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 evidence for or against postulate $$R'$$. If the assumption is to be proved at all, either new experiments must be devised or it must be proved by indirect means by showing that it is a consequence of experiment and accepted laws.

Now any one who accepts postulates M and $$R'$$ will perforce accept also all the logical consequences which necessarily flow from them. Of these logical consequences we shall now prove one which is of great importance in the theory of relativity:

I. The velocity of light in free space, measured on an unaccelerated system of reference S by means of units belonging to S, is independent of the direction of motion of S (MR').

Since by $$R'$$ the velocity of light is independent of that of the light-source we may suppose that the light-source belongs to the system S. Now let the velocity of light, as it is emitted from this source in various directions, be observed and tabulated. On account of the homogeneity of space mere direction through space will have no effect on these observed velocities; and therefore it they differ at all, the difference will be due to the velocity of S. Now if there were a difference due to the direction of motion of S this difference would put in evidence the motion of S. But by M it is impossible to detect such motion in this way. Hence the observed velocity must be the same in all directions. In other words, it is independent of the direction of motion of S; and thus the theorem is proved.

It is clear, however, that we cannot take the next step and prove that this observed velocity of light is independent of the absolute value of the velocity of S, as Tolman appears to conclude. To see this clearly, let us suppose that the absolute value of the velocity of S does affect the observed velocity of light. On account of $$R'$$ it will have the same effect on the observed velocity of light whatever may be the unaccelerated motion of the light-source. Hence, from all possible observations, the experimenter will have only a single datum from which to determine the effect of one phenomenon on another; namely, a datum in which the two phenomena are connected in a certain definite way. It is obvious then that he cannot determine the effect of one of the phenomena on the other; for he can never observe the one without the other being present also and the connection which exists between them is always the same however he may vary his experiment. And if the observer cannot determine an existing effect it is clear that he cannot prove the absence of any effect whatever.