402 Induced Magnetism [CH. xn 



Equations (397) and (395) (or (396)), combined with the condition that 

 fl must be continuous, suffices to determine H uniquely. The equations 

 satisfied by ft, the magnetic potential, are exactly the same as those which 

 would be satisfied by V, the electrostatic potential, if /z were the Inductive 

 Capacity of a dielectric. Thus the law of refraction of lines of magnetic 

 induction is exactly identical with the law of refraction of line of electric 

 force investigated in 138, and figures (43) and (78) may equally well be 

 taken to represent lines of magnetic induction passing from one medium to 

 a second medium of different permeability. 



468. At any external point Q, the magnetic potential of the magnetisation 

 induced in a body in which //, and K have constant values is, by equation (342), 



j 



rjj 



n a /i\ , an 9 /i\ an a ,/i\) 



^-^--+ ir -^--+^ z-l-ftdsdyd* ...(398). 

 da dx \rj dy dy \rj dz dz \rj) 



Transforming by Green's Theorem, 



(399) > 



shewing that the potential is the same if there were a layer of magnetic 

 matter of surface density K ^ spread over the surface of the body. This 



(JYl 



is Poisson's expression for the potential due to induced magnetism. 

 We can also transform equation (398) into 



.(400), 



dn \r 



shewing that the potential at any external point Q of the induced magnetism 

 is the same as if there were a magnetic shell of strength /cl coinciding 

 with the surface of the body. 



Body in which permanent and induced magnetism coexist. 



469. If a permanent magnet has a permeability different from unity, we 

 shall have a magnetisation arising partly from permanent and partly from 

 induced magnetism. If K is the susceptibility and / the intensity of the 



