.
We must now fill in a gap. From the principle of the constancy of the velocity of light it follows that the equation
has a significance which is independent of the choice of the inertial system; but the invariance of the quantity
does not at all follow from this. This quantity might be transformed with a factor. This depends upon the fact that the right-hand side of (29) might be multiplied by a factor
, independent of
. But the principle of relativity does not permit this factor to be different from 1, as we shall now show. Let us assume that we have a rigid circular cylinder moving in the direction of its axis. If its radius, measured at rest with a unit measuring rod is equal to