Note 8. 1 forces between influencing conductors 373 



distribution of electricity on a conductor on different parts of its surface by 

 means of the proof plane. The numerical results obtained by Coulomb led 

 directly to the great mathematical work of Poisson. I have not been able, 

 however, to trace, even in those parts of Coulomb's papers where it would 

 greatly facilitate the exposition, any idea of potential as a quantity which has 

 the same value for all parts of a system of conductors communicating with 

 each other. 



NOTE 8 [ART. 118]. 

 Cases of Attraction and Repulsion. 



The statements of Cavendish may be illustrated by the case of two spheres 

 A and B, whose radii are a and b, and the distance between their centres c. 

 If the charge of A is i, and that of B is o, the attraction is 



b 3 b 6 W b 9 + Aba 3 

 2 ? +3 ? +4 ? +5 -- 3T - + &c - 



an expression which shows that it depends chiefly on the value of b, the radius 

 of the sphere without charge. 



If the sphere B, instead of being without charge, is at potential zero, that 

 is, if it is not insulated, the attraction is 



b b 3 a 3 b* + 



+&c - 



This expression exceeds the former by 



b 



r + &c. 

 c c 7 



The number of times that the attraction of an uninsulated sphere exceeds 

 that of a sphere without charge is therefore approximately 



which is greater as the sphere is smaller. This agrees with what Cavendish 

 says in Art. 108. 



With respect to two bodies at the same potential, Cavendish remarks in 

 Art. 113, that it may be said that one of them may be rendered undercharged 

 in the part nearest to the other, and he shows that even in this case, the two 

 bodies must repel each other. But it may be shown that each of the bodies 

 must be overcharged in every part of its surface. For in the first place no part 

 can be undercharged, for the lines of force which terminate in an undercharged 

 surface must have come from an overcharged surface at which the potential 

 is higher than at the surface. But there is no body in the field at a higher 

 potential than the two bodies considered. Hence no part of their surface can 

 be undercharged. 



Nor can any finite part of the surface be free from charge, for it may be 

 shown that if a finite portion of the surface of a conductor is free from charge, 

 every point which can be reached by continuous motion from that part of the 



