Page:Relativity (1931).djvu/55

 moving with the velocity $$v$$ along the embankment. In the first place we require to determine the points $$A$$ and $$B$$ of the embankment which are just being passed by the two points $$A'$$ and $$B'$$ at a particular time $$t$$—judged from the embankment. These points $$A$$ and $$B$$ of the embankment can be determined by applying the definition of time given in Section VIII. The distance between these points $$A$$ and $$B$$ is then measured by repeated application of the measuring-rod along the embankment.

A priori it is by no means certain that this last measurement will supply us with the same result as the first. Thus the length of the train as measured from the embankment may be different from that obtained by measuring in the train itself. This circumstance leads us to a second objection which must be raised against the apparently obvious consideration of Section VI. Namely, if the man in the carriage covers the distance $$w$$ in a unit of time—measured from the train,—then this distance—as measured from the embankment—is not necessarily also equal to $$w$$.