116 



represent in all essential points the present status of the theory. The experimen- 

 tal material on the Stark effect of the series spectra has been largely increased since 

 the writing of the manuscript; first by the detailed investigations of Stark and 

 LiEBERT on the appearance of new lines in the helium and lithium spectra, which 

 have already been mentioned in Part II (cf. footnote on page 78), and which ful- 

 fill in all details the theoretical expectations described in the text. Further valuable 

 material has been produced by the investigations of Takamine^) on various spectra 

 as well as by a thorough-going investigation of the Stark effect of the mercury 

 spectrum, which this investigator has carried out in Copenhagen in collaboration 

 with Hansen and Werner, and the results of which have revealed a variety of 

 important details"). The effects found in all these investigations are in close 

 agreement with the theoretical anticipations, in that the main effect is the appe- 

 arance of new polarized components, the intensities and displacements of which 

 are closely connected with the relation of the spectral terms in question to the 

 corresponding hydrogen terms. 



Concerning the closer development of the theory subsequent to the writing of 

 the manuscript the analogous problem of the influence of external electric forces on 

 the fine structure of the hydrogen lines has been treated in detail by Kramers. 

 His results, which are based on a complete mathematical treatment of the mechan- 

 ical properties of the perturbed hydrogen atom, were already at hand at the final 

 redaction of the second part of this treatise as will be seen from the discussion in 

 Part II § 3, and have been meanwhile published in two papers^). In the first of these 

 papers it is shown, how we can arrive at a quantitative evaluation for the intens- 

 ities with which in an electric field the additional fine structure components appear, 

 which correspond to the new lines excited by the field in the series spectra of other 

 elements, and the displacements of the individual fine structure components, ini- 

 tially proportional to the square of the field intensity, are calculated. In the second 

 paper a complete discussion is given of the behaviour of the fine structure com- 

 ponents for increasing electric field and of their gradual change into the ordinary 

 Stark effect, where the displacement of the components has become directly propor- 

 tional to the field intensity. By the same procedure it is possible to account for 

 the effect of an external electric field on a hydrogen atom disturbed by an arbitrary 

 central field, and thereby essentially to develop the considerations given in the text 

 in their quantitative aspect. A calculation of this kind, concerning the initial displace- 

 ment of the components, has been recently used by Becker*) in order to discuss the 

 Stark effect of the alkali spectra. Although an agreement in the order of magnitude 



^) T. Takamine, Memoirs of the College of Science, Kyoto Imperial University, and Astrophys. 

 Jonrn. 50, p, 23 (1919;. 



~) H. M. Hansen, T. Takamine and S. Werner: D. Kgl. Danske Vid. Selsk. Skrifter (under press). 



') H. A. Kramers, Intensities of spectral lines, D. Kgl. Danske Vid. Selsk. Skrifter, 8, Række III. 

 3 (1919), and Zeitschr. für Phys. 3, p. 199 (1920). 



^) R. Becker, Zeitschr. für Phys. 9, p. 332, 1922. 



