was attained, nevertheless these calculations are open lo tlie ohjection, niciilioiud hy 

 Becke« himself, that they rest on assumptions concerning Ihc charactci- of (he orliil 

 of the outer electron in the stationary slates, which in many cases are not in agree- 

 ment with the ahove mentioned recent view on alomic siructure, in conse([uence of 

 wliich the main quantum numhers of the sliarp series lerms and of Ihc principal series 

 terms for sodium and the following alkali metals are lo he changed (comp. |)age W,\) 

 Wholly aside from difficulties of this kind, a complete theoretical Irealment of the 

 effect of an electric field on the series spectra cannot be given, however, on the basis 

 of such a calculation, because the deviations from a simple central licld cNJiibited 

 by the forces originating IVom Ihe inner system, ^yhich are responsible lor the com- 

 plex structure of the individual series lines, will as already pointed out in Ihe texl, 

 inlluence essentially the action of the external field. A detailed theorelical trealmeni 

 of this influence, which shows itself especially clear in the abovemenlioned new 

 investigations on tire mercury spectrum, is, however, not yet at hand. 



Note to § 4. The considerations given in the text on the anomalous Zeeman 

 effect are of a very summary character, this subject al the time of the redaction of 

 the manuscript being still very little developed. In the meantime an essential ad- 

 vance in the explanation of the experimental material in the sense of the quantum 

 theory has been made by tlie systematic investigations of Lande ') on the spectral 

 terms by combination of whicli the frequencies of the components of the anomal- 

 ous Zeeman etTect may be represented. Also the promising discussion given by 

 Sommerfeld") concerning the variations of these terms with increasing field, corres- 

 ponding to the Paschen-Rack effect must be mentioned here. The closer significance 

 of the stationary states to be associated with the combination terms appears, however, 

 still to offer fundamental difficulties and tlie interesting attempt, which Heisenberg^) 

 has made to get around these, does hardly possess sufficient connection with the 

 principles whicli underlie the other applications of the quantum theory to atomic struc- 

 ture. As pointed out in the text the difficulty consists in the first place in the fact, 

 tliat the ordinary electro-dynamic laws can no longer be applied to the motion of the 

 atom in a magnetic field in the same way as seemed to be the case in the theory of 

 the hydrogen spectrum''). Tlie conclusion mentioned in the text, that on the basis of the 



^) A. Lande, Zeitschr. für Pliys. 5, p. 231 (1921). 



^) A. Sommerfeld, Zeitschr. für Phys. 8, p. 257 (.1921>. 



") W. Heisenberg, Zeitschr. für Phys. 8. p. 273 (1921). 



*) The theoretical expectation discussed in l'art II, p. 72, thai in a mat;netic lield each of tlic 

 components of the fine striictnre of the hydrogen lines (and helium spark lines) will split up in a 

 normal triplet, is strongly supported by an investigation of Hansen and .Iacohsen (D. Kgl. Danske 

 Vidensk. Selsk. math.-fys. Meddelelser HI, 11, 1921) on the effect of a magnetic Held on the helium 

 spark line 4680 A. Although this investigation was very difticult due lo llie sensilivencss of Ihe line 

 structure of this line for electric forces present in the discharge, the result would at any rate seem to prove 

 that the effect of the field is of a type entirely ditt'erent from the anomalous Zeeman effect on ollier 

 spectra. Compare also 0. Oldenberg, Ann. d. Phys. 67, p. 2.53 (1922). 



D, K. D. Vidensk. Selsk. Skr.. iuUur\idensk. pfi mallicm. Atel.. S. Hiekke, IV, I. 1 ti 



