Appendix to Part III.') 



Note to § 1. The problem treated in this paragraph offers a simple application 

 of the point of view developed in Part I and denoted there as a formal connection, 

 or analog}% between the quantum theory and the classical electromagnetic theory 

 of radiation. In order to prevent the possible misunderstanding that it is here a 

 question of a direct connection between the description of the phenomena according 

 to the quantum theory and according to classical electro-dynamics, in later papers 

 of the author (compare Essay II) the law in which this analogy appears is design- 

 ated as the "correspondence principle". It is a question indeed of a purely quan- 

 tum theory theorem, which joins itself directly to the formulation of the funda- 

 mental principles of the quantum theory, and which affirms the existence of a 

 connection between the possibilitj' of any transition between two stationary states 

 accompanied by radiation, and the appearance in the motion of a certain harmonic 

 oscillation component which may be denoted as the oscillation "corresponding" to 

 the transition. The application of the correspondence principle to the theory of 

 series spectra given in this section has been already indicated in its outlines in 

 Part I pages 46 — 50, and especially used in Part II, pages 97 — 99 in the discussion 

 of the analogous problem of the fine structure of the hydrogen lines. 



A treatment of the laws of series spectra from a formally similar point of 

 view has been given meanwhile in a paper of Sommerfeld and Kossel^), and the 

 question is treated in detail in Chapter VI of Sommerfeld's book "On Atomic 

 structure and spectral lines" ^). As mentioned in this book, Roschdestwexsky had 

 already called attention to the small modification demanded by the quantum theory 

 in the combination scheme of the spark spectrum of magnesium given by Fowler 

 and referred to on page 104 of the text. This author has in the last years discussed 

 in a series of papers^) the quantum theory classification of the experimental ma- 

 terial of series spectra and has come to the conclusion, by a study of the empirical 

 laws, that the fixation of the main quantum number n in the sharp series terms 

 (S-terms) of the alkali metals is to be changed in such a way that in the first 



') Compare the introductorj' note to Part III, p. 101. In the following the three lectures men- 

 tioned in this note will for brevity be referred to as Essay I, II and III respectively. 



-) W. KossEL and A. Sommerfeld, Verb. d. Deutschen Phys. Ges. 2l, p. 240 (1919). 



^) A. Sommerfeld, Atombau und Spektrallinien, Vieweg. 3d ed., 1922. An euglish translation of 

 this book has just appeared. 



■*) D. S. Roschdestwensky. Transactions of the optical institute in Petrograd (Berlin). 



