Part I. 

 On the general theory. 



§ 1. General principles. 



The quantum theory of line-spectra rests upon the following fundamental 

 assumptions: 



I. That an atomic system can, and can only, exist permanently 

 in a certain series of states corresponding to a discontinuous series 

 of values for its energy, and that consequently any change of the 

 energy of the system, including emission and absorption of elec- 

 tromagnetic radiation, must take place by a complete transition 

 between two such states. These states will be denoted as the 

 "stationary states" of the system. 



II. That the radiation absorbed or emitted during a transition 

 between two stationary states is "un ifrequentic" and possesses a 

 frequency v, given by the relation 



£' -E" = h V, (1) 



where h is Planck's constant and where E' and E" are the values of 

 the energy in the two states under consideration. 



As pointed out by the writer in the papers referred to in the introduction, 

 these assumptions offer an immediate interpretation of the fundamental principle 

 of combination of spectral lines deduced from the measurements of the 

 frequencies of the series spectra of the elements. According to the laws discovered 

 by Balmer, Rydberg and Ritz, the frequencies of the lines of the series spectrum 

 of an element can be expressed by a formula of the type: 



V = /,--(«")-/;. (n'), (2) 



where n' and n" are whole numbers and /",(/?) is one among a set of functions 

 of n, characteristic for the element under consideration. On the above assumptions 

 this formula may obviously be interpretated by assuming that the stationary states 

 of an atom of an element form a set of series, and that the energy in the /i"" state 

 of the t"" series, omitting an arbitrary constant, is given by 



E,{n) = ~hf,{n). (3) 



We thus see that the values for the energy in the stationary states of an atom 

 may be obtained directly from the measurements of the spectrum by means of 

 relation (1). In order, however, to obtain a theoretical connection between these 



