be attached to this; for it is obvious that if we had tabulated, say, the coefficients for conductivity, surface-tension, viscosity, and specific volume, it would have been found that the changes produced in the first two would have been in the opposite sense to those pro- duced in the last two. But it is interesting to note that the expectation suggested by the above formule is distinctly realized. At very great dilution of electrolytes the temperature- coefficient becomes, approximately, ior Es l =f = tnd) | (Petri), ae the pressure-coefficient having the same form. The concen- tration-coefficient becomes ior w po =1/(P®an). . . 2 ee if we compare (9) and (10) with (7) and (8), it becomes obvious that the variation with concentration of the tempe- rature and pressure-coefficients will probably be more closely related at low than at high concentrations; but that the opposite will be true of the concentration-coefficients. Ac- cordingly, having plotted Grotrian’s coefficients and those of the above tables as functions of the concentration, I find that the temperature-coefficient curves are in general more closely similar at low than at high concentrations; but that this is not the case for the concentration-coefficient curves. In the case of the pressure-coeflicients the data are insufficient. A corresponding similarity holds for the absorption-spectra of solutions, though it cannot be expressed in coefficients. In a former paper * I have shown that for all solutions for which -* Trans, Roy. Soc. Can. ix. (1891), sec. 8, p. 27. Properties of Aqueous Solutions to their State of Ionization. 105. data were available the absorption-spectra were similarly affected by elevation of temperature and increase of concen- tration. The occasional constancy in the Difference between the Molecular Values of Properties of Solutions having the same Molecular Concentration. The difference between the values per gramme-equivalent of any property for two simple solutions, 1 and 2, of the same concentration will be (Py—P.) /n=h, hot (hy )ai— (la—he)ag. =. (11) Now a@ in all cases diminishes as » increases. Provided, therefore, the values of the (J—k)’s have the same sign, and the rates of change of the «’s with concentration are inversely proportional, or approximately so, to the (/—k)’s of their respective solutions, we shall have (P,—P,)/n exactly or approximately constant, 7. e. independent of the concentration. This approximate constancy will of course hold in all cases at extreme dilution. In the case of solutions of moderate strength this pheno- menon has been observed by Valson and Bender* for the density and refractive index, by Wagner + for viscosity con- stants, and by Jahn ft for the electromagnetic rotation of the plane of polarization ; and a very close approximation to con- stancy in the case of the densities of very dilute solutions is clearly shown in the results of Kohlrausch and Hallwachs’s § observations. It is obvious, from the values of / and & determined above for the density of sodium and potassium chlorides, that, as Bender found, this approximate constancy must hold for the densities of these salts. For /—k for NaCl has the value +0°01424, and for KCl +0-01316; while a glance at the first table shows that the ionization-coefficient of solutions of the former salt falls off somewhat more rapidly with increasing concentration than that of the latter. It is equally obvious that as the value of /—k for the thermal expansion of NaCl is ‘0391, and for KCl -0,13, the thermal expansions of these salts will not exhibit this constancy. We accordingly find from Bender’s observations For 7= Il IFS: 2. 2:5. Ge) a= 70,108 "0,85 0,815 0,78 * Wied. Ann. xxxix. (1890) p. 89. + Zeitschr. fiir phys. Chemie, v. (1890) p. 31. { Wied. Ann. xliii, (1891) p. 280. § Lbed. iii, (1894) p. 14. 106 Prof. J.G. MacGregor on the Relation of the Physical For viscosity 7—k for NaCl is —0:0022, and for KCl —0:0028. We may thus expect a closer approximation to constancy than in the last case ; and from Briickner’s obser- vations we find org — 9 0! 1:0. T1855, 2:0. 25. (P,—P,) /n= °00116 00122 -00126 -00128 -00135 For surface-tension /—k for NaCl is —0:096, and for KCl —0:116. The approximation will thus not be so close as in the last case. Rother’s observations give, by graphical inter- polation, hor — dip 1:5. 2, (P;—P,)/n= 016 0113 0105 For refractive index /—k for NaCl is ‘0054, and for KCl ‘0091. The approximation will thus be still less close in this case. Bender’s observations give for the D-line, tra = Lk, 2. 3. (P,—P,) fn "0.29 "O17 "0.24 The above account of this phenomenon may be further tested by the aid of Kohlrausch’s observations of conductivity; for in this case /--k is the molecular conductivity at infinite dilution (u,). The following values of differences of molecular conductivity will be sufficient :— (P,—P,)/n for Conductivity. HCl and 2H.SO, and AgNO, and HOlandNaCl.| ixco, | deNO,. NaCl. 0-01 2454 2333 1838 +55 0-1 2379 2365 1198 421 0-5 2260 2289 1171 29 10 2085 2120 1185 = 60 Compare with this the following table of values of mw, and @:— Properties of Aqueous Solutions to ther State of Ionization. 107 Tonization-Coefficients (a). : HCl NaCl 1K,CO, 4H,S0,. AgNO,. ip =3500. | p, =1030. | w,=1400. | p,=3700. | p,, =1090. 001) 976 034. 773 ‘772 933 0-1 927 840 628 563 "794 05 862 735 520 513 668 1-0 794 ‘675 ATI 492 582 The approximate constancy helds in the case of HCl and LK,COs, because w, for HCl being more than twice as great as for $K,CQO3, a for the latter falls off nearly twice as rapidly as for the former. In the case of AgNO; and NaCl there is no approximation to constancy, because the values of p,, being nearly equal, the rates at which & varies with n are very unequal, The Independence of the Contributions made to the Value of a Property by the Free Ions. The constant / for a salt ap will, according to the dissocia- tion conception, be composed additively of two parts, l, and l,, pertaining to the ions a and p respectively, and these con- stants /, and /, will be characteristic of the ions and will not depend upon the salt from which they have been dissociated. A certain amount of evidence has been accumulated which may be said to point in this direction. In the case of several properties it has been shown that for solutions of considerable dilution, the difference between the values of the property for solutions of two salts having a common ion and the same molecular concentration, is independent of what the common ion may be ; and the value of the difference divided by the numbers of gramme-equivalents per litre of the salts in solution has been taken to be approximately the difference between the constants 7, and /p. Results of this kind have been obtained by Valson and Bender for density and refracting power, by Kohlrausch for electrical conductivity, by Raoult for the depression of the freezing-point, by Traube* for the change * Ztschr. anorgan. Chemie, iii. (1892), p. 1. 108 Prof. J. G. Macgreger on the Relation of the Physical of volume on solution, by Réntgen and Schneider for com- pressibility, and by J abn’ for the electromagnetic rotation of the plane of polarization. Applying the above expression, we have for the difference in the values of a property per unit of molecular concentration, (Ez Teas Pp) / 2 = Kap (1 — tap) = Kop (1 = app) + Ls (ces — ap) + lacay — lyaap,(12) and at infinite dilution (Pap— Psp) /n=la— Is. e e ° e e (13) Had the experiments referred to been all carried out at extreme dilution, as were those of Kohlrausch, afterwards extended by Loeb and Nernst*, the evidence would be quite satisfactory. But in general they have been made at only moderate dilution, and it is obvious from (12) that the approximate independence of the common ion on the part of (Pa,—Ps,)/n, may be quite consistent with considerable variation in /,—ls. Itis clear that the first three terms of (12) may readily mask any variation in the last two, and that, if the last two did not vary, la—ls could not in all cases be the same. That no satisfactory conclusion can be drawn from experi- ments of this kind, unless conducted at extreme dilution, may be shown roughly in the case of density by the aid of the results obtained above. For we may assume that the ionization-constants for density obtained above will not be very different from those which would be derived from observations made at greater dilutiont. We know from Kohlrausch and Hallw achs’s observations that if ap and P represent NaCl and 3Na,CQs; respectively (Pap—Psp)/n will have the value 0-0139 for solutions containing ‘005 grm.- equivalents per litre, and that for NaCl and HCl it will have the value 0:0235. We may assume that for NaCl and KCl it will be about 02. From the values of & for these salts we find the first two terms of (12) to be -0,64. If we assume ie to have half the mean value of J for NaCl and KCl, the third term will amount to —‘0,98. ‘The first three Vee thus amount to about °0354, or say 4 per cent. of the value of (Pap—Po,)/n. ‘Thus, observations of the kind referred to, for density, could give no satisfactory result, even if conducted at this very great dilution. At a pater of -001 grm.- molecules per litre, the first three terms of (12), calculated * Ztschr. fiir phys. Chemie, ii. (1888), p. 948. + Mr. E. H. Archibald, one of my. sindlew) tells me that for magnesium sulphate, Kohlrausch and ‘Hallwachs’s data give k= 05663 and /=:066887. Properties of Aqueous Solutions to their State of Ionization. 109 in the same way, amount to ‘031, or about 0°5 per cent. of (Pap —P5p)/n. A proved independence of p at this dilution would be more satisfactory. Observations at such extreme dilutions, in the case of most properties of solutions, are probably impracticable. But they are fortunately unnecessary for the settling of the question under consideration. For if the values of the ionization-constants for any property have been obtained as above from observations over a range extending to great, though not necessarily extreme, dilution, the values so ob- tained may fairly be assumed to apply very approximately to much greater dilutions ; and from the values of l,+l,p, [5 +lp, la +1,, 4+l,, &c., thus obtained, it may readily be determined whether or not /,—J, is independent of the ions p, q, &c. Unfortunately, Kohlrausch and Hallwachs’s observations on density are not sufficiently numerous for this purpose. The Determination of the Tonization-Constants for the Free Ions. The values of the constants (,, ls, Jp, &c. may probably, in some cases at least, be determinable in the following way. The experiments just referred to would give J, +1,, s+J,, &c., as well as kop and ky,, &e. If now, guessing at the value of [,, we find the first three terms of (12) to be negligible at dilutions at which P., and P;, can be determined with sufh- cient accuracy, a determination of these quantities will give the value of laaa,—lsaz, ; and if aa and as, be known with sufficient accuracy, la, /,, and J, may then be found. It would of course be necessary to check our guess at the value of /, by substituting the value found in expression (12) and seeing whether or not with this value the first three terms would be negligible. The accurate determination of the ionization-constants for the various properties of a variety of solutions would form valuable material to serve as a basis for theory. I may therefore express the hope that observers who are so fortunate as to have the necessary instruments of precision at their dis- posal may be led by this paper to make the requisite observations. Phil. Mag. 8. 5. Vol. 43. No. 261. Feb. 1897. K Bevo XVI. The Relation of Circular Polarization, as occurring both in the Amorphous and Crystalline States, to the Symmetry and Partitioning of Homogeneous Structures, i.e. of Crystals. By Witi1amM Baritow~*, | general prevalence of the belief that circular polariza- tion is a property connected with the symmetrical arrangement of small parts of the bodies displaying it, dates from Reusch’s famous device for obtaining it with a stack of mica plates arranged asa staircase spiral. As we are now acquainted with the nature of the repetition in space which constitutes homogeneity of structure, and know how structures thus formed may be partitioned symmetrically f, the time seems to have arrived for comparing the various distinct classes of cases in which circular polarization occurs with the geometrical possibilities for homogeneous structures, unbroken aud broken, 7. e. for substances both in the crystalline and the fluid conditions. Adopting substantially the classification given by Pope, in a paper which he has recently published {, we may place the substances which possess the power of converting plane-pola- rized light into circularly-polarized light under five heads. 1. Those which exhibit circular polarization only in the amorphous state (that is, when dissolved, melted, or converted into gas). 2. Those among the substances showing circular polariza- tion in the crystalline state only which owe the property to complex grouping or intercalation of crystal individuals, such as occurs in many cases of pseudo-symmetry. 3. Those other substances showing circular polarization in the crystalline state only in which it is an inherent property of the homogeneous structure itself. 4, Those among the substances which rotate the plane of polarization both when amorphous and when crystalline - which owe the property, as displayed in the solid state, to complex intercalation of individual crystals. 5. Those other substances which possess the property both in the amorphous and in the crystalline state in which the circular polarization, when the latter state prevails, is a specific property of the homogeneous structure, and is not due to intercalation. On the threshold of an inquiry as to the relation between * Communicated by the Author. + ‘Mineralogical Magazine,’ 1896, xi. p. 119. t Trans. Chem. Soc. 1896, p. 971, On the Symmetry of Homogeneous Structures. Lit circular polarization and structure the very obvious con- clusion suggests itself that since circular polarization is essentially an enantiomorphous property, if it is traceable to arrangement of parts, the structures in which it ovcurs must be enantiomorphous, 2. e. not identical with their own mirror- images. Now if we adopt the conclusion, reached in my paper just referred to, that the partitioning which achieves the separation of a crystal into individual molecules must be one which is compatible with the coincidence-movements (Deckbewe- gungen) of the structure*, it is evident that, when a structure identical with its own mirror-image undergoes such a parti- tioning, the fragments produced will either themselves be identical with their own mirror-images, or will occur in equal numbers in two kinds which are enantiomorphs. And that in the former case there will be no enantiomorphism, and that in the latter the effect of such a property of one kind of fragment will, so far as the general mass is concerned, be just cancelled by the similar property, of opposite hand, of the other kind of fragment. ; We see therefore that we may confine our attention to those types of homogeneous structure which are enantiomorphs, not only when dealing with crystals, but also when considering those cases where the substances displaying the property in question are in one of the amorphous states. If circular polarization is in some way connected with structure, the following general principles may be laid down :— I. Circular polarization is due to the existence of certain arrangements of parts or particles of a structure, and these arrangements, which will be designated effective conjigurations, are of enantiomorphous form. Il. Absence of the property in a substance may be due either to the absence of effective configurations, or to the presence in equal numbers of two opposite kinds, whose effects just cancel one another, the arrangement of parts displayed by one kind being generally enantiomorphous, or nearly so, to that presented by the other kind. Let us now endeavour to arrive geometrically at a classi- fication of homogeneous structures according to the effeciive configurations which they contain, both when unbroken and when dislocated, which shall be parallel to the classification given above of substances possessing the property of circular polarization. 3 * Min. Mag. 1896, xi. p. 130. Ree 112. Mr. W. Barlow on the Relation of Circular Polarization Class 1 As a parallel to those substances which exhibit circular polarization in the amorphous state only, we have Enantiomorphous homogeneous structures which while un- broken contain effective configurations of two opposite hands whose effects just cancel one another, but which, after being symmetrically partitioned and dislocated, contain but one kind, the other being destroyed in the process of dislocation. An example from the cubic system will make this clear. A homogeneous structure with gyrohedral symmetry of type 8* is, as we know, not identical with its own mirror- image ; and if such a structure contains effective con figurations, we may suppose that they consist of particles so placed as to form a single kind of Sohncke’s 24-point-set, the centre A of the configurations occupying, therefore, the centres of half the cubes of a close-packed system of cubes filling space, sym- metrically chosen, z.e. so chosen that they are in contact at their edges only = But it can easily be shown that particles thus placed may equally well be regarded as forming other 24-point-sets whose centres lie at the centres B of the cubes of the other half of the system of cubes. And if the distance of a particle from the point A nearest to it 7s the same, or practically the same, as its distance from the nearest point B, the only material difference between the forms of the 24- point-sets thus related will be that one well be right- handed the other left-handed. If therefore the parts or particles of the effective con- figurations occupy positions thus about midway between the two kinds of singular points f A, B, the rotation produced by their arrangement about centres A may be neutralized by the effect of their arrangement, of the contrary hand, about eentres B. The homogeneous structure, when in the solid or unbroken state, will then, as a whole, produce practically no rotation. Not so, however, if it is symmetrically partitioned into fragments having one or other of the two kinds of singular points A, B for their centres, and then dislocated. “ For it is evident that this will destroy one of the two kinds of effective configurations, and leave the nae to. — - * Zeitschr. f. Kryst. 1894, xxiii. p. 18. - + The centres A form therefore a “ Gibieohes " flicheneenbeaeee Raumgitter,” or, as SELES ae it, ao regular oktaédrisches Raum- gitter. 1 Zeitschr. f. Kryst. xxiii. p. 60. to the Symmetry of Homogeneous Structures. 113 duce a rotation which is not counterbalanced by one of the opposite hand. | Points thus capable of being regarded as simultaneously forming two sets of distinct configurations which are enantio- morphous to one another or nearly so, are easily found in either of the enantiomorphous types én which all the cotnci- dence-movements taken together are identical with their own mirror-images, 1. e. in all of these types except Nos. 3, 4, 14, Peis, 17) bs, 19/21, 22. 26,20, 30, 31,32, 33, 42, 43, 44, 45, 46, and 47. In the last-named types the presence of helical structures of one hand without the helical structures enantiomorphous to them seems to prohibit any arrangement leading to certain compensation. Class 2. Parallel to those among the substances showing circular polarization in the crystalline state only which owe the property to complex grouping or intercalation of crystal individuals, such as occurs in many cases of pseudo-symmetry, we have Homogeneous structures, single individuals of which contain no effective configurations, but which, when differently-orientated twin individuals of them are intercalated, form such configura- tions where the twin individuals meet, but not in two kinds which are enantiomorphs. An example illustrating this may be presented by a twin combination of type 48 *. For suppose that two identical homogeneous structures of this enantiomorphous type, which contain no effective con- figurations, are so intercalated that while their orientations about an axis differ by 60°, one particular set of axes is common to both f, and further that at least one set of the singular points on these axes in one individual form, with the corresponding set in the other individual, a single continuous space-lattice. There are two ways in which this may happen, either the axes of one individual may have the same, or they may have the opposite orientation to that of the axes of the other individual. * Zeitschr. f. Kryst. xxiii. p. 31. + A case in which the system of axes taken alone always possesses higher symmetry than the structure to which it belongs has been selected. Where this is not the case, for twinning of the nature described to occur, higher symmetry of the system of axes will have to subsist as a special condition, e.g. for individuals possessing rhombic symmetry when twinning thus to have common axes, the axes, taken alone, must be so situated as to form a system in trigonal or hexagonal symmetry. 114 Mr. W. Barlow on the Relation of Circular Polarization For convenience of description let us suppose the axes to be vertical. Then wherever one of the specified singular points of the one individual is found next to and vertically over a corre- sponding singular point of the other individual, the parts of one individual will be found turned through 60° as compared with the corresponding parts of the other, and thus they will be related like two succeeding steps of a spiral staircase. And we may suppose that such a disposition, in the case in question, is an effective configuration. And since the individual structures thus related are identical, the effective configurations produced in this way will be all identical, and no configuration enantiomorphous to them will be present to set up circular polarization of the opposite hand to neutralize that which they set up. As the formation of the effective configurations is an inci- dent of the crystal grouping, they will not be found when the structure is partitioned and dislocated, but only where the twinning competent to produce them exists. Class 3. The parallel to the case of those of the substances showing circular polarization in the crystalline state only in which the property is inherent, is found in Homogeneous structures which contain effective configurations that are not counterbalanced by configurations enantiomorphous to them, and in which, when partitioned and dislocated, these configurations are wanting, their destruction having been brought about by the dislocation. An example to illustrate this case can be found in any enantiomorphous type which contains helical structure, the more prominent examples being furnished by those types in which the coincidence-movements due to the presence of helical structure are all of one hand. For the helical structures may be supposed to be effective configurations, and when symmetrical partitioning and disloca- tion of the similar fragments take place, they will necessarily disappear *. If, with the helical structure, all enantiomorphism dis- appears, so that the fragments of the enantiomorphous structure are, when taken alone, identical with their own mirror-images, it is evident that when a homogeneous struc- ture is reformed from the fragments, it may be either a right- handed or a left-handed enantiomorph. * See Min. Mag. 1896, x1. p. 188, to the Symmetry of Homogeneous Structures. 115 With this may be compared such a fact as that sodium chlorate, which is optically inactive in solution, can be ob- tained in a dextro- or levo-rotatory form at will. Class 4. To those among the substances that rotate the plane of polarization both when amorphous and when crystalline which owe the property, as displayed in the solid state, to complex intercalation of individual crystals, we find a paral- lel in Homogeneous structures which, like those of Class 1, while unbroken contain effective configurations of two opposite kinds whose effects just cancel one another, but which, after being symmetrically partitioned and dislocated, contain but one kind, the other being destroyed in the process of dislocation; and which also like those of Class 2, when differently orientated twin individuals of them are intercalcated, form additional effective configurations where the twinned individuals meet, but not in two kinds which are enantiomorphs. Type 49* will furnish an example of this if the following conditions obtain :— 7 a. The particles which furnish the effective configurations in the amorphous state, z.e. after partitioning and dislocation have taken place, form enantiomorphous 6-point-sets whose centres in the unbroken structure are a set of the principal singular points, i. e. of those lying at the intersections of trigonal and digonal axes. b. These particles are so placed that the 6-point-sets of opposite hand which, in the unbroken structure, they also form +, and whose centres constitute another set of principal singular points, are practically enantiomorphous to the first- named 6-point-sets, and the circular polarization produced by one set of 6-point-sets neutralizes, on the whole, in the un- broken structure, that of opposite rotation produced by the other set. c. Intercalation of twinned individuals, similar to that described as occurring in Class 2, produces, as in that case, effective configurations where the individuals meet. The origin of the circular polarization displayed in the amorphous state is in this class different from that to which it is traceable in the twinned condition. A new and striking instance of this class of circular polarization is given by Pope in the paper already referred to ft, viz., trans-m-camphotricarboxylic acid. * Zeitschr. f. Kryst. xxiii. p. 31, + Comp. B 112. { Trans. Chem. Soc. 1896, pp. 972 and 978. 116 On the Symmetry of Hamogeneous Structures. Class 5. Finally, a parallel to those among the substances which rotate the plane of polarization both when amorphous and when crystalline, in which the cireular-polarization, when the latter state prevails, is a specific property of the homogeneous structure, is afforded by Homogeneous structures which contain effective configurations that do not, on the whole, neutralize one another, and some of which are not destroyed when the structure is partitioned sym- metrically and dislocated. | A careful examination of the various types of enantiomor- phous homogeneous structure reveals the fact that in most of them the presence of effective configurations of any one kind, which are not helical structures, involves the presence in the same structure of other configurations formed of the same particles as those which compose the first-named con- figurations but differently allotted, which configurations, whether very similar or not, are of the opposite hand*. In such cises the two kinds of configurations need not, of course, neutralize one another, although probably in many cases they would practically do so. However, there are many other types whose parts are not thus balanced, and which certainly will not by any such property be made inactive. _It is one of these latter which is selected as an illustration. In astructure of type 12 f we may suppose that the effective configurations consist of particles so placed as to form Sohncke 24-point-sets whose centres A are the cube-centres of a close- packed system of cubes. These same particles may then equally well be regarded as forming 24-pvint-sets whose centres B occupy all the cube angles, but the two kinds of configuration cannot possibly in this case be supposed to neutralize one another because they are both of the same hand. They must, on the contrary, be expected to reinforce one another. Symmetrical partitioning into similar fragments, followed by dislocation, if it leaves one of the two sets of configurations intact, will destroy the other, and thus we may look for different specific rotation in the broken from that in the unbroken structure as the result of such a dislocation. : Cases are conceivable in which effective configurations of opposite hand are present in a structure, and those destroyed * Comp. p. 112. +t Zeitschr. f. Kryst. xxiii. p. 21. The Substitution Groups of Order 8p. TIF by dislocation are the doménant ones. In this event the sign of the specific rotation will change as we pass from the un- broken to the broken condition. ~ Wyrouboff’s discovery that in the case of rubidium tartrate, which is optically active in both states, the sense of the rotation is not the same in both, may be mentioned in this connexion*. We see from the foregoing that exactly corresponding to the five classes into which substances that possess the power of converting plane-polarized light into circularly-polarized light can be divided, there are five classes of structure dis- tinguishable by characteristic geometrical features. It can therefore hardly be doubted that circular polarization is a mechanical effect depending on the relative situation of the ultimate parts of bodies, and that the disappearance of the property and the changes in it observed when the state of a body displaying it alters are also mechanical effects entirely due to changes in geometrical configuration. XVII. The Transitive Substitution Groups of Order Spi p being any Prime Number. By G. A. Mituer, Ph.D.t is a recent paper published in this Journal} we determined all the possible operation groups of order 8p. The present paper is devoted to the more general problem of determining all the possible transitive substitution groups of this order. In solving this problem it is convenient to employ the results of the preceding paper together with the following two theorems. Txeorem I.— The number of transetive substitution groups which are simply isomorphic to an operation group (G) is equal to the number of different systems of subgroups of (G), such that each system includes all the subgroups that are transformed into each other when G is transformed by all the operations that are commutative to it, and none of these systems includes any invariant (self-conjugate) subgroup of G with the exception of edentity. The substitutions of these simply tsomorphic transitive groups can be directly obtained from G, and the degrees of these groups are the quotients obtained by dividing the order of G by the orders of the subgroups in the given systems §. * Journ. de Physique, 1894, p. 451. + Communicated by the Author. t August 1896, vol. xlii. pp. 195-200. § Cf. Dyck, Mathematische Annalen, vol. xxii. p. 90. 118 Dr. G. A. Miller on the Transitive Tororem II.—Every simple isomorphism of an operation group to itself can be obtained by transforming the group by means of operations that are commutative to it*. It is evident that identity forms one of the systems of sub- groups of theorem I., and that there is one and only one such system in each operation group. In other words, each operation group is simply isomorphic to one, and only one, regular substitution group. This substitution group is com- pletely determined by the simply isomorphic operation group and vice versdé. It may happen that this is the only transitive substitution group that is simply isomorphic to a given opera- tion group. This is clearly always the case when the operation group is a commutative group, as all the subgroups of such a group are invariant. Unless the contrary is stated, p is supposed to exceed 2, There are then 3 commutative operation groups of order 8p. These have been denoted by G,, G,, and Gy, in the paper to which reference has been made. The simply isomorphic regular groups may be conveniently obtained by forming three heads of order 8, each being obtained by writing one of the commutative groups of order 8 in p different systems of letters and placing the identical substitutions in correspon- dence, and by adding to each of these heads the substitution of order p which merely interchanges its systems of intransivity. G, contains the following subgroups :— Order of subgroups ...... 4p 2p pp 8 42a Number Tid ft ee Beast ek 1 a aa G, contains the following subgroups :— Order of subgroups ...... Ap, 2p p-8 A 2" Number i ith (ide asoe 8. \Soel-- Bout G, contains the following subgroups :— Order of subgroups ...... Ap 2p\\ p< 8 Aviat Number AU Tes ene ©. a Mo dale G;f contains the following subgroups :— Order of subgroups ...... 4n2pp8 4 7 a Number pt eet ke 3 3 1 p 2p+1 2p+1 1 G; contains one system of 2p subgroups of order 2 that does not include an invariant subgroup besides identity. It * Cf. Frobenius, Sttzungsberichte der Berliner Akademie, 1895, p. 184. + These group symbols have the same meaning throughout this paper as they have in the paper to which reference has been made. Substitution Groups of Order 8p. 119 is therefore simply isomorphic to two transitive groups whose degrees are 8p and 4p respectively. All the substitutions of the group of degree 8p are regular, and 8p—1 of them are of degree 8p. Their group properties are known from the cor- responding operations of G3. Hence the regular simply isomorphic group is completely determined. Since each one of the subgroups of order 2 in the given system is transformed into itself by 8 operations of Gs, the transitive group of degree 4p which is simply isomorphic to G3 must contain p substi- tutions whose class is 4(p—1). All its other substitutions, except identity, are of class 4p. It may be conveniently eonstructed by means of a cyclical substitution of order 4p, and any substitution that transforms this into its 2p —1 power. It may be observed that while the given 2p subgroups of order 2 are conjugate in the largest group that is commuta- tive to G;, these subgroups are not all conjugate in the largest group that transforms the given group of degree 4p into itself. G, contains the following subgroups :— Order of subgroups ...... 4p 2p p 8 4 2 1 Number Sores” aeB sis cs Sale Oe ley ea eo. Ou eee G; contains the following subgroups :— Order of subgroups ...... 4n 2p p 8 4 tee | Number SANS pene 3 39 1 p 2p+1 4p4+1 1 Hach of these two groups is simply isomorphic to two transitive groups whose degrees are 8p and 4p respectively. The two non-regular transitive groups may be constructed by means of a cyclical substitution of order 4p, and any substi- tutions that transform it into its 29+1 and 4p—1 powers respectively. The group that is simply isomorphic to G, contains 2 substitutions of degree 2p, and that which is simply isomorphic to G; contains 2p substitutions of degree 4p—2. G, contains the following subgroups :— Order of subgroups ...... ADA. SO pO Fe oo)” T Number meme ES 4.5: 1 AS ere a a Bae | G, contains the following subgroups :— Order of subgroups ...... Ap ap p 8 4 2.1 Number OEE pa bicer yes er LL Sat i as ae Pa G, contains the following subgroups :— Order of subgroups ...... Ae) OO we ee A Number ancy tae er ae PRY 9) Si IE 120 Dr. G. A. Miller on the Transitive Since each of these three groups contains only one sub- group of order 2, none of them can be simply isomorphic to any transitive group besides the regular group, for the degree of a simply isomorphic group can clearly not be less than 4p, since such a group has to contain an operation of order 4p. We have now considered the 8 operation groups which con- tain an operation of order 4p, and found that only three of them are simply isomorphic to a non-regular transitive group. G,) contains the following subgroups :-— Order of subgroups ...... 4p 2p p 8. 4 | Number petitart je dalees 7 7.1. p Op+1 494383 G,, contains the following subgroups :— Order of subgroups ...... 4p 2p.» 8-4 2a Number Aine teks 3 8.1. p 2p4+1 a G,, contains the following subgroups :-— Order of subgroups ...... Ap 2p ip 84) A ype! Number etre eet ee 8 5 1. p Yp+l Qed These three groups and Gy are the only operation groups of order 8p that contain the non-cyclical commutative group of order 4p, but not the cyclical group of this order. Gyo is simply isomorphic to one transitive group of degree 4p, Gy is not simply isomorphic to any transitive group besides the regular one, while Gj, is simply isomorphic to two non- regular transitive groups. The group of degree 4p which is simply isomorphic to Gj) may be constructed by adding to the non-cyclical commutative regular group of order 4p any substitution that transforms all its substitutions into their 20—1 power. It contains p substitutions of degree 4(p—1). The rest of its substitutions, excepting identity, are of degree 4p. The two groups of degree 4p which are simply iso- morphic to Gj, may be constructed by adding to the same regular group two substitutions that transform one of its sub- groups of order 27 into itself and interchange the other two subgroups of this order. One of these contains 2 substitu- tions of degree 2p, while the other contains 2p substitutions of degree 4p—2. The rest of the substitutions, except identity, are ol desrep Ap. FP | We have now considered the:12 operation groups of order 8 which exist for all values of p, and found the 18 simply isomorphic transitive substitution groups. Hence there are just 18 transitive substitution groups of order 8p that contain an invariant subgroup of order p when p—1 is not divisible’ Substitution Groups of Order 8p. 1A)! by 4. 7 of these are not simply isomorphic to any transitive group except to themselves, 4 are simply isomorphic to one other transitive group, and 1 is simply isomorphic to two other transitive groups. G,; contains the following subgroups :— Order of subgroups ...... Ae pee 4k 2 A Number ere 3 38 1 p 3p 2p+1 1 G,, contains the following subgroups :— Order of subgroups ...... pap: Pp yaesazn | Number ie WE ae, LL, aMNAy LLL Ae oiliest gy. Op OT 1 Since G,3 contains one system of subgroups of order 4 and two systems of order 2 that do not contain any invariant subgroup besides identity, it is simply isomorphic to four transitive substitution groups. Hach of the substitutions, except identity, in any one of these 2p subgroups of order 4 is transformed into itself by 8 substitutions. Hence the simply isomorphic group of degree 2p contains 3p substitutions of degree 2(p—1), 2p of order 4, and p of order2. This group may be constructed by means of the cyclical substitution of order 2p and a substitution which transforms it into any power that belongs to exponent 4 with respect to mod. 2p. Each of the two groups of degree 4p which are simply isomorphic to G,3 contains p substitutions of degree 4(p—1). In one of the groups these substitutions are the squares of its substitutions of order 4. Its substitutions of order 4 therefore consist of p—1 cycles of order 4 and two cycles of order 2. In the other group the substitutions of order 4 are composed of p cycles of order 4. These two groups may be constructed by making a cyclical group of order 2p simply isomorphic to itself, and adding to this intransitive head two substitutions which interchange its systems of intransitivity and at the same time transform a cyclic substitution of order 2p into a power which belongs to exponent 4 mod. 2p. G,, is not simply isomorphic to any transitive group besides the regular group. These two groups, Gi3 and Gy, are the only groups of order 8p which occur only when p—1 is divisible by 4 but not by 8. It remains to consider the single group (G5) which occurs only when p—1 is divisible by 8. G,; contains the following subgroups :— Order of subgroups ...... Ap. 2prp 8 4 :2..1 JTC Sr a eres Lwin Diva Ons aPtbred Since G,; contains one system of subgroups of each of the orders 8, 4, 2, 1 that does not include any invariant sub- group besides identity, it is simply isomorphic to one transitive 122 Dr. G. A. Miller on the Transitive substitution group of each of the degrees p, 2p, 4p, 8p. These groups can be directly constructed as each of them contains an invariant subgroup of order p, and a substitution of order 8 which transforms the substitutions of this sub- group into a power which belongs to exponent 8 mod. p. The group of degree p is the only primitive group of order 8p that contiins an invariant subgroup of order p. Hence there are 18 transitive substitution groups of order 8p that contain an invariant subgroup of order p when p—1 is not divisible by 4. When p—1 is divisible by 4 but not by 8 there are 23 such groups, and when p—1 is divisible by 8 the number of these groups is 27. The operation groups which do not contain an invariant subgroup of order p occur only when p is equal to7 or 3. When p=7 there is only one such group ((Gyg). G,, contains the following subgroups :— Order of subgroups ...... 4p 2p p -8 AZ Number “Oka tr 0; 0°36") aa As Gy, contains one system of subgroups of each of the orders p, 4, 2, 1 that does not include any invariant subgroup besides identity, it is simply isomorphic to one transitive sub- stitution group of each of the degrees 8, 2p, 4p, 8p. These groups can be readily constructed by means of the invariant subgroup of order 8, which contains 7 substitutions of order 2, and a substitution of order 7 which interchanges its sub- stitutions of order 2 cyclically. Hence there are 22 transitive substitution groups of order 56; 13 of these are regular. The group of degree 8 is primitive. The others are non- primitive since the subgroups of the orders 4, 2, 1 are clearly not maximal *. When p=3 there are three operation groups (Gy7, Gys, Gys) that do not contain an invariant subgroup of order 3. G,; contains the following subgroups :— Order of subgroups ...... Ay 2p -p 18 A 2a Number go fod wadene LAY ASS ee G,, contains the following subgroups :— Order of subgroups ...... Ap, V2p:- p48: MAG Number Fh eg or | ae ee: Bea ie Le image Gi, contains the following subgroups :— Order of subgroups ...... Ap “Dp ps 4 2 Number Sot ak Vetoes AS al * Dyck, Mathematische Annalen, vol. xxii. p. 91. Substitution Groups of Order 8p. 123 G,; contains one system of subgroups of each of the three orders 2p, p, 1, and two systems of each of the two orders 4, 2 that do not contain an invariant subgroup except identity. It is therefore simply isomorphic to the following transitive groups :— Degree of groups ......... Ae Bi 24° 6 12 INGERTNEE > = yet uae cose AR aS I These seven simply isomorphic transitive groups, in order, have been denoted as follows * :—(abcd) all, (abcd . efgh) pos. (ae .bg.cf.dh), (am.bn.cp.do.ex.fw.gu.hv.is.jt.kr.lq. Hy, (+abcdef os, (+abcdef)o4, (abedef. ghijkl)y., (ahe7 . bidg) ek. fl), (abed. efgh . ijkl), (afk . bgt. cej . dhl) (af.be.cg.dh. Gi, contains one system of subgroups of each of the three orders, p, 4, 1, and two systems of order 2 that do not con- tain any invariant subgroup except identity. It is therefore simply isomorphic to the following transitive groups :— Degree of groups ... .. 8 6 24 12 UNmabers 571) Sh 2. , 1 id el 97 These five simply isomorphic transitive groups, in order, have been denoted as follows :— (abed . efgh) pos. (ae. bf.cg. dh), (abedef)o4, (am. bn .co.dp. eq.fr.gs.ht.iu.ju.kw .la)Hy, (abcdef. ghijkl),, (ag bh. cr. dj. . fl), (abcd. efgh . kl), (afk. bgt. cej. dhl) (ab.cd il. jh) ¥. G, contains only two systems of subgroups that do not contain an invariant subgroup except identity. The orders of these subgroups are 3 and 1 respectively. The simply iso- morphic transitive groups have been denoted by (ab .cd .ef . gh) (ABCD) pos., (aceg. bdjh.ikmo .jlnp . qsuw. rtva)(abef. chgd .ijmn. kpol . qruv . sewt)(akr . bis. gq .dlt. cov. fmw.gnu.hpz). Hence there are 32 transitive substitution groups of order 24. 15 of these groups are regular. The group of degree 4 is primitive. All the others are nonprimitive. We have thus far excluded the special case when p=2. * Cf. Cayley, ‘ Quarterly Journal of Mathematics,’ vol. xxv. p. 71. + This group is not included in the list of transitive substitution pups of degree 12 recently published in the ‘Quarterly Journal of uthematics.” It seems to be the only transitive group of order 24 that has not yet been published. It contains three systems of nonprimitivity. 124 = The Transitive Substitution Groups of Order 8p. For the sake of completeness we shall consider these groups very briefly, although all of them are known. Since 4! is not divisible by 16 it follows from theorem I. that every subgroup of order 4 contained in a group of order 16 must include an invariant subgroup which differs from identity. All the subgroups of order 8 contained in such a group are known to be invariant. It remains therefore only to consider the subgroups of order 2. We may now show directly by means of the groups of order 8 that an operation group of order 16 cannot be simply isomorphic to more than one non-regular transitive group. We may regard a commutative subgroup of order 8 as the head of sucha group. When this is cyclical the truth of the statement is evident, since any operation of order 2 in the tail may be made to correspond to any other of its operations of this order. When the head contains four operations of order 4 and an operation of the tailis commutative to its three operations of order 2, the statement is true for the same reason. Finally, when the tail contains no operation that is commutative to the three operations of order 2 in the head, and also no operation of order 8, it must contain 4 operations of order 4 and 4 of order 2, since any operation of the tail and the subgroup of the head which is generated by its operations of order 2 must generate the non-commutative group of order 8 which contains five operations of order 2. In this last case we have that an operation of order 2 in the tail multiplied into two operations of order 4 in the head gives two operations of order 2. Hence the operations of the tail transform one of the cycles of order 4 in the head into its third power, and are commutative to the other two opera- tions of order 4 in the head. Hence any operation of order 2 in the tail may be made to correspond to either of the two non-commutative operations of this order in the head as well as to any other operations of the same order in the tail. As the only group which does not contain at least one of the two given commutative groups of order 8 is commutative, the statement is proved. _ We have now proved that every operation group of order 16 that contains non-commutative operations of order 2 is simply isomorphic to one and only one non-regular transitive group. Hence there are 20 transitive substitution groups of order 16; 14 of these are regular. . 7 Summary. . When p=2 there are 20 transititive substitution groups-of order 8p. -Six are of degree 8 and fourteen are of degree 16. On the Passage of Electric Waves through Tubes. 125 When p=3 there are 32 such groups. They occur as follows :— Degree of groups ......... 4 6 8 12 24 Number Bene asec ae eS? oO? ELS When p=7 there are 22 such groups. They occur as follows :— : | Deeree of Sroups —...... 0435-5 8 14 28 56 Number Seah. . (aaa He ck at ES When p—l1 is divisible by 8 there are 27 such groups. They occur as follows :— Dearee of sroups,t7ise;.......% p 2p Ap 8p Number SS Laie Anh at eo 9 1S When p—1 is divisible by 4 but not by 8 there are 23 such groups. They occur as follows — Wesree of sroups =.....:. 2p 4p 8p Number aria. oer IL 8 14 When p—1 is not divisible by 4 and p does not have one of the three values 2, 3, 7, there are 18 sae groups. They occur as follows :—- Deeree of groups ............ Ap Sp Number a ieee roe ote, 6 12 The three groups whose degrees are 4, 8, and p respectively are primitive. All the others are nonprimitive. When p=2 there are five commutative groups, but when » > 2 there are only three such groups. When p=2 there are three non-commutative groups that are not simply isomorphic to any non-regular transitive group. When p—1 is divisible by 4 there are five such groups. When this condition is not satisfied and p> 2 there are four such groups. Paris, December 1896, XVIII. On the Passage of Electric Waves through Tubes, or the Vibrations, of Dielectric Cylinders. By Lorp Ray eicH, /..S.* ! General Analytical Investigation. HE problem here proposed bears affinity to that of the ‘vibrations of a cylindrical solid treated by Pochham- mer +t and others, but when the bounding conductor ir * Communicated by the Author. T Crelle, vol. xxxi. 1876. Phil. Mag. 8.5. Vol. 43. No. 261. Feb. 1897. 13 10654 126 ~ Lord Rayleigh on the Passage of regarded as perfect it is so much simpler in its conditions as to justify a separate treatment. Some particular cases of it have already been considered by Prof. J. J. Thomson*. The cylinder is supposed to be infinitely long and of arbitrary section ; and the vibrations to be investigated are assumed to be periodic with regard both to the time (¢) and to the coordinate (z) measured parallel to the axis of the cylinder, i.e., to be proportional to &@"t?. | By Maxwell’s Theory, the components of electromotive intensity in the dielectric (P, Q, R) and those of magnetic induction (a, 6, ¢) all satisfy equations such as #R @R, aR_1 @R as | Ge” dg der Nadie an V being the velocity of light ; or since by supposition aR d?R oe aes a, aie da? dy? +?R=0, ° ° e ° e (2) where =p (V0? os ee The relations between P, Q, Rand a, 6, c¢ are expressed as usual by da, dQia dk di —— dz Re dy gy ° ° e e e e (A) and two similar equations ; while da dv! Vade daz + dy * dz =a e e e e e (5) Ae ai : dx dy - de ae e e ° e 2 (6) The conditions to be satisfied at the boundary are that the components of electromotive intensity parallel to the surface shall vanish. Accordingly | Ae Be Oucclic ine GAS ee PE tQ=0;. ie ee * ‘Recent Researches in Electricity and Magnetism,’ 1893, § 300. + The %? of Prof. J. J. Thomson (Joc. cit. § 262) is the negative of that here chosen for convenience. Electric Waves through Tubes. 127 da/ds, dy/ds being the cosines of the angles which the tangent (ds) at any point of the section makes with the axes of x and y. Equations (2) and (7) are met with in various two-dimen- sional problems of mathematical physics. They are the equations which determine the free transverse vibrations of a stretched membrane whose fixed boundary coincides with that of the section of the cylinder. The quantity # is limited to certain definite values, ’,?, k:”,..., and to each of these corresponds a certain normal function. In this way. the possible forms of R are determined. A value of R which is zero throughout is also possible. With respect to P and Q we may write pasa oe, ea) | d Q= Ge os Oe). . (10) where ¢ and w are certain functions, of which the former is given by i ar dQ dR sy RC stim CG ee ce There are thus two distinct classes of solutions; the first dependent upon @¢, in which R has a finite value, while W=0 ; the second dependent upon w, in which R and @ vanish. 7 For a vibration of the first class we have P=dd¢/dz, Ea TaNiGln earth ater eee le) and Weer Gi: maemieer ei.) 8e) GB) Accordingly by (11) am o= Bh, e e e e e e (14) and _imdk _imdR St eRe Q= a dy”? (15) by which P and Q are expressed in terms of R supposed already known. The boundary condition (7) is satisfied by the value ascribed to R, and the same value suffices also to secure the fulfilment of (8), inasmuch as dx dy a amdR Fas tds Bas" L2 128 Lord Rayleigh on the Passage of The functions P, Q, R being now known, we may express a, b,c. From (4) Ce dR m? +k’ dR i st eae See dy 3 so that a ee m+ k? dR _ mith d = At pes dy’ ~ Tpke? da? c=0.. (16) In vibrations of the second class R=0 throughout, se that (2) and (7) are satisfied, while 4? is still at disposal. In this case : P=dw/dy, QO=-d/dz, 2 - Sae By the third of equations (4) and dé. en idle dQ) a=. aE ON) ay ee ae henp 5 so that = —zpce/k?, and deg, ip de P= ie dy? C= 72 da? R=0;. ><. eee Also by (4) am de 2m de a= k2 da’ — k? dy” ° . . e (20) Thus all the functions are expressed by means of e, which itself satisfies (V7+h)c=0... .. =e We have still to consider the second boundary condition (8). This takes the form dedz dedy _ 0 Gyjds Sands) ae requiring that de/dn, the variation of ¢ along the normal to the boundary at any point, shall vanish. By (21) and the boundary condition dgjdn=0,- 4 voce. ee oe eee the form of c is determined, as well as the admissible values of 2, The problem as regards c is thus the same as for the two-dimensional vibrations of gas within a cylinder. which is bounded by rigid walls coincident with the conductor, or for the vibrations of a liquid under gravity in a vessel of the same form*. * Phil. Mag. vol. i. p. 272 (1876). Electric Waves through Tubes. 129 All the values of & determined by (2) and (7), or by (21) and (22), are real, but the reality of & still leaves it open whether min (3) shall be real or imaginary. If we are dealing with free stationary vibrations m is given and real, from which it follows that p is also real. But if it be p that is given, m” may be either positive or negative. In the former case the motion is really periodic with respect to z; but in the latter z enters in the forms ¢””, e-™, and the motion becomes infinite when z= +0, or when z=—o, or in both cases. If the smallest of the possible values of k? exceeds p?/V?, m is necessarily imaginary, that is to say no periodic waves of the frequency in question can be propagated along the cylinder. | Rectangular Section. The simplest case to which these formulze can be applied is when the section of the cylinder is rectangular, bounded, we may suppose, by the lines e=0, r=a, y=0, y=. As for the vibrations of stretched membranes,* the appro- priate value of R applicable to solutions of the first class is R=e+P9 sin (wra/a) sin (vry/B) 3 . eee (23) from a nich- the remaining functions are deduced so easily by (15), (16) that it is hardly necessary to write down the expressions. In (23) mw and v are integers, and by (13) ; Bam (K + @) Oi Sega oa a whence 2 snes ae Sai : papa (4+ a Det 9g _ The lowest frequency which allows of the propagation of periodic waves along the cylinder is given by nc ; eae ee ee ccs: Pee 6 ie (20) If the actual frequency of a vibration having its origin at any part of the cylinder be much less than the above, the resulting disturbance is practically limited to a neighbouring finite length of the cylinder. For vibrations of the second class we have e=e(™ 2) cos (umaz/a) cos (viry/8), »- - . (27) the remaining functions being at once deducible by means of (19), (20). The satisfaction of (22) requires that here again * ‘Theory of Sound,’ § 195. 130 Lord Rayleigh on the Passage of L, v be integers, and (21) gives yey? a + mi) ee identical with (24). If a>, the smallest value of & corresponds to p=1, v=0. When v=0, we have k=prr/a, and if the factor et?) be omitted, _im k P=0, Q=-— + sin ke, R=0; .. ae a solution independent of the value of 8. There is no solu- tion derivable from w=0, v=0, k=0*. a= sin kaz,;~ b=0, c=coskz, 5° Baa Circular Section. For the vibrations of the first class we have as the solution of (2) by means of Bessel’s functions, R=J,(kr)cosn?, 2 . .2 3) eee n being an integer, and the factor e+?) being dropped for the sake of brevity. In (81) an arbitrary multiplier and an arbitrary addition to @ are of course admissible. The value of & is limited to be one of those for which IerVS0.00 6 2 oo ee at the boundary where r=’. The expressions for P, Q, a, 6, ¢ in (15), (16) involve only dR/dx, dR/d;. For these we have = = Tos O— a sin 0=kJ,'(kr) cos n€ cos 8 + ~ J n(kr) sin n@ sin 0 Jn Jn =k cos(n— 104 J wie F +4kcos (n+ 164 Jn’ =| =1kcus (n—1)6 Jn_i(kr) —$h cos (n +1) dns (kr), . (88) according to known properties of these functions ; and in * For (18) would then become y°y=0; and this, with the boundary condition dyy/dn=0, would require that P and Q, as wellas R, vanish throughout. Electric Waves through Tubes. 131 like manner 4 ee laa dR : a = 7, sin 6+ 79 °° O= —sksin (n—1)0 Jn-i (kr) ~-tksin(n+1)6 Jniilkr). . (84) These forms show directly that dR/dz, dR/dy satisfy the fundamental equation (2). They appity when n is equal to unity or any greater integer. When n=0, we have ie elciaNs. fa! pees doth my Tu too) dR dR == —kJ,(kr) cos 8, i —kJ, (kr) sin @. (36) The expressions for the electromotive intensity are some- what simpler when the resolution is circumferential and radial: : : am ah circumf. component =Q cos @—P sin d= a amn = — F5- Sal kr) SIRE es od) radial component = P cos 0+ Q sin 0= o = am we If n=0, the circumferential component vanishes. J,/(kr)cosn8. . . . (38) Also for the magnetization circ. comp. of mag. =b cos @—asin 0= or = — “ans (kr) cosnO, . . (89) rad, comp. of mag. =a cos @+b sin 9= — “a = alt) Sa ee ee The smallest value of & for vibrations of this class belongs to the series n=0, and is such that kr=2°404, r being the radius of the cylinder. For the vibrations of the second class R=0, and by (21), Peery COS@LG,, «1s cvi) a) en (48) k being subject to the boundary condition Bee NaS) ind ce a) Le 29 sR = 39-31 — “9 approx. are tan Hence 0=42° approximately. The E.M.F. OC is there- fore 222°9 volts, and as the resistances are approximately equal, the point H (the letters of all the figures denoting corresponding points) bisects OC. As the reactances of all coils are approximately equal the point M also bisects AC, and hence P lies at the middle point of OA. The current OD is 6°9 amperes, in each circuit, making a total of 13°8 amperes in the main line. Any change made by introducing the two iron cores has the effect of moving the points upon the heavy portions of their respective circles in the directions of the P2 172 Currents in the Branches of a Wheatstone’s Bridge. Fig. 6.—Showing the actual variation of the quantities used from when the iron cores are all withdrawn until two of them are entirely in. O'HDC’ Seale 75 cm. = 20 volts. ‘75 cm. = 1 ampere. arrows as the cores are introduced, until the point P arrives at P’ when the cores are entirely in. The points H, CO, M, and D move to H’, C’, M’, and D’ when the iron cores are Inserted into one pair of coils. UO ee eae XXVIII. Applications of Physics and Mathematics to Secsmology. By C. Curzs, Sc.D.* Sections CONTENTS. 1-3. Introductory. 4, Influence of surface-load on observed level. 5. Direct pressure effect. 6-7. Relation between pressure and gravitational effects. 8-10. Pure pressure effects, general formule, application to rectangle. 11-18. Special cases of loaded rectangle. 14-18. Numerical results, and conclusions. 19-20. Pressure effects below the surface. 21-23. Luni-solar effects, explanatory. 24-26. Solution of problem. 27-30. Application to earth, working formule. 31. Numerical estimates. 32, Final conclusions. o3-34, Subsidiary remarks, Introductory. i ae existence of apparent movements in the earth’s surface-strata appeals in the first instance to seismologists. Prof. J. Milne, however, and others have been of late attempting to bring it home to astronomers and meteorologists that they too may have a vital interest in the matter. The presentations of the subject which have come under my notice take little or no heed of the theoretical aspects of the case, in which, as an elastician, I have long been interested. As the neglect of theoretical results may be due not so much to their defects as to the slowness with which mathematical investigations become generally known, I have decided to group together and discuss in a more or less popular way the theoretical conclusions which seem to me the most closely connected with the subject in question. § 2. The mathematical work by which these conclusions were deduced refers to material which is homogeneous, isotropic, and elastic; while the body in whose phenomena the seismologist is interested is the earth. Now it must not be supposed that I fail to appreciate the differences between the material of theory and that of nature. The certainty of the departure of many of the surface-strata from the attributes ascribed to isotropic elastic solids, and the uncertainty as to the density, solidity, and other physical properties of =9°°. of the earth’s mass I perfectly realize. The conditions under which the deep-seated materials of the earth exist are fundamentally different from those we are * Communicated by the Physical Society: read December 11, 1896. 174 Dr. C. Chree on Applications of Physies familiar with at the surface. ‘The enormous pressure, and the presumably high temperature, very likely combine to produce a state to which the terms solid, viscous, liquid, as we understand them, are alike inapplicable. But be the state what it may, the material must respond to the action of periodic forces ; such forces must produce varying strains and stresses ; and these strains and stresses can hardly fail to produce effects at the surface. No numerical estimate of these effects can claim to be in any sense final, as the mathe- matical work by which it is evolved must depend on physical data which are at best unproved. It appears desirable, how- ever, that such numerical estimates should be made, on the least objectionable physical basis available, if only for the reason that their existence supplies a guide and incentive to direct observation. In my opinion, for reasons previously discussed*, the treatment of the earth as an incompressible elastic solid is exposed to perhaps a minimum of objections. Most probably the material increases in density and temperature as we approach the centre, and a treatment which assumes the material to vary with the radial distance would possess higher a priori claims to regard than one which treats the earth as homogeneous throughout. The problem of a gravitating mass of varying elastic properties has, however, still to be published, and as the assumed law of variation would probably be mainly guess-work, the advantages for practical ends might be less than would appear at first sight. Variation of the material with the radial distance, I mayadd, could hardly affect the general character of the phenomena. Surface heterogeneity, in which the material varies rapidly with latitude or longitude, is not unlikely to modify largely the magnitude of some of the results at individual stations, but is most unlikely to produce a large effect on the order of magnitude of the mean lunar or solar tidal effects at a moderate number of stations scattered over the earth’s surface. The treatment of local surface pressures in the first part of the paper is in some respects on a less uncertain basis. We can assure ourselves, if need be, of the solidity of the ground surrounding a station ; and though the mathematical work treats the solid as going down to infinity, this only means in practice that the depth must be large compared to the shortest distance of the loaded area. There are reasons, however, even here for regarding the numerical results as in general but rough approximations. * Phil, Mag. Sept. 1891, p. 232. LU and Mathematics to Seismology. 175 They might possess high accuracy if the surface material were bare rock in horizontal strata, and the recording appa- ratus were supported directly on the rock ; but uncertainties are introduced when the load is applied at the surface of ordinary soil, and the support of the apparatus is stonework ee a building whose foundations go to an appreciable epth. § 3. The observed facts on which our investigations are most likely to bear are certain slow changes in the indications of spirit-levels or delicately suspended pendulums. Some of these Prof. Milne is disposed to attribute to meteorological agencies such as rainfall or evaporation. A relative excess of moisture to the west, say, of an observatory is, he considers, equivalent to a surface load on that side, tending to make the ground on which the building stands slope downwards from east to west. Such want of symmetry may arise from the peculiarities of the soil, or through the ground being sheltered by trees or modified by cultivation. In sunshine the shadow of the building itself, by retarding evaporation, may set up such a difference as Prof. Milne has in view. I am not sure that an excess of evaporation from the east, say, of a building is necessarily equivalent to the withdrawal of a surface load from that side, at least to the exact extent of the surplus evaporation. The withdrawal of moisture from the soil has a decided influence on its conductivity for heat— not to speak of electricity—and so may exert a very appre- ciable influence on the temperature near the surface, the consequences of which it would be difficult to follow. There is also, presumably, underground circulation both of air and moisture, which may not unlikely counteract to some extent differences of surface evaporation. Though these and other uncertainties exist, it is certainly worth while considering the numerical magnitude of the results to be expected from the agencies postulated by Prof. Milne. The theoretical results will also, I hope, suggest the way in which the best use may be made of experimental determinations of the effects of surface loading over limited areas of convenient shape. Influence of Surface Load on the observed Level. § 4. This influence is not so simple as might appear at first sight. The weight of the loading material is equivalent to a pressure normal to the surface, which we suppose hori- zontal. But, in addition, we must allow for the fact that the gravitational attraction of the loading material slightly alters 176 Dr. C. Chree on Applications of Physics the direction of “ gravity’ at the surface. Consider, for example, the influence of the ordinary ocean tide at a point inland near the shore. At high tide there is on the sea- bottom a pressure exceeding the mean by an amount corre- sponding to the height of the water above its mean level ; this will tend to make a naturally horizontal plane dip towards the sea. At the same time the surplus volume of water will give a horizontal component to what we may regard as normal “ gravity ” in the neighbourhood. This second effect has been called attention to, in this very case, in Thomson and Tait’s ‘ Natural Philosophy, art. 818, where will be found a numerical estimate for a specified set of conditions. What a spirit-level shows is the plane perpendicular to gravity—including “centrifugal force” and all disturbing forces. We are thus obliged to consider both effects before attempting numerical estimates. Direct Pressure Effect, Fundamental Formule. § 5. In the following calculations the earth is treated as an isotropic elastic solid, principal weight being attached to the results obtained by supposing the material incompressible. Also, as we are primarily interested in the consequences of pressure applied over limited areas, the loaded surface is treated as a horizontal plane, on the lower side of which the material extends to infinity. On these hypotheses we are enabled to make use of the very interesting and important results established by Professors Cerruti and Boussinesq. A convenient English abstract* of Boussinesq’s work is contained in Todhunter and Pearson’s ‘ History of Hlasticity,’ vol. li. part 2, arts. 1492 e¢ seg., from which the following formule are quoted, the only variation being the use of Thomson and Tait’s notation for the elastic constants. The origin of coordinates lies in the undisturbed surface, taken as the plane of zy, the positive direction of the z axis being downwards into the earth. The normal pressure applied to the element dw of surface is pdw, where p is supposed of course a known function of 2, y. u, v, w denote the components of elastic displacement, n the rigidity, and 7 Poisson’s ratio for the material. The displacements at any point x, y, z in the material are as follows: * Chapter ix. vol. i. of Love’s ‘ Treatise on,.,, Elasticity’ may also be usefully consulted. J —— Vv and Mathematics to Seismology. 