458 Mr. J. Larmor. A Dynamical Theory of [Dec. l y 



in it the very extensive class of viscous forces which are proportional 

 to absolute or relative velocities of parts of the system. This class 

 is the more important because it is the only one that will allow a 

 simple wave to be propagated through a medium with period inde- 

 pendent of its amplitude ; if the viscous forces that act in light pro- 

 pagation were not of this kind, then on passing a beam of homo- 

 geneous 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 derived from a dissipation func- 

 tion, it is natural to extend the same conclusion to the elastic 

 motions of slower periods than radiations, which constitute ordinary 

 electric disturbances. We thus arrive, 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 electrodynamics of 

 currents flowing in ordinary conductors ; though 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 dis- 

 sipation 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 later for the most general case by 

 MacCullagh. And, in fact, we could not make a more general sup- 

 position than this for the case of isotropic media ; while for crystal- 

 line media the utmost generality would arise merely from assuming 

 the principal axes of the dissipation function to be different from 

 those of the rotational elasticity, a hypothesis which is not likely to 

 be required. 



It has been pointed out, originally by Lord Rayleigh, that to fit 

 this theory to the facts of metallic reflexion it is necessary to take 

 the real part of the index of refraction of the metals to be a negative 

 quantity, which can hardly be allowed on other grounds, as it would 

 imply instability of the medium. We might indeed, following the 

 view of Willard Gribbs and others, imagine an interaction between 

 the light wave and the free vibrations of the atomic electric charges, 

 and through them the chemical vibrations of the atoms, owing to 

 proximity of their periods ; and we might possibly conceive the 

 electric medium to be, so to speak, held together by this kind of 

 support. But I think there is another and simpler alternative that 



* It is interesting to notice that, already in his memoir of 1864, Maxwell is 

 struck by the identity of the coefficients of the free aether for all periods, which 

 '' shows how perfect and regular the elastic properties of the medium must be when 

 not encumbered with any matter denser than air." 



