APPLICABLE TO MATHEMATICS, &C. 367 



Therefore, the condition PrzPa will give a 



common tangent to the two curves at the point 



P2-P 

 P.-Ps* 



There will be an equilibrium between two 



particles of the same kind which are attracted by 



P P 



the law —o- H , and repelled at the same time 



P P 



by the law —J- H ^ . When the distance of 



P — P 



the particles is p'p , the attractive force is 



P — P 

 effective when P > P3 and x > p^ p , the condi- 



tion P > P2 or P < P2 must necessarily exist, 



otherwise the attraction or repulsion will prevail 



P — P 



on both sides of x = p^ „ , If we extend this 



inquiry to the eqilibrium of three or more points 

 in a straight line, we shall have a system of two 

 or more equations which involve the respective 

 distances when in a state of rest. 



The formation of these equations is not diflScult, 

 but the determination of the distances between 

 the particles will be a matter of great labour, as 

 they will involve complex and intricate compu- 

 tation. 



