2.T 



Ö = -T . (3) 



to 



becomes noticeable. This period is a 4/'^ part of T and is equal to 

 the time taken by the dipole to make a complete revolution through 

 the angle 2.t. The projection of the moment of the dipole on a line 

 in the plane A^- F-say on the axis of X depends on the time in the 

 manner shown on (he figure (for the sake of economy the "large 

 nnmber" ƒ is here taken as being approximately 2). 



A A m-fi-AA 



rA 'VVUWV 



3. The quantum relation for our system is 



\pdq = nh (w = 0, 1 , 2 . . .) (4) 



fi 



where the coordinate g is the angle cp, p is the corresponding 

 momentum 1 co and the integral is taken over a complete perid T. 

 This gives in our case 



4f.2:jTp = nh (5) 



or 



P = n± ......... (6) 



If now the restricting boundary of the interval (1) is so chosen 

 as to make ƒ very large, then the differences between consecutive 

 values of p (see (6)) (and therefore also between consecutive values 

 of the energy) are very small. 



4. This result appears to be unacceptable. In fact if we pass to 

 the limit of /=oo i.e. if the restriction of the boundaries on the 

 dipole disappears then equation (4) gives certainly 



"=""1. <'' 



for now <9 is the period. Here (Equ. (7)) p changes by finite steps 

 whereas if the previous consideration be applied (Eqn. (6)) the steps 

 become infinitesimal for /=zco. This is the contradiction to be 

 discussed. 



5. Bohr's principle of correspondence offers a new point of view 

 for the treatment of this case. As before let / be a very large 



1* 



