230 BELL SYSTEM TECHNICAL JOURNAL 



the origin, and bending over to approach an asymptote which is a 

 horizontal Hne of the ordinate Nn. 



At this point a strictly classical physicist would certainly grin or 

 sneer, because he would say to himself: "The speaker started out by 

 assuming for simplicity that the atoms can point in only two directions, 

 and now he has gone on to his conclusions without remembering the 

 obvious fact that an atom may point in any direction whatever!" 

 Well, of course Langevin did make allowance for that supposedly 

 obvious fact; it complicates the affair to some extent, but not seriously, 

 and leads to a very similar curve for / versus fxII;kT. Quantum me- 

 chanics, however, flatly denies that it is a fact. I mentioned above 

 that the atomic gyroscope has some paradoxical properties of its own, 

 in addition to those which it shares with the laboratory gyroscope. 

 Here is one of them. The atomic magnet is supposed to be able to set 

 itself, not at any angle whatever with respect to the applied magnetic 

 field, but only at one or another of a small number of definite discrete 

 angles. This is because of its angular momentum: it is primarily the 

 angular momentum which is constrained to this very singular behavior, 

 and which the magnetic moment is automatically obliged to follow 

 because they are so closely linked together. If I am asked why the 

 angular momentum should behave like this, I can only reply that 

 according to what I am told, if one is sufficiently penetrated with the 

 spirit of quantum mechanics it seems self-evident, and if one is not 

 sufficiently penetrated with that spirit there is nothing which can be 

 done to help. Notice anyhow that it is compatible with the statement 

 that when the atom is freely flying along, the field just keeps it precess- 

 ing about the field-direction, instead of gradually aligning it; and there 

 is ground for being thankful that this derivation, and certain others, 

 are somewhat simplified by it. It may be asked, how many diff'erent 

 inclinations are permitted to the atom? This depends upon the angular 

 momentum of the atom, and we can tell it from the spectrum. There 

 are certain elements and certain compounds for which the case is just 

 as simple as I have described it; just two permitted orientations, the 

 parallel and the anti-parallel, and no more. There are others for 

 which the permitted inclinations are three in number, others for which 

 there are four, five, and other integers up to fifteen or twenty. All 

 these yield curves of / versus nH/kT having the same general traits, 

 but diff"ering in the rate at which they approach the asymptote. I will 

 refer to all such curves as "Langevin curves," although the only one 

 which Langevin proposed was the classical curve corresponding to the 

 case in which all orientations are permitted (or, as we may say, there 

 are infinitely many permitted orientations). 



