Measurement of Time and other Magnitudes. 653 



too far.) Having made a standard series, we can weigh any 

 other body by finding to which member of! the standard series 

 it is equal, according to (2). 



Why is this method of measurement adopted rather than 

 any other ? For this reason — that if we take the standard 

 body 3 and the standard body 4, place them in one pan, and 

 place in the other pan the standard bodies 2 and 5, then the 

 two pans will balance. That result would not be obtained 

 unless the system of measurement fulfilled certain conditions; 

 it would not be obtained, for example, if one arm of the 

 balance was longer than the other or one pan heavier than 

 the other. This test of obeying the laws of numerical 

 addition is that which a system of measurement must pass if 

 it is to be satisfactory: if two systems, both passing the 

 test, can be found for the same magnitude, then they must 

 lead to the attribution of the same value to all systems in 

 respect of this magnitude. I cannot compress the proof of 

 these statements within the compass of such a note as 

 this. 



Now let us turn to time. We require three similar 

 definitions. (1) The period occupied by the happening of 

 some definite process in a definite system is defined to be 1. 

 This period might be chosen to be the period occupied by the 

 fall of a body from one position to another, or the period 

 required for a lobster to turn red when placed in boiling 

 water. The objections to the last proposal are serious, but 

 not insuperable; it is only mentioned to indicate that the 

 period need not be that of any moving system and need not 

 therefore involve " space." The first example shows that it 

 need not be that of a uniformly moving body. 



(2) The period of a process, or the time-interval between 

 the events that are its beginning and its end, is equal to the 

 period of another process if, when matters are so arranged 

 that the beginnings are simultaneous, the ends are 

 simultaneous. 



(3) A period is the sum of two other periods A and B 

 if, when the beginnincr of A is simultaneous with the 

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

 then the end of B is simultaneous with the end of ( \ 



Let us now find some other period equal to that of the 

 unit, which is the period of a body falling from one position 

 to another. It is very convenient to choose the period of the 

 complete oscillation of a pendulum. Then we find by expe- 

 riment that if the period of fall is equal to one complete 

 oscillation of the pendulum, according to (2), it is equal to 



