GREEN 'S THEOREM. 1 9 



of the components relative to thfe internal masses, the total flow of 

 force which proceeds from the surface S is expressed by 



hvfs= |V/.*s+ p./ 



Since the flow of force is null for each of the external masses, 

 we have 



For each internal mass, on the contrary, we have 



J/ W </S = 



and consequently 



M being the algebraical sum of all the internal masses. 

 We have, finally, 



(7) 



Hence, for any closed surface, drawn in any manner in an electrical 

 field, the total flow of force, which proceeds from the surface that is, the 

 excess of the flow of forces which emerge, over the forces which enter, is 

 equal to the quantity of electricity, comprised within the surface, multiplied 

 by 47T. 



If i be the angle which the direction of the force F at any point 

 of the surface makes with the perpendicular, the perpendicular com- 

 ponent is expressed by 



F n = F cos i. 



If a be the perpendicular to the equipotential surface which 

 passes through the point in question, n the perpendicular to the 

 surface S measured towards the exterior, we have, further, 



F=-^ and F = - ; 

 da ^n 



c 2 



