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

$C_{0}B_{1}=\tau \left(c_{1}+{\frac {\mu ^{2}-1}{\mu ^{2}}}w\right)$,

$A_{0}D=\tau c$,

$A_{0}A_{1}=\tau w$.

If we write $C_{1}{\hat {A}}_{1}B_{1}=i$, and denote the total deviation of the wave-front by δ₁, we have

$A_{1}D=A_{0}D-A_{1}A_{0}\cos(\delta _{1})=\tau c-\tau w\cos {\delta _{1}}$,

$C_{1}B_{1}\tau \left(c_{1}-{\frac {wc_{1}^{2}}{c^{2}}}\right)$,