Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/139

 On the basis of this formula, Fresnel proceeded to solve the problem of refraction in moving bodies. Suppose that a prism A0 C0 B0, is carried along by the earth's motion in vacuo, its face A0 C0, being at right angles to the direction of motion; and

that light from a star is incident normally on this face. The rays experience no refraction at incidence; and we have only to consider the effect produced by the second surface A0B0. Suppose that during an interval τ of time the prism travels from the position A0C0B0 to the position A1C1B1, while the luminous disturbance at C0, travels to B1, and the luminous disturbance at A0 travels to D, so that B1D is the emergent wave-front.

Then we have
 * $$C_0B_1 = \tau\left(c_1 + \frac{\mu^2 - 1}{\mu^2}w \right)$$,
 * $$A_0D = \tau c$$,
 * $$A_0A_1 = \tau w$$.

If we write $$C_1\hat{A}_1B_1 = i$$, and denote the total deviation of the wave-front by δ1, we have
 * $$A_1D = A_0D - A_1A_0\cos(\delta_1) = \tau c - \tau w \cos{\delta_1}$$,
 * $$C_1B_1 \tau\left( c_1 - \frac{wc_1^2}{c^2}\right)$$,