MEASUREMENTS 187 



road over which we have travelled we estimate by the 

 time the journey has taken. Space gives us our only means 

 of measuring time, and time our best means of measuring 

 space. 1 Both temporal duration and spatial quantity 

 may be measured in their own terms. Even if the dial of 

 a clock were removed, we should still be able to measure 

 time by the ticking, though in this case the indirect measure 

 ment is no doubt by far the more convenient. Similarly 

 we may measure a mile by a chain, and here the direct 

 measurement is both more convenient and more reliable. 

 When we estimate the length of a road by the time the 

 journey has taken, our estimate, to be of any value as 

 a measurement, requires, first, that we should ascertain 

 the exact velocity at which we are travelling, and, secondly, 

 that the same velocity should be maintained throughout, 

 without either slacking or acceleration ; and we are unable 

 to measure the velocity in either case without measuring 

 both the time and the distance. If we measured space by 

 time only, the distance covered by a tortoise and an express 

 train in an hour would be the same. We ascertain by the 

 clock and the milestones that the express has covered 

 fifty miles in an hour, or by a tape that the tortoise has 

 progressed twenty yards, and we can then use either the 

 distance to measure the time, or the time to measure the 

 distance, on other occasions ; but only if we are quite sure 

 that the same velocity has been maintained. Similarly 

 with indirect measurements by a clock ; it is necessary to 

 measure the dial, and make certain that each fraction of 

 space corresponds with a certain number of seconds. What 

 gives the indirect measurement in this case its superior 

 convenience is that the velocity is determined by very 

 accurate machinery. The dial of a clock might be dis 

 pensed with if a man were deputed to count the beats and 

 proclaim the time at stated intervals, as the Muezzin pro 

 claims for the Faithful the hour of prayer, but the arrange 

 ment would not be equally convenient. Judgements like 

 those referred to in the above quotation are not really 

 1 Wundt, Human and Animal Psychology, English transl., p. 19. 



