POTENTIAL OF MAGNETIC SHELLS. 347 



If the shell is uniform we have 



v * * 



an expression which might have been obtained by the consideration 

 of layers of gliding (354). 



363. For a shell on a sphere of radius a, the point M being at 

 the outside, on the positive face of the shell, we have, in like manner, 



(8) V = - 



and, if the shell is uniform, 

 (8') V = * 



On the contrary, if the face turned away from the side of the 

 point M is negative, we must take the expressions 



<> 



364. In the case of a sphere, the potential p is a homogeneous 

 function of the degree - i of the radius 0, and of the distance r 

 from the point M at the centre, which gives the condition 



or 







