368 MAGNETIC INDUCTION. 



Since the internal action of a uniformly magnetised body is given 

 (354) by the partial differentials of the second order of the poten- 

 tial P of a homogeneous mass, the force can only be constant 

 provided the function P is represented by a polynomial of the 

 second degree that is to say, if the body is bounded by a surface 

 of the second degree. When the coefficient k is very small that 

 is to say, for all diamagnetic and feebly magnetic bodies we have 

 sensibly 



In this case the magnetisation induced in a uniform field is 

 under the same laws of induction as are dielectrics, so that all 

 the results to which we have attained in electrostatics are also 

 applicable to magnetism, without any other modification than the 

 substitution of the magnetic potential for the electrical potential, 

 and of the coefficient of magnetic induction for the specific inductive 

 capacity. 



386. SPHERE. For a uniformly magnetised sphere (355) we 

 have 



The magnetisation produced on a sphere by a uniform field 

 will be 



47T/X+2 



M I 



The coefficient h or - - is equal to unity for conductors of 



p+2 



electricity; it is always positive and less than unity for magnetic 

 bodies, and it differs little from unity when /*, is very great. This 

 coefficient, on the contrary, is negative and very small for dia- 

 magnetic bodies. 



The value of the magnetic moment of the sphere is 



The resultant force within the sphere is 



