SPHERE. 339 



355. SPHERE. For a sphere of volume , for instance, the 

 value of P at an external point at a distance r from the centre, is 



P--- 



~ r' 



from which follows 



and therefore 



ux 

 r 3 



as we have previously seen (157). 



In the interior of the sphere the action of a mass of unit density 



will be equal to - irr (44), which, if a is the radius of the sphere, 



O 



gives for the potential 



from which we get 



and consequently 



DP 4 



= --TTX 



^x 3 



4 T Y-0 



7T1, 1 U, 



that is to say, that the internal action of a uniformly magnetised 

 sphere is constant, parallel, and in a contrary direction to the direc- 

 tion of magnetisation, a result which has already been established 

 directly (157). 



The magnetic induction in the interior of the sphere is constant 

 and equal (324) to 



4 8 



~3* ~3^ ' 



Z 2 



