APPLICABLE TO MATHEMATICS, &C. 363 



This force will have to be overcome in order 

 to move the particles in either direction, from or 

 towards each other. 



m • P P P P 



Taking the equations — j- H ~ = &~-\ — - = 



we shall have from the first cT = — 5- and from the 

 second <r = - ^ , Therefore if the two parti- 

 cles be placed in the two points - ^ distance 



from each other they will have no attractive in- 

 fluence whatever on each other : and if placed in 



two points whose distance from each other is — — 



"3 



they will have no repulsive influence whatever on 

 each other. 



If we have the relation «- = -5^ , then the 

 above phenomena will take place at the same dis- 

 tance of the two particles from each other. 



These diff'erent states of equilibrium may 

 possibly suggest some useful reflections on the 

 characteristic diff*erence between fluids and rigid 

 bodies. 



