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

PERIODICITY IN NATURE 167
guaranteed by experience. Indeed, so far is
it from being a necessary law, that it is not
even exactly true. There are divergencies in
every case. For some instances these divergencies are easily observed and are therefore
immediately apparent. In other cases it requires the most refined observations and
astronomical accuracy to make them apparent. Broadly speaking, all recurrences depending on living beings, such as the beatings
of the heart, are subject in comparison with
other recurrences to rapid variations. The
great stable obvious recurrences-stable in
the sense of mutually agreeing with great
accuracy-are those depending on the motion
of the earth as a whole, and on similar motions
of the heavenly bodies.
We therefore assume that these astronomical recurrences mark out equal intervals of
time. But how are we to deal with their
discrepancies which the refined observations
of astronomy detect? Apparently we are
reduced to the arbitrary assumption that one
or other of these sets of phenomena marks out
equal times-e.g. that either all days are of
equal length, or that all years are of equal
length. This is not so: some assumptions
must be made, but the assumption which
underlies the whole procedure of the astronomers in determining the measure of time is
that the laws of motion are exactly verified.