177 > d _ = ail rpdw + (1— 2n) aE (fg (z+7)pdw : Pie =— of If viet (1—2n) 2 (Nog (2+7)pdo ‘ (2) w= {oan ([2dore JSeo}. eee. (3) Here v is the distance between the element dw where p is applied, and the point 2, y, z where u, v, w are measured. The integration extends to all parts of the surface where p differs from zero. The simplification in the formule when n='5, or the material is incompressible, should be noticed. The slope—?. ¢., inclination to the plane of xy—introduced into any horizontal plane depends only on the vertical dis- placement w. In particular, the slope of the surface depends only on wo, the value of the vertical displacement when z=0; and by (3) we obviously have wo={(1—n)/(2mn)} \\ (pir)dw. 2. . (A) In (4) v is the distance between the element dw and the point Xo) Yo on the surface to which wy refers. Relation between Pressure and Gravitational Effects. § 5. If we suppose ¢ the thickness, p the density of the material loading the surface, its gravitational forces are derived from the potential : Veer) [Gale ding, A eee) where y is the attraction between two unit masses at unit distance. The pressure exerted by the load is p=gpt, where gis gravity at the surface. Here we may regard g as the undisturbed value prior to the application of the load, as the alteration in the vertical component is negligible for our present object. Thus V=(y/9) J) (p/n) do. Comparing this with (4), we find for the surface value Vp of V the simple relation Vo=2rnyw/ig(il—n)}. ».« » » » (6) 178 Dr. O. Chree on Applications of Physics This holds true of Vy and wo all over the\surface, and so applies likewise to their differential coefficients with respect to #) and yy—so far at least as concerns points outside the loaded area. The direction-cosines of the normal to the surface after the application of the load are, to a first approximation, en SAUDE diy 4 dyy y 9 so that the slope at the point x, yp is given by _ 6 (dw\’ eo) 2 n=) +a) }-..-- @ Again, to a first approximation the presence of the loading- material has altered the direction-cosines of the line of action of gravity from ie eae ee g dix? 9 dy’ Thus gravity has become inclined to the vertical at the angle watt) +(G) }- ei rE Employing (6) in (7) and (8), we obtain the elegant relation Wi po=(—n)g/Amny), . . « ~ (9) The spirit-level measures Wy, +2, which always exceeds the true change of level Wy. Since ae MG fel ae (10) dae) | dyy Axo] dy’ the final directions of gravity and of the normal to the surface lie in the same vertical plane (z.e. plane through z). ‘This result may facilitate experimental investigations, as a rough idea of the direction of the resultant attraction of the loading- material will generally be obtainable by eye. ‘The possible influence of want of symmetry in the contour of the ground, or variability of the surface-strata, must of course be borne in mind. . The relation (9), so far as I know, is new. Its discovery was due to a faint impression that a formula I had obtained for the effect of a loaded rectangle resembled something I had seen: before, the something proving on investigation to be result (7) in Thomson & Tait’s Nat. Phil., art. 818. and Mathematics to Seismology. 1 § 7. To form an idea of the relative importance of yr, and yy, in the case of the earth, I have made the following selection of hypothetical values for 7 and n, the latter quantity being measured in grammes weight per square centimetre :— 12) SS =olVe< 1h (ii.) oe 35 x 10'; (iii.) 5 EXO According to the table in Lord Kelvin’s Encyclopedia Article on Elasticity, (i.) may be regarded as representing iron or steel, (11) as representing brass or slate of somewhat low modulus, while (1i1.) represents an incompressible material* such as seems most compatible with the hypothesis of a homo- geneous earth, naturally spherical but for rotation. According to Lord Kelvin’s table, the value of n in (iii.) is similar to what one should expect in rock of somewhat low elasticity. If a be the earth’s radius, p its mean density, gly =Arpa/3. Supposing p=5'5, and a=64 x 10" cms., we have approxi- mately goea=35 x 10° grammes weight per square centimetre. With the above figures, I find case (i.) Wy/y= 35/16= 2 roughly, (ii.) L025, (i11.) 390/33=11 roughly. The last result is likely, I think, to prove the nearest to what ordinarily occurs in practice, so that the gravitational effect may be expected to prove as a rule relatively small ; still it ought not to be disregarded without due consideration of the special circumstances. Pure Pressure Effects. § 8. In all cases when the largest dimension of the loaded area is small compared to its shortest distance from the point of the surface where the slope is required, a good first approxi- mation T to the surface vertical displacement—obvious on inspection of (4)—is wo (Lm lm), ose see | AE) where R denotes the distance from the centre of mass of the total load P. * See Phil. Mag. Sept. 1891, p. 250, remembering E/n=2(1+7). + See Todhunter & Pearson’s ‘ History,’ vol. ii. pt. 2, art. 1498, 180 Dr. C. Chree on Applications of Physics The corresponding approximation to the slope, viz., — —, =(1l—7)P/(27nR’), . . . (12) shows that at considerable distances from a small loaded area the slope varies approximately as the inverse square of the distance. In (11) and (12) the distribution of load is not assumed uniform. The fact that (11) holds only when the distance of the loaded area is so large that its effect is relatively small diminishes its value in practice. § 9. The determination of w from (3) entails the evaluation of two integrals, neither very manageable. [Tor points on the surface there is, however, only the single integral (4). This has been converted by Boussinesq into two alternative forms—one for points outside, the other for points inside the loaded area—which are convenient when the load, though not necessarily uniform, is distributed symmetrically round a point (see Todhunter & Pearson’s ‘ History,’ arts. 1501 and 1502). In this way the depression can be easily deter- mined at the centre and edge of a circular depressed area for a variety of laws of loading, and the depression at other points can be expressed in terms of infinite series or elliptic integrals (see Todhunter & Pearson, /. ¢., especially art. 1504). The slope in these cases, at any distance from the centre of the loaded area, can be obtained in the form of infinite series or elliptic functions; but results of this kind are more apt to repel than to enlighten the unmathematical reader. Fortunately, when the load is uniform, and the loaded area rectangular, it proves possible to express the components of slope dw/dx, dw/dy at any point of the surface in terms of ordinary Napierian logarithms. I shall accordingly devote attention almost exclusively to this case. § 10. Returning to (8), let x’, y' be coordinates of the element dw, so that dw =da'dy’, = (ew) + yy)? +2 The loading being supposed uniform, we have Anndw _ (| 2(- 171 of (l\, 75, pada a! i} da ) oe ihe zal) ans But a es eg) = and 7,(5)=- (5 : WJ and Mathematics to Sezsmology. 181 din dw __ Doak ee i is = is | where 7, and 7, are the inferior and superior limits of 7 in the integration with respect to x’. ie Suppose the origin vertically over the point where the slope is to be found, or z=y=0, and draw the axes of x and parallel to the sides of the loaded rectangle. Take for the coordinates of the corners of the rectangle— Hy Yrs Uy Yrs Lay Y25 Uy Yas and suppose Ly > X15 Y2 > Yie The following result is then easily obtained from (18) : darn (= ae =2(1—n) lo (yot V yo? + 212+ 2%) (n+ Vy? + 0? +2) p \du}z=: 5 (t+ VyP+eet+2) (yet Wye? + 09? +22) —— dx +2 {— — - 5) DP+O N\A y 2+ a2+e Sy2+al+2 1 WAI Yo 2 ( ) } ee 14 te +2? \ oy? 4 v9? 4 2? NV Yo? + fo? + 2? oe This combined with the corresponding expression for dw/dy, which can be written down by symmetry, supplies complete information as to the slope at all depths. By putting z=0 in (14), or by direct calculation, we get ee otiein) = 8 P jog a Vie he) (at Vy Pea?) ami (n+ Vy? +27) (yot NV ye? SEs) ae where 71, Y2 must be treated algebraically. Thus ABCD representing the loaded rectangle, DM, CN perpendiculars on Ow, we have, in the case shown in fig. 1 :— dw = a)p (OD DM) (OB-E BN). dt = Fan 8 (ORF AM)(OC+ON): * (162) in the case shown in fig. 2 :— dw (1—n)p, _(OD+DM)(OB—BN) ee fat) : ie eee, 8 (OA—AM) (O0+0N): {160)* * An equivalent but somewhat longer form for the logarithm (leading directly, however, to [17]) is given in eqn. (7) art. 818 Thomson and Tait’s ‘ Natural micas : ) . . (15) 182 Dr. C. Chree on Applications of Physics In the case of symmetry shown in fig. 38, where the centre of the rectangle lies on Oz, (OD + DM)/(OA—AM) =(0D+ DM)?/OM, &e., and (160) reduces to dw, __(1—n)p, (OD+DM ON 7g (tt 0)= "Plog (OoacN om °° OD) | oe Fig. 1. 7 - s : | | i : Al IB ! Se ke ee Ff) Fig. 2 ‘ J i D C Nad Nie hia 2 A B In this last case of course dw/dy=0, and Oz is the line of greatest slope at O. aot If in fig. 3 we draw DH and CK, bisecting the angles ODM, OCN, we easily throw (17) into the elegant form dw NK ere oss i (at O) = re log (Gr : (18) and Mathematics to Seismology. 183 It will frequently be possible to divide nearly the whole of a loaded area, not itself rectangular, into a small number of rectangles, so that the results obtained above could doubtless be utilized for obtaining approximate values of the slope in many cases where the loaded area is not rectangular. Subcases when one Dimension of Loaded Rectangle small, | § 11. In fig. 4, AB represents an elongated loaded area symmetrical about Or. If we suppose the breadth 20 small Fig. 4. « compared to the distance OA=c, and denote the length AB © by 2a, we easily deduce from (17) as a first approximation dw 7, et 0) =U. 2) P+2mn0A . OB, of Ue eecoee: (LO) where P=p. 2ax 26 is the total load over the area. If, further, ¢ be small compared to 2a, we have (at 0)=(1—n)pb/mne=(1—n)P+4mnac. . (20) When (20) applies, the slope along the axis of symmetry varies inversely as the shortest distance from the loaded area. _§ 12. In fig. 5, AB represents an elongated area perpen- dicular to the axis of symmetry Oy. J ‘Fig. 5. Supposing first that OD(=c) and the breadth 20 are com- parable, but both sma!l compared to the length 2a, we easily find from the formula corresponding to (17) dw dw a DaeP | 6728) 0 “dy (at U) cores log ; eS ee ere (21) 184 Dr. C. Chree on Applications of Physics If, further, the breadth be small compared to the shortest distance from O, we reduce (21) to o (at O) =2(1—n)pb/mne=(1—m) P/2anac, . (22) where P denotes as before the total load. Comparing (20) and (22) we observe that for equal distances ¢, the position of the loaded area in fig. 5 is twice as effective as the position in fig. 4. ae et ae ie eee la aaa | Mee mee ae ae — i i 8 A § 13. In fig. 6 the elongated loaded area has its centre at the origin of coordinates, and the axes of Ow and Oy are along its length 2a and breadth 26 respectively. The slope is required at a point Q(x, y) whose shortest distance from the area is considerable compared to 6. Draw through Q a parallel to AB cutting in M and N the lines AM and BN drawn perpendicular to AB. From (15) and the corresponding equation we have as first approximations to the components of slope dw _(1—n)pb( 1 1 3 = an , (28) _ dro _ (L—=n)pbAM ee 1 dy mn ~~ LQA(QA+QM) QB(QB+ any } 24 In (24), QM and QN are to be treated algebraically, and the formula must not be applied to cases in which either QA+QM or QB+QN tends to become very small (cf § 11). Numerical Illustrations. § 14. Suppose in the case of symmetry, illustrated by fig. 3, that the loaded area is a square 100 metres in the side, and that OM, its shortest distance from O, is 1 metre. and Mathematics to Seesmology. 185 Suppose the load to arise from a sheet of water 1 cm. deep, or that p=1 gramme wt. As in case (iii.) of § 7, let us put n='5, n=11x10' grammes wt. per sq. cm. Then we have approximately, in absolute measure, Ot = (mx 11x 10")"og,(10160/168) ; ae = or, as unit angle =206 x 10° seconds of are approximately, slope at O=0/"0012 approximately. . . (25) The result would be the same if the side and the least distance of the loaded square were altered in the same pro- portion, e. g. if the side were altered to 1000 and the shortest distance to 10 metres. The slope increases directly as the load. It would, however, require an abnormally large differential rainfall or evaporation to appreciably influence by direct pressure a level inside a building situated on strata similar to the material of our calculation. § 15. The differential effect of barometric pressure during the approach or retirement of a deep cyclonic depression would appear a more probable disturbing cause. We might very easily have a mean differential excess or diminution of pressure of 1 or 2 cm. of mercury over an area whose greatest dimension was very large compared to the shortest distance from the observing station, and consequently effects 10 or 20 times that appearing in (25) might not unreasonably be expected in disturbed weather. In the case of a large cyclonic area it would be desirable to apply a formula applicable to a loaded spherical surface, but (17) would probably give a very fair idea of the order of magnitude of the result. § 16. Asan illustration of a different kind, suppose in fig. 5 that O is a station near a long straight portion AB of a tidal river, and that we desire the difference of slope at O at high and low tide. It will suffice to take the difference of level at high and low water as the same all along AB. Suppose this difference to be 5 metres, and assume 7 and x to be the same as in the last example. Taking first c=4 x 2b, we get approximately from (21) dw 5x10?x7 was 1s , oO 95) ] (at O) —_— 5) BY) x 11 {07 oS: 10 X logig(1 29), Phil. Mag. 8. 5. Vol. 43. No. 262. Alarch 1897. Q 186 Dr. ©. Chree on Applications of Physics or in seconds of are slope at O=0"-033,.. . . "aa Taking next c=20, we replace (26) by slope at O=0710. . . . ae If, for instance, the river be 100 yards broad, the first station is 400, the second 100 yards from the bank. § 17. As rivers are seldom straight, I have supplemented the above by calculating the slope at the centre of a semi- circular channel of width 2), supposed small compared to the radius R. For a difference A in the level of high and low water, I find as a first approximation difference of slope at centre of semicircle=2(1—1)gbh/mnR. (28) To aid the imagination, the river may be supposed to enter and leave the semicircle by straight channels forming con- tinuations of the limiting diameter, so that the semicircular portion alone need be considered. It will be noticed that (22) and (28) are identical if c=, and p—gh. In other words, the semicircular tidal river has exactly the saine influence on the slope of the station at its centre as it would have if the channel were straight throughout and came within the same distance of the station. , § 18. The results of the last two paragraphs point to changes of water-level in tidal rivers and estuaries as more likely to appreciably affect the level of neighbouring observatories than any probable differential peculiarities of rainfall or evaporation. In making this observation I exclude of course the direct action of water on the foundations of the building. In all cases similar to those treated in §§ 14-17 the direct gravitational action of the load must be taken into account to obtain the full result. For instance, in the case of an anti- ’ eyclone, the horizontal attraction of the surplus air must be considered as well as the excess of pressure over the area covered by the anti-cyclone. Pressure Effects below the Surface. § 19. As the foundations of most buildings are below the ground-level, the slope at some little depth possesses con- siderable interest. The general formula (14) for the depression at any depth due to a loaded rectangle, though easily evaluated for specified numerical values of z, 2, &c., is somewhat com- e] and Mathematics to Seismology. 187 plicated. Its general character will be sufficiently compre- hended from the results in the case of symmetry, when Y= —p=b. Putting t= Cy ty 6-4 2a, we then convert (14) into Amn (dw\t=¥= “p (de), = 2(1—7) log (b+ VP +42) (—b+ VP + (e+ 2a)2+ 2) (—b+ vb? + 6? + 2”) (O+ a/b? + (c+ 2a)?+ 22) + 2b2?{ (6? + 2*)-1 (6? + 6? + 22) -3 = ((e +20)? +27) "(b? + (c+ 2a)? +2%)-2}, . . 29) So long as z/c is small the right-hand side of (29) can be expanded in a rapidly converging series of the form A+ B(e/c)?+..., where A and B are independent of z. There is no tendency in B/A to become very large for finite values of a/c and b/c. When we neglect B(z/c)? &c., we simply get the slope at the surface. We thus see that at depths small compared to the shortest distance of the loaded area the slope is nearly the same as at the surface itself. The value of B is easily obtained in special cases. As an example, take the sub-case of fig. 4, in which c/a and b/c are both supposed small. We then get for the slope Gia es. pd ce In (80) constant terms of the order (6/c)’ are omitted, though possibly more important than the variable term. Again, in the sub-case of fig. 5, when b/c and ¢/a are sup- posed both small, we find t—=y—0 2 = Ee (1-n+n5). rieke 1 341) dy y= mC In both these instances the slope ¢éncreases with the depth. The formulz hold only so long as z/c is small, so that the phenomenon is rather of theoretical than practical importance. Though somewhat opposed to & priort conceptions, this result would not appear exceptional. Thus, take the case of an 188 Dr. C. Chree on Applications of Physics isolated load pdw at a point P on the surface, and consider the vertical displacement at a point Q at depth z. Join QP=r, and draw QM=za' perpendicular on the vertical PM. Then denoting the angle QPM by a, we have at Q w==(pdw/4anr)§2(1—n) +cosat, . . . . . . . (82)* = (pdeo|Aarnce!) (2(1—n)(1 + 2) + (c/a!) (1 + 2a). Thus when 2/2’ is small, we find, neglecting powers of 2/a’ above the second, w= (pdw/2anzx'){1—n + 4n(z/2’)?33. . . (38) dw dy whence (pdo/2arnx'*){1—n+3n(z/a’)*t. . . (84) Here the slope —dw/da’ increases at first with the depth as in the case of (30) and (31). § 20. When the depth is of the same order of magnitude as the horizontal distance of the nearest point of the loaded area, individual cases of (14) or (29) require separate consideration. When the depth becomes large compared to the horizontal distance of the remotest point of the loaded area, we easily find from (14) as a first approximation (=) bah (5 —2n)p (Yo—Ys) (ae? — 24”) (35) GD [es Sarn 23 2 RS showing that the slope now diminishes as the inverse cube of the depth. If P denote the total load, x, y the coordinates of the C.G. of the loaded area, we have at once from (35) dw dx and by symmetry CD a i ou =(5—2n)Py/(4anz’). . . . (37) The line of greatest slope is thus in the vertical plane which contains the C.G. of the loaded area, and if R be the hori- zontal distance of the C.G., the slope is given by (dw/dR) =.= (5—2n) PR/(4anz*). . . . (88) The conditions assumed in (35) are practically tantamount to those of the elementary loaded area, and (38) can in fact be deduced from (32) by supposing @ small. r=y=0 a =(5—2n)P2/(4anz*), . . . (386) * Todhunter & Pearson’s ‘ History,’ vol. ii. eqn. (xxiv.) of art, 1497, and Mathematics to Seismology. 189 Luni-Solar Effects*. § 21. Another possible cause affecting the indications of pendulums and spirit-levels is the gravitational action of the heavenly bodies, especially the sun and moon. If we regard the earth as a sphere of mass Ei and radius a, and suppose the moon’s mass to be M and its distance from the earth R, there exists in the earth a system of bodily forces of which the principal come from a potential g (M/E) (a/R)? (r?/a) (8 cos? @—1)/2, . . « (89) where g is “gravity” at the earth’s surface, neglecting “ centrifugal force.’ The moon is supposed to lie in the line 0=0, the earth’s centre being origin, and r, @ ordinary polar coordinates. As explained in art. 812 of Thomson and Tait’s ‘ Natural Philosophy,’ there results at the earth’s surface a component force radially outwards g(M/E) (a/R)*(38 cos? @—1), and a component along the tangent T’=39(M/H)(a/R)* sin @cos 0, . . . . (40) directed towards the point under the moon (0=0). Both components being small compared to g, the direction of gravity is, owing to the direct attraction alone, deflected through the angle Oy’ =tan—!{3 (M/E) (a/R)? sin @cos@} . . (Al) from the vertical. The angle being very small may be re- placed by its tangent. Thomson and Tait suppose (M/E) (a/R)?=10-9/182, . . . . (42) and thence draw the following conclusion: —“ the plummet is deflected towards the point of the horizon under either moon (9=() or antimoon (9@=7), by an amount which reaches its maximum value... 0’:017 when the altitude is 45°.” They add— The corresponding effects of solar influence are of nearly half these amounts.” According to this conclusion direct luni-solar influence should make itself felt in any system of pendulum or spirit-level observations in which the accuracy is of the order 0”:02. § 22. The data on which the above calculation is based are pretty accurately known, which constitutes a reason for * Strictly the problem is a dynamical one; as yet only an “ equili- brium”’ solution is available. 190 Dr. C. Chree on Applications of Physics treating the direct effect by itself. It must, however, be borne in mind that the luni-solar influence is not confined to the pendulum bob, but extends to the material of the earth itself. Consequently the result calculated by Lord Kelvin and Prof. Tait is part only of a composite effect, which there is no very obvious way of analysing in practice into its components. In the actual earth the most obvious consequence of luni- solar action is the ocean tides, and, as we saw in § 4, any station near the sea-shore has its apparent level affected by these in two distinct ways. Even at an inland station ocean tides must exert some influence, though presumably it is very small. In addition, however, to ocean tides there must be tides in the earth’s mass, whether solid throughout or not, and it is to these I shall now call attention. The potential term (39) is only one of a series. The numerical values of the coefficients diminish rapidly as the order of the harmonic increases ; still itis desirable not wholly to neglect the higher harmonics, if only to make sure that the comparative smallness of the disturbing forces answering to them is not compensated in any instance by great effectiveness. I shall thus consider in the first place the results of the general problem when the degree of the harmonic appearing in the disturbing forces is unrestricted, making use of the results contained in a paper communicated to the Cambridge Philo- sophical Society * in 1887. § 28. Before entering, however, on this investigation, it is desirable to consider briefly the relation between the re- sults of theory and the phenomena we may expect to en- counter in direct observation. Surface-points on the undisturbed surface, regarded as spherical, transform into surface-points on the strained sur- face ; thus a very small surface-area, e.g. a square decimetre, may be regarded as a tangent plane in both conditions. Suppose, now, this area to have rigidly attached to it a spirit-level, consisting of part of a circular are filled with liquid and with a minute air-bubble. In the undisturbed condition suppose the bubble exactly at the central division O of the arc, while in the disturbed condition it is at an angular interval 6@ from O. This an observer would naturally attri- bute to a change 60 of level. The true interpretation is that in the disturbed condition the resultant of the forces at the surface makes with the normal the angle 60. In a rigid earth 5@ would be the angle of Thomson 1nd Tait’s calcula- *Sce the Society’s Transactions, vol. xiv. p. 278. and Mathematics to Seismology. 191 tion ; but in an elastic earth allowance must be made for the fact that the attraction of the disturbed earth is not along the normal. The effect on astronomical observations is still more com- plicated. Thus let an observer take the altitude of a star in the same vertical plane as the moon, using a mercury surface for his horizontal plane. The observed altitude will differ from the theoretical—z. e. the true altitude if the disturbing influence were absent—by an amount equal to the angle between the disturbed and undisturbed mercury surfaces. This is the algebraical sum of the inclination of the resultant gravitational force to the radius-vector in the disturbed con- dition and of the inclination of this radius-vector to its undis- turbed position. This explanation will show what the quantities are of which we require to know the theoretical values. § 24. To return to the problem. The earth is treated as truly spherical when undisturbed, “ centrifugal force’? being neglected, and as posssesed when disturbed of uniform den- sity p, and of uniform isotropic elastic qualities throughout, determined by the elastic constants m, n. The assumption of natural sphericity and the neglect of the centrifugal force answer merely to the neglect of small quan- tities of the second order of magnitude relative to those of the first ; the other assumptions have been discussed in § 2. In our ultimate applications the material will be supposed incom- pressible, 1. e. n/m=0, but it is undesirable to introduce unnecessary limitations in the mathematical results themselves, Further, absolutely incompressible material is merely a ma- thematical fiction, so it is desirable to have the means ready to hand to apply a correction to mathematical results based on such an hypothesis. Supposing the typical term in the potential of the disturbing forces to be Bla I A ee where o; is a known surface-harmonic of degree 7, and Vj a given numerical magnitude, we easily see that the equation to the strained surface will take the form RCo SOG is) es «1s § (4M) At the present stage all we know is that a; is small compared to a, the mean radius of the strained surface. The bodily forces consist in part of the disturbing forces, but mainly of the self-gravitational action of the “ earth.’ 192 Dr. C. Chree on Applications of Physics The complete value of the potential V is given by V=—f ga"? + 339 (1r/a)'ajo,/(20 +1) + Br’ Vi/oi*. . (40) In ordinary circumstances we are supposed to be given the unstrained surface, with full information as to the force system, and it is customary to regard the surface equations as applying to the unstrained surface. In the present instance— and I daresay as a rule in practice—the forces depend io some extent on the disturbed form of the body. It is thus con- venient, to say the least of it, to suppose that the surface equations apply in the present instance to the disturbed sur- face. This implies nothing more serious than the replacing the ordinary definition of strain, viz. ; (final length—initial length) /(initial length), y , (final length—initial length) /(final length}. The two definitions are equivalent so long as it 1s justifiable to apply the mathematical theory, which assumes the square of a strain negligiblet. § 25. The problem whose results I am about to use was more general than the one at present before us, inasmuch as the surface was not assumed to be naturally spherical. The notation employed in its solution was also somewhat different, the potential being given in the form =—t9a-4? +> aVior. . .-. Ge Thus in utilizing the results we must put Vi;=39a7/(2i4+1)4+Vij/a. . . . 24 In the general problem V; was unrestricted, but I contented myself with giving the two arbitrary constants a;Y;, aZ; explicitly in terms of o;V; and ga~‘a;. The expressions for the displacements freed from arbitrary constants were given (1. c. equations (13) to (15), pp. 280, 281) only for the case when V;=3ga-‘/(21+ 1), or when V; in (47) is zero. It is easy, however, to add the terms containing V;’.. For if in the equations (11) and (12) of p. 280, l. c., we substitute for V; the right-hand side of (47) and multiply up by a;,o;, we notice that V,/o; appears with the same coefficients as V possessed in the earlier equations (32) and (33) (/. ¢. p. 264), which determined the unknowns Y; and Z;—treated in that * See Prof. G. H. Darwin, Phil. Trans. 1879, Part 1. + See Phil. Mag. Sept. 1891, pp. 246-7. and Mathematics to Seismology. 193 instance as each the combined product of surface harmonic and arbitrary coefficient—for a perfect sphere acted on by bodily forces. Thus for terms in V; in the displacements, we have only to take the results (36), (37), and (88), J, ¢. pp. 264-265, and in them replace V; by V;,’o; and 8; by zero. Doing so, we find for the components of displacement, measured respectively in the directions of the fundamental polar elements dr, 7 d@, r sin 0 d6¢, the following results :— ae gpr { gia a?(5m +n) a 10a(m +n) 3m—n es A;O; . arrs +9p =n (2i - I) pL taf LOm* —1) — mn (Act + 423 + 347? + 297 + 10) +n? (82? + 82? + 131—2) } —7'-1g—*+27 1 10m?i(t + 2) — mn (42? 4+ 42? — 22 + 1) —n?(4i—3) } ] AE = i 5(m+n) ual [amet n —1'14m(-+1)—n} | 2n —I d ld C— dé >V,, ay) apa ° ° ° (49) where D;=5(m +n) {m(22? + 40+ 3) —n(2i+1)}, . . (50) a FLED: it1g—t Dp aE ay = In(2i-+ 1)D, [7H a—*{ 10m? (¢ — 1) (¢+ 8) —-mn(Ae? + 120? — 62 + 17) —n? (87? —17)} —r'—1a-*F2 510m (t+ 2) —mn(4e? + 47? — 21+ 1) —n? (4¢— 3) F] Te OV a 5(m+n)pV ici [aie tt aif 2nD; § 26. Before utilizing these results we must determine ai in terms of V;’, which is easily done as follows:—The surface being supposed originally spherical, the terms Sa;o% in (44) arose solely from the action of the disturbing forces, and so must be identical with the variable terms in the surface-value of wu. Thus writing a+ a,0; for v in the principal terms in (48), and a for r in the subsidiary, then equating the separate harmonic terms to the corresponding ones in Laie; and re- ducing, we find pa Vv /i§(2i+ 1L)m—n} + {2 (i—1)n( (22? + 42 +8) m— (i+ 1)n) 14.90% 157(20 + 1)m?— (82? + 627 — 21—Y) mn + (40 — 22? — 32 —3)n? n d(21+1)(8m —n)} (2774+ 474 3)m— (Qi+1)n}. eel > = oT rt fm(i+3) —n} |. (48) (51) .(52) 194 Dr. C. Chree on Applications of Physics If the self-gravitation were negligible, the denominator in (52) would become unity, the numerator remaining un- changed. ‘Thus self-gravitation reduces the change of form produced by the disturbing forces depending on the harmonics of degree 7 in the ratio gpa 15i( 22 + 1)m?— (87? + 67? — 27-9) mn + (42? — 22? — 37 — 3) n? n d(22+ 1) (8m—n) { (20? + 40+ 8)m— (2i4+1)n} If n/m=0, je oo or the material be incompressible, (52) reduces to pai*1V {i (27 + 1)/{2(¢—1) (222 + 47 +3) n} ee a= and the ratio (58) becomes 1: 1+ (gopa/n)i/(2?+414+3). .-. 2 (5) When 2=2, (52) becomes s pa? Vo! (Sm—n)/{n(19m—5n) } 56 ey ee 3(gpa/n) (LOm?—dmn + n?)/{5(8m—n)(19m—5n) }° Cy A result equivalent to (56), with the notation A=m—n, pb=n, was given by Prof. Karl Pearson, in Todhunter and Pearson’s ‘History,’ vol. il. part 2, p.425. An obvious misprint of 4u for 14 occurs, however, in the denominator of his formula. § 27. We may safely assume m—n positive, so the nume- rator in (52) has clearly the same sign as V;,/; also for a given value of V;’ it diminishes as 7 increases. Thus so long as the denominator in (52) exceeds unity there is no risk lest the relative smallness of the forces proceeding from any higher harmonic may be compensated in any way. It is obvious, however, that the coefficient of gpa/n in the deno- minator can be made negative by taking i large enough, for fyjinary values of n/m. For instance, if n/m=1/2,—the is negatsis of uniconstant isotropy,—the coefficient of gpa/n minator as When? exceeds 9, and with < infinite the deno- through the val jole would vanish and change sign as n passed If we take as befegP a/100. 9p4=35 X 10° or, ~ammes wt. per sq. cm., E(B & and Mathematics to Seismology. 195 this critical value of n has the very ordinary value 21 x 10° grammes wt. per sq. cm. Thus if such a value as m/n=2 were admissible the con- tingency of a,/V;,/ becoming enormously large for a high value of 2 would be quite a possible one. Unless, however, as I have previously pointed out, n/m be very small, the term in wu, independent of the angular coordinates, would in a body of the earth’s mass be enormously greater than is con- sistent with the mathematical theory of elasticity. Therefore, so long as the present calculation is justifiable, the denomi- nator in the value of a;/V;’ can differ but little from that occurring in (54), and we are thus thoroughly justified in neglecting all the higher harmonic terms in the potential relative to the term containing the second harmonic. § 28. Asa small departure of n/m from 0 would exercise but little influence on numerical values, it will be best, as we are dealing with data so uncertain, to neglect n/m altogether. Thus, putting hee Ors — beau 70) me = 0). Vy =9(M/E)(/R),. . 2. (5) we have for the displaced surface r=a+ta,Po, 5 C o : ° ; (58) where a,/a= - (gpa/n) (M/E) (a/R)? = £ oF e (gpaln) Sab @S))) An equivalent result is given in Thomson and Tait’s ‘ Natural Philosophy,’ art. 840. The result will also be found, along with that answering to 1=2, m=2n, in Mr. Love’s ‘'T'reatise on Hlasticity, vol. i. pp. 802, 303. The corresponding surface displacements are u = aPs(gpa/n)(M/B)(a/R)?/{1+2gpa/19n}, — (60)* ae - a sin cos A(gpa/n)(M/B) (a R)?/{1 + 2gpa/19n}.(61)* The term in u independent of the angular coordinates abso- lutely vanishes for n/m=0, and both components of the surface displacement, and so the resultant displacement itself, are reduced owing to the self-gravitation in the common ratio 1: 14+2gpa/(19n). aoe OBR na (62)* * The material being as here incompressible, it may be proved that for any value of ¢ in (45) the displacements are everywhere the same as In a sphere of radius a, over whose surface act purely normal tractions equal to pato;Vj'+ {1+ (ypa/n)i/(2i?-+4i+3) }. 196 Dr. C. Chree on Applications of Physics The angle through which the radius-vector is rotated from its undisturbed position, in the direction away from 6=0, is equal to v,/a, and so is known from (61). As v,/a is nega- tive for all values of @ between 0 and 7/2, this rotation is really towards the moon at every point of the illuminated hemisphere. § 29. We next require to find the inclination of the re- sultant force to the radius-vector over the surface. Employing (57) and (59) in (45) we find for the complete value of the potential V=—39(77/a)[1—2P, (M/E) (a/R)*(1 + 5gpa/19n) —(1+2g9pa/19n)]. . (63) The component forces along and perpendicular to the radius-vector are | = oY ea ud V. nee Ts de eT Thus at a point on the surface the principal terms, which alone we require, are R=—g, © = —3g sin 0 cos (M/E) (a/R)?(1 + 5gpa/19n) —=(1+2gpa/19n), . (64) and the inclination of the resultant force to the radius-vector is to a first approximation dy = 0/R=3 sin 0 cos 6(M/E) (a/R)3(1 + 5gpa/19n) =(1+2gpa/19n). . (65) For the apparent change of altitude, dz, in a star we haye, as already explained in § 23, da = dy + va/a=3 sin 0 cos (M/E) (a/R)? {1 + = (gpa/n) } (1+ 29pa/19n). . (66) § 30. For the apparent change of level dy, we require the inclination of the resultant force to the normal. To obtain this we may employ the result (65) in conjunction with the inclination dy, of the normal to the radius-vector, the latter being given to a first approximation by i= (—; ye = = sin 8 cos @(gpa/n) (M/E) (a/R)? (14 29pa/19n). (67) and Mathematics to Seismology. 197 Thus we have finally Sy=dy—3yy =3 sin 6 cos 0( M/E) (a/R)?+(1+2g9pa/19n). (68) This result can also be got by noticing that oy=tan-* (T/g), =T/g, to a first approximation, where T =Rsin 6,—O cos dy, = 39 sin 6 cos 0(M /E)(aR)?+(1+2gpa/19n) . (69) is the tangential component of the surface-force. Comparing (68) with (41) we have Ove: OW! ss 1:14+29pa/19n, . . . (70) or the self-gravitational forces reduce the apparent change of level, as calculated in Thomson and Tait’s ‘ Natural Phi- losophy,’ in precisely the same ratio as they reduce the ellipticity of the surface. This last result might probably be deduced at once from the fact that u, and v, are reduced in the same proportion, but 1 have preferred an explicit mathematical proof. Comparing (66) and (68), we have S2/8yr = 144 (2gpa/l9n),. . . (71) showing that the apparent change in star’s altitude —the star being, it will be remembered, in the same vertical plane with the moon—is always in excess of the apparent change of level. Numerical Estimates. § 31. As before, we shall take a= 64105 gpa = 35 x 10° grammes wt. per sq. cm., (M/E) (a/R)3 = 1/(182 x 10°). We shall consider only the greatest and least values of n specified in § 7, exhibiting the results side by side ; @, it will be remembered, is measured from the line joining the centres of the earth and moon. 198 Dr. C. Chree on Applications of Physics Numerical Results: Lunar Influence. 80x10" grammes wt. 11X10" grammes wt. per sq. cm. per sq. cm. 2gpa/19n = 35/76 700/209 1: 1+2gpa/19n (approx.) = 11 16 3:15 3 cos? 6—1 26— i 9g cms. — ems. v% =| —2. ~Ocosécms. | —61 sin 6 cos 6 ems. Polar less equatorial radius = - . ems. 102 ems, Apparent change level, ®) = O"*~ sin 26 ("004 sin 26 Apparent change of star’s| _ eee icine altitude, da = 0’-Oz1 sin 28 0'027 sin 20 The reduction effected by the self-gravitational forces in Thomson and Tait’s estimate, 0/"017 sin 20, for the apparent change of level increases conspicuously as the rigidity diminishes. In fact, for the lower value of n, di would be insensible unless with an instrument recording to 15 of a second of are. On the other hand, the changes in the shape of the earth and in the star’s apparent altitude are very decidedly larger for the lower value of n. Corresponding results of about half the numerical size of the above would be obtained in the case of solar influence. Final Conelusions. § 382. The results obtained indicate at least the directions in which luni-solar effects may be profitably looked for. If the earth’s elasticity for luni-solar influence be perfect, apparent changes of level or star’s altitude will be nd when the moon or sun, as the case may be, is either in the zenith or on the horizon, while they will be a maximum when the altitude is 45°. If the elasticity be not perfect, a lag in the tides may be expected. As regards star’s altitude, a hopeful feature is that the influence, being the same for all stars in the same vertical, should be easily separable from terrestrial refraction. The further fact that the apparent change is proportional to the cosine of the star’s azimuth measured from the vertical plane containing the moon, or sun, may prove of assistance. It would appear that luni-solar effects are not unlikely to prove of as much consequence as the direct pressure or gravitational effects of any ordinary differential meteorolo- and Mathematics to Seismology. ies) gical action in the neighbourhood of an observatory, though not nearly so important as ocean or estuary tides for obser- vatories situated within a few hundred yards of high-water- mark. The considerable fluctuation of. the calculated luni-solar effects with the value ascribed to the earth’s rigidity may lead eventually to interesting speculations as to the state of the earth’s interior. Subsidiary Remarks. § 83. Whilst attention has been confined to surface-pressure and luni-solar action, it is not intended to imply the non- existence of other agents capable of producing similar phenomena. The sun’s direct heating effect is doubtless in some cases a most effective agent in altering the level. A priori one would expect a diurnal variation from this cause, most sensible at stations on rocky ground exposed to the south. § 34. Before quitting the subject, it is desirable to consider what light existing seismological data throw on the credibility of the hypothetical theory adopted. lt appears pretty generally believed that wave-velocities calculated from observations near and distant from the epicentre of an earthquake are usually different, and the existence of at least two widely different wave-velocities seems on some occasions well established at the distant stations. One of the two wave-velocities has been regarded (on, I think, mistaken grounds) as postulating an elasticity incredibly high for an elastic solid medium. These phenomena are easily reconciled with the elastic solid hypothesis. When waves travel between two distant points through the interior of a sphere of large radius they may be expected to behave much as if the medium were infinite. Now in an infinite isotropic medium%, as is well known, there are two wave-yelocities, v; and v2, given in our previous notation by y= V(m+n)/p v= n/p. Thus, under the conditions supposed, we should expect two earthquake-waves with velocities similar to v, and vo. For definiteness, suppose that the velocities are actually v, and vs, * See, for instance, Love’s ‘Treatise on Elasticity, vol. i, pp. 183, 184. 200 Applications of Physics and Mathematics to Seismology. and suppose them to be respectively 12°5 and 2:5 kilometres per second, this appearing a fair estimate. Then, in absolute c.c.s. measure, V(m+n)/p =125x104, Wn/p = 25x 104. Taking p=5'5 for the earth, we have the approximate results, n = m/24 = 35x 107 grammes wt. per sq. cm. For E, Young’s modulus, and £, the bulk modulus (resistance to compression), we have similarly, EH = n(8—n/m) = 10 x 108 grammes wt. per sq. cm., k=m—n/s = 838x108 ” ” The rigidity and Young’s modulus—the quantities from whose magnitudes our conception of a material’s elasticity is usually derived—are in no ways remarkable, being much below the average magnitude observed in iron. The only abnormal feature is the enormous resistance to compression. Any one, however, who considers the enormous pressures presumably in continuous operation on the earth’s deep- seated material, will appreciate the probability that it responds uncommonly little to any slight increase in pressure. A difference between the velocities calculated at stations near and distant from the epicentre is only what we should expect. Lord Rayleigh* has shown that waves with a velocity somewhat less than Vn/p may be propagated through the material close to the surface of a medium bounded by an infinite plane; and a similar phenomenon may be expected in a sphere, so long at least as the distance from the epicentre is small compared to the radius. In such waves the velocity must depend mainly on the density and elastic properties of the surface material, which in general must differ largely from the corresponding quan- tities in the deep-seated material. Thus the velocities calcu- lated from the observed effects must depend largely on whether the waves propagated along the surface or those propagated through the interior are the dominant ones ; in other words, on whether the distance of the station from the epicentre is or is not small compared to the earth’s radius. * Proc. London Math. Soc. vol. xvii. (1886). See also Love’s ‘Treatise,’ vol. i. pp. 828-8380. | [> 20ta XXIX. The Spontaneous Change of Oxygen into Ozone and a Remarkable Type of Dissociation. By WILLIAM SUTHERLAND*. i 1886, in connexion with a physiological inquiry, Bohr (Wied. Ann. xxvil.) came across a singular discontinuity in the behaviour of rarefied oxygen, as well as a very pro- nounced departure from Boyle’s law; between 14° and 11°4° C. the discontinuity occurs at a pressure of about °7 millim. of mercury, above which Boyle’s law is replaced by (p+:'109)B=k, which was experimentally tested up to 15 millim., and below ‘7 millim. the pressure relation is (p+'07) B=Kk’, where k/=1:045h4, this being experimentally verified down to ‘1 millim.; thus the discontinuity consists in a change of volume from 4/'809 to k’/:77 at a constant pressure of -7 millim. It is to be remembered that Bohr’s pressures were all directly read with a cathetometer from the difference of level of mercury in two wide tubes, so that there is no question of the departure from Boyle’s law being only an apparent one, due to a fallacious step in a train of reason- ing. Ata pressure of ‘07 millim. the departure from Boyle’s law is no trifle, for a reliable M‘Leod gauge worked on the assumption of Boyle’s law would make a true pressure of 07 millim. appear to be twice as large. We have already seen in ‘‘ Thermal Transpiration and Radiometer Motion” ft that in Crookes’s study of radiometer repulsion for different gases with his torsion radiometer, oxygen at a pressure about *76 millim. or 1000/10° atmo exhibits a remarkable difference from other gases, showing a deflecting force 12 times as great as that of N, or COs, and 6 times as great as that of CO, and the anomaly continues till a pressure of about 300/10° to 200/10° atmo in Crookes’s list of pressures. Here are the complete results for the anomalous region, with the addition of what the deflecting force ought to be according to (26) of “ Thermal Transpira- tion and Radiometer Motion ” with the values of c’, A’’, and B’” there given for oxygen, as derived from the region of lower pressures, where all is apparently regular; the so- called pressures are given in terms of 1/10° atmo as unit. 0 A 1000 803 658 623 613 360 297 190 10* log. dec.... 1102 1093 1088 1086 108 1070 1058 1038 Weil, forces... 12 12 13 13 13 13 14 20 Defi. force cal. 4:2 52 6:3 6:6 67 Loe Be rSS * Communicated by the Author. { Phil. Mag. vol. xlii. Phil. Mag. 8. 5. Vol. 48. No. 262. March 1897. RR P 202 Mr. W. Sutherland on the Spontaneous Of course, Crookes in working his M‘Leod gauge to get the pressures just given, had no knowledge of Bohr’s sub- sequent discovery of the failure of Boyle’s law in oxygen at low pressures, so that the numbers given in the first row as the pressures are not the true pressures; though starting nearly true at 1000 they end up at 190, nearly twice as large as Bohr’s formula would give. But, as has been pointed out in “Two New Pressure-Gauges’’*, this erroneous yield of pressures does not affect our application of them in onr for- mule for log. dec. and deflecting force, because in these formule p merely replaces 1/B, and what the M‘Leod gauge really gives is 1/B, whether Boyle’s law holds or not; if Boyle’s law holds the values of 1/B are given in such a unit that they are equal to p, but if Boyle’s law fails, though they no longer give p, they give 1/B in an arbitrary unit. Thus, for example, according to the formula for log. dec. {(L—p)/U—#) — I} is proportional to A, the mean free path, which is directly as the volume B, so that (j=# = 1)/B = 2ar,/ByD, (—pw wherein Crookes’s values of p may be taken as correct rela- tive values of 1/B, so that we can form the products {(L—p)/(l—) —13/B from the values of /, the log. dec. in the last table, taking L as ‘1120 and w as ‘004, and 1/B as given by p; thus for 2ad,/ByD we have the values 17, 21, 19:7, 20°6, 20°9, 17:3, 18-1, and 15°6, which for a pure gas ought all to be the same, but as J is not very different from L at the higher pressures we cannot expect accurate constancy, but can state that there is no disturbance in 2aA,/B)D at all comparable to the dis- turbance in the deflecting force. To assure ourselves of this we will trace the values of 2a\)/B)D down to the lowest pressures. Bucene af AIO 582 6700-48 COD IG 12° 4 ¥6 3 10* 7... 10383 988 940 912 840 744 724 670 621 585 433 348 302 149, 153.4164 168 164 165. 162 15:7 13:8; 108 —70) 400 These show that 2aA)/By)D has an approximately constant value at about 16 down to about a so-called pressure of Z0/10° atmo, below which there is a rapid diminution. Being now in possession of the essential facts connected * Supra, p. 83. Change of Oxygen into Ozone, 203 with the abnormality of oxygen at low pressures we can consider the theory of it. Bohr’s results mean that pB de- creases with increasing volume B, and, according to the kinetic theory, pB=Nmv*/3, where N is the number of mole- cules in volume B; now it is not necessary that the molecules should be all alike, for whatever m may be mv’/2 is the same for all molecules at the same temperature; thus then the diminution of »B with increasing B discovered by Bohr would be most simply explained by supposing N to diminish with increasing B, seeing that mv’? must remain constant, that is to say, by supposing association or combination of the oxygen-molecules to oceur so as to produce molecules of the composition Os;. Let there be N, molecules of O, and N, of Oo:, then N,+a2N,=N, and pB=(N, 4+ Nz)mv?/3 = Nmv’?/3 — (a—1)Nomv’/3, to be compared with Bohr’s pB=k'—a'B, with the result that k' is identified with Nmv?/3 and «’B with (c—1)Nomv?/3, that is to say that N,/B at a given temperature is constant, which gives us the simple law of combination, that the number of molecules of O., per unit volume is to remain constant ; of course this law will not carry us up to the limit at which N, is zero; but we can state the law of combination in the following terms :—At a certain degree of rarefaction the molecules of O, begin to combine to form O,; and when these amount to a certain number per unit volume the effect of further rarefaction is to cause just so much further com- bination as keeps this number per unit volume constant; this process goes on till all the O, molecules are used up, that is, till eN2=N, after which the pure Oz, ought to obey Boyle’s law. Now the degree of rarefaction for the new appearance of Boyle’s law was not reached in Bohr’s experiments, but in Crookes’s observations of the deflecting force in oxygen we found the anomaly to disappear at a so-called pressure of between 300/10° and 200/10° atmo; but as these so-called pressures are nearly p+a', where a’, being ‘07 in millim. of mercury, is 92/10° atmo, the anomaly may be said to cease when p=2e'; thus to determine the value of « for which the combination is complete we have the conditions that then p= 2c’, and therefore (N,/B)mv*/3 = 2 (w@—1)(N2/B) mv?/3, to) 2 ond No=2N/3, R 2 so that 204 Mr. W. Sutherland on the Spontaneous Thus, then, a process of association or combination of the Q, molecules to form Q3, that is, ozone, explains one of Bohr’s equations, and the cessation of anomaly in Crookes’s experiments on deflecting force. It is necessary that in compressing pure O3 a pressure should be reached at which the QO; begins to dissociate into O,, and progressive increase of pressure produces progressive dissociation of O3 into Qs. This result is so contrary to the ordinary experience of dis- sociation amongst gases that it calls for the closest exam- ination before we proceed farther. Now the most striking result so far is that over a considerable range of values of B there is to be a constant value of N,/B, and this gives us at once an insight into the remarkable character of this disso- ciation ; for N,/B is proportional to the number of collisions of a molecule of O; with other molecules of O3 in unit time, and as long as this is below a certain value 6a'/mv’, as we have just seen, there is no dissociation, but when by com- pressing the pure O; a volume is reached at which N,/B= 6a!/mv*, that is, at which the number of encounters of O; with its fellow molecules attains a certain value, some of the molecules are on the point of being dissociated, and if the pressure is increased the dissociation proceeds until the number of collisions of an O; with its fellows falls to the value given by N,/B=6a'/mv’, at which the number of molecules of O, remains constant until further compression is attempted; thus, then, we have evidence that there is a certain periodic collision with one another which the O; molecules cannot stand, and this implies that the period is identical with some natural period of vibration in the molecule: we have a case of molecular resonance leading to the destruction of the resonating molecules. So far as we have gone it appears as though a collision of an QO; with an O, occurring between its collisions with other QO; is of no account, and we can understand how the presence of a number of O, molecules is really of little importance to the final result; for even if a collision with an O, has an inimical result as regards the dissociation, still, according to the laws of probability, there will be a number of successive collisions of some of the O, molecules with others without intermediate collisons with O, which would suffice to produce the destruction of the O3 molecules, and therefore the only effect of the QO, molecules is to make the process of disso- ciation slower. But at last a stage will be reached at which the dissociation is so slow that it is only able to neutralise the combination that goes on, and then further diminution of volume will Change of Oxygen into Ozone. 205 make the dissociation less rapid than the combination, and thus both on account of diminution of volume and com- bination N./B increases, so that the collisions of O; with O, cease to occur at the destructive periodicity, and the special cause of destruction or dissociation being removed, we have now to do with a more ordinary case, where the dissociation which takes place arises out of accidentally favourable col- lisions of O, with O3 or with O,, and combination out of accidentally favourable collisions of O, with O,; now the number of collisions per second of an O, with an OQ; is a2 = 2(N,/ B) (ag + ag) at* (Ke? at ae where a2 is radius and 3«?/2 mean squared velocity of mole- cule of O;; and the number of collisions per second of an Og with an QO, is V2 = 2(Ny/B) (ay + a)?ar8 (ep? + He?) 5 and as ag =2a,* and «,?/K,?=m,/m, = 2, the coefficients of N,/B and N,/B in the two expressions are nearly identical, and ,v2+ v, is proportional to (N,+N,)/B; but according 1o Bohr’s discovery (N,+N,)/B is constant after the disvontinuity occurs, so that it appears that on diminishing volume after the discontinuity, combination and dissociation are in equilibrium when the total number of collisions of an O3 per second has a certain constant value. Thus a periodicity in which the O, molecules play as im- portant a part as the O; molecules gets established as the one which the O; molecules can just stand, and diminution of volume goes on so as to keep (N.+N,)/B constant. But when the diminution of volume has gone a certain length another discontinuity appears which leads into the region of Bohr’s equation (p+a)B=k, to which the same explanation must apply as to his other equation, so that a new periodicity, which is to the former one as a to @, suddenly appears amongst the collisions of O3; with O3, as specially destructive to the O; molecules. But one consequence of our theory is that k ought to be the same in the two equations of the form (p+a)B=f, whereas Bohr’s values make k’=1:045k, because in the theory &£ in both cases stands for (N/B)mv?/3: accordingly we must revert to Bohr’s experimental data to ascertain whether & is necessarily different from k’. These are arranged in two series, the first at 14° C., and the second at 11°°5, Bohr giving the preference for reliability to the first ; but if we plot them both with B as abscissa and pB as 206 Mr. W. Sutherland on the Spontaneous ordinate the points thus obtained ought, according to Bohr’s equations, to lie on two straight lines, and if in these equa- tions k and k’ are the same, both lines ought to pass through the same point in the axis of pB: a glance at the points when plotted shows that two straight lines passing through such a point is the best representation for the second series of experiments, and although Bohr’s two equations for the first series, representing two lines cutting the pB axis in two distinct points, form a possibie expression of the mean locus of the points, still a representation which causes these points to coincide is quite as good, the difference between the two being less than the obvious errors of experiment. Thus for Bohr’s series I. we have the equations } (pta)B=k, (pt+e’)B=k, with a="1l and a’='043, while in series II. 2=-10 and a'=°057 ; the value of kis not given because the mass of the gas is unknown. It would appear as though @ increased with increasing temperature and @’ decreased, while theo- retically we should expect both a and 2’ to decrease, but the temperature interval between the two series is too small to allow of a safe inference as to the effect of temperature onaand a’. According to the theory the ratio of 2 to a! is that of the frequencies of encounters of O3; molecules with one another before and after the region of discontinuity, and from the above values it appears to be greater than 2 to 1 at 14° and less than 2 to 1 at 11°5, with very nearly a mean value of 2 to 1 like the octave in music. Thus, when pure O; is compressed, dissociation into O, begins when N,/B attains a certain value, and goes on in such a manner as to keep N,/B constant till a point is reached at which, on further reduction of volume, N, increases, but N, decreases in such a manner as to keep (N.+N,)/B constant, so that although volume diminishes pressure remains constant; thus the pro- cess of dissociation by encounters of the old periodicity proportional to N,/B ceases and there is fresh combination sufficient to keep (N,+N,)/B constant, but when by dimi- nution of volume and combination N,/B has risen to double its old constant value, dissociation begins again to occur on further diminution of volume, as though the molecules of O; were now resonating to the octave of the old periodic collision with a vigour that makes the presence of a great excess of O; of little account; this more rapid period is probably a natural period of vibration of QO, the other being an octave lower. An interesting point about the discontinuity is the similarity which it presents to the discontinuity of lique- Change of Oxygen into Ozone.. 207 faction, although, as we have just seen, the mechanism for keeping pressure constant is very different. But the simi- larity extends a little farther than to the one point of constant pressure, for Bohr found that on starting at a pressure below ‘7 millim. and suddenly diminishing the volume the pressure could be raised to °8 millim., although in the course of some hours it would fall back about ten per cent., a case which corresponds to that of supersaturation of a vapour with slow deposition of liquid ; on the other hand, when the pressure was at ‘7 millim. and the volume was increased the pressure remained at °7 millim. for a while and then began to fall off. These facts prove that dissociation goes on with great rapidity, while combination is slow, in agreement with our theory, because dissociation being produced directly by the collisions must be a very rapid process, whereas combination, as it must depend on collisions of the O, molecules under very favourable circumstances, being compelled to wait for the accidental occurrence of these rare conditions, must go on very slowly. We have now to see how the theory explains the ano- malous deflecting force discovered by Crookes, and also the slightness of the disturbance of the viscosity. Suppose that we have two chambers at temperatures 0, and @, connected by a tube and containing a mixture of O3 and QO, in the cooler chamber, there will be equilibrium between the O; and the O, when N,/B=3a,//2mv?, where , is the value of @’ appro- priate to the temperature @,; thermal transpiration will carry the mixture of N,/B molecules of O3 and N,/B of O, per unit volume along the tube to the hotter chamber, where the resulting increase of pressure, as well as the increase of tem- perature, will dissociate some of the N,, with still further tendency to increase the pressure ; now, when equilibrium is reached between the O; and the O, in the hotter chamber, N./B=38a,/2mv; in it ; and the final steady state of the whole system is determined by the conditions that N,/B in the cool chamber and in the hot chamber has the values given ; therefore, the circulation which was proved to accompany thermal transpiration will tend to carry fewer molecules of QO; from the hot chamber to the cold than from the cold to the hot, in the proportion of a,/mvz to ot,,/1Vay and therefore, to preserve the state of equilibrium, the circulation will have to carry more O, molecules from the hot chamber to the cold than from cold to hot, the gaiu of O3 in the hot chamber being dissociated to keep up the supply of O,, and the gain of O, in tlie cold chamber being combined to keep up the supply of O3 there, and thus the excess of N,/B, the number 208 Mr. W. Satherland on the Spontaneous of molecules of O, per unit volume in the hot chamber, over its value in the cold chamber must be 3/2 the corresponding difference in the values of N,/B, that is to say, the difference of the partial pressure of the O, in the hot and the cold must be 3/2 the difference of the partial pressure of the O, in cold and hot; so that the total excess of pressure in the hot chamber over that in the cold is equal to half the difference between the partial pressures «’ and a,; but we have just seen that with the temperatures constant these are constant over a large range of pressure from the pressure at which dissociation just begins up to the pressure at which the first discontinuity occurs. Thus, then, as the regions of the bulb on the two sides of the mica plate in Crookes’s experiment correspond to our hot and cold chambers, we see theoretically that the deflecting force ought to be constant from a pressure of about *7 millim. or 920/10° atmo down to about 2a or ‘11 millim. or 144/10° atmo, according to our equations with one value of & and °055 millim. as the value of «. Now in Crookes’s data already given we saw that the deflecting force remained practically constant at pressures from 1000/10° atmo down to between 300/10° and 200/10° in his list of apparent pressures, which are really »+a’ ; so that the deflecting force remains constant down to a pressure between 228/10° and 128/10° in close enough agreement with the 144/10° given above. When the degree of rarefaction is reached at which dissociation is just impossible in the hotter chamber, then the deflecting force will become that of pure O3, and its laws will be those of a single gas as given in “ Thermal Transpiration and Radiometer Motion”; in the region of pressure between that at which dissociation becomes impossible in the hot chamber and that at which it becomes impossible in the cool chamber, there will be a fall of deflecting force from that due to pure O; to the constant value which rules up to the pressure of discontinuity. As to the comparatively small variations of 2aX)/B)D which we found in our study of the log. dec., their smallness would be explained by the supposition that the viscosity of Q3 is very nearly the same as that of Os, for then the limiting con- stant value L of the log. dec. of QO, would also be approxi- mately a correct value for all the different values of L appropriate to all the different mixtures of O; and O,, which must have been experimented on at pressures between 1000/10° and 144/10° atmo. But it must be mentioned that Crookes drew attention to a slight irregularity in the values of the log. dec. of oxygen, for after maintaining a value nearly constant at about °1120 near a pressure of 20 millim., it rose to °1124 at 7°5 millim., after which it fell Change of Oxyyen into Ozone. 209 away in the usual manner; now as this irregularity occurs just at the region of pressure where Bohr’s experiments have shown us that dissociation is beginning, it is confirmatory of the other evidence. In the absence of experimental values of the viscosity of ozone, we can compare the viscosities of O; and O, by means of the kinetic theory, since for forceless spherical molecules of mass m and radius a the viscosity 1s proportional to mv/a? or to m3/a’, so that if we assume that O; is a sphere of double the volume as well as double the mass of O, regarded as a sphere, then the viscosity of Qs; is 2—* or ‘9 that of O,, so that we should be prepared to admit that the viscosities of ozone and oxygen are nearly equal. This being so, we have next to inquire as to the relative values of A, the mean free path, at some standard value of the number of molecules per unit volume of O3 and O, ; for spheres ) varies inversely as a?, and therefore » for O; ought to be about 2% or °63 of that for O,; so that if 2aA,/BoD tor pure O, is 20, it ought to fall to about 13 for pure O3, while we found actually a fall from about 20 to 15 and then a slight rise: therefore, seeing that we are not strictly correct in assuming viscosity, and therefore L, for mixtures of O, and O, to be the same as for O;, we cannot expect any closer agreement between the experimental results and our general theoretical reasoning about the comparative slightness of the perturbation in the log. dec. despite profound change going on in the gas, which in the end converts the oxygen into ozone. We have now to discuss the anomalous expansion of rare oxygen observed by Baly and Ramsay (Phil. Mag. [5] XXXVill.), whose experiments on hydrogen and nitrogen have been discussed in ‘‘ Boyle’s Law at Low Pressures” *, where it was shown that the apparent diminution of the coefficient of expansion of these gases at low pressure is perhaps not real; the increase which they found in the coefficient of expansion of oxygen at low pressures is therefore real, for probably the same cause is acting to produce an apparent | diminution of the coefficient as in the case of the other gases, The following are the reciprocals of the mean coefficients of expansion of oxygen between 12°C. and 132°, as given by Baly and Ramsay at various pressures calculated from the indications of a M‘Leod gauge according to Boyle’s law, and therefore exceeding the true pressure when above ‘7 millim. by ‘11 millim. and when below ‘7 millim. by ‘055 millim. Apparent 7p ......... 5:1 5:3 4:0 2°5 1-4 083 ‘O07 rue: pt. seddcemac tics 5:0 5:2 39 24 13 028 ‘OLS 261 260 262 251 283 244 240 , * Supra, p. 11. 210 Mr. W. Sutherland on the Spontaneous As we have seen, at all the pressures given we have to do at a temperature of 12° with mixtures of O, and O3, which on being raised to 132° will have the whole or part of the ozone dissociated into oxygen, and will therefore give a larger coefficient of expansion than belongs to a pure gas. In tact, if there is complete dissociation of the O3 at the higher temperature, the number of molecules is increased in the proportion of p+’ to p, so that the mean coefficient of expansion is increased to 1/273(1+4'/p) +2!'/120p ; thus with a’ ='055 the reciprocal of the coefficient of expansion becomes 263 at a pressure of 5 millim. and 231 at 1 millim., numbers which are in close agreement with those of experi- ment. At the two lowest pressures we ought to have to do with pure ozone at the lower temperature, and if it is entirely dissociated at the higher temperature the coefficient of expansion will be 3/273 x 2+ 1/240, and its reciprocal 104 in place of about 240 as found by experiment; accordingly it appears that at the lowest pressures the ozone probably is only partially dissociated at 132°C. Thus, although we cannot draw definite quantitative results from these experi- ments on the expansion of oxygen, we have ample qualitative evidence that dissociation accompanies the expansion of what has hitherto been considered to be pure rarefied oxygen, but which is either a mixture of oxygen or ozone, or, at a low enough pressure, pure ozone. In their experiments with oxygen Baly and Ramsay had an extraordinary experience which will be traced to disso- ciation. They had two M‘Leod gauges in connexion with a supply of oxygen whose pressure had been reduced to °75 millim., which is in the region of Bohr’s discontinuity ; on raising the mercury so as to shut off communication between the two gauges, and then compressing each of the equal volumes thus isolated at the same pressure into the fine graduated tubes of the gauges where both pressure and volume could be measured, they found that the mean value of pB in the one gauge was 8°8 times as large as in the other, whereas the two were expected to be equal ; it was only after putting the gauges frequently in communication with one another during 78 hours that the values of pB became equal. The total volume of each gauge was about 90 cub. centim., so that the original value of pB in both gauges was about 67°5, a rough estimate on account of the uncertainty in measuring p near the discontinuous region ; but after com- pression into the volume-tubes the value of pB in the one was 53°1 and in the other 6:04, so that practically the whole of the remarkable disturbance was confined to the one gauge. Change of Oxygen into Ozone. 