302 THE GRAMMAR OF SCIENCE 



impressions with regard to perceptual bodies. Once 

 established as a mechanical principle for particles, it was 

 natural to investigate whether its application to the whole 

 range of corpuscles would give results in agreement with 

 our perceptual experience. In so far as it did so, it 

 became recognised as a universal law of mechanism. 

 This process of discovering and then justifying the con- 

 ceptual law by aid of our perceptual experience applies to 

 all our further statements with regard to the laws of 

 motion, and I shall not think it necessary for my present 

 purposes to refer in each individual case to the experi- 

 mental discovery and justification. 



^ 8. — TJie Scientific Conception of Mass 



This fourth law of motion carries us a long way in 

 our description of the dance of corpuscles, but I have now 

 to ask the reader to follow me in a rather more difficult 

 investigation. This will, however, eventually repay us by 

 the number of new ideas to which it introduces us. As 

 the fourth law stands at present we should have to make 

 experiments on every possible pair of corpuscles in order 

 to form a scale of the ratios of their mutual accelerations. 

 In order to avoid this very laborious process we conceive 

 a standard corpuscle taken, which we will represent by 

 the letter O, and we suppose a record formed of the ratio 

 of the mutual accelerations of O and of each of the other 

 corpuscles with which we populate conceptual space. 



By the third law of motion the acceleration of Q due 

 to A will always be in the same ratio to the acceleration 

 of A due to Q, whatever be the field. Now we are going 

 to give a name to this ratio ; we shall call it the mass of 

 A relative to the standard O, or more simply the mass of 

 A. Thus we have : — 



-, , . Acceleration of O due to A 



Mass of A = -r i , ,]- , . ^ . . (a). 



Acceleration of A due to Q 



And similarly, if B be a second corpuscle, we have : — 



-. r -D Acceleration of Q due to B 



Mass of B = -r : T-^^ 7^ • . (&). 



Acceleration of B due to Q 



