effect of a magnetic field on the hydrogen spectrum which, although no complete 

 explanation of the observations was obtained, undoubtedly represents an important 

 step towards a detailed understanding of this phenomenon. 



In spite of the great progress involved in these investigations many difficulties 

 of fundamental nature remained unsolved, not only as regards the limited ap- 

 plicability of the methods used in calculating the frequencies of the spectrum of 

 a given system, but especially as regards the question of the polarisation and in- 

 tensity of the emitted spectral lines. These difficulties are intimately connected with 

 the radical departure from the ordinary ideas of mechanics and electrodynamics 

 involved in the main principles of the quantum theory, and with the fact that it 

 has not been possible hitherto to replace these ideas by others forming an equally 

 consistent and developed structure. Also in this respect, however, great progress 

 has recentlj' been obtained by the work of Einstein') and Ehrenfest^). On this 

 state of the theory it might therefore be of interest to make an attempt to discuss 

 the different applications from a uniform point of view, and especially to consider 

 the underlying assumptions in their relations to ordinary mechanics and electro- 

 dynamics. Such an attempt has been made in the present paper, and it will be shown 

 that it seems possible to throw some light on the outstanding difficulties by trying 

 to trace the analogy between the quantum theory and the ordinary theorj' of 

 radiation as cioselj* as possible. 



The paper is divided into four parts. 



Part I contains a brief discussion of the general principles of the theory and 

 deals with the application of the general theorj' to periodic systems of one 

 degree of freedom and to the class of non-periodic systems referred to 

 above. 



Part II contains a detailed discussion of the theory of the hydrogen spectrum in 

 order to illustrate the general considerations. 



Part III contains a discussion of the questions arising in connection with the ex- 

 planation of the spectra of other elements. 



Part IV contains a general discussion of the theory of the constitution of atoms and 

 molecules based on the application of the quantum theory to the nucleus 

 atom. 



Copenhagen, Xovemtjer 1917. 



'l A. Einstein, Verh. d. D. phys. Ges. XVIII, p. 318 (1916), Phys. Zeitschr. XVIII, p. 121 (1917). 

 "-) P. Ehrenfest, Proc. Acad. Amsterdam, XVI, p. 591 (19U), Phys. Zeitschr. XV, p. 657 (1914), Ann. 

 d. Phys. LI, p. 327 (1916) Phil. Mag. XXXIII, p. 500 (1917). 



