41 



325 



will in the following be indicated by the symbol (n' -> n") 



2n-- e' ;jj 

 /r'(l ^- "I'M) ' 



(105) 



If we put N — 1, formula (105) represents, as shown by Boiir. to a high degree of 

 approximation the series spectrum of hydrogen. Further, if we put N = 2, we should 

 on the theory expect that (105) would represent the line spectrum which would be 

 emitted by a helium atom which has lost one electron. Certain lines observed by 

 Pickering in stellar spectra ((7^4), (9^4), . . .), and by Fowler in a vacuum tube 

 containing a mixture of hydrogen and helium ((4-> 3), (5->3), . . .) were assumed by 

 Bohr to belong to this spectrum; and the theory was subsequently supported 

 by Evans' observation of these lines in the spectrum of a tube filled with care- 

 fully purified helium, which did not show the ordinary lines of the Balmer series 

 (f3->2), (4-^2), ...), but which, in addition to the series observed by Pickering 

 and by Fowler, showed a new series of lines lying close to the positions of the 

 Balmer lines and which on the theory correspond to (6-^4), (8 — 4), . ..'). 



In the theories given by Sommerfeld ^) for the effect of the relativity modifica- 

 tions, by Epstein') and by Schwarzschild') for the effect of a homogeneous electric 

 field, and by Sommerfeld ') and by Debye'') for the effect of a homogeneous magnetic 

 field on the hydrogen lines, every stationary state of the simplified hydrogen atom 

 appears, so to speak, as split up in a number of stationary states in which the values 

 ot the total energy differ only little from the values given by (103). Thus, in the case 

 of an electric field acting on the atom, the stationary states are fixed, as mentioned 

 above, by three entire numbers n^, n.^, n^, and to a stationary state of the simpli- 

 fied hydrogen atom characterised by a given value of n will "correspond" all 

 stationary states of the atom, perturbed by the electric field, for which /Jj -f n.^ + 

 is equal to this value. Also the three fundamental frequencies coy, and w,, 

 characterising the motion ot the perturbed atom, will only differ little from the 

 frequency of revolution w of the simplified hydrogen atom. The efiect on the spec- 

 trum, which will be due to the influence of one of the agencies mentioned, and 

 which may be calculated from (104), will consequently consist in the splitting up 

 of every hydrogen line in a number of components lying very near each other. As 

 well known, the above mentioned authors have in this way obtained results as 

 regards the frequencies of these components, which are in convincing agreement 

 with the experiments on the fine structure, the Stark effect and the Zeeman effect 

 of the hydrogen lines. 



') See E. J. Evans, Phil. Mag. XXIX, p. •2«4 .1915) 

 -) A. SoMMEiiFELD, Bci". Akad. München, 1915, p. 459. 

 ^) P. Epstein, Ann. d. Phys. L. p. 489 (1916) 

 *) K. ScHw AHZSCHILD, Ber. Akad. Berlin, 1916, p. 548. 

 ■■) A. SoMMEHKELD, Phys. Zeitsciir. XVII, p. 491 (1916). 

 P. Debye, Phys. Zeitschr. XVII, p. 507 (1916). 



1). K. n. Vlilensk. Selsk. Skr., nalurvldensk. og mnlheni Afd. 8. Hiukke. III. :i 42 