211 The phenomenon would be explained if we supposed that in the very unstable state of the gas at a pressure near “7 millim., where a mere change of volume suftices to dissociate some of the O; molecules, during the dissociation a number of free ions of O were liberated, and on account of slight want of electrical neutrality in the apparatus only in the one gauge. We have therefore to consider the effect of a number of atoms charged with electricity when mixed with a number of molecules. The atoms repelling one another on account of their electric charges will tend to accumulate near the walls of the vessel, while the molecules will remain evenly distributed through the vessel, for if they did not a diffusion stream would be set up in them until they were uniformly distributed. Thus then we can separate the mixture in imagination into two media determining the distribution of partial pressure amongst the atoms as if the molecules were absent, and then adding the uniform partial pressure due to the molecules. The differential equation for the distribution of pressure amongst atoms in a spherical vessel is easily written down, but I will defer its discussion to a more appro- priate occasion. For the present it will suffice to say that obviously the effect of electrical repulsion will be to force the majority of the atoms out to the surface, where a layer of rapidly altering density and pressure will be formed merging into the more gradually altering body of the medium. Let us consider the exaggerated case where, in the surface-layer, the pressure increases from one side of it to the other by P; then if Q is the total charge of the whole layer of surface 47R’, the repulsion experienced by unit area of the layer is (Q/R?)(Q/47R?), which is to be equal to P. If, then, in Baly and Ramsay’s experiments in one of the gauges at the moment at which they were isolated from one another the value of P, due to free oxygen ions in it, was about 8/9 of the recorded initial pressure of about *75 millim. then the mass of oxygen in this gauge, with the assistance of the ions, could equilibrate the pressure due to nine times as great a mass of oxygen in the other gauge, for we shall see immediately that the mass of the ions is negligible. Sup- posing Baly and Ramsay’s cylinder of 90 cub. centim. to be replaced by an equal sphere, then R is 2°78 centim., and P being 8/9 of °001 atmo is in round numbers 889 dynes per sq. cin., and therefore Q in absolute electrostatic units is 517, Now the electrochemical equivalent of oxygen is ‘00082, that is, there is one absolute electromagnetic unit of electricity or 3x10" electrostatic units in ‘00082 gram of oxygen ions, and therefore the mass of the ions containing our charge of 212 Mr. W. Sutherland on the Spontaneous 817 is 2°2/10" gram ; now the total mass of oxygen filling the other gauge at about -001 atmo is about 1:3/10* gram. Thus a conversion of less than a millionth of their mass of gas into ions collected into one of the gauges would explain the strange phenomenon encountered by Baly and Ramsay, if it is allowed that between the isolation of the gauges from one another and the compression into the fine tubes the charge Q got discharged, so that in both fine tubes after compression there was only pure oxygen, O,. We have also to account for the disappearance of the equal and opposite charge to Q. But it is not worth while occupying space to speculate on these minor matters, as the phenomenon is so important as to entitle it to a thorough experimental investi- gation. There are one or two consequences of the spontaneous formation and decomposition of ozone at low pressures which deserve to be touched on briefly. The first is, that as there is no theoretical reason why the presence of nitrogen should suppress the actions which we have been discussing, there ought to be slight departure from Boyle’s law in rarefied air ; in fact, let p, and p, be the partial pressures of nitrogen and oxygen in the air, then p,b=k,3; but p,.B=k,—aB, so that (pat po)B=pB=k, +k,—aB, and thus for air the equation is of the same form as for oxygen, but the departure from Boyle’s law will make itself conspicuous in a different region of pressure: Bohr found the departure in oxygen from a pressure of 15 millim. down to ‘7 millim. where the first discontinuity occurred, and so for air it might be looked for from about 75 millim. down to 3°5 millim. where a discontinuity should be expected, but of a different nature from that with oxygen, in fact p, becomes constant for a short range of volume, and so (p+p,) B=pB=k,+p,B till the region of volume is reached for which 2 in oxygen has the smaller value a', and then pB=k,+k,—«’B, which lasts until p,=2e’, at which point all the oxygen will have been changed into ozone, and therefore p, will be 4p, x 3/2, seeing that in the atmosphere at 760 millim. p,=4p, ; thus the pressure at which Boyle’s law will become re-established for the air, now a mixture of nitrogen and ozone, will be 132’ or about *715 millim. of mercury. The only accessible data suitable for comparison with these Change of Oxygen into Ozone. 213 conclusions about air are those of Amagat (Ann. de Chim. et de Phys. {5] xxviii.) who between 12 millim. and 1 millim. of mercury finds departures from Boyle’s law in the same direction as those indicated, but not of the amount that our theory requires, Amagat not considering the departures to be outside of the limits of experimental error, but it is hardly worth while occupying space with reproducing these data, since the Russian investigators Mendeléeff, Kirpitscheff, and Hemilian have found the departure for air to be always in the direction just indicated but of variable amount. One reason for this variability is shown in a pronounced form in the remarkable experience which Baly and Ramsay had with air in the capillary tube of one of their M‘Leod gauges, in which, while the pressure varied from 4°1 millim. to 8-0 the product pB fell from 100 to 9°4, a result to be explained, like the corresponding one for oxygen, by the supposition that in the unstable transition of part of the O, into O; some ions of O got liberated whose electrical repulsion produced about 91 per cent. of the initial pressure of 4°1 millim., the loss of the charge during the subsequent compression causing the part of the pressure due to the electricity to diminish, and pB, therefore, to diminish likewise. In view of the possibility of a perturbing cause of this magnitude it is obvious that special precautions will have to be taken in studying the compressibility of rarefied air to get rid of all electrical charge in the gas or the apparatus, and we can understand the baffling nature of the variations encountered by the Russian experimenters in their devoted work at this difficult experimental research. According to our reasoning the amount of ozone in the air at the surface of the earth ought to be «/760 or ‘11/760 per unit volume of air, or about one volume in 7000 if the air were protected from all chemical actions. The estimates of the actual amount of ozone in the air near the earth’s surface are very uncertain, but seem to indicate about one volume in a million; thus we are led to believe that oxi- dation must be responsible for the destruction of the greater part of the ozone that might theoretically be expected in the air near the earth. But as we rise in the atmosphere to a place where the pressure is p, the amount of ozone per unit volume ought to be a/p till a region of discontinuity is reached, after which the amount is @’/» till a point is reached where the pressure is about 715 millim. of mercury, at which and above which the whole of the oxygen exists as ozone, forming about one-seventh of the volume of the air there. These deductions have some hygienic importance 214 H. Willy Wien on the Division of Energy in and explain the reason for the current belief that the higher regions of the atmosphere and winds which come from them are richer in ozone than the surface air: they also show that there must be enough ozone in the whole atmosphere to have an important bearing on the blue colour of the sky. Hartley drew attention to this matter (Journ. Chem. Soc. xxxix. 1881), but as recent experiments have shown that oxygen in sufficient quantity shows a blue colour by transmitted light, the claims of ozone to a serious share in the blueness of the sky have been rather neglected ; but if it is remembered that the blueness of ozone is enormously stronger than that of oxygen under the same conditions, it becomes apparent that the quantity of ozone which has been theoretically shown to have a probable existence in the atmosphere must exercise a considerable influence on the colour of the sky and the colour of distant objects. From what we have seen we have also to contemplate the possibility of the existence of free ions of oxygen in the outer regions of the atmosphere, but a discussion of the effects of such must be reserved for a future paper. Melbourne, Aug. 1896. XXX. On the Division of Energy in the Emisston-Spectrum of a Black Body. By Witty WiEN*. LTHOUGH the influence of temperature on the radia- A tion of a black body and the division of this radiation into its component wave-lengths can be deduced from the electromagnetic theory of light by a purely thermodynamic method, the application of the same process to the division of the energy itself has not up to the present been successful. The cause of this lies in the fact that the dependence of intensity on wave-length must be completely determinable from the properties of the radiation, because the latter only depends on the temperature, and not on the special properties of single bodies. The radiation of a black body corresponds to the condition of thermal equilibrium, and consequently to the maximum of entropy. If, for example, a process were known by which a change of wave-length could be brought about without any expenditure of work, and without absorption in the sense of an increase of entropy, then the division of energy in the * Translation furnished by Mr. J. Burke from Wiedemann’s Annalen, vol. lyiii. p. 662 (1896). Communicated by Prof. G. F. FitzGerald, F.R.S. the E’'mission-Spectrum of a Black Body. 215 spectrum of a black body could be completely determined from the law of the maximum of entropy. As I have shown in an earlier paper, the entropy of radiation of a known intensity and colour can be determined, but there is no obvious physical process by which an alteration in colour such as that desired can be observed to be taking place. A determination of the distribution of energy is therefore im- possible without hypotheses. An attempt has been made by EH. von Lommel* and W. Michelson + to found a complete law of radiation on certain premises. For this purpose the latter makes the following stipulations :— (1) Maxwell’s Law of the division of velocities among a great number of molecules holds also for solids. (2) The period of oscillation 7, which is excited by a mole- cule, is connected with its velocity of propagation v by the equation = 4, v where p isa constant. (This assumption is based on a defi- nite conception with regard to the excitation of the radiation.) (3) The intensity of the radiation sent out from a molecule is proportional to the number of molecules having the same time of oscillation, is further an undetermined function of the temperature and a likewise unknown function of the kinetic energy, which by a further hypothesis is restricted to a power of v’. The law which Michelson obtains from these assumptions gives for the wave-length 2,, of the maximum of energy _ const. where @ denotes the absolute temperature. As for the rest, this law leaves the total emission as a function of the tempe- rature undetermined. I have now endeavoured to carry out the idea of Michel- son, of making use of Maxwell’s law of the division of velocities as a basis for the law of radiation, and at the same time to lessen the number of the hypotheses which, on account of our total ignorance of the cause of the radiation, are par- ticularly uncertain, by utilization of the results obtained by Boltzmann and myself by pure thermodynamic treatment. The remaining hypotheses, however, still possess some * Wied. Ann. iii. p. 251 (1877) T Journal de Physique [2] vi. (1887). 216 H. Willy Wien on the Division of Energy in uncertainty in their theoretical groundwork, but have the advantage that the deductions from them can be directly com- pared over a very wide range with the results of experience. Their confirmation or contradiction by experiment will there- fore decide the question of the correctness or otherwise of the hypotheses, and thus far be useful as a further development of the molecular theory. The law that in an exhausted vessel the radiation is the same as that from a black body at the same temperature as the walls of the vessel, holds also if the radiating body be a gas which is shut off from the vacuous space by transparent, and from the exterior by reflecting walls. But this gas must possess a finite absorptive power for all wave-lengths. There remains, however, no doubt that there are gases, such as carbonic acid and water-vapour, which, by mere elevation of temperature, emit heat rays*. Strongly superheated vapours may be regarded as gases, and by suit- able mixing of different substances, it is possible to conceive of a mixture of gases which possesses a finite absorptive power for all wave-lengths. In this case one must not, how- ever, consider that radiation which gases send out under the influence of electrical or chemical processes. If one radiating body be a gas, then Maxwell’s law of the division of velocities will hold if we take as our basis the kinetic theory of gases. The absolute temperature will be proportional to the mean kinetic energy of the gaseous molecule. This assumption has been rendered highly probable by the labours of Clausius Tt and Boltzmann {, and is still further supported by the researches of Helmholtz § on mono- cyclic systems, according to which researches both the kinetic energy and the absolute temperature have the property of being the integrating denominator of the differential of the added energy. To avoid the unecessary prolixity which would result from a consideration of the different constituents of a mixture of gases, let us imagine a mixture of such a kind that the homogeneous radiation under consideration is sent out by one only of the gases forming the mixture. The number of molecules whose velocity lies between v and v +dv is proportional to the quantity v2 vee o dv, * Paschen, Wied. Avn. 1. p. 409 (1893). +t Pogg. Ann. cxlii. p. 483 (1871). t Wien. Ber. [2] liii. p. 195 (1866). § Gesammelte Abhandlungen, iii. p. 119. the Emission-Spectrum of a Black Body. 217 where a denotes a constant, which can be deduced from the mean velocity * 6 by means of the equation =2__ 39 Uv = 7m. The absolute temperature is therefore proportional to a. But the vibrations sent out by a molecule whose velocity is v are completely unknown in their dependence on the condition of the molecule. A now-a-days generally accepted view is that the electric charges of the molecules can excite electro- magnetic waves. We make the hypothesis, that each molecule sends out vibrations of a wave-length which only depends on the velocity of the molecule moved and whose intensity is a function of this velocity. j It is possible to obtain this deduction by several different special hypotheses with regard to the process of radiation ; as, however, such premises at this preliminary stage are com- pletely arbitrary, it appeared to me to be the safest method to make the necessary hypothesis as simple and general as possible. As the wave-length » of the radiation sent out by any molecule is a function of v, v is also a function of X. The intensity ¢, of the radiation whose wave-length lies between A and (A+ dd) is therefore proportional (1) To the number of molecules which send out radiations of this period ; (2) To a function of the velocity v, therefore also to a function of 2. Consequently BAY) P= (Aje @ where F and f denote two unknown functions, and @ denotes the absolute temperature. Now the change of radiation with temperature is composed, according to the theory given by Boltzmann f and myself t, of an increase of total energy in proportion to the fourth power of the absolute temperature and of a change of wave- length of the whole energy comprised between » and (\+dn) in such a direction that the wave-length belonging to it alters in inverse ratio to the absolute temperature. If we imagine the energy at any temperature plotted as a function of the wave-length, then the curve obtained would remain * » is the square root of mean square of velocity.—Transl. + Wied. Ann. xxii. p. 291 (1884). t Wien, Ber. d. Berlin. Akad. 9th Feb., 1893. Phil, Mag. 8. 5. Vol. 43. No. 262. March 1857. S 218 H. Willy Wien on the Division of Energy in unaltered at a different temperature, if the scale of the draw- ing were so changed that the ordinates were decreased in the relation of 1/64 and the abscissee increased as 9. ‘The latter is with our value of ¢, only possible if X and @ occur in ex- ponents only as the product XA. If c denote a constant, then ‘haba DED ERE: | The increase of total energy determines the value of F(A). Indeed the relation must hold | F(A)e ~xdr=const. 64. 0 F(A) can be found by the method of undetermined coefficients. We imagine F(A) expanded into a series and make \=¢/y0, then fa) G2 2 @” n F(A) =H a) =a+ay1— + a = Wee oie Z ce eee C ne ips FO? pee S et ee, a Integration of this gives Ey es ~ eC 2 eC a dy <3 Q@x-1( *” Bae {Poo aAdA= af, F( De I= 2nan aa é Vy 2dy. J m—1 Therefore const. = Sate T (n—1). All the coefficients are therefore nothing except one of them, the coefticient of 6°—'= 6 ; therefore n=), Consequently F (A) = = Accordingly the equation for ¢, is p= ne eo x0. From this follows :— WO ME has v6 FR ae as OS (5 ) &d 2 Coins (3 12¢ c” ) 7? ae the Emission-Spectrum of a Black Body. 219 for ss ae db = PERG SGN ; or. i oCe~* . Cen aie ad . ee ‘ Az 18 negative, therefore the value corresponds to a maximum. Let this value be called A». The corresponding value of ¢ is C n= ae cue As both @ and dd/dd vanish for X=, the curve is an asymptote to the X-axis. ~ Further, d?¢/da’=0 for the roots of the equation 30A26? —12cr8 + c?=0 ; i, (1 ae ye. 6 For these two points the curve has points of inflexion. If we put A=A,, (1+), then e 5 Og Se P= A546) “BU +e) therefore for therefore € log - = —5( log ee rez) =~ 5Ge 344 If we put —e for e, then loge =—5(Je+$et+}e...) In this case the absolute total of the series is greater and therefore $/¢, less than when e¢ is positive. So far as «<1, the ordinates at an equal distance from the maximum are less on the side of small wave-lengths. In an earlier work* I showed that the energy curves of black bodies at different temperatures cannot cut one another. From this it may. be deduced that the curve must fall away slower toward the side of the long waves than the curve const. rn? But this is in reality the case with our curve: d¢,/dXd is in absolute magnitude always less than 5C/A*, and only reaches * Wied. Ann. lii. p. 159 (1894). S 2 220 Dr. T. Muir on Lagrange’ s the maximum value for d=o. For infinitely increasing temperature , would equal C/A’, and the maximum of energy would approach infinitely near to the wave-length zero. W hile I had deduced the formula for ¢, from the theore- tical considerations just brought forward, Prof. Paschen found independently that the formula ON = da e O, where @ is a constant, was the one which reproduced best the results of his observations, and was kind enough to communi- cate this to me and to allow me to publish his formula here. Prof. Paschen intends to determine the value of the constant a from a complete calculation and comparison of his experi- ments. If ais not equal to 5, the total emission would not follow Stefan’s law. Charlottenburgh, June 1896. XXXI. On Lagrange’s Determinantal Equation. By Tuomas Muir, LL.D.* 16 oe proofst have been given of the reality of the roots of the equation a—wx b Cc b fr nn rn = y) and more than one extensiont of the theorem has been made. Apparently, however, no departure from axi-symmetry of the determinant has ever been contemplated until quite recently. This new and important step is due to Professor Tait, who in a paper read before the Royal Society of Edinburgh in May is led to the conclusion that the cubic equation A Cc =P pa iD 'p mis Bio SISBRIo * Communicated by the Author. + For three of them see Salmon’s ‘Modern Higher Algebra,’ 4th edit. — pp. 28, 48-56. } See Sylvester, Crelle’s Journal, \xxxviii. pp. 6-9. Routh, ‘ Dynamics of a System of Rigid Bodies,’ part ii. 4th edit. pp. 86-88, 41. Muir, ‘Messenger of Math.’ xiv. pp. 141-143. 221 has all its roots real, and thereupon adds that “a somewhat similar process shows that the roots of the equation Determinantal Equation. a—e ob c d Ce fi —0 g h ~—w are always all real, provided the single condition cdh= bf be satisfied.” On examination of this latter statement in the light of former researches of my own, I found that it was scarcely correct to say that only one condition was necessary, the further requirements being that b and d be of like sign, ¢ and g of like sign, and therefore also f and h of like sign,—in other words, that the determinant should, so far as sign is concerned, be axi-symnetric; and from this I passed to the consideration of similar equations of higher degree, with the following results :-— 2. Taking the equation of the nth degree, but for short- ness’ sake writing it only of the fifth, viz. a—-k& Ay a3 A As, OG Le Wa) ee Cy Co Com Cy Go =O dy de din. de ey ey é3 6, €5—x and multiplying the wows Ly Or, Wa) Os, Wa, Ws respectively, and the columns by o[', a7', 71, w7!, oF} respectively, we have the equation in the form Qj—X& = Wwy'dg @0;'d3 Wwl'd, w0>'a; wo 1b; bo —2 ww 5' bs M071 D4 Wooo! De @307'C, W307" Co C3—-& @:07'C, @30>165 @,@7'd, wwy'dy ww; 'd3 dy—« ord; OsO,"e, @s@,1ey Ws '3 Ws ey es—e The determinant here is in substance exactly the same as before ; but we have now five disposable quantities, @,, @s, @3, 4, @;, and the question is whether these can be so deter- mined as to make the array of elements axi-symmetric. The conditions for this clearly are —1 — --1 —l, — —! @, 07 'A2=@20 71'bj, Wo; !as=@3;07'C), ... 229 Dr. T. Muir on Lagrange’s or, better, @dg=07b;, OPd3;=03¢, 7 ay= wed), Ofds= w5"ey @2b3=3"Co, O° bg= Os do, @3°b; = 5 ee 3 @3C4=07d3, O3 C= 573 5 w2ds5= 54 ? from which it is evident that, whatever the full and final answer to our question may be, it will be necessary that a, have the same sign as jy, a3 ” ” ” C1; a) —in other words, that conjugate elements of the original deter- minant be alike in sign. As, however, we have got to ascertain whether a set of non- zero values can be found for @, @, @3, @;,@; which will satisfy all the equations, it is desirable to arrange them for- mally as a set of (ten) homogeneous equations in these five unknowns. The result of this is x0)" — byw,” =0, a) 30)" —¢,o; rome ==) | ayo, —d,w," == (), ds," SO =), | b3@.” —Co@3” = (0); | byw,” —d,o, = r bso? — €20; =0, C4O3” — dso," ==) | C53" —e,0;7 =0, | d;@,’. —e,0 =0(. J Now the equations being homogeneous, only the ratios of the five unknowns have to be found,—that is to say, only four magnitudes are wanted, and for this the first four equations are evidently sufficient. The existence of the remaining equa- tions implies that conditions of consistency have to be fulfilled; and these conditions are at least six in number, for each of the remaining equations determines a ratio already deter- mined, and does so in terms of coefficients not previously met with, Thus equation (6) determines @,/w,’, which has already been got from equations (1) and (2): hence we have the condition. ait hte 1 43 ety Determinantal Equation. 993 ag —b, Gis) Oks —¢, =a), bz; = —y a. Ag)3 Cy = A301 C9, the others being Ayb yd, =a4bydp, an) b; ey = a5), C25 A3C4Qy = a,0,d3 305€, = A5C) &3, ade; = As 164 Further, no other conditions are necessary : for, these being complied with, the values of the ratios obtained from the first four equations will satisfy the remaining six. 3. Any conditions of consistency, therefore, which may be obtained from the last six equations only must be depen- dent on the conditions already obtained. For example, from (5), (6), (8) we have the condition b3Cqlg = DyCodls 5 but this is merely a result derivable by multiplication and division from three of the previous six conditions, viz. the three A641 = Agl A 35 Abscy = A3b4Co, d4bid, => dyb,d, S The number of such dependent conditions is four, viz. from (5), (6), (8) b3C4dy = bacods, from (9), (7), (9) D305 €2 = D5 C963, trom (6), (7). (10) sbidse> =U5dse,, and from (8), (9), (10) eadse3 =csd3¢4. 4. Again, the ten conditions regarding the signs of the elements, viz. agi = 4+, a3¢y= +, eeeoe are not all independent. Only the first four are necessary when taken along with the six equations of § 2. For the conditions Agb3C, =A3b1 C2, dgbj= +, agqy=+ give b3c,=+4, dgb,dy=aybydg, aob;= +, ad=+ give yd,=+4, Agbsé) =Asb,@2, deb, = +, Asq=+ give bsag=+4+, bzegda =bycods, b3ceo=+, bad =+ give qd3;=+4, bsC5 02 =O5Cze3, bsco—=+, bse2=+ give cse=+, bid sé, =bsdoes, bidg=+, bseg=+ give dyey=+. 224 Dr. T. Muir on Lagrange’s 5. The state of matters thus is that the quintic equation Qa ag b; bo—x Sietsve —) will have all its roots real if ten conditions be complied with: V1Z. siz as to magnitude, and four as to sign. Azb3 Cy = A301 Coy ab=+, dybyd = agb, ds, a3¢;=+, Ag); €) = Azb ea, asdj=+, 3 Cad = a4Cd3, ase) = 15 3 C5 €1 = A5Cy C35 gd €) = Azd 4, and that the six conditions as to magnitude imply four others like themselves, viz. — b3 Cda= ba Cod, bs C52 = Ds C23, bids €, = bsdyeq, cds €3 = C53 C4 5 and the said six together with the four conditions as to sign imply six others similar to the latter, viz. bse;= +, bydg= +, bség=+, qdzs=+, C503 = +, de, =+. 6. The law of formation of the magnitude conditions is not readily apparent, but a change to the double-index notation for the elements of the determinant suffices to clear up the difficulty. Writing | a.c3d,e; | in the form 14 12 A ire ral 22 Zoe te Determinantal Equation. 225 the conditions in question are Peace l= 21.32. 13, 23.31 .AQ=32 .43. 24, 12.24.41=21.42.14, 23.35 .52=332 . 53 . 25, fee 2 i 52), 15; 24.45 .52=42.54.25, Lig Ss ee Sul wu SSS aa. SO. ion ocoL ol 53). 15, Pipe or A te 54. 15; Hach condition is thus seen to have its origin in a triad of the five indices 1, 2, 3,4,5. For example, from the triad 123 we form the elements 12, 23, 31, and from these the conju- gate elements 21, 32, 13, and so arrive at the condition 12) 25 Sa 3.135, which, in order that the distinctive character of its formation may be more apparent, would be still better written BZ oe 2a od i ZA dere 2.3) In this way the number of conditions is seen to be Cs,3, the necessary conditions being Cz». in number, and the depen- dent conditions C,3. 7. The general theorem may consequently be enunciated as follows :— The nthic equation 4 12 13 21 22—x DS as eae i 31 32 Soi ee |e will have all its roots real, tf in the case of every pair pm, v of the indices 2, 3, 4, ..., n we have by ny 73 78 | pee ee ee aye and ie pela no these conditions implying that in the case of every triad m, v, p of the indices 1, 2, 3,..., n we shall have and 226 Dr. P. Zeeman on the Influence of Magnetism 8. Finally, it should be carefully noted that the essence of the whole matter lies in the fact that when the specified con- ditions hold, the given determinant is transformable into an axi-symmetric determinant in which «x is involved in the same way as before. Mowbray Hall, Capetown, S.A., November 30,1896. XXXII. -On-the Influence of Magnetism on the Nature of the Light emitted by a Substance. By Dr. P. ZeEMAN*. iL, Se years ago, in the course of my measurements concerning the Kerr phenomenon, it occurred to me whether the light of a flame if submitted to the action of mag- netism would perhaps undergo any change. The train of reasoning by which I attempted to illustrate to myself the possibility of this is of minor importance at presenty, at any rate I was induced thereby to try the experiment. With an extemporized apparatus the spectrum of a flame, coloured with sodium, placed between the poles of a Ruhmkorff elec- tromagnet, was looked at. The result was negative. Probably I should not have tried this experiment again so soon had not my attention been drawn some two years ago to the following quotation from Maxwell’s sketch of Faraday’s life. Here (Maxwell, ‘ Collected Works,’ il. p. 790) we read :—“ Before we describe this result we may mention that in 1862 he made the relation between magnetism and light the subject of his very last experimental work. He endeavoured, but in vain, to detect any change in the lines of the spectrum of a flame when the flame was acted on by a powerful magnet.” If a Faradayt thought of the possibility of the above-mentioned relation, perhaps it might be yet worth while to try the experi- ment again with the excellent auxiliaries of spectroscopy of the present time, as 1 am not aware that it has been done by others§. I will take the liberty of stating briefly to the readers of the Philosophical Magazine the results I have obtained up till now. 2. The electromagnet used was one made by Ruhmkorff and of medium size. The magnetizing current furnished by accumulators was in most of the cases 27 amperes, and could * Communicated by Prof. Oliver Lodge, F.R.S., with the remark that he had verified the author’s results so far as related to emission spectra and their polarization. | Fi: + Cf. § 15 and § 16. nh t See Appendix for Faraday’s own description of the experiment. § See Appendix. on the Nature of the Light emitted by a Substance. 227 be raised to 35 amperes. The light used was analysed by a Rowland grating, with a radius of 10 ft., and with 14,938 lines per inch. The first spectrum was used, and observed witha micrometer eyepiece with a vertical cross-wire. An accurately adjustable slit is placed near the source of light under the influence of magnetism. 3. Between the paraboloidal poles of an electromagnet, the middle part of the flame from a Bunsen burner was placed. A piece of asbestos impregnated with common salt was put in the flame in sth a manner that the two D-lines were seen as narrow and sharply defined lines on the dark ground. The distance between the poles was about 7 mm. If the current was put on, the two D-lines were distinctly widened. If the current was cut off they returned to their original position. The appearing and disappearing of the widening was simultaneous with the putting on and off of the current. The experiinent could be repeated an indefinite number of times. ue 3 4. The flame of the Bunsen was next interchanged with a flame of coal-gas fed with oxygen. In the same manner as in § 3, asbestos soaked with common salt was introduced into the flame. It ascended vertically between the poles. If the current was put on again the D-lines were widened, hecoming perhaps three or four times their former width. 5. With the red lines of lithium, used as carbonate, wholly analogous phenomena were observed. 6. Possibly the observed phenomenon (§§ 3, 4, 5) will be regarded as nothing of any consequence. One may reason in this manner: widening of the lines of the spectrum of an incandescent vapour is caused by increasing the density of the radiating substance and by increasing the temperature. Now, under the influence of the magnet, the outline of the flame is undoubtedly changed (as is easily seen) hence the temperature and possibly also the density of the vapour is changed. Hence one might be inclined to account in this manner for the phenomenon. 7. Another experiment is not so easily explained. A tube of porcelain, glazed inside and outside, is placed horizontally between the poles with its axis perpendicular to the line joining the poles. The inner diameter of the tube is 18 mm., the outer one 22mm. The length of the tube is 10 cm. Caps are screwed on at each end of the tube +; these caps are closed by plates of parallel glass at one end, and are sur- rounded by little water-jackets. In this manner, by means * Cf., however, also Pringsheim (Wied. Ann. xlv. p. 457, 1892). + Pringsheim uses similar tubes in his investigation concerning the adiation of gases, J. ¢. p. 480. 228 - Dr. P. Zeeman on the Influence of Magnetism of a current of water, the copper caps and the glass plates may be kept sufficiently cool while the porcelain tube is rendered incandescent. In the neighbourhood of the glass plates, side-tubes provided with taps are fastened to the copper caps. Witha large Bunsen burner the tube could be made incandescent over a length of 8cm. The light of an electric lamp, placed sideways at about two metres from the electromagnet, in order to avoid disturbing action on the are, was made to pass through the tube by means of a metallic mirror. The spectrum of the are was formed by means of the grating. With the eyepiece the D-lines are focussed. This may be done very accurately, as in the centre of the bright D-lines the narrow reversed lines are often seen. Now a piece of sodium was introduced into. the tube. The Bunsen flame is ignited and the temperature begins to rise. A coloured vapour soon begins to fill the tube, being at first of a violet, then of a blue and green colour, and at last quite invisible to the naked eye. The absorption soon diminishes as the temperature is increased. The absorption is especially great in the neighbourhood of the D-lines. At last the two dark D-lines are visible. At this moment the poles of the electromagnet are pushed close to the tube, their distance now being about 24 mm. The absorption-lines now are rather sharp over the greater part of their length. At the top they are thicker, where the spectrum of the lower, denser vapours was observed. Immediately after the closing of the current the lines widen and are seemingly blacker; if the current is cut off they immediately recover their initial sharpness. The experiment could be repeated several times, till all the sodium had dis- appeared. The disappearance of the sodium is chiefly to be attributed to the chemical action between it and the glazing ofthe tube. For further experiments therefore unglazed tubes were used. 8. One may perhaps try to account for the last experiment (§ 7) in this direction:—It is true that the tube used was not of the same temperature at the top and at the bottom ; further, it appears from the shape of the D-lines (§ 7) that the density of the vapour of sodium is different at different heights. Hence certainly convection-currents caused by difference of temperature between the top and bottom were present. Under certain plausible suppositions one may cal- culate that, by the putting on of the electromagnet, differences of pressure are originated in the tube of the same order of magnitude as those caused by the difference of temperature. Hence the magnetization will push e.g. the denser layer at_ the bottom in the direction of the axis of the tube. The lines on the Nature of the Light emitted by a Substance. 229 become widened. For their width at a given height is chiefly determined by the number of incandescent particles at that height in the direction of the axis of the tube. Although this explanation still leaves some difficulties, certainly some- thing may be said for it. 7 9. The explanation of the widening of the lines attempted in § 8 is no longer applicable to the following variation of the experiment, in which an unglazed tube is used. The inner diameter of the tube, about 1 mm. thick, was 10 mm. The poles of the electromagnet could be moved till the distance was 14 mm. ‘The tube now was heated by means of the blowpipe instead of with the Bunsen burner, and became in the middle part white hot. The blowpipe and the smaller diameter of the tube make it easier to bring the upper and lower parts to the same temperature. This is now higher than before (§ 7), and the sodium lines remain visible conti- nuously*. One now can wait till the density of the sodium vapour is the same at various heights. By rotating the tube continuously round its axis I have still further promoted this. The absorption-lines now are equally broad from the top to the bottom. When the electromagnet was put on, the absorption- lines immediately widened along their whole length. Now the explanation in the manner of § 8 fails. 10. I should like to have studied the influence of magnetism on the spectrum of a solid. Oxide of erbium has, as was found by Bunsen or Bahr, the remarkable property of giving by incandescence a spectrum with bright lines. With the dispersion used, however, the edges of these lines were too indistinct to serve my purpose. 11. The different experiments from §§ 3 to 9 make it more and more probable that the absorption- and hence also the emission lines of an incandescent vapour are widened by the action of magnetism. Now if this is really the case, then by the action of magnetism on the free vibrations of the atoms, which are the cause of the line-spectrum, other vibrations of changed period must be superposed. That it is really inevitable to admit this specific action of magnetism is proved, I think, by the rest of the present paper. 12. From the representation I had formed to myself of the nature of the forces acting in the magnetic field on the atoms, it seemed to me to follow that with a band-spectrum and with external magnetic forces the phenomenon I had found with a line-spectrum would not occur. It is, however, very probable that the difference between a band- and a line-spectrum is not of a quantitative but of a * Pringsheim, Z. ¢. p. 456, 230 - Dr. P. Zeeman on the Influence of Magnetism qualitative kind*. In the case of a band-spectrum the mole- cules are complicated, in the case of a line-spectrum the widely separated molecules contain but a few atoms. Further mvestigation has shown that the representation I had formed of the cause of the widening in the case of a line-spectrum im the main was really true. 13. A glass tube, closed at both ends by glass plates with parallel faces and containing a piece of iodine, was placed between the poles of the Ruhmkorff electromagnet in the same manner as the tube of porcelain in § 7. A small flame under the tube vaporized the iodine, the violet vapour filling the tube. By means of electric light the absorption-spectrum could be examined. As the temperature is low this is the band- spectrum. With the high dispersion used, there are seen in the bands a very great number of fine dark lines. If the current round the magnet is closed, no change in the dark lines is observed, which is contrary to the result of the expe- riments with sodium vapour. The absence of the phenomenon in this case supports the explanation, that even in the first experiment, with sodium vapour (§ 7), the convection-currents had no influence. For in the case now considered, the convection-currents origi- nated by magnetism, which I believed to be possible in that case, apparently are insufficient to cause a change of the spectrum ; yet, though I could not see it in the appearance of the absorption-lines (cf. § 7), the band-spectrum is, like the line-spectrum, very sensible to changes of density and of temperature. 14. Although the means at my disposal did not enable me to execute more than a preliminary approximate measurement, I yet thought it of importance to determine approximately the value of the magnetic change of the period. The widening of the sodium lines to both sides amounted to about 41, of the distance between the said lines, the inten- sity of the magnetic field being about 10* C.G.S. units. Hence follows a positive and negative magnetic change of naw of the period. 15. The train of reasoning mentioned in (1), by which I was induced to search after an influence of magnetism, was at first the following:—If the hypothesis is true that in a magnetic field a rotatory motion of the ether is going on, the axis of rotation being in the direction of the magnetic forces (Kelvin and Maxwell), and if the radiation of light may be imagined as caused by the motion of the atoms, relative to * Kayser in Winkelmann’s Handbuch, ii. 1, p. 421, on the Nature of the Light emitted by a Substance. 281 the centre of mass. of the molecule, revolving in all kinds of orbits, suppose for simplicity circles; then the period, or, what comes to the same, the time of describing the circumference of these circles, will be determined by the forces acting be- tween the atoms, and then deviations of the period to both sides will occur through the influence of the perturbing forces between eether andatoms. The sign of the deviation of course will be determined by the direction of motion, as seen from along the lines of force. The deviation will be the greater the nearer the plane of the circle approximates to a position per- pendicular to the lines of force. 16. Somewhat later I elucidated the subject by representing to myself the influence exercised on the period of a vibrating system if this is linked together with another in rapid rotatory motion. Lord Kelvin (now 40 years ago*) gave the solution of the following problem :—Let the two ends of a cord of any length be attached to two points at the ends of a horizontal arm made to rotate round a vertical axis through its middle point at a constant angular velocity, and let a second cord bearing a material point be attached to the middle of the first cord. .The motion now is investigated in the case when the point is infinitely little disturbed from its position of equili- brium. With great angular velocity the solution becomes rather simple. Circular vibrations of the point in contrary directions have slightly different periods. If for the double pendulum we substitute a luminiferous atom, and for the rotating arm the rotational motion about the magnetic lines of force, the relation of the mechanical problem to our case will be clear. It need not be proved that the above-mentioned considera- tions are at most of any value as indications of somewhat analogous cases. I communicate them, however, because they were the first motive of my experiments. 17. A’ real ‘explanation of the magnetic change of the period seemed to me to follow from Prof. Lorentz’s theory ft. In this theory it is assumed that in all bodies small elec- trically charged particles with a definite mass are present, that all electric phenomena are dependent upon the configura- tion and motion of these “ions,” and that light-vibrations are vibrations of these ions. Then the charge, configuration, and motion of the ions completely determine the state of the gether. The said ion, moving in a magnetic field, experiences mechanical forces of the kind above mentioned, and these must * Proc. Roy. Soc. 1856. + Lorentz, La Théorie électromagnétique de Maxwell. Leyde, 1892 ; and Versuch einer Theorie der electrischen und optischen Erschein ungen Rd hewegten Korpern, Leiden, 1895. 232 Dr. P. Zeeman on the Influence of Magnetism explain the variation of the period. Prof. Lorentz, to whom I communicated these considerations, at once kindly informed me of the manner in which, according to his theory, the motion of an ion in a magnetic field is to be calculated, and pointed out to me that, if the explanation following from his theory be true, the edges of the lines of the spectrum ought to be circularly polarized. The amount of widening might then be used to determine the ratio between charge and mass, to be attributed in this theory to a particle giving out the vibrations of light. The above-mentioned extremely remarkable conclusion of Prof. Lorentz relating to the state of polarization in the magnetically widened lines I have found to be fully confirmed by experiment (§ 20). 18. We shall now proceed to establish the equations of motion of a vibrating ion, when it is moving in the plane of (a, y) in auniform magnetic field in which the magnetic force is everywhere parallel to the axis of z and equal to H. The axes are chosen so that if wis drawn to the east, y to the north, z is upwards. Let ebe the charge (in electromagnetic measure) of the positively charged ion, m its mass. The equations of relative motion then are :— 2 Le ee Ee dt? at a d°y ’ ax ( ) The first term of the second member expresses the elastic force drawing back the ion to its position of equilibrium ; the second term gives the mechanical force due to the magnetic field. They are satisfied by naae® e e e e i] e 2 y=Be'S a mv a=—k?a+eHsB 5 2h, bea pide eee ms’ B= —h?B—eHsa where m, k, e are to be regarded as known quantities. For us the period T is particularly interesting. IY H=0, it follows from (3) that s=2 —— Vm * These equations are like those of the Foucault pendulum, and of course lead to similar results. provided that 2a — on the Nature of the Light emitted by a Substance. 233 i i, 4) If H is not 0, it follows from (3) approximately that ele ee eH ) oak val 2k m) Putting T’ for the period in this case, we have , 2rvm ) Ta—7"(1+ Sega Hence the ratio of the change of period to the original period becomes eH és. aed 2kyjm mm" An’ (6) A particular solution of (1) is that representing the motion of the ions in circles. If revolving in the positive direction (viz., in the direction of the hands of a watch for an observer standing at the side towards which the lines of force are running) the period is somewhat less than if revolving in the negative direction. The period in the first case is determined by the value of (5) with the minus sign, in the second with the plus. The general solution of (1) shows that the ions describe, besides circles, also slowly rotating elliptical orbits. In the general case, the original motion of the ion having an arbitrary pesition in space, it is perfectly clear that the projection of the motion in the plane of (z, y) has the same character. The motion resolved in the direction of the axis of z is a simple harmonic motion, independent of and not disturbing the one in the plane of (7,7), and hence one not influenced by the magnetic forces. Of course, the consideration of the motion of an ion now given is only to be regarded as the very first sketch of the theory of luminiferous motions. 19. Imagine an observer looking at a flame placed in a magnetic field in a direction such that the lines of force run towards or from him. Let us suppose that the said observer could see the very ions of § 18 as they are revolving; then the following will be remarked :—There are some ions moving in circles and hence emitting circularly polarized light; if the motion is round in the positive direction the period will, for instance, be longer than with no magnetic field; if in the negative direction, shorter. There will also be ions seemingly stationary and really moving parallel to the lines of force with unaltered Phil. Mag. 8. 5. Vol. 43. No. 262. March 1897. ih 234 Dr. P. Zeeman on the Influence of Magnetism period. In the third place there are ions which seem to move in rotating elliptical orbits. If one desires to know the state of the sether originated by the moving ions one may use the following rule, deduced by Prof. Lorentz from the general theory:—Let us suppose that in a molecule an ion P—of which the position of equilibrium is P»—has two or more motions at the same time, viz. let the vector P,P always be obtained by adding the vectors PoP which should occur in each of the component motions at that moment; then the state in the ether at a very great distance in comparison with P,P will be obtained by superpusing the states which would occur in the two cases taken separately. Hence it follows in the first place that a circular motion of an ion gives circularly polarized light to points on the axis of the circle. Further, one may choose instead of the above-considered elliptical orbits a resolution more suited to our purpose. One may resolve the motion of the ion, existing before the putting on of the magnetic force, into a rectilinear harmonic motion parallel to the axis of z and two circular (right-handed and left-handed) motions in the plane of (2, y). The first remains unchanged under the influence of the magnetic force, the periods of the last are changed. By the action of the grating the vibrations originated by the motion of the ions are sorted according to the period, and hence the complete motion is broken up into three groups. The line will be a triplet. At any rate one may expect that the line of the spectrum will be wider than in the absence of the magnetic field, and that the edges will give out circularly- polarized light*. 20. Aconfirmation of the last conclusion may be certainly taken as a confirmation of the guiding idea of Prof, Lorentz’s theory. To decide this point by experiment, the electromagnet of § 2, but now with pierced poles, was placed so that the axes of the holes were in the same straight line with the centre of the grating. The sodium lines were observed with an eye- piece with a vertical cross-wire. Between the grating and the eyepiece were placed the quarter-undulation plate and nicol which | formerly used in my investigation of the light normally reflected from a polarly magnetized iron mirrorf. The plate and the nicol were placed relatively in such a * IT saw afterwards that Stoney, Trans. Roy. Soc. Dublin, iv., en- deavours to explain the existence of doublets and triplets in a spectrum by the rotation of the elliptical orbits of the “ electrons” under the in- fluence of perturbing forces. + Zeeman, ‘ Communications of the Leyden Laboratory,’ no. 15. on the Nature of the Light emitted by a Substance. 235 manner that right-handed circularly-polarized light was quenched. Now according to the preceding the widened line must at one edge be right-handed circularly-polarized, at the other edge left-handed. By a rotation of the analyser over 90° the light that was first extinguished will be transmitted, and vice versd. Or, if first the right edge of the line is visible in the apparatus, a reversal of the direction of the current makes the left edge visible. The cross-wire of the eyepiece was set in the bright line. At the reversal of the current the visible line moved! This experiment could be repeated any number of times. 21. A small variation of the preceding experiment is the following. With unchanged position of the quarter-wave plate the analyser isturned round. The widened line is then, during one revolution, twice wide and twice fine. 22. The electromagnet was turned 90° in a_ horizontal plane from the position of § 20, the lines of force now being perpendicular to the line joining the slit with the grating. The edges of the widened line now appeared to be plane polarized, at least in so far as the present apparatus permitted to see, the plane of polarization being perpendicular to the line of the spectrum. ‘his phenomenon is at once evident from the consideration § 19. The circular orbits of the ions being perpendicular to the lines of force are now seen on their edges. 23. The experiments 20 to 22 may be regarded as a proof that the light-vibrations are caused by the motion of ions, as introduced by Prof. Lorentz in his theory of electricity. From the measured widening (§ 14) by means of relation (6), the ratio e/m may now be deduced. It thus appears that e/m is of the order of magnitude 10’ electromagnetic U.G.S. units. Of course this result from theory is only to be considered as a first approximation. 24. It may be deduced from the experiment of § 20 whether the positive or the negative ion revolves. If the lines of force were running towards the grating, the right-handed circularly-polarized rays appeared to have the smaller period. Hence in connexion with § 18 it follows that the positive ions revolve, or at least describe the greater orbit. 25. Now that the magnetization of the lines of a spec- trum can be interpreted in the light of the theory of Prof. Lorentz, the further consideration of it becomes specially attractive. A series of further questions already present themselves. It seems very promising to investigate the motion of the ions for various substances, under varying circumstances of temperature and pressure, with varying 936. . Dr. P. Zeeman on the Influence of Magnetism intensities of the magnetization. Further inquiry must also decide as to how far the strong magnetic forces existing according to some at the surface of the sun may change its spectrum. The experiments described have been made in the Physical Laboratory at Leyden, to the Director of which, Prof. Kamer- lingh Onnes, I am under great obligations for continuous interest in the present subject. Amsterdam, Jan. 1897. Appendix. Since the publication of my original paper in the Proceed- ings of the Academy at Amsterdam, and while the present paper was in the press, I have become acquainted with two attempts, till now unknown to me, in the same direction, and also with the original account of Faraday’s experiment referred toin§1. The last is to be found in Faraday’s ‘ Life’ by Dr. Bence Jones, vol. ii. p. 449 (1870), and as it is extremely remarkable I will reprint it here :— “1862 was the last year of experimental research. Stein- heil’s apparatus for producing the spectrum of different sub- stances gave a new method by which the action of magnetic poles upon light could be tried. In January he made himself familiar with the apparatus, and then he tried the action of the great magnet on the spectrum of chloride of sodium, chloride of barium, chloride of strontium, and chloride of lithium.” On March 12 he writes :—“ Apparatus as on last day (January 28), but only ten pairs of voltaic battery for the electromagnet. “The colourless gas-flame ascended between the poles of the magnet, and the salts of sodium, lithium, &c. were used to give colour. A Nicol’s polarizer was placed just before the intense magnetic field, and an analyser at the other ex- treme of the apparatus, Then the electromagnet was made, and unmade, but not the slightest trace of effect on or change in the lines in the spectrum was observed in any position ‘of polarizer or analyser. “Two other pierced poles were adjusted at the magnet, the coloured flame established between them, and only that ray taken up by the optic apparatus which came to it along the axis of the poles, 7. e. in the magnetic axis, or line of magnetic force. Then the electromagnet was excited and rendered neutral, but not the slightest effect on the polarized or unpolarized ray was observed.” on the Nature of the Light emitted by a Substance. 237 “This was the last experimental research that Faraday made.” , In 1875 we have a paper by Prof. Tait, who has kindly sent me a copy, “ On a Possible Influence of Magnetism on the Absorption of Light, and some correlated subjects ” (Proc. Roy. Soc. of Edinburgh, Session 1875-76, p. 118). Prof. Tait remarks that a paper by Professor Forbes, read at the Society, and some remarks upon it by Maxwell, have recalled to him an experiment tried by him several times, but which hitherto has led to no result. Then the paper proceeds :— “The idea is briefly this—The explanation of Faraday’s rotation of the plane of polarization of light by a transparent diamagnetic requires, as shown by Thomson, molecular rota- tion of the luminiferous medium. The plane-polarized ray is broken up, while in the medium, into its circularly-polarized components, one of which rotates with the sether so as to have its period accelerated, the other against it in a retarded period. Now, suppose the medium to absorb one definite wave-length only, then—if the absorption is not interfered with by the magnetic action—the portion absorbed in one ray will be of a shorter, in the other of a longer, period than if there had been no magnetic force; and thus, what was originally a single dark absorption line might become a double line, the components being less dark than the single one.” Hence here the idea is perfectly clearly expressed of the experiment, tried in vain; an idea closely akin to that of § 15 above, both being in fact founded on Kelvin’s theory of the molecular rotation of the luminiferous medium, though not directly applicabie to the experiment of § 9, in which case the lines of magnetic force are perpendicular to the axis of the tube. In the second place I have to mention two papers by the late M. Fievez, to which attention has been drawn by M. van Aubel, in a letter to Prof. Onnes and intended for communi- cation to the Academy of Sciences, Amsterdam. Prof. Onnes read the letter at the January meeting, and made at the same time some explanatory remarks of which in the following I make free and extensive use. The papers referred to are :— M. Fievez, “ De |’ Influence du Magnétisme sur les caracteres des Raies spectrales” (Bulletin de ? Acad. des Sciences de Bel- gique, 3° série, tome ix. p. 881, 1885); and Fievez, “ Hssai sur Origine des Raies de Fraunhofer, en rapport avec la Constitution du Soleil” (/. ¢. 8° série, tome xii. p. 30, 1886). Here experiments are described as in §§ 4 and 13 of the present paper. Nothing, however, is observed about the widening of the absorption-lines, nor about the polarization 238 Influence of Magnetism on the Nature of Light. of the emitted light. The results obtained by M. Fievez merit careful attention and consideration. He has observed with a flame in a magnetic field not only widening but reversal and double reversal of the lines of the spectrum, the lines at the same time becoming more brilliant. Unfortu- nately quantitative details are not given. The facts observed in some cases by Fievez are qualitatively not in accordance with my observations or what is to be deduced from my results. Hence even in the cases where the results are qualitatively in accordance, the question remains whether Iievez has observed the same phenomenon. The field used by Fievez seems to have been more intense than the one I had at my disposal. Is it possible perhaps to account in this manner for the “ double renversement (¢’est-a-dire apparition d’une raie brillante au millieu de la raie noire élargie)”’? I think the answer must be in the negative. Tor, arguing from § 19, a line must widen, or else, the field being very intense, become a triplet. We cannot but understand from Fievez’s description of the experiment that the light was emitted perpendicular to the lines of force. Now the double reversed line of Fievez is not the triplet to be expected from theory, for it is expressly stated by Fievez that the line expe- rimented upon is not the simple line of the spectrum, but one previously widened and reversed (by some agency independent of magnetism). By the action of magnetism a brilliant line in the centre of the black line appears. Hence perhaps one may interpret the case of double reversal as a direct action of mag- netism, but then only as a doubling of the absorption-line and not as a division of the original line into three parts. As the application of Lorentz’s theory given in § 18 is confessedly only a very first sketch, further theoretical and experimental evidence is wanted before we are able to decide whether in the experiment of Fievez a specific action of magnetism on light or perturbing circumstances have been prevalent. Indeed one may make the same objection to M. Fievez’s ex- periment as I myself have made to my own analogous experi- ment in § 6. The whole of the phenomena observed by Fievez can readily be attributed to a change of temperature by the well- known actions of the field upon the flame (change in its direction or outline, magnetic convection, Wc.) ; and the last sentence of his paper states that ‘‘les phénomenes qui se manifestent sous l’action du magneétisme sont identiquement les mémes que ceux produits par une élévation de tempéra- ture.” The negative result obtained by Fievez with absorp- tion-spectra would without further consideration (as in § 12) eS ee a ae Notices respecting New Books. 239 point in the same direction. The inference to be drawn from Fievez’s experiments alone would rather be, I think, that the temperature of the flame is changed in his experiments than that a specific action of magnetism on the emission and ab- sorption of light exists. By experiments already in progress I hope to settle the dubious points. Summarizing we may say:—Had the experiments of Fievez come to my knowledge they would have been a motive for me to further investigation, Fievez not having prosecuted his inquiry up to a decisive result. At least at present it remains even doubtful whether the phenomenon observed by Fievez with a magnetized flame is really to be attributed to the specific action of the magnetic field on the period of the vibrations of light, which I have found and undoubtedly proved by the experimental confirmation of Lorentz’s pre- dictions. Amsterdam, February 1897. XXXITT. Notices respecting New Books. Das Wesen der Elektrizitat und des Magnetismus, auf Grund eines einheitlichen Substanzbegriffes. By J. G. Voat. Leipsic: Wiest, 1897. HE author of this treatise is obliged to borrow from the Eng- lish language expressions strong enough to characterize the ordinarily accepted notions concerning the ether and matter, which he designates as “absurd” and “stupid.” His philosophic mind refuses, much more emphatically than that of a certain eminent British statesman, to admit the existence of an ether and of atoms in a state of perpetual vibration. He sees no difficulty, however, in filling space with a continuous, contractile xther, containing nuclei which undergo periodic fluctuations of density ; matter consists of the permanently condensed portions of this ether. We are not told how these centres of condensation differ from the rest of the ether, or by what process they pull the surrounding medium; their only function is to perpetually expand and contract. In fact, the theory is only the opposite extreme of the kinetic theory ; every point in the ether is supposed to be the seat of potential- or strain-energy instead of kinetic energy. The author avoids any mathematical statement of his theory, sometimes by remarking that he is not a physicist, which is an obvious fact, and sometimes by explaining that his work is intended as a popular exposition. The volume is printed in German characters, and its illustrations are so extremely bad that the author finds it necessary to make an apology for them. J. L, H. [ 240 | XXXIV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 151.] Dec. 16th, 1896.—Dr. Henry Hicks, F.R.S., President, in the Chair. ‘ae following communications were reals — ‘On the Subdivisions of the Carboniferous Series in Great Britain, and the True Position of the Beds mapped as the Yoredale Series.’ By Dr. Wheelton Hind, F.R.C.S., F.G.S. In this paper the author gives a summary of our knowledge of the local divisions of the Carboniferous system, and criticizes the present classifications in vogue, laying special stress upon the local variations in the lithological characters of the rocks, and summing up to a large extent the fossil evidence which is available. He maintains that the Yoredale Beds are largely the equivalents of the beds which have elsewhere been referred to the Mountain Limestone Series, though some local beds which have been included in the Yoredale Series may rather be the equivalents of the Millstone Grit. He advocates the abolition of the term ‘ Yoredale Series’ as applied toa subdivision of the Carboniferous strata comparable in importance to such divisions as Carboniferous Limestone and Millstone Grit, but believes that the term may be usefully employed to denote the changes in character of the beds due to causes which operated locally, and to represent the Carboniferous Series as it occurs in Wensleydale, Swaledale, Teesdale, and the upper parts of Wharfedale and Ribblesdale. He would divide the rocks of the Carboniferous System into an Upper Carboniferous or Anthraciferous Series, and a Lower Car- boniferous or Calcareous Series; and indicates the occurrence of three very different faunas in the Carboniferous rocks, viz.:—(i) a Coal-Measure fauna rich in fish-remains, with the molluscan genera Carbonicola, Anthracomya, and Naradites (essentially a freshwater fauna); (11) the Lower Coal-Measure and Grit fauna, largely marine but littoral, with Aviculopecten, Posidonella, Nautilus, Goniatites, and peculiar gasteropoda ; and (111) a Limestone fauna, essentially marine, very rich in brachiopods, and containing Pecten, Avicula, Edmondia, Sanguinolites, and many other lamellibranchs, gasteropods, such as Huomphalus, Pleurotomaria, Murchisonia, and Loxonema, and certain peculiar cephalopods. 2. ‘Note on Volcanic Bombs in the Schalsteins of Nassau.’ By Prof. E. Kayser, Ph.D., For.Corr.G.8. ‘The bombs forming the subject of this communication occur in two localities in the neighbourhood of Oberscheld near Dillenburg. They are generally rounded, though sometimes angular, and vary in size from that of a nut to that of aman’s head. Each consists of a kernel of coarse-grained rock representing a fragment of limestone -altered by metamorphism, surrounded bya rind of amygdaloidal rock due to the inclusion of the fragment in molten Java. They demonstrate the pyroclastic origin of the Schalsteins, and also prove the similarity between the old ‘Devonian volcanoes and those which are now active. THE LONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] APRIL 189%. XXXV. On the Electrification of Gases exposed to Rénigen Rays, and the Absorption of Réntgen Radiation by Gases and Vapours. By KH. RurHerrord, I.A., 1851 Exhibition Science Scholar, University of New Zealand, Trinity Col- lege, Cambridge*. i a recent paper by Prof. J. J. Thomson and myself ‘ On the Passage of Electricity through Gases exposed to Rontgen Rays” (Phil. Mag. Nov. 1896), a method of obtaining electrified air by means of the Réntgen rays was very briefly explained. The present paper deals with further experiments which have been made to investigate more fully the way in which electrified gases can be obtained by means of the Roéntgen rays, and also to examine the properties of the charged gas. The opacity of gases for Rontgen radiation has also been examined. A gas becomes a temporary conductor under the influence of the Roéntgen rays, and preserves its power of conducting some short time after the rays have ceased to act; since the conduction in the gas is probably due to the convection of charged particles which travel through the gas with a velocity of the order of 1 cm. a second for a potential gradient of one volt per cm., it is not surprising that we can separate the positive from the negative conducting particles before they give up their charges to the electrodes. * Communicated by Prof. J. J. Thomson, F.R.S, Phil, Mag. 8. 