115 



the origin of the complex structure of the series hnes it has become clear through 

 investigations in recent years, especiallj' by Sommf.rfkm)") and Landi':-), that here 

 we have to do with the appearance of a third quantum condition in the fixation 

 of the orbit of the outer electron. This arises simply from the deviation from cen- 

 tral symmetry of the field, in which the series electron moves and corresponds to 

 the fixation of the stationary states of a hydrogen atom in an external field with 

 axial symmetry (cf. Part II, page 54), of which we meet a characteristic example 

 in the case of a hydrogen atom in a homogeneous external electric or magnetic 

 field, when the relativity modifications of the equations of motion are taken into 

 account (cf. Part II page 78 and 92). By the introduction of the third quantum con- 

 dition the orbital plane of the series electron is fixed relative to the axis of the inner 

 system, in such a way that the total angular momentum of the atom is equal to 



ft r^ , where ^t, is a whole number, the third quantum number, which, together 



with the quantum numbers n and r, completely determines the state of motion of 

 the series electron. Through this circumstance it is possible to a certain extent to 

 restrict the transition possibilities by making use of considerations on the conserv- 

 ation of angular moments during the radiation process of the kijnd set forth in 

 Part I, page 34, and independentlj' developed by Rubinowicz (compare Part II, note 

 on page 60). Thus we can conclude that in a transition the total angular momen- 

 tum of the atom must remain constant or increase or decrease by - — . This re- 



striction in the possibilities of variation of the quantum number (i, which is in 

 agreement with the observations, follows also directly from the correspondence prin- 

 ciple, as is easily shown by a simple consideration, quite similar to the considerations 

 in Part I, page 33 and Part II, page 59. It may, however, be pointed out, that the 

 restriction in the variation possibility of the quantum number t, which is respon- 

 sible for the remarkable limitation in the applicability of the general principle of 

 combination of spectral lines, appearing in the characteristic structure of the series 

 spectra discussed in § 1, can not be derived from considerations of the conservation 

 of angular momentum, but is to be looked upon as a characteristic consequence 

 of the correspondence principle. In contradiction to what has often been assumed 

 (cf. Essay II, page 58; see also Sommerfeld's book, Ch. 6, § 2) and to what also 

 has been indicated in the conclusion of the paragraph to which the present note 

 refers, considerations of conservation of angular momentum can be used only to 

 throw light on such limitations in the combination principle of spectral lines, which 

 show themselves in the laws holding for the number of components of the complex 

 structure of the individual series lines. 



Note to § 3. The conclusions in this section rest upon the general considera- 

 tions of disturbed systems developed in Part 1, pages 49-50, and Part 11, >; 2, and 



') A. Sommerfeld, Ann. d. Phys. 63, p. 221 (1920). 

 ') A. Lande, Zeitschr. f. Phys. 5, p. 231 (1921). 



