Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/310

The equations of the electromagnetic field in the metal may be written

${\begin{cases}\ &\mathrm {curl} &\mathbf {H} &=&4\pi \mathbf {S} ,\\-&\mathrm {curl} &\mathbf {H} &=&{\overset {.}{\mathbf {H} }},\\\ &\ &\mathbf {S} &=&\mathbf {\iota } +{\overset {.}{\mathbf {D} }}=\kappa \mathbf {E} +\epsilon {\overset {.}{\mathbf {E} }}/4\pi c^{2},\end{cases}}$

whore k denotes the ohmic conductivity; whence it is seen that the electric force satisfies the equation

$\epsilon {\overset {..}{\mathbf {E} }}+4\pi \kappa c^{2}{\overset {.}{\mathbf {E} }}=c^{2}\nabla ^{2}\mathbf {E}$.

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

1. Cf. p. 180.
2. Cf. p. 181. Cf. also Rayleigh, Phil. Mag. (5) xii (1881), p. 81, and H. A. Lorentz, Over de Theorie de Terugkaatsing, Arnhem, 1870.
3. Cf. p. 181.
4. Cf. p. 182.