by the electron in unit of time as a consequence of the radiation, would be equal to 

 2-!;aFand aF respectiveh'. Due to the principles of conservation of energy and of 

 angular momentum holding in ordinary electrodynamics, we should therefore expect 

 that the ratio between the energy and the angular momentum of the emitted radiation 

 would be 2 7ri^, ^) but this is seen to be equal to the ratio between the energy /ii/ and 

 the angular momentum ^~- lost by the system considered above during a transition 



for which we have assumed that the radiation is circularly polarised. This agree- 

 ment would seem not only to support the validity of tlie above considerations but 

 also to offer a direct support, independent of the equations (22), of the assumption 

 that, for an atomic system possessing a-n axis of symmetry, the total 



It 



angular momentum round this axis is equal to an entire multiple of x— . 



2 7t 



A further illustration of the above considerations of the relation between 

 the quantum theory and the ordinary theory of radiation is obtained if we consider 

 a conditionally periodic system subject to the influence of a small perturbing 

 field of force. Let us assume that the original system allows of separation of 

 variables in a certain set of coordinates q^, ■ ■ ■ qs, so that the stationary states are 

 determined by (22). From the necessary stability of the stationary states we must 

 conclude that the perturbed system will possess a set of stationary states which 

 only differ slightlj' from those of the original system. In general, however, it will 

 not be possible for the perturbed system to obtain a separation of variables in any 

 set of coordinates, but if the perturbing force is sufficiently small the perturbed 

 motion will again be of conditionally periodic type and may be regarded as a super- 

 position of a number of harmonic vibrations just as the original motion. The dis- 

 placements of the particles in the stationary states of the perturbed system will 

 therefore be given by an expression of the same type as (31) where tlie fundamental 

 frequencies wk and the amplitudes Ct,....t., may differ from those corresponding to 

 the stationary states of the original system by small quantities proportional to the 

 intensity of the perturbing forces. If now for the original motion the coefficients 

 Ct,,...ts corresponding to certain combinations of the r's are equal to zero for all 

 values of the constants a^, ... us, these coefficients will therefore for the perturbed 

 motion, in general, possess small values proportional to the perturbing forces. From 

 the above considerations we shall therefore expect that, in addition to the main 

 probabilities of such transitions between stationary states which are possible for the 

 original system, there will for the perturbed system exist small probabilities of new 

 transitions corresponding to the above mentioned combinations of the r's. Con- 

 sequently we shall expect that the effect of the perturbing field on the spectrum 

 of the system will consist partly in a small displacement of the original lines 

 partly in the appearance of new lines of small intensity. 



A simple example of this is afforded by a system consisting of a particle moving 

 in a plane and executing harmonic vibrations in two perpendicular directions with fre- 



') Comp. K. ScHAPOscHNiKow, Pliys. Zeitschr. XV, p. 454 (1914) 



5* 



