14 



BELL SYSTEM TECHNICAL JOURNAL 



tangent law, 



L ^ ctnh^^-— . 



/o kT (JLaH 



In deriving this the assumptions are made that the elementary mag- 

 nets, each of moment fXA, are subject to thermal agitation and momen- 

 tarily may have any orientation with respect to the direction of the 

 field, and that they are too far apart to influence each other. Quantum 

 theory alters the second of those assumptions by stating that in such 

 an ensemble of elementary magnets (atoms) there will be only a limited 

 number of possible orientations, in the simplest case only two, one 

 parallel and the other antiparallel to the direction of the field. In this 

 case the equation corresponding to Langevin's is 



-7- = tanh -^;=r • 

 io kl 



(3) 



These two theoretical relations are plotted for variable H and con- 

 stant T (room temperature) in Fig. 8, the constants being those for 



Fig. 8- 



I 2 3 4 5 6 7 



FIELD STRENGTH IN MILLIONS OF OERSTEDS (H) 



-With no helpful mutual action between atoms, enormous fields 

 would be necessary to saturate a magnetic material. 



iron (/o = 1740, iia = 2.04 X lO-^" erg/gauss). It is obvious that 

 with the highest fields so far attained in the laboratory (about 300,000 

 oersteds) the magnetization would attain only a small fraction of its 

 final value Jo if this law were obeyed, and in this range / would be 

 sensibly proportional to the field-strength : 



I = 



CH 

 T '' 



