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In Einstein's book, "Relativity: The Special and General Theory", he uses the Fizeau experiment to show how the Lorentz Transform correctly predicts the addition of velocities.

I have some difficulty understanding the interpretation of the results, however. Suppose that liquid M is in reference frame F, and liquid N is in reference plane F'. Also, N is moving at velocity

*v*wrt M. When light travels through M, assume the velocity is measured as

*u*wrt F. If light were traveling in N, I would also expect it to travel at velocity

*u*but this time wrt F' since firstly, the medium (N) is at rest in F', and secondly, Einstein says that the speed of light does not depend on the frame of reference. According to this principle, I would also expect light traveling in N to travel at speed

*u*wrt both F and F'.

This is analogous to the moving train wrt a platform example, where a light shone from the front of the train would have a measured speed of

*c*in both the reference frame of the train, and of the platform.

Why then does Einstein use a principle of additive velocities to calculate the new speed of the light?

thanks for the help,

Aaron