∂f₄₁/∂x₁ + ∂f₄₂/∂x₂ + ∂f₄₃/∂x₃ = ρ₄ }
Note 9.
On the Constancy of the Velocity of Light.
Page 12—refer also to page 6, of Einstein’s paper.
One of the two fundamental Postulates of the Principle of Relativity is that the velocity of light should remain constant whether the source is moving or stationary. It follows that even if a radiant source S move with a velocity u, it should always remain the centre of spherical waves expanding outwards with velocity c.
At first sight, it may not appear clear why the velocity should remain constant. Indeed according to the theory of Ritz, the velocity should become c + u, when the source of light moves towards the observer with the velocity u.
Prof. de Sitter has given an astronomical argument for deciding between these two divergent views. Let us suppose there is a double star of which one is revolving about the common centre of gravity in a circular orbit. Let the observer be in the plane of the orbit, at a great distance Δ.
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/c² and from A to B is T + 2Δu/c². Now if 2uΔ/c² be comparable to T, then it is impossible that the observations should satisfy Kepler’s Law. In most of the spectroscopic binary stars, 2uΔ/c² 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/c² = 0. 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 kuΔ₀, u₀ being the maximum value of u, the velocity of light emitted being
u₀ = c + ku,