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 L. If two systems of reference $$S_1$$ and $$S_2$$ move with unaccelerated relative velocity and if a line segment l is perpendicular to the line of relative motion of $$S_1$$ and $$S_2$$ and is fixed to one of these systems, then the length of l measured by means of the units belonging to $$S_1$$ will be the same as its length measured by means of the units belonging to $$S_2$$.

The essential content of these two postulates may be stated in simpler terms (but less accurately) if one allows the explicit introduction of the observer. Thus V is roughly equivalent to the following statement: Two observers whose relative motion is uniform will agree in their measurement of that uniform relative motion. As an approximate equivalent of L we have: Two observers whose relative motion is uniform will agree in their measurement of length in a line perpendicular to their line of relative motion.

It will be observed that these two postulates are nothing more than explicit statements of notions which underlie the classic theories of mechanics. The first is assumed in supposing that there exists such a thing as the relative motion of two bodies which are not at rest relatively to each other. The second is nothing more than the statement of a portion of the idea which lies at the bottom of our conception of such a thing as the length of a rod or other object.

Since these two postulates are universally accepted, the question might naturally arise, Why state them at all? Is it not enough simply to take them for granted? The answer is that there are other notions which have heretofore met with the same universal acceptance and which do not agree with the postulates of relativity. Therefore it seems to be desirable — in fact, to be essential to proper logical procedure — to state explicitly just those assumptions concerning the relation of the two systems of reference which we shall have occasion to employ in argument. Only in this way is one able to see exactly on what basis our strange conclusions rest.

We shall make a digression here to say one further word about postulate L. In part II. we shall draw the conclusion that length in the line of motion is not independent of the velocity with which the system is moving. In view of this the question arises as to why we must assume that length in a line perpendicular to the motion is independent of the motion. The answer is that we are under no such necessity, that we are at liberty to assume that length in a line perpendicular to the motion is dependent on the velocity of such motion. In fact, the general formulation of such an hypothesis has already been made by E. Riecke. This hypothesis, however, is undoubtedly more complicated and less elegant than the one which we have made; and the latter, as we shall see, is in