652 CONSTANTS OF MAGNETISATION. 



It follows that 



With a magnet, M = ; in this case the mean value of the potential 

 on the surface is also zero. 



1215. If we have determined by any method the external 

 potential of the magnet, and the internal potential of the fictive 

 layer, by the aid of the potential on the surface, the density at 

 each point (498) will be given by the equation 



(8) 47ro- + + = 0, 



the external and internal perpendiculars being counted from the 

 surface. 



The determination of these potentials reduces to problems of 

 electrical influence. 



Suppose that the function U represents the potential of unit mass 

 at a point P, and of the layer which this mass, if it were electrical, 

 would produce by induction on the surface S, which is supposed to 

 be a conductor, and in connection with the earth, and let u be the 

 density of this layer on the element d. 



We shall apply equation (5) to the volume bounded by the 

 surface S and the surface S' of a sphere of infinitely small radius, 

 having the point P as centre. 



For the surface S', the value of U tends to become equal to 



, and, when r' tends towards zero, 

 r 



r dv r i dv , pv 



J In J r' t>r' J <>*' 



(V *TS'=-V fj^rVo- 

 J T>n P j V T 



The value of the second member of the equation (5) for the 

 surface S', reduces then to - 471- V p . 



