134 



PARTICULAR CASES OF EQUILIBRIUM. 



We thus obtain 





1-7* "I-/ 



I-?* 



Vj = m< 



+ PB~ (I " 



j y'Z y4 



PA + PA^ + PAj 



...+ 



fn 



] 



Denoting by a and /3 the two series containing the distances 

 PA, PA X . . . , P B 1? PB 2 . . . , which are determinate functions of the 

 co-ordinates of the point P, we have simply 



151. Two EQUAL MASSES OF OPPOSITE SIGNS INFINITELY NEAR 

 EACH OTHER. Let us suppose that the two equal masses of opposite 

 signs +m and -m of problem (144) are infinitely near or, what 



Fig. 39- 



amounts to the same thing, let us consider the condition of the field 

 at a distance which is very great compared with the distance za of 

 the two points A and A'. The value of the potential at a point P 

 (Fig. 39) 



r' 



rr 



