Van der Waals 9 Equation of State to Magnetism. 713 



equation to include the liquid as well as the gaseous state 

 can be applied to the paramagnetic equation to include the 

 ferromagnetic as well as the paramagnetic state. 



The salient facts which Van der Waals embodies in his 

 equation are the reaction of the gaseous molecules one upon 

 the other, giving rise to an intrinsic pressure and the density 

 limit. Written in terms of density his equation is 



where p is the density, treated as the reciprocal of the 

 volume, p is the limiting density, and it is the intrinsic 

 pressure. According to Van der Waals this intrinsic pres- 

 sure is a function of the density, and may be put equal to 

 ap 2 , where a is a constant. This expression for the intrinsic 

 pressure makes the equation a cubic in p, and gives to the 

 calculated isothermals and isopiestics of a fluid an appro- 

 priate shape. 



The equation to a ferromagnetic will be an analogous 

 extension of the paramagnetic equation 



Hj =R'T, 



thus j must be replaced by ( y — =- ) in order to make 



allowance for the effects of a limiting intensity of magneti- 

 zation I , and H must be replaced by (H + H,) in order to 

 take account of the effect of an intrinsic field H< set up by 

 the interaction of the molecular magnets one upon another. 

 This intrinsic field will be some function of the intensity I 

 and may be put H t =/(I). The general magnetic equation 

 can then be written 



(H+/(I))( I 1 -^)=R'T. 



The verification of this equation is embarrassed by the 

 effects of magnetic hysteresis, but I have shown in a former 

 paper in this Magazine * that when hysteresis is eliminated 

 there is evidence for the constancy of R' in the ferromagnetic 

 state, that the form of the isothermals is obtained when a 

 limiting intensity of magnetization is inserted as above, and 

 that it is necessary to introduce an intrinsic field of force 

 into the equation if the shape of the isodynamic curves is to 

 be appropriately represented and if E/ is to have a unique 

 value in both states. In another paper | I have shown that 



* Phil. Mag. xxvii. p. 357, Feb. 1914. 

 t Phil. Mag. xxiii. p. 36, Jan. 1912. 



Phil. Maq. S. 6. Vol. 30. No. 179. Nov. 1915. 3 A 



