TIME MEASUREMENT. The problem of the measurement of time demands a reference to its philosophical foundation, if it is to be viewed otherwise than as an empiric treatment of a practical necessity. Without touching the contention of relativ ists that time is in a certain sense merely a fourth dimension added to space, we may take it that to any individual it appears differ ent and separate from his space, and is simpler than space to treat because it has merely one dimension. The difficulty arises precisely because of this fact, that it is fundamental and there is nothing similar or simpler to compare it with. Duration, per manence, existence even, all presuppose the lapse of time and therefore some means for its detection, or, what is the same thing, some primitive measure of it. The fact upon which all these ideas are based is the possibility of repetition of experience. When ex periences are iepeated, closely enough, we associate them with the ideas of things and reality. Such appears to be the psychological history of the construction of our world. We look then for the measurement of time to some process with recognizable repeti tions, which may be counted. This replaces the impalpable idea of duration by counted steps and thus brings time into the class of measured quantities. Pulse beats, the alternations of day and night, the periods associated with definite spectral lines are in stances of natural processes that have actually served this pur pose, besides artificial instruments such as the balance watch and the pendulum clock; but to isolate the essential features we may idealize an instrument for the measurement of time as a gyroscope (A) mounted without friction inside a case (B), which may or may not itself rotate, and is held, friction free, at the common axis (o) ; or more abstractly still we may imagine two particles A, B, revolving at different angular speeds about a common centre 0. Each new passage of A past B is a repetition, giving a countable step of time. This may be used for measurement of time precisely as a pair of compasses is used for measuring space. If we do not know that the revolution of A with respect to B is constant, that corresponds to the use of a pair of compasses not known to be stiff at the joint ; the measure can still be made for what it is worth and may be the only one possible. If the lapse of time
measured falls between two integral counts, we have the problem of subdividing the standard unit by constructing a smaller one which is standardized by comparing it with the standard. No new problem, theoretical or practical, is introduced thereby, and known methods are applicable to its treatment. The parallel and contrast between the measurement of time and of one dimensional space may be probed further. Measurement of the latter is ef fected practically through the construction of an (arbitrary) standard yard or metre, from which copies are taken and com parisons made. If a copy A' B' is compared with the standard A B, the mark A' is seen to agree with the mark A, at a particular time, and the mark B' to agree with the mark B, at a different time, the difference being the time taken by the observer to travel from A to B. If we introduce mirrors at A', B', so that the congruences may be observed simultaneously, this does not abolish the time differ ence but only reduces it by making light the traveller. The dif ference is essential in kind. Now consider the standard for time measurement, a gyroscope in which there is a mark A, rotating within a case on which there is a mark B. Compare this with a copy A', B'. The cases B, B' may be in rotation, and the marks B, B' cannot be brought into permanent coincidence. Thus the step of time between two passages of A' across B' may be com pared with that occupied between two passages of A across B, only with an allowance for the time taken for a signal to pass across the space between B and B'. If B and B' are the same, as they may be if both are effectively the sphere of stars, then the allowance for the passage of the signal is abolished, and the com parison of the two standards of time is more perfect than that of two standards of distance ; the reason for this is that for the two ends of a standard of space we cannot have the same time, but for two ends of a standard of time we can have the same point of space. We can pass to and fro in space but not in time.