Pagina 203 de 212

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

image055

or with sufficient accuracy by

image056

This expression may also be stated in the following form:

image057

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

image058

From this it follows that

image059