360 MAGNETIC INDUCTION. 



The intensity of magnetisation I, and its components A, B, and C 

 parallel to the axes then become 





Adding these last equations after having multiplied them by <&?, ^, 

 </s respectively, we get 



If the value of k is constant throughout the body, the first member 

 of the equation is the exact differential of a function < of the 

 coordinates, and we have 



A- 3 * B- 3 * r- 3 * 



** ^ > *-* ">T~ > * T~ 



It follows from this (332) that the magnetisation is lamellar. 

 376. THE INDUCED MAGNETISATION is SUPERFICIAL. On the 

 other hand the general expression for magnetic density 



c)B 



here reduces to 



, /yu ^ 2 u yu\ 

 = -* ++ = ~ 



Since, from Poisson's equation, we have AU = 4?r/o, we get 



= 0, or /> = 0; 



that is to say that the magnetic density is zero throughout the whole 

 extent of the body. The magnetisation is then also solenoidal, and 

 there is no free magnetism except on the bounding surface of the 

 body. 



