326 



CONSTITUTION OF MAGNETS. 



The energy of the second shell in the field of the first has the 

 same value, and is expressed in the same way, 



as a function of the flow of force which proceeding from the first 

 would traverse the second ; from it we infer 



(24) M = M'. 



Thus when two magnetic shells of equal strengths are in presence 

 of each other, the flow of force which starts from one and traverses 

 the other, entering by the negative face, is the same for both. 



It will be observed how analogous this property is with the 

 theorem demonstrated above (63) relative to the electrostatic in- 

 duction between two conductors. 



342. Equation (22) shows that the energy of a shell in a mag- 

 netic field only depends on the flow of force which crosses the 

 surface bounded by the contour of the shell, and that it is inde- 

 pendent of the form of this surface. This energy, and therefore the 

 force exerted on the shell, may be expressed then as a function 

 of the curve of the edge. 



In like manner the reciprocal energy of two shells given by 

 equation (23) only depends on the two edges; this energy and 

 the reciprocal force may then be expressed as a function of the 

 two curves which bound the shells. 



343. ACTION OF A FIELD ON A SHELL. Consider a shell S 

 (Fig. 80) placed in any given magnetic field. When the shell ex- 

 periences an infinitely small displacement, the increase of the 

 potential energy is 



