Van der Waals i Equation of State to Magnetism. 719 



to the temperature o£ transformation, secondly, an abrupt 

 transition through a region of instability, and, thirdly, a 

 region in which the magnetic intensity declines less and less 

 quickly and approaches the temperature axis asymptotically. 

 Curie's researches showed that the curve tracing the change 

 of state loses its abruptness and becomes less steeply inclined 

 to the temperature axis as the field becomes stronger*. This 

 result is immediately deducible from the equation under 

 discussion, where it is seen that when H is extremely large 

 the expression would then always be negative and the region 

 of instability would disappear. We should expect to find a 

 critical field where the change occurred from abrupt to rapid 

 continuous loss. 



Although there is this general agreement between the 

 ferromagnetic equation and experimental results, the re- 

 duced curve of I=/(T) traced from the equation does not 

 fit very well the experimental curve at all temperatures. 

 Van der Waals' equation, however, seems to be faulty in the 

 same way when it is applied to the determination of the 

 variation of liquid density with change of temperature, and 

 there is no doubt that an improved equation of state which 

 would fit the experimental curve of p=f(T) would at the 

 same time more correctly represent the experimental magnetic 

 curve of I=/(T) for the following reason. 



The critical temperatures of nickel and water are nearly 

 alike, and it is possible, therefore, conveniently to compare 

 the behaviour under variations of temperature of the magnetic 

 intensity of nickel as a typical ferromagnetic with the density 

 of water as a typical liquid. When values of these quantities, 

 treated as fractions of the maxima, are plotted against a scale 

 of reduced temperatures, the curve for nickel is almost in- 

 distinguishable from the curve for water f. Thus an equation 

 which is correct for one would be correct for the other. 



7. From a knowledge of the value of a' it is possible to 

 calculate the magnitude of the intrinsic field for any intensity 

 of magnetization. At the maximum intensity I we have 

 H; = «'J 2 , and for iron we get 



Hi=7-6x(1685) 2 = 2-2xl0 7 . 

 Similarly for nickel we get 



Hi=(92)x(5101 2 =2-4xl0 7 , 

 and for cobalt 



Hi=21x(1300j 2 =3-6xl0 7 . 



An intrinsic field of this magnitude was shown to be 



* Curie, G£uvres, p. 332. 



t Phil. Mag. xxiii. p. 36 (1912). 



