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 that the time units of the two systems of reference $$S_1$$ and $$S_2$$ are of different lengths. Just how much they differ is a secondary matter; that they differ at all is the surprising and important thing. As postulates M, V, L are generally accepted and have not elsewhere led to such strange conclusions it is natural to suppose that the strangeness here is not due to them.

Referring to the argument carried out above, we see that no unusual conclusions were reached until we had introduced and made use of assumption A. Moreover we have seen that this assumption itself is a logical consequence of M and $$R'$$. Further, $$R''$$ is not involved either in theorem III. or in its corollary. But these already involve the strange features of our results. Hence the conclusion is irresistible that the extraordinary element in these results is due to postulate $$R'$$ — or to speak more accurately, to just that part of it which it is necessary to use in connection with M in order to prove A as a theorem.

This result is important, as the following considerations show. Postulates V and L state laws which have been universally accepted in the classical mechanics. Postulate M is a direct generalization from experiment, and the generalization is legitimate according to the usual procedure of physicists in like situations. Postulate $$R'$$ is the statement of a principle which has long been familiar in the theory of light and has met with wide acceptance. Thus we see that no one of these postulates, in itself, runs counter to currently accepted physical notions. And yet just these postulates alone are sufficient to enable us to conclude that corresponding time units in two systems of reference are of different magnitude. In the next section we shall show on the basis of the same postulates that the corresponding units of length in the two systems are also different. Thus the most remarkable elements in the conclusions of the theory of relativity are deducible from postulates M, V, L, $$R'$$ alone; and yet these are either generalizations from experiment or statement of laws which have usually been accepted. Hence we conclude: The theory of relativity, in its most characteristic elements, is a logical consequence of certain experiments together with certain laws which have for a long time been accepted.

One other remark, of a totally different nature, should be made with reference to the characteristic result of theorem IV. It has to do with the relation between the time units of the two systems. This relation is intimately associated with the fact that each observer makes his measurements on the hypothesis that his own system is at rest, while the other system is moving past him with a velocity v. If both observers should agree to call S fixed and if further in this modified "universe" our