5. Vol. 43. No. 263, April 1897. U a % bas if »o {- % v a af tan 242 Mr. EH. Rutherford on the Electrification | The method of separation used was to direct a rapid current of air or other gas along the surface of the charged electrode of a vessel exposed to the Rontgen rays; a large metal cylinder was taken, either of thin metal to allow the rays to readily pass through the side, or a piece was cut out and a sheet of very thin metal substituted to serve the same pur- pose. Fig. 1. —Y), Indactor D Z YO Ba tlery A (fig. 1) was the metal cylinder, B Ca glass tube fixed centrally inside the cylinder. The wire D E was fixed in the glass tube BC and supported by thin metal spikes in the centre of the tube. Several inches of wire, BD, projected from the glass tube. A current of gas was sent from a pair of bellows or a gas reservoir along the tube CB, and then along a metal tube into an insulated conductor connected with one pair of quadrants of an electrometer, the other pair being connected to earth. The wire DE was connected to one pole of a battery of small lead cells, the other pole being to earth. The outside of the cylinder was connected to earth, and the bulb and Ruhmkorff coil were placed inside a metal tank, so as to completely screen the outside apparatus from electrostatic disturbances. A hole was cut in the tank, and the bulb arranged so as to allow the rays to fall on the part BD of the charged wire. When the bulb was not working, however rapid a current of air was sent along the charged electrode, no electrification was obtained in the inductor, but the moment the rays were turned on the inductor became charged opposite in sign to the charged wire. The deflexion of the electrometer continuously inc-eased as long as the rays and blast of air were acting. The inductor was generally placed some feet from the generating vessel A, the air passing to the inductor through a metal tube of 3 cm. diameter. Since the electrification of dh ln i te in ms to of Gases exposed to Réntgen Rays. 243 the inductor is opposite in sign to the charged wire, the effect can in no way be due to conduction through the Réntgenized air from the charged electrode to the inductor, since the inductor would then be charged to the same sign as the electrode. A small plug of glass wool placed in the metal tube between the generator and the inductor completely stopped all electri- fication, and the inductor received no charge, however rapid a blast of air was sent through the apparatus. On account of the large quantity of air blown through the inductor in order to obtain a convenient deflexion on the electrometer (an amount sufficient to fill the inductor many times over), only a small proportion of the charge could be blown out. If, however, a gentle current of electrified air was blown into the inductor for two or three seconds, and the rays then stopped, it was found possible to blow out most of the charge again, after a short interval, provided there was a fairly wide opening in the inductor. If the opening was stopped with a plug of glass wool, it was found impossible to blow out the slightest amount, since the electrified particles gave up their charge freely to the glass wool. Since the glass wool has the power of completely dis- charging the electrification both positive and negative, a short wide metal cylinder lightly packed with glass wool was used instead of the inductor for testing the amount of the electrification in most of the experiments that follow. The amount of electrification obtained varied with the potential of the charged wire and the velocity of the current of air. The relation between the amount of electrification and the E.M.F. of the charged wire is shown in the Table below :— Amount of Electrification E.M.F. in volts. 5 ate in scale-divisions. eee 17 60 30 100 70 130 200 82 The amount of electrification increases up to a certain point and then diminishes. The maximum amount of elec- trification is closely connected with the value of the E.M.F. which is just sufficient to give the saturation-value of the U2 244 Mr. E. Rutherford on the Electrijication current through the gas. In the above table the saturation- value of the E.M.F. was about 70 volts, and this corresponds to the maximum amount of electrification. Since the velocity of the conducting particles increases with the E.M.F. but the current through the gas remains constant, when the E.M.F. is raised above its saturation- value it is to be expected that a greater proportion of the conducting particles would reach the electrode. This agrees with experiment, for as the E.M.F. is increased above a certain value the amount of electrification obtained steadily diminishes. The amount of electrification obtained for a given E.M.F. increases at first with the velocity of the blast, and then tends to a maximum value, which cannot be increased, however rapid a blast is sent along the wire. An experiment proving conclusively that the amount of electrification is intimately connected with the conduction of electricity through the gasisas follows :—The electrode along which the air was blown was carefully insulated and connected to one pair of quadrants of the electrometer. The two pairs of quadrants were charged up to the same potential and then insulated from each other, and the rate of leak of the charged wire determined. The rate of leak steadily diminished with increase of velocity of the blast ; when the air issumg from the glass tube had a velocity of about 1000 cm. per second the rate of leak was only one fourth of its value when the air was still, and the amount of electrification in the air passing from the wire, as tested by the glass wool cylinder, was nearly equal to the quantity of electricity corresponding to the difference between the two rates of leak. We should not expect them to be exactly equal, since some of the Réntgenized air containing both positively and nega- tively charged particles is also blown out. The charged gas obtained in this way is thus due te an excess of the positive or negative conducting particles, what- ever they may be, to which conduction in gas under the Roéntgen rays is due. In all these exp rriments precautions were taken against dust. Tt was found that the amount of electrification obtained was independent of the quantity of dust in the air provided the velocity of the issuing blast was kept constant. The air in one case was sent through a long tube filled with glass wool into the gas reservoir, which was then allowed to stand fora couple ot days without being disturbed. The air in passing from the reservoir to the generator was again passed through glass wool, but the effect obtained was exactly the same as if of Gases exposed to Réntgen Rays. 245 the dust-charged air from the room were sent directly through the apparatus. Electrification from Charged Insulators. If the central electrode through which the air was blown was coated with paraffin or sealing-wax, it was found that the amount of electrification obtained was at first about equal to the amount with the bare electrode. If the bulb was kept working the amount of electrification diminished after a time. The central electrode was then connected to earth, and when the x-rays were acting electrification could still be obtained, but of opposite sign to that obtained before. If the wire with the coating of dielectric on its surface was kept charged to a high potential and the rays continued for some time, on applying a smaller H.M.I’. to the wire in the same direction the sign of the electrification is generally changed. The explanation of these and similar phenomena is simple if we consider that the conducting particles of the gas either give up their charge to the surface of the insulator, or adhere to the surface which becomes charged opposite in sign to the wire itself. If the bulb is kept working, the electromotive intensity acting on the gas is diminished, owing to the effect of the oppositely charged insulator. The amount of electrifica- tion obtained therefore diminishes if the H.M.F. is not well above the saturation-value. If the central electrode be then connected to earth, the charged insulator causes a current through the gas in the opposite direction, and thus changes the sign of the charge in the gas blown out. If the charge on the insulator is large, as is the case if the central wire has been raised, for example, to a potential of 200 volts and exposed to the rays for some time, on applying an H.M.F. of 30 volts, say, in the same direction the electrification changes sion. In this case, the electromotive intensity due to the charged insulator is greater and opposite in sign to that due to the 30 volts, and so the current through the gas is reversed. The sign of the electrification obtained when the wire is covered with insulating material is thus dependent on the amount and sign ot the charge on the surface of the dielectric. From a charged wire coated with paraffin or sealing- wax which had been exposed to the Roéntgen rays for several minutes, it was found possible to obtain electrified air, by dir ecting a current of air along its surface, several hours after the central electrode had been connected to earth. 246 Mr. E. Rutherford on the Electrification Properties of the Charged Gas. Since the charged gas obtained is due to the separation of the oppositely charged conducting particles to which con- duction in a gas under the w-rays is probably due, we should expect the positively and negatively electrified gas to closely resemble Rontgenized air in its properties, and such is found to be the case. The gas completely loses its charge in its passage through the pores in a plug of glass wool; while Roéntgenized air, after being forced through glass wool, loses all trace of con- ductivity. The gas readily gives up its charge to any conducting or insulating surface against which it impinges. The greater amount of electrification is discharged in the passage of the gas down a long tube. If the electrified air is allowed to impinge against the surface of an insulated metal plate, it gives up a portion of its charge to the metal. The facility with which the gas is discharged is to be expected, since no evidence of polarization has been found in the conduction of the gas exposed to the Rontgen rays when metal electrodes are used. ; A remarkable property of the electrified gas is that positive and negative electrification are not discharged with equal facility by all metals. When the charged gas was passed through a long zine tube, the amount of negative electrifica- tion on the issuing gas was always less than the amount of positive for the same velocity of the blast. By insulating the zinc tube it was found that it received a greater charge of negative than of positive. In order to test this difference, cylinders of zinc, tin, and copper were made of the same size, and the charged gas forced through them. It was found that zinc and tin discharged negative electrification more rapidly than positive, the difference in general amounting to about 20 per cent. Copper apparently discharged the positive and negative with about equal facility, but many experiments seemed to point to the conclusion that even in the case of copper negative was slightly more readily dis- charged than positive. If the electrified gas impinged against insulated plates of different metals, the same general results were obtained. Not only was there a difference in the discharging powers of positive and negative electrification for any particular metal, but a copper plate, for example, discharged positive more readily than a zine plate placed exactly in the same of Gases exposed to Réntgen Rays. 247 position, while the zinc plate discharged more negative than the copper. Other metals, like aluminium, lead, were tested, and in all cases negative electricity was discharged with slightly more facility than positive. The variable discharging power of the different metals agrees in some respects with the results obtained by Minchin (‘ Blectrician, March 27, 1896), who found that under the influence of the Réntgen rays insulated metal plates were all charged up toa small potential. According to his results copper was charged positively and zinc negatively, while sodium was highly negative. He also found that the potential to which some of the metals could be raised depended on the degree of polish of the exposed surface. In the experiments on the discharging power of the metals, the results were dependent to some extent on the brightness of the surface, especially in the case of tin and zine. The amount of electrification discharged by a metal tube one inch in diameter and a foot long is very large, amounting in some cases to over one fourth of the whole charge on the gas. It must be remembered, however, that the current of air conveying the charged gas is travelling at a high velocity, and is, in consequence, in a state of violent eddying motion, so that probably a large proportion of the gas approaches near the surface in its passage along the tube. The charge is taken from the gas not only when it passes through metal tubes, but also when it passes through tubes coated with an insulator. A metal tube was taken and coated with a thin layer of paraffin, and it was found that the charge on the cylinder was about the same as with the clean metal. It was difficult to determine with certainty whether insulators exhibited similar properties to metals in regard to discharging power. The amounts of positive and of negative electrification discharged were approximately the same, but the differences were too small to make certain of. The conductivity of the charged gas was tested by placing an insulated wire kept at a constant potential inside a metal vessel through which the electrified gas was blown. It was found that when the electrification was of the same sign as the charged wire, the gas gave up its charge to the outside vessel, and when of the opposite sign, to the charged wire. The current through the gas was only temporary, and ceased as soon as the current of electrified gas was stopped. 248 Mr. KE. Rutherford on the Electrification Electrification of Different Gases. All the gases which were experimented with could be electrified in the same way as air. A gas-bag was filled with the gas to be tested, and then forced along the electrode as in the case of air, care being taken to allow the gas to run through some time before the rays were turned on, in order to remove the air as far as possible from the generating vessel. The amounts of electrification obtained for a given velocity of the gas and intensity of the rays varied with the conduc- tivity of the gas under the #-rays. Gases that have a greater conductivity than air gave more electrification than air. Oxygen and coal-gas gave slightly less electrification than air, while carbon dioxide gave slightly more—the amounts being sensibly proportional to their conductivities. . The vapour of methyl iodide was tried, which has a ver high conductivity—over 20 times that due to air. Only a partial test could be made of it, as sufficient quantity of the vapour was not obtainable. Some of the liquid was placed in the generator (fig. 1), and gently heated to its boiling- point, till the vessel was filled with vapour. The rays were then turned on, and a rapid current of air sent for 3 or 4 seconds along the central electrode. The amount of electri- fication obtained was over 5 times the amount from air in the same time. After a few seconds the highly conducting vapour was blown out and the electrification became sensibly that due to air alone. If a current of the vapour could have been sent instead of a current of air, it is probable that the amount of electrification obtained would have been over 20 times that of air in the same time. The experiments on hydrogen were interesting as bearing on the question of the relative velocity of the conducting particles of hydrogen and air. For a given small weight on the gas-bag the amount of electrification from air was 2°5 times that due to hydrogen in the same time. As the weight was increased the ratio fell to 1-5. This is as we should expect if the velocity of the hydrogen ions was greater than those of air. For small velocities of the blast a much smaller proportion of the hydrogen than the air ions escape. As the velocity is increased the amount of electrification from the air increases slowly, as nearly all of the ions are blown out, while the amount from hydrogen increases rapidly as the velocity increases. In a previous paper (Joc. cit.) it was shown that hydrogen was saturated for a much lower value of the H.M.F. than of Gases exposed to Réntgen Rays. 249 air, while the velocity of the hydrogen ion was much greater than that of air. The experiments on the amount of electri- fication with variation of H.M.F. and velocity of the blast confirm the previous results which were obtained in an entirely different way. Velocity of the Ions.—An approximate determination of the velocity of the conducting particles for air can be made by de- termining the rate of leak of a charged wire connected to an electrometer when air is blown at varying velocities from a tube of known diameter along the charged wire. If we assume the current of air of high velocity from the tube to be confined within narrow limits for a short distance from the orifice, the velocity of the ions in order that a known proportion of the ions should reach the electrode can easily be deduced. The velocity of the blast issuing from a tube °8 cm. in diameter was 800 ecm. per second, and the wire was charged to a potential of 35 volts. With this velocity the rate of leak of the wire was only one third of the natural leak; so that two thirds of the conducting particles of one sign were blown out. The length of the exposed wire B D (fig. 1) was 6°3 cm., and knowing the diameter of the wire B D and of the cylinder, it can be shown that the velocity of the conducting particles for air is about 1 cm. per second for a potential gradient of one volt. This is of the same order as the rough determination made in the previous paper by Professor Thomson and myself. The positive and negative conducting particles of air travel with the same velocity, for when the sign of the charged wire is reversed the rate of leak is the same as before with the same velocity of the blast. When different amounts of positive and negative electrification were obtained, it was at first thought that part of the difference might be due to inequality in the velocity of the ions, but later experiments showed that it was entirely due to the greater facility with which metals discharged the negative electrification. Volume-Density of Electrification of the Charged Gas. Only a very minute portion of the gas conveys the charge in the cases we have been considering. In the paper pre- viously referred to it has been shown that assuming the conducting particles convey an atomic charge, only about one billionth of the gas is required to be split up to give the conductivity observed. In the previous experiments the conducting air is still further diluted by the blast along the electrode which conveys the charged particles with it. From data of the capacity of the electrometer and velocity of the blast it can be shown that the amount of charge per c.c. 250 Mr. F. Rutherford on the Electrification of air was about 10-‘ electrostatic units. In the case of the better conducting gases and vapours the volume-density is greater. For the vapour of methyl iodide the volume- density would be over 20 times as great. The facility with which the electrified gas is discharged by metals and insulators may at first sight lead to the conclusion that we are dealing with electrified dust, which, as is well known, is completely discharged by glass wool, and also readily gives up its charge to whatever it comes in contact with. Jt has been shown, however, that the amount of electrification is quite independent of the amount of dust in the air, and that therefore ihe electrification can be in no way due to electrified dust. The theory has been advanced that the discharge of elec- tricity from the surface of a-metal under the action of ultra- violet light is due to the disintegration of metallic particles or vapour from the surface, and that these carry off the charge. The discharge of electrification by the Réntgen rays might pos- sibly be due to a similar cause, and this was fully investigated. In the first place, there are many experiments which negative this view. It has been shown in a previous paper that the current through a gas conducting under the 2-rays increases with the distance between the electrodes although the surface exposed to the gas is unaltered. The amount of electrification obtained from a gas was found to be quite independent of the nature of the electrodes. The inside electrode (fig. 1) of the cylinder was coated with paraffin or wax, and provided we de not allow the charge to collect on the surface of the insu- lator, the amount of electrification was unaltered. Similarly, if the inside of the cylinder was coated with an insulator, no difference in amount could be detected immediately after the rays were turned on ; but after the rays had been acting for a short time the amount decreased, owing to the charging of the surfaces of the insulators. These conclusions show that the conductivity in a gas is independent of the nature of the surface of the electrodes, for it is extremely improbable that the same amount of dust would be dislodged by the rays from the surface of all metals and insulators. The most conclusive experiments on this subject are some which I recently made on the diminution of the intensity of the Roéntgen rays due to the absorption in their passage through gases and vapours. Absorption of Energy by Gases and Vapours. Since gases all conduct under the influence of the x-rays, it was interesting to investigate the relative absorption in of Gases exposed to Réntgen Rays. 251 order to make the gases conductors, and whether the absorption was in any way related to the constitution or conductivity of the gas. The absorption of energy in gases like air, hydrogen, oxygen is small and is not easily detected unless a delicate null method is used. Two equal and similar conical-shaped vessels A B C, A’B’C’ (fig. 2), much larger in diameter at the top than the bottom, ie 2: yp were placed in such positions that the axis of each cone passed as nearly as possible through the anode of the focus- bulb. From experiments it was found that the z-rays appeared to emanate in all directions from the anode. The upper parts of each vessel, A B, A’B’, were made of lead, and were separated from the lower portions BC, B/C’, which were made of glass, by thin ebonite plates. Thin ebonite plates also covered the ends of the glass cylinders at C and C’, so that the vessels BC, B’C’ were air-tight, and could be ex- hausted when required. The lead cylinders A B, A’B’ were used to compare the rate of leak after the rays had passed through the glass cylin- ders. Insulated wires D H, D/H’ formed the electrodes, and these were connected to opposite pairs of quadrants of the electrometer, and both quadrants were at first charged up to the same potential, which in practice was generally 200 volts. oe. outsides of the vessels AB, A’B’ were connected to earth. Zoe Mr. E. Rutherford en the Electrification The position of the bulb was so adjusted that the rate of leak in each cylinder was exactly the same, so that since the potential of each pair of quadrants fell at the same rate, the needle of the electrometer remained at rest while the rays were kept acting. If another gas was introduced into one of the glass vessels BC it was found that the balance was dis- turbed, owing to the variation of intensity of the rays in the vessel AB, which was caused by the less or greater absorption of the rays in their passage through the gas. In the experi- ments the only rays which caused conduction in the lead cylinders had to pass through the gas, and all stray radiation was carefully screened off. If we assume that the absorption of energy in passing through a thin layer of gas of thickness dl is proportional to the intensity of the rays I at that point and to the length of the gas dl traversed, the decrease of intensity of the rays due to absorption of energy in the gas is equal to Aldl, where X is a constant for any particular gas but varies for different gases, and may be called the coefficient of absorption of the gas. Experimentally it was found that the rate of leak of a gas is proportional to the intensity of radiation at any point. From these considerations it can readily be shown that the ratio of the rate of leak when the rays pass through a length lof the gas, to the rate of leak when the gas is removed and a vacuum substituted is e~” where e=2°7, and this result is independent of any metal or insulators which the rays pass through in both cases before reaching the testing vessels. The ratio of the rates of leak can be readily deduced from the movement of the electrometer needle, and since the length of the gas traversed is known, the coefficient > is thus determined. 3 Experiments were first made to see whether air absorbed any appreciable amount of energy of the radiation. The balance was obtained and then one of the glass vessels was exhausted by an air-pump; the electrometer slowly moved in one direction while the rays were kept acting. If the other vessel was also exhausted, the balance was again restored, and if air was then let into the vessel first exhausted, the electro- meter needle moved in the opposite direction. The variation of the rate of leak after passing through 10 em. of air was about one per cent., but it was a difficult matter to determine such a small variation with accuracy. It will be at once seen that the approximate value of A/ is 10-?, and therefore for air A=10-*; since 1 10 em. If we suppose wz-radiation to be emitted by the sun, assuming the radiation would have to pass through four miles of Gases exposed to Réntgen Rays. 253 of homogeneous atmosphere, the intensity at the surface of the earth would be approximately 10-7 of the intensity of the radiation before it reached the earth’s atmosphere. This is an excessively minute proportion, and it is not surprising therefore that experiments, made even on the highest moun- tains, to detect any Réntgen rays in solar radiation (Cajori, Phil. Mag. Nov. 1896) should have been unsuccessful, even if the intensity of the x-radiation at the hmits of our atmosphere, were greater than could be produced at the surface of a Crookes tube. Gases like oxygen, coal-gas, carbon dioxide, whose leakage- rates are about the same as that of air, absorb about the same amount of energy. Sulphuretted hydrogen, which has a conductivity six times as great as air, diminishes the intensity of the radiation by about 4 per cent. in passing through 10 cm. of the gas. Chlorine, whose conductivity is eighteen times that of air, dimi- nishes the intensity about 12 per cent. for the same distance. The absorption of energy in these cases is not necessarily selective, for the same results were obtained whatever gas was used in the testing vessels. After the radiation had passed through sulphuretted hydrogen the same diminution in intensity was obtained whether air or sulphuretted hydrogen was used in the testing vessels. Mercury vapour, which is one of the best conductors of electricity under the «x-rays, is also one of the best absorbers of the ra _v+dy—b : v—b ’ since N/(N —dN) =(v+dv)/v. Taking logarithms and expanding, and writing for a” its value 30; or ay > where R is the ordinary gas constant Vaporization of Liquids. 295 (=1:979J), and M the molecular weight of the liquid, we have RT wd ‘= JM (—b)” or integrating from the interior of the liquid to that of the vapour, RT Atay Wa iee b re JN { Ls ear + - 3}, “Vtech? in which v and v’ are the specific volumes of the liquid and saturated vapour respectively. By the method of its derivation, eq. (9) is general, and gives the relation between the specific volumes and the differences of potential JL, due to any system of bodily forces acting on a vapour the size of whose molecules is not negligible compared with their free paths. The assumptions employed above as to the effect produced by the volume of the molecules are the same as those which lead to van der Waals’s characteristic equation for fluids : (p +5)@-3) = a Hquation (9) may therefore also be derived from this, and the ordinary hydrostatical equations of equilibrium in a somewhat simpler way, although this gives no account of the molecular actions which constitute the process. oi As the assumptions involved in the term -, are not necessary, let e dL p(v—b) =a Bothy eae, © (li0) be the relation between the pressure and volume of the fluid in the region of varying density, —p being the actual pressure (molecular included with external). 6 may be not necessarily independent of the temperature, but if it be not variable with v, we can differentiate (10) at constant temperature and obtain RT dv =O 2% th The ordinary equation of hydrostatical equilibrium in the surface-film is YD ENN iin wer ear re ne) where dV is the element of potential of the bodily forces on the liquid, and p the density. Substituting for dp from (11), 296 Mr. 8. R. Milner on the Heats of and integrating from the interior of the liquid to that of the vapour, we obtain which, with JL; written for V’—V, is the same equation as (9) for the internal heat of vaporization. Another expression for the latent heat might similarly be obtained from the other term of the characteristic equation by writing the pressure in the liquid as p=p + = p being the vapour-pressure. In the film of varying density, » would also contain terms dv Ae 3 the densities are constant these would vanish from the final result, and the internal latent heat would become * Li edp 1 | es, Al v depending on but on integration between places where * Tt seems to have been usual to assume that the total latent heat of a yapour is given by We pdv. Thus Nernst (‘Theoretical Chemistry,’ p. 209), writing the pressure in the liquid a p=p + a makes the internal heat of vaporization leva ayl 1 : “du= 4 (= —=) Juco ne ; a result only half as great as (13). Consideration of the process, how- ever, seems to show that the internal heat is the same thing as the difference of potential V'—V, and that therefore its value is given by eee or ie dp. For the molecules in moving from the liquid to the v p v vapour and doing work against the molecular forces change their kinetic energies by an amount V’—V, or fo dp per gram into potential energy. This amount of heat is therefore taken from the system, and remains in the vapour as potential energy. At the same time, as they move up through the region of varying density, they expand and lose kinetic energy = \p dv (although it is not necessary for a molecule to have the extra energy indicated by this to be able to pass from one layer to the next considered in the deduction of (9)—the expansion may be considered Vaporization of Liquids. 297 This expression, however, does not seem to give very accurate results; it is of a different form from (9), although of course were van der Waals’s equation strictly true it would be equi- valent to it. Equation (9) for the heat of vaporization contains what is to a certain extent an arbitrary constant b. 6 is not, however, in reality completely arbitrary, as it can be calculated approxti- mately from the critical volume, although the approximation is very rough, or it could, if necessary, be estimated with sufficient exactness by substituting in van der Waals’s equation the specific volumes of the liquid at two different pressures. As, however, there seems some theoretical reason to believe that 6 is slightly variable with the temperature*, it seems better, instead of calculating the heats of vaporization of dif- ferent liquids with approximate values of 0, to test the formula by calculating 6 for different temperatures of the same liquid from the other quantities of the equation, either to see if it keeps constant or to determine its variation. The values obtained in this way may be tested by applying them in the equation a Bn RT (p+ a)e—8= ap to see if they give satisfactorily constant values of a (this equation being used here for the liquid state only, where it holds very approximately, although the constant may change considerably through such a large range as that from the liquid to the vapour). The only two cases in which the heats of vaporization have been measured with any accuracy at different temperatures are water and benzene. Below are the values of } and a cal- culated for these substances by means of (9), the headings of the columns denoting the quantities expressed by those letters in the earlier part of the paper. (Volumes are given in c.cs., the latent heat in gr. calories, and a is in units such that = is a pressure in dynes per sq. cm.) q as going on after the molecules have reached the upper layer). The work \p dv done in this way, however, goes to increase the kinetic energies of other molecules of the system, and is immediately made up to the expanding molecules by radiation, so that the system as a whole does not lose this heat. If part of this work to the extent p(v'—v) is done on the atmosphere, as when evaporation is actively going on, it must of course be supplied to the liquid as extra heat. * Sutherland, Phil. Mag vol. xxxvi. (1898) p. 507. 298 Mr. 8S. R. Milner on the Heats of Water. Es v. v'. Hise. b. a. 0 1-000 210600 HTD 0-838 TiIGI1e 25 1:003 43960 5560 822 rer(il 50 1:012 12050 5360 813 7-66 7d 1:026 4102 5163 °803 (B35, 100 1-043 1650 496°5 “799 766 125 1:062 755°5 477-0 "794 772 Benzene, C,H,. Mol. wt. 77°84. t. v. Oe a3. b. a. 0-2 1S 8141 100°10 0-8852 1:66 x 10° 17-3 1:1341 3523 96°96 “8864 1-605 32:0 11544 1874 94:30 "8862 1-614 48-4 1:1784 1001 91°32 "8862 1628 67:0 1:2070 538°0 80-01 "8854 1-640 .86°4 12382 304-7 84:57 "B85 1-654 95°6 1:2541 238°3 82-94 *8830 | 1-666 110°4 1:2812 164-2 80°39 8837 1-682 121°6 13037 126-7 78°55 "8848 1697 t The latent heats have been calculated trom the empirical formulze / 5 Water . . L,=606°5 —0:70¢ ——s hee 4 Benzene* . 1,=107-05—0:158¢— 2 9), _ It will be seen that these cases, the only two in which the latent heats have been measured experimentally, give opposite results as regards the constancy of the numbers 6 anda. In water, while b shows a gradual decrease of about 5 per cent. in 125°, a remains fairly constant; in benzene 6 seems to remain constant, while a increases. The regularity of the variation of the numbers (such as the fall to a minimum with subsequent increase in a in water) is due to the fact that L; has been calculated from an empirical formula the constants of which may not be quite accurate. The increase at high temperatures in the value of 6 for benzene is also due to extrapolating the empirical formula for L; too far. The mea- ‘surements of Griffiths and Marshall extended only up to 40°, so that the constancy of 6 at higher temperatures may be con- sidered doubtful, since the linear form of their equation may * Griffiths and Marshall, Phil. Mag. January 1896. Vaporization of Liquids. 299 not hold above 40°. To obtain more reliable values at higher temperatures, I have calculated the latent heats of benzene by means of Clausius’s equation, nob (: dp ) Li= ze v) Tae Dp), by which the latent heat may be obtained up to the critical point. By this means one may calculate the latent heats at different temperatures of some other substances for which they have not been experimentally measured, but in which »v, v’, and p are known, and so obtain a fair number of cases by which to test the validity of (9). The data have been obtained almost completely from papers by Ramsay and Young, or Young and Thomas, in the Philosophical Magazine, Philosophical Transactions, and Journal of the Chemical Society. The values of = and of L have been given in one or two cases by the observers, being obtained from an empirical equation for the vapour-pressure. In the other cases ug has dt been determined by tabulating the differences in log, p for 20° (the curve for logp being nearly a straight line, these differences do not differ greatly from the differential coeffi- cients), and calculating - from them by the relation dp ad 859 logo p. 1 og 20 (43 a method which gives dp/dt somewhat more accurately than taking differences on the vapour-pressure curve itself. The values of the latent heats have generally been smoothed by a curve before using in the equation for 0. Below are given the values of 6 anda for a number of substances, with L; determined in this way. Benzene. i v. v'. Lj. b. a, 0-2 eis 8141 101:0 0°8900 aly fe} 1°1341 3923 98-7 *8962 1671 x 10° 32°0 1°1544 1874 95:9 *8970 1:682 48°4 1:1784 1001 92:9 *8975 1-690 67:0 11-2070 538:0 89:0 *89 10 1-683 110°4 1:2812 164:2 80°1 “8820 1675 163°4 1:4008 53°93 68°3 “8600 1:673 181°4 1:4523 38°84 64:0 8512 1677 202°3 15225 26°97 59-0 8490 =| 1:707 300 Mr. 8. R. Milner on the Heats of It will be seen that the latent heats calculated from Clausius’s equation are slightly different from those given by Griffiths and Marshall, so that while 6 diminishes con- siderably at high temperatures, its substitution in van der Waals’s equation gives a very constant value of a through a wide range of temperature. The calculation of b becomes very uncertain at low and at high temperatures, so that no reliance can be placed on the result at 202°8 ; 6 would have to be still smaller than it is to bring a down to the normal value. Ethyl Oxide, (C,H;),0. Mol. wt. 84:0. | i v. v'. iby b. a. 0 1358 | 1209 86°16 1-054 20 1-401 5347 80-44 1043 | 1-803 10° 40 1-451 268-0 75°36 1-038 | 1-790 60 1502 | 147-7 70°81 1-081 | 1-786 80 1-562 86-60 | 6591 1-025 | 1-793 100 1-638 53:55 | 60-32 1012 | 1-778 120 1-735 34-09 | 54-90 1015 |1-816 140 1-857 29-98 | 47:32 | 0977 |1-768 160 2-021 1447 | 39°75 ‘977 |1-818 170 2-147 1145 | 3416 ‘951 | 1-808 180 9°343 8815 | 27-09 912 ) 4 190 2-730 6172) 1811 976 } | be V. Oe Li. b. a. 20 1:265 5899 266°5 1:036 5°82 x 10° 40 1:291 2276 2589 1:043 5°46 60 1324 993°8 249'6 1:052 DOU 80 1:360 479°8 2386 1:060 5-64 100 1-401 251°0 295-2 1:063 5°62 120 1-449 140-0 211°0 1:066 5:58 140 1:506 82°25 195:3 1:066 5:51 160 Soy (Ff 50-16 178°2 1:067 5°45 180 672 31:40 158-2 1:065 5°35 190 ivoo 24-94 147-4 1:066 5-32 200 1-808 19°70 1849 1:065 5:40 210 1:903 15e 119°5 1:055 Vaporization of Liquads. 301 Stannic Chloride, SnCl. Mol. wt. 259-3. | t. Vv, | Ole Li. b. a. | 140 0-5248 61:9 26:0 0:364 2°26 x 10° 160 O41] 39°9 24°5 363 2:26 180 “D095 26:6 23-0 359 2:25 200 5806 18°35 21°5 306 2-24 220 6065 12°94 20:0 307 2:28 240 6383 9°23 18-2 "354 2:29 260 6781 6°58 16:0 “B47 2:28 280 ‘7338 4°63 132 335 2°26 Methyl Formate, HCOOCH;. Mol. wt. 59°86. t: v. u. Li. b. a. 60 1:0949 167°0 96:2 0-7760 1°732 « 10° 80 1°1360 95°05 87°8 “7590 1°668 100 11831 58°45 82:0 "7560 1°682 120 1:2392 37°25 79-1 A475 1681 140 1:3092 24°25 15:5 "7390 1-688 160 1°4013 16:05 68:9 "7130 1-660 180 1-5336 10°60 48-0 6880 1°650 200 1°7675 6:56 34:0 6650 1:687 Ethyl Formate, HCOOC,H;. Mol. wt. 73°83. é. | v. v'. Li. b. a. 100 AS 7e7/ 97:0 76°88 0°8455 1°638 x 10? 120 1:2827 60:4 71:33 "8384 1:625 140 1°3427 39:1 65°64 °8326 1°622 160 1:4169 25°8 58°89 "8194 1°606 180 1°5129 17-4 50°69 "7900 1°560 200 1:6484 11:60 42°50 "7680 1°563 220 1°8902 7:25 30°34 T485 1597 Methyl Acetate, CH,;COOCH;. Mol. wt. 73°83. te v. Oe Li. b. a, 100 1:2163 103°5 79-67 0°8519 1:694 x 10° 120 1:2670 63:4 73°87 8478 1680 140 1:3276 40:7 67°78 *8421 1663 160 1:4020 26°80 61:22 8370 1:654 180 1:4991 17:60 53°22 “8329 1:648 200 1°6393 11°55 43°72 ‘8067 1639 220 1°8936 7-06 30°43 ‘7780 1:660 302 Mr. S. R. Milner on the Heats of Propyl Formate, HCOOC;H,;. Mol. wt. 87°80. % v. Qs" Li. b. a. 80 1:199 325 79°3 0:898 1:59 x 10° 100 1-238 184 75:3 “899 1-59 120 1-280 I s5) 10D *8938 1°56 140 1:329 70-4 66°7 "899 1:59 160 1°387 499 61:1 “888 1:56 180 1°455 30°9 545 860 iy | 200 1-542 21:2 49°0 "856 1°52 220 1-660 14:5 42-4 "849 ] ° 1°52 240 1-839 9°6 34:3 “860 f : 1:58 Hthyl Acetate, CH,;COOC,H;. Mol. wt. 87°80. te v. Os Li. b, a. | 80 1-213 285 77:4 0-903 1-58 x 109 100 1:254 162 74:5 ‘916 1:63 120 1302 97-0 70:0 918 1:63 140 1:°358 60°6 65:2 ‘918 1:63 160 1-422 38°8 58°4 900 1°57 180 1:503 29°79 5271 887 1°55 200 1-610 17-25 455 886 1°56 220 1-770 11°23 375 885 1:57 It will be seen by inspection of the tables, that while the value of 6 calculated from the heat of vaporization by equation (9) as a rule diminishes fairly considerably with the tempera- ture, that of a determined by its substitution in van der Waals’s equation remains approximately, and in some cases very accurately constant. The experimental quantities in the last two or three cases seem somewhat less accurate than in the others, and the numbers 6 obtained from them do not lie at all well on a curve—and as a shows itself very sensitive to the slightest changes in 0, its values here show somewhat large divergences. Still an inspection of the numbers at low and at high temperatures shows that the considerable diminution in 6 that takes place is of such an amount as to make the a determined from it approximately constant. The slow fall to a minimum and subsequent rise of a@ in some cases may be due either to some extent to experimental inaccuracy, or more probably to equation (9) not holding completely through a wide range of temperature,—as, indeed, with its assumptions it can hardly be expected todo. 2 id. Vaporization of Liquids. 303 Several other substances tried give a similar diminution of 6 and constancy of a. I have only come across two so far which have failed to do so, propyl alcohol and carbon tetra- chloride. In the first of these a shows a gradual and continuous decrease, and in the second an increase, for which it is difficult to see any reason. It may be as well to give the data for these substances :— Propy! Alcohol, C;H;,OH. Mol. wt. 59°86. ts | v. v'. Ti. b. a. 80 1:330 958-0 161°5 1:120 4:12 x10? 100 1:365 443 15271 1:130 4:09 120 1-406 225 141°0 1-182 3°93 140 1°455 124 130°4 Wen 37/ o'8l 160 F515 723 piel 1ei6y 3°60 180 1591 44-5 104°8 1:139 3°52, 200 1:689 28°3 91-4 1-120 3°30 220 1:823 18-0 out 1:095 a2 Carbon Tetrachloride, CCl, Mol. wt. 153°45. & v. v'. IDE: b. a. 60 0°6594 2982 43°0 0:4765 4°29 x 108 80 6773 163°5 41-2 "4760 4°33 100 ‘6972 97°5 39°55 A757 4:49 120 "7193 61:2 37°76 "4749 4°48 140 "7435 40°3 55°76 4720 4°51 160 "7703 27-4 33°50 -4665 4°53 180 *8019 19:05 80:90 “4565 4°49 200 8412 13°48 28:20 "4505 4°54 220 *8907 9°62 25°31 “4460 4:59 240 "9575 6°83 22°02 “4460 4-72 260 1:0628 4:66 ANS 4370 471 The examples given in the previous Tables seem sufficient to substantiate for the majority of liquids the validity of the assumptions on which the equation for the heat of vaporiza- tion is based. It is clear that, with the two exceptions mentioned, the internal heat of vaporization of these liquids will be accurately expressed by the equation pe Btn v' —b b b Par 434s 8a T yb ——5} (9) in which 6, although not constant, has a value satisfying 304 The Heats of Vaporization of Liquids. van der Waals’s equation, RT v being the volume of the liquid, and a an absolute constant. This is not quite the same thing as if b were eliminated between (9) and (14), which would give a Se Meret a lV ae Lis F5p log —2 + 5(5— 7) — gr») Peer as there is reason to believe that a varies a good deal from the liquid to the vapour, although it remains fairly constant in the liquid. However, at low temperatures, a/v? is negligible with regard to p, and p with regard to a/v*, so that in this case the total heat of vaporization would be sufficiently expressed by RT a a Le JM log pe 1 Je (transferring 3 p(v'—v) to the left-hand side of the equation). A calculation indeed shows that an equation of this form expresses it with considerable accuracy at low temperatures. Finally, the equation for the heat of vaporization throws ML T is roughly constant for different liquids, L being the heat of vaporization at the absolute temperature T of the boiling-point. an interesting light on Trouton’s well-known law that From equation (9) it will be seen that 7 is a quantity depending on », v’, and 0. But v’, which is the only quantity which would vary considerably from substance to substance, only enters in the logarithm, and in the denominator of a small term, and will consequently not greatly affect the result; again p and therefore is not greatly different for different v y) v—b liquids at corresponding temperatures, which may be consi- a : ML dered the same as their boiling-points. 7? therefore, at the boiling-point will not vary more than 20 or 30 per cent. for most liquids, which is about the extent to which Trouton’s law applies. [ 305 ] XLII. Notices respecting New Books. Vorlesungen wher theoretische Physik. HH. von HELMHOLTZ. Band V. EHlektromagnetische Theorie des Lichts, herausgegeben von ArTHuUR Konig und Carn Runner. Leipzig: Leopold Voss, 1897. HE publication of Helmholtz’s course of lectures on theoretical physics will be welcomed by physicists of every nationality. To be students under a Maxwell or a Helmholtz is a privilege accorded to the comparatively few, and of these fortunate disciples only two or three may feel themselves able to undertake the presentation of the thoughts and ideas of their master in their original form. We heartily rejoice that in the present case such volunteers have been found as Prof. Runge and Dr. Konig ; these will be assisted in the preparation of subsequent volumes by Dr. Krigar-Menzel. The volume now issued as a first instalment of the work is not the initial part of the course, but 1t was more easily edited than the rest because one of the students took down the lectures in shorthand at the time of their delivery. Nearly half the volume was revised by Helmholtz himself. After a short introduction dealing with the emission and wave theories of light and leading up to the mention of Hertzian vibrations, the equations of plane transverse and longitudinal waves are briefly discussed. Maxwell’s equations of the electro- magnetic field are then obtained in a very simple manner, starting from the experimental facts that magnetic lines of force form closed curves round an electric current, and that a change of linear magnetization gives rise to electric currents in closed circuits surrounding it; the co-existence of electric and magnetic polari- zations is thus established. The equations are afterwards trans- formed and applied to the case of a disturbed ether, with or without conducting matter, and it is shown that the waves set up correspond in type to the transverse waves in an elastic medium, the electric and magnetic dispiacements being at right angles to each other. The transition to optics is effected by means of Huyghens’s principle, which Helmholtz deduces from electro- magnetics by a generalization of Green’s theorem, introducing time as a fourth variable in addition to the three space-coordinates. Diffraction, interference, reflexion, and refraction are treated as in ordinary optics, the author returning to electromagnetics in the discussion of polarization and dispersion. A connexion between ether and matter is necessary in order to explain dispersion and magnetic rotation of the plane of polarization ; the author assumes that the molecules of matter contain two ions with equal positive and negative charges, and that under the influence of the electric field these ions may be drawn asunder or rotated round their centre of mass, which remains fixed. In an alternating electric field some of the energy of the Phil. Mag. 8. 5. Vol. 43. No, 263, April 1897. 2A 306 Notices respecting New Books. field is therefore used in maintaining the vibrations of these pairs of ions, which are damped by electrical and mechanical forces. By writing down the equations of energy and applying the principle of least action, results are obtained which represent the facts of dispersion and absorption with a fair degree of accuracy. The motion of the charged ions in a magnetic field gives rise to movements of the ether which set up electric and ponderomotive forces ; the effects of these are compounded with the electric and magnetic vibrations in the light waves, giving rise to two circularly-polarized waves which travel with different velocities. The theory has recently received some confirmation from Zeeman’s observations on the existence and polarization of broadened spectral lines from a source of light in a magnetic field. The volume is well printed, and appears to be remarkably free from the typographical errors which often occur in works of a mathematical character. The series, when complete, will rank as one of the most important treatises on modern physics. J. L.H. Magnetic Fields of Force. By H. Exserr, Professor of Physves m the University of Kiel. Translated by C. V. Burron, D.Sc. Part I. London: Longmans, 1897. So much has been written lately concerning scientific education in Germany, to the disparagement of this country, that it is encouraging to meet with a modern text-book for German students in which the principles adopted are essentially of British origin. By the labours of Faraday and Maxwell we were early taught the usefulness of the conception of lines of force, in explaining both electric and magnetic phenomena; it has, however, required the work of Hertz to finally eradicate from Germany and from science the theories of distance-action. Professor Ebert presents in this volume the principal facts pertaining to magnetism and electro- magnetism, and shows how they may be explained qualitatively and quantitatively by assuming that the magnetic field contains energy, and that force exists at every point in it. Venturing a step turther, he quotes Lord Kelvin’s deduction from the phe- nomenon of magnetic rotation of the plane of polarization, that lines of force are kinematically comparable with axes of rotation, and advances the theory that magnetism is due to a rotational motion. This leads to an interesting chapter on vortex motion and on cyclic motions in general; the latter subject, which was first treated by Helmholtz and Boltzmann and has received further development in Hertz’s ‘ Principles of Mechanics,’ serves as an introduction to the second part of the author’s work. We regret to note that the dimensions of magnetic quantities are specified on the assumption that permeability is a mere ratio. This is all the more remarkable in a treatise which traces magnetic phenomena to a motion of the ether, because the nature of such motion determines to some extent the absolute dimensions of the permeability of the medium. Dr. Burton has performed the duties of translator with great Notices respecting New Books. 307 skill; he has resisted the temptation to render a too literal trans- lation, without committing the more serious error of obscuring the author’s meaning.—J. L. H. Towa Geological Survey. Vol. V. Annual Report, 1895, with Accompanying Papers. 8vo. 452 pages, with 7 maps, 14 plates, and 72 figures in the text. Des Moines, 1896. THis volume contains reports on six Counties, drawn up on a uniform plan. They treat of the situation and area; previous geo- logical work in the district; the physiography, namely topography and drainage; stratigraphy, namely general relations of the strata, and the geological formations locally represented; typical expo- sures, including unconformities and deformations; economic pro- ducts and water-supply. The Geology of Jones County is reported on by Dr Samuel Calvin, the State Geologist. Harlier observations on the district by D. D. Owen, J. Hall, J. D. Whitney, C. A. White, and W. J. McGee are duly noted. The topography is described as dependent chiefly on the superficial deposits, modified by the drainage-courses. Of the solid or indurated strata, there are some fragmentary relics of Carboniferous beds, and large areas of Pleis- tocene and Silurian (Niagara limestones). The last at some places have enormous Corals, exposed by weathering into monumental masses. ‘The soils, including Geest, a “product of secular rock decay ;” building-stone, extensively quarried; lime; clays; and other products, as well as water-supply, are carefully dealt with. In Washington County, by Mr. H. F. Bain, Assistant State Geo- logist, the rock-masses are of Carboniferous (Mississippian) age. In Boone County (by Dr. 8S. W. Beyer) the Upper (Des Moines) Carboniferous series has useful coal-seams at some places. In Woodbury County (Mr. H. F. Bain) the Cretaceous system sup- plies the hard rocks; and these have always been of much interest to Geologists in the State; especially the upper series, namely the Colorado stage (consisting of the Niobrara Chalk and Benton Shale), and the Dakota stage with its interesting fossil flora. The Pleistocene deposits (‘ preglacial, glacial, and post-glacial”) are here, as else- where throughout these Reports, caréfully defined and illustrated with a map, views, and sections. In Warren County (Professor J. L. Tilton), besides the Pleistocene deposits, there are Carboni- ferous (Pennsylvanian and Mississippian series) strata yielding some coal. Appanoose County (Mr. H. F. Bain) has many coal-mines in active work. These Reports are full of well-described facts and careful con- siderations, useful to both student and teacher in geology, and, of course, highly valuable to the people of Lowa State. Most of the plates and many of the figures, giving views of exposures and of various parts of the country, have been reproduced from satisfactory photographs. The geological sections are some- what diagrammatic but useful. The maps are doubtlessly exact. Tbe several tables of contents and the general index are very good and of great service to those consulting the work. 308 Notices respecting New Books. Autobiographical Sketch of James Crow, LL.D., F_RS., §e. With Memoir of his Life and Work, by JAMES CAMPBELL IRons, M.A. 8vo. 550 pages, with two portraits. 1896. Stanford, London. TH autobiography (pages 9-41) given in James Croll’s own words, as dictated to his wife three years before his death, contains the principal incidents of his life, as recollected and thought over himself, down to 1887. His chronic headaches, pressure of work, and disinclination for the task allowed of no diffuse treatment of the many interesting points in this brief per- sonal history. In the body of the book Mr. J. C. Irons, with the intimate knowledge of a warm and sympathetic friend, has elaborated this short life-sketch, enlarging it with collateral information from friends and correspondents into a very complete biography of James Croll, and a useful and interesting résumé of his intellectual work. In his youth he had very little schooling and much hard work ; first, in his father’s croft, and afterwards as a wheelwright and joiner. He was not a sharp lad; but a taste for reading came when he got the first number of the ‘ Penny Magazine,’ at Perth, in 1832, Dick’s ‘Christian Philosopher, and Joyce’s ‘ Scientific Dialogues.’ Making a systematic attempt to learn something of the physical sciences, he was more attracted to the laws and con- ditions on which their facts and details depend than to the results and phenomena themselves. Thus directing his attention mainly to general principles, he found himself better able to grasp the meaning and bearings of the subject of study; and he states that his early acquaintance with the general principles of physical science was of great service in his researches in after years. He felt, however, that the strong natural tendency toward abstract thinking somehow unsuited him for the practical details of daily work. | Habitually meditative, with strong religious sentiments, and brought up in the thoughtful communion of his Scotch co-religio- nists, he felt keen interest.in the controversies between Armi- nianism ard Calvinism, toMhe former of which he was attached. But after careful study of Edwards’s work on ‘Free Will, and Tappan’s ineffectual criticism of that book, and after having “‘gone over thirty or forty treatises on the freewill controversy,” he found Edwards’s conclusions to be sound; and ‘“* became convinced that some moderate form of Calvanism was nearest the truth, not only of philosophy, but also of Scripture.” Had he been able to afford it, he would have been inclined to devote his time to the study of Philosophy, his mind having been benefitted and ideas enlarged, first by Edwards and then by Kant. A long-standing disease of the left elbow-joint became too bad in 1846 for manual labour; and James Croll found a friend (Dr. Irons) in Perth, who helped him with stock and advice to set up as a tea-dealer at Elgin. In 1848 he married Isabella Macdonald of Forres. With strong and persistent effort he gave up smoking ; Notices respecting New Books. 309 he had always been an abstainer from drink. After this time the elbow-joint became badly inflamed, and ultimately was anchylosed. Having had to give up his business on account of bad health, he tried engagements with Assurance and other Societies at various towns, and a Temperance Hotel at Blairgowrie; and ulti- mately was engaged on the ‘Commonwealth’ newspaper at Glasgow (1858). Of late years he had had some leisure tor read- ing, but it brought on pain in the eyes (instead of at the top of the head), and this continued for several years. His principal reading was on questions relating to “liberty ” and “ necessity ; ” and this led to Theology and Metaphysics. His thoughts on the metaphysics of Theism were published in 1857 in his ‘ Philosophy of Theism.’ In 1859 James Croll was appointed to the charge of the Ander- sonian College and Museum in Glasgow. He had already suffered from what appeared to be a heart-affection, interfering with active exertion; but in 1865, whilst stooping, a sudden twitch in the upper left side of the head was followed by a dull pain, which became unbearable if mental work was continued for any length of time. Though his general health was good, any overwork was followed by disability for some days. Nor could he ever atter- wards concentrate his thoughts to the overcoming of a difficulty at one stretch. The free use of scientific books belonging to the Institution itself and to the Glasgow Philosophical Society decided the balance in his mind between the love of physics and the love of philosophy, in favour of the former, at least for a time. Among the modern subjects of physical research, which were then discussed by a goodly band of sympathetic scientists at Glasgow, that relating to the cause of the Glacial Epoch especially attracted Croll’s atteution. Once more settled, and with congenial surroundings, in the old Glasgow college, he was expecting to do some steady work in his favourite lines of thought; but the painful condition of head and eyes sadly checked him. He gave his energies conscientiously to the daily duties of the place (in which his brother helped him) ; and, courageously fighting against difficulties, as he had all his life through, he managed to write several papers, long or short, whilst he remained as keeper at the Andersonian College. The first of these, relating to Ampéere’s Electrical Experiment, was published in the Philosophical Magazine, April1861. Other papers followed (many of them in the Phil. Mag.), treating of Electricity, Heat, Gases, Chemical Affinity, Tides, Climate, the Glacial Epoch, Sub- mergence and Emergence of Land, and the Eccentricity of the Earth’s Orbit. In 1867 Mr. Croll was asked to give his services as Resident Surveyor and Clerk, or Secretary, in the Office of the Geological Survey of Scotland, at Edinburgh. After some hesitation he allowed himself to be nominated, and submitted to the regular Civil Service examination. Though he did not satisfy the every- day examiner in ordinary “arithmetic” and “ English,” his great calculations regarding the eccentricity of the earth’s orbit and the 310 Notices respecting New Books. precession of the equinoxes during many millions of years, and his book on the Philosophy of Theism, with his numerous published papers, were duly accepted (after some pressure against ‘red tape”) as sufficient evidence of arithmetical capacity, and proof of ability to write good English. Thus the Director-General of the Survey secured the services of a highly-prized scientific and philo-. sophic worker, in spite of the rigid rules of the Treasury and Civil Service Commission. His researches on the causation of physical phenomena were continued in his spare time, chiefly in his walks, and evenings at home; and many other papers were published on the above- mentioned and other subjects, as Gravitation, Denudation, Inter- glacial periods, Glaciers, Gulf-stream, Oceanic Currents, Ice-sheets, Thickness of Sedimentary Rocks, Age of the Earth, Molecular Motion, Kinetic Energy, the Sun, Nebule, Climate and Cosmology, and Evolution. In 1875 the essence of his published notes and memoirs, and the results of his observations, had been embodied in the highly esteemed volume ‘Climate and Time; A Theory of Secular Changes of the Earth’s Climate.’ This was written with great difficulty, for the cephalic pains greatly limited his oppor- tunities of writing down his thoughts, and his health often failed. In 1876 St. Andrew’s University gave him the degree of LL.D., he became a Fellow of the Royal Society, Hon. Memb. New York Acad. Sci., of the Bristol Nat. Soc., Psychol. Soc. Gt. Brit., Glasgow Geol. Soc., Lit. Antiq. Soc. Perth, and the Perthshire Soc. Nat. Sci. The Geological Society of London awarded him the balance of proceeds of the Wollaston Fund in 1872, of the Murchison Fund in 1876, and of the Barlow-Jamieson Fund in 1884. In 1880 Dr. Croll got a strain in the office, which, with his other painful affections, disabled him. On resigning his appoint- ment he was, to his grief, not favoured with any more than a very meagre pension fixed for his thirteen years’ service on the most stringent rules. Applications made to Government for a grant from the Civil List were without effect. After giving to the world a few more papers or memoirs on the physical subjects in which he had been so much interested, Dr. Croll published in 1885 in one volume, entitled ‘Discussions on Climate and Cosmology,’ 8vo, Edinburgh, the results of his labours since the publication of ‘Climate and Time’ in 1875. With scrupulous and self-denying economy Dr. Croll utilized the proceeds of his published books in procuring an annuity, small as it was, for himself and his devoted and beloved wife. Some aid came from friends and from the Royal Society’s special fund; and he settled quietly at Perth not far from the place of his first home. Suffering, but patient; clear-headed and desirous of imparting his knowledge, but unable to do so except by dictation to his always helpful wife, he remained long enough to see the printed sheets of his latest book. He was always amiable, candid, consistent, and conscientious. The high respect with which he was regarded by all, and the warm Notices respecting New Books. 311 affection and sympathy felt for him by his friends, were well known in his lifetime, and are now plainly shown by the voluminous, but valuable, correspondence and the obituary notices preserved in this Biography. _ he titles of 92 of Dr. Croll’s books and memoirs, from 1857 to 1890, are catalogued at pages 527-535. The following remarks are applicable to some of them, more particularly of 1857, 1864- 75, and 1883-90. “‘ His first work, entitled ‘The Philosophy of Theism,’ published in 1851, at the age of thirty-six, endeavoured to define the relation ot Theism to the determination of molecular motion. He tried to show that, for the production of any organism, two things are necessary,—first, motion; second, the determination of motion. Mere vital force might account for motion, but the determination of motion implies an idea, design, and a directing mind” (page 507). “To Dr. Croll belongs the rare merit of showing that, though glacial cycles may not arise directly from cosmical causes, they may do so wndirectly. His first contribution to the subject was pub- lished in 1864, but the development of his theory resulted in a series of brilliant researches extending over a period of eleven years, to 1875. He was led to investigate the problem of the eccentricity of the earth's orbit and its physical relations to the Glacial Period. By means of Leverrier’s formule, he calculated tables of eccentricity for three million years in the past and one million years in the future, with the view of determining the periods of high eccentricity, which according to his theory were coincident with cycles of extreme cold. He was further led to consider the various physical agencies affecting climate, resulting from periods of high eccentricity, of which by far the most impor- tant is the deflexion of the ocean-currents”’ (see page 510). The cause of these was a subject of much discussion ; and “these various lines of research are intimately associated with the fundamental question of the physical cause of climatic change.” “Dr. Croll’s investigations into the geological history of terres- trial climate had led him to consider the question of the origin of the sun’s heat, and thence to reflect on the possible condition and development of nebule and stars. The latter chapters of the” ‘ Discussions’ &c. above mentioned ‘were devoted to these sub- jects, which he would fain have discussed more at length, had not the increasing failure of his bodily powers warned him that, if he wished still to return to that philosophy which was his first love, he must husband his remaining strength. Nevertheless the attrac- tion of these astronomic problems proved insuperable. He continued to work at the subject, enlarging the scope of the investigation until it embraced not the earth and the sun merely, but the origin and development of the whole material universe. At last he fol- lowed his usual method,—gathered together his various contribu- tions to the subject, trimmed, enlarged, and modified them, and published them in a separate volume, entitled ‘Stellar Evolution in its Relation to Geological Time.’ The publication of that work marks the close of his labours in more definite scientific inquiry. 312 Geological Society :— He was now free with such remaining strength as he could com- mand to re-enter the field of philosophic speculation, in which he had spent his earliest years of mental exertion, and which for nearly thirty years, through all the engrossing attractions of geo- logical inquiry, had never Jost its fascination for him. Accordingly he betook himself once more to the study of such subjects as force, matter, causation, determinism, evolution, &c., and proceeded to apply the facts and principles with which he had in the interval been dealing so actively to the problems in philosophy that had aroused his thoughts in the early years of his life. In spite of his increasing infirmity, he persevered in committing to writing the ideas which he had now formed, and he sent to press his last work, ‘The Philosophical Basis of Evolution,” in 1890. (See page 004.) He died December 15, 1890: aged 69 years. XLII. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. (Continued from p. 240.] January 6th, 1897.—Dr. Henry Hicks, F.R.S., President, in the Chair. HE following communications were read :— 1. ‘On the Structure of the Skull of a Pliosaur.’ By C. W. Andrews, Esq., B.Sc., F.G.S. 2. «On the Pembroke Earthquakes of August 1892 and November 1893. By Charles Davison, Sc.D., F.G.S. Part I. of this paper deals with the earthquakes of August 1892, of which eleven are recorded, the principal being the third. The author gives an account of the preliminary shocks and after-shocks, and a detailed account of the principal earthquake, describing the disturbed area, the relationship of the earthquake to a north-and- south fault, hading to the west, that of sound to shock, and the occurrence of sea-waves. Part II. treats of the earthquakes of November 1893 ; there were four undoubted earthquakes, of which the first was the chief one. Descriptions are given of the phenomena. Part III. treats of the origin of the earthquakes and their connexion with faults; and the author points out the possible value of the study of earthquakes in supplementing geological surveys. For more than fifty years prior to the earthquakes of 1892-93 there appear to have been no slips of importance along the fault-system of the area. After this prolonged interval of repose, the earlier movements took place along transverse (north-and-south) faults, and the later along longitudinal (east-and-west) ones. The three faults of the latter series which the author connects with the disturbances lie successively one to the north of the other, as if the abrupt displacement of a rock-mass over one thrust-plane impelled Changes of Level in the Bermuda Islands. 