of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in [chapter:VII]Section VII) disappears.
We were led to that conflict by the considerations of [chapter:VI]Section VI, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance per second relative to the carriage, traverses the same distance also with respect to the embankment in each second of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance relative to the railway line in a time which is equal to one second as judged from the embankment.
Moreover, the considerations of [chapter:VI]Section VI are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity.