APPLICABLE TO MATHEMATICS, &C. 357 



place among the particles. Substituting the value 

 of f(a?) in equations (2) and (3), we shall find the 

 velocity with which the particles approach or 

 recede according as m > m* or m < m\ 



The points of equilibrium here mentioned are 

 not produced by means of the antagonist forces 

 of attraction and repulsion, but they are points at 

 which both the attraction and repulsion are equal 

 to nothing. 



Let us now proceed to investigate the subject 

 in a more general manner, by proposing difi'erent 

 Laws for the attractive and repulsive forces. 



Let a particle M placed 



at A, attract and repel a a» "B 



particle M' placed at B, 



with forces which vary as m ^(x) and Wi *(.r) re- 

 spectively. Where the distance A B is repre- 

 sented by X. 



By referring to page 351, we shall find that 

 "^ I = the efiective attractive force of A on B. 



— -^ = the effective repelling force of A on B. 



