346 Dr. J, 11. Ashworth on Magnetic Hysteresis 



(b) The tangent to the curve of equation (4) at any 

 point is 



dm _ 1^ 1 , fi v 



dx ~ x 2 sin h 2 x' ' ^ ' 



and this must be put equal to the coefficient of oc in equation 

 (5), hence 



x u 2 sinh 2 x u fiNIo ' * ' ' [ '> 



where x u is the value of x for instability. When T is 

 chosen x u is thus determined, and x u being known, m u is 

 found from equation (4). 



(c) The field for instability (H„) is the value of H in 

 equation (5) when the reduced intensity is m u ; thus 



H u =-Tx u -m u NI . ....... (8) 



or T» -. 



H tt =-Ta -NI [coth* B -i), ... (9) 



and H tt is thus determined when T is given and x u found. 

 If T is less than the critical temperature then the first term 

 is less than the second and H M is negative. 



(5) We can trace the variation with temperature of this field 

 for instability by plotting H w , the intercept which the line 

 tangent to the curve cuts off" from the vertical axis against 

 the tangent of the inclination of the line as it varies with the 

 temperature. When this is done we get the curve traced in 

 the inset to figure 4, plotted to arbitrary scales, and it is 

 seen to be like the one found for the variation of these two 

 quantities as deduced from the ferromagnetic equation. 

 The remarks made in reference to that curve apply in the 

 same way here. 



(6) As both the ferromagnetic equation and the kinetic 

 theory have been developed in a general manner, it follows 

 that all ferromagnetic bodies should conform to the theory 

 of corresponding states both for I=/(T) and for I = $(H). 

 There is evidence for the truth of this in the relations of 

 residual magnetic intensity to temperature, but the proof is 

 not yet complete that corresponding states hold in the 

 relations of intensity to field-strength. Experiments on this 

 subject are in progress as already mentioned. 



