MAGNETIC SHELLS. 315 



If, while the point was fixed, the shell altered its shape so as to 

 pass from the position S' to the position S (Fig. 77), the potential at 

 P would undergo the same increase of 



Fig. 77- 



As a matter of fact, the change of potential does not take place 

 suddenly on a geometrical surface, since the shell has necessarily a 

 finite thickness, and it is easy to see that the potential at P varies 

 continuously while the point traverses the magnetised layer. 



For, let the shell SS' (Fig. 78) be divided into two parallel layers 



Fig. 78. 



of thicknesses x and h - x, and of power ^ and $ 2 , and consider 

 the point P at the surface of separation of these two shells. The 

 value of the potential at P is 



V = o>3> 2 - (477 - co)*! 



We have further 



and, consequently, 



x x 



V = (0< - 47T^> - = <( CO- 47T - 1. 



h n 



The perpendicular action of the shell at the point P is 



This expression, as might have been foreseen, is the perpen- 

 dicular component of the induction at the point P. For we have 



