It is a different matter when the distance has to be judged from the railway line. Here the following method suggests itself. If we call _A′_ and _B′_ the two points on the train whose distance apart is required, then both of these points are 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_. XI. THE LORENTZ TRANSFORMATION The results of the last three sections show that the apparent incompatibility of the law of propagation of light with the principle of relativity (Section VII) has been derived by means of a consideration which borrowed two unjustifiable hypotheses from classical mechanics; these are as follows: (1) The time-interval (time) between two events is independent of the condition of motion of the body of reference. (2) The space-interval (distance) between two points of a rigid body is independent of the condition of motion of the body of reference.