400 Dr. N. Bohr on the Quantum Theory of 



The possible necessity for an alteration of this kind in 

 assumption C may perhaps not seem unlikely when it is 

 remembered that the laws o£ mechanics are only known to 

 hold for certain mean values of the motion of the electrons. 

 In this connexion it should also be remarked that when 

 considering periodic orbits only mean values are essential 

 (comp. I. p. 7). The preliminary and tentative character of 

 the formulation of the general assumptions cannot be too 

 strongly emphasized, and admittedly they are made to suit 

 certain simple applications. For example, it has been already 

 shown in paper IV. that the assumption B needs modification 

 in order to account for the effect of a magnetic field on 

 spectral lines. In the following sections some of the recent 

 experimental evidence on line spectra and characteristic 

 Rontgen rays will be considered, and I shall endeavour to 

 show that it seems to give strong support to the main 

 principles of the theory. 



2. Spectra emitted from systems containing only one 

 electron. 

 In the former papers it was shown that the general 

 assumptions led to the following formula for the spectrum 

 emitted by an electron rotating round a positive nucleus 



tf(M + ro)W n 2 2 ) W 



Ne, —e, M, m are the electric charges and the masses of the 

 nucleus and the electron respectively. The frequency of 

 rotation and the major axis of the relative orbit of the 

 particles in the stationary states are given by 



AT9 47rVMm 1 1 /i«(M + ifi) 2 ,.. 



6) n = JN- M — i -g, Za n =r- n z . . . (4) 



The energy necessary to remove the electron to iufinite 

 distance from the nucleus is 



9 7rVMm 1 

 W — X 2 (K\ 



VVn_1> h 2 (M + m)?i* W 



This expression is also equal to the mean value of the kinetic 

 energy of the system. Since — W„ is equal to the total 

 energy A n of the system we get from (4) and (5) 



■ar"** ( 6 ) 



If we compare (6) with the relation (1), we see that the 



W 



