Page:The principle of relativity (1920).djvu/247

 Let the observer be in the plane of the orbit, at a great distance Δ.

c - u B A c + u

The light emitted by the star when at the position A will be received by the observer after a time, Δ/(c + u) while the light emitted by the star when at the position B will be received after a time Δ/(c - u). Let T be the real half-period of the star. Then the observed half-period from B to A is approximately T - 2Δu/c^2 and from A to B is T + 2Δu/c^2. Now if 2uΔ/c^2 be comparable to T, then it is impossible that the observations should satisfy Kepler's Law. In most of the spectroscopic binary stars, 2uΔ/c^2 are not only of the same order as T, but are mostly much larger. For example, if u = 100 km/sec, T = 8 days, Δ/c = 33 years (corresponding to an annual parallax of ·1´´), then T - 2uΔ/c^2 = o. The existence of the Spectroscopic binaries, and the fact that they follow Kepler's Law is therefore a proof that c is not affected by the motion of the source.

In a later memoir, replying to the criticisms of Freundlich and Günthick that an apparent eccentricity occurs in the motion proportional to kuΔ_{0}?], u_{0} being the