282 



NA TURE 



[January i8, 1894 



traction of the conduct irs on the dielectric system, is d\<Hd<p ; 

 therefore the component of the traction, somehow produced, of 

 the dielectric system on the conductors is -dVHjdcp. 



The stress in the ather between two electrified bodies consists 

 of a tangential traction on each element of area, equal in mag- 

 nitude to the tangential component of the electric force at that 

 place and at right angles to its direction. The stress in the 

 material of the dielectric is such as is produced in the ordinary 

 manner by the surface tractions exerted on the material by the 

 conductors that are imbedded in it. The stress in the dielectric 

 of Faraday and Maxwell has no real existence ; it is, in fac', 

 such a stress a; would be felt by the surface of a conductor used 

 to explore the field, when the conductor is so formed and placed 

 as not to disturb the electric force in the dielectric. The mag- 

 netic stress of Maxwell is simply a mathematical mode of expres- 

 sion of the kinetic reaction of the medium. 



The transfer of a charged body across the field with velocity 

 not large compared with the velocity of electric propagation 

 carries with it the whole system of electric displacement belong- 

 ing to the body, and therefore produces while it lasts a system 

 of displacement currents in the medium, of which the circuits 

 are completed by the actual flow of charge along the lines of 

 motion of the different charged elements of the body. 



According to the present theory of electrification, a discharge 

 of electricity from one conductor to another can only occur by 

 the breaking down of the elasticity of the dielectric cether 

 along some channel connecting them ; and a similar rupture is 

 required to explain the transfer of an atomic charge to the 

 electrode in the phenomenon of electrolysis. We can con- 

 ceive the polarisation increasing by the accumulation of 

 dissociated ions at the two electrodes of a voltameter, until 

 the stress in the portion of the medium between the ions and 

 the conducting plate breaks down, and a path of discharge is 

 opened from some ion to the plate. While this ion retained 

 its charge, it repelled its neighbours ; but now electric attrac- 

 tion will ensue, and the one that gets into chemical contact 

 with it first will be paired with it by the chemical forces ; while 

 if the conducting path to the electrode remains open until this 

 union is complete, the ion will receive an opposite atomic 

 charge from the electrode, which very conceivably may have to 

 be also of equal amount, in order to equalise the potentials of 

 the molecule and the plate. This is on the hypothesis that 

 the distance between the two ions of a molecule is very small 

 compared with the distance between two neighbouring mole- 

 cules. A view of this kind, if thoroughly established, would 

 lead to the ultimate averaging of atomic changes of all atoms 

 that have been in combination with each other, even if those 

 charges had been oiiginally of different magnitudes. The I 

 assignment of free electric charges to vortex atoms tends i 

 maikedly in the direction of instability ; though instability I 

 under certain circumstances is essential to electric discharge, 

 yet it must not be allowed to become dominant. 



The presence of vortex atoms, forming faults so to speak in 

 the sether, will clearly diminish its eflective rotational 

 elasticity; and thus it is to be expected that the specific 

 inductive capacities of material dielectrics should be greater 

 than the inductive capacity of a vacuum. The readiness with 

 which electrolytic media break down under electric stress may 

 be connected with the extremely high values of their inductive 

 capacities, indicating very great yielding to even a small 

 electric force. 



In all that has been hitherto said we have kept clear of the 

 complication of viscous forces ; but in order to extend our 

 account to the phenomena of opacity in the theory of radiation 

 and of electric currents in ordinary conductors, it is necessary 

 to intrcduce, such forces and make what we can of them on 

 general principles. It is shown that the introduction of the 

 dissipation function info dynamics by Lord Rayleigh enables 

 us to amend the statement of the fundamental dynamical 

 principle, the law of Least Action, so as to include in it the 

 veiy extensive class of viscous forces which are proportional to 

 absolute or relative velocities of parts of the system. This 

 class is the moie important because it is the only one that will 

 allow a simple wave to be propagated through a medium with 

 period independent of its amplitude ; if the viscous forces that 

 act in light proj agalion were not of this kind, then on passing 

 a beam of homogeneous light through a metallic film it should 

 emerge as a mixture of lights of different colours. The viscous 

 forces being thus proved by the phenomena of radiation to be 

 xierived from a dissipation function, it is natural to extend 



NO. 1264, VOL. 49] 



