It is clear that we have the problem of 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′_, and finally, the light plays the part of the 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 (A) or (B), according as the Galilei transformation or the Lorentz transformation corresponds to the facts. Experiment[10] decides in favour of equation (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 (B) to within one per cent. [10] Fizeau found image015 where image016 is the index of refraction of the liquid. On the other hand, owing to the smallness of image017 as compared with 1, we can replace (B) in the first place by image018 or to the same order of approximation by image019 which agrees with Fizeau’s result. 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 trom electrodynamics as an astoundingly simple combination and generalisation of the hypotheses, formerly independent of each other, on which electrodynamics was built. XIV. THE HEURISTIC VALUE OF THE THEORY OF RELATIVITY Our train of thought in the foregoing pages can be epitomised in the following manner. Experience has led to the conviction that, on the one hand, the principle of relativity holds true and that on the other hand the velocity of transmission of light _in vacuo_ has to be considered equal to a constant _c_. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates _x, y, z_ and the time _t_ of the events which constitute the processes of nature. In this connection we did not obtain the Galilei transformation, but, differing from classical mechanics, the _Lorentz transformation_. The law of transmission of light, the acceptance of which is justified by our actual knowledge, played an important part in this process of thought. Once in possession of the Lorentz transformation, however, we can combine this with the principle of relativity, and sum up the theory thus: