Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/309

and similarly the equation

$\mathbf {E} =4\pi c^{2}\mathbf {D} /\epsilon$

is replaced by

$\mathbf {E} =4\pi (c_{1}^{2}D_{x},c_{2}^{2}D_{y},c_{3}^{2}D_{z})$.

The other equations are the same as in isotropio media; so that the propagation of disturbance is readily seen to depend on the equation

$(\mu _{1}{\overset {..}{H}}_{x},\mu _{2}{\overset {..}{H}}_{y},\mu _{3}{\overset {..}{H}}_{z})=-\mathrm {curl} \{c_{1}^{2}(\mathrm {curl} H)_{x},c_{2}^{2}(\mathrm {curl} H)_{y},c_{3}^{2}(\mathrm {curl} H)_{z}\}$.

Now, if μ₁, μ₂, μ₃ are supposed equal to each other, this equation is the same as the equation of motion of MacCullagh's aether in crystalline media,^[1] the magnetic force H corresponding to MacCullagh's elastic displacement; and we may therefore immediately infer that Maxwell's electromagnetic equations yield a satisfactory theory of the propagation of light in crystals, provided it is assumed that the magnetic permeability is (for optical purposes) the same in all directions, and provided the plane of polarization is identified with the plane which contains the magnetic vector. It is readily shown that the direction of the ray is at right angles to the magnetic vector and the electric force, and that the wave-front is the plane of the magnetic vector and the electric displacement.^[2]

After this Maxwell proceeded to investigate the propagation of light in metals. The difference between metals and dielectrics, so far as electricity is concerned, is that the former are conductors; and it was therefore natural to seek the cause of the optical properties of metals in their ohmic conductivity. This idea at once suggested a physical reason for the opacity of metals—namely, that within a metal the energy of the light vibrations is converted into Joulian heat in the same way as the energy of ordinary electric currents.

1. Cf. pp. 164 et sqq.
2. In the memoir of 1864 Maxwell left open the choice between the above theory and that which is obtained by assuming that in crystals the specific inductive capacity is (for optical purposes) the same in all directions, while the magnetic permeability is aeolotropic. In the latter case the plane of polarization must be identified with the plane which contains the electric displacement. Nine years later, in his Treatise (§ 794), Maxwell definitely adopted the former alternative.

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