Electric and Magnetic Fields on Spectral Lines, 517 



be found when a closer examination is made of the effect 

 of the electric field on the motion of the electron *. This 

 problem, however, will not be considered further at this 

 stage. 



The problem of the influence of an electric field on the 

 spectra of other elements is naturally far more complicated 

 than for hydrogen, and cannot be discussed in detail until 

 the theory for such spectra is further developed. It seems, 

 however, possible on the present theory to obtain a simple 

 explanation of the characteristic difference, observed by Stark, 

 in the effect of tin field on the lines of the different series of 

 the helium spectrum. 



According to the last section, the different series of lines 

 in the spectrum of an element correspond to different series 

 of stationary states of the atom in which one of the electrons 

 moves in an orbit outside the others. For any high value 

 of n this orbit is approximately the same as that of the 

 electron in a hydrogen atom. In the discussion we assumed 

 fhat the effect of an electric field on the energy of the 

 stationary states of the hydrogen atom, is connected with a 

 considerable variation in the position and eccentricity of the 

 orbit of the electron in the presence of the field. The possi- 

 bility of such a variation is dde to the fact that without the 

 field every elliptical orbit is stationary. When, however, 

 there are perturbing forces from the inner electrons the latter 

 condition is not satisfied, and thus the effect of an external 

 electric field on the stationary states may be expected to be 

 much smaller than for the corresponding states of the 

 hydrogen atom. 



A measure of this effect of the inner electrons on the 

 motion of the outer may be obtained by considering the 

 function <f> r (n) , The nearer this function approaches unity 

 the smaller is the disturbance due to the inner electrons, and 

 the more the motion of the outer approaches to that of the 

 electron in the hydrogen atom. Now for the elements of 

 low atomic weight, such as helium and lithium, <f> r (?i) has a 

 value very nearly unity for the Diffuse series, while for the 

 Sharp series or the Principal series, the value is not at all as 

 close. On our theory we should, therefore, expect a much 

 greater influence of an electric field on the first series than 



* Note added during the proof . — In Verh. d. Deutsch. Phys. Ges. 1914, 

 p. 20, K. Schwavzschild has discussed the problem of the effect of the 

 field on the motion of the electron in some detail. In contrast to the 

 above considerations he attempts to apply the results on the explanation 

 of the Stark effect without leaving- ordinary electrodynamics. 



