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

168 INTRODUCTION TO MATHEMATICS
Before explaining how this is done, it is interesting to observe that this relegation of the
determination of the measure of time to the
astronomers arises (as has been said) from
the stable consistency of the recurrences with
which they deal. If such a superior consistency had been noted among the recurrences characterisitc of the human body, we
should naturally have looked to the doctors
of medicine for the regulation of our clocks.
In considering how the laws of motion
come into the matter, note that two inconsistent modes of measuring time will yield
different variations of velocity to the same
body. For example, suppose we define an
hour as one twenty-fourth of a day, and take
the case of a train running uniformly for two
hours at the rate of twenty miles per hour.
Now take a grossly inconsistent measure of
time, and suppose that it makes the first hour
to be twice as long as the second hour. Then,
according to this other measure of duration,
the time of the train's run is divided into
two parts, during each of which it has traversed the same distance, namely, twenty
miles; but the duration of the first part is
twice as long as that of the second part.
Hence the velocity of the train has not been
uniform, and on the average the velocity
during the second period is twice that during
the first period. Thus the question as to