4 



number and suppose that the permissible values of p are truly 

 given by Equ. (6). We want to know the requirements made by 

 the principle of correspondence as to the "probability of a transition" 

 from the state n = n^ to the state ?i =: ?i, (say as the result of absorption 

 in a tield of radition). The Principle of correspondence regards the 

 probability of the transitions as analogous to the amplitudes of 

 "corresponding" harmonics in a Fourier series expansion of the 

 function represented graphically on the figure. This function repre- 

 sents the dependence on the time of the X or Y component of 

 the dipole's moment. The Fourier expansion of the function may 

 be put into the form 



X— :S Ascosls-^] (8) 



The harmonics "corresponding" to the transition 7i^ — ► 7i, are 

 given by : 

 , 5 = n, — n, (9) 



From an inspection of the figure or by means of a short calcul- 

 ation it becomes apparent that for a large value of ƒ the amplitudes 

 of all the harmonics are small with the exception of those harmonics 

 whose period is nearly equal to the "quasiperiod" ê i.e. with the 

 exception of those for which 



7' 



-^0. (10) 



s 



or 



s = ^f (11) 



Therefore if ƒ is large all the transitions have a very small 



probability with the exception of those for which very nearly 



n,-n,^4f (12) 



and therefore (in virtue of (6j) 



h h 



P,—Px={n, — n;, ^— (13) 



4/. Z7t In 



which is the same as the interval between consecutive values of p 

 prescribed by (7) for infinitely large values of ƒ. 



6. If therefore we should take a collection of identical samples 

 of our system having all the same very large value of f, being all 

 at rest i.e. in the state /^ = at the time t = and if we should 

 subject each sample independently to the action of a black body 

 radiation — then we should find at a later time t that: 

 , A. Out of the very dense succession of the p levels which are 



