356 



72 



a-priori probabilities of the different stationary states are not equal to each other but 

 they are, in the case under consideration, proportional to the values of n.^ Hence if we 

 consider the ensemble of stationary states for which the value of /j=. n^-f-ng is 

 the same, the numbers of atoms in the luminescent vacuum tube present in these 

 states may be expected to be approximately proportional to the values of in 

 these states. From this it follows that the intensitilies with which on ordinary 

 electrodynamics the different radiations of frequencies t^(Oj-\-(U2 , where i Tj -|- 1 has 

 a given entire value, would be emitted from the atoms in states corresponding to 

 a given value of n are not simply proportional to the squares of the amplitudes 

 of the vibrations of these frequencies in these states, but proportional to these 

 squares multiplied by n^. From the formal connection between the quantum theory 

 and the ordinary electrodynamical theory of radiation we are therefore, in analogy 

 with the considerations in § 5, led to expect that, as a first approximation, an 

 estimate for the relative intensities of the fine structure components {n[, n'^ -* n'^, n'^) 

 of a given line may be obtained by comparing the intensity of each component 

 with the quantities n'„R'^ and n'^R"', where R' and R" represent, just as in § 6, the 

 relative amplitudes of the circular harmonic vibrations of frequency {n\ — n'^) co^ 

 -j- (n; — n;) occurring in the motions in the initial and final states, i. e. the 

 ratios between these amplitudes and the half major axes of the orbit. 



In the tables IX and X we have given schemes for the theoretical estimate of 

 the intensities of the fine structure components of a number of spectral lines. 

 Tabel IX refers to the lines (3 -* 2), (4 — 2) and (5 2), which correspond to 

 //„(6563 Å), H^.(4861 Å) and H^(4340 Å) in the hydrogen spectrum; Table X refers 

 to the lines (4^3), (5^3), (6^4) and (7-4), corresponding to 4686 Å, 3203 Å, 

 6560 Å and 5411 A in the helium spectrum. 



The first column contains the transitions giving rise to the different compo- 

 nents, characterised by their symbol {n\, n'^ n'[, n'g). 



The second and third columns contain the values of 7^ = n\ — and = n'a — n.y 

 For each line the components corresponding to r., = + 1 and = — 1 are separated 

 by a dotted line. 



The fourth and fifth columns contain the values of R' and R" which may be 

 found from (37) by introducing (117), and which accordingly have been calculated 

 by means of the formula 



R{^lco, + w,) = l/(l + -)^r-i(r^)-(l-0./r+i(^^')). (123) 



where 



e' = = , s = l/T^^ , r = r,+ 1. 



n^-|-/i2 n ' 1 I 



In order to apply (123) in case of transitions for which u is equal to — 1 we must 

 obviously introduce for r the negative value r -= — (n' — n"). 



I MoHH, loc. cit. Part I, p. 27. 



