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 already pointed out, that one who accepts theorem I. can hardly refuse to assume $$R''$$. But theorem I. is a logical consequence of postulates M and $$R'$$, as we have shown. Moreover, from what follows it will be seen that we have occasion to make no further assumptions which can in any way run counter to currently accepted notions. Consequently, it would seem that the experimental evidence for or against the whole theory of relativity must center around postulates M and $$R'$$. We have already given some account of the experimental evidence for these postulates. In connection with theorems to be derived later (in this paper and in another which the writer has in preparation) further reference will be given to the existing experimental evidence and some other possible lines of research in this direction will be pointed out.

It is generally conceded that the strange conclusions which flow from the theory of relativity are due to postulate R (or to postulate $$\overline{R}$$, in the customary formulation). In view of the theorem I. above and our discussion of its consequences, it is now clear that the strangeness in the conclusions of relativity is due to that part of R which is contained in $$R'$$. It is important therefore to have a careful analysis of this postulate and especially to know alternative forms, which, in view of the other postulates, are logically equivalent to it. One such form has already been given by Tolman (l. c., p. 36), who has also urged the importance of the general problem. In the second paper of this series the alternative form due to Tolman will be subjected to a fresh analysis. As already pointed out in the Introduction, other alternative forms will also be given.

§ 4. The Postulates V and L. — It has been customary for writers on relativity to state explicitly only the postulates M and R. But every one, as a matter of fact, has made further assumptions concerning the relations of the two systems. These assumptions in some form are essential to the initial arguments and to the conclusions which are drawn by means of them. To the present writer it seems preferable to have these assumptions explicitly stated. Among the several forms, any one of which might be chosen, there is one which seems to us to be decidedly simpler than any of the others; and it is this one which we shall employ here. We state the postulates V and L as follows:

V. If the velocity of a system of reference $$S_2$$ relative to a system of reference $$S_1$$ is measured by means of the units belonging to $$S_1$$ and if the velocity of $$S_1$$ relative to $$S_2$$ is measured by means of the units belonging to $$S_2$$ the two results will agree in absolute value.

This velocity we shall call the relative velocity of the two systems. The direction line of this velocity will be called the line of relative motion of the two systems.