138 PARTICULAR CASES OF EQUILIBRIUM. 



We obtain then, by substitution, 



155. In valuing the force at each point, the electrical masses 

 only affect the result by their moment 2ma = t3, which may remain 

 finite for suitable values of m, although the distance 20. is infinitely 

 small. The total flow of force proceeding from the two infinitely 

 near centres is not therefore determined, but the flow from a sphere 

 of given radius R may be easily calculated. 



From equation (20) the value of the perpendicular component at 

 point P, corresponding to the angle w, is 



trr 

 F = 2 cos o>. 



The surface of the bow whose angular aperture is 2o>, being equal to 

 27rR 2 (i cos <o), that of the elementary zone corresponding to the 

 angle dv> is 



sin wtfo). 

 The flow of force which traverses this zone is therefore 



47TS7 . 



d Q = sin o> cos w #w, 



R 



and the total flow corresponding to the angle o> is 



O = sin w cos w d(& = sin 2 o>. 



R J R 



This expression is nothing more than that of the line of force, of 

 the order N, which terminates at the contour of the zone in question, 

 and it might have been written directly. 



If o) be made equal to , we shall have the total flow on one side 



of the transverse plane OB the value of this flow is ; it is seen 

 to be inversely as R. 



To trace on a meridian plane the lines of force which correspond 



