354 



70 



and the factor iV^ in (122), the distances between the comjjonents will for a given 

 helium line be much larger than for a hydrogen line in the same part of the 

 spectrum. In conformity with this, it has for the lines of the Balmer series in 

 hydrogen been possible only to establish the existence of narrow doublets, the 

 members of which must be expected each to correspond to several components of 

 the theoretical fine structure, while for some of the helium lines, especially for the 

 lines (4 3) and (5 -> 3), Paschen has been able to detect a considerable number 

 of components. For these lines Paschen was able to identify in detail all compo- 

 nents found by him with components or groups of components to be expected on 

 Sommerfeld's theory and the experimental value for the constant a, which may be 

 found from the observed frequency differences of the components, was in good 

 agreement with the theoretical value [a = = 7.30 • 10~^|. Moreover the absolute 

 values of the frequencies gave, when the calculations were based on the complete 

 expression (119) for v, values for the constant A' which, within the limit of experi- 

 mental errors, were the same for each of the different hydrogen lines (A' = c. 109677.7) 

 as well as for each of the ditferent helium lines {K = c. 109722.1), while the ratio 

 between these two constants was in agreement with the theoretical value J-i — 7^ .') 

 While Sommerfeld's theory thus afforded a convincing interpretation as regards 

 the frequencies of the fine structure components, it was, however, in the simple 

 form in which it was given unable to account for the in tent i lies with which 

 these components appeared. Especially it seemed difficult to explain the remarkable 

 differences shown by the spectrograms of the fine structure of one and the same line 

 which were made under different experimental conditions. Thus, in the case of the fine 

 structure of the helium line 4686 Å, the intensity distribution for the different compo- 

 nents on Paschen's photographs showed pronounced differences if a steady voltage had 

 been applied to the vacuum tube containing the gas ("Gleichstrombild") or if the 

 Ihe tube had been exposed to an interrupted spark discharge ("Funkenbild"). In a 

 recent paper Sommerfeld-) has made an attempt to explain the intensities of the 

 line structure components by comparing the intensity of every component with the 

 product of the a-priori probabilities of the initial state and of the final state of the 

 corresponding transition, obtaining in this way what he called a "typical intensity 

 distribution", and by discussing the possible modifications in this distribution which 

 the experimental conditions might produce. By such considerations, however, it 

 was not found possible to obtain a satisfactory agreement with the observations, and 

 Sommerfeld was led to the conclusion that the intensities cannot be explained "statis- 

 tically" but claimed an explanation which takes into account the mechanism of 

 the transition process and which therefore might be called "dynamical". From the 

 l)oint of view of Bohr's theory this conclusion is evident; in the limit of large n's, 

 for instance, the intensities can according to this theory directly be Ôbtained from 



') F. Paschen, loc. cit. p. 935. 



■-) A. Sommerfeld, Ber. Akad. Mûticheu, p. »3; 1917. 



