MAGNETIC RESONANCE. II 387 



Much was said in Part I about the magnetic resonance of nuclei 

 having more than two permitted orientations. We may seem to be wan- 

 dering off the course if we revert to these, but this case is very pertinent. 



There are nuclei with three, four, ... up to ten or maybe more allowed 

 orientations. One would expect them to display a multitude of peaks; 

 but there is never more than one. This is for two reasons, which I give 

 after introducing the symbol (27 + 1) for the number of orientations. 

 First, it is impossible to turn a nucleus from any orientation to any 

 other except the nearest to the original one. This reduces the number of 

 possible peaks to one fewer than the number of orientations. But second, 

 all of these 27 possible peaks are of the same frequency for given H, or 

 at the same field strength for given v, so that they all coalesce into a 

 single peak. 



The formula for this apparent single peak which is strictly 27 coinci- 

 dent peaks has been derived in Part I, and this is it: 



hv = {n/I)H (4) 



Now it is necessary to interpret 7 and /x; and the interpretation is dif- 

 ferent according as one uses the old quantum theory or the new quantum 

 mechanics. The old quantum theory deals more simply with these prob- 

 lems, and would be preferable if this field could be isolated from all the 

 rest of physics; but the new quantum mechanics is worth the extra 

 trouble that it causes. 



In the old quantum theory, there are two definitions of 7 that reduce 

 to the same thing. First, 7 is the angular momentum of the nucleus in 

 terms of the unit /i/2x; that is to say, the angular momentum of the 

 nucleus is 7/i/2x. Second, Ih/2Tr is the maximum possible projection, 

 upon the field-direction, of the angular momentum of the nucleus. This 

 is because, among all of the allowed orientations of the nucleus, the 

 one which is most nearly parallel to the field-direction is exactly parallel 

 to the field-direction. So it was shown in Fig. 1. 



In the new quantum mechanics, the second of these definitions re- 

 mains valid and the first does not. This is because the orientation which 

 is most nearly parallel to the field-direction is not exactly parallel 

 thereto. It is inchned, in fact, to the field-direction by the angle 

 arc cos I/\^I{I + 7), and the angular momentum of the nucleus is 

 V7(7+ l)(V27r). 



Thus there is one definition of 7 which is valid under both theories, 

 and that is, that 7 is the maximum possible projection upon the field- 

 direction, of the angular momentum of the nucleus in terms of the unit 

 h/2Tr. Similarly it is always correct to say that m is the maximimi pos- 