313 the advance of those immediately below. There can be little doubt that the fault-slips of 1892 affected the conditions of stress along the neighbouring transverse fault, so that the displacements along it occurred earlier than they might otherwise have done. 3. ‘Changes of Level in the Bermuda Islands.’ By Prof. Ralph S. Tarr. The author gives a summary of previous writings bearing upon the geology of the Bermudas; but his own researches point to a rather more complicated series of changes than those which have been inferred by other writers. The formation of the ‘ base-rock ’ or ‘ beach-rock ’ occurred at some period which cannot be accurately ascertained at present, owing to the fragmentary nature of the included fossils. It may have been formed in Pleistocene or even late Tertiary times. After its formation it was converted into a dense limestone and then eroded, probably by subaerial agents, and finally attacked by the waves at an elevation of at least 15 feet above present sea-level ; during this stage it was covered by beach- deposits of pebbles and shells, which were accumulated in a period so recent that the contained fossils are of the same species as the organisms living in the neighbouring sea. Then followed an uplift, during which land-shells lived on the beach-deposits ; but these were soon covered by blown sand—the principal accumulations of the islands, and the outline of the islands was perfected by the action of the winds. ‘This was done at an elevation which was at one time certainly as much as 40 or 50 feet above present sea- level. The author adduces evidence of a depression since this accumulation, causing land to disappear and the outline of the area to become very irregular; and he proves that these changes cannot be accounted for solely by erosion, as some have maintained, There are indications that the land is at present quiescent. It appears, then, that most of the work of construction of the Bermudas has been done in recent times. January 20th.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read:— 1. ‘On Glacial Phenomena of Paleozoic Age in the Varanger Fiord.’ By Aubrey Strahan, Esq., M.A., F.G.S. The Gaisa beds of the Varanger Fiord consist of slightly altered quartz-grits, with red sandstones and shales, and rest upon a deeply denuded surface of the metamorphic rocks. In a section, first noticed by Dr. Reusch, a heterogeneous mixture of grit and clay with boulders of granitic and other rocks is seen to be intercalated between the quartz-grits, the bedding of the overlying grit proving that this boulder-rock was contem- poraneously formed, and not subsequently wedged in. The surface of the grit below the rock is characteristically glaciated. Proof is given that the striated surface is not the floor of a thrust-plane, Phil. Mag. 8. 5. Vol. 48. No. 263. April 1897, 25 314 Geological Society. and that the boulder-rock is not a fault-breccia or a crush-conglome- rate, but a ‘till.’ In the absence of fossils the Gaisa formation is doubtfully assigned to an early Paleozoic age. It exhibits the same sedimentary characters as the rocks of later date in other parts of the world in which glacial phenomena have been observed. The glacial episode is attributed to a temporary change of climate rather than to the high latitude in which the section lies. 2. ‘The Raised Beaches and Glacial Deposits of the Varanger Fiord” By Aubrey Strahan, Esq., M.A., F.G.S. The Raised Beaches range up to nearly 300 feet above the sea. Though a number of impersistent shingle-banks occur at various heights, the highest is constant, and can be traced along the same level either as a shingly terrace or by a zone of wave-worn rocks. Evidence is furnished by the relative size of different parts of the beach that the prevalent wave-action was from the west, and by the greater abundance of erratics on or below the beach than above it, that floating ice was at work. At the head of the fiord a blue clay dotted over with stones is now being formed, and the raised beach there consists of a similar material. Both here and elsewhere this clay simulates a Boulder Clay; but for reasons given it is believed to be a marine fiord- deposit, into which many stones have been dropped by floating ice. Deposits of true glacial age, in the form of mounds of gravel, are described, and shown to have yielded the material out of which parts of the Raised Beaches are formed. The glaciation of the fiord is attributed to floating ice, and is shown to have taken place before the formation of the Raised Beaches, at a time when the sea sur- rounded this part of Finmark, by way of the Varanger Fiord, the Tana Valley, and the Tana Fiord. February 3rd.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read :— 1. ‘The Subgenera Petalograptus and Cephalograptus.’ By Miss G. L. Elles. 2. ‘On some Superficial Deposits in Cutch.” By the Rev. J. F. Blake, M.A., F.G.8. The author arranges the deposits of which he treats under the following heads :—1. Subrecent Concrete; 2. Boulder Beds asso- ciated with the former; 3. Quartzite Reefs; 4. Infratrappean Grits; 5. Laterite; 6. Alluvium and Rann. 1. The Subrecent Concrete consists of a calcareous, porous, lami- nated sand with milioline remains, which extends to a height of about 700 feet above the Rann, and has a discontinuous distribution. The author gives reasons for regarding this as an eolian deposit, partly derived from recent marine accumulations and blown inland and uphill by the prevalent winds. Intelligence and Miscellaneous Articles. 315 2. The Boulder Beds are next described, their distribution noted, and their occurrence with eolian deposits recorded. The author argues that the xolian deposits once had a greater slope, and acted as carriers, so that, under the influence of rain, the stones from the hills slipped to their present position. 3. The Quartzite Reefs are described as filling up cracks; the material is of xolian origin and derived from the surrounding rocks, and owing to this material having been formerly at a lower level than the latter, water stood on it for a sufficiently long time to permit of the materials being cemented by a siliceous deposit, and converted into quartzite. 4, The Infratrappean Grits are maintained to be superficial deposits on the pre-trappean land-surface, some being the ordinary results of weathering, others due to the washing down of débris to a water- covered level, and others again simply eolian drift. It is thus seen that there has been constancy in the meteorological conditions of Cutch from recent times as far back as the Cretaceous period. 5. The Laterite-deposits of the district occur to a height of only 120 feet above the Rann. There is evidence that they were laid down in water at a time when the surface of the country was not very different from the present one. ‘The material may have been partly derived from Jurassic rocks, but some of the constituents, as the eroded agates, must have come from the trap-rocks. 6. The Rann is an area which has recently been abandoned by the sea, owing to unequal movements, but there is evidence that deposit has also taken place in it, and the depression has become shallower, so that in course of time the whole surface will be made of alluvial or xolian soil. XLIV. Intelligence and Miscellaneous Articles. GALVANOMETER DESIGN. To the Editors of the Philosophical Magazine. GENTLEMEN, eS me to acknowledge the courtesy and entire correct- ness of Professor Gray’s recent letter (Phil. Mag. January 1897) respecting my note on Galvanometer Design (Phil. Mag. December 1895). Professor Gray perfectly apprehends my point of view in the matter, and very clearly indicates the nature of the omission which constitutes my error. That this was its nature I had already discovered in reflecting upon the note by Professors Ayrten and Mather (Phil. Mag. November 1896). It had been my intention to briefly point out the fact as soon as some additional experimental data could be obtained. But as this would probably cause some further delay, owing to my inability to participate in active work, I take the opportunity afforded by Professor Gray’s remarks to recognize the correctness of the 316 Intelligence and Miscellaneous Articles. demonstration by Messrs. Ayrton, Mather, and Sumpner in their original paper. It may be well, however, to note that this con- clusion does not vitiate the inferences which were the main point of my former paper, namely, the comparative inefficiency of the central portion of the coil, even if wound in reverse order, and the consequent importance of employing exceedingly short needles. Sitas W. Honman. Boston, Mass., February 18, 1897. ON MAGNETIC AFTER-ACTION. BY PROF. IGN. KLEMENCIC. The magnetic induction which is observed in soft iron wires which have been annealed for some time, and are placed in weak fields, is made up of two parts; a fact established by Ewing (Phil. Trans. 1885, p. 569, and Proc. Roy. Soc. 1889) and Lord Rayleigh (Phil. Mag. 1887). One part follows the production or cessation of magnetizing force; the second part begins after the termination of the former, and develops itself very slowly, so that the intensity of magnetization attains its final value only after some minutes. The phenomenon of a time retardation was denoted as ‘‘creeping” or viscous hysteresis; it is here called ‘magnetic after-action.” Itis very probable that the establishment of magnetic after-action in the middle of the wire proceeds more rapidly than at the ends. Magnetic after-action occurs mostly in weak fields; it diminishes with the strength of the field, and the more rapidly the thinner the wire under investigation. No regular connexion between the magnetic after-action and the thickness of the wire could be made out, probably owing to unequal annealing. Strong magnetizations of the wires in no wise affect their mag- netic after-action. Magnetic after-action is a transitory phenomenon, which is only observed in freshly-annealed bars.— Wiener Berichte, March 1897. MAGNETIC INFLUENCE ON LIGHT-FREQUENCY. The footnote on page 232 (March no.) was by the communicator, not the author, of the paper; and he notes that the simplest way of putting the elementary theory, for an ion or electron revolving in an orbit of fixed size but any shape, is to write the radial magnetic force as d(mrw*)= ¢ Bu, whence 27n=dw= eB/2m, n being the magnetically-caused change of frequency, and B the density of magnetic induction, or »H.—EDps. THE LONDON, EDINBURGH, anv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] i s* MAY 1897. a eee XLV. On the Resolving Power of Telescopes and Spectroscopes for Lines of Finite Width. By F. L. O. Wapsworts *. 2) es question of the theoretical resolving power of optical instruments has been discussed by a number of writers— most fully and comprehensively by Rayleigh ¢, who has shown that the theoretical angular resolving power of any instru- ment having an aperture of width 0 is a =m Be where @ is the b angle between two fine lines or points which can just be separated (two stars for example), A 1s the mean wave-length of light, b the linear aperture of the instrument, and m a constant varying from unity for a rectangular aperture to about 1°1 for a circular aperture. It is possible to determine at once from this expression the spectral resolution or separation of a spectroscope, by remembering that the function of the dispersing train, which may consist either of prisms or of a transmission or reflection grating, is simply to form a series of spectral images of a single source,—the slit of the spectroscope. Of these images only those will be resolved or separated for which the difference in angular dispersion is equal to or exceeds the angular resolution @ of the spectroscope aperture. In the case of the spectral images * Communicated by Lord Rayleigh, F.R.S. T “Resolving or Separating Power of Optical Instruments,” Phil. Mag. Oct. 1879, p. 261. “ Resolving Power of Telescopes,” Phil. Mag. Aug. 1880. ‘The Manufacture and Theory of Diffraction Gra‘ings,” Phil. Mag. 1874, p. 5. Also articles on Optics, vol. xvii, and Wave Theory, vol. xxiv. Enc. Brit. Phil. Mag. 8.5. Vol. 43. No. 264. May 1897. 2C 318 Prof. F. L. O. Wadsworth on the Resolving Power of of a slit this resolving power is in general less than the theoretical resolving power for infinitely narrow lines: (1) because of the finite angular width of the slit; (2) because of the dispersion of the spectroscope train, which for radiations which are not monochromatic produces the same effect as a widening of the slit. Theoretically we shall distinguish between four cases :— 1. The resolving power (theoretical) of a spectroscope train for an infinitely narrow slit and monochromatic radiations, 2.¢., infinitely narrow spectral lines. This is the quantity usually denoted by r. 2. The resolving power (also theoretical) for a wide slit and monochromatic radiations. Usually denoted by gp, the “purity ” of the spectrum. 3. The resolving power (limiting) for an infinitely narrow slit, but for lines of finite width AX. This quantity we will denote by R. 4, The resolving power (practical) for a wide slit and non- monochromatic radiations ranging for each line over a small value AX as in (3). This quantity, which represents the practical resolving power or purity of the spectrum, will be denoted by P. Let D= aed be the angular dispersion of the spectroscope train. The spectroscopic resolution for any case is defined by the ratio = where dd is the difference in wave-length of two lines of mean wave-length, >, that are just resolved. Therefore for the first case or poy, 1... a perfectly general relation which holds good whatever may be the nature, form, or arrangement of the spectroscope train. d@ dé dn . Introducing the values of D = > dna obtain at once the usual expressions . sin — Z nih a/ 1=ntsin’ 2 ee . . a | | J r=2Nb dn = (¢;—¢,) dx Telescopes and Spectroscopes for Lines of Finite Width. 319 for a train of N prisms of refracting angle ¢ through which the rays pass at minimum deviation, and mn T= Tiros QO eS om eee (3) for a grating of n lines. In the case of the grating the expression for the resolving power may be put into a form which will bring out more clearly one fact that is not generally emphasized in the theory of the gratings, z.e., that for a given position of the grating, the resolving power is independent of the number of lines n and is determined, as in any optical instrument, simply by the linear aperture 6. This proposition may be very simply proved trom the fundamental equation of the ditfraction- grating, Mr =s(sinz +sin @). Multiplying both sides by n we get mnd=ns(sinz+sin@). . . . . « (4) But mn=r and ns=b the linear aperture of the grating. Hence r= (SUELO EIST) IT ahh Sect So (5) an expression which is independent of n and depends only on 6 and on the position into which the grating is turned. The maximum value of v is that for which 2=@=90°. Then we have fax. = 2 x ’ which shows that the resolving power of a grating is an expression of the same form as the corresponding expression for a microscope, telescope, and reflecting mirror. The maximum resolving power is the same (though expressed in different units) as that for a mirror of the same horizontal aperture. This theoretical maximum, however, can never be realized, because for large angles of incidence and diffraction the angular aperture of the grating becomes very small, and the light consequently excessively faint. In practice the angle of incidence i never exceeds 60° for an angle of diffraction 8=0, nor more than 45°-50° when the angles of incidence and diffraction are equal (Littrow type). Hence maximum practical resolving power, which we will call 7, varies from rae 2C 2 320 Prof. F. L. O. Wadsworth on the Resolving Power of If we take the higher limit we find that the limit of resolving power of the best and largest gratings now in use (ruled surface 54 inches) is for the middle part of the spectrum (A='00055 mm.) about 375000 units, just sufficient to “resolve”? a double line whose components are about 016 tenth-metres apart. The view at one time held that higher resolving powers than this were unnecessary because of the discontinuities in a train of light-waves is now known to be erroneous. Michelson’s recent work has shown that some of the spectral lines which appear single in the most powerful spectroscopes yet constructed, are in reality very complex, consisting of three, four, or even more components whose distance apart in some cases is probably not much more than 0-006 tenth-metres. ‘To resolve these by means of a grating, we need, therefore, instruments having at least three times the aperture of those now in use. Were the interferometer or wave-comparer universally applicable in spectroscopic analysis, there would be little occasion to attempt to rival its performance by gratings, but it is unfortunately only applic- able to the more intense of the bright lines of a spectrum. For the more detailed study of faint lines, and absorption- lines, gratings of larger resolving power than have yet been constructed would seem to be the first essential. The mechanical difficulties to be overcome are very formidable. | The chief difficulty does not seem to lie in the production of a screw of sufficient accuracy, since. by Rowland’s method we are enabled to produce a screw of the required length in which the errors of run, periodicity, &e. are less than those unavoidably introduced by eccentricities in the mountings and divided head*; but in avoiding the errors of spacing caused by unequal wear of the ways on which the ruling- point carriage moves, and in maintaining sufficiently constant temperature conditions during the ruling. How great these difficulties actually are may be better appreciated when it is remembered that to rule a 15-inch grating (of 20000 lines per inch) the ruling-engine would have to run continuously for nearly two weeks (a 6-inch grating requires five days and nights), that in such a grating a dis- placement of one five-hundred-thousandth part of an inch in the position of the lines in any part of the grating would greatly impair the definition and resolution in any order higher than the second, and that such a change would be brought about by the smallest amount of unequal wear, or even by a slight change in thickness of the film of oil on one of the ways of the ruling-carriage, or by an unsymmetrical * See Rowland’s article on the Screw, Hnc. Brit. vol. xxi. Telescopes and Spectroscopes for Lines of Finite Width. 321 change of temperature of the grating or of parts of the ruling- engine of less than °C. But the immense value that such large gratings would have in rendering possible a more detailed study of the complex character of spectral lines, and a more exact determination of their wave-length under varying conditions of production, would seem sufficient to amply justify any expenditure of time and money necessary to make their production possible and practicable*. It is worth while remarking that the independence of resolving power of the fineness of ruling, already pointed out, makes it possible to considerably reduce the time and diffi- culties of ruling large gratings by very considerably increasing the grating space, provided only that ruling-points can be found (by trial) which will produce gratings sufficiently bright in the higher orders. The two objections usually urged to coarse-ruled gratings are the increased overlapping of the different orders of spectra, and the increased accuracy of spacing required. I have recently shown how the first objection may be overcome by a very simple and efficient optical device placed in front of the spectroscope slitt. The second objection is not a valid one. It has been shown (Rayleigh) that in a given grating the allowable error in the spacing s is +s in the first order, $s in the second, 75s in the third, or in general = s. But for a given resolving power, i.¢e., for a given aperture and given position of erating, we have from (4) — =constant, or for two gratings of the same aperture but of different spacing, s and sj, my _ SOLS 8 The limiting absolute error of ruling is therefore the same in both fine and coarse-ruled gratings. If, for example, the absolute error of spacing of the ruling-machine is imsono inch, equally good definition would be obtained by ruling the grating with 20,000 lines to the inch, and using the first order spectrum only, or by ruling it 4000 lines to the inch, and using the fifth spectrum. But the last grating would * The writer has just finished the design of a large ruling-engine, the money for the construction of which has been given by a friend of science in Chicago. Work on it has been begun in the instrument-shop of the Observatory, and every possible precaution will be taken to ensure success. + The ‘ Astrophysical Journal, March 1896, vol. iii. p. 169, 322 Prof. F. L. O. Wadsworth on the Resolving Power of require only 1 the time for ruling, and hence in general would be only 4 as difficult to make as the first one. The question of the relative brightness of the spectra in the two gratings would be, as already stated, almost entirely a question of the selection of a ruling-point. Let us now consider the resolving power of a spectroscope for wide slits (width s) and monochromatic radiations. The formula ordinarily given for this is » : i aee 2 Se ee e e e e ° e (6) This is based on the assumption that for distinct resolution of wide lines, the angular distance between the contiguous edges of the two lines must be equal to the resolving power of the aperture through which they are viewed. According to this assumption the angular distance between the centres of the two lines of width s, which would be just resolved, would have to be a(oh +mrf)=(-+m5)= t(sptmr), » (7) where is the angular magnitude of the aperture 4 as viewed from the line s, f is the distance of the line itself from the lens, and 7” the focal length of the observing telescope. But I have recently found that it can be shown, both by theory and by experiment, that this assumption is incorrect, and that the resolving power of an instrument for wide lines is considerably greater than is indicated by the above expression. As this point has apparently escaped notice heretofore it may be considered a little in detail. The diffraction-pattern due to a line of width s, or angular width a= , 1s found by integrating the effect due to each linear element over the whole width of the line. In the case of a rectangular aperture the diffraction-pattern due to each linear element is represented, as 1s well-known, by the equation sin?™ ¢ JE Ot rarer 2 5 e ° ° . (8) aes ¢ being the angular distance from the centre of the diffrac- tion-image. ‘The intensity at any point y due to the effect of Telescopes and Spectroscopes for Lines of Finite Width. 323 all of the elements of a line of uniform brightness will there- fore be wolq sin?” (y— 9) PS0) == .... 0) eee a sin? =’ TX dy=f (yy). + (10) Om) x | The value of the definite integral (10) cannot be found directly in terms of y and a, but it can easily be evaluated by mechanical quadrature for different values of these variables. For c=a, which is about as small a value as is ever used in practice, the values of I’=/(y) are given in Table I. For the sake of comparison the values of I (from 8) are also included. TABLE I. y: I'=f(y). I. y: IV=/'G)). J. 0 1:00 1:00 8 24 055 2 92 87 10 11 000 4 71 D7 1:2 044 024 6 "45 25 15 030 "045 The diffraction-curves represented by these values are plotted in fig. 1 (p. 324). Like I, the curve I’ does not fall off regularly, but passes through a series of maxima and minima whose position is given by the general equation* myo Vee 9 1 7 2, TO o = —-| =) = — Augie Ya, tan— = 5 tan Jy tor 2Qm T¢= < dm. TO (oy tan 5— for 2m << 2m+ iL * This part of the problem, z.e., that of locating the position of the minima in the diffraction-patterns of a slit and of a circular aperture of finite width, was worked out by the writer (at the suggestion of Professor Michelson) about six years ago, while a student at Clark University. The results were published in Professor Michelson’s paper on “ Applica- tion of Interference Methods to Astronomical Measurements ” (Phil. Mag. July 1890, p. 1, see pp. 14-17). 324 Prof. F. L. O. Wadsworth on the Resolving Power of In this case c=a, and we have therefore bai cor Dy, a or y — lage Dae 02 ese or the minima occur at points 4« further from the centre than when the source is a line of negligible width*. Piece 2.0 1.0 oO j 10 20 The integral was evaluated in the same manner for different values of o both smaller and larger up to o=3a. The diffrac- tion-patterns of two sources of width o=a and o=8a are shown in fig. 2, in dotted lines. In order that a double line may be resolved it is necessary * Since the position of the minima in this case depends on the angular magnitude of the source o as well as on the aperture of the telescope, it follows that by covering the objective of the latter by a rectangular opening of known size, and then measuring by means of a micrometer the positions of the minima of the diffraction-pattern, the value of o may be determined from the above equations, Experiments on a large number of slits of varying width and holes of varying diameters (for which the positions of the minima are slightly different) showed that when the source was sufficiently bright to give well-marked minima, single observations gave results which were at least five times as accu- rate as could be obtained by direct micrometric measurement of the image with full aperture of the telescope. This method is, however, con- siderably less accurate than the refractometer method of Professor Michelson which is fully described in the earlier part of the paper referred to, and the observations are therefore not given at length. Telescopes and Spectroscopes for Lines of Finite Width. 325 that the intensity at the centre of the diffraction-pattern of the double source (shown in full lines in fig. 2) should be Fig. 2. eat Soe iw about 0°8, the intensity at the maxima corresponding to the centres of the two geometrical images. In order that this may be the case the distance between these centres in the three cases c=a, c=2a, and c=3a must be for o= a,angular distance between centres=1:°27a=oc + 0'27a, g=2a, ,, ” ” » =22la=o+0-2la, = ae 99 3 » =3'20ae=o+0°20a, or in general " " ea ea ay From these and intermediate values the curve in fig. 3 (p. 326), which represents the relation between the angular width of the lines and the angular distance 6 between the con- tiguous edges necessary for distinct resolution, was plotted. In order to test these results experimentally a fine black wire was stretched across the centre of an ordinary double motion slit, thus forming two parallel slits whose widths could be simultaneously varied (by opening the slit), while the distance between the contiguous edges (which was equal to the diameter of the wire) remained constant. The two slits were uniformly illuminated by the light of the sun or an electric arc passing through a screen of white paper, and were viewed by a telescope over whose objective was placed a rectangular opening of width 0. The slit was set at various measured widths, and the dis- tance of the telescope from it varied until the two halves of the slit were just resolved. If D represents the distance of 326 Prof. F. L. 0. Wadsworth on the Resolving Power of the telescope from the slit, d the diameter of the wire, and S the whole length of the slit, we have evidently o Sd b be ea Ba and 0». 48-0 a Dia As a check, a few measurements were also taken with the telescope at a fixed distance from the slit, the aperture 6 being varied until the two elements were just resolved. The effect Fig. 3. 1.0 20 3.0 of varying the brightness of the slits by interposing additional screens and by removing them altogether was also tried, as well as the effect of varying the magnifying power of the telescope. As long as the images were bright enough to be clearly seen there was no appreciable effect produced by either of these changes. The results are presented in the following table :— | TABLE II. S. D. d. b. a/a. | o/a. 1:97 | 12760 | 0:045| 205 | 28 ‘13 | Sunlight, screened. 1:46 | 12760 as ts 21 13 Y “1 0:97 | 12760 2g - Sh) “1S 4 J 0:60 9900 E * POA ale ; Z 0°36 6700 = ae 84 | °25 mS screened and unscreened. 0-167} 4210 Pa) ie 55 | °40 is vibration very bad. 07150} 3280 - A 58 | “bl a unscreened, cloudy. 0:100 2770 9 9 ‘37 ‘60 ” ” ”? 0:075| 2370 -23 | - 70 e 0-250; 11000 | 0-20 | 260 | -11| -86 | Are light, screened. 0°500 | 11000 0°20 17:0 “42 "56 oe ” 29° Telescopes and Spectroscopes for Lines of Finite Width. 327 These results are plotted (crosses) in fig. 3. The agree- ment with the first part of the curve obtained by theory is very good, but beyond the point e=a the experimental values are considerably less than the theoretical ones. These last were obtained, it will be remembered, on the assumption that in order to obtain resolution the difference in intensity between the centre and edges of the diffraction-pattern of a double source must be at least 20 per cent. These results indicate that when the lines are broad a falling off in intensity at the centre of considerably less than this is noticeable. Indeed this is what we should expect, since we know that on an extended bright background (such as a planetary surface) faint markings may be distinguished where the variation in intensity from the background itself is not more than from. two to five per cent. We are therefore certainly on the safe side in following the curve deduced from theory. The value of %, the angular resolution of the telescope for the wide lines, is, moreover, practically the same whichever curve be followed, because, for the values of o for which the two curves begin to depart to any extent from each other, the value of 6 is small com- pared to o itself*, 3 The theoretical curve of fig. 3 may, up to the point c=3a, be closely represented by the hyperbola of the form 1 1 Wen a (2) 2 Oo a a 9 CE Be 2o+a’ whence we get Sate) r But o= ; and a= j (for rectangular aperture m=1). Sub- stituting these values we get Hs Os oe AEN: (14) The angular distance between two lines of width ¢ which can just be resolved is then Baotd=7 (+55), atts) * For the value of c=1-5a, for which the difference between the two curves 1s greatest, the two values of 3 differ by only about four per cent. For o=3a the difference in 3 is only about two per cent, 328 Prof. F. L. O. Wadsworth on the Resolving Power of An examination of this result develops the interesting fact that the aperture required to separate the components of a double line is less when the lines have a small finite width than when they are tnjinitely narrow. For, as may be easily proved, the expression for 2 becomes a maximum when sur A ENE! ete Wee 2 a2) ae Thus for a line of angular width c=}, we have Xu b or, what amounts to the same thing, a telescope of given aper- ture has 10 per cent. greater resolving power for lines of width + than for lines infinitely narrow. To find the width of line for which the resolving power of the instrument is the same as the theoretical resolving power we put >='91- =9le, 2 POUT ae” which gives at once syy=0, or $A, or it is just as easy toresolve the components of a double line when these have a width equal to one-half the angular resolu- tion of the telescope as when their width is zero. This in- creased resolving power resulting from increasing the width of the lines from 0 up to dais due to the same effect as is produced by stopping out the central portion of the telescope objective, z.é., by a strengthening of the centre of the result- ing diffraction-pattern relative to the edges. For the spectroscopic resolution we have, as in the first case, dé i » A (dr)o =>, aes (s¥ ais Isp +r r) . «= (15) r r (Gey ey ae e « ° (16) v TO sb EX or which differs from the expression ordinarily given for the i xX purity of a spectrum by the presence of the {hol oti aac as a coefficient of the second term of the denominator. The Telescopes and Spectroscopes for Lines of Finite Width. 329 existence of this factor necessitates a considerable modifica- tion of certain statements based on the old formula for purity. Instead of diminishing continuously with increased slit-width, the purity of the spectrum first actually increases up to the point sp= sn, and is still equal to the theoretical resolving power of the instrument when sw=3d*. As the slit is widened still further, the purity begins to diminish, although much less rapidly than is indicated by the old formula for purity. In his remarks on the practical purity of a bright line-spectrum in the article “ Spectroscopy” (dine. Brit. vol. xxii. p. 374), Schuster says :—‘* The maximum illumination for any line is obtained when the angular width of the slit is equal to the angle subtended by one wave-length at a distance equal to the collimator aperture. In that case sy=) and the purity is half the resolving power. Hence when light is a consideration we shall not asa rule realize more than half the resolving power of the spectroscope.” Hquation (16) shows, however, that under this condition for maximum illumination+ the purity is really 75 per cent. of the theoretical resolving power instead of 50 per cent. as indicated by Schuster. A similar erroneous conclusion (based upon the commonly accepted formula for purity) was drawn by the writer in one of his earlier papers{, in which it was stated that the purity in case of stellar spectra could never exceed one-third the theoretical resolving power (unless the slit-width is made less than the diameter of the diffraction-image of the star). Hqua- tion (16) shows us that this limit should be nearly one-half instead of one-third. Third Case.—If the radiation is not monochromatic, but is made up of wave-lengths ranging over a interval from A toX+AX, the dispersion of the spectroscope train will spread out the image of an infinitely narrow slit into a band in which the distribution of intensity (supposing the dispersion over the small range Ad to be strictly proportional to X) will be the same as in the source of radiation. This image will be further broadened by diffraction, and the distribution of intensity in the image formed by the spectroscope objective * Unfortunately it is not generally possible to profit by this fact, because for such narrow slits the spectrum is in most cases too faint to be well seen. | T As is readily seen, this condition holds only for absolutely mono- On uat ae sources of radiation (see ‘ Astrophysical Journal,’ January 1895, pp. 62, 63). { ‘Astrophysical Journal,’ January 1895, pp. 68, 69. 830 Prof. F. L. O. Wadsworth on the Resolving Power of will be given by an expression similar to (9), but containing a term /(¢%) which represents the distribution of intensity in the source of radiation. | The law of distribution (in a normal source) is not yet definitely known. The one ordinarily assumed is that which follows from Maxwell’s kinetic theory, which is * FAC) ee where « is a constant whose value varies with the substance emitting radiation, and with the temperature and pressure in the source. A law of distribution more recently proposed by Michelson is f Ch ee I) $e (18) If the first law is assumed, we have for the intensity in the ‘diffraction-pattern . vay sin? (y— 9) I, -| epee ae 2 db= (x, ,%)3 - (19) 2 {z(y-4)} and if the second, >sin? rp sin? (y—$¢) I,= Resi wears 2 dp=y,(7, Y at,). - (20) --2 ¢’ a (y—-9) } i Fig. 4. 2.0 10 o 1.0 _ 20 I have not succeeded in integrating either of these integrals * See Rayleigh, Phil. Mag. April, 1889, p. 298; also Michelson, Phil. Mag. September 1892. + ‘ Astrophysical Journal,’ Nov. 1895, p. 251. Telescopes and Spectroscopes for Lines of Finite Width, 331 in finite form. They may be integrated by developing into a series, but I have found it easier and quicker to integrate by mechanical quadrature. Owing to the very close corres- pondence between the curves represented by (17) and (18) (see fig. 4), the result will be practically the same whichever law be adopted. The expression for I, is the one which has actually been integrated, and the resulting curves Wi(«, 7, a, ) for two values of « are given in fig. 5. The dotted lines represent the curves /(¢) and the full lines the resulting diffraction-pattern yj (7). Fig. 5. For convenience the values of « are expressed in terms of the “ half-width” of the line (Michelson) and «@ the limiting resolving power of the spectroscope objective. The “ half- width ” 6 is defined to be the value of ¢ for which fo=}. Hence 7 Nap. log 2 k= anceael Bi). (21) What we may call the effective width of the line w is the width ab (fig. 4), which is equal to 46. At the points a and b the intensity /() is only about one-twentieth the intensity at the centre, and the part of the curve beyond this point may therefore be considered as having but little effect either on the eye or on the photographic plate. The values of w in the curves of fig. 5 are w=2a, w= 4a. In fig. 6a the diffraction-curve for a double source, of which each component is of width w= 2a, is shown. Adopt- ing the same rule as before, 7. ¢. that for resolution the intensity at the middle of the diffraction-pattern must not be 332 Prof. F. L. O. Wadsworth on the Resolving Power of more than 0°8 the intensity at the two maxima on each side, we find that for resolution the distance between the com- ponents in different cases must be w= a, dish fi2ae=Q;, w= 2a, 9 = L40a=ONp, w= 38a, » =190a=O:;, w=A4a, pe 2:452=Q,. For lines so wide that the broadening by diffraction can be entirely neglected we find (fig. 6) that the distance between the components necessary for resolution is 2°36=0°575 w= Fw. Fig, 6a. Fig. 66. Expressing the preceding results in the form = tot), we have for 10 = 0; Fw) = 1-00, QO=a= = 4 Xu for w=a, J(w) =0°55, O= qv +0535, 4 Xu for w= 2a, J(w) =0°31, O=7w +031 i) A X for w=3da, f(w)=0°18, ai qw +0185, for w=4a, f(w)=0°15, X= Fw + O15 *, for wana, fw) =0-00, A= Fw 40°00. The coefficients /(w) of the last term are plotted in fig. 7 as a function of w. The first portion of this curve may, as in Telescopes and Spectroscopes for Lines of Finite Width. 333 the case of fig. 3, be closely represented by an empirical hyperbola (dotted curve) whose equation is Ww I a RG or ROT nee! e “ é (22) whence (23) The angular width, w, of the line, since this is produced by the dispersion of the spectroscopic train, is w=DAr= 5 Ad, sit aed eld asl DAI 1/4 N | = 7 (77+ a) ree. (25) and therefore for the spectroscope resolution dé ma r)s=, and sa hon " Se me bat wat (06) Cy oe ee ( q@TAr+t Anan a formula very similar in form to that derived for the purity P in the case of a wide slit and monochromatic radiations. Phil, Mag, 8, 5. Vol. 48, No. 264. May 1897. 2D 334 Prof. F. L. O. Wadsworth on the Resolving Power of - ’ Since the spectrum lines must always have a certain ‘‘ width,” the expression for R last. deduced, which for convenience we will call the limiting resolving power, is more generally useful in determining the greatest resolving power of a spectroscope under practical conditions than the usual expression for 7 (the theoretical resolution of the instrument). For. very small values of rAd, i. e. for very small resolving powers or very narrow lines, the value of R will, as in the case of p, slightly exceed r. But for large values of either r or AX the limiting resolving power will be very much less than the theoretical power of the instrument, particularly for large values of r. No matter how narrow the line may be there is a limit beyond which an increase in the theoretical resolving power is without effect in increasing R. This maximum value of R will evidently be or the maximum resolving power that can be attained with any instrument with infinitely narrow slit is not more than one and three-quarter times the ratio between the mean wave-length and “ width ” of the spectral lines under exami- nation *. Our knowledge of the width of spectral lines under different conditions is at present very limited. Various hypotheses, of which the most noted are those of Lommel, Jauman, Galitzin, and Michelson, have been advanced to account for the broadening of the lines under varying con- ditions of temperature and pressure, and to give us a numerical measure of the amount, but they are all more or less unsatis- factory. Michelson’s recent experimental work: with the interferometer has given us our most definite knowledge of the widths of some few bright lines in the spark-spectra of some of the metals under different pressures. In each case the exponential law of distribution is assumed, and the quantity given is 6, the “ half-width ” which has already been deiined. It has been assumed as before that the effective range of wave-length Ad is about 46. Table III. contains a brief summary of some of the results obtained. ° pote Ae thy: * As will be presently seen, however, we may attain a somewhat greater practical purity P than this. 33 ” 2 Tae Telescopes and Spectroscopes for Lines of Finite Width. 335 ° TasueE III. Substance. Line \. Character of Source, __| Pressure in mm. | 0 (tenth-metres). Anr- 46. Hydrogen ........., Ha* 6565 ~ Vacuum tube. Very low. 047 An'=0'°328* % > 09 50 098 Ad’ =0°532* 5 . $3 100 134 AX'=0:696* ” "SDD cP) 200 230 AX’ =1:06* Nodiuimisse.;cs<0nve D,* 5890 Vacuum tube. Very low. "005 0-020 Not stated, Not stated. 100 09 0°36T ile 5h “ 200 "16 0:64t Di sas70 Bunsen flame. Atmospheric. |About ‘05 ¢ 025" Cadmium ........ Red 6489 Vacuum tube, temp. about 280°. Very low. ‘0065 0:026 Green 5086 x 3 7 % “0050 0:020 Not stated. Not stated, probably spark. 100 05 0:200T 9 9? ” ‘ 200 08 0°32t ” ” ” 400 “14 0:56 Mercury ........... Green 5461 Vacuum tube, temp. about 100°. Very low. 003 t 0:12 * The red hydrogen line is a double, the distance between the components being about 0°14 tenth-metre. The value given for 0 is for each component, and the total effective width of the double line is therefore AX\’'=40+0:14. The same is true of each of the D lines (according to Michelson each is made up of at least four components), the distance between the centres of the principal components being 0:07. When the density is low, these components are therefore separated by much more than their own width; byt when it is high (as in the Bunsen flame) each component broadens and overlaps the other, so that the total effective width is, as in the case of the Ha line, A\’=46 +0:07. + There would seem to be some discrepancy between these results, which are given in the Astrophysical Journal for November 1895, p. 251, and the results previously obtained with the vacuum tube (Phil. Mag. September 1892, p. 280). + Calculated from data given in Phil. Mag. September 1892, p. 280. . 2D2 336 Prof. F. L. O. Wadsworth on the Resolving Power of For convenience the values of R, Rmax. and 7/R, have been computed for various values of AX, ranging from 0°01 to 1-0 tenth-metre, and for values of x from 25000 to 1000000. They are given in Table IV. The vertical columns show the decrease in the value of R with an increase in AQ for a given value of r; the horizontal lines show the increase in R with r for a given width of line. The last column gives the maximum resolving power Rmax. that can be attained when the lines have the width AX given in the first column. We see that in general we shall very nearly reach this limit when the theoretical resolving power r is about twice Ras. The additional gain in R, obtained by a further increase in 7, would not be worth the expense of the larger instruments required and the sacrifice in brightness necessary. Indeed, in most cases it would hardly be advisable to use a value of » greater than one to one and one-half times Rx, as with this we shall have already attained from ? to % of the limiting resolving power. The finest lines so far found (see Table IV.) have a width AA of not less than 0:01 tenth-metre. For this width the value of Riyaz, is 950000, and the maximum theoretical power which it would be advisable to use would therefore be about 1400000, corresponding in the case of a grating to an aperture of from 18 to 20 inches. On the other hand, for some of the wider lines, such as those of hydrogen in the vacuum tube, and of many bright metallic lines in are spectra, there would be no advantage whatever for visual work in using a resolving power greater than 20000 to 25000, for which a grating of 4-inch aperture, or 5 60-prisms of 14 inches aperture would suffice. For solar spectrum work, in which the lines are not likely to be narrower than = tenth-metre*, our present 5 and 6 inch gratings will do nearly all that we could hope to attain with larger apertures +, unless indeed there should be some marked advantage in particular cases in the use of the first and second orders of spectra, rather than the higher orders. The preceding conclusions are all based on the assump- * In the case of faint lines the apparent width may sometimes be much less than this, because of the rapid falling off in intensity towards the edge of the line. Indeed, for faint lines, it is not likely that the apparent width of the line is greater than 26, and in some cases even less, Hence estimates of pressure based upon direct visual observations of the widening o lines may be considerably in error. + The latter would, however, be advantageous in photographic work in giving increased accuracy and increased photographic resolution by reason of the greater linear dispersion. See ‘ Astrophysical Journal,’ vol. 1, p- 238, and vol, ii. p. 264. Telescopes and Spectroscopes for Lines of Finite Width. 837 TABLE LV. X= 5500 tenth-metres. sos ae a Ieee ele ee ee See et i ee Oe AX, r= 25000. 7=50000. r= 100000. 7= 200000. - rv = 500000. r= 1000000. tenth- Rmax. metres. 7/R. R. r/R. R. r/R. R. r/R. R. 7/R. R. r/R. R. 0-01 0:98 25400 | 0:97 51600 | 0-95 105600 | 0-94 212800 | 1:04 480000 1:39 | 722000 |} 962000 0:02 0:97 25800 | 0:95 52800 | 0-94 106400 | 1:00 200000 | 1:39 361000 2:29 | 437000 || 481000 0:04 0:95 26400 | 0:94 53200 | 1:00 100000 | 1:24 161700 | 2:29 219000 4:27 | 234000 || 240000 0:06 0:94 26600 | 0:96 52400 | 1:10 90900 | 1°56 128500 | 3:27 153000 6:30 | 159000 |) 160000 0:08 0°94 26600 | 1:00 50000 | 1°24 80800 | 1:91 104600 | 4°27 117000 8:35 | 120000 |} 120000 9°10 0:95 26400 | 1:04 48000 | 1:39 71900 | 2:29 87300 | 5:28 95000 | 10-41 96000 96000 0-12 0:96 26200 | 1:10 45500 | 1°56 64300 | 2°67 75000 | 6°30 79400 | 12°50 80000 80000 0-14 0:97 25800 | 1:16 |. 42900 | 1:73 57700 | 3:06 65000 | 7:33 68000 | 14:50 69000 || 69000 0-16 1:00 25000 | 1:24 40400 | 1:91 52300 | 3-46 58000 | 8°35 60000 | 16°60 60000 |} 60000 0-18 1:02 24600 | 1:31 38100 | 2°10 47700 | 3:86 52000 | 9°38 53000 | 18°70 53000 || 53000 0-20 1:04 24000 | 1:39 36000 | 2°29 43700 | 4:27 46800 | 10°41 48000 | 20°75 48000 || 48000 0:25 1:12 22400 | 1:60 31200 | 2:77 36100 | 5:28 37900 | 13:00 38000 | 25:9 38000 || 38000 0°30 1:20 29800 | 1:85 27000 | 3:27 30600 | 6:30 31800 | 15°60 32000 | 31°1 32000 |; 32000 0°35 1:29 19300 | 2:05 24400 | 3:76 26600 | 7:33 27000 | 18°17 27000 | 36°3 27000 || 27000 0°40 1:39 18000 | 2°29 21800 | 4:27 23400 | 8:35 24000 | 20°75 24000 | 41°4 24000 || 24000 0:50 1:60 15600 | 2°77 18000 | 5:28 18900 | 10:41 19000 | 25°90 19000 | 51:8 19000 |} 19000 0:60 1:82 13700 | 3:27 15300 | 6°30 15900 | 12:47 16000 | 31:1 16000 | 62:2 16000 |; 16000 0°80 2°29 10900 | 4:27 11700 | 8:35 12000 | 16°61 12000 | 41°4 12000 | 82:9 12000 |; 12000 1:00 277 9000 | 5:28 9500 | 10°41 9600 | 20°75 9600 | 51°38 9600 | 103°6 9600 9600 338 Prof. F. L. 0. Wadsworth on the Resolving Power of- tion that the maximum practical resolving power 7, which has been assumed to be equal to 1°5A/b, and which corre- sponds to an angle of deviation of about 90° (@=7=45° to 50°), can be utilized. When for any reason this is not the case, whether because of the inaccuracies of ruling, the faintness of the higher orders of spectra, or the character of the mount- ing, a correspondingly larger aperture must be made use of. If, for example, we consider the maximum angle of deflexion to be 60° (which from purely mechanical considerations is about the largest possible angle that can be used in the ordinary Rowland mounting), we have for 74 who T= 35° In order to attain the same resolving powers, R, as before, the apertures must be increased about 75 per cent. If we assume a maximum angle of 45°, which in practice is not often exceeded in our present gratings, the apertures would have to be increased by over 100 per cent., and we should therefore need to attain the full limiting resolving power nae For lines AN=:01 tenth-metre, an aperture 0 of at least 1 metre An 02 55 PA b aera, eS AX=-05 5, (solar work) ,, b 5 4o em, Fourth Case-—In order to determine the limit of resolution or the practical purity P in this, the most important case, we must first determine the diffraction-curve resulting from a superposition of all the elements of the slit, each one of which has a dispersion-pattern similar to those represented in full lines in fig. 5. If, as before, these elements are equal in intensity, i.é., if the illumination over the whole width of the slit is uniform, the intensity-curve of the diffraction-image will be 1= | nes w, a)dE=p/(o, y, w, a), . (28) P] where - 262 sin? ~ (y— 9) Wi (y; w, @) -\ 2 Gy 4 dp, . (29) ze —(Eo-#)] as derived from (19) and (21). Since the function ¢, is not known in finite terms, ¥,, can- not be directly found. -We may, however, approximate very ee Telescopes and Spectroscopes for Lines of Finite Width. 839 closely indeed to it by replacing the function ,, by. the function sin? 5 Y See he Cae ° (30) [07] which between the points y=40 and y=20, or over all that part of the curve shih 1s ayer m determining the resolution of a double line, coincides, as seen in fig. 5 (dashed curve), almost exactly with the curve W(x, y, ). . The expression for I,, then becomes ( aH’ (E=9) Fae ESD) which is exactly similar in form to (9), the only difference being that 2 has been replaced by ©. he We may therefore obtain at once the limit of resolution for this case from (12) and (14) by replacing « by Q, giving us ane L,= // Fatt eae nate 0? , ea) > =limitin g angular resolution=o + Replacing o and O, by their values in terms of s, yr, R, 7, and \ and reducing, we finally obtain for &y, =| p+ e i) =|, % Paee(33) | 2s +25 | and for purity r Xu ee meee (cree (dd) 4 " (x) ey) 2s +N R This expression differs from (16) only in the presence of the factor R as a coefficient of X in the denominator. When this ratio is unity P=p, or the practical purity is equal to the theoretical purity for monochromatic radiations. By an inspection of Table IV. it will be seen that while 340 Prof, F. L. O. Wadsworth on the Resolving Power of - e e e she e for narrow lines and small resolving powers the ratio — 1s R very nearly unity, and that formula (16) therefore represents very closely the purity of the spectrum, the same is by no means true for wide lines and large resolving powers. In the extreme case figured in the table the value of this ratio rises as high as 100. In order to show more clearly the influence of this factor on the purity of the spectrum under different conditions, Table V. has been prepared, showing the values of P for different slit apertures, from 0°005 mm. to 0°3 mm., different widths of lines from 0-01 to 1:00 tenth- metres, and resolving powers varying from 25000 to 1000000. For comparison the values of p are given for each slit-width and resolving power, and also the value of p’ calculated from the old formula for purity (6). An inspection of the table shows at once how greatly in error estimates of purity based upon this old formula may be in some very common cases. Take for example the case of a spectroscope having a re- solving power of 100000 (5-inch grating, 20000 lines, 2nd order) ; working with angular slit-width such that sy=-005 (s=); mm., y~=7), as in the concave grating). The value of p (16) is about 158000, while the value of P varies from 163000 to 10000. The value of p’ (the old formula for purity) for the same case is only 105000. It is therefore in this case from 50 per cent. to 1000 per cent. in error. In case of larger resolving-powers (r=1000000) it may be as much as 60 times too great. In general, of course, the large values of rAd that give rise to the smaller values of P will not be used for visual work, as there is, as already indi- cated, but little gain in practical resolving power or purity when the value of 7 is greater than the value of Ryax. given in Table V. But in photographic work it is, as has already been shown in a previous paper, a great advantage to use (for extended sources) a short camera and very high resolving power, in order to attain a given degree of photographic purity. Another point which is of considerable practical importance in this connexion is that for these large values of - the purity of the spectrum may be maintained constant or even actually improved over a wide range of those slit- widths actually used in practice. For the maximum value of P (as of p) will be attained when sy = D(R)’ Telescopes and Spectroscopes for Lines of Finite Width. 341 For r=200000, AN= 1°00, ‘= 20°75, and the maximum value of P is therefore attained when the value of sf is about 415% or about ‘0023, corresponding for the usual spectro- scope (r=) to a slit-width of about ,4;mm. Under the same circumstances the practical purity is still as great when the slit-width is j4; mm. as when it is zero. For still higher resolving powers the maximum allowable widths of slit are still greater. Hven with such low values of ~ as R 2 or 3 (corresponding to lines as fine as those sometimes found in the solar chromosphere, 7. ¢., 0°2 to 0°25 tenth- metre), and resolving powers of only 100000, the purity remains undiminished up to values of sy=A to 13d (0005 to 0008), or to slit-widths (with the concave grating) of from =); mm. to 4; mm. One further case remains to be considered, viz. that of a wide slit and non-monochromatic radiations in which the slit-image is not uniformly brought across the whole width. The expression for the intensity in the diffraction-pattern then becomes l=, On (2p Gone 6. ee Sfp) where / (&) expresses the intensity at any part of the slit at a distance € from its centre. The only case of importance of this kind is the case of stars. If the star-image is perfect, 2. e. unaffected by atmospheric or instrumental aberration, the distribution in intensity for any one wave-length is repre- sented by the law Ys sin 2, E T.\) a being the resolving power of the telescope-lens which forms an image of the star. As before, the integration could only be effected by me- chanical quadrature or by development into a series (Wv, not being known in finite terms). It has not been thought worth while to go through the necessary labour of integration for the reason that, practically, such conditions are never realized, at least in stellar spectrographic work. There might be moments at which, if the star were kept perfectly centred on the slit, the full resoiving power resulting from Tapite V. wv Sw w r r r r radians. °™ 48 25000 | 50000 | 100000 | 200000 ( (01 | 20000 | 40200 | 81200 | 163200 005} jy) | -05 | 20300 | 40600 | 77800 | 132400 | | P 4 -10 20300 | 38900} 66200} 91400 010| 3; 00052 | +50 | 15100 | 19400] 20700 | 20400 | (1:00 | 9700 | 10300 | 10200 10000 020| 2.) ls (from 16) 19800 | 39600 | 79100 | 158200 | \p' (from 6) 13100 | 26200 | 52400 | 104800 | ; ( (01 | 12400 | 24800 | 49700 | 99400 | 1 -05 | 12400 | 24800 | 48700 | 90900 010| 35 P 2 -10 | 12400 | 24400 | 45500 | 74300 0001 4 =| +50) 10900 | 16600 | 20200 | 21500 015| 3, 1:00 | 8300 | 10100 | 10800 | 10300 3 (from 16) 12300 | 24600 | 49100 | 98200 ee "(from 6)| 8900 | 17800 | 35500 | 71000 ( (01 | 6700 | 13400 | 26700 | 53500 | -03 | 6700 | 13400 | 26600 | 51900 020) 2, | P 4 -10} 6700 | 13300 | 25900 | 47800 | 0-002 4 ~— |: -50.| 6400 | 11400} 17100 | 20600 030} Js | (100, 5700, 8500} 10300 | 10600 7 | 2 (from 16) 6650 | 18350 | 26700 | 53400 \p' (from 6) 5400 | 10800 | 21600 | 48200 - ¢ (01 4500 | 91000] 18100 | 36200 ! -05 | 4500 } 91000 | 18000 | 35600 030) # | | P 4 -10/ 4500} 9000} 17800} 34200. 0-003 4 =| 50} 4400; 8300} 14100] 19100 045| 2, J ; {1:00} 4200} 7600] 9500] 10500 p (from 16), 4500} 9100 18100 | 38200 p' (from 6), 3900) 7800| 15300 | 31000 , (01 2700} 5400 | 10900 | 21800 | 05 2700 5400! 10900 | 21800 050) #5] P 4 -10| 2700 5400 | 10800 | 21400 0:005 | 50} 2700.' 5300} 9700| 15400 075| | 1:00 | 2600 4900} 7700} 9900 p (from 16) 2700 | 5400 ) 10900 | 21800 (p' (from 6)) 2500) 5000/ 9900] 19800 (01 | 1400} 2800} 5500] 11000 | 05 | 1400 | 2800} 5500] 11000 10 | P 4 -10| 1400! 2800} 5500 | 10900 | 0:010 2 ‘50 | 1400} 2700| 5300] 9800 ee aes a 00 | 1400] 2600] 4900] 7800 oe 16)| 1400 | 2800} 5500! 11000 Ln erm (from 6)| 1300} 2600] 5200) 10400 SIRT PON SPY Ey ee OL 700 | 1400] 2800] 5600 700 | 1400} 2800} 5500 '-20 | a | P 700 | 1400] 2800] 5500 | 0-020 | 700 | 1400}. 2700! 5300 30 a U1 00 | 700 | 1400! 2600; 4900 ‘ p (from 16) 700 | 1400 2800 | 5600° \p' (from 6); 650 2600 , 5200 243000 166000 101500 20400 10000 245000 177000 133000 113600 85700 21000 10300 133500 108000 90200 83100 75700 21100 10400 90500 77500 54500 52900 48800 20600 10500 54500 49500 27500 27200 26500 | 454000 202000 108000 19900 9800 491000 395000 259000 171000 103000 20600 10000 267000 216000 178000 141000 95300 20800 10100 181000 155000 108000 97300 77100 21100 10300 109000 99000 54900 53000 Aa On the Measurement of Alternate Currents. 343 the superposition of two such diffraction - patterns as are represented by (35) might be realized, but in general the star-image will be so broadened and disturbed in position by continual atmospheric disturbance (to say nothing of chro- matic aberration in the case of the image being formed with a lens), that the effect on the photographic plate will in the long run be practically the same as would be produced by a uniformly illuminated slit. r Yerkes Observatory, University of Chicago, February 1897. XLVI. On the Measurement of Alternate Currents by means of an obliquely situated Galvanometer Needle, with a Method of determining the Angle of Lag. By Lord Rayusias, oN gars T is many years} since, as the result of some experiments upon induction, I proposed a soft iron needle for use with alternate currents in place of the permarently magnetized steel needle ordinarily employed in the galvanometer for the measurement of steady currents. An instrument of this kind designed for telephonic currents has since been constructed by Giltay ; but, so far as I am aware, no application has been made of it to measurements upon a large scale, although the principle of alternately reversed magnetism is the foundation of several successful commercial instruments. The theory of the behaviour of an elongated needle is sufficiently simple, so long as it can be assumed that the magnetism is made up of two parts, one of which is constant and the other proportional to the magnetizing force. If internal induced currents can be neglected, this assumption may be regarded as legitimate so long as the forces are small. In the ordinary case of alternate currents, where upon the whole there is no transfer of electricity in either direction, the constant part of the magnetism has no effect ; while the variable part gives rise to a deflecting couple proportional on the one hand to the mean value of the square of the mag- ‘netizing force or current, and upon the other to the sine of twice the angle between the direction of the force and the * Communicated by the Author. : + Brit. Assoc, Report, 1868; Phil. Mag. vol. ili, p. 43 (1877). { Phil.-Mag. vol. xxiii. p. 225 (1887). 344 Lord Rayleigh on the Measurement of Alternate Currents length of the needle. The deflecting couple is thus evanescent when the needle stands either parallel or perpendicular to the magnetizing force, and rises to a maximum at the angle of 45°. For practical purposes the law of proportionality to the mean square of current would seem to be trustworthy so long as no great change occurs in the frequency or type of current; otherwise eddy currents in the iron might lead to error, unless the metal were finely subdivided. It is hardly to be supposed that for ordinary purposes a suspended iron needle would compete in convenience with the excellent instruments now generally available; but having found it suitable for a special purpose of my own, I think it may be worth while to draw to it the attention of those interested. In experiments upon the oxidation of nitrogen by the electric are or flame it was desired to ascertain the relation between the electric power absorbed and the amount of nitrogen oxidized. A transformer with an unclosed magnetic circuit was employed to raise the potential from that of the supply to the 3000 volts or more needed at the platinum ter- minals. Commercial ampere-meters and volt-meters gave with all needed precision the current and potential at the primary of the transformer; but, as is well known, these data do not suffice for an estimate of power. The latter depends also upon the angle of lag, or retardation of current relatively to potential-difference. If this angle be @, the power actually employed is to be found by multiplying the product of volts and amperes by cos @, so that the actual power may be less to any extent than the apparent power represented by the simple product. Various watt-meters have been introduced for measuring the actual power directly, but I could not hear of one suitable for the large current of 40 amperes used at the Royal Institution. Working subsequently in the country I returned to the problem, and succeeded in determining the angle of lag very easily by means of the principle now to be explained. The soft iron needle of 2 centim. in length, suspended by a fine torsion-fibre of glass and carrying a mirror in the usual way, is inclined at 45° to the direction of the magnetic force. This force is due to currents in two coils, the common axis of the coils being horizontal and passing through the centre of the needle. As in ordinary galvanometers, the mean plane of each coil may include the centre of the needle ; but it was found better to dispose the coils on opposite sides and at dis- tances from the needle which could be varied. A plan of the arrangement is sketched diagramatically in the woodcut, where MM, SS represent the two coils, the common axis HK passing by means of an obliquely situated Galvanometer Needle. 345 through the centre of the needle N. If the currents in the coils are of the same frequency and of simple type, the mag- netizing forces along HK may be denoted by A cos nt, B cos (nt—e), ¢ being the phase-difference. If either force act alone, the deflecting couple is represented by A? or by B?; but if the two forces cooperate the corresponding effect is Gi a 2a cose, . . CE) reducing itself to (A+B)? or (A—B)? only in the cases where e is zero or two right angles. The method consists in measur- ing upon any common scale all the three quantities A?, B?, and C?, from which e can be deduced by trigonometrical tables, or more simply in many cases by constructing the triangle whose sides are A, B, and C. The determination of the phase-difference between the currents is thus independent of any measurement of their absolute values. The best method of estimating the deflecting couples may depend upon the circumstances of the particular case. The most accurate in principle is the restoration of the needle to the zero position by means of a torsion-head. But when the conditions are so arranged that the angular deflexions are moderate, it will usually suffice merely to read them, either objectively by a spot of light thrown upon a scale, or by means of a telescope. In any case where it may be desired to push the deflexions beyond the region where the law of pro- portionality can be relied upon, all risk of error may be avoided by comparison with another instrument of trustworthy calibration, one coil only of the soft iron apparatus being employed. In certain cases the advantages which accompany the restoration of the zero position of the needle may be secured by causing the deflexions themselves to assume a constant value, e.g. by making known changes of resistance in one or both of the circuits, or by motion of the coils altering their efficiencies in a known ratio. In the particular experiments for which the apparatus was set 346 Lord Rayleigh on the Measurement of Alternate Currents up the coil MM (see woodcut) was reduced to a single turn of about 17 centim. diameter and conveyed the main current (about 10 amperes) which traversed the primary circuit of the transformer. This, it may be mentioned, was a home- made instrument, somewhat of the Ruhmkorff type, and was laced at a sufficient distance from the measuring apparatus. The shunt-coil SS was of somewhat less diameter and con- tained 32 convolutions. The shunt-circuit included also two electric lamps, joined in series, and its terminals were con- nected with two points of the main circuit outside the apparatus, where the difference of potentials was about 40 volts. Provision was made for diverting the main current at pleasure from MM, and by means of a reverser the direction of the current in SS could be altered, equivalent to a change of e by 180°. The measurements to be made are the effects of MM and of SS acting separately, and of MM and 8S acting together in one or both positions of the reverser. The best arrangement of the details of observation will depend somewhat upon the particular value of e to be dealt with. If this be 60°, or thereabouts, the method can be applied with peculiar advantage. For by preliminary adjust- ment of the coils, if movable, or by inclusion of (unknown) resistance in the shunt-circuit, the deflexions due to MM and SS may be made equal to one another ; so that in the case supposed the same deflexion will ensue from the simultaneous action of the two currents in one of the ways in which they may be combined. This condition of things was somewhat approached in the actual measures relating to the electric flame. ‘Thus in one trial the coils were adjusted so as to make the deflexions due to each of the currents acting singly equal to one another. The value was 40 divisions of the scale. When both currents were turned on, the deflexion was 264 divisions. Thus A?=B?=A40, A? + B’—2AB cos e= 263 ; whence cos e= 67, Ore—15. In a second experiment the deflexion due to both currents acting together was made equal to that of the main acting alone. Here A°=40, B=71, A?4+B?—2AB cos e=40; whence cos e="665. The accuracy was limited by the unsteadiness of the electric flame and of the primary currents (from a gas-driven De by means of an obliquely situated Galvanometer Needle. 347 Méritens) rather than by want of delicacy in the measuring apparatus. 