POISSON'S THEORY. 301 



masses will be developed by induction; as the force and the potential 

 are now everywhere null on the exterior, the layer induced has, on 

 any external point, a potential equal and of opposite sign to that of 

 the original masses. A layer equal and of the opposite sign dis- 

 tributed on the external surface according to the same law, will 

 produce a potential equal and of the same sign as those of the 

 system in question, and will form therefore a system equivalent for 

 external points. This conclusion obviously applies to magnetism, 

 the two kinds of masses obey the same elementary law. 



The external actions exerted by the magnet enable us to calculate 

 the density of this fictive surface layer, but will teach nothing respect- 

 ing the real distribution of magnetism. In order to investigate this 

 distribution, it would be necessary to determine experimentally the 

 forces which act on the interior of the magnet, and make cavities 

 into which test needles could be introduced; but the withdrawal of 

 a mass, however small, modifies the force in the cavity, for the 

 adjacent masses are suppressed, whose effect cannot then be 

 neglected. The magnet is equivalent then to two fictive layers, 

 one on the outer and the other on the inner surface of the 

 cavity; the sum AV of the three secondary differentials of the 

 potential is become null in this region, while it was originally 

 equal to -47rp. 



316, POISSON'S THEORY. Hitherto we have made no hypothesis 

 as to the manner in which magnetic masses are distributed in the 

 magnetised substance. To establish the theory of magnetisation by 

 induction, Poisson considers a magnetised body as made up of 

 magnetic particles disseminated in a medium impervious to magnet- 

 ism. These particles are spherical and equidistant if the body is 

 isotropic and homogeneous ; each of them contains equal quantities 

 of positive and negative fluids, part in the neutral state in the interior, 

 and part in the free state on the surface. The magnetic moment of 

 each particle, of volume u, may be represented by uq, the factor q 

 depending on the degree of magnetisation. If we consider a volume 

 dv> which is very great compared with the dimensions of the particles, 

 but infinitely small in reference to the dimensions of the magnet, all 

 the particles which it contains will have their magnetic axes sensibly 

 parallel, and the magnetic moment of the volume element will be the 

 sum of the moments of the particles. Calling ^, as we have already 

 done (167), the ratio of the space occupied by the particles to the 

 total volume dv, the total volume of the particles contained in this 

 element is proportional to hdv> and its magnetic moment will be 

 hqdv. This element will act on any point at a finite distance like 



