THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



The simplest case of measurement is that of stretches. 

 Even when the terms are not quantities, if the number of 

 terms in one stretch is double that in another it is natural to 

 consider the first stretch as double of the second. This is our 

 meaning, for example, when we say that one man's flock of 

 sheep is double, or twice as great as, another's. 



In the case of terms which are quantities, measurement 

 would seem possible only when each term can properly be 

 regarded as the sum of parts. This is not true, for example, of 

 pleasures. If it gives me equal pleasure to entertain A and to 

 entertain B, to entertain both together gives either two 

 pleasures tke former two or else a single new pleasure the 

 N .pleasure of entertaining A and B together which cannot be 

 considered as the sum of the former pair. Nevertheless when, 

 as in this case, the physical source of a quantity is duplicated 

 there is a great and ^natural tendency to consider the quantity 

 to be doubled also. Thus most people would consider the 

 loudness of two equal notes to be twice the loudness of one. 

 It is hardly necessary to quote Leibniz's doctrine of petites 

 perceptions to show how strong the tendency is, and we shall 

 find important examples of its influence in science.* 



In the case of distances we meet with a similar difficulty ; 

 for the distance from a term A to a term C cannot strictly be 

 regarded as the sum of the distances from A to an intermediate 

 term B and from B to 0. Here, however, it seems even more 

 natural than in the last case to consider the distance AC twice 

 the distance AB or BC if these are equal. Thus the interval 

 from the note C on the piano to G is equal to the interval from 

 G to D in the next octave. This being the case, we may con- 

 sistently regard the interval from C to D as twice the interval 

 from C to G. 



There remain the cases of Space and Time, in which with- 

 out doubt we have wholes composed of parts. Here, though 



* Infra, p. 97. 



