WEBER'S THEORY. 399 



point, and the magnetisation which results therefrom is the stronger, 

 the more these particles are deviated from their original direction. 

 If the axes of all these particles were parallel the magnetisation 

 would have reached its maximum value. 



But this position can never be attained, owing to the reciprocal 

 reactions of the molecules. Wilhelm Weber has shown how these 

 reactions may be allowed for. 



426. WEBER'S THEORY. Let us assume with Weber that each 

 unit of volume contains n magnetic molecules, and that the moment 

 of each of them is equal to m. If all these molecules were parallel, 

 the magnetic moment of unit volume would be M = nm> and the 

 magnetisation of the medium would be at its maximum. 



When the medium is in the natural state, the molecules are 

 turned indifferently in all directions. To express this property let us 

 draw through the centre of the sphere a radius parallel to each of 

 the axes of the n molecules ; the extremities of these radii will be 

 arranged on the sphere in a uniform manner. 



The number of molecules the axes of which make, with a 

 determinate direction, which we take for the axis of x, an angle 



smaller than a is - (i - cos a) ; and the number of molecules whose 

 angles with the axis of x are between a and a + da is equal to 



sin ada. 

 2 



Let us now suppose this medium to be in a uniform field whose 

 intensity X is parallel to the axis of #, and consider the action 

 which it exerts on a molecule whose magnetic axis makes an angle a 

 with the direction of the field. 



If this molecule were free it would set parallel to the force of the 

 field, and, all the other molecules undergoing an analogous rotation, 

 the medium would attain the maximum magnetisation under the 

 influence of any external force however feeble. 



As this is not the case, it must be assumed that each molecule is 

 impelled to resume its original direction by an antagonistic force, 

 which arises either from the constitution of the medium itself, or by 

 the reactions which the magnetised molecules exert upon each other. 



The simplest hypothesis is to suppose that this antagonistic force 

 D is constant, and acts in the original direction of the axis of each 

 molecule. 



The new direction of the axis of a molecule in its position of 

 equilibrium is then given by that of the resultant of the forces 

 DandX. 



