POTENTIAL OF A LAMELLAR MAGNET. 319 



on the form and position of the edge of the open shells that is 

 to say, of the infinitely thin zones cut on the surface by two adjacent 

 shells, and not at all on the form of the shells. 



For a point in the interior, the force in a slit between two shells, 

 or the magnetic induction, will be obtained by combining the action 

 determined by these successive zones, with a force in the opposite 

 direction to the magnetisation at the point in question, and equal to 

 4 TT I. The potentials by means of which these forces may be expressed, 

 are directly obtained from the following considerations. 



Let us first of all disregard the closed shells, and suppose that 

 after having removed all the open shells which the magnet contains, 

 we replace them by shells respectively of the same power terminated 

 by the same edge, but applied on the surface itself; this operation 

 would be realised physically if each of the shells were formed of 



Fig. 79. 



an elastic membrane, fixed by its edge, which could be stretched so 

 as to be applied on the surface of the magnet without modifying its 

 magnetic strength. Let us assume, for instance, that in Fig. 79 all 

 these shells have their positive faces turned upwards, and that they 

 are made to cover the point A of the surface of the magnet 

 where the function <& has its maximum value. 



The entire surface will then be occupied by a series of shells, the 

 superposition of which forms a complex shell, and produces at every 

 point outside, the same potential as the magnet itself. 



Let us now consider a point P in the interior. The potential 

 has not changed by the fact of the transformation of those shells 

 which passed between A and P ; but for each of the other shells 

 which have been traversed by the point P, the potential is less by 

 Let then-^p be the potential of magnetisation at P, and 