1) a8 ‘Wher the phase-difference is about. a quarter of a period, cos¢ is small, and its value is best found by observing the éffect of reversing the shunt-current while the main current continues running. ‘The difference is 4AB cose, from which, combined with a knowledge of A and B, the value of cos e€ is advantageously derived. Imfcose is absolutely zero, the re- versal does not alter the reading. If the currents are in the same, or in opposite phases, it is possible to reduce the joint effect to zero by suitable adjust- ment of the coils or of the shunt resistance. The application of principal interest is when the shunt- current may be assumed to have the same phase as the potential-ditference at its terminals, for then cos ¢€is the factor by which the true watts may be derived from the apparent watts. We will presently consider tke question of the negligibility of the self-inductiou of the shunt-current, but before proceeding to this it may be well to show the applica- tion of the formule when the currents deviate from the sine type. — ~ If a be the instantaneous current, and v the instantaneous potential-difference at the terminals, the work done is Javdt. The readings of the soft iron galvanometer for either current alone may be represented by Pei \aidh ae Bea i edd, |. (2) where h, k are constants depending upon the disposition of the epparatus. When both currents act, we have the readings C/? or C= {\(ha ko) -abewes O21 Ais: (3) Taking the first alternative, we find — CPW lade + hkl avdt +h \e'dt, or > Ripe a aa a . C,2— A?— BP = fav dt (4) ge Nacdi ede h yo aie The fraction on the right of (4) is the ratio of true and apparent watts; and we see that, whether the currents follow the sine law or not, the ratio is given by cose, where, as before, ¢ is the angle of the triangle constructed with sides proportional to the square roots of the three readings. 348 On the Measurement of Alternate Currents. Another formula for cose is C222 TAR 5 +n sr In the final formula (4) the factors of efficiency of the separate coils (A, k) do not enter. This result depends, how- ever, upon the fulfilment of the condition of parallelism between the two coils. If the magnetic forees due to the coils be inclined at different angles x, y' to the length of the needle, we have in place of (3), cos €= CG cos y+ v cos yx’) (asin y+ sin x’) dé =| [$a’sin 2y + 40’ sin 2y/ + av sin (y+y’) |dt; . (6) while A?=tsin 2y\ardt, B’=}sin2y'fo'dt... (7) Accordingly Savdt (2 A?—B? {sin 2y. sin 2y/} {(ardtx\vdt} 2AB sin (x +7’) in which the second fraction on the right represents the influ- ence of the defect in parallelism. If y and y’ are both nearly equal to 45°, then approximately V{sin2y.sin2y'} |, ne aoe Se We have now to censider under what conditions the shunt- current may be assumed to be proportional to the instantane- ous value of the potential-difference at its terminals. The obstacles are principally the self-induction of the shunt-coil itself, and the mutual induction between it and the coil which conveys the main current. As to the former, we know™ that if the mean radius of a coil be a, and if the section be circular of radius c, and if n be the number of convolutions, L=dantaf log = — 7 }. . +) To take an example from the shunt-coil used in the experi- ments above referred to, where © (8) O—oems) (e— tb cni.,' - n=32, L is of the order 10° cm. The time-constant of the shunt- circuit (rT) is equal to L/R, where R is the resistance in C.G.S8. * Maxwell’s ‘Electricity, § 706, Temperature and Ohmic Resistance of Gases. 349 measure. If 7 be the resistance measured in ohms, R=r x 10°, so that fea ail oy exe What we are concerned with is the ratio of 7 to the period of the currents ; if the latter be ;}5 second, the ratio is 1/100r, so that if 7 be a good number of ohms—it must have exceeded 100 in the particular experiments—there is nothing to fear from self-induction. It would seem to follow generally that if the voltage be not too small, sav not falling below 10 volts, there should be no difficulty in obtaining sufficient effect from a shunt-coil whose self-induction may be neglected. It may be remarked that since the efficiency of the coil varies as n, while L varies as n?”, it will be advantageous to keep n (and 7) down so long as the self-induction of the whole shunt-circuit is mainly that of the coil. If the main and the shunt-coils were wound closely together, the disturbance due to mutual induction would be of the same order of magnitude as that due to self-induction. If the coils are separated, as is otherwise convenient, the influence of mutual induction will be less, and may be neglected under the conditions above defined. As to the effect of self-induction, if present, we know that the lag ¢ is given by Taman Up Mvae seu tes sul ss |e a le) where p=27 x frequency. The angle of lag of the main current (9), which it is the object of the measurements to determine, is then given by Cer BS VOW 8 Nien foe sie) (CED) e being the phase-difference of the two currents as found directly from the observations. XLVIL. The Temperature and Ohmic Resistance of Gases during the Oseillaiory Electric Discharge. By JoHn TROWBRIDGE and THEODORE Wm. RicHarps”*. | our papers f on “ The Spectra of Argon and The Multiple Spectra of Gases ” we have emphasized the importance of considering the electrical condition of the circuit in which is placed the Plucker tube containing the gas under examination. We have pointed anew to the fact that in general the continuous discharge of an accumulator produces one spectrum, while * Communicated by the Authors. f Phil. Mag. vol. xliii. pp. 77, 135. Plal. Mag. 8. 5. Vol. 43. No. 264. May i897. 10) bo 350 Messrs. Trowbridge and Richards on the Temperature the oscillatory discharge of a condenser produces another. In considering this question one is immediately struck by the fact that, although the gas acts as if it presented a resistance of several hundred thousand or even several million ohms to the current, while under the influence of the continuous discharge, nevertheless this same tube allows oscillations which are wholly damped by a few hundred ohms to pass through it under the influence of a condenser. These considerations led us to measure the resistance of such a tube to the oscillatory discharge, and we found by means of a novel method that in fact a mass of gas at low tension containedin a capillary tube may act as though it opposed a resistance of only five or six ohms to the spark of a large condenser. In order the more clearly to grasp the situation, the potential-differences between the ends of the tube during a continuous discharge may well be considered first. A number of measurements of such potential-differences have been made by Hittorf* and others, but it may be well to give two of the many series of measurements which we have made, in order to facilitate comparison with the discharge of the condenser through the same tubes. The tubes employed throughout this research were of the ordinary type devised by Pliicker, consisting of two cylindrical bulbs separated by a capillary 1:3 mm. in diameter and 7 cm. long. The electrodes were of aluminium. Unless otherwise stated all the experiments here recorded were made with tubes of exactly this shape and size; and most of the experiments were made with a single tube. The voltmeter used for measuring the potential-differences was a Thomson electro- static electrometer, and the current used was not much over a milliampere. As the voltmeter was only graduated to 1800 volts, the readings above that amount are merely approximations. Hach gas evidently has its minimum of potential-ditference, that of hydrogen lying at about 1 mm. of pressure, and that of nitrogen at about 0'°3 mm. These minima, as well as the total potential-differences, are undoubtedly modified by the strength of the current; but the results given above are com- parable with one another because they were all made under the same conditions. Hittorf found a minimum at about 0°35 mm. for nitrogen, and he pointed out by means of his extra electrodes that.the fall of potential was very irregular, the greater part of it residing at the kathode. His results have been confirmed by others, and Wood ¢ has shown that the heat evolved at different parts of the tube follows the same irregularities as these potential-differences. * Wied. Ann, xx. p. 705. t Ibid. lix. p. 238. and Ohmie Resistance of Gases. Bie Potential-differences between Electrodes of Spectrum tube. Hydrogen. Nitrogen. Pressure in mm. Voltage. Pressure in mm. Voltage. 70 2600 (?) 85 very high. 6:0 2100 (?) 50 very high 4:0 1900 4:0 2600 (?) 3°5 1500 30 2100 (?) 2-0 1340 25 1750 15 1260 kT 1600 1°25 1220 4 1410 115 1150 1-2 1340 1:00 1100 AO} 1180 “70 1140 0-7 1140 “50 1220 06 1080 “13 very high. 0-5 1040 0:3 980 0°25 1030 0°13 1700 0:06 2800+ (?) Neglecting the factors of the potential-difference which reside at the electrodes, the sum of which increase with the exhaustion of the tube, we find that according to Hittorf’s results the resistance of the gas itself steadily diminishes as the exhaustion proceeds ; for example, with a current of two milliamperes he found a fall of potential of about 120 volts between two parts of the middle of the tube eight centimetres apart, the tension of the nitrogen being 0°35 mm. When the current was about one milliampere, and the tension of the gas was only about 0:001 mm., the voltage sank to fifteen. These two figures correspond to resistances of 60,000 ohms and 15,000 ohms respectively, the resistance of the gas diminishing as the pressure is decreased. Of course we have no certainty as to how much of this opposition to the current is due to true resistance, and how much to a kind of polariza- tion, but it is convenient for present purposes to count it all as resistance. In any case this opposition, if maintained, is far too great to permit the passage of oscillations, even under the most favourable conditions. In order to prove that the opposition is not maintained, but is in fact broken down by the spark, it was only necessary to photograph the dis- charge with the help of a rapidly revolving mirror, after the method of Feddersen. Unfortunately, the light in the tube itself is too faint for direct instantaneous photography ; but 2H 2 352 Messrs. Trowbridge and Richards on the Temperature the light of the spark between two cadmium electrodes in the same circuit is quite bright enough for the purpose, and of course any oscillations which crossed the spark-gap must also go through the tube. Our next step, therefore, was to make a series of such photographs of a spark discharged through hydrogen, at first when the gas glowed with a white light and showed its many-line spectrum, and afterwards when it exhibited the characteristic red tint and a spectrum of only four lines in the visible portion of the spectrum. In order to obtain the white light in the hydrogen tube, it was necessary to increase either the impedance or the resistance in the circuit containing the tube. With a definite very small amount of impedance we increased the resistance until the red glow disappeared in the tube, and discovered on developing the photographs which were obtained by means of the revolv- ing mirror that the discharge was non-oscillatory. When, however, the resistance in the condenser circuit was diminished, the red glow began to appear, and the photographs taken when all the resistance except the tube itself was removed showed that the discharge was oscillatory. This also was evident from the peculiar crackle of the spark, which Hertz remarked was essential in performing his experiments on electric waves. The apparatus used in this and subsequent experiments is sketched in the accompanying diagram (fig. 1). An examination of our photographs showed the interesting fact that there were in general not more than two or three complete oscillations ; the remaining ones which could have been obtained from the given capacity and _ self-induction having been damped by the resistance of the gas. The question immediately arose, What is the resistance of the gas at the instant of the discharge? For if an idea of this can be obtained we can get an estimate of the amount of beat developed in the gas during each oscillation. A Thomson Hlectrostatic Voltmeter connected to the ends of the hydrogen tube indicated a difference of potential of over 1800 volts, and this difference of potential could only be obtained by substituting for the Geissler tube a resistance of many thousand ohms. The indications, however, of this instru- ment in this case are of no value ; for we discovered that a resistance of from ten to twenty ohms was sufficient to pro- duce the same amount of damping which the gas exerted. The resistance of the gas, therefore, could not be greater than these amounts*. It is evident, therefore, why the voltmeter gives erroneous readings. On account of the inertia of the moving parts, and the very short time of the discharge, it * “Damping of Electrical Oscillations,” Proc. Amer, Acad. 1891. and Ohmic Resistance of Gases. _ BIO does not indicate the fall of potential through the small resistance of the tube during the instant when the discharge passes, but maintains an indication of a high difference of potential. In order to apply systematically this new method of measuring resistances, our next step was to prepare a series Fig. 1. To, = ce B, battery of 5000 to 10,000 storage cells. C, condenser of 1000 to 18,000 electrostatic units. R, small resistance to damp oscillations. S, spark-gap between cadmium terminals. T, Pliicker tube containing gas. W,, chief water resistance of 5 to 50 megohms. of standards—photographs of the oscillatory sparks of con- densers of different sizes, damped by known resistances which were substituted for the Geissler tube in the condenser circuit. In all these experiments, of course, the small resistance on the left-hand side of the sketch was cut out by a suitable key. Three large leyden-jars, each 30 cm. in diameter and 50 cm. high, having a capacity of 6000 electro- static units apiece, were used either singly or together to act as the condenser; the waves generated by these large capacities were much too long to interfere with one another upon so short a circuit. The resistances were wires of manganin 0-1 mm. in diameter, stretched on both sides of long strips of thin vulcanite plate, the idea of this arrangement being to eliminate self-induction and yet to prevent the short-circuiting of the high potential. The spark-gap usually consisted of cadmium terminals arranged in the focus of a revolving 354 Messrs. Trowbridge and Richards on the Temperature mirror driven very rapidly by means of a small electric motor. In a few cases zinc terminals were used, with no appreciable difference in the results (Righi*). The terminals were re-pointed from time to time, and were always kept at a distance of 1°3 mm. apart. With this apparatus the photographs of perhaps 500 sparks were taken, and the results are recorded in the following table. As a general rule the spark containing the highest number of oscillations upon any plate was taken as the representative one. The first column below records the resistance through which the discharge had to pass before reaching the spark- gap, while the second, third, and fourth record the number of half-oscillations observed upon the photographs. Resistance Standards. Capacity =6000. | Capacity =12,000.| Capacity = 18,000. pee sae Not on hale Nostornalr No.of hal me oscillations. oscillations. oscillations. 0 is 37 32 1 a 21 (2) 21 2 16-0 14 13 3 12:0 1] 10 4 9:5 35 7 5 8-0 7 6 6 75 6 5 7 65 5 4 10 5-0 4 3 15 3-0 3 20 2-0 2 17 30 1:0 These figures correspond in general tendency with the less precise determinations made by Feddersen 7; they show, as his determinations did, that the larger the capacity the fewer the number of oscillations. This tendency is especially noticeable between two and ten ohms, the part of each curve which is most capable of accurate determination. While noi perfectly regular, these curves manifestly furnish the means of mea- suring approximately any small resistance through which a spark, followed by as much as one-half of an oscillation, is able to pass. i Having now our scale of measurement, we substituted for our known resistances a Pliicker tube attached to an admirable automatic Toepler air-pump (of Kiss, Budapest), as well as to receivers containing pure hydrogen and nitrogen. These gases could be delivered individually into the tube at any * Nuovo Cimento (2) xvi. p. 97. + Pogg. Ann, exiii. p. 487. 399 The bulbs of the pump, aggregating over ith the , were always in communication wit so that the discharge and Ohmic Resistance of Gases. Pliicker tube while the circuit was closed, desired pressure. a litre in volume Fig. 2.—Ohms are plotted horizontally ; half-oscillations are plotted vertically. serasesaerarace BoSoReoedoD BeBeuetce rrr a RY Pe ring AN QBaa Py at HHH Seaeenae | Sr 8, Wa ae BN) O) Pave EDs Wt <4 boos EEE EEE EEE am BReSoas [yy seeietoet ssccties HH HH Bae EEE eee HE UE Saae Py Ty tty rt ‘mer A . Sar eeeae ae aeeeene [ TY | SRST 88) 2) SER PEEEE EEE EEE EEE EEE eee EERE ERY] gen The hydro ant pressure. Spee i io) Hoa SO) (oes Oods oS HOR & Sn o OSs eee ee SO Seeaenes = ON S orl me iernipe a a era ae, 4 x ON aq Aae Pp 2 oO Loam = ane aol ea ~ n~ o Oo Jas) eine an Pro 4 og Oo i) a S. = ee on ® Se are) or = fo) His} _— en took place under essentially const was made electrolytically and puri a solution of potash and over fused pota ® aS ray lo) mM wm ob) y (aby HAA ae “ oe ts shes cs oO 356 Messrs. Trowbridge and Richards on the Temperature and over the same two driers as the hydrogen. The length of the spark-gap remained always the same, excepting for the very lowest and the very highest pressures of gas, through which the electricity refused to pass unless the spark-gap was narrowed. In the first column of each table below is recorded the tensions of gas, in the second, third, and fourth are recorded the numbers of half-oscillations obtained with the three different capacities respectively, while in the fifth, sixth, and seventh of these columns are to be found the resistances corresponding to these oscillations, each value being taken from its proper curve in fig. 2. In order to give a better idea of the comparison and the way in which the oscillations are damped, reproductions from two photographs are appended (p. 360). The Resistance of Hydrogen. Number of half-oscillations. | Resistance in ohms. Pressure of gas. Capacity| Capacity| Capacity| Capacity] Capacity; Capacity =6000. |=12,000.|=18,000.) ==6000. |=12,000./=18,000. ee millim. (ohms.) | (ohms.) | (ohms.) 13°5 0 sant aeeal | ek de over 100 10-0 23 vic 2 50 ? Bs 15 5:0 1 2 2 | ~30 20 15 3°6 2 sae) nL UN sawler 20 ae 30 3 3 15 10 2:0 2 3 3 20 15 10 18 ie 3 ae st 15 Se 1:25 3 3 4 15 15 i 115 + ae ae 10 3 0-85 54 9 0°75 63 oe 55 0°60 7 6 ais 5 5 0-40 6 ee: 6 bes 0°31 63 7 6 7 D 5 0-21 6 a6 6 Zp 0-15 5 53(?)| 6+ 10 bes 5 0:10 ee ab sok ne 7 0:05 43 | nospark.| no spark. 11 and Ohmic Resistance of Gases. 351 cH gaehecrsrieceaet H ecbefenduatart| gestastey otantassotantcutertetectests a — Suse oneeeseenstclaussccsssesssnaen BEEEEEEEEE EEE Eee oe EEE SEE Seo eee —— || ——— ERSSEaa as a a iit ay ae Breapembesosos's QRaS8 Be) yt ‘= TTA [I [Ty See eeeensennnnt a OESGERDRESESEEaBES4 Ht ates BS Ly Srsdi ened ttesitessatieee Sees feet eseeceerrtr an seonssesersal PEELE ge er BE REE BSCE Ee sD 9 se esse, 520 4Reeees PE HH GSS) SSRSean gtarapnoo0e aes a | A | »s a augoe0/Guaeneaae 45 GECcooecse0 Aseogg00 BEER FEC H Py BERR EEE EB EEE EEE ECE ESSE DESORARE SERS Seees ft | A HRSaGHaao 4 HH Beg gaeeaueoR Hescossaatifftaece Hescosataa ftesaeett : : | tH -H Hl ci Bee ee qeBeeeae BaNdh acces selnvecdl : seeEeteesaase “EERE Ser ae oH oH sean eel nae ie Effettessesseeeeeeeresoe 0 5 Gea ig) nu roa 906-35 Ohms are plotted horizontally. Millimetres of pressure are plotted vertically. 358 Messrs. Trowbridge and Richards on the Temper.ture The Resistance of Nitrogen. Number of half-oscillations. | Resistance in ohms. | Pressure of gas. f 5 : Capacity| Capacity| Capacity) Capacity) Capacity; Capacit ST EOGie = 12,000.) =18,C60. 8000 1b 000. — 18,006. es ——— | millim. (ohms.) | (ohms.) | (ohms,) 95 see 1 bias ee 30 ats 50 1 (faint)) 14 ls 30 25 23 4-2 ior 13 ie 25 oe 27 2 er 3 20 Ken 10 2 2 2 2 (?) 20 20 15 Ie7 5c 3 Sai 15 eck 1:3 és 3 5 15 aoe 1-04 3 2t oF 15 10 8 0-70 He 4 ses sae 10 ie: 0°50 33 5 4 an fo) (4 0:30 4 See 6 12 a 5 0-26 53 Sos 53 (?) a 5d 0:22 as 8 des 4:5 O15 63 83 fi 4 0:07 5 8 10 4:5 0:05 7 5) 0:03 8 4 0:02 9) 8 0-01 5 , 8 Besides these measurements of hydrogen and nitrogen, several photographs were made of sparks sent through some of Lord Rayleigh’s argon contained in sealed tubes. Since the capillaries were not in every case equal in diameter, the results are not wholly comparable with one another, or with those in the two tables given above. Two half-oscilla- tions each were observed in the photographs of argon at 1, 2, and 3 mm. pressure contained in tubes with very fine capillaries, while six half-oscillations were observed in tubes about like those used for nitrogen and hydrogen. ‘This shows that the form of the tube influences very materially the resistance. As a very small jar will provide enough elec- ticity to give the blue spectrum of argon, the resistance of a tube containing the gas at 1 mm. pressure was deter- mined with a capacity of about 1000 as well as with the usual capacities 6000, 12,000, and 18,000 electrostatic units. Somewhat over six half-oscillations were observed in each case, corresponding to resistances of about thirteen, eight, six-and- a-half, and five ohms respectively. 0:005 |.no spark. no ae no spark. very high very high and Ohmic Resistance of Gases. 3909 ecucer sence nagoe DHHe Ft tt Boge) at onnaa a a ‘i r fo = Go a a ea a LI I | He (rst at seaevaged cazetssrerserarseuarasz Pod sdosssuessseezabecretsereraezsiaee PE eee ee CT SaaNe i! Aa oH s | 2 gueene seseare CH mceseters marae Sdeeate SnesuaeaG HH Segucee igs cucese sees teeeuoe7dasee deb” 2a ceeegneseasseascesesceettecce EE Se pee Sseadeyceneaseeeesstitittazattt Seeedagfasseuy danh adaaeet a tantevectanfactcrectesterectantasteiters cat Hite ab job ceananad’ cos panespeasscvanccrsteerareatatcavszasaed a i | 3 a Sean peeuaacuaean PEA aS FEC 36-7 audeeanee’™ ceuaseene SEES Eee GsusdiH -agdeceaacuuatfecetstoce seserevasesatatetaecsssrecaneees 5 10 15 20 25 Se as aE Ohms are piotted horizontally. Millimetres of pressure are plotted vertically. ‘QouRysIsar SVE] Jo JuTOd ye ueSorpdy Jo aourjstser suryo g A pedmrg ‘9 “oI ‘peduep ION “g “Stal ‘SNOLLVITIOSQ £0 SHAVUNOLOHG so) colt 260 Messrs. Trowbridge and Richards on the Temperature and Ohmic Resistance of Gases. 361 The evidence of all these experiments is unequivocal, and may be summed up under the following heads :— I. The resistance of a gas at low pressure to the oscillatory discharge is equivalent to only a very small ohmic resistance. Il. This resistance is in general greater the less the quantity of electricity. III. Down toa very small pressure this resistance decreases with the tension of the gas. At a pressure considerably below the minima in the potential curves given on p. 351, the resistance seems to reach a minimum, but the irregularity of the sparks in this region makes this last minimum somewhat uncertain. The minima of resistance probably vary with the quantity of elec- tricity discharged as well as with the specific properties of the gas. The minimum for nitrogen is attained at a much lower pressure than that of hydrogen. IV. The form of the tube has an important effect upon the resistance of the gas. V. With the oscillatory discharge it ts evident that the electrodes produce far less effect than with the continuous discharge. These conclusions are not wholly without support in the literature of the subject. J.J. Thomson’s researches with tubes without electrodes * show that a rarefied gas must have an extremely low resistance to the oscillatory discharge of electricity, and Jaumann + found that the “ electric strength ” | of a gas increased as the quantity of electricity diminished. But all earlier accurate measurements have been made with continuous currents, whose relations are very different from those of the sudden discharge of a condenser which we have studied. The continuous current meets with great opposition, especially at the negative electrodes, where much heat is developed. The oscillatory discharge meets with very little opposition, and correspondingly we find that here the greatest heat is developed in the gas itself, especially in the capillary tube, the electrodes remaining comparatively cool. This experiment we have tried repeatedly, sending exactly equal amounts of electricity through the tube in each fashion, and observing great differences in the heating effects. Moreover, even in the continuously glowing gas itself apart from the electrodes, the potential-difference, if due to resistance alone, corresponds to vastly greater resistance than that opposed to * “Recent Researches in Electricity and Magnetism,’ p. 92. T Suitz.-berichte Wien. Akad, vol. xevil. p. 765. 362 Messrs. Trowbridge and Richards on the Temperature the condenser discharge, according to Hittorf’s results already uoted. : It is clear that the quantity of electricity going through the tube in a given time is almost incredibly different in the two cases. This difference has not been enough emphasized in the literature upon the subject. Suppose that the battery and other resistance are so regulated as to supply a milll- ampere of current, and the condenser is of such a size that when it is connected the spark passes ten times a second. These conditions were frequently those of our experiments. The spark, judging from our photographs, certainly does not last more than one millionth of a second, hence the current- strength at the instant of the discharge must be at least 100,000 times as great as that of the continuous discharge without the condenser, or must amount to 100 amperes. Jaumann’s observation that the opposition to the current is less as the current increases, and our conclusion (III.) that _ the resistance is less with the larger capacity, are in reality observations which may be represented as the two extremities of a long curve. This curve is formed by the relation of milliamperes to megohms on one end, and of hundreds of amperes to ohms upon the other. The part of the curve between these two extremities is very hard to investigate with our present means, and indeed it seems to behave differently with different gases. For these two conditions are represented in any given case by the two spectra of the gases, and as we increase the current we observe varying relations between these spectra. In the case of hydrogen the spectrum of four visible lines gradually increases in brilliiancy with the gradual fading of the many-lined spectrum of the lower temperatures as the current is increased; and only when the current-strength becomes very great do the extra lines disappear. In other words, the change from one condition to the other is gradual. In the case of nitrogen, upon the other hand, the change is abrupt: and often when the gas is near its sensitive point some sparks will go through with little opposition, while others give the banded spectrum and the non-oscillatory photograph, showing that the resis- tance was large. Argon is like nitrogen in the suddenness of the transition, but its transition takes place with much weaker currents than with either hydrogen or nitrogen. We have repeatedly found argon to give the pure blue spectrum under the influence of the discharge of the full battery with very little resistance in the circuit without any condenser, or with less than eight amperes ; for the resistance of each cell of the battery is about the quarter of an ohm. » eMial and Ohmic Resistance of Gases. 363 One of the great difficulties of investigating the inter- mediate part of the curve lies in the fact that no tube is strong enough to stand the continuous application of tempera- tures as high as those developed by the corresponding current. On the other hand, the repeated. instantaneous discharge, which the tube will stand, cannot be estimated when the resistance rises above the very small amount necessary to damp out the oscillations. The question whether the change in the spectrum, upon increasing the current, is due to greater heat or to the oscil- latory motion, is one which is not easily settled, because the last trace of the return oscillation requires hundreds of ohms for its damping; and under these conditions this oscillation is not easily photographed. The fact that argon offers no less resistance than hydrogen or nitrogen to electric oscillations, but nevertheless is much more sensitive to increased current, tends to show that the important factor in the question is not the oscillatory nature of the discharge, but only the great quantity which is always attendant upon oscillatory discharges. Since gases do not strictly follow Ohm’s law, we cannot assume that the formula R= \ | a in which R=resistance, L=self-induction, and C=capacity, and which gives the limiting value of R for non-oscillatory discharges, rigidly holds. If, however, we obtain a white glow in hydrogen which is due to the unidirectional discharge of a large eine denser through a large resistance besides that of the tube and then proceed to increase the electromotive force. and consequently the strength of the current in our unidirectional discharge, we can determine whether this form of discharoe is competent to produce the red glow in hydrogen. : The apparatus which was used for this purpose consisted of a step-up transformer consisting of two secondaries of many turns of fine wire, which were slipped upon a long primary. When the secondaries were coupled in series the electromotive force of the discharge was doubled without any considerable change in capacity. As a matter of fact the glow was seen to be perceptibly redder with two coils than with one, showing that the change in the quantity is the essential feature in the change of the spectrum. While this conclusion interferes with the strict application of the word talantoscope to an argon-tube, the use of the tube as a talantoscepe nevertheless remains; for while the oscilla- tions and the blue spectrum are not strictly dependent upon one another they are both dependent upon the same final cause, 364 Messrs. Trowbridge and Richards on the Temperature The conclusion that the large quantity of electricity, and therefore the high temperature caused by the discharge, is the cause of the very much diminished resistance of the tube and the corresponding spectrum, leads us at once to consider the energetics of the problem. On the assumption that the 1D) departure from Ohm’s law is not large*, since C= R and the amount of impedance in the circuit is so small as to be neglected, we shall have an amount of energy developed in the tube for perhaps the millionth part of a second equal to CE. With an electromotive force of 10,000 volts and a resistance of ten ohms, a current of 1000 amperes must he obtained, and this multiplied by 10,000 and divided by 746 gives the electrical horse-power if the current were maintained for a second. The corresponding value is over 10,000, and this corresponds to an excessively high temperature for a very brief space of time. Of course a bolometer or any other thermometer in the tube could not indicate this energy, for it is of very short duration, and even in its .brief existence undoubtedly does not affect the whole mass of the gas through which the dis- charge passes. J.J. Thomson has called attention to this factt. In the case of the continuous discharge the tem- perature is undoubtedly vastly lower, but even here it is probable that the pale brush does not concern all the particles — of the rarefied gas, for otherwise the discharge in a wide tube should be as bright as the discharge in a narrow tube. Therefore calculations or experimental determinations of the average temperature of a large tube, such as those of Warburg { and Wood, while interesting as relative considera- tions, give no clue as to the kinetic energy of the molecules which actually carry the current. For such a clue one must refer to experiments of the sort we describe. All the results recorded in this paper support the well- known hypothesis that the current when disruptive is carried by dissociated molecules. The continuous discharge is best * Moreover, we find that the electrostatic capacity of the Geissler tube is not sufficient to affect the period of the oscillatory movement. To decide this, we arranged a rocking key which interposed first the Plucker tube, and then, immediately afterwards, a wire of self-induction equal to that of the tube, and photographed the oscillatory discharge through the two circuits. No change could be perceived in the period of the two discharges. If the electrostatic capacity of a Geissler tube were large, an argon tube would not be so sensitive as it is to slight changes in the electrostatic capacity in the circuit. + ‘Recent Researches,’ p. 167. { Wied. Ann. liv. p. 265. — and Ohmic Resistance of Gases. 365 explained by conceiving of a polarized condition, in which the molecules are in some way bound together by the electric energy which is striving to force itself through them. As the current increases the amount of the heat increases, until it reaches a stage when some of the gas is freed from this bondage—when the molecules not only separate from their electric embrace, but split into their component atoms. Then, if a large quantity of electricity is at hand to discharge itself, the rate of discharge increases with enormous rapidity, resulting in more dissociation, and the resistance is almost entirely broken down. A good resumé of the present state of this hypothesis is given in ‘ Nature, January 28th, 1897, p. 310, and to this statement our determination of the re- sistance makes an important addition. Hydrogen and cxygen cannot be dissociated to any appre- ciable extent at ordinary temperatures and pressures, otherwise water would form when they were mixed. We have no vapour-densities of hydrogen or oxygen at temperatures which show dissociation, but this is no reason for believing that at temperatures of 3000 degrees or more dissociation does not take place. Indeed, the burning of hydrogen and oxygen gives us every reason for believing that the tendency of both hydrogen and oxygen molecules to dissociate increases with the temperature. Chlorine, bromine, and iodine are all known to dissociate at high temperatures and to conduct electricity well under those conditions. Another point in favour of ascribing the red glow of hydrogen to dissociation is to be found in the fact that rarefied aqueous vapour gives the pure “ four-line”’ spectrum much more easily than hydrogen itself. In order to give any hydrogen spectrum at all, the vapour must be dissociated. Of course the dissociation takes place only at the moment of the discharge, the atoms combining again when cold. It is caused by the heat of the discharge, and not by electrolysis, although that too may take place at the electrodes. In short, there is every reason to believe that at temperatures as high as those with which we are dealing, the hydrogen is split apart into hydrogen atoms, and that these atoms, or perhaps the energy involved in the act of splitting them, are re- sponsible for the “ four-line” red spectrum. The fact cannot be too strongly emphasized that this sort of dissociation is very different indeed from the electrolytic dissociation of solutions. | _ In order to find if the structure which is dissociated by the spark is the molecule or some more complex structure, mereury vapour was subjected first to the continuous discharge Phil. Mag. 8. 5. Vol. 48, No. 264. May 1897. 2F 366 Messrs. Trowbridge and Richards on the Temperature and then to the oscillatory. Since the spectra obtained were widely different, the conclusion, at least in the case of the mercury, is that the structure is complex; for mercury molecules are monatomic. This conclusion is reinforced by many other facts known about the continuous discharge. Hence the existence of two argon spectra does not give any reason for disbelieving the evidence of specific heat with regard to the monatomic nature of argon. From the point of view of a mechanical conception of the causes producing the two spectra of a gas, it is easy to imagine that when the atoms are bound together in the polarized con- dition, the electricity by a succession of readjustments may travel step by step from one end of the tube to the other, at a comparatively low temperature, and so cause quite a different set of electromagnetic vibrations from those depend- ing upon the breaking down of this polarized system. The evidence that the second spectrum given by the oscillatory discharge is due either to the act of separating the atoms from one another, or to the passage of the electricity through the atoms already set free by the heat, has been given above. Hittorf’s experiments, in which he was able to send a very strong continuous current through a gas without the pro- duction of light, would seem to indicate that the light is due to energy involved at the moment of dissociation, but the spectra of the solar prominences lead to the opposite inference, and conclusive evidence upon this point is wanting. The dissimilar behaviour of different gases is easily accounted for by considering the two causes which are supposed to resist the dissociation : in the first place, the “ polarized” condition of the molecules, and in the next place, the chemical affinity of the atoms for one another. This last force is usually admitted to be greater in the case of nitrogen than in that of hydrogen, hence the difficulty, the irregularity and the abruptness of the transition in the former case. One should expect that a monatomic gas, like argon, where the polarization alone pre- vents the passage of the current, would be easier to change in this respect, as indeed it is. The fact that the second spectrum of mercury is not very easily obtained militates against this explanation, however. Assuming, then, that the red spectrum of hydrogen is due to the sudden occurrence of the reaction Ep gla Ee it is very interesting to note that our results agree with the necessary deductions from the law of mass action as applied and Ohmic Resistance of Gases. 367 to this case. If the reaction is supposed to take place iso- thermally at a very high temperature, it is manifest that the progress of the reaction from right to left must increase as the concentration of the hydrogen—in other words, the ten- sion of gas—is diminished. This we find to be the case : the resistance of the gas increases, and the purity of the ‘“four-line”’ spectrum diminishes as the tension of the gas increases, except when the gas is exceedingly rarefied. In this case it is probable that the number of atoms present, even if all were free, would be insufficient to carry all the current. Hence we should expect to find this minimum at a lower pressure when the capacity of the condenser employed was less; but, unfortunately, the spark is too uncertain at these very low tensions, even with 20,000 volts from the complete battery, to give definite results. Since hydrogen undoubtedly requires a very large amount of heat for its dissociation, it follows that when the tempera- ture is raised while the pressure is kept constant, more atoms should be set free. We find, as a matter of fact, that the resistance diminishes as we increase the capacity of the condenser—that is to say, the heat of the discharge. The case is exactly analogous to the dissociation of nitric peroxide observed by HE. and L. Natanson *. Our work leads one to infer that since a very high tempera- ture is needed to produce the “‘four-line”’ spectrum of hydrogen, this high temperature must be present whenever this spectrum appears, for example, in the solar prominences and in many fixed stars. The higher the tension of the gas, the higher the temperature required ; hence one must know the atmospheric pressures in these heavenly bodies before attempting to guess at the actual temperature attained ; but there can be no doubt that this temperature is in any case far beyond the reach of any earthly means except the electric discharge which we have been considering. Harvard University, Feb. 23rd, 1897. * Wied. Ann, xxiv. p. 454, and xxvii. p. 606. 22 prses 3 XLVI. On a Supposed Proof of a Theorem in Wave-motion. To the Editors of the Philosophical Magazine. GENTLEMEN, ye p. 281 A this volume of the Philosophical Maga- zine, Mr. Thomas Preston announces an extension Y of Fourier’s theorem whereby a scalar function of any number of variables may be expanded in a series of sines and cosines of linear functions of the variables, with coefficients expressible as definite integrals. This remarkable theorem is of much interest from the mathematician’s point of view, and is likely, when handled correctly, to be of use to physicists also. But, in applying it, it is essential that we should attend to the fact that it deals with scalar quantities only, and cannot be employed in physical problems except so far as the mathe- matical discussion of the problem, throughout whatever is its extent in space, admits of being brought into a scalar form. Another consideration must also be kept in mind, viz.: that what presents ilself in optics as diffraction is encountered in every real wave-motion. Both of these considerations, and the distinction between forced wave-motion and wave- motion which the medium is able to propagate, seem to have been overlooked in two attempts which Mr. Preston has made to employ his theorem to prove certain physical theorems which treat of real wave-motious, one attempt on p. 283 and the other on p. 285; and unfortunately the oversights vitiate the proofs which he offers. They also affect what is said in the third paragraph of his paper, on p. 281. This paragraph contains two statements, of which the first is erro- neous owing to the omission of these considerations, and the second can “only be rendered correct by interpreting the word ‘function’ to mean a function containing vectors as well as scalars, in which case the observation although true would have no relation to what follows it. In the first paragraph of his paper, on p. 281, Mr. Preston quotes the enunciation of a theorem in wave- propagati on as follows :-— ‘‘ However complex the contents of the objective field, and whether it or parts of it be self-luminous, or illuminated in any way however special, the light which emanates from it may be resolved into undulations each of which consists of uniform plane waves.” This enunciation is taken from a paper on Microscopic Vision, and is in reality a general theorem in wave-motion On a Supposed Proof of « Theorem in Wave-motion. 369 though presented there in its optical form only. It may be freed from limitation while keeping the enunciation sub- stantially the same, and then becomes :— Tf space be occupied by any uniform medium capable of propagating waves, and if a disturbance however complex is called into existence within a defined portion oj the space, then the undulations which emanate from the disturbance and spread through the rest of space may be resolved into undulations of the medium each of which consists of uniform plane waves. This may be called Theorem A. It is a theorem which the present writer proved geometrically and of which a symbolical proof is much wanted. A correct symbolical proof, when- ever it is discovered, will probably lead to useful determi- nations of the coefficients of the expansion in Theorem A, involving vectors as well as scalars, but otherwise somewhat like (though necessarily more complex than) the expressions for the coefficients of a Fourier’s expansion. To accomplish this would be an important service. Mr. Preston endeavours to supply this desideratum in the paper now under discussion. Each of the plane waves of Theorem A has been shown by the present writer to be of unlimited extent in its plane and uniform over its whole extent. It is therefore a wave which as it travels forward remains unchanged whatever be the medium that occupies the space, provided only that the medium be uniform. Observe also that what the waves are does not depend exclusively upon what the disturbance is, but upon this in conjunction with the physical properties of the medium. Accordingly any expressions for the coefticients of the terms of the expansion which supposes these coefficients to be functions of the disturbance only, such as the values given by Mr. Preston at the top of p. 283, must be wrong. They can only belong to some kinematical resolution consisting of forced vibrations ; a mathematical exercise of little use in physics, since it supplies no information about the real resolution into plane waves effected by nature which is what is dealt with in Theorem A. Of the consequences of Theorem A, that which is of most value to the physicist, is that the radiations owéside the region of disturbance resolve themselves into undulations of uniform plane waves. It is of somewhat less importance to the physicist, though equally true, that the theorem also resolves the disturbance itself into these same undulations, if the dis- turbance be of such a kind that it expends all its energy in propagating waves. (See the condition numbered 3, on page 141 of this volume.) The truth of this second part of the theorem is shown in the paper on Microscopic Vision referred 370 Dr. G. J. Stoney on a Supposed Proof to by Mr. Preston, where it is demonstrated that the undula- tions of plane waves are competent to form what is there called the Standard Image: an image which is identical with the original disturbance if the latter be one which expends all its energy in the propagation of the waves. (See p. 339 of the Philosophical Magazine for October 1896.) Accordingly the theorem may be enunciated under either of two aspects. It is immaterial into which form it is put, since each implies the other, so that either being established both are proved. Mr. Preston adopts the second form in paragraph 2 of his paper, on p. 281, where he puts the enunciation into the following terms, to which I have made additions within brackets which are introduced to make the meaning unmistakable :— “ Any disturbance however complex within a given region of space”? [provided only that tt be one which expends all tts energy in generating waves| “may be resolved into a system of plane-wave components” [which are real]; that is, which belong to the undulations actually generated in the medium that pervades the space—undulations which if unobstructed spread from the disturbance through the whole of space. Such being Theorem A, we have now to compare it, or rather contrast it, with Theorem B, which Mr. Preston sup- poses to be its analytical expression. Theorem B will be found at p. 283 of Mr. Preston’s paper, and is as follows :— f(a, Y, 2 t) = XA cos (pet gy t+rz+ st) (B) +> B sin i ee eae ne in which the coefficients, the A’s and B’s, have the purely scalar values assigned to them at the top of the same page. Accordingly vectors have no place anywhere in equation (B) ; and as a consequence /(x,y¥, z, t) is incompetent to represent the “disturbance however complex within a given region,” which is what we have to analyse. In fact any single ex- pression, like the first or the second member of equation (B), which purports to represent a “disturbance however com- plex,’ must include the vectors of the transversals as well as their scalar values. Moreover, in using equation (B) the coordinates w, y, z must be restricted to points within the “ given region of space.” The supposition then that the scalar equation given by Mr. Preston can possibly be the analytical expression of Theorem A, falls to the ground. It may at first sight appear as if these difficulties could be met by the familiar expedient of representing the motion within a given space not by the one function F(a, y, z, ¢) which is not scalar, but by three purely scalar equations, of a Theorem in Wave-motion. 371 such as E=/i(4, y, 2, ¢), n=o(2,Y, 2, t), S=/3(2, ¥, 2, ¢), (where &, 7, and € may be displacements, or velocities, or so on, in the three coordinate directions); and by then expand- ing each of these by Mr. Preston’s theorem. But on a close scrutiny we find that though this furnishes an apparent solu- tion, in the form of forced vibrations, or rather a group of such solutions, this group unfortunately does not include the solution which would be selected by nature under any con- ceivable circumstances. The analysis furnishes undulations which could not propagate themselves through any medium. The motions which it furnishes are the non-natural motions of a mere forced kinematical resolution, of no use in physics. That this is so can be made plain by taking any very simple example, such as the following. Let the “ given region of space” within which the disturb- ance is maintained be a thin circular disk perpendicular to the axis of z; let the origin of coordinates be at the centre of the disk, let the disturbance maintained within it be of the simple kind represented by £=f(vt—2) +/(ul +2), and let the medium be the eether. The undulations which will be generated by this disturbance will propagate themselves both forwards and backwards and both within and beyond the disk ; and as from symmetry the two groups of undulations will be exactly alike, it will suffice to ascertain what those travelling forwards will be. This is easily done from the circumstance that they closely approxi- mate to being identical with the radiations forwards from a circular opening in a screen of the size of the disk, when the light from a star, or rather that part of it polarized in one direction, is allowed to fall perpendicularly on the back of the screen. Before reaching the screen the light from the star of any one wave-length is as near an approximation as can be realised to being a single undulation of uniform plane waves with each wave of infinite extent in its own plane. A cylindrical beam out of this undulation is what reaches the opening in the screen. Until it reaches the opening it is an absolutely single train of uniform plane waves. But at the opening it ceases to be this single beam. From that situation forwards it spreads in a highly complex way over what we may call a 372° Dr. G. J. Stoney on a Supposed Proof cone of dispersion, and becomes that sheaf of innumerable radiations which produce the well-known diffraction effects. That they form avery complex system and are infinite in number may be seen from the considerations in the subjoined footnote”. Let us now turn to the events that would arise if the dis- turbance €=/(vwt—z)+/f(vi+<) were maintained throughout the disk-like region of space. Here a highly complex sheaf of radiations almost identical with that described in the last paragraph would be emitted forwards by the disturbance in the disk, and an exactly similar one back- wards. What Theorem A tells us is that these two complex systems of radiations can be resolved into znnumerable undu- Jations, each of perfectly uniform plane waves, each of infinite extent laterally, and each advancing in its own direction through space without undergoing change. Further, that if all of these were made to cross the disk, they by their mutual interference would unite to produce within that small portion of space the extremely simple motion represented by E=/(vi—z) +/f(vt +z), while everywhere else in space, whether in the plane of the disk or outside it, they by their inter- ference develop not that motion, but the radiations which emanate from itt. ‘This is information of importance. I¢ is a true analysis of events that are really going on. Contrast this with the kinematical information supplied by Theorem B, viz. :—The motion within the disk represented by 272 E=/(ut—2) + (ol +2) can be forcibly resolved into two mathematical series, the * The innumerable direct and diffracted undulations which advance from the opening in the screen and which are furnished by Theorem A, could be each concentrated into a point by an aplanatic lens of infinite aperture placed in front of the opening in the screen so as to receive all the light which emerges from it. In practice the lens need not be of infinite aperture, since the same resultant effect is produced by a lens whose aperture is somewhat larger than the opening in the screen. This furnishes as the image of the star a spurious disk surrounded by rings. Accordingly every point of this complex image is the concentration of one of the undulations of uniform plane waves of infinite extent laterally, which are furnished by Theorem A. { Along with the radiations which converging upon the disk would produce in it the motion =/(vt—z)+/(rt+z). In fact, each infinite undulation necessarily consists of a moiety of the undulation flowing in towards the region of disturbance, of a small portion travelling across it, and of the rest travelling past or from it. But practically. the presence of the inflowing portions causes no inconvenience, because in the appli- cations of the theorem the radiations that are outward bound, and those inward bound, are easily discriminated. ) of a Theorem in Wave-motion. 373 terms of which represent mere artificial undulations which advance in only two directions, one perpendicularly forwards the other perpendicularly backwards across the disk, which may not be carried one step outside it, which inside it are of a kind that no medium could propagate, which are in fact a mere mathematical fiction, and not any physical analysis whatever of events going on in nature. Yet these two analyses, one by Theorem A the other by Fourier’s Theorem, though so utterly unlike, are identified with one another in the first of the two statements made in the third paragraph of Mr, Preston’s paper. _ In the paper preceding Mr. Preston’s it is shown on p. 273 that Theorem A may be expressed symbolically by the equation Fiz, y,2,t)= \j = | sin (27 ON : — +2)] -sin @d0dg, (A) where r=acos6@+ysin@cos¢+zsin@sind, and in which the M’s are directed quantities. The values of v and the vector components of the M’s depend on the properties of the medium, and may be expressed as functions of 0 and @ when we know the equation of the wave-surface in the medium. On the other hand the e#’s and the scalar components of the M’s depend on the originating disturbance. Now what is wanted is such an analytical proof of Theorem A as will give us symbolical expressions for these quantities as functions of @and qd; and it may be hoped that Mr. Preston, with his experience in dealing with this class of problem, will yet be able to substitute the really valuable proof which will accom- plish this for the illusory proof which, on a first view, he has mistaken for it. _ I have made a slight attempt by adopting polar coordinates, but hitherto without success, to find some use for Mr. Preston’s extension of Fourier’s Theorem. It is perhaps not impos- sible that a fuller search in this direction may bear fruit. ‘But whatever the issue, it is plain that Mr. Preston’s extension of Fourier’s Theorem, though it may be of limited applicability in physics, is of interest as a mathematical theorem. : I am, Gentlemen, Faithfully yours, G. JOHNSTONE STONEY. 8 Upper Hornsey Rise, N., April 12, 1897. he B74 oq XLIX. Liquid Coherers and Mobile Conductors. By Rotto APPLEYARD™*. iP a communication tf made three years ago to the Physical Society, I described some experiments illustrating the change in electrical resistance of certain complex bodies under the influence of oscillatory discharges. All the substances dealt with were solids ; and the coherence was invisible. The change of condition had therefore to be demonstrated either by measuring the resistance before and after discharge, or by connecting the coherers permanently in series with a battery and galvanometer. The three experiments now brought before you have regard to “‘coherers”’ formed of liquid dielectrics, and mobile con- ductors. By choosing a transparent dielectric and an opaque conducting substance, it is possible to examine the process of coherence by direct observation. But it may be well to premise that the similarity of results obtained with solid and liquid “ coherers,” respectively, in no way proves a similarity of process. The two sets of phenomena are probably related, but are not necessarily identical. The term “dielectric ”’ is here to be understood as signifying merely a substance of low conductivity. Experiment 1—A glass tube about eighteen inches long, and haif-an-inch wide, is sealed at one end and corked at the other. Platinum electrodes are inserted at each end. The tube is nearly filled with about equal volumes of paraffin-oil and mercury. If it is laid upon a flat table and shaken, horizontally, for a few minutes, the mercury breaks up into small spheroids; and, by a little manipulation, these can be disposed as a chain of particles lying evenly between the platinum electrodes. The resistance of the chain of mercury spheroids, measured under these conditions, is several megohms. If we now connect the electrodes to a battery of about two hundred volts, the whole regime is suddenly altered. At the moment of applying the current, the spheroids of mercury, within the tube of oil, are visibly impelled, as though a mechanical tap had been administered to the glass ; and, almost simultaneously, they coalesce into large globules. The resistance is now represented by a few ohms. Exactly the same result can be brought about by sup- porting the tube near a Hertz oscillator; or, still more simply, by passing a spark into one or other, or both, of the * Communicated by the Physical Scciety: read March 26, 1897, + “Dielectrics,” Phil. Mag. xxxviii. p. 396 (1894); Pree. Physical Society, xili. p. 155 (1895., | Liquid Coherers and Mobile Conductors. . 375 electrodes. In order to retard the spontaneous coherence of the mercury, resulting from mutual pressure of the spheroids, it is well to keep the tube horizontal. If, however, it is desired quickly to convert a body of mercury from the sub- divided to the ordinary state, sparks may be passed into the tube while it is more or less vertical. The running-together of subdivided mercury is more leisurely to be observed with large globules. These form separate, elongated, conductors. The way in which they unite will be referred to in describing Experiment 3. Haperiment 2.—A glass tube, similar to the first, but some- what wider, is nearly filled with a mixture of paraffin-oil and water, and vigorously shaken. I propose to call this a “ rain” tube. Ifit is kept at rest, the oil, in the common course of events, floats to the top in a few minutes. The “ rain” tube, however, shows that the separation, especially towards the final stage, is accelerated by the passage of a spark, or by a direct current from a battery of about a thousand volts. Ifthe conditions are right, the water particles suspended in the oil cohere, at the moment of electrification, to form larger drops. The frictional resistance to falling is thereby diminished, and the water is consequently precipitated in and through the oil. Jt may sometimes be seen descending in a rapid suc- cession of globules, precisely as large rain-drops are precipitated after thunder. About equal parts of oil and water is a good proportion. The containing vessel may be either a tube ora flask ; it should not be more than three-quarters full of liquid. This free space facilitates the mixing when the tube or flask is shaken. The phenomenon is rendered much more striking by colouring the oil with alkanet-root. I have to thank Prof. McLeod for suggesting this pigment. Heperiment 3.—The behaviour of a mobile conductor, when electrified in a partially conducting liquid, is readily examined by pouring a little mercury into a flat photographic dish con- taining a stratum of paraftin-oil and water. The presence of the oil is necessary to prevent the mercury from running together too freely of its own accord. A battery of from, say, one volt to two hundred is required, and a pair of wires to dip into the dish. A reversing-key, such as is used for cable transmission, may be included in the circuit. Suppose we begin with a large globule of mercury in each of any pair of corners of the photographic dish, several inches apart ; and let the globules be connected one to each pole of the battery, by means of the dipping wires. A momentary tap of the key causes instantaneous deformation of the mercury in each corner, especially of that connected to the negative pole ; and there is evident attraction between the globules, 376 Messrs. Richards and Trowbridge on the Effect of Great Sometimes the mercury gets into a lethargic condition; but it can always be roused by mechanical agitation of the surface. Now let the current be kept on for a few seconds ; the negative globule sends forth a tentacle towards the positive globule, the length of the tentacle depending upon the current and the distance between the globules. Under favourable cir- cumstances it may extend from corner to corner, and thus establish contact ; or fissure may occur, the tentacle breaking into spheroids ; and these spheroids may cross over between the globules. This is the order of things usually to be observed, but the action is sometimes erratic. Let us now bring back the scattered globules of mercury to their respective corners, and distribute a few isolated spheroids in the interspace. Jn addition to the effects previously noticed at the terminal globules, we now see that, when the current is applied, each intermediate ‘spheroid extends a “ finger ” towards the positive globule. This is the process of mobile coherence ; the short “ fingers,” or long “tentacles,” form links between consecutive spheroids, and finally a complete conducting circuit is established. By successive applications of the current, any elongated bodies of mereury between the terminal globules can be made to creep along like caterpillars; the successive forward motions of the ‘tentacle, or tail, cause a corresponding retro- gression of the globule as a w ‘hole. Any small spheroids scattered about the dish may be urged in a direction depending upon the direction of the successive current impulses; and a “ finger ” will always appear on the side towards the positive electrode. So that by choosing a ‘convenient stray spheroid, and operating a battery-reverser as a transmitting-key, a telegraphic receiver is improvised from no other apparatus than a drop of mercury and a little oil. By some such means the awakening genius of primi- tive man may have contrived all the subtle machinery of a telegraph-instrument upon the smooth surface of an oyster- shell. L. The Effect of Great Current-Strength on the Conductivity of Electrolytes. By Y THEODORE WILLIAM RICHARDS and JoHN TROWBRIDGE * ci our paper on the temperature and ohmic resistance of gases during the oscillatory electric discharge ft, “we have described a method of determining resistance by * Communicated by the ae T Page 349, supra. : Current-Strength on the Conductivity of Electrolytes. 377 measuring its damping effect upon electric oscillations. The method is obviously one which will apply to electrolytes also, provided that the resistance to be measured is less than twenty ohms; and it seemed to be very well worth while to determine if the intense current involved in the discharge of a large condenser is capable of causing any change in the condition of an electrolyte. In our first experiment, two copper plates of sixteen square centimetres area were clamped at a distance of three centi- metres apart by means of vulcanite. Upon being immersed in a saturated solution of pure cupric sulphate at 15° C., the plates allowed about ten oscillations from one of our large leyden-jars, nine from two jars, and eight from three jars to pass through it. According to the scale of standards, given in our last paper (see fig. 2, p. 355), each of these results corre- sponds to a little less than four ohms’ resistance. By means of Kohlrausch’s method, using a very small inductorium, this cell gave an extremely poor minimum at a point corresponding to a resistance of about ten ohms. The plates, which had purposely been left very dirty, in order to test the efficiency of the method, were now scrupulously cleaned with alkali and acid, and were then both carefully plated with pure copper. With Kohlrausch’s method the cell now gave an excellent minimum at exactly four ohms’ resistance, and further clean- ing and plating caused no further change. New photographs of the sparks from the two jars sent through the cell showed again about nine half-oscillations, corresponding to about 3°8 ohms. It is evident, then, that the resistance of concentrated cupric sulphate is not essentially altered by great alterations in the strength of the current. Hxperiments with zincic sulphate gave similar results, and a solution of cadmic sulphate between cadmium electrodes which possessed a resistance of 4°7 ohms according to Kohl- rausch’s method, gave nine, seven, and six half-oscillations with one, two, and three jars respectively, corresponding to about 5 ohms in each case. ; 5. Woe Undoubtedly the reason why the strong instantaneous cur- rent, which alters so much the resistance of gases, has so little effect upon solutions, is because of the great mass and specific heat of the material which must be warmed in the latter case. The average temperature of the solution rose during our experiments only at the rate of about 1° in three minutes. A similar, although smaller, heat-capacity prevents the wire resistances which are used as standards from becoming seriously altered in resistance by the heat. We had used 378 Prof. J. Trowbridge on the Electrical mianganin wire in our tests ; but in order to be sure that our fine short wires had not been overheated, we constructed a five-ohm resistance of four strands of coarse manganin wire about 0°25 millim. diameter and 3°5 metres long. This was stretched upon each side of a thin vulcanite plate to avoid self-induction, but it allowed essentially the same number of oscillations to pass as did the short fine wire. A short german- silver wire, with a very high temperature-coefficient, showed a conductivity only a very little less ; thus the error from the heating of the wire may be neglected. In order to show that common electrolytic polarization does not interfere with the accuracy of our method, we measured with the help of our 20,000 volt storage-battery and conden- sers the resistance between two bright platinum plates similar in size to the copper ones described above in a cupric sulphate solution. This was found to be four ohms, and after plating the electrodes with copper the resistance remained unchanged. Kohlrausch’s method gave no satisfactory result with both electrodes free from copper, but when both were plated it indicated a resistance of 3°9 ohms. Our method may therefore be a useful one for the approxi- mate determination of conductivities in cases where impurities or polarization render Kohlrausch’s method unsatisfactory. For accuracy, of course pains must be taken to develop all the photographs in the same fashion, and in general to arrange the conditions of the exposure alike in all cases. Our conclusion that the conductivity of electrolytes is not greatly affected by great changes in current-strength only emphasizes all the more strongly the conclusion of our last paper, that the conductivity of gases is very much affected by changes in the current-strength. Harvard University, March 8, 1897. LI. The Electrical Conductivity of the Atther. By Joun TROWBRIDGE*. HE electrical conductivity of the ether has been main- tained by Ediund and has been apparently disproved by various recent investigations—notably those of Prof. J. J. Thomson{. The latter writer, in his treatise entitled ‘ Recent Researches in Electricity and Magnetism,’ also remarks, p. 98:—“‘Again, if we accept Maxwell’s Electromagnetic * Communicated by the Author. t Roy. Soe, Proc. vol. xlv. 1888, p. 280, Conductivity of the Atther. 