93 



377 



initial state (n' -^ 3) can liardly any more be considered as a perturbation of tiie fine 

 structure, but may ratber be described as an effect of the same order of magnitude 

 as tbe influence of the relativity modifications. On the other hand, as seen from the 

 value of H"'^ corresponding to the transition (21 ; 1-^11; 1), the motion in the final states 

 is yet ratber stable against perturbing forces of tbe order of magnitude in question. 

 Owing to this, as well as to tbe smallness of tbe frequency dilTerences involved in tbe 

 theoretical fine structure, it has therefore only been possible to observe a doublet 

 consisting of two diffuse components. In fig. 13 tbe theoretical fine structure has 

 been schematically represented in the same way as in the figures 10 and 11. The 

 lengths of tbe new components correspond to a perturbing field of 100 Volt Tbe 

 arrows indicate the position of the centres of gravity of tbe cornjjonents observed 

 by Paschen. The theoretical distance between the two strong original components 

 (03^02) and (12-* 11) is 0,142 A, while the width of the observed doublet was 

 about 0,12 Å. ') Tbe reason for this discrepancy must mainly be sought in tbe 

 appearance of tbe new component (21 ^ 11), as well as in tbe splitting up of the 

 components (03-* 02) and (12-* 11) into several components under tbe influence of 

 the perturbing forces. -) This point will be discussed more closely in the later paper 

 on the transmutation of the fine structure into the Stark efîect, referred to above, 

 but it has been mentioned here in order to draw attention to the difficulties which 

 are involved in an exact determination of the constant K for hydrogen, appearing 

 in formula (120), from measurements on tbe wave length of the hydrogen lines. As 

 regards the measurements of the relative intensities of tbe components of tbe H,, 

 doublet, Meissner finds that the relative intensities of tbe component of larger and 

 of that of shorter wave length may be represented by the numbers 7 and 5 respec- 

 tively.'') This seems again to indicate that tbe a-priori probability for a transition 

 between two circular orbits (03-* 02) is less than would be expected from tbe estimate 

 aflbrded by table IX, which is based on the method discussed in § 5. As regards 



the other lines in the Balmer series of hydrogen, H FI^ doublets the width of 



which is of the right order of magnitude have been observed, but these lines are dis- 

 turbed to a yet higher degree by small electric fields in tbe vacuum tube than H,^ . 

 In general it will be seen that, when different investigators have found different 

 values for the width of the doublet of one and the same hydrogen line, this may 

 be due to the presence of perturbing fields of different intensities in the luminous 

 gas. Especially, when certain authors find that the doublets of the higher members 

 of the Balmer series are smaller than should be expected from Sommkrfeld's theory 

 of tbe fine structure of tbe spectral lines emitted by tbe undisturbed hydrogen 



') See Haschen, loc. cit. p. 933, compare also Sommerfeld. Ann. d Pliys. LI, p. Ü8 (1916). 



^1 From the formula for J> given in note 3 on page 77 it is simply seen that in first approxima- 

 tion all components in which (03 02) will split up under the influence of an electric field are dis- 

 placed in the direction of shorter wave length, while those of (lif — 11) are displaced in the direction of 

 longer wave length. 



■I See F. Paschen, loc cil. p. 933. 



