the Intrinsic Field of a Magnet. 415 



and the first term in the denominator instead of being 

 negligible, as in the former treatment of the ferro-magnetic 

 equation*, is of importance. By thus recognizing the 

 influence of the applied field the correspondence between the 

 curve deduced from the equation and the curve constructed 

 from experimental data is found to be improved. 



The equation to the critical temperature (T c ) remains the 

 same as before — namely, 



8 6I 8 a% f 



c ~ 21 R'/n 27. R' l } 



Secondly, let the temperature be constant and the applied 

 field be variable ; then, A' being constant in the absence of 

 external constraints, the right side of equation (3) is 

 constant, and the consequences formerly derived from the 

 ferro-magnetic equation are the same f except that the small 

 factor b replaces the large factor a\ with the result that 

 appropriate numerical values of I and H are now obtained. 



For example^ the relation of I to H is given by the 

 equation 



,§=(K)/{?-Hg)1- • • < 6 > 



which shows that hysteresis is in evidence, since the second 

 term in the denominator, involving the small quantity 6, is 



TT 



comparable with the first term ^ . If b were to diminish to 



a negligible quantity, as it may be made to do under certain 

 conditions, then the equation represents the anliysteretic 

 curve of I = ^> (H). 



Again, the equation to the critical field (H c ) is 



H«=~Mo 2 : (7) 



and this correctly gives the critical field as about the order 

 of a tenth of a unit, instead of the order of 10 6 formerly 

 calculated with a instead of b. 



Lastly, when both the molecular and the magnetic intrinsic 

 fields become small enough to be negligible then the ferro- 

 magnetic equation reduces to 



?=R'T, ........ (8) 



* Ashworth, Phil. Mag. vol. xxx. p. 711. 

 t Ashworth, Phil. Mag. vol. xxxiii. p. 334. 