379 Theory of Light, a vacuum cannot be a conductor or it would be opaque, and we should not receive any light from the sun or stars.” The experiments which have been made hitherto on this subject have been conducted with comparatively feeble electrostatic forces. By means of a storage- battery of 10,000 cells in connexion with a Planté rheostatic machine* I have studied the resistance of highly rarefied media under dis- ruptive discharges, and I am led to the conclusion that with a sufficiently powerful electrical stress, what we term a vacuum can be broken down, and that the disruptive discharge during its oscillations encounters very little resistance. In the case of a highly exhausted Crookes tube I have measured this resistance and find it in the special case I considered less than three ohms. My experiments lead me to the conclusion that the chief resistance is encountered at the surface of the electrodes, and that when this is overcome the ether offers little resist- ance. The method I have employed seems to me to be a very useful one for the study of electrical discharges. It may be termed the damping of the additional Spark Method, or the comparison of resistances by the estimation of the damping of electrical oscillationst. The electrical circuit is provided with two spark-gaps. One of these is placed in a gas, or under the conditions which are to be examined, while the other is photographed according to Feddersen’s method by a revolving mirror. With cadmium terminals this method enables one to estimate the resistance of a spark in air or in rarefied media to one half an ohm. Having at my command a battery giving a voltage of twenty thousand, with an internal resistance of only one quarter of an ohm per cell, and capable therefore of giving a very powerful current, I first studied the behaviour of Crookes tubes which were connected to the terminals of this battery. I found that no Réntgen rays could be obtained with a voltage of twenty thousand. On heating the Crookes tubes, they were filled with a pale white light, which showed very faint bands in the green when examined by the spectro- scope. Then the entire strength of the battery appeared to be manifested in the tubes, the electrodes became red-hot— the medium broke down and offered no resistance to the current of the battery. This white discharge showed even at its culminating point no Réntgen rays. I then employed * Comptes. Rend. t. \xxxv. p. 794, Oct. 1877. + “Damping of Electrical Oscillations on Iron Wires” (Phil. Mag. Dec. 1891). 2 380 Prof. J. Trowbridge on the Electrica the Planté rheostatic machine. ‘This apparatus,-I think, has not received sufficient attention from physicists. In connexion with a large battery it is very efficient and it enables one to form an estimate of the high electromotive force that one employs in the study of the Réntgen rays. I have slightly modified the form of the machine as it is given by Plante. The main- principle consists in charging leyden-jars in multiple and then discharging them in series. The proportion of the length of spark to the number of jars is very close. Knowing the electromotive force of the battery which charges the jars we can estimate the voltage necessary to produce sparks of different lengths. -I speedily found that at least one hundred thousand volts were necessary to produce the Roéntgen rays, and they were produced more intensely as I increased the voltage, certainly to the point of five thousand volts. In order to ascertain whether the discharges through the Crookes tubes when the Réntgen rays were apparently pro- duced most strongly were oscillatory, I first placed a Geissler tube in the circuit with the Crookes tube and carefully observed the appearances of the two electrodes of the Geissler tube. They were quite alike and indicated an oscillatory discharge. J then replaced the latter tube by a small spark- gap and photographed the spark in a rapidly revolving mirror. The photograph showed at least ten oscillations with a period of about one millionth of a second with the Crookes tube and the circuit I employed. Furthermore, applying the method of estimating resistances by the method of damping, I found that the resistance of the rarefied medium was less than five chms. The energy, therefore, at the moment of the emission of the Rontgen rays was not far from three million horse- power acting for one millionth of a second. I employed also a Crookes tube with an aluminium mirror of about two centi- metres focus. ‘The resistance of this tube to the discharge was the same as that in which the mirror had a focal length of six centimetres. Incidentally, there seems to be no advantage in shortening the distance between the kathode and the anode by employing a mirror of short focus. Struck by- the fact. that the distance between the electrodes did not appear to make any appreciable difference in the resistance of the Crookes tube, I replaced the latter by a spark-gap of six inches in length in air, and photographed the spark in another gap in-air in the- same circuit. This latter gap was one quarter of an inch. The photographs showed on an average the same number of oscillations whether the secondary spark- gap was six inches in length or one inch in length. I feund Conductivity of the Atther. 381 moreover, that on increasing the electromotive force the resistance of the sparks in air decreased. By quickly drawing apart the terminals of my large battery I can produce a flaming discharge in air of about three feet in length. Righi has also observed the same phenomenon with sparks from an electrical machine. We see that no increase in resistance results. I then placed the secondary spark-gap in a receiver and studied the resistance offered by rarefied air at the point when long ribbon-like white disruptive discharges can be obtained. This point is at about 100 millim. pressure. The resistance of such discharges of about six inches in length in a receiver containing air at this pressure is two or three ohms more than sparks of one quarter of an inch in air; the latter have a resistance of from two to three ohms. On measuring by the above method the resistance of sparks of different lengths in the receiver at this pressure, no difference in resistance could be perceived between a spark of six inches in length and one of three inches in length. The secondary spark-gap was next placed in a chamber of air which was compressed to fouratmospheres. This amount of compression made no difference in the resistance to the disruptive discharges. The additional spark was also obtained in hydrogen gas generated by electrolysis at atmospheric pressure, and no appreciable difference in resistance between this gas and air was noticed. The length of spark which could be obtained with a given voltage was somewhat more in hydrogen than in air. It was interesting, in the next place, to determine by this method whether differences in the material of the spark-gaps made any difference in the resist- ances observed in the case of disruptive discharges*. I accord- ingly employed terminals of platinum, iron, aluminium, brass, cadmium, and zine, and could perceive no difference. More- over, any difference of resistance between spheres and between pointed terminals, or between a point and a plane, seemed to be inappreciable. With powerful discharges such differences, if they exist, apparently disappear. The additional spark was next placed ina heated flame. It is well known that the spark-length can be thus greatly increased. On photo- graphing a spark in an additional gap the resistance appeared to be slightly increased in the flame ; doubling the length of this spark, however, made no change in the resistance that ‘was encountered in the heated medium. The phenomenon was exactly analogous to that observed in the receiver ex- hausted to 100 millim. I was interested to observe whether * Righi, Nuovo Cimento (2) xvi. p. 97 (1876); De La Rue and Hugo -Miiller, Phil. Trans. clxix. pt. i. p. 98 (1878). ~ Phil. Mag. 8. 5, Vol. 48. No. 264. May 1897. 2G nN A eee 382 The Electrical Conductivity of the Aither. heating the spark in the primary of a Thomson-Tesla trans- former produced any marked change in the high-tension spark of its secondary. It was evident that it was detrimental. The high-tension sparks immediately ceased to jump at the extreme sparking-distance of the terminals. Following this train of thought I next placed a spark-gap of the primary of the above-mentioned transformer between the poles of a very powerful magnet, giving a field of certainly ten thousand lines to the centimetre. It is well known that when such a field is excited, the primary spark appears to be blown out with a loud report and a great increase of length of spark is obtained in the secondary of the transformer. Applying the same method, I photographed the spark of the additional spark-gap and found no difference in resistance whether the magnetic field was excited or not: or when the spark jumped across the magnetic lines or in the direction of the latter. Is it possible that the ether being already under a magnetic stress, the addition of a powerful electrostatic stress serves to suddenly break down the ether? It is well known that a blast of air imitates the action of the magnetic field. It probably does so by blowing out the voltaic are which tends to form. It may be that the electrodynamic repulsion com- pels the spark not to follow, so to speak, the voltaic are and its current of heated air. The loud report may indicate a sudden stress in the medium, and in the case of the Crookes tube the highly rarefied medium within it would effectually prevent our hearing a similar report. I next placed the primary spark of the Thomson-Tesla transformer near a Crookes tube which was giving out the Rontgen rays. I could not perceive any mutual effect. The effect, moreover, of ultra-violet light on the resistance of sparks in air could not be detected. The method I have outlined enables one to form an estimate of the energy incident upon the production of the Rontgen rays. It can also measure with greater accuracy than has been possible hitherto the resistance of sparks in air and different media. It shows conclusively that the discharge in a Crookes tube at the instant when the Réntgen rays are being emitted most intensely is an oscillatory discharge. In popular language, it can be maintained that a discharge of lightning a mile long, under certain conditions, encounters no more resistance during its oscillations than one of a foot in length. In other words, Ohm’s law does not hold for electric sparks in air or gases. Disruptive discharges in gases and in air appear to be of the nature of voltaic ares. Hach oscilla- tion can be considered as forming an arc. It is well known On Stationary Electrical Waves in Wires. 383 that a minute spark precedes the formation of the voltaic arc in air. The medium is first broken down and then the arc follows the drawn apart carbons. I believe that this process occurs also in a vacuum, and that absolute contact is not necessary to start the arc. My experiments lead me to con- clude that under very high electrical stress the ether breaks down and becomes a good conductor. Jefferson Physical Laboratory, Harvard University, Cambridge, Mass., U.S. — LIL. On the Effect of Capacity on Stationary Electrical Waves in Wires. By W.B. Morton, M.A.* HILE working recently at stationary electrical waves in wires produced in Blondlot’s manner, I was led to make some measurements on the ettect produced when a capacity is inserted at a point of the secondary circuit. The positions of the successive nodes were explored in the usual way by a bridye, the indicator being a vacuum tube which was placed across the wires and which showed a maximum of brightness when the bridge was at a node. When two opposite points of the parallel secondary wires were joined to the plates of a small air condenser, the effect was to bring closer together the nodes on the two sides of the condenser, the amount of this shortening of the apparent half wave-length depending on the position of the inserted capacity. The effect was nil when the condenser was at a node, and maximum when it was mid- way between two nodes. ‘This influence of the increased capacity of the wires is of course of the same nature as the shortening of the wave-length when the wires pass from air into a dielectric liquid. Drude and others have made use of this way of measuring directly the index of refraction of different liquids for the electric waves; but the influence of an isolated capacity does not seem to have been much studied. Salvioni has published { some measurements on the effect of capacity inserted at a point between the end con- denser and a bridge. When the second condenser was put in it was necessary, in order to restore resonance, to alter the distance of the plates of the end condenser. Von Geitlert got rid of the reflected waves by using a terminal resistance * Communicated by the Physical Society : read April 9, 1897. + Rend. Acc. Linc. 1892, pp. 250-253; Wied. Bebl. xvii. p. 485. { Wied. Ann. xlix. pp. 184-195 (1893); cf Barton and Bryan, Proc. Phys. Soc. xv. p. 23. 2G2 384 Mr. W. B. Morton on the Effect of Capacity so that no standing oscillations were formed in the wires. He found that when a condenser was inserted it caused reflexion of the waves, and a series of nodes and loops could be found in front of the condenser. Mazzotto* in a recent research has availed himself of the effect of an isolated capacity to produce.a gradual change in the wave-length of the oscilla- tions. He uses pieces of wire hung on to the parallel wires. The theory of electric waves in wires has recently been treated in an exhaustive manner by Drudet. His method consists in following out in detail the various reflexions undergone at the bridges by a wave-train which starts from the end of the wires. The state of affairs at a point of the circuit is obtained by summation of a series of separate dis- turbances due to the different direct and reflected trains. The calculations are rather complicated. In obtaining a formula with which to compare my observations I have used a method adapted from some work of Mr. Heaviside’st. A'part from the actual results obtained, the investigation is perhaps of some interest as showing how easily some problems con- nected with oscillations in wires can be attacked by this method. y The experiments were made, for the most part, at the end of the parallel secondary wires remote from the oscillator, the arrangement being as shown in the diagram. A Goa Sy B So > anes a a ee C is the end condenser of capacity S,. 8, an interposed condenser. The vacuum tube was placed across the plates of S,. The plates of S, and 8, were kept at a constant distance apart while the position of 8, was varied. A nodal position B of the bridge having been found so that the tube shone, B was left on the wires, and A laid on and adjusted so that the tube remained bright. Then A, B are nodes of the same system. Owing to the finite length of the bridge the potential-difference at its ends is not quite zero, the trué— node falling at the centre of the bridge. Accordingly, if the bridge B is taken off the wires the nodes will fall a short dis- tance to the left of B—roughly half the length of the bridge. This distance Drude has called the ‘“‘ bridge-shortening.” In * Nuov. Cim. [4] ii. pp. 296-311 (1895) ; Wied. Beil. xx. p. 392. + Abhandl. der Siichs. Ges. der Wiss. xxiii. pp. 64-168 (1896) ; Wied. Ann. \x. pp. 1-46 (1897). { ‘Electrical Papers,’ ii. p. 194 et seq. on Stationary Electrical Waves in Wires. 385 order to restore maximum brightness in the tube, the bridge A must now be displaced in the same direction through twzce the “ bridge-shortening.”” ‘The difference in the positions of A, according as Bis on or off the wires, gives us therefore a means of finding the correction to be applied to the observed bridge-positions to get the true nodes in the wires. We want to express that the circuits AB and BC are in resonance. Jn order to find approximately the period of oscillation of such circuits we can proceed as follows :—Sup- pose a simple harmonic potential-difference Vj sin nt to be kept up between the wires at one end of the circuit, and find an expression for the oscillations produced in the circuit. The amplitude of these oscillations will become infinite when n corresponds to the natural period of the system. A formula has been obtained by Cohn and Heerwagen for a circuit like BC. I have not found any discussion of the circuit AB. We neglect the resistance of the wires and put S for their capacity and L for their induction per unit-length, both sup- posed constant. This will be only approximately true as we approach the ends of the circuits. The equations connecting the current C and potential-difference V are _ WV _ 7a de PF at _ dG _ dV dix dt dx being the element of length, a2V AV ee daz =L8S 9 or if V varies as sin nt P = = — LSn*7V=—<@’V, CE ea 3 where g=n VLS=; = oe vis the velocity of radiation, and » the wave-length along free wires; “. V=(A cos gv+B sin ga) sin nt. This gives — Ce iG (A sin gu—B cos gx) cos né. Take first the circuit BC. Here we have V=V>sin nt when «=0, and C=8,5 when w=c, 386 Mr. W. B. Morton on the Effect of Capacity 25 A=Y;; Z and : ~ = (A sin ge—B cos ge) = S.n(A cos ge + B sin ge). Putting tan a= LS gn’ — LS8,v’¢ = og we get B=A tan (qce+<@), / — and vay, £28 fa(e Memegen ss cos (qc+a) The amplitude becomes infinite when ge+a= ~ ; cot ge=tan a; ’ 27rc iis, 20 Se 2. @. Ce = Re . ot ° = fee (1) This is Cohn and Heerwagen’s formula. Taking now circuit AB, suppose the impressed potential- difference to act at A. Let V,= (A, cos gz+B, sin gz) sinnt between e=0 and «=a, V.= (A, cos gx + B, sin gz) sin nt between c=a and c=b. The conditions to be satisfied are :— at x=0, V,=V,sin nt, at £=@,i). Vi= V5, T and C,—C,= Si — at z=at+b, V=0. Putting in the values we get AGW a A, cos ga + B, sin ga= A, cos ga+ B, sin ga = n{(—Ay+ A,) sin ga + (B,—B,) cos ga}, A, cos g(a+b)+ Bosin g(a+b) =0, gS; s: On solving these equations for the constants we find t has been put for _ sin g(a+b—2) —tsing(a—2z) sngb. . ae sin g(a+6) —¢ sin ga sin gb Yoon sin g(a +b—2) a Te ~ sin g(a+6) —tsin ga sin gb Vo 2 on Stationary Electrical Waves in Wires. 387 Equating the denominator to zero we find Cab ga 1 COUGO— le ele or QTra Oh) Ds TSS cot > + cot = Sie (2) This formula, which connects the frequency of the oscillation with the position and capacity of the condenser, might have been deduced from formula (1). For we can imagine the capacity 8, divided into two parts, o and o’, in such a way that when these parts are attached to the parts a and b of the circuit respectively, the two partial systems oscillate indepen- dently with the same frequency. We have thus from formula (1), Fp MM 6) te Se wot 2 2 ya eS On adding we get equation (2). In seeking to test the agreement between the theory and the observations, formula (2) was written r 27ra gd 1 ats | cot oF COE a | = Gee constant. A small error in observation of the node position causes an error in the left-hand side very large in proportion, and of amount varying with the position of the condenser in the circuit. In view of this the method adopted was to find the mean value of By from the observations and, using it, to cal- culate the values of b corresponding to each a. A comparison of the observed and calculated values of } shows a sufficiently good agreement, the discrepancy being greatest when the condenser is too near a bridge. One set of observations involving only the circuit AB and formula (2) were taken on a small apparatus at the end near the oscillator. One bridge was kept fixed and the wave- length was the same throughout. Thus only the quantity d was liable to the error in determining the node. The uncer- tainty in this determination amounted to about 5 millim. The wires were about 15 millim. apart, and the condenser consisted of two small copper strips, 1 centim. by 5 centim., hung on the wires. The half wave-length was 37°5 centim, The following table gives the results measured in centimetres :— 388 Mr. W. B. Morton on the Effect of Capacity TABLE I. b a | a. Cale Obs 2-0 34:7 33-1 6-0 19:8 175 80 134 12:9 10:0 103 105 12-0 85 8-7 14-0 77 79 20-0 59 5:9 30-0 3-7 3:9 33-0 2-7 3:1 The other observations were made at the end of the wires of a large oscillator in the manner already described. In the calculation both formule had to be used. First, a measure- ment without the interposed condenser gave directly a value of A for a given value of c. Then from formula (1) by use of these values the constant Be was found. In working up the Ss subsequent observations with condenser §, in position, know- ing c gave A from formula (1), then 2, a, b in (2) gave a value of = Using the mean of such values the calculated b’s were got as already indicated. ; The parallel wires were about 20 m. long, 2 millim. dia- meter, and 10 centim. apart. The plates of condensers §,; and S. were of 83 and 20 centim. diameter respectively. Uncer- tainty of node position from one to two centimetres. TaBeE II. Distance of plates of S,, 0°5 centim.; of S,, 3°7 centim. : st S Without S,, c=44:5; at+b= 9 = 302'5. Hence c= 13°2; c > a. b. b Obs Cale Obs. Cale. Obs 451 | 3046 44 | 2995 | 2960 51°3 326°6 54-9 82°5 178 50°7 324°5 79°7 553 54:7 50°1 322°4 113°5 433 42°9 48°5 3168 161°5 34-4 30°7 46°3 308°9 224°3 28:1 27°9 on Stationary Electrical Waves in Wires. 389 . | TaseE IIT. oi The same capacities, a different node-system. Without 8,, c=54'9; + =3875, giving the same value, Se —* =193'2 S Cc. 3 | a. b. b. Obs. | Obs. Cale. Obs. aan 5 360°6 54:9 1 179: 5 169°9 62:9 365°0 79:7 Sis 54:7 62°7 364°4 100°9 6a°7 67°35 60:9 358°7 149'1 49-0 501 56°3 343°3 278°7 26°4 Dies 55°38 340°0 305°7 19:0 19:9 TABLE LY, Distance of plates of 8; =1 cm., of 8, unchanged =3°7 cm. ‘Same node-system ‘as in Table III. C. 5 a. b. b. Obs. 2 Obs. Cale. Obs. Cale. 581 349-4 83:9 192'8 187-6 58:5 350°6 148-1 110°7 111-5 57-5 347-1 1945 81:3 81:0 56:5 344-0 240°5 60:0 61:0 55:3 340 0 288-2 36°4 36'8 55°0 3390 321°3 15-4 15-2 TABLE V. Distance of plates of S;="5 cm., of 8,==6°2 cm. Without 8,, c=60°0; * =300-0; Se eae ieen. 60°5 301-4 2629 19°6 20°8 S & aN a b, . Obs. 2 Obs. Cale. Obs. Cale. 62:8 307°8 27-6 2331 231°7 65-9 316°4 366 186°5 180-0 655. 315°3 49:1 113-2 122°9 67:0 319-4. 68-0 77-2 735 66-0 316-7 1188 48:3 49-7 65:5 315°3 157:1 40°4 40:5 63:9 310-9 196'6 33-7 34-6 | | CO On Stationary Electrical Waves in Wires. Notices respecting New Books. 391 The general course of the changes referred to is best seen from the annexed figure, which corresponds to the last series of observations. The ordinates are distances of the inserted condenser from an arbitrary origin near the end of the wires. the abscissas of the points on the two curves are the distances of nodes B and A from the same origin on twice the scale, the crosses between the curves showing the position of the condenser. It will be seen that the apparent half wave-length, or distance AB, is least when the condenser bisects the distance. When the condenser coincides with either node, AB is the full half-wave. When the condenser passes out- side A B, the curve of A turns in again. I have to express my thanks to Prof. Ebert of Kiel, in whose laboratory and under whose kind direction the expe- riments were carried out of which these observations form part. Queen’s College, Belfast, 27th February, 1897. LIII. Notices respecting New Books. Grundzuge emer thermodynamischen Theorie elektrochemischer Krifte. Dr. Atrrep H, Bucurrer, Freiberg in Saxony: Craz and Gerlach, 1897. HE dissociation theory of electrolytes has received so much attention during recent years, and the casein its favour has been so ably stated by Arrhenius, Nernst, and Ostwald, that we need to be reminded of the existence of the older chemical or association theory of solution. The author of the present volume expresses his objections to the newer theory, and especially to the way in which it sets aside previously established ideas concerning chemical combination. He indicates how the laws of thermodynamics, so freely used by the founders of the dissociation theory, can be applied with equal success in the development of the older ideas. According to his view, an electrolyte consists of molecules of salt, molecules of solvent, and complex molecules containing both salt and solvent ; the relative proportion of the complex molecules increases with increasing dilution and the conductivity of the solution depends upon their presence. The aim of the treatise seems, however, to be destructive criticism of the views of the new school, rather than the construction of a theory in accordance with the requirements of the chemist. JE. He 392 Notices respecting New Books.. Phi ysies : ap Elmo Text-book for University Classes, ie _ C. G. Knorr, D.Se., F.R.S.E. London: Chambers, 1897. Some time ago Dr. Knott published an elementary treatise on magnetism and electricity intended chiefly for university medical students in their science year. He now presents a re-issue of that work as a portion of a treatise on experimental physics for junior students, and has added sections on mechanics, heat, sound, and light. The volume is divided into two parts, purely material phe- nomena being discussed in the first part, which is consequently devoted to mechanics, heat, and sound; while the second part treats of the ether, and includes magnetism, electricity, and radia- tion. In order to compass the whole subject in the space of 650 small pages much compression and some omissions are, of course, necessary, the effects of which are most obvious in the chapters devoted to heat, and especially in the treatment of fusion and evaporation. Some of the statements require revision ; for example, we read on page 229 that ‘“ water can be kept liquid at any high temperature by simply heating it in a closed vessel capable of standing the pressure,” whereas critical temperature is mentioned and defined on the next page but one. A collection of exercises is appended to each chapter and is a good feature of the book; its usefulness might, however, be in- creased by giving the answers to the numerical problems. J.U. H. Theory of Physics. By JosrrH S. AMEs, Ph.D. New York: Harper, 1897. | Accorpine to Dr. Ames three things are necessary in the teaching of physics—a text-book, a course of lectures, experimental demon- strations and tutorial classes, and laboratory work by the students themselves. He believes that the demonstrations and laboratory work afford sufficient instruction in the details of experiments, and a separate text-book may in any case be provided for them. As a supplement to the lectures, however, the student requires a text-book in which the facts of the subject and the explanations of them are arranged in logical order: such a book may, in the opinion of the author, relieve the student from the necessity of taking lecture-notes. The present volume has been written in accordance with these ideas; almost all points which would be mentioned in a first-year course are to be found in it, experimental details being altogether omitted. The result is not, as might be expected, a mere cram-book, but a very concise and readable treatise. Perhaps the greatest fault in the book is the suggestion that it should serve instead of lecture-notes, because the taking of notes has an educational value, not only by i impressing facts upon the student’s memory, but also by training him to observe the relative importance of the various facts and arguments, to which a Notices respecting New Books. 393 text-book could only impart differing degrees of prominence by- the employment of large and small types, footnotes, and other, equally unsatisfactory devices. Jieclue Tr. Elektricitat direkt aus Kohle. By EttENNE DE Fopor. Vienna = Hartleben, 1897. : ae . weeps . Tun great waste which accompanies the conversion of the chemical energy of coal into electrical energy, by means of the steam- or gas-engine and dynamo, has led many mventors to consider the possibility of directly producing electricity from cheap combustible materials such as coal or carbon. The author gives an account of attempts to accomplish this, classifying them according to the manner in which the carbon has been employed; thermoelectric, thermomagnetic, and hydroelectric machines are thus included, as well as primary batteries having a carbon electrode. dsab, da Atomismus, Hylemorphismus und Naturwissenschaft. By Dr. A. Micuexirscn. Graz: Michelitsch, 1897. | es Ueber den Urstoff und seine Energie. I. Teil: Die theoretische Bedeutung der Gesetze von Dulong-Petit und Kopp. By Dr. H.« Ketrer. Leipsic: Teubner, 1896. , as TuxEseE pamphlets both deal with the question of the ultimate con- stitution of matter. That of Dr. Michelitsch is philosophical and metaphysical in character ; he seeks to show by a consideration of the laws of nature that a single primary substance ( Urstoff’) exists, and that the various kinds of matter are merely different forms cf it. Matter consists of substance and form: in chemical reactions substance persists, but the old form is destroyed and a new one created, the substance possessing the power of assuming its form, just as the power to form the fruit is contained in the seed. The author objects to the atomic theory of matter on the ground that - it-does not afford a sufficient distinction between mixture and combination; the rearrangement of atoms during chemical com- bination merely consists in alteration of their positions in. space; anda similar change would take place on mechanically mixing the substances. | | : ; | te Dr. Keller, unlike Dr. Michelitsch, accepts. the atomic hypo- thesis, and finds in the law of Dulong and Petit that the atomic heats of all elements are equal, an argument in favour of the existence of a primary atomic substance. The atoms of all elements consist of an integral number of atoms of the primary substance (Urateme), which act as centres of force, and are capable of rota tory or vibratory motion. The temperature is due to the energy of vibration of these primary atoms; the author shows, however, that in gases this atomic vibration determines the velocity of trans- lation of the molecule, the energies of the two kinds.of motion 394 Geological Society :— being proportional to each other, so that the results of his theory are not inconsistent with the ordinary kinetic theory of gases. L. H. Anleitung zur mikrochemischen Analyse organischer Verbindungen. By H. Benrens. Part IV. Leipsic: Voss, 1897. A PREVIOUS volume of this work on the investigation by means of the microscope of aromatic amines was noticed some months ago; the present work relates to uric acid and urea and their derivatives, and the more important organic acids. J. L. H. LIV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 315.] February 24th, 1897.—Dr. Henry Hicks, F.R.S., President, in the Chair. HE following communications were read :— 1. ‘On the Nature and Origin of the Rauenthal Serpentine.’ By Miss Catherine A. Raisin, B.Sc. This serpentine has been already described by Herr Weigand as one of those which occur in regions of gneiss or schist related in their origin to these rocks. In order to test this hypothesis as to the formation of the serpentine, the author has examined the district and has studied its rocks with the microscope. Herr Weigand asserted that transitions could be recognized from typical gneiss to a peculiar amphibolite, and that the latter rock has been changed to serpentine. The author could find in the field no evidence ofa passage from gneiss to amphibolite, and calls attention to the general difficulty of “the supposition. She states that when the serpentine is examined microscopically, the greater part shows the usual appearance of serpentine derived from olivine, and can be distinguished from included parts, which have resulted from change in hornblende or other pyroxenic constituents. Further, that several accessory minerals occur which are usually found in peridotites. The rock also contains a peculiar chlorite. This she thinks the result of the modification of a biotite, for the latter mineral occasionally occurs as a constituent in a neighbouring serpentine, and, both there and in the Rauenthal, forms appa- rently intermediate can be detected. It seems to her that the chemical analyses already published are not in harmony with the supposed change of a hornblende-rock into serpentine. While it is true that a hand-specimen sometimes shows a trans- ition (generally rapid) from a rock consisting mainly of hornblende Coal: a new Explanation of its Formation. 395 to one which has consisted mainly of olivine, she maintains that this appearance is far more consonant with partial differentiation of the original magma, followed by fluxional movements and flow- brecciation. It is not that a mass of amphibolite passes into one of serpentine, but that a specimen of the latter is occasionally streaked by the former. By comparison with other serpentines of the Vosges and else- where, which are admittedly developed from olivine-rocks, so much likeness is found between them and the Rauenthal mass, that the origin must be similar. 2. ‘On Two Boulders of Granite from the Middle Chalk of Betchworth (Surrey).’ By W. P. D. Stebbing, Esq., F.G.S. The author notices cases of occurrence of boulders in Chalk which have been previously described; and records the occurrence of two boulders which were obtained from the Chalk of the Tere- bratulina-gracilis zone. ‘The largest weighed 7 lb. 7 0z., measured 5'°8 x 6°25 x 4-125, and consisted of decomposed granite; valves of Spondylus latus and Serpula were still attached. The other, also granite, though of a different character, weighed 3 lb. 12 0z., and measured 3°6x5'"8x4"°5, Prof. Bonney has furnished a description of the microscopic characters of the two boulders, which are possibly of Scandinavian origin. The author discusses the mode of transport to their present position, and favours the agency of floating ice, 3. ‘Coal: a new Explanation of its Formation; or the Phe- nomena of a New Fossil Plant considered with reference to the Origin, Composition, and Formation of Coal-beds.’ By W. &. Gresley, Esq., F.G.S. The author argues that the brilliant black lamine in coal and similar materials to those that form these lamine, which are found in earthy coals, shales, and clays, point to the former existence of an aquatic plant, having the general shape of the modern Platy- certum alcicorne, which grew 2n situ. He believes that much coal was formed by this aquatic ‘coal-plant, which grew amongst the mechanical sediments and the débris of the terrestrial vegetation that accumulated on the floors of sheets of water. March 10th.—Dr. Henry Hicks, F.R.8., President, in the Chair. The following communications were read :— ; ‘Volcanic Activity in Central America in relation to British Earthquakes,’ By A. Gosling, Esq., H.M. Minister & Consul- General in Central America, The author of the communication points out that.the volcano of 396 Geological Society. Izalco, in the Republic of Salvador, which has been in active eruption for over one hundred years, suddenly ceased to be so within a fortnight of the period at which the communication was sent (Dec. 20th, 1896), and he notes the occurrence of seven shocks of earthquake in England on December 17th, 1896. He quotes remarks concerning the volcano, which were contributed by him to the ‘ North American Review’ in January 1896. 2, @ hie Red Rocks near Bonmahon on the Coast of Co. Water- ford.” By F. R.C. Reed, Esq., M.A., F.G.S. _ The rocks which are considered in this paper have been regarded by some authorities as deposits interstratified. with the Lower Paleozoic rocks of the district, while others have maintained that they are of Old Red Sandstone age. Jt is the object of the author to show the correctness of the latter supposition, and he brings forward evidence to prove that the red rocks rest unconformably upon the Lower Paleozoic rocks, or are faulted against them, and that the breccias of the red rocks contain fragments of the Lower Paleozoic rocks, and also of intrusive rocks which break through the latter. The red rocks also resemble deposits which are known to be of Old Red Sandstone age. The Old Red Sandstone rocks of the district form an irregular and incomplete elliptical ring around a denuded plateau of older rocks. The incompleteness is due to the concealment of the southern part of the ring beneath the sea; but if the southern part of this ring be as irregular as the northern portion, faulted patches of the Old Red Sandstone rocks may well come in among the older rocks of the cliffs in the positions where the beds which are discussed in this paper occur. : 3. ‘On the Depiy of the Source of Lava.’ By J. Logan Lobley, Esq., F.G.S8. The author contends that lava cannot have been brought to the surface from a depth of 30 miles, as fissures which would serve as conduits could not exist at that depth, and, moreover, the lava would be consolidated before it reached the surface, owing to contact with cool rock for a considerable period. He argues that the pressure of the overlying rocks would cause the rocks even at a depth of 10 miles to be practically plastic, as shown by M. Tresca’s experiments, and that no continuous fissure could occur in such rocks. Estimates of the volumes of ascending lava-columns were given, with a diagram comparing them with a 30-mile thickness of rocks, THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE... »* [FIFTH SERIES.] Mee JUNE 1891. NEN LV. The Thermo-electric Properties of some Liquid Metals. By Wii1iaM Becxit Burnis, lately 1851 Exhibition Sccence Research Scholar, Nottingham * | ae object of the experiments here to be described was to compare the thermo-electric properties of solid metals with those of the same metals when melted. The four metals employed, tin, lead, bismuth, and mercury, were each thermo- electrically compared with copper, the tested metal being contained in a hard glass tube, so that the observations could be pushed to temperatures considerably above those of the melting metals, and the changes in the thermo-electric pro- perties during the process of melting observed. ‘Two sets of experiments were made, the first set with the greater part of the metal under test at ordinary temperatures, and the second set with all the metal under test at high temperatures. In the first set of experiments with tin, lead, and bismuth, the glass tube containing the metal was W-shaped, the metal filling the central part, but only rising about one-third of the height in the outside limbs. To fill this tube one end was dipped into a crucible full of the melted metal, which was then allowed to cool. The crucible and tube were immersed in a bath of linseed oil, which was raised to a temperature above that required to melt the metal. When the metal was quite liquid, air was withdrawn from the upper end of the tube till the metal bad risen to the right height. The tube was next slowly withdrawn from the still hot oil, to prevent * Communicated by the Physical Society: read Feb. 26, 1897. Phil. Mag. 8. 5. Vol. 43. No. 265. June 1897. 2 H " > Re ae : ~~ 398 Mr. W. B. Burnie on the Thermo-electric cracking due to the freezing of the metal, and allowed to cool. The superfluous metal was then melted out of the open limbs. The two copper-metal junctions were to be in the two open limbs of the tube, and a number of thick copper wires were so arranged round the outside of the tube as to conduct away the heat from all parts not in the immediate neighbourhood of the hot junction. By this means all the metal except a small portion was kept solid, and the level of the melted metal was always higher in the open than in the closed limb. This was necessary, as the solid metal was not a satisfactory cork for the tube, and a slight liquid pressure was needed to keep good contact between the liquid and solid metal. The temperature-differences between the hot and cold junctions were measured with a thermo-element of platinum and a platinum-rhodium alloy (Pt 90 per cent., Rd 10 per cent.). This thermo-element was calibrated between the temperatures of 0° C. and 263°°5 C. by comparison, in linseed oil, with a Reichsanstalt standardized thermometer. The calibration curve was then extrapolated as far as 430°C. by means of an equation. For reasons which will be explained later, it was useless to adopt any more accurate method than this for the first set of experiments. The thermo-element was insulated within and from without with asbestos paper, and each junction was bound to one of the standard copper wires. These copper wires were also insulated with asbestos, so that only their ends, which were in close proximity to the junc- tion of the temperature-measuring thermo-element, were uncovered. Some experiments were made to determine the electrical insulating properties of asbestos paper at high temperatures, and it was found that the errors introduced by the electrical conductivity of the supposed insulator were, up to 600° C., negligibly small. Other experiments were made to deter- mine whether or not the temperature of the junction in asbestos differed greatly from the temperature of the metal surrounding the asbestos. One junction of the temperature- determining thermo-element was immersed in melted lead, and the other in melting ice. The parts of the wires just outside the lead were alternately heated with a burner, whereby the temperature-difference between the junction and the metal would be decreased, and cooled with an air blast, whereby the temperature-difference would be increased. Readings of the temperature-difference between the two junctions were meanwhile taken ; and it was found that by varying the temperature of the leading-in wires the tempera- Properties of some Liquid Metals. 399 ture of the hot junction was not altered by more than {5 of a degree. As the leading-in wires were hotter, when warmed by the flame, than the melted lead, 75 degree was greater than the greatest error introduced during the experi- ments by the heat-insulating capability of the asbestos aper. : Hach of the copper wires with its thermo-element junction was melted into the metal in its respective limb, and held in the centre of the tube by asbestos paper. One limb of the W was heated in a sand bath, and the other was kept cold in melting ice. | , The two standard copper wires and the two free wires from the temperature-determining thermo-element were led to a paraffin switch-block, so that either pair could be connected, through a reversing key and a resistance, to a reflecting gal- vanometer. This resistance was so great as to render no correction necessary for the resistance variations, due to heat, . in the circuit. For each reading the temperature of the hot junction was made nearly constant; then, using each thermo- electric combination alternately, galvanometer deflexions were noted with the current direct, and the current reversed. After the necessary correction, the mean of the readings of the platinum-platinum-rhodium thermo-element gave the temperature, and the mean of the readings of the thermo- element under test gave the H.M.F. in arbitrary units. After each complete experiment, the constant of the tempera- _ ture-measuring thermo-element was determined by removing the crucible containing sand, putting in its place one contain- ing melted lead, and allowing the lead to cool, meanwhile taking readings. The curves for copper-lead, copper-tin, and copper-bismuth, which were obtained by this method, are given in figs. 1, 2, and 3 respectively. The abscissee are temperatures and the ordinates E.M.F.’s in arbitrary units. These curves will be discussed when the mercury experiments have been de- scribed. The W-shaped tube was not suitable for the application of a freezing-mixture, and so in the mercury experiments the junctions were each in a small test-tube about half filled with the metal. An inverted U-tube also full of mercury, with one end dipping into the metal in each of the test-tubes, connected the two. One of the test-tubes was surrounded by melting ice, and the other was cooled with a mixture of solid carbon dioxide and ether. A mass of copper wire was ' wrapped round the tube to be cooled, in order that it might warm up slowly after the evaporation of the carbon dioxide. 2H 2 D = = — ie ke Ss Sl a= == < = o_ = ea] 400 Mr. W. B. Burnie on the Thermo-electric As the temperatures to be measured approached the neutral point of the thermo-element used in the last experiments, an iron-constantan thermo-element was employed to measure Fig. 1.—Copper-Lead Thermo-element. : : = | ; . i. o jAfter guid: cocling. e Afler slou- cocltniy Temperature C. the temperature-differences between the two junctions. This thermo-element was calibrated by the observation of the gal- vanometer deflexions when one junction was in melting ice E.M.F. in Arbitrary Units. Properties of some Liquid Metals. 401 and the other junction first in melting mercury and then in boiling carbon dioxide and ether. As these two deflexions were nearly proportional to their respective temperature-differ- ences, the calibration curve equation was assumed to be of the form, deflexion =at+t?, where ¢ is the temperature, and a and } constants. These two constants were determined from the two observations, and the calibration curve for the thermo- Fig. 2.—Copper-Tin Thermo-element. o After quick| cooling se After slow. cooling 0 100 200 300 Temperature C. element was plotted from the equation. The element and the standard copper wires were insulated as in the last experiment, and bound to the glass tubes dipping into the mercury. The freezing-mixture was contained in a double- walled test-tube, the inner and outer walls being separated by cork distance-pieces, and the whole being wrapped in flannel. The electrical connexions were the same as in the last experiment. | Fie. 3.-—Copper-Bismuth Thermo-element. 500 402 Mr. W. B. Burnie on the Thermo-electric In the experiments, the tube containing the cold junction was cooled as far as possible with the freezing-mixture, and allowed to warm slowly up. Readings of the galvanometer were meanwhile taken every thirty seconds, as follows :— ne 3S Ww + ie OSs es SS 5 Ss a3 G =) se. & SERS) » ~s 6 § N49 Re RS S s Se Te Sy =) <= ee fo} re) >) 5 _ 3 x a) ay = O) = ro) S N =) > lal ro) 400 300 200 100 E.M.F. in Arbitrary Units. First, a reading from the temperature-determining thermo- element with the current direct; then a reading from the same element with the current reversed ; then a reading from E.M.F. in Arbitrary Units. Properties of some Liquid Metals. 403 the copper-mercury element with the current direct; and lastly, a reading from this element with the current reversed. The cycle then began again. From the means of each pair of readings, reduced, two curves were plotted, one giving the relation between temperature and time, and the other giving the relation between E.M.F. in arbitrary units, and time. The curves (fig. 4) give the relation between H.M.F. and eer deduced from these two curves, for two experi- ments, o LY* Experiment e2’ il Fane rime nt oo —20 —40 —60 Temperature C. In figs. 2, 3, 4 two curves are in each case given. These two curves were obtained from the same metal. The eftect is most marked with bismuth (fig. 3). At the conclusion of one experiment the apparatus was cooled very rapidly by removing the sand and blowing air on to the tube containing the melted metal. Another set of readings was then taken, with the temperature of the hot junction rising, and the lower of the two curves in fig. 3 was obtained. At the conclusion of this experiment the apparatus was cooled very slowly, about two hours being occupied, and the result of the next AOL Mr. W. B. Burnie on the Thermo-electric experiment was the upper curve. It was found possible, moreover, with intermediate rates of cooling to produce intermediate curves. This effect is probably due to the Fig. 5. B = — JUNCTION IN MELTING ICE HEATING 4 CIRCUIT variations in the crystalline structure of the metal under test, dependent on the rapidity of its solidification ; and it may be that the various thermo-electric properties which have been Properties of some Liquid Metals. 405 observed for different pieces of bismuth are largely due to this same cause. With tin the effect was less marked, and with lead it was unnoticeable. In the mercury experiments it was not possible to regulate the rate of cooling ; but the two most widely differing curves obtained are given in fig. 4. As this effect of its previous treatment upon the metal rendered accuracy impossible, the experiments were repeated with three of the metals, viz. tin, lead, and bismuth, with a method so arranged that the whole mass of the metal to be tested was in a molten state, and thus homogeneous. The apparatus is shown in fig. 5. The metal was con- tained in a U-tube A A, A, A, and was heated by a current of electricity in german-silver wires HHH. The metal was introduced into the tube by means of a glass pipette, both tube and pipette being-warmed in a bunsen flame. The part of the glass tube where the junctions were to be, A A, was covered with copper to render the heat distribution more uniform. The german-silver wire was insulated with asbestos paper, and wound spirally round the tube in two sections, M M,, M,; M,. Over this were wrapped several layers of asbestos paper and asbestos string, DD. The connexions of the heating circuit are shown in fig. 5. In the paraffin switch-block, P,,if TC and T, C, were connected, the same current from the heating battery passed through both ammeters, G, G,, both resistances, W, W.2, and both sections of the heating coil. This caused a saving in current when it was merely required to melt the necessary con- nexions into the metal, or to burn out the asbestos insulation. If, however, TO was connected the current passed through the ammeter Gy, the resistance W,, and the long section of the heating coil; and if T, O, was connected the current went through the other ammeter, resistance, and heating-coil section. By adjusting the resistances W, and W, the tempe- ratures at the junctions could be varied as required. ‘The diameter of the german-silver wire was 0°5 mm., and the largest current required was 4 amperes. ‘The U-tube is shown about one half actual size. . For measuring the temperatures a platinum-silver thermo- element was employed, as this gave H.M.F.’s of the same order of magnitude as those to be measured. This element had three junctions, as shown in fig. 5, so that either the temperature of one of the junctions or the temperature- difference between the two junctions of the thermo-couple under test could be measured. ‘The thermo-element was calibrated with linseed oil up to 288° C.; and one point on the calibration curve, at 441°4 C., was determined with ~~ a a) =| aS 0) i] ) =| fH 5) Si = ‘=| om a o @ =>) = Ss 7 We} bp | [x 406 Mr. W. B. Burnie on the Thermo-electric sulphur vapour. Hach limb was calibrated separately, but they were found to be similar. The part of the calibration curve from 288° C. to 430° C. was plotted from the equation :— E.M.I’. (in volts) x 10’=0:1407 ¢ + 0:001227 2. S =) oO E.M.F., Volts x 10°. This equation was obtained from the point on the curve determined with sulphur, and the point where t=220°7 C. on the curve as drawn in between 0° C. and 288°C. By the application of the method of least squares to all the calibra- Properties of some Liqud Metals. 407 tion observations a somewhat different equation was obtained, Viz. :— E.M.F. (in volts) x 10° =0°1463 ¢ + 0:001238 # ; Fig. 7.—Copper-Lead Thermo-element. & = Z oC > = a = 0 250 300 350 400 Temperature C. but as the calibration curve was not exactly a parabola the upper equation was judged the better. The junctions and standard copper wires were insulated as E.M.F., Volts x 105. 100 80 {f 60 ee oO 20 f=) 408 Mr. W. B. Burnie on the Thermo-electric in previous experiments and melted into the metals. The two standard wires and the three free wires from the tem- perature-determining thermo-element were led to a paraffin switch-block, P,, which was connected to an arrangement of Fig. 8. Sage EPO -Bismuth Thermo-element. 250 300 350 400 Temperature O. a galvanometer, G, a standard cell, 8, a key, K, a bridge battery, ie na at es. W, and W;, sw eeheniceke P, and P3, and a metre bridge, as ot in fig. 5, for measuring the H.M.F.’s. Properties of some Liquid Metals. 409 The current in the long heating section was adjusted before each reading till the temperature of the fixed temperature junction was at a certain point, slightly above the melting- point of the tested metal. Readings were taken with the temperature of the variable temperature junction both above and below the melting temperature of the metal. With tin and lead this latter was easy, but with bismuth, owing to the crystallization effect before mentioned, the readings were rather uncertain. Above the melting-point, however, they were perfectly constant. The curves plotted from the results of the experiments by this method are given in figs. 6, 7, and 8 respectively. In each of these curves we see that in a small variation of temperature, about the melting-point, there is a considerable change in the direction of the thermo-electric curve. The effect is smallest with lead, with tin it is larger, and with bismuth it is very remarkable ; that metal changing, during melting, from an exceedingly active thermo-electric metal to one very similar to lead in its thermo-electric properties. With mercury also (fig. 4) we see that a great change takes place at the melting-point. This indicates that there is a difference between the Peltier effect for the solid and for the melted metal. But the change in curvature is not sufficiently marked for us to be able to say whether the specific heat of electricity remains proportional to the absolute temperature. To decide this point a direct determination of the Thomson effect is needed. The worked-out observations from which the curves in figs. 6, 7, and 8 were plotted are given below. Copper-Tin Element. (Fig. 6.) Temperature of constant temperature junction 239° C. Temperature of variable temperature E.M.F. in junction. volts x 10°. 255°8 2°86 276 Ger 286°1 9:0 306°1 13°2 323°2 16°92 393°7 23°63 201 2°0 272°2 6°35 315°1 15°45 yd 1S —od1 200°1 —11°15 179°5 — 16°86 410) = Thermo-electric Properties of some Liquid Metals. Copper-Lead Element. (Fig. 7.) Temperature of constant temperature junction 3836°1 C. Temperature of variable temperature E.M.F. in junction. volts x 10’. 346'1 5°215 307 11°13 370°6 17:92 385°2 26:9 400°5 35°86 4138°3 47-4 440°3 63:2 35971 12°25 392°8 8°5 380°2 23°75 310°3 —11°9 307°3 —13°4 280-5 —23°6 251 —395 Copper-Bismuth Element. (Fig. 8.) Temperature of constant temperature junction 278°5 C. Temperature of variable temperature E.M.F. in junction. - volts x 10°. 287 2°6 291-4 3°97 308 9°01 315°7 12:05 306°7 24°5 385° 1 33°68 405-9 } 40°15 453°6 56°25 388°'3 34°18 339°2 18:94 309°2 9°73 259 les Ui 254°6 —41-2 In each case a constant has been added to the E.M.F.’s before plotting. These experiments were conducted in the Physical Labora- tory of the Hidgendssisches Polytechnikum, Ziirich, under the supervision of the director, Prof. Dr. H. F. Weber, to whom my best thanks are due. fe. LVI. On the Photography of Ripples. By J. H. VINCENT, BSc., A.R.C.Sc., Assistant Demonstrator in Physics at the Royal College of Science, London, S.W.* [Plates I.-IIT. | mies * of the phenomena described in this paper have » ve been exhibited at public lectures by Mr. C. V. Boys, using the stroboscopic method, which was first applied to the study of ripples by Lord Rayleigh. I am indebted to Mr. Boys for having recommended to me the work of photograph- ing these effects, and also for many valuable suggestions. Lord Kelvin defines a ripple as a wave whose length is less than that of the wave which is propagated with the minimum velocity. For ordinary mercury, waves less than 1:3 centim. long are ripples. Capillary ripples are those whose length is so small as to render negligible, in the value of the velocity squared, the term due to gravity. These definitions are rendered clearer by reference to Mr. Bovs’s Logarithmic Wave Chart. The portion of the curve, repre- senting the relation of the velocity and wave-length, to the left of the point of minimum velocity, refers to ripples. The straight-line portion to the left of the chart represents capil- lary ripples. In order to obtain ripples it is necessary to use vibration- frequencies above a certain value. Thus in the case of ordi- nary clean-looking mercury, with its damp and _ probably greasy surface, the surface-tension of which may be between 300 and 400 C.G.S. units, a frequency of about 15 per second causes the biggest waves which the above definitions include as ripples; while frequencies of about 200 and upwards give rise to waves whose propagation is practically controlled by surface-tension, and these waves are capillary ripples. Now the duration of the sensation produced by a luminous impression on the retina lasts for about one eighth of a second; thus we are unable to see ripples on the surface of mercury. The frequencies employed are generally many times the maxi- mum visible frequency. It is not the high velocity of propa- gation which renders ripples invisible ; ripples produced by a disturbance of a frequency of about 200 do not travel very quickly, a foot a second being about the order of magnitude of the velocity on the surface of ordinary mercury. * Communicated by the Physical Society: read Feb. 26, 1897. 412 Mr. J. H. Vincent on the Diagram of Apparatus. 4 nat. size. T. Mercury trough. A. Standard of retort-standard. B. Wooden block through which passes the bent down portion of A. C. Upper bar of wooden stand. IR. India-rubber loop. S. First spark-gap. LL. Lenses. D. Camera. F. Tuning-fork and stand. Photography of Ripples. 413 Description of the Apparatus. A rectangular wooden trough, about 1 centim. deep and 12 x 15 centim. area, contains the mercury upon the surface of which the ripples are produced. This trough rests upon the rectangular base of a retort-stand, the upper portion of whose standard is bent at right angles over the base so as to be parallel with the latter. This horizontal portion is passed through a rectangular block of wood, and the whole is then slung from a gallows-like wooden structure one metre high. The spark-gap from which the light proceeds to illuminate the mercury surface is placed near the top and to one side of the wooden stand. Light from this gap falls upon a lens to _ the left of the stand, so that the emergent light is parallel ; after reflexion the light is collected by a second lens similar in all respects to the first, so that an image of the spark would be produced at the primary focus of the second lens; the focal length of these lenses was 44 centim. The camera is placed in such a position as to enable the first achromatic lens of the combination to collect the rays and converge them so as to come to a focus at the aperture in the lens stop. The stop used was the smallest of the set belonging to the camera (64). The camera is then focussed upon a fine thread laid on the surface of the mercury. In addition to the first spark-gap, which was about °5 centim. across, a second yap was used in order to increase the brightness of the spark in the first gap. The second gap was varied from time to time, but was generally 1°5 centim. across. The first gap was shunted by a piece of stout thread soaked in calcium-chloride solution. This prevented small sparks due to induction. The knobs of a Wimshurst machine were con- nected, one with a terminal of the second spark-gap and the inside coats of a battery of four half-gallon leyden-jars ; the other Wimshurst terminal was connected to the outer coats, one side of the first spark-gap, and to earth. A wire joining the other terminals of the two gaps completes the spark arrangements. Method of Causing the Ripples. The ripples are due to the agitation of the surface of the mercury by a style of glass attached to one prong of a vibra- ting tuning-fork. ‘The fork was in most cases struck with a rubber-shod hammer; but in the last two experiments, in which a strip of cover-glass attached to the fork acts asa line- source, 1t was found that the irregular large waves caused by the concussion entirely masked the phenomena which it was sought to photograph. In these cases the fork was main- tained in synchronous vibration with another similar fork Phil. Mag. 8. 5. Vol. 43. No. 265. June 1897. rd! Al4 Mr. J. H. Vincent on the which was electrically excited. The two forks, placed ap- proximately parallel, are tied together by a piece of thread about two feet long, so that the thread is at right angles to both forks. This thread is then adjusted to an appropriate tension by trial, when the maintained fork causes the other to vibrate for any length of time. This simple device, which — has been used in the ‘Royal College of Science laboratory for some time, is due to Mr. W. Watson. Description of Photographs. The plates used were of various kinds, and any of the well- known plates gave good results. Some of the negatives were intensified previous to printing. The figures are about 4 natural size. My best thanks are due to Mr. R. Chapman, who has assisted me throughout with great zeal. Photographs showing a series of circular waves set up by a single style attached to a fork of known frequency were taken with a view to quantitative measurements of surface- tension, wave-length, and velocity. A bar of wood was so placed that two needle- -points which it carried nearly touched the surface of the mercury. These points are a known dis- tance apart, and by measuring the negatives we may find the scale of reduction of lengths along this line. The particulars of the motion are obtained from the equations Ob. uel 2ar Die from which we find, in a particular experiment, n=180 per second, X='165 centim., v=29°7 centim. a second, T=306 dynes per linear centim. This low value of the surface-tension was obtained from mercury which had stood in the apparatus for some days. The values obtained in a similar way previously were 420, 421, 365. The tension falls as the mercury gets more con- taminated. The value of the surface-tension of pure dry mercury is usually quoted at 540. Fig. 1. Two styles are attached to the same prong of a fork, the frequency of which is 120. One centre is unfortunately hidden by the fork. The approximately straight dark lines which are seen to radiate from the region between the centres of oscillation are lines of minimum disturbance; they are hyperbolas of which the centres of disturbance are the foci. This photograph illustrates the interference phenomena in Optics produced by Young’s or Fresnel’s methods. Fig. 2. The frequency of the fork is 256. | Both styles are Wig = nr? = Photography of Ripples. 