464 



As the inferior limit in the integral has been chosen, as the 

 function 'f may be determined by considering that for i/m = 

 Urm is given as a function of T, viz. by equation (5). The two 

 equations obtained in this way determine ?^,„i when T and Mm are 

 given. The following form can be given to these equations. If we 

 call u^\- and T* the values of ii^ and T which according to (5) 

 belong to a definite value of .r, the following values of Uym and T 

 now correspond to it : 



a 



p 

 Sha 



— ^ «^ 



^ , (23) 



a I 



7' = T* 



"" e "/' 



Sha 



In these equations the integration '"; w^hich occurs in (22) has been 

 carried out. It is easily seen that iinn is greater than the value of 

 Ur (for Mm = 0) which belongs to the same value of T. So also 

 that if u^i.=zkT*, Unn is equal to the value of Uy (for Mm=zO) 

 at the temperature 7\ 



For determining the spontaneous magnetization, J/,n in (23) must 

 be replaced by o, and further it has to be remembered that betw^een 

 a, a, and Uim according to (12) and (17) the following relations exist *) : 



Ö _ Cha 1 1 tlnn „ . 



wft Sha a 3 ic^c 



The calculations can be performed by calculating at a given value of 



— the corresponding value of T: (24) gives the values of a and 



71^1 



— corresponding to — ; then according to (23) 



a 



Sha — a — 



J/*!- = /fi-m e nil', (25a) 



a 



according to (5) by the aid of the equations 



1) In Langevin's 3f,„, «-diagram this integral can be read as the surface which 

 has the curve (7) and ihe il/,^^-axis as its boundaries. 



-) It follows from equation (23) that the determination of the Curie point by 

 equation (16) is not ('hanged as a consequence of the influence of the field on the 

 rotational energy. This may also be deduced directly. 



