34^ PARTICULAR CASES. 



But the expression I/^S represents the potential U of the 

 positive surface of the shell ; we have then 



(3) 



The value of the potential Q of a layer whose density at each 



3? 

 point is equal to the magnetic strength <, is U- or ~(3dn ; from this 



follows 



-g- 



If - be the distance of the point M from the element dS, the 



f r 



potential Q is equal to I j&ds, which further gives 



(5) V 



The factor p represents the potential of unit mass placed at the point 

 M on the element ^S. 



361. If the shell is uniform the factor ^ is a constant. If P is 

 the potential of a layer of density equal to unity, we shall have 

 Q = 3>P, and expressions (4) and (5) become 



> "- 



362. Let us consider, for instance, a shell bounded by a plane 

 surface ; this may be replaced by a plane shell of the same strength, 

 bounded by the same surface. Let us place this shell in the plane 

 of yz, the positive face on the side of the #-axis. The abscissa of 

 the point M being x, we have evidently dx = - dn, and therefore 



(7) 



