SOME CONTEMPORARY ADVANCES IN PHYSICS-X 131 



upon the direction of the field — for this is precisely what M cos a is — 

 either does not change at all or else changes by ±co/i. Sometimes 

 it acts in the first of these ways, sometimes in the second, sometimes 

 in the third; but never in any other. 



This would result, if the behavior of the atom floating in the mag- 

 netic field were governed by two vwXqs; first, that it may orient itself 

 only in certain "permitted" directions such that M cos a, the pro- 

 jection of its magnetic moment upon the field-direction, assumes 

 "permitted" values which are integer multiples of wh; second, that 

 whenever a transition occurs M cos a either retains the value which 

 it had initially, or else passes to one or the other of the two adjacent 

 permitted values. 



The first of these rules is stated more rigorously than is quite neces- 

 sary; all that is required is to say that M cos a is permitted to take 

 only such values as belong to an equally-spaced series with intervals 

 equal to oih. The second rule is necessary. 



The theory of the normal Zeeman effect is simply, that the atom 

 does behave according to these rules. Radiation of the frequency Vo 

 occurs, either when the magnetic moment of the atom does not change 

 and the atom does not turn, or when the magnetic moment changes 

 and simultaneously the atom turns just so as to keep the projection 

 of the magnetic moment on the field-direction constant. We shall 

 later see that the latter of these two alternatives is the accepted one. 

 It must be supposed that the atom, so to speak, capsizes when it 

 emits the frequency Vo while floating in a magnetic field ; it flops over 

 at the same moment as it passes from one stationary state to another. 

 Radiation of the frequency vo-\-^v or of the frequency Vo — ^v occurs, 

 as we shall see, when the magnetic moment of the atom changes; in 

 some cases the atom capsizes during the process, in others it does not. 

 I now translate the foregoing rules from the language of magnetic 

 moments to the language of angular momenta. The first rule is, 

 that the atom may orient itself only in certain permitted directions 

 such that P cos a, the projection of the angular momentum upon the 

 direction of the magnetic field, assumes permitted values which are 

 consecutively spaced at intervals of {2nc/e)u)h. 



Now it is a fact of experience, that in the cases of the normal Zeeman 

 effect, 



w = e/4x)uc. (14) 



The rule therefore reads, that the projection of the angular momentum 

 of the atom upon the direction of the magnetic field is constrained to take 

 certain pennitted values, spaced at intervals of h/2ir. 



