_ 41 



(22), but it will be shown how Ihe conditions which fix the slalionary stales ol 

 the perturbed atom may be obtained by a direct examination of Ihe small deviations 

 of the motion of the electron from a simple Keplerian molion. In Ihis way it 

 seems possible to obtain a more direcl illustration of the princi[)les discussed in 

 Parti; and we shall see moreover that the treatment in question may be used also 

 in cases where the method of separation of variables cannot be applied. 



In Part III the problem of the series spectra of other elements will be treated 

 from a similar point of view. As pointed out by the writer in an earlier paper, a 

 simple explanation of the pronounced analogy between these spectra and the hy- 

 drogen spectrum is offered by the fact, that the atomic systems, involved in the 

 emission of the spectra under consideration, in a certain sense may be regarded as 

 a perturbed hydrogen atom. On the other hand, a clue to the interpretation of the 

 characteristic difference between the hydrogen spectrum and the spectra of other 

 elements was first obtained by Sommekfeld's theory of the stationary slates of cen- 

 tral systems referred to above. As shown by Sommerfeld, it is possible on this 

 theory to account in general outlines for the well known laws governing the fre- 

 quencies of the series spectra of the elements; and, as it will be shown in Part III, it 

 is also possible, on the basis of the formal relation between the quantum theory and 

 the ordinary theory of radiation, in this way to obtain a simple interpretation of the 

 laws governing the remarkable differences in the intensities with wliich the various 

 series of lines appear, which on the combination principle would constitute the 

 complete spectra under consideration. As regards the detailed discussion of these 

 spectra, however, it is necessary to bear in mind that the part played by the inner 

 electrons in the atoms of the elements in question forms a far more intricate pro- 

 blem than the perturbing effect of a fixed external field on the hydrogen atom. 

 For the treatment of this problem the theory of conditionally periodic systems 

 based on the conditions (22) does not seem to suffice, while, as it will be shown 

 in Part III, it appears that the method of perturbations exposed in the following 

 lends itself naturally also to this case. 



§ 2. The stationary states of a perturbed periodic system. 

 In Part I it was shown that the problem of the fixation of the stationary 

 states of a periodic system of several degrees of freedom, which is subject to the 

 perturbing influence of a small external field, cannot be treated directly on the basis 

 of the general principle of the mechanical transformability of the stationary states 

 by considering the influence, which on ordinary mechanics a slow establishment 

 of the external field would exert on the motion of some arbitrarily chosen statio- 

 nary state of the undisturbed system (see Part I, p. 23). This is an immediate 

 consequence of the fact, mentioned in the former section, that the stationary stales 