the same conclusion to the elastic motions of slower periods 

 than radiations, which constitute ordinary electric dis- 

 turbances. We thus anive, by way of an optical path, at 

 Joule's law of dissipation of electric energy, and Ohm's linear 

 law of electric conduction, and the whole theory of the electro- 

 dynamics of currents flowing in ordinary conductors ; though 

 j the presumption is that the coefficients which apply to motions 

 of long period are not the same as those which apply to very 

 rapid oscillations, the characters of the matter-vibrations that 

 are comparable in the two cases being quite different. If it is 

 assumed that the form of the dissipation function is the same 

 for high frequencies as for low ones, we obtain the ordinary 

 theory of metallic reflexion, which differs from the theory 

 of reflexion at a transparent medium simply by taking 

 the refractive index to be a complex quantity, as was done 

 originally by Cauchy, and la'er for the most general case 

 by MacCullagh. And, in fact, we could not make a more 

 general supposition than this for the case of isotropic media; 

 while for crystalline media the utmost generality would arise 

 merely from assuming the principal axes of the dissipation func- 

 tion to be diff'erent from those of the rotational elasticity, a 

 hypothesis which is not likely to be required. 



The considerations which have here been explained amount 

 to an attempt to extend the regions of contact between three 

 ultimate theories which have all been already widely developed, 

 but in such a way as not to have much connection with one 

 another. These theories are Maxwell's theory of electric phe- 

 nomena, including Ampere's theory of magnetism and involving 

 an electric theory of light. Lor 1 Kelvin's vortex-atom theory of 

 matter, and the purely dynamical theories of light and radiation 

 that have been proposed by Green, MacCullagh, and other 

 authors. It is hoped that a sufficient basis of connection be- 

 tween them has been made out, to justify a restatement of the 

 whole theory of the kind here attempted, notwithstanding such 

 errors or misconceptions on points of detail as will unavoidably 

 be involved in it. 



Lord Kelvin has proposed a gyrostatic adynamic medium 

 which forms an exact representation of a rotationally elastic 

 medium such as has been here described.' If the spinning 

 bodies are imbedded in the aether so as to partake fully in its 

 motion, the rotational forcive due to them is proportional jointly 

 to the angular momentum of a gyrostat and the angular velocity 

 of the element of the medium, in accordance with what is stated 

 above. But if we consider the rotators to be free gyrostats of 

 the Foucault type, mounted on gymbals of which the outer 

 frame is carried by the medium, there will also come into play 

 a steady rotatory forcive, proportional jointly to the square of 

 the angular momentum of the gyrostat and to the absolute an- 

 gular displacement of the medium. An ideal gyrostatic cell has 

 been imagined by Lord Kelvin in which the coexistence of pairs 

 of gyrostats spinning on parallel axles in opposite directions 

 cancels the first of these forcives, thus leaving only a static for- 

 cive of a purely elastic rotational type. The conception of an 

 sether which is sketched by him on this basis,- is essentially the 

 same as the one we have here employed, with the exception 

 that the elemental angular velocity of the medium is taken to 

 represent magnetic force, and in consequence the medium fails 

 to give an account of electric force and its static and kinetic 

 manifestations. A gyrostatic cell of this kind has internal 

 freedom, and therefore free vibration periods of its own ; it is 

 necessary to imagine that these periods are very small compared 

 with the periods of the light waves transmitted through the 

 medium, in order to avoid partial absorption. The propaga'.ion 

 of waves in this aether, having periods of the same order as the 

 periods of these free vibrations, would of course be a pheno- 

 menon of an altogether different kind, involving diffusion 

 through the medium of energy of disturbed motion of the gyro- 

 stats within the cells. 



The electric interpretation of MacCullagh's optical equations, 

 which forms the basis of this paper, was first stated by Prof. G. 

 F. Fitzgerald (/%?■/. Trans., \%%o). An electric development of 

 Lord Kelvin's rotational aether has been essayed by Mr. Heavi- 

 side, who found it to be unworkable as regards conduction- 

 current, and not sufficiently comprehensive {Phil. Trans., 1892, 

 § 16 ; " Electrical Papers," vol. ii. p. 543). A method of repre- 

 senting the phenomena of the electric field by the motion of 



1 Lord Kelvin (Sir W. Thomson), Comptes Rcttdus, September i5, 1889; 

 "Collected Papers," vol. iii., 1S90, p. 467. 



2 Lord Kelvin (Sir W. Thomson), "Collected Papers," vol. iii., 189O1 

 pp. 4.36-472. 



