BARLOW'S PROBLEM. 



There are produced then, as we have seen in the case of 



electricity (165), two magnetic layers, one M : on the internal 



surface S : (Fig. 85), and the other M 2 on the external surface S 2 of 

 the volume in question. 



Fig. 85. 



The internal actions F! and F 2 of these two layers are determined 

 by the equations 



-F, 



where /5 denotes the ratio ( ) of the cubes of the radii. 



\a 2 / 



The action of these two layers is constant in the interior of the 

 small sphere S p and its value is 





but it is not constant within the magnetic substances, nor without. 

 We have then, for the total action <f> - F on the interior, 



9 I 



B B 2 



