CONTEMPORARY ADVANCES IN PHYSICS 



353 



-J = coth a = L((i), 



(11) 



the symbol /max. being used for NM, the total magnetic moment 

 which the assemblage of A^ molecules would have if they were all 

 directed perfectly parallel to the field. 



This function L{a) is represented by the curve of Fig. 12, which 

 departs from the origin with slope a/3 = AIH/SkT, and bends over 



•w 

 /" 



x = 



_ ^H 



KT 



Fig. 12 — The I-vs.-a curve of Langevin's theory of paramagnetism, and the data 

 for gadoHnium sulphate. (After P. Debye.) 



toward its asymptote L = I without passing through any point of 

 inflection. It has thus a resemblance to the initial curve; but one 

 must not be misled by this, for Langevin's theory is not a theory of 

 ferromagnetism. It is based on assumptions appropriate to a gas, 

 and gases are not ferromagnetic; it gives no account of remanence, 

 and remanence is an essential feature of ferromagnetic bodies. With 

 a gas of which the molecules are permanent magnets, we should 

 expect / to vary with H in the manner indicated by the curve. 



Now as a matter of fact, in oxygen and other paramagnetic gases I 

 is apparently proportional to //, up to the greatest fieldstrengths 

 which can be applied : 



/ = aJL (12) 



This however does not necessarily mean that equation (11) is not 

 valid ; it may mean simply that the greatest available fields (some tens 

 of thousands of gauss) are not great enough to pass beyond the 

 sensibly-straight initial portion of the curve. If so, then 



<To'^ = 'Jn.^x.AI/SkT = NAP/SkT 



(13) 



I 



