XIII

It is clear that we have the problem of [chapter:VI]Section VI again before us. The tube plays the part of the railway embankment or of the co-ordinate system $K$, the liquid plays the part of the carriage or of the co-ordinate system $K^{\prime }$, and finally, the light plays the part of the

040 man walking along the carriage, or of the moving point in the present section. If we denote the velocity of the light relative to the tube by $W$, then this is given by the equation eqn:(A) or eqn:(B), according as the Galilei transformation or the Lorentz transformation corresponds to the facts. Experiment Fizeau found $W=w+v(1-{\displaystyle \frac{1}{n^2}})$, where $n={\displaystyle \frac{c}{w}}$ is the index of refraction of the liquid. On the other hand, owing to the smallness of ${\displaystyle \frac{vw}{c^2}}$ as compared with $1$, we can replace eqn:(B) in the first place by $W=(w+v)(1-{\displaystyle \frac{vw}{c^2}})$, or to the same order of approximation by $w+v(1-{\displaystyle \frac{1}{n^2}})$, which agrees with Fizeau's result. decides in favour of equation eqn:(B) derived from the theory of relativity, and the agreement is, indeed, very exact. According to

recent and most excellent measurements by Zeeman, the

influence of the velocity of flow $v$ on the propagation of light is represented by formula eqn:(B) to within one per cent.

Nevertheless we must now draw attention to the fact that a theory of this phenomenon was given by H. A. Lorentz long before the statement of the theory of

relativity. This theory was of a purely electrodynamical nature, and was obtained by the use of particular hypotheses as to the electromagnetic structure of matter. This circumstance, however, does not in the least diminish the conclusiveness of the experiment as a crucial test in favour of the theory of relativity, for the electrodynamics of Maxwell-Lorentz, on which the

original theory was based, in no way opposes the theory of relativity. Rather has the latter been developed from electrodynamics as an astoundingly simple combination and generalisation of the hypotheses, formerly independent of each other, on which electrodynamics was built.