14 ON POTENTIAL. 



moved through MM' or ds, along any curve whose tangent MT 

 makes the angle a with the direction of the force, the corresponding 

 electrical work is 



since the force is expressed by 



we have 



If rj and r 2 represent the distances OA and OB, the work of 

 displacing unit mass from A to B is 



B m m 

 W. = . 



*1 >2 



Comparing this equation with equation (i) we see that the two 

 terms and represent respectively, to within a constant, the value 



r \ '2 



of the potential at A and at B ; hence the potential of a single mass 

 m at a point at distance r is equal, except for a constant, to } 



that is, to the quotient of the acting mass by its distance from the 

 point in question. 



Let us now suppose that there are several acting masses m, m\ 

 m", . . . , the total work of the displacement of unit of electricity is 

 equal to the algebraical sum of the partial works corresponding to 



each of the masses ; denoting then by ^ the sum of the quotients 

 of the different masses by their distances from the point of departure 



A, and by the analogous sum for the point of arrival B, 

 r z 



If the point B is in connection with the earth, the potential V B is 



zero. On the other hand, the expression Jf becomes zero, if the 



r 2 



point B is at a great distance from the masses in question, whether 

 in the air or on the ground ; and since the earth, like any conductor 



