travels the distance w relative to the railway line in a time which is
equal to one second as judged from the embankment.

Moreover, the considerations of Section 6 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.



ON THE RELATIVITY OF THE CONCEPTION OF DISTANCE


Let us consider two particular points on the train * travelling
along the embankment with the velocity v, and inquire as to their
distance apart. We already know that it is necessary to have a body of
reference for the measurement of a distance, with respect to which
body the distance can be measured up. It is the simplest plan to use
the train itself as reference-body (co-ordinate system). An observer
in the train measures the interval by marking off his measuring-rod in
a straight line (e.g. along the floor of the carriage) as many times
as is necessary to take him from the one marked point to the other.
Then the number which tells us how often the rod has to be laid down
is the required distance.

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^1 and B^1 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