126 



PARTICULAR CASES OF EQUILIBRIUM. 



The equipotential surfaces whose equation is 



- (--- 



\r r 



are surfaces of an ovoidal form, with a single sheet, tending to merge 

 into spheres in proportion as they approach the centres of action. 

 All of them, which correspond to positive values of V, envelope the 

 point A, while those which correspond to negative values envelope 

 the point A'. They are separated by a symmetrical plane at zero 

 potential. 



The equation of the lines of force is 



N 



cos to cos a>' = i cos 6 = 



These lines of force are all limited, proceeding from the point 

 A, and terminating at the point A' ; they are evidently symmetrical in 

 reference to the plane of zero potential, which is perpendicular to the 

 axis AA' at 0, the middle of the distance AA' (Fig. 34). 



T' 



Fig. 34- 



145. The angles ft and ft' which the force makes with the radius 

 vectors are still determined by the equation (10), which gives 



(12) 



sin ft 



146. The expression of the force is 



"cos ft cos ft' 