415 attached to the same prong. The photograph shows two series of interference-curves, one a family of hyperbolas analogous to those shown in fig. 1, and the other a family of ellipses. The hyperbolas are the radiating light lines seen on the side of the photograph remote from the fork. They are fixed in position, the little dark facets moving along between pairs of hyperbolas. The light oval curves in the region between the centres of disturbance are ellipses, since they are the loci of points of intersection of the two series of circles whose radii grow uniformly, and at the same rate with time. Their method of production here is similar to a well-known geometrical construction for ellipses. Unlike the system of hyperbolas, these ellipses are not at rest. They travel outwards in such a way that any ellipse occupies a position which was filled previously by its predecessor a whole period before. That semiaxis of any ellipse which passes through a centre of dis-. turbance grows with the same velocity as that with which the ripples are propagated. The other semiaxis grows witha velocity which is infinite at the commencement, but which gradually decreases to the same uniform velocity of growth as that of the first. The law of decrease of velocity is the same as the law of decrease of the lengths of whole-period elements of a linear wave with respect to a point. In order to render these ellipses stationary it would be necessary to change one of the sources into a sink to which the circular waves converge. This could be experimentally realized with ripples by causing a circular are and a style to be agitated by the same prong of a fork, when the effects would be analogous to M. Meslin’s experiment in Optics. Fig. 3. Frequency 256. This photograph is very similar to fig. 1; but in addition to showing interference phenomena like those of Fresnel and Young, it also illustrates interference effects in which the direction of propagation of light is parallel to the line joining the point-sources. Thus in the photograph, if we consider the disturbance anywhere on aright line drawn perpendicular to a line joining the two point-sources produced, we see that the places of no disturbance are symmetrical about the line joining the sources. ‘They are points on the system of hyperbolas already mentioned. In M. Meslin’s method of producing interference-fringes the screen is placed between the two point-centres, one a source and the other a sink. ‘fhe bands are circular, and are sections of ellipsoids of revolution, and not of hyperboloids, such as the fringes in the photograph would become if the whole picture were rotated about the line joining the point- 212 416 Mr. J. H. Vincent on the sources. These fringes are not seen on the screen in M. Meslin’s experiment with the split lens, even when the screen is placed beyond the second focus, because the pencils do not there overlap. It seems that modifications of M. Meslin’s experiment could be devised so as to enable complete circular fringes to be seen, and also to render the ections of hyperboloids visible. For example, it appears probable that if a circular portion of a convex lens were cut out and the central portion moved towards the original point- source, the sections of hyperboloids of revolution would be visible on a screen placed beyond the second focus. Fig. 4. The two sets of ripples are produced by a fork of frequency 128 and another of frequency about 112. These two forks then produce 16 beats a second. The curved light lines represent places of minimum disturbance at the instant when the spark occurred. ‘These lines are not stationary as in No. 3, but rotate towards their convexities. The centre of disturbance from which they move is the one of higher frequency. If we consider a point anywhere on the surface of the mercury, beats occur at that point with the same frequency as the passage of these lines of minimum disturbance takes place over the point. Thus, 16 of these lines cross any point per second. Fig. 5. This shows ripples produced by two forks, the higher of which has a frequency four times as great as the lower, the frequency of which is 128. If we neglect the effect of gravity, ceo eu 2nT Ap from which it follows that the wave-length of the ripples from the higher ferk should be half that due to the lower. This relation is approximately true for these ripples. Fig. 6. Frequency 180. This photograph shows a point-source and a reflecting-line, the latter is a side of a triangular piece of microscope cover- glass, which is kept in position by a small splinter ef wood. The interference-lines which are shown are due to the mutual action of the primary and the reflected waves. The phenomena exhibited are analogous to Lloyd’s single-mirror fringes in - Optics. Faint signs of diffraction invading the geometrical shadow of the obstacle can be seen. The region of shadow is covered by faint lines parallel to the nearest side of the triangle acting as a line-source. ‘The wave-length is the same as that of the primary waves, and the effect is due to forced vibrations. Fig. 7. This photograph illustrates reflexion and forced Photography of Ripples. A17 vibrations. The light curved lines in the region between the source and the nearest side of the triangle are similar to those between the two sources in fig. 2. They are due to the interference between the source and its virtual image. Fig. 8. Frequency 256. Here we have a shallow circular reflector with the source placed approximately at the principal focus. The reflected waves are circles of large radii; the very slight outward cur- vature at the ends shows that even when the reflector has an arc of about 60° the effect of spherical aberration is small. Since the reflected waves come from a virtual point-source, we have, as interference-lines, a series of confocal ellipses and confocal hyperbolas ; the latter are fixed, but the former travel away from the line joining the source and its image. If the reflected waves had been rectilinear, both these sets of curves would have become parabolas. Fig. 9. Frequency 256. The centre of disturbance here coincides very closely with the principal focus of the central portion of the semicircular reflector. The reflected ripples are straight lines in the middle, but are bent outwards from the reflector towards the ends. This illustrates spherical aberration. Fig. 10. Frequency 256. The obstacle is a small round cover-slip floating on the mercury. The ripple-shadow is slightly encroached upon by the waves bending round the edge of the obstacle. One side of the disk acts as a convex circular mirror, and the inter- ference-fringes are due to the mutual action of the source and its virtual image situated within the circumterence of the disk. Fig. 1i. The frequency in this and fig. 12 is 120. Here straight-line waves are originated by the agitation of a slip of cover-glass, one side of which dips into the mercury. The waves are reflected from the shallow circular mirror, and converge to the principal focus. Two series of parabolic interference-fringes are shown. They are confocal, and have their concavities directed towards the source and reflector respectively. Fig. 12. Similarly excited waves are reflected at an angle of about 45° from a straight edge. The long black mark running from one end of the dipping edge to the corner of the print is due to a depression in the surface caused by a floating needle, put there to screen off the circular waves coming from the end of the strip of glass. Dittraction is well shown in this photograph. F Oe LVIL. Conductance produced in Gases by Réntgen Rays, by Ultra- Violet Light, and by Uranium, and some consequences thereof. By J. Carrutuers Beartiz, D.Sc., F.RSE., 1851 Exhidition Scholar, Research Fellow of the University of Glasgow, and M. SMoLucHOWSKI DE SmoLan, PA.D., Research Fellow of the University of Glasgow *. $1. Wt propose in the following paper to give the results | of experiments carried out by us at Lord Kelvin’s suggestion, and with his help, in the Glasgow University Physical Laboratory. Weshall give first results which relate to the conductance produced in gases by Rontgen rays, by ultra-violet light, and by uranium. Secondly, results bearing on the quasi-conductance produced in solid dielectrics by Roéntgen rays. ‘Thirdly, we shall give an account of experi- ments which we made to measure the difference of potential between wires of the same metal connected metallically with two plates of any two metals between which Rontgen rays, ultra-violet light, or “‘ uranium rays ” pass. § 2. On the Conductance produced in Air, at ordinary pressure and at different voltages, by Rontgen rays, by uranium, and by ultra-violet tight. To measure the conductance produced in air by Roéntgen rays and by uranium, we used an arrangement consisting of two quasi leyden-jars, A and B, with their inside coatings connected together. The outside coating of A was connected to the case of a quadrant electrometer, the outside coating of B, which was insulated on a block of ee to the insulated ne of the electrometer (see fig. 1). In all the experiments in Stat the two-leydens arrange- ment was used the leyden B remained the same. It con- sisted of a cylindrical lead can, 25 centim. long, 4 centim. diameter. A metal bar about 1 centim. diameter, 25 centim. long, was supported centrally on paraffin filling the whole space between the metal bar and the containing jead. The metal bar was connected by a wire to the internal coating of A. To protect this wire from inductive effects it was sur- rounded by a tube of lead connected to the case of the electrometer. In the experiment with Réntgen rays the leyden A con- * Communicated by Lord Kelvin, having been read before the Glasgow Philosophical Society, April 14th, 1897. The chief results were described in several papers communicated to the Royal Society of Edinburgh since the beginning of the present year. Conductance produced in Gases by Réntgen Rays &e. 419 sisted of an aluminium cylinder, 16 centim. long, 3 centim. in diameter. This cylinder was connected to the case of the electrometer. The insulated metal inside it, which was a flat strip of aluminium about 10 centim. long and 14 centim. "Tl old rn PE [ZEST ‘Go “tv fomngenyy, wo.rT | Mill ae = Z ! ! i j wide, cut from the same sheet as the surrounding aluminium tube, was supported at one end by a small piece of paraffin so placed as to be out of reach of the action of the Réntgen 420 Drs. Beattie and De Smolan on the Conductance lamp*. ‘The rays from the lamp were allowed to pass from a lead cylinder surrounding it and connected to the case of the electrometer by a small hole about :3 square centim. in area. They fell on the aluminium sheath transparent to them and rendered the air between it and the insulated aluminium within conductive. To get a definite difference of potential, the two pairs of quadrants of the electrometer were placed in metallic con- nexion. Then one terminal of a battery or of an electrostatic induction machine was connected to the internal coatings of the two quasi leyden-jars, and the other terminal to the case of the electrometer. The difference of potential pro- duced was measured by a multicellular voltmeter in the case of voltages under 500 volts, and on a vertical single-vane voltmeter for higher differences. When the desired difference of potential had been estab- lished, the metallic connexion of the battery, or of the electric machine, with ihe internal coatings of A and B was broken, and this charged body left to itself. To find the loss due to impertect insulation the pair of quadrants in metallic connexion with the outside coating of B was insulated in the ordinary way, and the deviation of the electrometer reading from the reading obtained when the quadrants were metallically con- nected—which we shall call the metallic zero—per minute was observed. ‘To find the loss when the rays were acting, the two pairs of quadrants were again placed in metallic connexion and the Roéntgen lamp set going; then the pair of quadrants connected to the outside coating of B was insulated from the other pair, and the deviation from the metallic zero again observed per minute. We tried various differences of potential, ranging from a few volts to 2200 volts. The results we obtained showed that the rate of leak did not appreciably increase from a voltage of about 6 volts to 2200 volts. Positive and negative charges leaked away at the same rate. These results confirm and extend through a very wide range of voltage the result announced by Thomson and McClelland in a paper communicated to the Cambridge Philosophical Society March 1896. To test the conductivity induced in air by uranium, we first used the two-leyden method described at the beginning of this section. The leyden A was a cylinder of aluminium with one end covered with aluminium. This cylinder formed * The Rontgen lamp was a focus tube of the Jackson pattern. produced in Gases by Réntgen Rays §c. 421 the external coating of the leyden-jar. The internal coating was a disk of aluminium insulated on paraffin. The uranium, which was a disk 5-5 centim. diameter, *5 centim. thick, was placed inside a cardboard cylinder with one end open and the other covered with aluminium, thin enough to be transparent to the uranium influence, so as to touch the aluminium end (see fig. 2). Fie. 2. oD ELECTROMETER (ec a ee Nl ate ee Ee VILL LLL! PARAFFIN LEYDEN ALUMINIUM TUBE This cardboard cylinder could be moved backwards and forwards in the aluminium cylinder, so that the distance between the insulated disk in the latter and the aluminium end of the former could be varied. The uranium thus acted through the aluminium end of the cardboard box and made the air between the end and the insulated aluminium disk conductive. The leakage was in this way made slow enough to be easily observed in the electrometer. The rate of leak was not perceptibly increased when the piece of uranium was heated nor when the sunlight fell on it. The aluminium end of the cardboard box and the outside coating of the aluminium cylinder were connected to the case of the electrometer. The insulated aluminium disk was connected to the inside coating of the levden B. These inside coatings were charged to a known potential and then left to themselves. The air-space between the insulated aluminium disk and the aluminium end of the cardboard box was 2 centim. The voltages used were therefore voltages per two centim. of this air-space. With this arrangement the leakage per minute—the necessary correction due to the natural leakage with uranium removed having been made— at various voltages was :— 422 Drs. Beattie and De Smolan on the Conductance (a) Voltage. rae ee arr? 6 56-0 10 aaa zt 113-0 88 128-0 176 156-0 750 219-0 1250 229-0 2000 260-0 3000 276-0 [Sensibility of electrometer 24 sc. divs. per volt of subsidence of difference of potentials between coatings of A.] We also investigated the conductivity produced in air by a second piece of uranium 3 centim. long, 1 centim. broad, and about °5 centim. thick. This was mounted firmly in a glass bulb 6 centim. long, 3 centim. diameter, on a platinum wire fused into one end of the bulb. The uranium in the bulb was surrounded throughout two-thirds of its length by a zinc cylinder 1°5 centim. in diameter. This zine cylinder was kept in position by a stiff platinum wire fused into the other end of the glass (see fig. 3). Two glass tubes were Fig. 3. BATTERY TO ELECTROMETER TO SHEATHS fixed on to the bulb; by means of these any desired gas could be introduced or any desired vacuum produced. Round the outside of the glass bulb a strip of tin-foil was placed and connected to the case of the electrometer. This prevented vitiation of our results by a leak between the two electrodes over the outside of the glass. The balb was first evacuated and then filled with dry air. The uranium was then con- nected to the insulated terminal of the electrometer and the zinc to one terminal of a battery or of an electrostatic induc- tive machine, the other terminal being connected to the case of the electrometer. For voltages up to 100 volts the ter- minal was kept connected to the zinc while the leakage due produced in Gases by Réntgen Rays §c. 423 to the presence of the uranium was being observed. For higher voltages the zinc was first brought to the voltage given in the table and then disconnected and left to itself. (5) Leakage per minute Voltage, in se. divs. 9 92 29 120 99 129 ey 138 200 130 300 137 A15 136 [Sensibility of electrometer 140 sc. divs. per volt. | The appended curves (fig. 4) were drawn by taking the leakage per minute as ordinate,. the voltage as abscissa. Curve (a) represents the results of the first series of experi- Fig. 4. ments (a) reduced to voltages per 2 millim. between the outside coatings of A. Curve (b) gives the results of the second series of experiments (6). It will be seen that with uranium, as with Réntgen rays, the leakage through air is not proportional to the E.M.F. We found also that both positive and negative charges leaked away at the same rate. 494 Drs. Beattie and De Smolan on the Conductance With ultra-violet light we have as yet only observed the rate of leak from a charged body for voltages up to two or three volts. The method we employed is one originally used by Righi. A cage of brass wire gauze was made and connected to the case of the electrometer. Inside it the insulated metal was placed on a block of paraffin, and connected to the insulated terminal of the electrometer by a wire protected against inductive effects. The light from an are lamp was then let shine through the gauze so as to fall on the insulated metal perpendicular to its surface (see fig. 5). Fig. 5. ELECTROMETER \ WIRE GAUZE, eta Ries pie aoe tls t 1 METAL DISC = (eh oe ee niece ee With this arrangement we found when the insulated metal was zinc, aluminium, or copper, and when a positive or negative charge was given to any one of these metals when insulated, that positive and negative charges leaked away at the same rate when the light from the are lamp fell on the charged metal, the positive or negative charges being reckoned from the steady electrometer reading which is obtained when the two quadrants of the electrometer are insulated and the ultra-violet light shining. Our results on leakage through air from a body illuminated by ultra-violet light agree with those obtained by Branly. § 3. Effect of Réntgen Rays on the Conductance of Parafjin and of Glass. In our first experiments with paraffin we used a brass ball of about an inch in diameter, connected to the insulated terminal of the electrometer by a thin wire soldered to the ball. The ball and the wire were both coated to the depth of about an eighth of an inch with paraftin. The ball was then laid on a block of paraffin in a lead box with an aluminium window, both of which were in metallic connexion with the case of the electrometer. The paraftined ball was then charged positively, and the rays caused to play on it. After two minutes the electrometer produced in Gases by Réntgen Rays §c. 425 reading was steady at 0°5 of the initial reading. The electro- meter was then discharged by metallic connexion and again charged positively. Its reading remained steady after three minutes at 0°63 of the initial charge. In the third and fourth experiments the readings after three minutes were °81 and ‘90 of the initial charges respectively. The ball was next charged negatively. When the rays were played on it a steady reading was obtained after four minutes at *18 of the initial charge. In the second, third, and fourth experiments the steady readings after four minutes were *45, ‘70, and °78 of the initial charges re- spectively. The paraffin was then removed and the brass ball polished with emery-paper; whether the charge was positive or negative it fell in about five seconds to one definite position, ‘437 of a volt, on the positive side of the metallic zero, when the rays were played on the charged ball. These experimental results demonstrate that, for the low potentials—usually 2 or 3 volts—we here used, the Rontgen rays did not produce conductance between the brass bail, when it was coated with paraffin, and the surrounding metal box. We have already seen in § 2 that air is rendered temporarily conductive by the rays, and Roéntgen’s com- parison of the effect of the rays with that of a flame shows that our experimental results are explained by the augmenta- tion of the electrostatic capacity (quasi- condenser) of the brass ball by the outside surface of its coat of paraffin being put into conductive communication with the surrounding lead box and the connected metals. In our second series of experiments we endeavoured to eliminate the influence of the varying capacity of the quasi- condenser. [or this purpose we placed a strip of metal connected to the insulated terminal of the electrometer inside an aluminium cylinder ; the space between the metal and the cylinder was first filled with air, afterwards with paraffin. The aluminium cylinder was connected to the case of the electrometer, and inductive disturbances were avoided by sur- rounding the copper wire connected to the insulated terminal with a lead sheath in metallic connexion with the electrometer case. In our first experiments with this apparatus we had air, instead of the main mass of paraffin, separating the insulated metal from the surrounding aluminium cylinder, as shown in fig. 6, and we had only small disks of paraflin serving as insulating supports for the ends of the metal, and not played on by the Roéntgen rays. When the metal thus supported 426 Drs. Beattie and De Smolan on the Conductance was charged, whether positively or negatively, the Réntgen rays diselectrified it in about five seconds; not, however, to Fig. 6, Le Litllda ) L.S. the metallic zero, but to a zero depending on the nature of the insulated metal and of the metal surrounding it. On the other hand, if the interior insulated metal had initially no charge given to it, yet when the Rontgen rays were played on it through the walls of the surrounding aluminium cylinder, the reading on the electrometer deviated to the same zero to which in the previous case it had fallen, and there remained steady. With paraffin between the aluminium cylinder and the insulated metal within (see fig. 6) we found no perceptible increase of conductance produced by the Rontgen rays above the natural conductance of the paraffin when undisturbed by them. If the insulated metal was not charged and the Rontgen rays played on it through the aluminium and the paraffin, no deviation from the metallic zero took place when the two pairs of quadrants of the electrometer were insulated from one another. To make a similar series of experiments with glass we used a piece of glass tubing 9°5 millim. internal diameter, 70 centim. long, and 10 millim. external diameter. The inside of this tube was coated with a deposit of silver, which was placed in metallic connexion with the insulated terminal of the electrometer. ‘The outside of the glass was covered with wet blotting-paper connected to the case of the electro- meter. No increase of conductance was produced in the glass when the Rontgen rays were played on it. We next removed a part of the wet blotting-paper from the outside of the glass, and, after charging the insulated interior metal deposited on the inside of the glass, we heated the exposed part with a spirit flame, in this way making the glass a conductor. The charge was completely removed in produced in Gases by Réntgen Rays §e. 427 24 minutes. We thus see that our method is amply sensitive to the conductance produced in glass by heating. The differences of potential concerned in the experiments described in the last paragraphs were not more than two or three volts per centimetre of paraffin or per half-millimetre of glass. ~ To extend our experiments to higher voltages we used the two-leyden method described in § 2. In the experiments on paraffin the leyden A was the aluminium cylinder filled with paraffin in which an insulated metal—now connected to the inside coating of B—was embedded, already referred to. With this arrangement we found that with a difference of potential up to 2500 volts per centimetre of paraffin, no increase of conductance was produced by the Rontgen rays. In the experiments with glass the leyden A consisted of the glass tube already used. Its inside coating of silver was now connected to the inside coating of B. With glass also we could not find any increase of conductance produced by the Réntgen rays with differences of potential reaching up to 2000 volts per half-millimetre of glass. § 4. Analogous Hifects produced by Flame and by Réntgen Rays. Two similar sticks of paraffin, which we shall call C and D respectively, each of about 4 sq. centim. cross section, were coated throughout half their lengths with tinfoil. These tin- foils ought to be each metallically connected to the case of the electrometer. To obtain a sufficiently delicate test for their electric state, a metal disk of 3 centim. diameter was fixed horizontally to the insulated terminal of the electrometer. The two pieces of paraffin were first diselectrified by being held separately in the flame of a spirit-lamp. Their non- tinfoiled ends were then pressed together, and their electric state tested after separation. It was found that they were still free from electric charge. After this, D was charged by being held over the pointed electrode of an inductive electric machine. The quantity of electricity given to it in this way was roughly measured by noting the electrometer reading when the paraffin was held at a distance of 4 centim. above the metal disk connected to the insulated terminal of the electrometer. The free ends of C and D were again held together, and, after separation, both pieces were tested separately. The charged one, D, had suffered no appreciable loss, and the other, C, induced an electrometer reading of a few sc. divs. in the same direction, when held as near as possible to the 428 Drs. Beattie and De Smolan on the Conductunce metallic disk without touching it. This showed that an exceedingly minute quantity of electricity had passed from D to C when they were in contact. C was then diselectrified by being held in the flame. The ends of Cand D were again put together—D still having the charge previously given to it—and in this position were passed through the flame. They were tested with their ends still pressed together, and it was found that when held as near as possible to the metal disk without touching it, no reading was produced on the electrometer. After this they were separated and tested separately ; and it was found that D, when held over the disk, gave a large reading in the same direction as before the two with their free ends together had been passed through the flame, and C (which was previously non-electrified) gave a large reading in the opposite direction. Exactly similar results were obtained with the two paraffin sticks when Roéntgen rays were substituted for flame, and when glass or ebonite was used instead of paraffin. The explanation clearly is this :——The flame or the Rontgen rays put the outer paraffin surfaces of C and D temporarily in conductive communication with the tinfoils, but left the end of D, pressed as it was against the end of C, with its charge undisturbed. This charge induced an equal quantity of the opposite electricity on the outer surfaces of the paraffin of C and D between the tinfoils ; half on C, half on D. When the application of flame or of Rontgen rays was stopped, this electrification of the outer parathin surfaces became fixed. D, presented to the electrometer, shewed the effect of the charge initially given to its end, and an induced opposite charge of half its amount on the sides between the end and the tintoil. C showed on the electrometer only the effect of its half of the whole opposite charge induced on the sides by the charge on D’s end. We have here another proof that paraffin is not rendered largely conductive by the Rontgen rays. Had it been made so, then the charge given to the end would have leaked through the body of the paraffin to the outside, and have been carried away either by the tinfoil or by the conductive air surrounding the non-tinfoiled parts. To show that the induced charges were fixed on the sides, the two sticks, © and D, were next coated with tinfoil throughout their whole length, only one end of each being uncovered. The uncoated end of D was then charged and pressed against that of C, and the two were held either in the flame of a spirit-lamp or in the Réntgen rays. When taken produced in Gases by Réntgen Rays &c. 429 out of the flame or the Réntgen rays, and then separated and tested separately, it was found that D had retained its charge practically undiminished, and that C had acquired a very slight charge of the opposite kind. § 5. Leakage of Electricity from an Electrified Body in gases other than air at ordinary pressure, due to the presence of uranium. We were able to investigate the rate of leak in different gases by means of the smaller piece of uranium mounted in a glass bulb as described in § 2 (fig. 3). The gas used was first stored in a reservoir over water. It was then bubbled through strong sulphuric acid and passed over caustic potash, ealeium chloride, and phosphoric anhydride into the glass bulb. The bulb was first exhausted to an atmospheric pressure of about 6 millim.; then the gas to be used was passed into it. It was again evacuated and refilled. This was repeated about twenty times. Finally, it was strongly heated so as to draw off any adhering layers of the gas which had previously been in the bulb, and then allowed to cool in an atmosphere of the gas at 760 millim. pressure. One of the tubes was then sealed up ; the other was closed by a well- fitting and well-greased glass stop-cock. The following tables give the results obtained with the gases we have experimented on :— Hydrogen. Leakage per minute Voltage. in se. divs. 2 volts. 32 dis 37 22 39 34 ,, 38 OOR 39 TaN 38 Oxygen. ae 125 Jonas 157 Carbonic Acid. 4 ,, 94 CA ae. 167 238 183 AD) ae 180 2900 ,, Spark discharge. [Sensibility of electrometer 140 sc. divs. per volt. ] Phil. Mag. 8. 5. Vol. 43. No. 265. June 1897. 2K Leakage per minute in scale-divisions. 200 150 | 100 430 Drs. Beattie and De Smolan on the Conductance The results given for these three gases are comparable to the second series of results given in § 2 for conductance produced in air by uranium. We see that the rate of leak is greater in oxygen than in air. No comparative figures need be given as these would vary according to the voltage chosen. The leakage in hydrogen is less than in air ; in carbonic acid it is less for 4 volts but greater for 90 volts than it is in air. For the latter voltage the leakage in carbonic acid is greater even than the corresponding leakage for oxygen. The appended curves show the peculiarities of the leakage in the different gases (fig. 7). une Pie ST. Voltage. § 6. Leakage in different Gases at different Pressures due to Uranium. The method of filling the glass bulb with any given gas has already been described in §5. The vacuums up to 2 millim. were produced by a double-barrelled air-pump ; higher vacuums were produced by a Topler pump. The following tables give the results obtained with the gases we have used :-— 210 produced in Gases by Réntgen Rays ec. 431 Air. a. : y: B. Me Leakage Leakage ze i Atmospheric per minute per minute pressure in mms. for 4 volts. for 96 volts. 760 100 131 *132 Ae 240 44 46 183 "192 190 40 39 "210 *205 121 24 26 197 214 64 12 13°5 OT "212 58 11-0 10-0 "189 172 23 44 3°75 "191 163 3°6 1-2 1:2 "339 839 It will be seen from the last two columns of the table that the rate of leak at 4 volts and at 96 volts is nearly propor- tional to the atmospheric pressure. The results obtained at 3°6 millim. are not very trustworthy. With lower pressures no appreciable leakage at these two voltages was observed. Hydrogen. a. B Atmospheric Leakage per minute a Va pressure in mms. at 4 volts. 760 oe O41 1°43 197 11 °056 7h 66 4 ‘061 -50 Shae 1) ley *5D With lower pressures no leakage was observed. The rate of leak is at higher pressures somewhat approximately pro- portional to the pressure, at lower ones to the square root of the pressure. Oxygen. a. : B Atmospheric Leakage per minute a ins pressure in mins. for 4 volts. 760 125 "16 4-5 205 48°5 "25 373 64 15:0 “24 2°9 2 2:0 1:00 of a Carbonic Aud. Atmospheric Leakage per minute Leakage per minute pressure in mms. for 4 volts. for 100 volts. 760 94 167 62 18 21 2 not observable. 2K 2 Leakage per minute in scale-divisions. 432 Drs. Beattie and De Smolan on the Conductance The curves for air, oxygen, and hydrogen, given in fig. 8, were obtained by taking the atmospheric pressure in millim. as abscissa and the leakage per minute for four volts as ordinate. Atmospheric pressure in inillims. § 7. Measurement of the Difference of Potential between wires of one metal connected with two mutually insulated metals when the air between them is rendered cenductive by Rontgen rays, by ultra-violet light, and by uranium. _ The fact that gases are made conductive by Réntgen rays, by ultra-violet light, and by uranium supplies us with a means of measuring the difference of potential between wires of one metal connected with twe mutually insulated con- ductors. This method has already been used by Righi. He determined the difference of potential of wires of one metal connected to two mutually insulated conductors by rendering the air between them conductive under the influence of ultra-violet light. Minchin, Righi, and Murray have made experiments of a similar kind with Rontgen rays. In our experiments to measure this difference of potential between wires of one metal connected to two mutually insulated conductors by rendering the air between two mutually insulated conductors conductive by means of Rontgen rays, we used a cylinder of unpolished aluminium connected to the case of the electrometer. Along the axis of this a conductor was placed, supported by its ends on small blocks of paraffin. This insulated conductor was connected — produced in Gases by Réntgen Rays &c. 433 by a copper wire to the insulated terminal of the electrometer. Suitable means were taken to protect this connecting wire from inductive effects (see fig. 9). Fig. 9. oa Lead Tubs WLLL From ‘ Nature,’ Feb. 11, 1897. ) The Rontgen lamp was placed in a lead cylinder connected to the case of the electrometer. The rays passed into the cylinder of aluminium through a window in the lead cylinder 2 centim. broad and 4 centim. long. ‘This window could be screened or unscreened at will. 3 The course of the experiment was the same with each insulated conductor. The conductor was charged first positively, then negatively ; the Roéntgen rays were then caused to shine on it through the aluminium cylinder sur- rounding it and the electrometer-readings taken at fixed intervals, until a steady reading on the electrometer was obtained. The point at which the electrometer-reading remained steady with the rays acting we shall call the rays- zero. Finally, the insulated conductor was discharged by metallic connexion in the electrometer and re-insulated ; the rays were again caused to shine on it till the deviation from the metallic zero reached the rays-zero and there remained steady. This deviation from the metallic zero was not stopped by placing an aluminium screen over the window of the lead cylinder surrounding the Rontgen lamp ; on the other hand, it was stopped if a lead screen was used. In the following table, column II. gives the potential- differences of the rays-zero from the metallic zero for twelve 434 Drs. Beattie and De Smolan on the Conductance different metals insulated within the unpolished aluminium cylinder as described above. Column ILL. gives the differ- ences for two of the same metals in the interior but with the surrounding aluminium cylinder altered by its inner surface being polished by emery-paper. iq. IRE ib Bs Insulated metal. Magnesium tape........ — 0°67L of a volt. Amalgamated zinc ...... — 0:66 x Polished aluminium .... —0465 _,, Polished zine Ses 2 hw = 0-545 5 2). Unpolished aluminium .. —0°349 _,, + 0°35 of a volt. Polished deadd-=, sae St =—0'257 —.,, Polished coppers... 27. +0°129 _,, Polished iron nail ...... +0:182 ,, Palladwm ware a2... 0s -.- +0:255 __,, Groldlewine voc. 06 0.01 hae oe 40-264, +0°930 ,, Carbon eee ortc. es ek “07420902 ae It will be noticed that the difference of potential depends very much on the state of polish of the two mutually insu- lated conductors. To make similar experiments with ultra-violet light we used the brass wire gauze cage arrangement described in § 2. That is, we have now air between the wire gauze and the insulated conductor rendered conductive by ultra-violet light. The insulated conductor was 2 centim. distant from the gauze. The steady electrometer-reading after the two pairs of quad- rants were insulated and the ultra-violet light shining (which we shall hereafter refer to as the ultra-violet-light-zero) was observed. The difference of potential indicated on the elec- trometer between the rays-zero and the metallic zero does not give, however, the contact-force between the gauze and the insulated conductor within. The reason for this we shall see in the next section. The following table shows the steady potential-differences in the electrometer due to the conductive effect produced by ultra-violet light in the air between the brass wire gauze and the insulated conductor. Insulated metal. Potential-difference. Polished Wine oe see eee oe —0-75 of a volt. Polished aluminium ...... — 0°66 5 German ‘silver: 7-2 2 eee —0:19 * Gilded brass +. See +0:04 a Polishedscopper.2:. eee +0-12 5 Oxadizedicopper -225,92-F-.- +1:02 - produced in Gases by Réntgen Rays §c. 435 When the insulated metal was charge either positively or negatively and the ultra-violet light let fall on it, the electrometer-reading deviated until the ultra-violet-light-zero was reached. The rate of deviation was the same for a posi- tive or a negative charge if we reckon the charge from the ultra-violet-light-zero. We have used two different methods to measure the poten- tial-difference between wires of the same metal connected to two mutually insulated metals when the air between them is rendered conductive by the presence of uranium. The more convenient method is to take uranium as one of the mutually insulated metals. To do this we fixed a metallic disk, 3 centim. diameter, to the insulated terminal of the quadrant- electrometer. Opposite this disk, and separated from it by air, we placed the disk of uranium, 5:5 centim. diameter, con- nected to the case of the electrometer. With this arrangement we found, after contact between the quadrants was broken at the electrometer, a deviation from the metallic zero. This deviation took place gradually till a steady reading was reached. This steady reading we shall call the uranium-conductance- zero, or shortly the uranium-zero. If the insulated conductor had a charge given to it of such an amount as to cause the electrometer-reading to deviate from the metallic zero beyond the uranium-zero, the reading quickly fell to this conductance zero and there remained steady. When no charge was given to the insulated metal the steady uranium-zero was reached in about half a minute. The following table gives the potential-differences found in this way :— Motul. A ae ange Polished aluminium (1) immediately after being polished .......... sean Polished aluminium (1) next day ...., — 0-90 Rolished almminivmms(2)) a sek «a: — 1:00 manaloamated: VANG 2! s.005 42% oe ae ne — 0°80 Polishedezime is 5 West aes faa ets 2 —0:°71 Whapolishted) 71ers te ek ry tation — 0°55 Rolished eddy ii tik oe sca eae Ss — 0°54 HERA Ole, cee te a tt Me eer EMG Pe — 0-49 Unpolished aluminum (1).......... — 0-41 olisbed copper. tosh.) es eS —O:17 STU WOE, GOTT OY ES 0: ak PSR nes Sm + 0:05 Unpolishedscopper\...... 4. ek es + 0:07 Car pOnyses eye) ely. iso's te A + 0°20 Oxidized copper (@)ae.. gists. den as +042 Oxidized copper D)aig.¢ <6 with screens of lead, zinc, and tinned iron ; lead ones with copper, zinc, and tinned iron; bismuth with copper, lead; zinc, and tinned iron; and zine with those of. lead: no screening effect was detected in any of the eleven instances.’ As the radiant influence was not manifestly intercepted by screens, it appears to partake so far of the nature of gravity. | I have to express thanks to Messrs. Stock & Taylor,: of Birmingham, for the loan of 74 ewt. of lead ; to Messrs,, Osler for the preparation and loan of bars of glass, brass, and plaster ; and to the Magnesium Company, Patricroft, Man- chester, for preparing and lending the bars of magnesium, bismuth, and antimony. | | [ 458 ] LIX. On a Supposed Proof of a Theorem in Wave-Motion. To the Editors of the Philosophical Magazine. GENTLEMEN, i ie a letter printed at page 368 of this volume, under the above title, Dr. Stoney directs attention to a communi- cation* in which I expressed the possibility of expanding any function of any number of variables in the form S(t, y-.-) = 2A cos (let+my+...) + 2Bsin (let+my+...). . (1) He admits this to hold good for “ scalar functions,” but for such functions only ; and he concludes that the applications of it “to prove certain physical theorems which treat of real wave-motions ” are erroneous. In reply, I may state first of all that I fear Dr. Stoney has misunderstood my communication. What I intended to convey was, that if we take the variables to be wz, y, z, t— namely, the coordinates of a point in space and the time— then the above expansion enables us to resolve any specified disturbance, existing throughout any given region, into a system of simple harmonic plane waves. When I say a specified disturbance, I mean simply that the disturbance at every point of the region is expressed in the ordinary way in terms of its three component velocities or displacements in the form E=Fyi(z,y,2,t), n= Fi(v,y,2,t), $= F3(z,y,2,¢), and I did not think it necessary to state such an obvious proceeding. Each of these functions can be expanded, as Dr. Stoney admits, and the components of the simple har- monic plane waves are then to hand. Of course a velocity (or a displacement) is a directed quantity, and a function which represents a velocity is a vector function ; but it is here a vector function of scalar variables, and accordingly the analysis which I have employed holds good. In fact, if F be such a vector function, we may write it in the form F = iF, +)F, +kF5, where Fj, F,, and F; are scalar functions which, by admission, may each be expanded in the form (1), so that F is thrown at once into a sum of simple harmonic terms of the type (iA, +jAg+kAs;) cos (la+myt+...) = Acos (le+my+t...), * “Qn the General Extension of Fourier’s Theorem,” p. 281 of this volume. On a Supposed Proof of a Theorem in Wavre-Motion. 459 where A is a directed quantity and is obviously determined by the definite integral given on p. 283, being related to F in the same way as A, is to Fy, &e. Dr. Stoney in fact admits as much as this, but he then goes on to say on p. 371 that “on a close scrutiny we find that although this furnishes an apparent solution, in the form of forced vibrations, or rather a group of such solutions, the group unfortunately does not include the solution which would be selected by nature under any conceivable circum- stances. The analysis furnishes undulations which could not propagate themselves through any medium. The motions which it furnishes are the non-natural motions of a mere forced kinematical resolution, of no use in physics. That this is so can be made plain by taking a very simple example... ;” and he then takes an example and discusses it in a manner which shows clearly that his letter was written under some misunderstanding as to my interpretation of the expansion. What I state is, that when the disturbance which _ exists throughout any given region is specified, then a system of plane waves can be determined which will produce the same disturbance at every point of that given region. Now in his example Dr. Stoney takes the given region of space to be a circular disk having its plane perpendicular to the axis of 2, and he specifies the disturbance throughout the disk to be E = f(vt—2) +f(ot +2) 5 so that in this case the specified disturbance throughout the given region is already in the form of plane waves, and these can be resolved into simple harmonic components when the form of the function fis given; and nothing more remains to be done. As to what happens outside the disk, this is quite another question and belongs to the class of problems dealt with by Sir G. G. Stokes in his classical paper on the Dynamical Theory of Diffraction. So far there has been no necessity whatever for considering the nature of the medium or the manner in which it pro- pagates waves, plane or curved, or even whether it propagates waves at all. We simply ask for the disturbance, and this being given we can determine the equivalent simple harmonic plane-wave system. _ But if the given disturbance happens to be the actual dis- turbance existing in some medium capable of propagating plane waves unaltered, then the specification of this dis- turbance will involve the properties of the medium. The equivalent plane-wave system will represent the actual dis- turbance, and these waves will be propagated through the medium and will continue to represent the disturbance. 460. ..° Notices respecting New Books. Thus when the disturbance is given and the plancae en com- ponents are determined so as to satisfy the initial conditions throughout all space, then this same plane wave system will continue to represent the subsequent disturbance in all its stages, and the waves will be propagated as plane waves. > As Dr. Stoney contrasts the method adopted in my com= munication with that employed by himself elsewhere, I feel bound before concluding to take this opportunity of pro- testing against the method adopted by Dr. Stoney in his proof of the theorem on p. 276. I object to the ease and freedom with which he rides off to infinity on a spherical wave and comes back on a plane wave. One does not feel quite sure as to what has happened in the meantime. Why go to infinity in order to find out what is going on about home? Why deal with a very long cylinder of finite width rather than a very narrow one of moderate length? If it is true that a curved wave may be replaced by its tan gent planes, considered as infinite plane waves, this should be demonstrated about home rather than at infinity. A spherical sector of moderate area certainly approximates to the corresponding area in the tangent plane as the radius of the sphere increases: But this sector travels out as part of a complete spherical wave, while, when reversed, it returns as a segment of a wave. How does it return? — Is it supposed to be geometrically reversed, so as to focus at the original centre, or dees it diffuse through- out space by diffraction during the whole time of its return ? Is it evident by any method that this sector, when reversed, will produce the same effect at the original centre as the whole tangent plane wave would? — Such are some of the difficulties which I recognize i in Pe method, and these are real and great difficulties to those who are less deeply versed than Dr. Stoney in the aie aspect of the Cee : I am, Gentlemen, : Bardavie, an Faithfully yours, Orwell Park, Dublin. : THOMAS PRESTON. “LX. Notices respecting New Books. The Phase Rule. By Witprr D. Bancrort. Ithaca, New York, The Journal of Physical Chemistry, 1897. WE have been chiefly indebted to Dutch and German wie : for the great advances made in our knowledge of physical chemistry during the pest few years. Now, however, the school of physical chemists in America has shown its existence and activity by the publication of.a monthly journal of which Professor Geological Society. 461 Trevor and the author are joint editors, and the present volume is issued by the publishers of the journal. The work consists of a general discussion, without mathematics, of the conditions of equilibrium of chemical mixtures, in which the amount of any component, the temperature, and the pressure are considered as variable. Van’t Hoff, in his ‘Studies in Chemical Dynamics,’ and others have examined a few such cases of equili- brium quantitatively, while Roozeboom has done much experi- mental work of a more qualitative character; but, so far as we are aware, no attempt has been made until now to classify the phenomena. The author defines a phase as a mass of uniform concentration, and its components as the substances of independently variable concentration contained in it. For a mixture of phases in equili- brium every phase will furnish an equation involving functions of its components together with the temperature and pressure. The number of equations will thus be equal to the number of phases, while the number of independent variables will be +2 if the mixture contains n components. A system consisting of »+2 phases will thus give as many equations as there are variables ; such a system can only exist at a single temperature and pressure and is called non-variant. An equilibrium mixture of ice, water, and steam belongs to this type. If the number of phases is only n+1 the system is monovariant, and is fully determined by the specification of one of its variables; with » phases the system is divariant, and so on. The scope of the present volume is limited to non-, mono-, and di-variant systems, with at most four components ; and in the discussion of changes of equilibrium the general theorem of Le Chatelier is made use of, namely, that whenever a system is disturbed from without, it adjusts itself to the new conditions by the occurrence of a corresponding reverse change within itself; for example, an increase of external pressure will cause an increase in the amount of the denser phases. The author demonstrates the extreme usefulness of this theorem in predicting the effect of any given change. The value of Mr. Bancroft’s treatise lies not so much in the fact that it presents the results of a large amount of experimental work in physical chemistry, but rather that it indicates a scientific method of classifying all such work; he has, in fact, taken the first step towards the formation of order out of chaos in this department of science. J, Lone LXI. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 396.] March 24th, 1897.—Dr. Henry Hicks, F.R.S., President, in the Chair. rIXHE following communications were read :— 1. ‘Notes on some Volcanic and other Rocks which occur near the Baluchistan-Afghan Frontier, between Chaman and Persia.’ Phil. Mag. 8. 5. Vol. 43. No. 265. June 1897. 2M 462 Geological Society :— By Lieut.-Gen. C. A. McMahon, V.P.G.S., and Capt. A. H. McMahon, C.LE. In the first part of this paper Capt. McMahon describes briefly the physical geography of the Baluchistan deserts, which extend along the south of the Helmund River, between Quetta and Persia. Taking first the plains and their drainage-system, he shows how the wide alluvial plains of Shorawak and Chagai were probably in earlier times one large lake. North and west of these plains, as far as Persia, lie vast deserts of sand, which in places are gradually encroaching upon and burying the mountain-ranges which rise up like islands in the desert. He shows how the sand has intercepted all the drainage from the mountains and prevented it from making its way, as it would otherwise do, into the Helmund River and the God-i-Zirreh Lake. Turning next to the mountains, Capt. McMahon describes a well-defined line of fault, which he traced for a distance of about 120 miles from north of Chaman, along the Khwaja Amran and Sarlat mountain-ranges to Nushki. East of this fault all the rocks appear to be sedimentary; while those to the west are all, with few exceptions, volcanic and igneous. The mountain-ranges in the desert described appear to be all voleanic, and reference is made to the Koh-i-Taftan, 12,600 feet high, lying south-west of them, which is still an active volcano. The curious, grotesquely-shaped peaks of the Koh-i-Sultan range are then briefly described, and especially that named Neza-i-Sultan —a gigantic natural pillar of volcanic agglomerate many hundreds of feet high. After thus describing the general character of the country, Capt. McMahon points out the very remarkable force and activity with which certain natural agents are at present at work there— namely, water, wind, sand, and extremes of heat and cold. In the second part of the paper Gen. McMahon describes the microscopical characters of the rocks, which consist of lavas, ashes, pumice, igneous intrusive, and sedimentary rocks. The localities in which ores of lead and copper, gypsum, sulphur, ete. occur abundantly are also mentioned. Some andesites are described, which are especially interesting from a petrological point of view. Rosenbusch mentions that a brown hornblende occurs in some rocks in which the angle of extinction varies from small to nil. Some of the andesites described abound in amphibole, red-brown in transmitted light, which possesses - the optical properties and specific gravity of anthophyllite, and which uniformly exhibits straight extinction. It is an original, and not a secondary mineral. These anthophyllite-bearing augite-andesites also contain olivine —a mineral rare, but not unknown, in this class of rocks. 2. ‘On the Association of Sigillaria and Glossopteris in South Africa.’ By A. C, Seward, Esq., M.A., F.G.S., University Lecturer in Botany, Cambridge. 3. ‘Notes on the Occurrence of Sigillaria, Glossopteris, and other Plant-remains in the Triassic Rocks of on ae By David Draper, Esq., F.G.8. The Glacio-Marine Drift of the Vale of Clwyd. 468 April 7th.—Dr. Henry Hicks, F.R.S., President, in the Chair. The following communications were read :— 1. ‘On the Morte Slates and Associated Beds in North Devon aud West Somerset.—Part II.’ By Henry Hicks, M.D., F.RS. P.G.S. With Descriptions of the Fossils by the Rev. G. F. Whid- borne, M.A., F.G.S. In the Brat part of this paper, read by the author before the Society i in February 1896, he described the Morte Slates as they occur in North Devon, and the fossils found in them. In this, the second part, he refers mainly to the rocks classified as Morte Slates in West Somerset. He shows that the latter differ in some im- portant characters from those in North Devon, and have an entirely distinct fauna. The fossils obtained from North Devon show that there the beds must in the main be classed with the Silurian rocks ; but in West Somerset, so far as discoveries have yet been made, the fossils indicate that they should be classed with Lower Devonian rocks. The author’s contention that the Morte Slates which extend through the centre of North Devon and West Somerset from Morte Point to the north of Wiveliscombe, a length of about 40 miles, are the oldest rocks in the area and form an axis with newer rocks lying to the north and to the south, is therefore fully proved by stratigraphical and paleontological evidence. The fossils are care- fully described by Mr. Whidborne, and he shows that there are numerous forms in common between them and those considered to be characteristic of the Lower Devonian rocks in the continent of Europe and in America. 2. ‘The Glacio-Marine Drift of the Vale of Clwyd. By T., Mellard Reade, Esq., C.E., F.G.S. The local drift of the higher parts of the Vale of Clwyd is replaced by marine drift towards the mouth; and it is the object of this paper to give the results of a detailed examination of these marine drifts, rather than to explain the phenomena. The first part of the paper gives the results of an examination of the boulder- clay from Craig, west of Llandulas, to the Vale of Clwyd, south-east of Abergele. Mechanical analyses of the clays are given; but the point of greatest interest is the occurrence of abundance of forami- nifera, especially in the plastic brown and red Boulder Clays, which often contain intensely striated erratics. These foraminifera have been examined by Mr. Joseph Wright. Most of them occur in the boulder-clays of Crosby and Wirral; but some of them are very rare in British localities other than those now recorded, namely, Rhabdogonium tricarinatum, Sphecordina bulloides, Pullenia sphe- roides, and Pulvinulina Menardit. The glacial sands and gravels of the east side of the Vale of Clwyd are also described, and especial attention is called to an esker-like mound of sand (g ravel), occurring south-east of Diserth Castle, formed of bedded deposits, the bedding of which generally follows the outer form of the ridge. The ridge has Boulder Clay upon the flanks, and is described as rising through the Boulder Clay. [ 464 ] LXII. Intelligence and Miscellaneous Articles. To the Editors of the Philosophical Magazine. GENTLEMEN, a abe me to call your attention to the fact that in January 1897 Messrs. Stroud and S. B. Henderson published in No. 260 of this Journal a paper entitled “A Satisfactory Method of Measuring Electrolytic Conductivity by means of Continuous Currents,” in which several authors are quoted who have em- ployed methods similar to that described in the paper above mentioned. \ Messrs. Stroud and Henderson must have forgotten or over- looked my statement in Wiedemann’s Annalen, vol. xxiii. pages 482-490, in which not a similar, but in fact the very same method is described by me. The fig. 1 on page 21 of the paper in your journal is quite the same as the fig. on page 482 in my statement. J have employed for the equal resistance only 20 8. E., whereas Messrs. Stroud and Henderson have used 1000 ohms. Certainly I was aware of the advantage of a higher degree of resistance, and the reason for the little power I used was, as I expressly mentioned on page 483, the fact that I had no greater resistance at my disposal. I remain, Yours faithfully, F. NEESEN. THE HEATS OF VAPORIZATION OF LIQUIDS. To the Editors of the Philosophical Magazine. GENTLEMEN, Mr. Griffiths has kindly drawn my attention to a slight error on page 298 of my paper in your April issue, viz.: that the mea- surements by himself and Miss Marshall of the latent heat of see extended up to 50° C., instead of 40° as I inadvertently stated. I may also take this opportunity of noting that on page 290 of the paper on “The Variation of the Dissociation Coefficient ” the last three equations are reduced to the ordinary form by expressing the gas-constant R in gram-calories, instead of in the work-units used previously. This explains the disappearance of J from the previous equation, and should have been stated at the time. I am, Gentlemen, Your obedient servant, S. R. Miner. University College, Bristol, May 1, 1897. [ 465 j : “Ke » INDEX ro VOL. XLII. AETHER, on the electrical con- ductivity of the, 378. Alternate currents, on the measure- ment of, by means of an obliquely situated galvanometer-needle, 345. Appleyard (R.) on liquid coherers and mobile conductors, 374. Argon, on the spectra of, 77. Atomic theory, on the genesis of Dalton’s, 1538. Barlow (W.) on the relation of cir- cular polarization to the symmetry and partitioning of homogeneous structures, 110. Barton (Dr. E. H.) on the absorption of electric waves along wires by a terminal bridge, 39. Battelli ((Prof. A.) on photographic action inside discharge tubes, 133. Beattie (Dr. J. C.) on conductance produced in gases by Rontgen rays, ultra-violet light, and ura- nium, 418. Bismuth, on the thermo -electric properties of, 397. Blake (Rev. J. F.) on some super- ficial deposits in Cutch, 314. Bonney (Prof. T. G.) on the geology of the Furka Pass, 73. Books, new:—Bedell’s The Prin- ciples of the Transformer, 69; Geological Survey of Canada, An- nual Report, Vol. VIL, 69; The Scientific Papers of John Couch Adams, Vol. 1.,71; Kerntler’s Die elektrodynamischen Grundgesetze und das eigentliche Elementar- gesetz, 149; Ayrton’s Practical Electricity, Vol. I., 149; Voget’s Das Wesen der Elektrizitat und des Magnetismus, auf Grund eines einheitlichen Substanzbegriffes, 239; Helmholtz’s Vorlesungen uber theoretische Physik, Bd. V., 305; Ebert’s Magnetic Fields of Force, Pt. 1.,306; Iowa Geological Survey, Annual Report for i895, 307; Autobiographical Sketch of James Croll, 308; Bucherer’s Grundzuge einer thermodyna- mischen Theorie elektrochemischer Krafte, 391; Knott’s Physics, 392 ; Ames’s Theory of Physics, 392; de Fodor’s Elektricitat direkt aus Kohle, 393; Michelitsch’s Atom- ismus, Hylemorphismus und Na- turwissenschaft, 393; Keller’s Ueber den Urstoff und seine Energie, Th. I., 398; Behrens’s Anleitung zur microchemischen Analyse organischer Verbindun- gen, Pt. [V., 394; Bancroft’s The Phase Rule, 460. Bose (Prof. J. C.) on a complete apparatus for the study of the pro- perties of electric waves, 55. Boyle’s iaw at very low pressures, 11. Bressa prize for 1898, 152. Bryan (G. B.) on the absorption of electric waves along wires by a terminal bridge, 39. Burch (G. J.) on the tangent lens- gauge, 256. Burnie (W. B.) on the thermo- electric properties of some liquid metals, 397. Capacity, on the effect of, on sta- tionary electrical waves in wires, 383. Chree (Dr. C.) on applications of physics and mathematics to seis- mology, 173. Circular polarization, on the relation of, to the symmetry and _ parti- tioning of homogeneous structures, LO: Coherers, on liquid, 374. Conductance produced in gases by Rontgen rays, ultra-violet light, and uranium, on the, 418. Conductivity of electrolytes, on a method of measuring the, 19, 464; on the effect of great current- strength on the, 376; of the zther, on the, 378. Conductors, on mobile, 374. Crehore (Dr. A. C.) on the currents in the branches of a Wheatstone’s bridge, 161. Crystals, on the relation of circular polarization to the symmetry Xe. of, 110. Currents in the branches of a Wheat- stone’s bridge, on the, 161. , on the measurement of alter- nate, by means of an obliquely situated galvanometer-needle, 343. Current-strength, on the effect of great, on the conductivity of elec- trolytes, 376. 466 Cylinders, on the vibrations of di- electric, 125. Dalton’s atomic theory, genesis of, 153. Davison (Dr. C.) on an error in the method of determining the mean depth of the ocean from the velocity of seismic sea-waves, 33; on the accessory shocks of the Japanese earthquake of 1891, 75; on the Pembroke earthquakes of Aug. 1892 and Nov. 1893, 312. Determinantal equation, grange’s, 220, Discharge tubes, on photographic action inside, 133. Dissociation, on a remarkable type oto Ole ae. Dissociation-coefficient, on the varia- tion of the, with temperature, 286, 464. Electric discharge, on the tempe- rature and ohmic resistance of gases during the oscillatory, 349. wayes, on the absorption of, along wires by a terminal bridge, 39; on a complete apparatus for the study of the properties of, 55 ; on the passage of, through tubes, 125; on the effect of capacity on stationary, in wires, 383. Electrification of gases exposed to Rontgen rays, on the, 241. Electrolytes, on the effect of great current-strength on the conduc- tivity of, 376; on a method of measuring the conductivity of, 19, 464. Emich (Prof. F.) on the explosion of thin layers of explosive gases, 151. Emission-spectrum of a black body, on the division of energy in the, 214. Energy, on the division of, in the emission-spectrum of a black body, 214. Explosion of thin layers of explosive gases, on the, 151. Fourier’s theorem, on the general extension of, 281, 368, 458. Galvanometer-needle, on the esti- mation of waste space round a, 36, 315; on the measurement of alter- nate currents by means of an obliquely situated, 343. Gases, on the multiple spectra of, 185; on the explosion of thin layersof explosive, 151; on the elec- trification of, exposed to Rontgen on the on ~ La- INDEX. rays and the absorption of Rontgen radiation by, 241; on the tempe- rature and ohmic resistance of, during the oscillatory electric dis- charge, 349; on conductance pro- duced in, by Rontgen rays, ultra- violet light, and uranium, 418. Geological Society, proceedings of the, 73, 150, 240, 312, 394, 461. Glacial epoch, on another possible cause of the, 150. Gore (Dr. G.) on the influence cof proximity of substances upon voltaic action, 440. Gosling (A.) on voleanic activity in Central America in relation to British earthquakes, 396. Gray (Prof. A.) on the estimation of waste space round the needle of a galvanometer, 36. Gresley (W.S.) on the formation of coal, 395. Harden (A.) on the genesis of Dal- ton’s atomic theory, 153. Heats of vaporization of liquids, on the, 27, 291, 464. Henderson (J. B.) on a method of measuring electrolytic conducti- vity by means of continuous cur- rents, 19. Hicks (Dr. H.) on the Morte slates in N. Devon and W. Somerset, 463. Hind (Dr. W.) on the subdivisions of the Carboniferous series in Great Britain, 240. Holman (Prof. 8. W.) on galyano- meter design, 315. Hull (Prof. E.) on another possible cause of the glacial epoch, 150. Ionization, on the relation of the physical properties of aqueous solutions to their state of, 46, 99. Kayser (Prof. E.) on volcanic bombs in the Schalsteins of Nassau, 240. Klemengic (Prof. I.) on magnetic _ after-action, 316. Lag, on a method of determining the angle of, 343. Lagrange’s determinantal equation, on, 220. Lead, on the thermo-electric pro- perties of, 397. Lens-gauge, description of the tan- gent, 206. Light emitted by a substance, on the influence of magnetism on the nature of the, 226, 316. . Liquids, on the heats of vaporization of, 27, 291, 464. INDEX. Lobley (J. L.) on the depth of the source of lava, 396. MacGregor (Prof. J. G.) on the re- lation of the physical properties of aqueous solutions to their state of lonization, 46, 99. McMahon (Lieut.-Gen. C. A. & Capt. A.H.) on some volcanic rocks be- tween Chaman and Persia, 461. Maenetic after-action, on, 316. force acting on moving electri- tied spheres, on the, 1. Magnetism, on the influence of, on the nature of the light emitted by a substance, 226, 316. Marshall (Miss D.) on the heats of vaporization of liquids at their boiling-points, 27. Mercury, on the thermo-electric pro- perties of, 397. Metals, on the thermo-electric pro- perties of some liquid, 397. Miller (Dr. G, A.) on the transitive substitution groups of order 8p, p . being any prime number, 117. Milner (S. KR.) on the variation of the dissociation-coethicient with temperature, 286, 464; on the heats of vaporization of liquids, 291, 464. Mortun (W. B.) on the effect of capacity on stationary electrical waves in wires, 383. Muir (Dr. T.) on Lagrange’s deter- minantal equation, 220, Neesen (F’.) on a method of measur- ing electrolytic conductivity, 464. Ocean, on an error in the method of determining the mean depth of the, from the velocity of seismic sea- waves, 35. Oxygen, on the spontaneous change of, into ozone, 201. Ozone, on the spontaneous change of oxygen into, 201. Photographic action inside discharge- tubes, on, 133, Photcgraphy of ripples, on the, 411. Polarization, on the relation of cir- cular, to the symmetry and parti- tioning of homogeneous structures, 110. Pressure-gauges for the highest vacua, on two new, 88. Preston (T.) on the general extension of Fourier’s theorem, 281, 458. Radiometer motion, on, 142. taisin (Miss C. A.) on the Rauenthal serpentine, 394, 467 Rayleigh (Lord) on the passage of electric waves through tubes, or the vibrations of dielectric cylin- ders, 125; on the passage of waves through apertures in plane screens, 259; on the measurement of alter- nate currents by means of an obliquely situated galvanometer- needle, with a method of deter- mining the angle of lag, 348. Reade (T. M.) on the glacic-marine drift of the Vale of Clwyd, 468. Reed (F. R. C.) on the red rocks near Bonmahon, 396. Resolving power of telescopes and spectroscopes for lines of finite width, on the, 317. Reynolds (Prof. O.) on thermal trans- piration and radiometer motion, 142. Richards (T. W.) on the spectra of argon, 77; on the multiple spectra of gases, 155; on the temperature and ohmic resistance of gases during the oscillatory electric dis- charge, 349; on the effect of great current-strength on the conduc- tivity of electrolytes, 376. Richarz (F.) on the action of Rontgen rays on a jet of steam, 75. Ripples, on the photography of, 411. Rontgen rays, cn the action of, on a jet of steam, 75; on the electrifica- tion of gases exposed to, and the absorption of, by gases and vapours, 241; on conductance roduced in gases by, 418. Roscoe (Sir H. E.) on the genesis of Dalton’s atomic theory, 153. Rutherford (14.) on the electrification of gases exposed to Rontgen rays, and the absorption of Rontgen radiation by gases and vapours, 241, Schuster (Prof. A.) on the magnetic forces acting on moving electrified spheres, 1. Seismology, applications of physics and mathematics to, 173. Smolan (Dr. M.S. de) on conductance produced in gases by Rontgen rays, ultra-violet light, and uranium, 418. Solutions, on the relation of the physical properties of aqueous, to their state of ionization, 46, 99, Spectra of argon, on the, 77; on the multiple, of gases, 135, Spectroscopes, on the resolving power of, for lines of finite width, 317, 468 Spheres, on the magnetic force acting on moving electrified, 1. Squier (Lieut. G. O.) onthe currents in the branches of a Wheatstone’s bridge, 161. Steam, on the action of Rontgen rays on a jet of, 75. Stebbing CW aP; D. ) on two boulders of oranite from the middle chalk of Betchworth, 395. Stoney (Dr. G. J. ’ on a new theorem in wave-propagation, 139, 273, 368. Strahan (A.) on the seolog'y of the Varanger Fiord, 313, 314. Stroud (Prof. Ww.) on a method of measuring electrolytic conduc- tivity by means of continuous currents, 19. Substitution groups, on the transitive, of order 8p, p being any prime number, 117. Sutherland (W.) on Boyle’s law at very low pressures, 11; on two new pressure-gauges for the high- est vacua, 83; on the sponta- neous change "of oxygen into ozone and a remarkable type of dissociation, 201. Tangent lens-gauge, description of the, 256. Tarr (Prof. R. 8.) on changes of level in the Bermuda Islands, 315. Telescopes, on the resolving power of, for lines of finite width, 317. Temperature, on the variation of the dissociation-coefficient with, 286, 464. Thermal transpiration, on, 142. Thermo-electric properties of some liquid metals, on the, 397. Thomson (Prof. J.J.) on the absorp- tion of Réntgen radiation by gases and vapours, O55. Tin, on the thermo-electric properties of, 397. Trowbridge (Prof. J.) on the spectra of argon, 77; on the multiple spectra of gases, 185; on the temperature ‘and ohmic resistance of gases during the oscillatory INDEX. electric discharge, 349; on the effect of great current-streneth on the conductivity of electrolytes, 376; on the electrical conductivity of the ether, 378. Tabs, on the passage of electric waves through, 125. Ultra-violet light, on conductance produced in gases by, 418. Uranium, on conductance produced in gases by, 418. Vaporization, on the heats of, of liquids, 27, 291, 464. Vapours, on the absorption of Rént- gen radiation by, 241. Vincent (J. H.) on the photography of ripples, 411. Voltaic action, on the influence of proximity of substances on, 440. Wadsworth (Prof. F. L: O.) on the resolving power of telescopes and spectroscopes - for a of finite width, 317. Walker (Dr. T. 08 ihe geology of the Sebel nickel district, 73. Wave-propagation, disease of a new theorem in, 159, 273, 281, 368, 458. Waves, on the passage of, through apertures in plane screens, 259. ——,, electric, on the absorption of, along wires by a terminal bridge, 39; on a complete apparatus for the study of the properties of, 55; on the passage of, through tubes, 125; on the effect of capacity on stationary, in wires, 383. Wheatstone’s bridge, on the currents in the branches of a, 161. Wien (W.) on the division of energy in the emission-spectrum of a black body, 214. wien! on the absorption of electric waves along, 39; on the effect of capacity on stationary electrical waves in, 3883. Zeeman (Dr. P.) on the influence of magnetism on the nature of the light emitted by a substance, 226. END OF THE FORTY-THIRD VOLUME. Printed by Taytor and Fraycrs, Red Lion Court, Fleet Street. ] . Vol. 43. PI. 5 S . Mag il Ph Sow Sie “Say, ae: a Phil. Mag. S. 5. Vol. 43. Pl. II y) tt eRe ay nw iw ’ ea oe <3 PUEEH LET Fig. 6. 4, 7,