402 



ON MAGNETS. 



In the first case, in which we have X< D, the limits of the 



integration are R 2 = 



and R = D- 



In the second case, in which we have X>D, the limits of 

 the integration are R 2 = X + D and R x = X - D. 

 All reductions being made, we get then : 



When X<D, 

 X = D, 



X>D, 

 X=oo, 



= M. 



iD 2 "] 

 ~3^J ; 



According to this theory, the magnetisation is at first propor- 

 tional to the magnetic force until it is equal to the reaction of the 

 medium, in which case the magnetisation attains two-thirds of its 

 maximum value. When the magnetic force has become greater, 

 the magnetisation increases less rapidly, and tends towards a finite 

 limit. 



The curve OL (Fig.. 90), which represents the magnetisation as 

 a function of magnetic force, consists then of a rectilinear part OA 

 which is prolonged by the curve AL, the asymptote to a horizontal 

 straight line CD. 



to 



Fig. 90. 



429. Weber's own experiments agree satisfactorily with this law. 



More recent researches, however, have shown that the value 

 of k cannot be considered constant even for small forces. This 

 coefficient at first increases regularly up to a maximum, and then 

 diminishes. 



