Electric and Magnetic Fields on Spectral Lines. 515 

 This gives n= 2Wm v - ^ 1 E <A 



2«„=^(l + E T /^\ . . . (17) 

 Introducing this iu (14), (15), and (16) we get 



0)„ = -T-; r-- 



and 



A »= C --^^( 1 ± E I6^?^> * ' (19) 

 T^^(iq=E T ^^). . . . (20) 



It should be remembered that these deductions hold only 

 for large values of n. For the mechanical interpretation 

 of the calculations we need therefore only assume that the 

 eccentricity is very nearly unity for the large orbits. On 

 the other hand, it appears from (17), (18), and (19) that 

 the principal terms in the expressions for 2a n , co n , and A n are 

 the same as those deduced in the former section directly from 

 the Balmer formula. If we therefore suppose that these 

 quantities in the presence of an electric field can be expressed 



a- 



by a series of terms involving ascending powers of E— , we 



may regard the above deduction as a determination of the 

 coefficient of the second term iu this series, and may expect 

 the validity of the expressions lor every value of n. It may 

 be considered, in support of this conclusion, that we obtain 

 the same simple relation (11) between the frequency of 

 revolution and the mean value of the kinetic energy as was 

 found without the field, cf. p. 510. 



In the presence of an electric field we shall therefore 

 assume the existence of two series of stationary states of the 

 hydrogen atom, in which the energy is given by (19). In 

 order to obtain the continuity necessary for a connexion 

 with ordinary electrodynamics, we have assumed that the 

 system can pass only between the different states in each 

 series. On this assumption we get for the frequency of the 

 radiation emitted by a transition between two states cor- 

 responding to n-2 and n l respectively : 



1 /a a ^ ZwVm/ 1 1 \( , „ W 3 A 



.... (81) 



