Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/207

where w denotes the velocity of the ponderable body. If the body is an ordinary isotropic one, and if we consider light propagated parallel to the axis of z, in a medium moving in that direction; the light-vector being parallel to the axis of x, the equation reduces to

$\rho {\frac {\partial ^{2}e_{x}}{\partial t^{2}}}=n{\frac {\partial ^{2}e_{x}}{\partial z^{2}}}-\rho _{1}A\left({\frac {\partial }{\partial t}}+w{\frac {\partial }{\partial z}}\right)^{2}e_{x}$;

substituting

$e_{x}=f(z-Vt)$,

where V denotes the velocity of propagation of light in the medium estimated with reference to the fixed aether, we obtain for V the value

$\left({\frac {n}{\rho +\rho _{1}A}}\right)^{\frac {1}{2}}+{\frac {\rho _{1}A}{\rho +\rho _{1}A}}w$.

The absolute velocity of light is therefore increased by the amount ρ₁Aw/(ρ + ρ₁A) owing to the motion of the medium; and this may be written (μ² - 1) w/μ², where μ denotes the refractive index; so that Boussinesq's theory leads to the same formula as had been given half a century previously by Fresnel.^[1]

It is Boussinesq's merit to have clearly asserted that all space, both within and without ponderable bodies, is occupied by one identical aether, the same everywhere both in inertia and elasticity; and that all aethereal processes are to be represented by two kinds of equations, of which one kind expresses the invariable equations of motion of the aether, while the other kind expresses the interaction between aether and matter. Many years afterwards these ideas were revived in connexion with the electromagnetic theory, in the modern forms of which they are indeed of fundamental importance.

1. Cf. p. 115 sqq.