It will be observed that science, in the case of mechanics, has followed the same course as in geometry. Initially our information is empirical and suffers from all the inaccuracies of human observation and all the various contingencies that characterise physical phenomena. But this empirical information is idealised, then crystallised into axioms, postulates or principles susceptible of direct mathematical treatment. To be sure, as we proceed in our purely theoretical deductions, unless we are to lose all contact with reality, we must check our results by physical experiment; and this necessity is still more apparent in rational mechanics than in geometry. If peradventure further experiment were to prove that our mathematical deductions in mechanics were not borne out in the world of reality, we should have to modify our initial principles and postulates or else agree that nature was irrational. With mechanics, the necessity of modifying the fundamental principles became imperative when it was recognised that [Pg 76] the mass of a body was not the constant magnitude we had thought it to be; hence it was experiment that brought about the revolution. On the other hand, in the case of geometry, it was the mathematicians themselves who foresaw the possibility of various non-Euclidean doctrines, prior to any suggestion of this sort being demanded by experiment. And now let us revert once again to the problem of time. Theoretically, the law of inertia should permit us to obtain an accurate determination of congruent intervals, but as it was quite impossible to observe freely-moving bodies owing to frictional resistances as also to the gravitational attraction of earth and sun, it was advantageous to discover some other physical method of determination. This was soon obtained. The principles of mechanics enable us to anticipate that if a perfectly rigid sphere, submitted to no external forces, is rotating without friction on an axis fixed in a Galilean frame, its angular rate of rotation will be uniform or constant, as measured in the frame. By “constant,” we mean constant as measured in terms of the standards of time-congruence defined by a free body moving under ideal conditions according to the principle of inertia. Hence we are in possession of a method of measuring time, more convenient than that afforded by the motions of free bodies along straight courses. It may be noted that the definition of congruent durations as given by the rotating sphere is in perfect accord with the definition in terms of causality as formulated in the passage quoted from Weyl.