the disc may regard his disc as a reference-body which is at rest ; on
the basis of the general principle of relativity he is justified in
doing this. The force acting on himself, and in fact on all other
bodies which are at rest relative to the disc, he regards as the effect
of a gravitational field. Nevertheless, the space-distribution of this
gravitational field is of a kind that would not be possible on Newton s
theory of gravitation.[18] But since the observer believes in the
general theory of relativity, this does not disturb him; he is quite in
the right when he believes that a general law of gravitation can be
formulated a law which not only explains the motion of the stars
correctly, but also the field of force experienced by himself.
[18] The field disappears at the centre of the disc and increases
proportionally to the distance from the centre as we proceed outwards.
The observer performs experiments on his circular disc with clocks and
measuring-rods. In doing so, it is his intention to arrive at exact
definitions for the signification of time- and space-data with
reference to the circular disc _K _, these definitions being based on
his observations. What will be his experience in this enterprise?
To start with, he places one of two identically constructed clocks at
the centre of the circular disc, and the other on the edge of the disc,
so that they are at rest relative to it. We now ask ourselves whether
both clocks go at the same rate from the standpoint of the non-rotating
Galileian reference-body _K_. As judged from this body, the clock at
the centre of the disc has no velocity, whereas the clock at the edge
of the disc is in motion relative to _K_ in consequence of the
rotation. According to a result obtained in Section XII, it follows
that the latter clock goes at a rate permanently slower than that of
the clock at the centre of the circular disc, _i.e._ as observed from
_K_. It is obvious that the same effect would be noted by an observer
whom we will imagine sitting alongside his clock at the centre of the
circular disc. Thus on our circular disc, or, to make the case more
general, in every gravitational field, a clock will go more quickly or
less quickly, according to the position in which the clock is situated
(at rest). For this reason it is not possible to obtain a reasonable
definition of time with the aid of clocks which are arranged at rest
56