Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/450

 for the specific inductive capacity in terms of the number and circumstances of the electrons.

Returning now to the case in which the dielectric is supposed to be in motion, the equation for the polarization may be written

from this equation, Fresnel's formula for the velocity of light in a moving dielectric may be deduced. For, let the axis of be taken parallel to the direction of motion of the dielectric, which is supposed to be also the direction of propagation of the light; and, considering a plane-polarized wave, take the axis of parallel to the electric vector, so that the magnetic vector must be parallel to the axis of. Then equation (III) above becomes

equation (IV) becomes (assuming B equal to II, as is always the case in optics),

The equation which defines the electric induction gives

and equations (1) and (2) give

Eliminating D., Px, and Ily, we have

or, neglecting w/cº,

Substituting $$E_x = e^{n(t - z/V)\sqrt{-1}}$$, so that denotes the velocity of light in the moving dielectric with respect to the fixed aether we have