49 



333 



involved in tlie transitions. It is therefore of great importance tliat, just in the case 

 of spectral lines which arc split up in components, it is possible to obtain some 

 direct information as regards the relative intensities of these components in a way 

 which is quite independent of the preceding considerations. In fact, a simple 

 consideration of continuity or, as Bohh calls it, a consideration of the necessary 

 •'stability of spectral phenomena"'), assures us at once that the intensities of the 

 polarised components in which an unpolarised spectral line splits up under the 

 influence of small external forces will be such, that the ensemble of all compo- 

 nents together will show no characteristic polarisation in any direc- 

 tion, if small quantities proportional to the intensity of the external forces are 

 neglected. If we consider for instance the Stark eflect or the Zeeman effect of the 

 hydrogen lines, viewed in a direction perpendicular to that of the electric or of 

 the magnetic field, the sum of the intensities of the components polarised parallel 

 to the field must be equal to the sum of the intensities of the components polarised 

 perpendicular to the field. The information about the intensities given by this state- 

 ment becomes more valuable the smaller the number is of the components in 

 which the line is split up, but in general this occurs just in the cases where the 

 /j's involved in the different transitions are small numbers and where consequently 

 the estimate of the a-priori probabilities of spontaneous transitions, based on a 

 consideration of the amplitudes of the harmonic vibrations in whicli the motion of 

 the atom may be resolved, becomes especially uncertain. 



§ 6. The Stark effect of the hydrogen Unes. 



In this section we will discuss in detail the estimate for the relative intensities 

 of the components of the Stark effect of the hydrogen lines, which can be obtained 

 from the calculations in § 3 on the basis of the considerations given in § 5, and it 

 will be shown that it is possible to account in a convincing way for the relative 

 intensities of the components which have been observed by Stahk-) in the case of 

 the hydrogen lines Ha, H;j, Hy and //,;. 



If the intensity of the electric field acting on the atoms is so large that the 

 relativity modifications in the laws of mechanics governing the motion of the 

 electron may be neglected, the hydrogen atom will form a mechanical system 

 which allows of separation of variables in parabolic coordinates (Epstein). This 

 separation has been performed in § 3 and, as mentioned in the preceding section, 

 the stationary states of the atom will be fixed by the three conditions 



/j = nj/j, = n^h, I,, = /jj/i, (110) 



') Bohr, loc. cit Part U, p. 8.i. 



1 .1. Stark, Elektrische Si)ekl ralanalyse chemischer Atome, l.eipzig, Hirzel (Htl4). This monograph 

 contains a survey of Stark's investigations on the effect of an electric lidcl on spectral lines until. 1914 



I). K. 1). VltlciiNli. Sclsk.Ski-., n;.liiiviilfnsk.()t<nialliem. AT.I . 8. HirUko. III. 3. 4:{ 



