234 BELL SYSTEM TECHNICAL JOURNAL 



tween the magnetic moments calculated from magnetic data after this 

 fashion, and those derived from the spectra, are accurate within an 

 experimental uncertainty of a few promille. I think that these are 

 among the most impressive results in the whole structure of modern 

 physics. Then in addition the rare-earth elements help us out again, 

 owing to the peculiarity which their atoms have of behaving, even when 

 they are incorporated into solid compounds, as though they were the 

 atoms of a gas. They have supplied us with a number of beautiful 

 agreements of this same character. 



Now as a transition to the next part of this paper, I must acquaint 

 you with another fact which belongs to this last part. I have more or 

 less been allowing you to suppose that with solids as with gases, the 

 susceptibility is generally proportional to I'T. Actually it is much 

 more common, among solids, to find a law of the type, 



X = const./(r - e), (9) 



where 6 stands for a constant differing from one substance to another. 

 This constant is evidently of the dimensions of temperature; it is a sort 

 of "critical" temperature, known as the paramagnetic Curie point; the 

 formula usually holds for a broad range of values of T above and not 

 too close to Q. (There are plenty of cases where even this formula will 

 not fit, but we will not concern ourselves with them.) You see that 

 this might be taken as meaning, that for temperatures greater than 6 

 the substance is more strongly magnetized by any particular field 

 strength than, by our previous theory, we should expect it to be. It 

 might even be taken as suggesting, that in addition to the applied field 

 which we produce ourselves by a horseshoe magnet or something of the 

 kind, there is an extra field arising within the substance itself, which 

 helps along with the magnetization. Now this is just the suggestion 

 which physicists have accepted. Of course it is necessary to make some 

 specific assumption about this extra or internal field, in order to arrive 

 at the empirical law which I just wrote down. The required assump- 

 tion turns out to be simple and gratifying. It is necessary and suffi- 

 cient to assume that inside the magnetized substance, there arises an 

 extra field which is proportional to the magnetization I itself. Hitherto 

 we have been supposing that the torque acting upon an atomic magnet 

 is directly and entirely due to the applied field //, and we have been led 

 to the law that x varies inversely as T. Now we are going to suppose 

 that the torque is due to a field (// + .4/) ; and this will lead us, by way 

 of the equation 



/ = A'Mtanh {II + AI):kT (10) 



