RECIPROCAL ACTION OF TWO SPHERES. 165 



Suppose that the action of the two spheres is the same as if the 

 masses were respectively concentrated at the centres, and that the 

 potential of each of them is equal to that obtained for the centre, by 

 replacing the adjacent sphere by an equal mass situate at the centre. 

 We shall have thus 



N M 

 ~ +J 



MN 

 <: 2 R 2 ' 



TJV __ - _ (U 2 + V 2 ) 



U (U 



and for equal charges 



F- 



If we make <r=4, Sir W. Thomson's formulae give 



I-J = 0-80258, 

 2 (fi- a) = 0-05846, 

 2(b-a) = 0-03766. 



The corresponding values in the approximate formula are 



= = 0-0625, 



=^ = 0-04. 

 i) 2 25 



Thus, when the distance of the surfaces is equal to the diameter 



