130 BELL SYSTEM TECHNICAL JOURNAL 



and for the "extra magnetic energy" of the atom due to the field 



AU=-MH cos a (9) 



In this last expression it is tacitly assumed that the extra magnetic 

 energy is zero when the atom is oriented crosswise (at right angles) to 

 the field. This is not an arbitrary, but a quite essential convention, 

 justified from the atom-model."^ Suppose now that the atom passes 

 between two stationary states S' and S", in which its internal energy, 

 its magnetic moment and its inclination are denoted by U', M', a' 

 and U", M" and a", respectively. Were there no magnetic field, 

 the frequency radiated would be 



vo = {U"-U')/li (10) 



but owing to the field, the frequency radiated is 



VH = Vo+Av = {U"- U')/h-\-H iM' cos a'-M" cos a")/h (11) 



the term Aj/ representing the displacement of the line by the field. 

 The question is, whether this term can be equated^to the observed 

 displacements. 



Consider the most tractable cases, those in which the so-called 

 "normal Zeeman effect" is observed. In these cases a line of fre- 

 quency Vo is replaced by three, of which the frequencies are 



Vo-\-wH, Vo, vc — coH (12) 



corresponding to three values for the displacement Ap, which are 

 expressed by 



Av=+o:H, 0, -c^H (13) 



The quantity co occurring in these expressions is a specific numerical 

 constant. Comparing these with the expressions for Az^ in (11), we 

 see that if our model is to be used to interpret the observations, then 

 for the first of the three observed lines M' cos a' must be greater 

 than M" cos a" by the amount ^ co; for the second, AI' cos a' must 

 be equal to M" cos a"; for the third, M' cos a' must be less than 

 M" cos a" by the amount coh. 



Another way of putting these statements is, that in order to interpret 

 the normal Zeeman effect in this manner it must be supposed that 

 whenever a transition occurs, the projection of the magnetic moment 



'" The action of the magnetic field upon the revolving electron imparts to it an 

 extra angular velocity about the direction of the field (the Larmor precession) and 

 hence an extra kinetic energy which (to first order of approximation) is proportional 

 to —cos a and is zero when a = ir/2. This extra kinetic energy is the extra magnetic 

 energy AU. It is profitable to derive the entire theory in this manner. 



