Introduction. 



In an attempt to develop certain outlines of a theory of line-spectra based on 

 a suitable application of the fundamental ideas introduced by Planck in his theory 

 of temperature-radiation to the theory of the nucleus atom of Sir Ernest Rutherford, 

 the writer has shown that it is possible in this way to obtain a simple interpre- 

 tation of some of the main laws governing the line-spectra of the elements, and 

 especially to obtain a deduction of the well known Balmer formula for the hy- 

 drogen spectrum'). The theory in the form given allowed of a detailed discussion 

 only in the case of periodic systems, and obviouslj' was not able to account in 

 detail for the characteristic difference between the hydrogen spectrum and the 

 spectra of other elements, or for the characteristic effects on the hydrogen spectrum 

 of external electric and magnetic fields. Recently, however, a way out of this diffi- 

 culty has been opened by Sommerfeld^) who, by introducing a suitable generalisa- 

 tion of the theory to a simple type of non-periodic motions and by taking the 

 small variation of the mass of the electron with its velocity into account, obtained 

 an explanation of the fine-structure of the hydrogen lines which was found to be 

 in brilliant conformity with the measurements. Alreadj' in his first paper on this 

 subject, Sommerfeld pointed out that his theory evidently offered a clue to the 

 interpretation of the more intricate structure of the spectra of other elements. Briefly 

 afterwards Epstein"') and Schwarzschild ^), independent of each other, by adapting 

 Sommerfeld's ideas to the treatment of a more extended class of non-periodic 

 sj'stems obtained a detailed explanation of the characteristic effect of an electric 

 field on the hydrogen spectrum discovered by Stark. Subsequently Sommerfeld"') 

 himself and Debye") have on the same lines indicated an interpretation of the 



1) N. Bohr, Phil. Mag., XXVI, pp. 1, 476, 857 (iyi3|, XXVII, p. 506 (1914), XXIX, p. 332 (1915), XXX. 

 p. 394 (1915). 



-) A. SoMMEKFELD, Ber. Akad. München, 1915, pp. 425. 459, 1916, p. 131. 1917, p. 83. Ann. de Phvs.. 

 LI. p. 1 (1916;. 



3) P. Epstein, Phys. Zeitschr. XVII. p. 148 (1916), Ann. d. Pliys. L. p. 489, LI, p. 168 (1916i. 



<) K. ScHWARzcHiLD, Ber. Akad. Berlin, 1916, p. 548. 



=) A. Sommerfeld, Phys. Zeitschr. XVII, p. 491 (1916). 



•■■) P. Debye, Nachr. K. Ges. d. Wiss. Göttingen, 1916, Phys. Zeitschr. XVII, p. .■)07 (1916\ 



r 



