16 Prof. J. Larmor on Electromagnetic Induction 



The solution can be conducted as above. Taking an external 

 field, 



then 



where Q is a function of r; and substituting in equation (10), 

 we find 



therefore 

 where 



And we adapt our previous solution for Q by writing cos for k. 

 Thus, in the case of a solid sphere in a field of force given by 



P =A ^Y^coss<k 



we have, by (6), when we neglect squares of > 



-r. 2ttcds ( r 2 a 2 \ 



approximately inside the sphere, and 



4cTtcosA a 2n+3 



F -~(2n + l)(2n + 3)c ^+rY;sin^ . . (12) 



outside the sphere. 



This solution may be expressed as before. 

 We have found that a magnetic potential 



X2 = A r 1 YJ 4 cos scf) 



generates a steady system of currents in the rotating con- 

 ductor whose external potential is 



a 2n+s 



where 



. 47rws n 



A=-A - 





a (n + l)(2w + l)(2w + 3) 



This potential is the same as would be produced by a dis- 

 tribution of magnetic matter over the surface of the sphere 



