350 BELL SYSTEM TECHNICAL JOURNAL 



Weiss' Theory 



There is another theory of magnetization, built upon an entirely 

 different basis from Ewing's — a basis involving the notion and in 

 fact the definition of temperature. To import temperature into 

 theories of magnetism is clearly most desirable, considering how 

 great is the influence of that variable upon the I-vs.-H curves; an 

 influence so great, indeed, that when a sample of any ferromagnetic 

 substance is made sufficiently hot, all the distinctive features of 

 ferromagnetism depart from it. In developing Ewing's model, it is 

 easy to say that as the temperature is raised the little magnets are 

 more vigorously agitated, the bonds which are responsible for rema- 

 nence and coercivity are more frequently ruptured; but such state- 

 ments, though plausible, lack precision and hold out no promise of 

 numerical agreements between theory and experience. That being 

 the case, it seems unreasonable to expect numerical agreements from 

 a theory offering a much less definite and specific picture of the interior 

 of a ferromagnetic body than even Ewing's. Such agreements, 

 nevertheless, emerge from the theory of Langevin and Weiss. 



Langevin took as his point of departure the theory of temperature 

 developed by the great savants Maxwell and Boltzmann (the same 

 from which, by the way, the quantum-theory arose through the 

 modifications made by Planck). To introduce as much, or as little, 

 of this theory of temperature as is required for our present purpose, 

 we envisage a sample of oxygen gas, A^ molecules per unit volume, 

 in thermal equilibrium at absolute temperature T. Let each molecule 

 be visualized as a rigid body of mass m, having three principal axes 

 of rotation and corresponding moments of inertia /i, h, h- The 

 molecules are darting to and fro, with translatory velocities which 

 may be specified by giving the three components u, v, w of each in 

 some coordinate-frame. They are likewise revolving, with angular 

 velocities which may be specified by giving the three components 

 r, s, t of each along the principal axes of the molecule in question. 

 The kinetic energy of the molecule is given by 



= Ku +K, + K,, + Kr-\-K,-\- Kt, (1) 



each of which six terms may be regarded as the kinetic energy asso- 

 ciated with the variable which its subscript denotes. We will further 

 suppose that each molecule is a magnet of moment M. When the 

 gas is pervaded by a magnetic field //, each molecular magnet has a 

 potential energy Ve given in terms of the variable d, the angle which 

 its axis makes with the field, by the equation 



