We see, then, that a great variety of methods for determining time have been considered. Some were mechanical, others astronomical, [Pg 78] others optical, while still others appealed to radioactive phenomena. In each case our definitions were such as to confer the maximum of simplicity on our co-ordination of a certain type of phenomena. For instance, if in mechanics and astronomy we had selected at random some arbitrary definition of time, if we had defined as congruent the intervals separating the rising and setting of the sun at all seasons of the year, say for the latitude of New York, our understanding of mechanical phenomena would have been beset with grave difficulties. As measured by these new temporal standards, free bodies would no longer move with constant speeds, but would be subjected to periodic accelerations for which it would appear impossible to ascribe any definite cause, and so on. As a result, the law of inertia would have had to be abandoned, and with it the entire doctrine of classical mechanics, together with Newton’s law. Thus a change in our understanding of congruence would entail far-reaching consequences. Again, in the case of the vibrating atom, had some arbitrary definition of time been accepted, we should have had to assume that the same atom presented the most capricious frequencies. Once more it would have been difficult to ascribe satisfactory causes to these seemingly haphazard fluctuations in frequency; and a simple understanding of the most fundamental optical phenomena would have been well-nigh impossible.