A SYSTEM OF PARTICLES. 245 



9. In the preceding investigation, it has been supposed that the 

 force, which a particle exerts on another particle of the same medium, 

 as well as that which it exerts on a particle of the other medium, 

 is repulsive. 



Had we adopted the contrary course, considering the action either 

 attractive or repulsive as it might happen to be, we should clearly 

 have arrived at the following conclusions, the force varying inversely 

 as the square of the distance. 



d'a „ /I 3Sa;\ , M^il 3Aa;^ 



7 _ 



= P^ -, 





d"(^' r^^l^ 3Aa;-\ , , _, 31 (1 3Sx'\ ^ ^, 

 -dF = ^^(R^--W-)^^^Q''[?-~^)^^' 



where ia, ^/3, ^7 represent the variation of motion for two particles of 

 A estimated in the directions x, y and s. 



An, A/3, A 7 represent the variation of motion between the given 

 one of A, and one of B. 



A' a', A'/3', A'7' represent the variation of motion between two of B. 



A a', A/9', A 7' represent the variation of motion between the given 

 one of B, and one of A. 



I I 2 



