Van der Waals' Equation of State to Magnetism. 721 



The calculated magnitude of the intrinsic field depends on 

 the value assigned to a', and this may be derived either from 

 the expression for the critical temperature or from the ex- 

 pression for the temperature coefficient. It is important, 

 however, to notice that neither of these expressions deter- 

 mines a' without a knowledge of E/, as it is the ratio of a' 

 to R' which appears in both. Thus, even if the magnitude 

 of the intrinsic field is denied, so long as the ratio of a' to R' 

 remains constant, the relations of intensity oi magnetization 

 to temperature which have been derived from the ferro- 

 magnetic equation remain true. The progressive transfor- 

 mation from the ferromagnetic to the paramagnetic state 

 demonstrated b}^ Curie is, however, evidence in favour of 

 the view that R' is an unique constant, and if its magnitude 

 is that which it has in the paramagnetic state then a' is 

 determined, and the intrinsic field must be of the order 

 10 7 gausses. 



8. Curie's work was followed by a kinetic theory of para- 

 magnetism developed mathematically by Langevin *, and 

 Langevin's theory has been extended by Prof. P. Weiss t 

 to include ferromagnetism by making the intrinsic field the 

 subject of an hypothesis. He assumes that the magnitude of 

 the intrinsic field is directly proportional to the first power 

 of the intensity of magnetization, and writes H t = NI, where 

 N is a numerical constant. From this hypothesis he derives 

 three important formulae which it is interesting to compare 

 with corresponding ones derived from the ferromagnetic 

 equation. Firstly, for the critical temperature he writes 



T,=NA, O) 



where A is Curie's constant referred to magnetic moment 

 per unit volume, and N is the constant mentioned above. 

 The ferromagnetic equation gives 



T _ 8 ,j 1 

 c_ 27 °R'' 



S 1 



These expressions agree if N= — a'I , since A=^,. 



Secondly, for corresponding states Prof. Weiss gives the 

 equation 



T I 3 



T = fh 08) 



where c= p^ -, fi being the magnetic moment of the 



* Langevin, Attn. Chim. Phys. 8 ser. t. v. p. 70 (1905). 

 t Weiss, C. R. t. cxliii. No. 26, p. 1136. 



