important periodicities was the first step in natural science. This consistency arises from no abstract intuitive law of thought; it is merely an observed fact of nature
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.
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 characteristic 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
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.