where ω represents the angular velocity of rotation of the disc K′ with respect to K. If v0, represents the number of ticks of the clock per unit time (“rate” of the clock) relative to K when the clock is at rest, then the “rate” of the clock (v) when it is moving relative to K with a velocity v, but at rest with respect to the disc, will, in accordance with Section XII, be given by
or with sufficient accuracy by
This expression may also be stated in the following form:
If we represent the difference of potential of the centrifugal force between the position of the clock and the centre of the disc by φ, i.e. the work, considered negatively, which must be performed on the unit of mass against the centrifugal force in order to transport it from the position of the clock on the rotating disc to the centre of the disc, then we have
From this it follows that
