An introduction to mathematics, by A. N. Whitehead.

PERIODICITY IN NATURE 169
whether the train has been running uniformly
or not entirely depends on the standard of
time which we adopt.
Now, for all ordinary purposes of life on the
earth, the various astronomical recurrences
may be looked on as absolutely consistent;
and, furthermore assuming their consistency,
and thereby assuming the velocities and
changes of velocities possessed by bodies, we
find that the laws of motion, which have
been considered above, are almost exactly
verified. But only almost exactly when we
come to some of the astronomical phenomena.
We find, however, that by assuming slightly
different velocities for the rotations and
motions of the planets and stars, the laws
would be exactly verified. This assumption
is then made; and we have, in fact thereby,
adopted a measure of time, which is indeed
defined by reference to the astronomical
phenomena, but not so as to be consistent
with the uniformity of any one of them. But
the broad fact remains that the uniform flow
of time on which so much is based, is itself
dependent on the observation of periodic
events.
Even phenomena, which on the surface
seem casual and exceptional, or, on the other
hand, maintain themselves with a uniform
persistency, may be due to the remote influence of periodicity. Take, for example, the