POISSON'S HYPOTHESIS. 369 



and the induction 



The former of these expressions also represents the total external 

 force on a point near the equator, and the second on a point near 



the pole. The ratio of these two forces is therefore equal to - . 



In the case in which /x is very great, the formulae become simpler, 

 and we have sensibly 



387. POISSON'S HYPOTHESIS. If we suppose with Poisson that 

 a magnetic body is made up of a system of small spheres, which 

 are absolute magnetic conductors (/x = oo ), disseminated in a non- 

 magnetic medium, the ratio of the volume occupied by all the 

 spheres, to the total volume, is expressed (167) by 



Taking the value /* = 500 for iron, we get 



.- 



500 167 



But the maximum value which the ratio h can have with equal 



7T I 



spheres is j= = i - -. We must therefore suppose that 



in the present case the volumes of the spheres are not the same, 

 and that the greater intervals are occupied by spheres of smaller 

 diameter. It appears, however, difficult to suppose that the adjacent 

 spheres do not act on each other, and that the magnetisation of 

 each of them, as is assumed on Poisson's theory, could be solely 

 dependent on the external field. 



B B 



