461 



§ 3. a. intivductloii of th(\ quantain-theor)j into Weiks's theory for 

 tlir ferroniagnetlc state. Wo suppose tlial tlie introdnclion of the 

 qiuintuni-theory only brings this change in tlie statistics of the 

 orientations of the elementary magnets under the influence of the 

 magnetic field, that in the relations which Langevin ^) has deduced 

 for it kT has to be replaced by the vahie ?^,. for the rotation energy 

 which is now valid ''). 



According to Langevin the magnetic moment il/„i of unit of mass 

 under the influence of the magnetic field H is : 



I Cha 1 ) 



M,n = ''Hi ^r ; ....... (7) 



( on a a ) 



n is the number of freely rotating molecular ') magnets in the imit 

 of mass, a is the molecular magnetic moment; a is determined by 



liH 

 « = — (8) 



The value of w,-, which may be changed by the magnetic field is 

 treated in tliis section under b. 



From (7) and (8) follows for the susceptibility of paramagnetic 

 substances, as long as no saturation ^) begins to be appreciable : 



X = ^ (9) 



OosTERHUis has also accepted this relation. 



1) P. Langevin. Ann. chim. phys. (8) 5 (1905;, p. 70. 



2) In the application to solids we imagine the molecules to rotate freely, or at 

 least to be so weakly bound to a definite equilibrium orientation that the maximum 

 increase, which the potential energy can undergo by the deviation of a molecule 

 from the equilibrium orientation is still small compared with the mean kinetic 

 energy of rotation which the molecule has at the temperatures at which we consider 

 the magnetization. In cases in which the changes in potential energy .'ire appreci- 

 able more intricate relations appear. Cf. P.Weiss, G.R. 156 (1913), p. 1674, 1836, 

 for a treatment of such cases in the assumption of the equipartion value for the 

 rotation energy. 



3) Under "magnetic molecule" we understand in this communication the elemen- 

 tary particle which rotates freely as a whole and has a magnetic moment; at 

 present we do not enter into the question whether it is the same as the chemical 

 molecule or not. According to WErss each chemical molecule KcgOj would contain 

 3 magnetic molecules. 



•i) It deserves to be noticed that in the assuirsption of a zero-point energy saturation 



phenomena at low temperatures are to be expected to make their appearance at 



higher values of H than according to Langevin's theory, in which a is determined 



H 

 by the value of — . 



