POISSON's THEORY OF INDUCED MAGNETISM. 155 



France, Tome V., the investigation of this theory in its 

 most general form. He supposes that portions of the 

 iron, occupying a space equal to k x entire volume of 

 the iron (k being a fraction) are magnetic. In each of 

 these spaces the two magnetic fluids can be separated 

 to a constant distance in the direction in which the 

 aggregate of external magnetism (both that of a distant 

 body and that of the surrounding iron) acts on them, 

 the amount of fluid so carried over to opposite sides 

 being proportional to the intensity of the magnetism : 

 this supposition amounts to exactly the same as that of 

 the small magnets in the last articles. He then inves- 

 tigates symbolically (in a triple integral) the aggregate 

 effect of all these little magnets upon any one : and, 

 adding that aggregate to the external force, the total 

 force upon that magnet and the direction of that total 

 force are symbolically expressed. These must be the 

 same as the force and direction assumed for it in the 

 investigation ; and the equations expressing this identity 

 are the equations on the solution of which the solution 

 of the problem depends. 



It will be seen at once that this is a problem of very 

 great complexity. In the general case, no advance 

 whatever can be made to a solution of it. Only in the 

 case of a sphere (solid or hollow), and a spheroid, can a 

 result be obtained. One inference is, that the external 

 attraction of the sphere is not much diminished by the 

 hollow, until the hollow becomes so large as to leave a 

 comparatively thin shell. For other purposes, it is 

 conceived that a very oblate spheroid may in some 



