108 



the outer electron bj' a comparison with a simple sj'stem consisting of an electron 

 moving in a lixed central field we may assume, however, that the above general 

 considerations as regards the appearance of the different series and their intensities 

 will remain valid. In fact we may assume that the motion of the outer electron, 

 due to the central character of the atom, can be resolved into a number of harmonic 

 vibrations in a similar way as the motion of an electron in a simple central field. 

 Moreover it will be observed that the considerations in Part I on page 33 about the 

 change of angular momentum during the transitions are quite independent of the 

 number of moving particles if only the field in which they move possesses an axis 

 of svmmetrv. 



§ 3. Effect of electric fields on series spectra. 



The general analogy of the spectra under consideration with the spectrum to 

 be expected for a simple system consisting of an electron rotating in a central field 

 of force is also brought out very instructively by the effect of electric fields on these 

 spectra, which has recently been investigated by Stark ^) in case of a great number 

 of elements. In case of a simple central system we shall except that the effect of 

 the fields consists partly in the appearance of new spectral lines of intensities in- 

 creasing with the electric field, partly in the splitting up of the different lines in a 

 number of components polarized parallel and perpendicular to the direction of the 

 electric force, just as in the problem of the influence of an external electric field 

 on the fine structure of the hydrogen lines, considered in Part II. For a given field 

 these efl^ects will be the smaller the more the orbit of the electron in the stationary 

 states involved in the transitions deviates from a purely periodic orbit. Now for the 

 spectra of the elements a measure for these deviations may be sought in the devi- 

 ations from unity of the values of the function (pr(n) defined by (88)^). For most 

 spectra the latter de^dations are considerable for small values of r and n, and in 

 agreement with this Stark found that for the greater number of elements the effect 

 on their spectra was exceedingly small or undetectable for electric fields of the in- 

 tensities applied by him. In case, however, of the elements of smallest atomic 

 numbers, viz. helium and lithium, the deviations from unity of fj(n) are much 

 smaller, the difference ^^(n) — 1 being of the same order as 0,001 already for r = 3, 

 and just for these elements Stark has found considerable effects which are of a 

 very interesting nature. 



In the first place the appearance of a number of new separate lines outside 

 the usual series was observed in the presence of the field. These lines correspond 



*) See J. Stare, Elektrische Spektralanalyse chemischer Atome, Leipzig 1914. 

 ^ See X. Bohr, Phil. Mag. XXVII, p. 517 (1913) and XXX, p. 409 (1915). 



