THE LAWS OF MOTION 



307 



reader that our definitions of mass and force would 

 ultimately lead us to the same conclusions as he will find 

 in current physical text-books. In the first place we 

 will investigate an elementary problem which will lead us 

 to a mode of testing the equality of masses. Suppose we 

 had two corpuscles or rather particles A and B of masses 

 m^ and w^ in the same field, and we will suppose them 

 placed in a horizontal line, A to the left and B to the 

 right Now, owing to the presence of some system to 

 the left of A, which we need not definitely describe, we 



^ g L 'b^ ^ r ^ fab 



-^ 



B -^ 



->■ 



Fig. 23. 



will suppose A to have an acceleration represented by g 

 units horizontally to the left. Similarly B, owing to 

 some other system, shall have a horizontal acceleration of 

 g units to the right. Further, A and B will mutually 

 accelerate each other, and we will represent B's accelera- 

 tion of A from left to right by the symbol fi,^ and A's of 

 B by 7^^, which will be in the opposite sense. We are 

 going to choose a particular " physical field " for the 

 acceleration of A and B ; they shall be linked together 

 so that their distance cannot change, but the link itself 

 shall be conceived as producing no accelerations in either 

 A or B. We might conceptualise this link by aid of a 

 limit to actual perception, namely, by a fine weightless 



