654 Measurement of Time and other Magnitudes. 



the period of any other complete oscillation. Hence all 

 oscillations are of unit period. By (3) the interval between 

 the beginning of the first and the beginning of the third 

 oscillation is 2, that between the beginning of the first and 

 the beginning of the fourth is 3— and so on. The choice 

 of the pendulum is convenient because it automatically adds 

 time-intervals without interference ; but a succession of 

 falling bodies, each releasee] by the end of the fall of the one 

 before, would serve almost equally well. 



This system of measurement can be proved by experiment 

 to be satisfactory. If any process A has a period equal to 



3 oscillations of the pendulum, another B a period equal to 



4 oscillations, a third one equal to 2, and a fourth D one 

 equal to 5: then it is found that, if the beginning of A is 

 made simultaneous with the beginning of (J, the end of A 

 with the beginning of B, the end of C with the beginning 

 of D, then the end of D will be simultaneous with the end 

 of B. This proposition is true of whatever nature the four 

 processes may be. 



Accordingly the pendulum provides us with a satisfactory 

 standard series of time-intervals represented by integial 

 numerals. The fractions can be obtained by other pendulums, 

 but there is probably no need to repeat what has been said. 

 Any other time-interval can be measured by determining to 

 what member of the standard series it is equal. 



All the principles involved and their experimental proof 

 are of precisely the same nature whether the magnitude to 

 be measured is weight or time. There is even a similarity 

 in the definition of the unit, Just as we take a certain body 

 and for various reasons, good or bad, call its weight 1000 

 and not 1 : so we take a certain system with a definite period 

 and call its period 86400 and not 1. We do not need to 

 realise concretely the system of which the magnitude is 

 defined to be 1 : but we must realise concretely some 

 system of which the magnitude is defined to be something. 



Having established our system of time-measurement, we 

 define uniform motion as that of a body which covers equal 

 distances in equal times: and we proceed to investigate 

 experimentally, and not mentally, what bodies have uniform 

 motion. 



Of course this is all as elementarv as ABC. 



