The equations of the electromagnetic field in the metal may be written
whore k denotes the ohmic conductivity; whence it is seen that the electric force satisfies the equation
.
This is of the same form as the corresponding equation in the elastic-solid theory[1]; and, like it, furnishes a satisfactory general explanation of metallic reflexion. It is indeed correct in all details, so long as the period of the disturbance is not too short—i.e., so long as the light-waves considered belong to the extreme infra-red region of the spectrum; but if we attempt to apply the theory to the case of ordinary light, we are confronted by the difficulty which Lord Rayleigh indicated in the elastic-solid theory.[2] and which attends all attempts to explain the peculiar properties of metals by inserting a viscous term in the equation. The difficulty is that, in order to account for the properties of ideal silver, we must suppose the coefficient of Ë negative—that is, the dielectric constant of the metal must be negative, which would imply instability of electrical equilibrium in the metal. The problem, as we have already remarked,[3] was solved only when its relation to the theory of dispersion was rightly understood.
At this time important developments were in progress in the last-named subject. Since the time of Fresnel, theories of dispersion had proceeded[4] from the assumption that the radii of action of the particles of luminiferous media are so large as to be comparable with the wave-length of light. It was generally supposed that the aether is loaded by the molecules